CHEMICAL INTERACTIONS BETWEEN SILICATES AND THEIR … · predictive power of rock physics models and seismic interpretation by including the ... I am forever grateful to Gary Mavko

CHEMICAL INTERACTIONS BETWEEN SILICATES AND

THEIR PORE FLUIDS:

HOW THEY AFFECT ROCK PHYSICS PROPERTIES FROM

ATOMIC TO RESERVOIR SCALES

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF GEOPHYSICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Danica Dralus

August 2013

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/pm879nw9130

© 2013 by Danica Elizabeth Dralus. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/pm879nw9130

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Gerald Mavko, Primary Adviser


Tapan Mukerji


Kenneth Peters

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

iv

v

Abstract

This thesis focuses on physico-chemical interactions between rocks and fluids that

lead to changes in acoustic and transport properties. The goal was to improve the

predictive power of rock physics models and seismic interpretation by including the

effects of chemically-induced changes in rock properties. This thesis explores three

fluid-rock interactions to understand their effects from the subatomic level to basin

and reservoir scales.

The first fluid-rock interaction is the dissolution of opal-CT and its precipitation in

the more stable quartz phase. Marine diatoms deposit biogenic silica as amorphous

opal-A. These deposits interact with saturating aqueous solutions, transforming to

microcrystalline opal-CT and eventually quartz. Deposits undergoing these miner-

alogical changes display corresponding changes in acoustic, transport, and storage

properties. Enhanced permeability and preserved porosity during these transitions

may result in the formation of diagenetic hydrocarbon traps, even in the absence of

structural traps. Successful exploitation of diagenetic traps in oil and gas exploration

requires an understanding of how quickly the opal-CT to quartz phase transition

occurs and a method for predicting trap locations.

In this study, the kinetics of the opal-CT to quartz phase transition were de-

termined using a series of hydrous pyrolysis experiments designed to approximate

subsurface conditions. The acquired data were fit well by a nucleation and growth

model with one- to two-dimensional crystal growth. The zero-order kinetics parame-

ters were then utilized in a basin and petroleum system model to predict the location

of the opal-CT to quartz transition along a cross section of the southern San Joaquin

vi

Basin, California. Predicted transition depths were within 1200 ft of observed transi-

tion depths in nearby oil fields, a significant improvement over predictions based on

published kinetics.

The second fluid-rock interaction is the adsorption of carbon dioxide in zeolitic tuff

samples. Zeolites are aluminosilicates with large, cage-like structures and electrically

charged frames, which make many of them strong adsorbents of carbon dioxide. This

study examined the effects of carbon dioxide adsorption on the acoustic properties

and strain behavior of zeolite-rich tuff samples. A tuff containing chabazite, one

containing clinoptilolite, and one that had not undergone zeolitization were measured

in a hydrostatic pressure vessel during exposure to pressurized helium and carbon

dioxide. Ultrasonic acoustic velocities exhibited classical dependence on differential

pressure. However, the zeolitic samples exhibited significantly reduced strains when

saturated with carbon dioxide. The tuff without zeolite showed no anomalous strains

when saturated with carbon dioxide. The interaction between the carbon dioxide

molecule and the chabazite frame was modeled using electronic Density Functional

Theory (DFT).

The third fluid-rock interaction is the induced precipitation of salt in sandstone

samples. Ionic salt precipitation in reservoir rocks can lead to formation damage

and impermeable zones. Successful seismic monitoring of salt precipitation requires

knowledge of how the salt deposition alters the acoustic and transport properties of

the rock. In this study, Fontainebleau Sandstone samples were saturated with brine

and subjected to evaporative drying to induce salt precipitation. Acoustic velocities,

porosity, and permeability were measured before and after salt precipitation. The

changes in porosity and permeability resulting from salt precipitation mimicked the

natural diagenetic trend for Fontainebleau Sandstone.

vii

Acknowledgements

Mind you, I am not asking you to bear witness to what you

believe false, which would be a sin, but to testify falsely to what

you believe true – which is a virtuous act because it

compensates for the lack of proof of something that certainly

exists or happened.

– Umberto Eco, Baudolino

Much like a child, a dissertation takes a village of support and nurturing to grow.

My research chapters contain acknowledgements for specific tasks, but I would like

to thank a few people for their continued support over the years.

I am forever grateful to Gary Mavko for agreeing to serve as my adviser. He

gave me the greatest gift an adviser can give: the gift of freedom. Not only did he

allow me to explore my own interests and forge a path for myself, but he funded my

sometimes-crazy endeavors. I am a better scientist for his generosity.

I would like to thank Ken Peters for serving as a co-adviser. His infectious enthu-

siasm inspired me to tackle new problems and learn new skills.

Many people supported my research by consulting on specific projects and pro-

viding technical assistance. Mike Lewan (USGS) designed and oversaw the kinetics

experiments. Tiziana Vanorio supervised the rock physics laboratory and pressure

vessel experiments. Jennifer Wilcox and Shela Aboud supervised the density func-

tional theory simulations. Tapan Mukerji, Jack Dvorkin, Les Magoon, Oliver Schenk,

Carolyn Lampe, and Steve Graham were always available to answer my questions

and suggest new avenues of research. Allegra Hosford Scheirer was never more than

an quick email away. She seemed to have an endless supply of research suggestions,

viii

encouraging words, and red ink, all of which I appreciate.

Financial support for my work was primarily provided though industrial affiliates

programs: the Stanford Rock Physics and Borehole Geophysics Project and the Basin

and Petroleum Systems Modeling Group. I appreciate our affiliates’ investment and

continued interest.

Students, post doctoral scholars, and staff make life in the trenches bearable. To

all the people (and there are many) who sat through my seminar talks, dragged me

out for coffee, helped me locate account numbers, and kept me company through the

elevator doors when I was stuck: Thank you! In particular, I’d like to thank Fuad

Nijim who keeps the rock physics group running smoothly. Kevin Wolf taught me

to be less wound up about things, Richa and Jolene Robin-McCaskill helped me to

laugh and keep things in perspective, Justin Brown was never afraid to say what

we were all thinking, and Tess Menotti suffered through my geology questions with

grace. Through it all, Stephanie Vialle was there to teach me geochemistry, discuss

rock physics, and brighten my day. Thank you, all.

Words cannot express how much my family means to me. My sisters, Darlene,

Donna, and Dawn, have shared in all of my successes and failures and have continued

to love me unconditionally. They are three of my best friends. My mother, Denise,

is a constant source of joy in my life. My father, John, did not live to see me return

to graduate school, but I think he’d be proud. I am also lucky to have a wonderfully

supportive extended family, from aunts and cousins to step-families and in-laws.

Last but not least, I would like to thank my husband, Stuart, and our three cats,

Ani, Gibbard, and Barney. I love you more than you realize.

If at first you don’t succeed, that’s one data point.

– Randall Munroe

CONTENTS ix

Contents

Abstract v

Acknowledgements vii

List of tables xiv

List of figures xxv

1 Introduction 1

2 Experimental determination of kinetics for the opal-CT to quartz

phase transition 7

2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Monterey Formation sample characterization . . . . . . . . . . 12

2.3.2 Hydrous pyrolysis . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2.1 Hydrous pyrolysis methods . . . . . . . . . . . . . . 16

2.3.2.2 Comparison to Ernst and Calvert (1969) . . . . . . . 21

2.3.2.3 Hydrous pyroysis results . . . . . . . . . . . . . . . . 22

2.3.3 XRD analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Kinetics Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.4.1 Chemical analysis methods . . . . . . . . . . . . . . . . . . . . 37

2.4.2 Determining reaction rates . . . . . . . . . . . . . . . . . . . . 41

x CONTENTS

2.4.3 Determining kinetic parameters . . . . . . . . . . . . . . . . . 47

2.4.4 Implications for transformation rates . . . . . . . . . . . . . . 49

2.5 Additional Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3 Incorporating silica phase transition kinetics into a basin and petroleum

system model of the San Joaquin Basin, California 59

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.3 San Joaquin Basin Model . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 Silica Phase Transition Descriptors . . . . . . . . . . . . . . . . . . . 67

3.4.1 Transition temperature nomogram . . . . . . . . . . . . . . . 67

3.4.2 Transition kinetics . . . . . . . . . . . . . . . . . . . . . . . . 70

3.4.3 Modeled parameters . . . . . . . . . . . . . . . . . . . . . . . 71

3.5 Basin Modeling Results . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.6 Synthetic Seismic Section Across the Opal-CT to Quartz Boundary . 77

3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4 Anomalous strain behavior in CO2-saturated zeolitic tuffs 87

4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.1 Sample Selection and Preparation . . . . . . . . . . . . . . . . 90

4.3.2 Sample Characterization . . . . . . . . . . . . . . . . . . . . . 92

4.3.3 Velocity Measurements . . . . . . . . . . . . . . . . . . . . . . 92

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.4.1 Establishing a Baseline . . . . . . . . . . . . . . . . . . . . . . 94

4.4.2 Exploring Fluid/Rock Interaction . . . . . . . . . . . . . . . . 96

4.4.3 Relating Strain to Zeolite Content . . . . . . . . . . . . . . . . 102

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

CONTENTS xi

5 Density Functional Theory study of CO2 adsorption in chabazite 113

5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.3 Overview of DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.4 DFT Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.4.1 System calibration . . . . . . . . . . . . . . . . . . . . . . . . 117

5.4.2 Lattice parameter . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.4.3 Bader charge analysis . . . . . . . . . . . . . . . . . . . . . . . 123

5.4.4 DOS/LDOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.4.5 Joined systems . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6 Anthropogenic salt deposition in sandstones 131

6.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.4.1 Porosity – Permeability Trend . . . . . . . . . . . . . . . . . . 136

6.4.2 Mass, Porosity, Salt Volume, and Permeability Changes . . . . 137

6.4.3 Elastic Property Changes . . . . . . . . . . . . . . . . . . . . 139

6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

References 153

xii CONTENTS

LIST OF TABLES xiii

List of Tables

2.1 Sample characterization for Monterey Formation plugs. The opal-

CT-rich porcelanite plugs were cored in two directions, perpendicular

and parallel to the bedding plane. The quartzose chert sample was

only cored perpendicular to the bedding. All samples show acoustic

anisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Summary of the material and procedural differences between Ernst and

Calvert (1969) and this study. MF = Monterey Formation. . . . . . . 21

2.3 Recovered pyrolyzed material for XRD analysis. . . . . . . . . . . . . 25

2.4 XRD results for recovered pyrolyzed materials. . . . . . . . . . . . . 30

2.5 Rate constants for all six pyrolysis series calculated assuming zero-

order and first-order reactions. Initial quartz concentrations were con-

strained to zero. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.6 Nucleation and growth reaction rates for the six hydrous pyrolysis runs.

Initial quartz concentrations were not scaled a priori ; instead, Equa-

tion 2.11 was used to account for the initial quartz concentration. The

top section of the table contains values calculated from the uncon-

strained fit to the data. The lower section fixes n and finds the best

fit value of kT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.7 Pre-exponential factors and activation energies for the zero-order, first-

order, and nucleation and growth reactions. . . . . . . . . . . . . . . 50

2.8 Predicted rate constants and reaction half lives at low temperatures.

Recall that the nucleation and growth equations use n = 1.30 for the

Ernst and Calvert data and n = 2.45 for this study. . . . . . . . . . . 51

xiv LIST OF TABLES

2.9 Sample characterization for Wakkanai Formation plugs. . . . . . . . . 55

3.1 PetroMod input parameters used to model the opal-A to opal-CT to

quartz phase changes in this study. When using the Keller and Isaacs

(1985) nomogram, clay content is the input parameter. The transition

temperatures, shown in gray, are derived based on the specified clay

content. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.2 Opal-CT to quartz phase transition depths for the Antelope Shale, Mc-

Donald Shale, and Kreyenhagen Formation predicted using PetroMod

simulations. Distance is measured along the strike of the cross section.

“All qtz” means the layer is predicted to be fully converted to quartz

at present day. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.1 Sample characterization for the seven samples described in this chapter. 94

4.2 Relative strains experienced by the yellow and green tuff samples under

CO2 saturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.1 Result of Bader charge analysis for the chabazite framework with one

aluminum atom per unit cell. Shown are each atom, the number of

valence electrons the isolated ion would have, and the number of va-

lence electrons assigned to it using Bader decomposition. As expected,

aluminum and silicon lose electrons, and oxygen gains them. . . . . . 124

6.1 Data summary for salt precipitation experiments. Dimensions were

measured once. Other properties were measured before and after in-

duced salt precipitation. . . . . . . . . . . . . . . . . . . . . . . . . . 135

LIST OF FIGURES xv

List of Figures

2.1 Cartoon of the transitions from opal-A to quartz. High energy, low

stability, amorphous opal-A dissolves easily in an aqueous solution and

precipitates as microcrystalline opal-CT. Opal-CT is still less stable

than quartz, so continued dissolution results in the precipitation of

low energy, high stability quartz. . . . . . . . . . . . . . . . . . . . . 9

2.2 Pictures of representative core plugs of (a) Monterey Formation porce-

lanite cored perpendicular to the bedding plane, (b) Monterey Forma-

tion porcelanite cored parallel to the bedding plane, and (c) Monterey

Formation chert cored perpendicular to the bedding plane. Note the

millimeter-scale laminations in all three samples. Also note the abun-

dance of healed fractures in the chert sample. . . . . . . . . . . . . . 13

2.3 Uncapped pyrolysis vessel containing ground Monterey Formation porce-

lanite. The buffered aqueous solution is being added by pipette. . . . 19

2.4 Gas chromatograph oven used for pyrolysis. Seven vessels are loaded

in this oven on a raised platform for more even heat distribution. . . 20

2.5 Phase diagram of water showing the temperatures used in the Ernst

and Calvert (1969) study compared to those in this study. Although

the range is smaller in this study, all temperatures are below the critical

temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.6 An example of recovered pyrolysis material still in the pyrolysis vessel. 24

2.7 Pyrolysis vessel after liquids and solids were removed. Note the white

scale formation on both the base and lid of the container. The scale

was mechanically removed before subsequent experiments. . . . . . . 26

xvi LIST OF FIGURES

2.8 Plot of pH after pyrolysis for Monterey Formation porcelanite for sam-

ples run with buffered solutions having pH values of 7 and 10. The

colored bands show the ranges of the resulting pH values. Recall that

porcelanite pyrolyzed with (non-buffered) salt water resulted in a fluid

pH of less than 4.0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.9 XRD spectra for the 310◦C pyrolysis samples. The primary peak for

each component is labeled. The bottom spectrum (gray) corresponds

to the unaltered Monterey Formation sample before pyrolysis. The sec-

ond spectrum (blue) shows the sample after four days of pyrolysis and

3% conversion. Note that the dolomite peak completely disappeared,

replaced by a strong calcite peak. In addition, the broad opal-CT peak

showed increased crystallinity. The third (green) and fourth (orange)

spectra correspond to 10% and 28% opal-CT conversion, respectively.

The opal-CT peak decreased in amplitude as the quartz peak grew. . 32

2.10 Ternary diagrams showing compositions of the pyrolyzed samples as

determined by the Rietveld method (Rietveld, 1969) for pyrolysis tem-

peratures of 310◦C, 333◦C, and 360◦C. If the fraction of carbonate had

remained constant, the silica phase transformation would have pro-

gressed along the orange pathway. An overall decrease of carbonate is

evident. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.11 Representative XRD spectra showing the regions (gray boxes) used for

integrated peak heights. The two left boxes were summed to represent

opal-CT. The right box contains the primary quartz peak. . . . . . . 34

2.12 Calibration plots for XRD analysis of opal-CT and quartz abundance.

(left) Calibration data for this study compared to Ernst and Calvert

(1969). (right) Calibration data compared to whole-pattern matching

results. Data are from the pyrolysis experiments where the peak-height

ratios were measured and the percent quartz was determined using the

Rietveld method. MF = Monterey Formation . . . . . . . . . . . . . 35

LIST OF FIGURES xvii

2.13 Percent quartz determined using the Rietveld method compared to

values obtained using integrated peak-height ratios and the calibration

curve (Figure 2.12). The Rietveld method consistently overestimates

the amount of quartz by as much as 20%. The diagonal 1:1 line is

shown for visual reference. . . . . . . . . . . . . . . . . . . . . . . . . 36

2.14 Cartoon showing the reaction progressions for zero-order, first-order,

and nucleation and growth reactions (Equations 2.5, 2.7, and 2.10, re-

spectively). Reaction rates are arbitrarily scaled to aid in visualization.

Note that the Avrami equation takes the same shape as a first-order

reaction when n = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.15 Plots of experimental data and the linear fit of the form of Equation 2.5.

The R2 values for each line are shown on the plots. . . . . . . . . . . 42

2.16 Plots of experimental data and the linear fit of the form of Equation 2.7.

The R2 values for each line are shown on the plots. . . . . . . . . . . 44

2.17 Plot of experimental data and the linear fit of the form of Equa-

tion 2.11. The R2 values for each line are shown on the plot. The

gray line superimposed on the 400◦C data reflects the subset of data

used by Stein and Kirkpatrick (1976) to match the observed quartz

morphology (see text). . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.18 Plot of experimental data and the linear fit of the form of Equa-

tion 2.11. Thin solid lines are the fits shown in Figure 2.17. The

dashed lines show the fit with n values (slope) fixed at 1.30 for the

Ernst and Calvert data and 2.45 for this study’s data. The R2 values

for each new fit are shown on the plot. . . . . . . . . . . . . . . . . . 47

2.19 Arrhenius plots (Equation 2.12)for zero-order, first-order, and nucle-

ation and growth reactions. The R2 values for the linear fits are shown

on the plots. The cross-over temperature (the highest temperature at

which this study’s data predict faster transformation than Ernst and

Calvert data) is marked for the zero- and first-order reactions. The two

nucleation and growth fits are not directly comparable because they

assume different values of n. . . . . . . . . . . . . . . . . . . . . . . 49

xviii LIST OF FIGURES

2.20 Hydrous pyrolysis data compared to the predicted reaction progress

using zero-order, first-order, and nucleation and growth reactions de-

termined by data from this study and Ernst and Calvert (1969). . . . 53

2.21 Photograph of representative core plug from the Wakkanai Formation

porcelanite. No lamination can be seen in this sample. The dark color

arises from the presence of clay and a non-zero TOC. . . . . . . . . . 54

2.22 Two possible ways clay could affect kinetic plots (see Figure 2.19). If

clay acts as a catalyst at all temperatures, the kinetics could be repre-

sented by dashed line 1. If clay also affects the temperature dependence

of the reaction, dashed line 2 might be more accurate. The reaction

rate at a single observed temperature could be the same under either

scenario while laboratory experiments at high temperatures would see

very different rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1 Schematic transition of a siliceous layer from porcelanite to medium

and low porosity quartz phases ending in chert. Porosity generally

decreases with burial; permeability increases in the intermediate region

before decreasing again. The permeability in the quartz region is due

almost entirely to fractures. . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Schematic shows how a single depositional layer can comprise multiple

petroleum system elements. . . . . . . . . . . . . . . . . . . . . . . . 62

3.3 San Joaquin Basin map (from Peters et al., 2007) showing the approx-

imate locations of the SJ-6 seismic line (Bloch, 1991) and the nearby

Rose and North Shafter oil fields. . . . . . . . . . . . . . . . . . . . . 65

3.4 SJB cross section along the SJ-6 seismic line. . . . . . . . . . . . . . . 67

3.5 Stratigraphic column of the southern San Joaquin Basin Province, from

Hosford Scheirer and Magoon (2007). . . . . . . . . . . . . . . . . . 68

3.6 Nomogram for predicting the temperatures at which the opal-A to

opal-CT and opal-CT to quartz phase transitions occur based on the

relative amount of detritus (from Keller and Isaacs, 1985). The circles

indicate calibration data. . . . . . . . . . . . . . . . . . . . . . . . . . 69

LIST OF FIGURES xix

3.7 Modeled temperature profile for the present-day San Joaquin Basin,

SJ-6 cross section, using this study’s zero-order kinetics. Only the

source rocks are colored. . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.8 Silica phase map for the present-day SJ-6 cross section in the San

Joaquin Basin using Ernst and Calvert (1969) zero-order kinetics. Only

the source rocks are colored. . . . . . . . . . . . . . . . . . . . . . . 76


Joaquin Basin using this study’s zero-order kinetics. Only the source

rocks are colored. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77


Joaquin Basin using the Keller and Isaacs (1985) nomogram with 20%

detrital material (clay). Only the source rocks are colored. . . . . . . 78


Joaquin Basin using the Keller and Isaacs (1985) nomogram with 45%

detrital material (clay). Only the source rocks are colored. . . . . . . 79

3.12 Deviations of the predicted opal-CT to quartz transition depths com-

pared to the observed transition depths. Positive values indicate pre-

dicted depths are shallower than the observed depths. The Keller and

Isaacs (1985) nomogram with an assumed clay content of 20% yields

the best prediction in this case. The kinetics from this study show

significantly improved predictions over the Ernst and Calvert kinetics. 80

3.13 Sythetic seismic sections were based an extraction at 19.58 mi along

the SJ-6 seismic line. . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.14 Downsampled pseudologs for the extraction shown in Figure 3.13. The

locations of the Antelope Shale and McDonald Shale, which are mem-

bers of the Monterey Formation, are indicated. In this log, both are in

the opal-CT phase. Values are resampled at 10 m intervals. . . . . . . 82

3.15 Synthetic seismiogram for the pseudologs in Figure 3.14. The central

Monterey Formation reflections are indicated on the plot. . . . . . . . 82

xx LIST OF FIGURES

3.16 Synthetic seismic response through the Monterey Formation. Droplets

indicate the saturating fluid: black for live oil, blue for brine (both at

pressure). The oil/water interface in (b) has the same seismic char-

acteristics as the opal-CT/quartz interface in the (c). Therefore, the

fluid effect and mineral effects are difficult to distinguish. . . . . . . 83

4.1 Cartoon of the hydrostatic pressure vessel apparatus for measuring

strain and ultrasonic acoustic velocities at pressure. Each one inch

diameter sample was jacketed and subjected to a confining pressure.

The pore pressure was controlled independently from the confining

pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.2 Experimental data for the non-reactive Fontainebleau Sandstone. P-

and S-wave velocities are shown on the left; strains are on the right.

Both plots show the classical dependence on differential pressure with

no variation resulting from CO2 injection. Data acquired by Tiziana

Vanorio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.3 Acoustic velocities for GA at varying differential pressures and pore

fluids. Dry data are represented by red circles; CO2-saturated data are

represented by blue diamonds. Also shown are velocities predicted by

Gassmann fluid substitution (gray triangles). The dry and saturated

velocities are nearly indistinguishable. . . . . . . . . . . . . . . . . . 97

4.4 Strain as a function of differential pressure for sample GA. After the

CO2 was released from the pore space, additional strain data were

taken as the confining pressure was decreased. The CO2-saturated

data were expected to follow the dry decreasing (unloading) curve.

CO2-saturated pores show decreased strain for the same differential

pressures, interpreted as swelling. . . . . . . . . . . . . . . . . . . . . 98

LIST OF FIGURES xxi

4.5 Difference between dry strain and CO2-saturated strain as a function

of differential pressure for sample GA. The dry strain was interpolated

using the fit to the dry decreasing data shown in Figure 4.4. The error

bars were estimated assuming a 1% uncertainty in the voltage across

each linear potentiometer. The strain difference is statistically signifi-

cant and approximately constant through the entire range of differen-

tial pressures, which correspond to pore pressures from 1 to 7 MPa.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.6 Strain as a function of differential pressure for sample VRtgn5. Dry

data were taken for increasing and decreasing confining pressure. At a

confining pressure of 1 MPa, the sample was saturated with 0.9 MPa

CO2; the strain was measured. Both the confining and pore pressures

were increased by 1 MPa, and the measurement was repeated. The

strains under CO2-saturated conditions are less than under dry condi-

tions, again indicating swelling. . . . . . . . . . . . . . . . . . . . . . 100

4.7 Strain as a function of pore pressure for sample VRtgn5. The red line

denotes the dry strain at 0.1 MPa differential pressure as predicted by

the fit to the dry decreasing data shown in Figure 4.6. The light red

bar is the estimated uncertainty. CO2-saturated strains are statistically

significantly less than those of the dry system, and they are essentially

independent of pore pressure for pressures under 6 MPa, that is, for

gaseous CO2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.8 Strain for the compacted zeolite powder as a function of CO2 exposure

time. The initial large strains were most likely a result of grain rear-

rangement in the compressed powder. Strain does not exhibit a clear

dependence on exposure time at this scale but may over much shorter

times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.9 Description of the stress cycling to which each colored sample was

subjected. Upper black lines are confining pressure, lower lines are

pore pressure (colored by fluid type), and the difference between the

upper and lower lines is the differential pressure. . . . . . . . . . . . . 104

xxii LIST OF FIGURES

4.10 P-wave velocities for the green, yellow, and gray tuff samples. Veloc-

ities of the highly porous Campi Flegrei tuffs (yellow and gray) show

very little pressure sensitivity in this range. The denser green tuff is

pressure sensitive. For all three samples, the velocities appear to de-

pend only on differential pressure; they show no change with saturating

fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.11 Full strain behavior for the gray (non-zeolitized) tuff including 95%

confidence intervals. The dashed red line indicates the sample length

once the sample was fully relaxed after the experiments. After an initial

plastic deformation, strains were consistent for dry and fluid-saturated

cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.12 Strain behavior for the gray (non-zeolitized) tuff, decreasing differential

pressure curves only, including 95% confidence intervals. Strains for the

gray tuff showed no dependence on pore fluid type, only on differential

pressure. In this series of unloading curves, the non-zeolitized tuff

shows a classical stress dependence on differential pressure. The CO2

curve overlies the helium and dry curves. The final dry curve reflects

additional deformation that may be the result of thermal damage after

high pressure CO2 exposure. . . . . . . . . . . . . . . . . . . . . . . . 107

4.13 Full strain behavior for the yellow (chabazite-rich) tuff including 95%

confidence intervals. The dashed red line indicates the sample length

once the sample was fully relaxed after the experiments. After an initial

plastic deformation, dry and He-saturated measurements of strain are

similar. Injection of gaseous CO2 causes a decrease in strain (swelling). 108

4.14 Strain behavior for the yellow (chabazite-rich) tuff, including 95% con-

fidence intervals, decreasing differential pressure curves only. The he-

lium curve overlies the initial dry curve, but the CO2 curve shows

reduced strain at the same differential pressures. It is less strain than

the final unconfined dry measurement. The final dry curve reflects a

small additional deformation from high pressure CO2 exposure. . . . 109

LIST OF FIGURES xxiii

4.15 Full strain behavior for the green (clinoptilolite-rich) tuff including

95% confidence intervals. The dashed red line indicates the sample

length once the sample was fully relaxed after the experiments. After

an initial plastic deformation, dry and He-saturated measurements of

strain are similar. Injection of gaseous CO2 causes a decrease in strain

(swelling). Increasing the CO2 pressure to the liquid phase causes a

sharp decrease in strain that is largely reversed upon release of the CO2. 110

4.16 Strain behavior for the green (clinoptilolite-rich) tuff, including 95%

confidence intervals, decreasing differential pressure curves only. After

the initial dry pressure curve, strains are identical for dry and He-

saturated conditions. Injection of gaseous CO2 causes a decrease in

strain (swelling) that is doubled under liquid CO2 injection. Upon

release of the CO2, the sample does not return to its maximally-

compacted state. The green tuff did not appear to be damaged by

high pressure CO2 exposure. . . . . . . . . . . . . . . . . . . . . . . . 111

5.1 The unit cell for a calcium chabazite molecule. (yellow = aluminum,

cyan = silicon, dark gray = oxygen, red = calcium, light blue = water)

The hydrated molecule is shown on the left; note the ring of coordi-

nated calcium atoms and the tight cluster of water molecules. The

zeolite framework, which contains only aluminum, silicon, and oxygen,

is shown on the right. The top row is the view along the 111 axis.

Subsequent rows are rotated up 45◦ and then 35◦. . . . . . . . . . . . 119

5.2 Energy cutoff calibration for chabazite with one aluminum. As higher

energy states are included, the solution converges on the “true” system

energy. An energy cutoff of 450 eV would be appropriate for this example.120

xxiv LIST OF FIGURES

5.3 Plots of total energy of the dehydrated chabazite framework as a func-

tion of the lattice parameter for frames containing no aluminum atoms

(blue) and one aluminum atom (red) per unit cell. Dashed lines are

the best fit to each data set. The estimated minimum-energy lattice

parameter a0, the resulting value of the fitting parameter β, and the

bulk modulus calculated from them are shown on the plot for each

case. The single-aluminum case has a larger cell size (larger a0) and a

less favorable energy state than the no-aluminum case. . . . . . . . . 122

5.4 Example of Bader charge mapping from Henkelman et al. (2006). (a)

Each point traces a path of steepest ascent in charge density until

a local maximum is reached. (b) Points that terminate at the same

maximum are assigned to the same Bader region. . . . . . . . . . . . 123

5.5 Example of a density of states (DOS) plot for chabazite with one alu-

minum atom per unit cell. The energy has been translated so that the

Fermi level is at 0 eV. . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.6 Example of a local density of states (LDOS) plot for the three types of

atoms in the chabazite frame containing one aluminum atom per unit

cell. Lower energy states are typically associated with s orbitals while

the higher states are primarily associated with p orbitals. . . . . . . . 126

5.7 The combined carbon dioxide and chabazite framework system. (yellow

= aluminum, cyan = silicon, dark gray = frame oxygen, green and

black = carbon dioxide molecule) From the left, the carbon dioxide

molecule was brought closer to the aluminum atom. The oxygen atoms

attached to the carbon were allowed to relax at each stage; the oxygens

bend away from the aluminum as they approach it. CO2 is repulsed

by the frame and is does not adsorb. . . . . . . . . . . . . . . . . . . 128

5.8 CO2 adsorbed to a coordinated calcium ion. (yellow = aluminum, cyan

= silicon, dark gray = frame oxygen, red = calcium, green and black

= carbon dioxide molecule) . . . . . . . . . . . . . . . . . . . . . . . 129

LIST OF FIGURES xxv

6.1 CT scans of the three Fontainebleau Sandstone samples before induced

salt precipitation. Sample IDs and pycnometer porosities are listed

below each image. Permeabilities range from (a) 1050 mD to (c) 11 mD.

Courtesy of Ingrain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.2 Permeability as a function of porosity for Fontainebleau Sandstone

samples. Light gray data are from Bourbie and Zinszner (1985); dark

gray data are from Gomez (2009). Colored data are samples measured

in this study before (open circles) and after (closed circles) induced

salt precipitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6.3 Property changes resulting from salt deposition. (6.3a) Absolute poros-

ity change versus initial porosity. (6.3b) Relative porosity change ver-

sus initial porosity. (6.3c) Absolute mass change versus initial porosity.

(6.3d) Relative mass change versus absolute porosity change. (6.3e)

Volume of salt precipitated estimated by mass difference and by pyc-

nometer measurements. (6.3f) Absolute permeability change compared

to absolute porosity change. . . . . . . . . . . . . . . . . . . . . . . . 138

6.4 Elastic property changes resulting from salt deposition. (6.4a) Acous-

tic velocity versus porosity. (6.4b) Absolute velocity change versus

absolute porosity change. (6.4c) Vp/Vs ratio versus porosity. (6.4d)

Absolute Vp/Vs ratio change versus absolute porosity change. . . . . . 140

6.5 Elastic parameter changes resulting from salt deposition. (6.5a) Pois-

son’s ratio versus porosity. (6.5b) Absolute Poisson’s ratio change ver-

sus absolute porosity change. (6.5c) Bulk and shear moduli versus

porosity. (6.5d) Absolute modulus change versus absolute porosity

change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

xxvi LIST OF FIGURES

1

Chapter 1

Introduction

Rock physics is the link between geophysical observables and the intrinsic physical

properties of rocks. It provides a framework for understanding the connections be-

tween porosity, permeability, compressibility, pore shape, fluid saturation, resistivity,

and acoustic impedance.

Nearly all current rock physics relations assume that the interactions between a

pore fluid and its host rock are purely mechanical. They describe how a saturating

fluid can support a rock under pressure, but they neglect, for example, the gradual

change in pore structure as the mineral grains become part of an aqueous solution

through dissolution. The purpose of this dissertation is to help develop the ability

of rock physics to interpret geophysical observables that change due to fluid-rock

interactions. This involves identifying systems where the rock matrix may be affected

by a saturating fluid, experimentally quantifying the induced changes in mechanical

properties, and determining the time scales over which the changes occur.

Pore fluids are known to alter rock matrices under a variety of conditions. For

example, carbonates are particularly susceptible to change from interaction with aque-

ous solutions. Water-saturated carbonates experience decreases in acoustic velocity

due to dissolution (Baechle et al., 2009; Vanorio et al., 2010; Vialle and Vanorio, 2011),

while water-saturated basalts experience increases in acoustic velocity due to carbon-

ate precipitation (Adam et al., 2013). Carbonates also experience water weakening

that may be due to electrostatic repulsion (Risnes and Flaageng, 1999) or pressure

2 CHAPTER 1. INTRODUCTION

solution (Hellmann et al., 2002). In addition, heterogeneity in pore microgeometry

can affect the reactivity of carbon dioxide in carbonates (Vialle et al., 2013).

Many silicates interact chemically with saturating fluids resulting in changes to

the mechanical properties of the rock. Changes in ultrasonic acoustic velocities have

been observed during zeolite synthesis as stable crystal structures form from reacting

fluid phases (Schmachtl et al., 2000). Strain changes can also result from adsorption

of carbon dioxide in zeolites (Pulin et al., 2001). Precipitation of salt in siliceous

reservoirs can dramatically decrease permeability (van Dorp et al., 2009).

This dissertation focuses on two types of silicates: silica polymorphs and zeo-

lites. Three fluid-rock systems are considered: an aqueous solution with opal-CT and

quartz, carbon dioxide with zeolites, and brine with quartz. These first pair results

in the slow dissolution of opal-CT and precipitation of quartz. The change in phase

causes changes in grain density, permeability, and acoustic velocities. The second

pair results in adsorption of carbon dioxide and changes in strain behavior of the

zeolitic rock. The third pair results in precipitation of salt, which affects the porosity,

permeability, and acoustic velocities of the sample.

Observing changes in rock properties is a first step in understanding fluid-rock

interactions. However, the ultimate goal is to incorporate these observations into

rock physics models to improve their efficacy and broaden their application. The way

these data are incorporated depends on the rock physics model in question.

One of the more common applications of rock physics is the location and moni-

toring of fluids in the subsurface. This is often accomplished by watching for changes

in the compressional and shear wave velocities and linking them to changes in the

pore fluid type. A typical workflow involves converting acoustic velocities to bulk

and shear moduli, predicting the change in moduli when the pore fluid is replaced by

another, and converting the predicted moduli back to velocities.

The bulk and shear moduli of materials are often inferred from acoustic velocities

through the relations

K = ρ(V 2p − 4

3V 2s

); µ = ρV 2

s , (1.1)

3

where ρ is the bulk density of the sample, Vp and Vs are the P- and S-wave velocities,

and K and µ are the bulk and shear moduli (e.g., Mavko et al., 2003).

A widely used method for predicting changes in moduli due to fluid substitution is

Gassmann’s relations (Gassmann, 1951). They essentially separate the bulk modulus

of a system into contributions from the dry rock frame Kdry, the mineral grains

composing the rock Kmin, and the pore fluid Kfluid,

Ksat =φ(

1Kmin− 1

Kfluid

)+ 1

Kmin− 1

Kdry

φKdry

(1

Kmin− 1

Kfluid

)+ 1

Kmin

(1

Kmin− 1

Kdry

) ; µsat = µdry , (1.2)

where φ is the porosity. These relations are based on several assumptions about the

composition of the rock and the frequency of the wave being transmitted. As with

the majority of classical rock physics models, Gassmann’s relations also assume that

the pore fluid does not chemically influence the intrinsic properties of the solid frame

of the rock; that is, there can be no change in φ, Kdry, or Kmin. This is highlighted by

the fact that there is no direct pathway for a fluid substitution from fluid A to fluid B;

the bulk modulus of the dry frame must be calculated as an intermediate step, at least

implicitly. The same relation couples Kdry with both Kfluid A and Kfluid B, allowing

for no change in dry properties. In addition, because the fluids do not support shear

waves, the Gassmann-predicted shear modulus is unaffected by a fluid change.

Systems with strong fluid-rock interaction may render Gassmann’s relations in-

sufficient to predict elastic property changes. For example, flooding a brine-saturated

sandstone reservoir with CO2 can cause the rapid precipitation of salt as the CO2 and

water reach chemical equilibrium (Mackay and Jordan, 2005; Merdhah and Yassin,

2009). During seismic monitoring of the reservoir, Gassmann’s relations could be

used to predict the seismic response of the CO2-saturated reservoir given the brine-

saturated data. However, it would fail to predict the stiffening effect of salt deposition

at grain contacts of the rock.

Perhaps an even more fundamental model in rock physics is that of effective pres-

sure. For many rocks, particularly those with significant porosity, acoustic velocities


are strongly dependent on pressure. When a rock is saturated with a fluid, mechani-

cal coupling allows the fluid to partially support the rock. In that case, the acoustic

velocities are functions of the effective pressure, typically expressed as

Peff = Pc − αPp , (1.3)

where Pc is the confining pressure, and Pp is the pore fluid pressure. In most practical

applications, the coefficient α is assumed to be unity, a good approximation for poorly

consolidated materials. If the coupling of the fluid-rock system is purely mechanical,

α is given more specifically by

α = 1− K

Kgrain

, (1.4)

where K and Kgrain are the bulk moduli of the rock and the grains composing it,

respectively (Nur and Byerlee, 1971).

As in the case of Gassmann’s relations, the effective pressure formulation may not

hold if chemical interactions actively alter the composition of the rock. That is to say,

the value of α may depend on the specific fluid and rock under consideration, or it

may become a function of time. For example, zeolites are strong adsorbents of CO2.

Zeolitic rocks may follow a well-defined effective pressure law for an inert gas such

as helium. However, the adsorption of CO2 would alter the rock matrix and cause

swelling compared to the helium-saturated case at the same effective pressure.

These are only two of the many theoretical relations between geophysical ob-

servables and rock properties used in the field of rock physics; the list of empirical

relations is long as well. But these examples show that chemical effects may present

real challenges to even the most commonly used rock physics tools. While the effects

are often second-order, they must be understood and constrained if geophysicists are

to analyze new systems with confidence.

5

Chapter Descriptions

This dissertation covers three fluid-rock interactions in five chapters. Silica phase

changes due to dissolution in aqueous solution are explored in Chapters 2 and 3.

Carbon dioxide adsorption of zeolite is treated in Chapters 4 and 5. Induced salt

precipitation is handled in Chapter 6.

Chapter 2 describes a series of experiments conducted to determine the kinetics

of the opal-CT to quartz phase transition. Hydrous pyrolysis experiments combined

Monterey Formation porcelanite with a buffered aqueous solution to approximate

realistic subsurface conditions. After pyrolysis, the transformed material was analyzed

using powder X-ray diffraction to determine the amount of quartz present. The

phase transition data were then modeled as zero-order, first-order, and nucleation

and growth reactions. Kinetics parameters were determined for each reaction type,

and these parameters were compared to those from previous experiments (Ernst and

Calvert, 1969).

Chapter 3 incorporates the kinetics determined in the previous chapter in a basin

and petroleum system model of the southern San Joaquin Basin, California. The

depth of the opal-CT/quartz transition was modeled using zero-order kinetics from

this thesis, zero-order kinetics from a previous publication (Ernst and Calvert, 1969),

and a nomogram developed for the Santa Barbara Basin (Keller and Isaacs, 1985).

The modeled silica phase transition depth was then compared to the observed tran-

sition depth in nearby oil fields.

Chapter 4 presents the results of experiments designed to characterized the me-

chanical changes in zeolitic tuffs resulting from carbon dioxide saturation. Three tuff

samples, one containing chabazite, one containing clinoptilolite, and one without ze-

olite, were subjected to pressure cycling in a hydrostatic pressure vessel. The pore

space of each sample was in communication with the atmosphere, saturated with

helium, or saturated with carbon dioxide. Changes in strain and acoustic velocities

were monitored throughout the experiments.

Chapter 5 introduces electronic Density Functional Theory (DFT) and describes


how DFT models can supplement rock physics models. To model the strain result-

ing from interaction between zeolite and carbon dioxide in the previous chapter, a

dehydrated chabazite frame was simulated, and the bulk modulus of the frame was

calculated from the results. The interaction between the dehydrated frame and a car-

bon dioxide molecule was also simulated, and the adsorption energy was calculated.

Chapter 6 describes evaporative drying experiments designed to induce salt pre-

cipitation in Fontainebleau Sandstone samples. Samples were saturated with brine

and heated until the water evaporated. To quantify the effect of salt precipitation on

the rock matrix properties, porosity, permeability, and ultrasonic acoustic velocities

were measured under dry conditions both before and after salt precipitation.

7

Chapter 2

Experimental determination of

kinetics for the opal-CT to quartz

phase transition

2.1 Abstract

Biogenic silica, deposited as amorphous opal-A, is thermodynamically unstable at

near-surface conditions. Through interaction with aqueous solutions, it transforms

to microcrystalline opal-CT and eventually to a stable quartz phase. The rate and

conditions under which opal-CT converts to quartz can have a profound effect on the

transport and storage properties of the rock matrix, which control hydrocarbon trap-

ping in petroleum systems, particularly where structural traps are absent. Published

kinetics currently used to describe this silica phase transition and predict the depth

at which it occurs were derived under chemical conditions unlikely to be found in the

subsurface. In this study, kinetic parameters for the opal-CT to quartz phase tran-

sition were determined using realistic subsurface pore fluid compositions to improve

transition depth predictions.

This study consists of two parts. In the first part, naturally occurring opal-

CT-rich porcelanite and quartzose chert from the Monterey Formation near Lompoc,

California were characterized by geophysical methods. The porcelanite was then used

8 CHAPTER 2. SILICA PHASE TRANSITION KINETICS

in a series of hydrous pyrolysis experiments buffered with various aqueous solutions.

After pyrolysis, the solid material was analyzed using powder X-ray diffraction to

determine the relative amounts of opal-CT and quartz as function of pyrolysis time

and temperature.

In the second part, the fractional silica phase data were used to derive rate con-

stants for each experimental temperature using zero-order, first-order, and nucleation

and growth reaction kinetics. The rate constants were then used to determine the

pre-exponential factor and activation energy for an Arrhenius description of the reac-

tion kinetics. The implications for transition times at low temperatures characteristic

of geologic conditions are discussed.

2.2 Introduction

Siliceous deposits are common throughout the world, particularly around the Pacific

Rim from Japan to Sakhalin to California. In deep ocean basins that contain little

detrital silica, most of the silica is biogenic. Marine diatoms deposit amorphous

silica (opal-A), which is thermodynamically unstable. Through interaction with pore

fluids, the less stable opal-A is gradually transformed into microcrystalline opal-CT

and ultimately to the stable quartz phase during burial diagenesis (e.g., Murata and

Larson, 1975; Oehler, 1975; Williams et al., 1985). Figure 2.1 shows a cartoon of this

reaction progression.

This phase progression occurs in siliceous deposits worldwide and can profoundly

affect the acoustic, transport, and storage properties of the rock. The average mineral

density increases through the phase transitions from 2.1 g/cc (opal-A) to 2.3 g/cc

(cristobalite and tridymite forming opal-CT) to 2.65 g/cc (quartz). Coupled with

compaction trends, this change in mineral density produces sharp increases in bulk

density and decreases in porosity at both the opal-A/opal-CT and opal-CT/quartz

boundaries (e.g., Murata and Larson, 1975; Beyer, 1987; O’Brien et al., 1989; Comp-

ton, 1991; Nobes et al., 1992; Guerin and Goldberg, 1996). Generally, during dia-

genesis diatomite (opal-A) undergoes a porosity reduction from 45% to 25% after

conversion to opal-CT; its matrix permeability also drops from around 10 mD to

2.2. INTRODUCTION 9

ener

gy opal-A

opal-CT

quartzstability

this study

Figure 2.1: Cartoon of the transitions from opal-A to quartz. High energy, low stability,amorphous opal-A dissolves easily in an aqueous solution and precipitates as micro-crystalline opal-CT. Opal-CT is still less stable than quartz, so continued dissolutionresults in the precipitation of low energy, high stability quartz.

negligible values. The conversion to quartz results in an additional matrix poros-

ity reduction (Isaacs, 1981). Increasing amounts of opal-CT and quartz also cause

the rock to become more brittle, so fracture permeability often increases as matrix

permeability decreases (Chaika and Williams, 2001).

Acoustic velocities typically increase across the opal-A/opal-CT and opal-CT/quartz

boundaries as measured in both well logs and the laboratory (e.g., Bohrmann et al.,

1992; Nobes et al., 1992; Tribble et al., 1992; Chaika and Dvorkin, 1997). These ve-

locity changes can even be seen on seismic surveys as a Bottom Simulating Reflector

(BSR) (McManus et al., 1970; Hein et al., 1978; Bohrmann et al., 1992). Velocity

changes can be obfuscated by fracturing and fluid effects, though converted-wave data

can often separate these effects from lithology changes (Kidney et al., 2003).

The typical diagenetic trends observed in these siliceous deposits can be obscured

by the presence of organic material and migrating hydrocarbons. For example, hydro-

carbons can preserve matrix porosity in the opal-CT phase, or hydrocarbon cracking

can induce additional fracturing that increases permeability and porosity in the quartz

phase (Reid and McIntyre, 2001; Grau et al., 2003). In addition, there are regions


of oil-rich siliceous deposits where no strong seismic reflections occur at the opal-

CT/quartz boundary even though the opal-A/opal-CT boundary is evident (Chaika

and Williams, 2001).

The opal-CT/quartz boundary can be difficult to detect seismically, often because

of a diffuse transition zone as well as the fluid effects already discussed. Because this

is particularly true in hydrocarbon-rich basins, which are likely to be the subject of

seismic surveys, it is helpful to be able to predict the approximate depth of the opal-

CT to quartz phase transition based on geochemistry as well as seismic data. This

means understanding the reaction mechanism for the phase transition, determining

its kinetic parameters, and identifying and quantifying the common variables that

can affect the transition rate.

The silica reaction pathway consists of dissolution and precipitation reactions as

indicated in Figure 2.1. The phase transformations are not solid state based on

textural arguments (Williams et al., 1985), 18O/16O isotope fractionation analysis

(Murata et al., 1977), and kinetics comparisons between the strength of the Si-O

bond and the activation energy of the hydrothermal dissolution reaction (Mizutani,

1970, 1977; Williams et al., 1985). The two parameters most likely to contribute

significantly to reaction rate are temperature and pressure. While pressure can affect

the opal-CT to quartz phase transition at high pressures (over 50 MPa), temperature

is the dominant parameter at natural basin pressures (Carr and Fyfe, 1958; Ernst

and Calvert, 1969; Williams and Crerar, 1985; Huang, 2003).

Dissolution and precipitation reactions are affected by temperature and pressure,

but they are also influenced by the chemistry of the aqueous solution. Either disso-

lution or diffusion can be the rate-limiting step for these reactions, so both the silica

dissolution rate and the silica solubility can contribute to the overall reaction rate.

Silica solubility in aqueous solution remains relatively constant for pH less than ten,

but it can increase more than a hundred-fold as the solution becomes increasingly

basic. In contrast, although salinity causes only a slight increase in silica solubility,

it can significantly increase the dissolution rate. For example, the dissolution rate of

quartz in a 0.1 N NaCl solution is nearly seventy times faster than that in water (Iler,

1979). The contribution of salinity to silica solubility is small, and it is extremely

2.2. INTRODUCTION 11

complicated to model (Fournier et al., 1982; Fournier and Marshall, 1983).

In addition to pH and salinity, the presence of other dissolved minerals can alter

the reaction environment. Amorphous silica combined with sea water and calcium

carbonate results in lower silica solubility than that of amorphous silica with either

distilled water or sea water. In natural systems, carbonates often release magnesium

into the pore fluid when they dissolve. Mg(OH)2 flocculates opal-CT providing nu-

cleation sites for opal-CT crystal growth (Iler, 1979). This has the effect of increasing

the opal-A to opal-CT transition rate. Since the opal-CT to quartz transition com-

monly expels pore water enriched in magnesium, the rapid migration of this fluid can

promote opal-A to opal-CT transformation in shallow sediments near dikes and faults

(Ireland et al., 2009).

Clays occur in many natural sediments. Clays adsorb silica,thus maintaining low

silica saturation in the fluid. This retards the opal-A to opal-CT phase change but

provides conditions well suited for slow quartz precipitation, resulting in accelerated

opal-CT to quartz phase change (Williams and Crerar, 1985).

In addition to all of the pore fluid controls on dissolution, morphology and texture

of the rock itself can affect dissolution rates by altering reactive surface area and

diffusion pathways.

The chemical parameters controlling the phase transition reaction rate occur on

the atomica scale and are clearly numerous and difficult to isolate. Nonetheless, phase

transition kinetics are implemented in basin-scale models to predict the opal-CT to

quartz transition depth, typically using kinetics from Ernst and Calvert (1969). They

measured the fraction of opal-CT-rich porcelanite converted to quartz as a function

of temperature and time for samples saturated with distilled water and confined at

a pressure of 200 MPa. They determined the reaction rate of conversion at each of

three temperatures assuming a zero-order reaction and used these values to estimate

an activation energy of 23.2 kcal/mol. Based on their kinetic results, they estimated

that the phase transition would take approximately 4 Ma at 50◦C. These results are

quite useful as foundation for understanding the kinetics of this reaction, but they

do not reflect the myriad of geochemical influences on solubility and dissolution rate

encountered in natural sediments.


The goal of this study is to determine kinetics of the opal-CT to quartz phase

transition under conditions that more closely mimic those in sedimentary basins at

the time of transformation. This involves the use of hydrous pyrolysis experiments

like those of Lewan (1985) and Ernst and Calvert (1969). However, the experiments

here use naturally-occurring, mineralogically diverse samples, buffered aqueous solu-

tions with natural magnesium sources, low pressures, and sub-critical temperatures.

Ultimately, the kinetic data derived here will be used to predict the opal-CT to quartz

transition depth in the San Joaquin Basin by incorporating them into a dynamic basin

model as shown in Chapter 3.

This chapter is divided into two main sections. Section 2.3 explains the laboratory

data used in the study, including sample characterization, hydrous pyrolysis experi-

ments, and XRD analysis of the heated material. Section 2.4 discusses the analysis

of the data and determination of the kinetic parameters for the reaction. In addition,

Section 2.5 briefly describes parallel experiments on an opal-CT-rich porcelanite from

a Japanese siliceous reservoir rock.

2.3 Experiments

2.3.1 Monterey Formation sample characterization

The primary source of siliceous rock was a weathered portion of the Miocene Monterey

Formation (MF) exposed in a quarry near Lompoc, California. The sample was

obtained through the courtesy of John Roulston (World Minerals, Inc., Lompoc,

California). Blocks of diatomite, porcelanite, and chert were collected from the quarry.

The diatomite was friable and unsuitable for standard geophysical characterization.

The porcelanite and chert were both sturdy enough to be cored. Figure 2.2 shows

photographs of three such cores. Note the millimeter-scale horizontal laminations

visible in the photographs.

The sample described here as chert contains both opal-CT and quartz, but quartz

was the dominant phase. Although the opal-CT component would undergo a phase

2.3. EXPERIMENTS 13

(a) perpendicular (b) parallel (c) perpendicular

Figure 2.2: Pictures of representative core plugs of (a) Monterey Formation porcelanitecored perpendicular to the bedding plane, (b) Monterey Formation porcelanite coredparallel to the bedding plane, and (c) Monterey Formation chert cored perpendicularto the bedding plane. Note the millimeter-scale laminations in all three samples. Alsonote the abundance of healed fractures in the chert sample.

transition if subjected to hydrous pyrolysis, its small initial volume would make de-

termining the relative proportions of opal-CT and quartz very difficult. Therefore,

the quartz content of the chert was deemed too high for it to be a suitable starting

material for the pyrolysis experiments.

The sample described here as porcelanite was chosen as source material for the

hydrous pyrolysis experiments. It comprises nearly equal parts opal-CT and dolomite

with a small amount (∼2-4 wt%) of quartz. While these samples contained more

dolomite than is typically found in the Monterey Formation (Isaacs, 1981), we chose

to include the naturally-occurring carbonate for two reasons. First, it would not

likely interfere with the phase transition because it contains no silica. Second, the

carbonate could potentially act as an pH buffer for the aqueous solution used in the


Table 2.1: Sample characterization for Monterey Formation plugs. The opal-CT-richporcelanite plugs were cored in two directions, perpendicular and parallel to the bed-ding plane. The quartzose chert sample was only cored perpendicular to the bedding.All samples show acoustic anisotropy.

Porcelanite Chert

quantity units ⊥ to bedding ‖ to bedding ⊥ to bedding

bulk density [g/cc] 2.087± 0.007 2.076± 0.007 1.89± 0.02grain density [g/cc] 2.477± 0.003 2.457± 0.003 2.0365± 0.0014

porosity [–] 0.157± 0.003 0.155± 0.003 0.074± 0.011Vp [km/s] 4.140± 0.008 4.364± 0.008 3.58± 0.02Vs [km/s] 2.631± 0.007 2.735± 0.005 2.432± 0.015ν [–] 0.16 0.18 0.07

hydrous pyrolysis. A subsample of the porcelanite was treated with an HCl solution

and dried in a muffle oven at 500◦C for 24 hours to provide an XRD spectrum of

the siliceous components of the starting material. Note that the heat treatment of

opal-CT in the absence of water serves to improve its crystallinity but does not result

in a phase transition (Williams et al., 1985).

Once the porcelanite was selected as a starting material for the pyrolysis exper-

iments, plugs were cored for geophysical analysis. The porcelanite was cored both

parallel and perpendicular to the bedding plane. Due to difficulty during coring, the

chert was cored perpendicular to the bedding plane only. The porcelanite remaining

after coring was then prepared for the pyrolysis experiments.

Basic geophysical characterization of the Monterey Formation samples (both the

opal-CT-rich porcelanite and the quartzose chert) is shown in Table 2.1. The bulk

density was calculated from caliper measurements of dimensions of the samples and

measurements of mass. The grain density and porosity were determined using a he-

lium pycnometer. The permeabilities for all samples were below the 1 mD lower

detection limit of the nitrogen permeameter and were therefore not quantified. The

compressional (Vp) and shear (Vs) wave velocities were measured under benchtop

conditions using a pulse transmission method (Birch, 1960). A Panametrics 5052 PR

pulse generator provided the signal to Panametric transducers (either V103 for 1 MHz

P-waves or V154 for 0.7 MHz S-waves). The signal was recorded using a Tektronix

2.3. EXPERIMENTS 15

TDS 420A digital oscilloscope. Samples were unconfined, but an axial stress of ap-

proximately 3 psi was applied to facilitate coupling between the transducers and the

sample surface.

Chaika and Williams (2001) classified two types of opal-CT-rich and quartz-rich

Monterey Formation reservoir rocks depending on clay content. Based on depositional

history, they anticipated San Joaquin Basin samples to fall into group 1, the high clay

group, and all coastal California samples to fall into group 2, the low clay group. This

was largely supported by data, although some San Joaquin Basin samples showed

low-clay characteristics. All samples in this study were from the coastal California

region. They have bulk densities and porosities consistent with the low-clay trend.

The quartzose chert, which still contains a significant fraction of opal-CT without

apparent clay, has a much lower measured grain density than anticipated from its

mineral composition. Because the helium pycnometer equilibrated within minutes and

remained stable for tens of minutes, the low grain density measurement may indicate

the existence of inaccessible porosity. It is also possible that there are two porosity

regimes: one associated with relatively higher permeability flowpaths (e.g., fracture

network) and another associated with much lower permeability pathways (e.g., matrix

permeability). In contrast, the grain density of the porcelanite is consistent with its

mineralogy and observed porosity.

The benchtop acoustic velocities are reasonable for these types of rocks (e.g.,

Chaika, 1998). Anisotropy, likely due to bedding, is apparent in the porcelanite.

If weak transverse anisotropy is assumed, the Thomsen parameters ε and γ can be

estimated from the velocities (Mavko et al., 2003),

ε ≈ Vp(90)− Vp(0)

V p(0)= 0.054 γ ≈ Vsh(90)− Vsh(0)

Vsh(0)= 0.040 .

2.3.2 Hydrous pyrolysis

At their most basic, hydrous pyrolysis experiments consists of mixing a material with

an aqueous solution, sealing the mixture in a non-reactive container, and heating

the container for a specified time. The general workflow for the hydrous pyrolysis


performed here is similar to that described by Lewan (1985) and by Ernst and Calvert

(1969).

The experiments performed by Ernst and Calvert (1969) pyrolyzed Monterey For-

mation opal-CT to understand the same transition to quartz studied here. However,

their experimental conditions were not representative of subsurface conditions. This

study includes several modifications to their original set-up. These are contrasted in

§2.3.2.2.

All of the hydrous pyrolysis experiments described here were conducted at the

Denver Federal Center of the U.S. Geological Survey (USGS) under the guidance of

Michael D. Lewan.

2.3.2.1 Hydrous pyrolysis methods

The pyrolyzed material used in this study was the quarried Monterey Formation

porcelanite discussed in §2.3.1. After the large blocks of porcelanite were cored, the

remaining material was successively crushed, ground, and sieved. Particles having

diameters between 177 and 250 micrometers (between 60 and 80 mesh) were reserved

for pyrolysis; the rest were set aside for future work. The raw material was found to

comprise approximately 2 wt% quartz, 47 wt% opal-CT, and 51 wt% dolomite based

on XRD analysis.

The aqueous solution included in the pyrolysis vessel is key in controlling the silica

phase transition rate, so it must be chosen carefully. Silica in distilled water equili-

brates to a pH of ∼3 (Iler, 1979). This is far from the estimated pH of subsurface

waters likely to be circulating in siliceous deposits at the time of silica phase conver-

sion; that pH is ∼8.0. In addition, alkaline conditions (i.e., higher fluid pH) are more

favorable for silica dissolution than acidic conditions. For dissolution and precipita-

tion reactions, the pH of the fluid may very well control the reaction rate. Therefore,

the aqueous solution used in these hydrous pyrolysis experiments was selected in an

attempt to mimic naturally-occurring subsurface fluids.

Little is known about the behavior of most aqueous solutions (including buffered

solutions) at high temperatures (>100◦C). Various aqueous solutions were tested for

pH before and after heating to see if they were returned to an anticipated pH after

2.3. EXPERIMENTS 17

pyrolysis.

Initially, a commercially available salt solution (Oceanic Natural Sea Salt Mix)

was mixed with distilled water to create a simulated seawater solution having a com-

position similar to natural subsurface fluids. The solution itself started with a pH

near 8.0, but it measured only 3.6 after being mixed with Monterey Formation opal-

CT and heated for 14 days at 225◦C. Similar tests at 275◦C and 325◦C returned fluid

pH measurements of 3.5 and 3.9, respectively. This was deemed too acidic to be

representative of natural conditions, so the simulated seawater was not used.

After seawater was excluded, a series of commercially-available buffered aqueous

solutions were tested. General buffers with pH values of 9.0 and 10.0 were heated

to 325◦C for 80 hours without rock; they measured 8.4 and 8.8, respectively, after

pyrolysis. Subsequent tests showed buffers with initial pH values of 7.0 and 10.0

resulted in post-pyrolysis values near 8.0 when Monterey Formation porcelanite was

included in the pyrolysis vessel. Therefore, most of the hydrous pyrolysis experiments

were run using a colorless general buffer with pH of 7.0 containing a mixture of dibasic

sodium phosphate and monobasic potassium phosphate. A few select data were taken

using a colorless general buffer with a pH of 10.0 containing sodium bicarbonate and

sodium carbonate.

Once the aqueous buffer was selected, temperatures were chosen for the rock pyrol-

ysis. At least three pyrolysis temperatures were required for kinetics analysis. Ideally,

realistic reaction rates would be measured at representative basin temperatures. Un-

fortunately, the Ernst and Calvert (1969) data suggest this reaction occurs so slowly

at 60◦C that it would require 1.7 million years to convert all of the opal-CT to quartz.

Much higher temperatures are required in the laboratory to force conversion on an

experimental time scale. Based on the Ernst and Calvert (1969) kinetics, a tempera-

ture of 300◦C would require ∼230 days for full conversion to quartz. Therefore, 310◦C

was selected as the lowest pyrolysis temperature for the experiments shown here. At

temperatures higher than 374◦C, water can enter a supercritical phase. The effect

this would have on the dissolution rate and solubility of silica is unknown, so pyroly-

sis temperatures were kept below this value. Thus, the highest pyrolysis temperature

selected was 360◦C. A third temperature of 333◦C was chosen because it evenly splits


the high- and low-temperature difference on a logarithmic scale.

The hydrous pyrolysis vessels chosen for these experiments consisted of a threaded

316 stainless steel cap and plug for a 1.5 inch diameter pipe from Swagelok (SS-2400-C

and SS-2400-P). Each vessel had a volumetric capacity of 25 cc. Five grams of ground

porcelanite were added to each vessel. The amount of aqueous solution needed to be

large enough to allow ample fluid to facilitate the phase transition but small enough

that the reactor remained under 90% full of rock and liquid water, plus steam at the

target temperature, a criterion meant to reduce the likelihood of pressure build-up

and seal leakage. The volume of the liquid phase at the target temperature can be

predicted using steam tables and the state equation

vTl =(M o

wγTv − (vr − vs))γTl(γTv − γTl )

, (2.1)

where vTl is the volume of the liquid at temperature, M ow is the mass of the aqueous

solution added at room temperature, vr and vs are the volumes of the reactor and

solid sample, γTl is the specific volume of the liquid phase, and γTv is the specific

volume of the vapor phase. These calculations yielded appropriate aqueous solution

masses of 13.30 g, 12.25 g, and 10.50 g for temperatures of 310◦C, 333◦C, and 360◦C,

respectively. The vapor pressures of water at these three temperatures are approxi-

mately 10 MPa, 13 MPa, and 19 MPa, respectively, so the experiments shown here

were considered low pressure compared to those of Carr and Fyfe (1958) (>100 MPa),

Ernst and Calvert (1969) (200 MPa), and Huang (2003) (0.05-3 GPa).

Figure 2.3 shows a photograph of an uncapped pyrolysis vessel containing five

grams of ground porcelanite with the buffered solution being added by pipette.

The ground porcelanite and buffered aqueous solution for each experiment were

combined in the pyrolysis vessels, capped tightly, and weighed. The vessels were

stacked in a Hewlett-Packard 5890 A gas chromatograph oven, offset and on a raised

platform to encourage hot air circulation and to facilitate even heating. A photograph

of this set-up is shown in Figure 2.4. After the oven was filled, it was set to its des-

ignated temperature and allowed to heat. Each oven took approximately 30 minutes

to reach its target temperature.

2.3. EXPERIMENTS 19

Figure 2.3: Uncapped pyrolysis vessel containing ground Monterey Formation porcelanite.The buffered aqueous solution is being added by pipette.

Because the goal of the hydrous pyrolysis experiments was to sample opal-CT at

various stages of transformation, each vessel was assigned a different time for removal.

Records were kept of the times each oven was opened and how long it took to reheat

to its target temperature (typically less than five minutes).

Once removed from the oven, samples were allowed to cool to room temperature, a

process that took three to four hours. When cool, the samples were weighed to check

for mass changes indicating leaks; no vessels experienced mass loss during pyrolysis.

Room temperature vessels were opened and allowed to vent for several minutes.

The appearance of the recovered material was noted as were any strong odors. The

vessel contents were poured into a 1 L millipore beaker with a fritted glass surface

fitted with a Pall Life Sciences GN-6 Metricel membrane filter with 0.45 µm holes.

A vacuum was applied to the beaker to separate the pyrolysis fluid from the solids.

Once the recovered pyrolysis fluid was weighed, its pH was measured using an Orion

pH meter (model 720A calibrated to 10.0 and 7.0 buffered aqueous solutions) and it

was transferred to a vial for storage.

The pyrolysis solids were scraped into a beaker and flushed repeatedly with deion-

ized water. The wash water was removed under vacuum. The solids were moved to

Petri dishes where they were weighed before being transferred to a vacuum oven for

dehydration. Samples were dried under 135 mbars of vacuum at ≤100◦C until dry,


Figure 2.4: Gas chromatograph oven used for pyrolysis. Seven vessels are loaded in thisoven on a raised platform for more even heat distribution.

typically overnight. Dry samples were weighed again before being lightly hand-ground

using an agate mortar and pestle and transferred to glass vials in preparation for XRD

analysis.

The XRD analyses used to quantify the phase transition rate were performed at

Stanford University. Procedures and results are discussed in §2.3.3. To understand

the extent to which the experiments captured the phase transition, a few XRD spectra

were acquired to spot-check pyrolyzed samples at the USGS. The pyrolysis times were

adjusted as needed based on those results.

An additional sample of pure Monterey Formation opal-CT was prepared for XRD

calibration. Approximately 50 g of the porcelanite used as starting material for the

pyrolysis experiments was combined with HCl solution and allowed to soak. Once

the dolomite dissolved, the mixture was centrifuged to remove the liquid, and the

remaining opal-CT was rinsed with distilled water and dried. The material was

placed in a 500◦C muffle furnace for approximately eight hours to induce the improved

crystallinity achieved by dry heating opal-CT.

2.3. EXPERIMENTS 21

Table 2.2: Summary of the material and procedural differences between Ernst and Calvert(1969) and this study. MF = Monterey Formation.

Ernst and Calvert (1969) this study

material MF opal-CT MF opal-CT + dolomiterock preparation ground ground, sieved (60-80 mesh)aqueous solution distilled water buffered solution pH 7.0amount of water 30 mg rock / 10 mg water 5 g rock / 10 g watertemperatures 300◦C, 400◦C, 500◦C 310◦C, 333◦C, 360◦C

2.3.2.2 Comparison to Ernst and Calvert (1969)

The procedures and materials in these pyrolysis experiments were very similar to

those of Ernst and Calvert (1969). While Ernst and Calvert focused on the opal-CT

to quartz transition in pure water, this study aimed to understand the opal-CT to

quartz transition as it likely occurs in the subsurface. To that end, this study trades

the physical insight of a simplified system for data that can be used in practical

subsurface modeling of silica phase transitions. The key differences between the Ernst

and Calvert study and this study are explained in this section and are summarized

in Table 2.2.

The solid materials used in the two studies are similar. Both were quarried coastal

Monterey Formation samples from Lompoc, California. Ernst and Calvert used nearly

pure opal-CT to avoid interactions between the pyrolysis fluid and any other mineral

phases. This study used the raw porcelanite as quarried with no attempt to remove

non-opal-CT components. Other mineral phases were allowed to affect the fluid

chemistry and alter the reaction kinetics as they would in situ. The porcelanite used

here was ground and sieved in hopes of mitigating grain size effects on dissolution

and growth (e.g. Ostwald ripening; Iler, 1979); the Ernst and Calvert samples were

ground to an unspecified size.

The pyrolysis fluids used in the two studies were also different. As discussed in

§2.3.2.1, silica in equilibrium with distilled water produces a fluid with very low pH,

much lower than the pH of most subsurface water. Ernst and Calvert used distilled

water as their pyrolysis fluid; and while they did not report the post-pyrolyis pH of


that fluid, it was likely near 3 or 4. Because silica dissolves more slowly in acidic

solutions, the low pH of their fluid may have retarded the phase transition. Instead,

a buffered aqueous solution with a pH of 7.0 was used in this study to ensure the

pyrolysis fluid maintained a reasonable pH.

The proportions of solid materials to liquids varied in the two studies. Ten mil-

ligrams of distilled water were used for each 30 mg of opal-CT in the older report.

Assuming that there would be ample fluid circulation in siliceous deposits over the

million-year time scale of phase transition, the proportions used here were at least

10 g of water for each 5 g of rock.

Finally, the three pyrolysis temperatures were different in the two studies. Ernst

and Calvert chose 300◦C, 400◦C, and 500◦C for their experiments. Temperatures that

span such a large range allow for a more robust linear regression during analysis of

the kinetics, but their two higher temperatures were above the critical temperature

of water. Because an aqueous solution is crucial for the silica phase transition, and

because all laboratory temperatures used are far from subsurface conditions, the

temperatures used in this study were kept below the critical temperature for water

even though it limited the range of temperatures for regression analysis. Figure 2.5

shows a graphical representation of all six temperatures in relation to the phase

diagram of water.

2.3.2.3 Hydrous pyroysis results

Based on the Ernst and Calvert (1969) kinetics data, full transition of the most

rapidly converting samples (those pyrolyzed at 360◦C) was predicted to take more

than a month. However, through spot-checked XRD of early samples, the 360◦C

samples were found to be fully converted after only three days. The removal times of

vessels were adjusted accordingly. The lowest temperature experiments ran for up to

24 days.

All of the pyrolysis vessels maintained their seals during pyrolysis. The mass of

each sealed container was measured before and after heating; nearly all maintained

their mass within 0.1 g as measured to the nearest 0.1 g. The largest deviations were

0.3 g. Once opened, most vessels experienced a small mass loss due to escaping gas.

2.3. EXPERIMENTS 23

temperature (°C)

pres

sure

(atm

)

374

220

solid

liquid

vapor

temps for this study temps for

Ernst & Calvert

0

0

Figure 2.5: Phase diagram of water showing the temperatures used in the Ernst andCalvert (1969) study compared to those in this study. Although the range is smallerin this study, all temperatures are below the critical temperature.

This was generally on the order of 0.5 g.

Qualitative descriptions of the recovered material were noted. Generally, there

was little odor upon opening the pyrolysis vessels smell because the samples contained

little organic material. Small bubbles were observed in many samples. The recovered

liquid was typically clear or slightly yellow. The solid material was usually light brown

or slightly gray with white clumps often forming a crust on the top of the sample.

Figure 2.6 is a photograph of one recovered sample.

After the qualitative descriptions were recorded, the pyrolysis liquid was filtered

and the solid material collected as described in §2.3.2.1. A summary of the recovery

data for the samples used in the kinetics analysis is given in Table 2.3. Pyrolysis

fluid was more difficult to recover than solid material. Some of the fluid mass was

lost as vapor when the vessel was opened. In addition, the small rock grains were

able to retain a significant amount of fluid even under vacuum. In fact, samples often

retained 10 g to 15 g of rinse water after being exposed to a vacuum. This water

was later removed by evaporative drying in a vacuum oven. Ultimately, the pyrolysis

fluid recovery was only between 30% and 58%.

The recovery of the solid material had a higher yield, between 86% and 93%. Some

of the mass was lost as the material was transferred from the vessel to the filtration


Figure 2.6: An example of recovered pyrolysis material still in the pyrolysis vessel.

apparatus and then to the drying dish. Some mass, however, was likely dissolved in

the pore fluid at the time it was filtered and recovered. This suggests that the density

of the pore fluid was probably higher after pyrolysis than before. This mass loss due

to dissolution will be discussed further in §2.3.3 in the context of sample composition

changes.

For some experiments, some mass adhered to the pyrolysis vessel itself. A light-

colored scale formed on the interior surfaces of many of the vessels, a sample of which

can be seen in Figure 2.7. The scale was scraped so that as much material as possible

could be salvaged for the XRD analysis; however, the remaining thin film had to be

removed mechanically using a wire brush.

The final data acquired at the time of pyrolysis were the pH values of the pyrolysis

fluid after temperature cycling. Figure 2.8 displays the results of those tests for all of

the recovered samples regardless of whether XRD was ultimately performed on the

corresponding solid material. Data for vessels filled with the pH 7.0 buffer are shown

in blue; data relating to the pH 10.0 buffer are shown in orange. Vessels containing

the pH 7.0 buffer resulted in final pH values between 7.33 and 8.25. Vessels containing

the pH 10.0 buffer resulted in final pH values between 7.48 and 7.99. The data reveal

no pH trend correlating either to length of time in oven or to oven temperatures.

2.3. EXPERIMENTS 25

Table 2.3: Recovered pyrolyzed material for XRD analysis.

temp timeinitial recovered recovery initial recovered recovery

solid mass solid mass rate solids fluid mass fluid mass rate fluids(◦C) (hrs) (g) (g) (%) (g) (g) (%)

310◦C

96 5.002 4.401 88.0 13.296 7.1 53.4168 5.001 4.381 87.6 13.289 7.0 52.7270 5.014 4.347 86.7 13.324 7.7 57.8408 5.016 4.321 86.1 13.326 6.8 51.0576 5.079 4.402 86.7 13.333 7.3 54.8

333◦C

24 5.001 4.501 90.0 12.274 5.8 47.348 5.002 4.428 88.5 12.249 6.0 49.072 5.001 4.393 87.8 12.268 6.3 51.496 5.001 4.353 87.0 12.245 5.9 48.2120 5.002 4.391 87.8 12.262 6.0 48.9144 5.001 4.315 86.3 12.271 6.0 48.9168 5.002 4.335 86.7 12.263 5.8 47.3

360◦C24 5.000 4.667 93.3 10.568 4.9 46.448 5.001 4.415 88.3 10.535 4.9 46.576 5.000 4.331 86.6 10.527 3.4 32.3

2.3.3 XRD analysis

Quantification of the Monterey Formation sample composition before and after pyrol-

ysis is the link between the pyrolysis experiments and analysis of the kinetic param-

eters that describe the phase transition. This study, like Ernst and Calvert (1969),

relies on powder X-ray diffraction (XRD) measurements of the recovered solids to

determine the relative amounts of opal-CT and quartz.

XRD spectra were taken at Stanford University using the School of Earth Science’s

Rigaku Geigerflex X-ray powder diffractometer operating at 35 kV and 15 mA. The

recovered solid samples were hand-ground to a fine powder using an agate mortar

and pestle. Approximately 0.5 g of material was placed in a glass mounting plate

and loaded horizontally into the machine. A continuous scan was used for acquisition

with a 0.03◦ step and a 1.5 second dwell. Both finer steps and longer acquisition times

were tested, but neither appreciably changed the relative constituent abundances.

Figure 2.9 shows spectra for the 310◦C pyrolysis experiments at select points


Figure 2.7: Pyrolysis vessel after liquids and solids were removed. Note the white scaleformation on both the base and lid of the container. The scale was mechanicallyremoved before subsequent experiments.

in the transition. For illustrative purposes, the primary peak for each component

is labeled. The bottom spectrum in gray corresponds to the unaltered Monterey

Formation sample before pyrolysis. The broad peak near 2θ CuKα = 21.6◦-21.9◦

(4.05-4.10A) represents the microcrystalline opal-CT phase comprising a mixture of

tridymite and cristobalite. The second spectrum (blue) shows the sample after four

days of pyrolysis; approximately 3% of the opal-CT had converted to quartz. Notice

that the dolomite peak completely disappeared, replaced by a strong calcite peak.

In addition, the broad opal-CT peak sharpened to a more precise peak, implying

increased crystallinity. The third (green) and fourth (orange) spectra correspond to

10% and 28% opal-CT conversion, respectively. The height of the opal-CT peak

decreased in amplitude at each time step while the quartz peak noticeably increased.

The relative component weights were determined using two different methods. The

first method utilized modern computing techniques to decompose the XRD spectrum

into weighted spectra of the components (Rietveld method). That technique allowed

2.3. EXPERIMENTS 27

0 100 200 300 400 500 6006

7

8

9

10

11

time [hours]

pH

pH 7 buffer

pH 10 buffer310ºC

333ºC

360ºC

using pH 7 bu�er

310ºC

333ºC

360ºC

using pH 10 bu�er

Figure 2.8: Plot of pH after pyrolysis for Monterey Formation porcelanite for samplesrun with buffered solutions having pH values of 7 and 10. The colored bands show theranges of the resulting pH values. Recall that porcelanite pyrolyzed with (non-buffered)salt water resulted in a fluid pH of less than 4.0.

for determination of the amounts of all major components. The second method used

a peak-height ratio technique in conjunction with a calibration curve; this was the

analysis technique of Ernst and Calvert (1969) and was only useful to determine the

relative amounts of opal-CT and quartz.

The Rietveld method is a whole-pattern matching algorithm in which the sample

spectrum is decomposed into weighted fractions of other known spectra (Rietveld,

1969). There are numerous parameters in the whole pattern matching algorithm that

can be adjusted for precise analysis. These adjustments can affect the reported weight

percentages of the components. However, the Monterey Formation samples comprise

combinations of just opal-CT, quartz, dolomite, and calcite. The spectra for all but

the opal-CT are relatively simple and distinct. The broad peaks associated with the

microcrystalline opal-CT make it difficult for the Rietveld analysis to decompose the

spectrum and assign precise absolute values to the sample composition. However,


the method has the advantage of providing an estimate of the relative amounts of all

components, not just opal-CT and quartz.

General trends in the Rietveld data are illustrative here. Figure 2.10 shows ternary

diagrams of Rietveld sample composition from the three pyrolysis temperatures col-

ored by pyrolysis time. Dolomite and calcite fractions are combined along the car-

bonate axis. If the pyrolysis fluid were unchanged by pyrolysis, or if silica and calcite

dissolved in even amounts, the silica phase transformation would progress from right

to left on the plot as indicated by the orange line. However, these data indicate the

carbonate fraction decreases sharply at first and continues to decline slightly during

pyrolysis, following the blue curve. This represents a loss of carbonate to the pyroly-

sis fluid and/or the unrecoverable scale on the vessel. The relative loss of carbonate

serves as a reminder that the complicated mineralogy of real rocks may affect fluid

composition and silica diagenesis in ways that cannot be replicated in the laboratory

using only pure opal-CT as pyrolysis material.

The second method used to determine the amounts of the sample components, a

peak-height ratio technique, compares the height of the primary quartz reflection to

that of the primary opal-CT reflection. Ernst and Calvert (1969) used the 1011 re-

flection of α-quartz (2θ CuKα = 26.7◦, 3.34A) and the 101 reflection of α-cristobalite

(2θ CuKα = 21.9◦, 4.05A). A calibration curve plotting peak-height ratios for con-

trolled mixtures (as discussed below for this study) of the two silica phases was used

to translate peak ratios to mineral mixtures. Figure 2.12 contains a reproduction of

the Ernst and Calvert calibration curve in addition to the calibration data from this

study.

This study also used the 1011 reflection of α-quartz for the peak comparison.

However, the samples in this study show a greater tridymite contribution than those of

Ernst and Calvert. Therefore, a combination of the 101 reflection of α-cristobalite and

the 404 reflection of α-tridymite (2θ CuKα = 21.6◦, 4.107A) was used to represent the

opal-CT phase. The breadth of the opal-CT peak is related to non-Bragg diffraction

due to the intergrowth of the tridymite and cristobalite phases (Elzea and Rice, 1996).

To capture the diffuse nature of the opal-CT contribution to the XRD spectrum, the

analysis of peak height was replaced by an integrated peak area. Care was taken

2.3. EXPERIMENTS 29

to exclude a minor quartz peak (2θ CuKα = 20.85◦, 4.257A) and a minor calcite

peak (2θ CuKα = 23.02◦, 3.860A) that occur within the broad opal-CT peak region.

Ultimately, the opal-CT “peak height” was a sum over intensity from 2θ CuKα =

19.65◦ − 20.67◦ and 21.06◦ − 22.80◦. Similarly, the quartz “peak height” was a sum

over intensity from 2θ CuKα = 26.25◦ − 27.09◦. A diagram showing these regions is

shown in Figure 2.11.

A calibration curve is required to translate peak-height ratios into relative abun-

dances of quartz and opal-CT. For this study, the HCl-washed opal-CT was mixed

with a pure Arkansas quartz sample (obtained from the USGS) in known weight ra-

tios. The XRD spectrum of each mixture was analyzed for integrated peak heights.

The peak-height ratios are plotted as a function of known quartz fraction in Fig-

ure 2.12. The left plot shows the calibration data for this study superimposed on the

calibration curve from Ernst and Calvert (1969). Despite the different methods for

obtaining peak-height ratios, the two studies produce calibration data that follow a

single trend described by the equation

R = −0.0020P 2q + 0.14Pq − 3.8 , (2.2)

where R is the peak-height ratio and Pq is the weight percent quartz. Given measured

integrated peak-height ratios, Equation 2.2 was solved for Pq to estimate the quartz

fraction.

The raw and HCl-washed Monterey Formation samples have a quartz fraction of

approximately 3% as determined by petrographic methods as well as Rietveld analy-

sis. When applied to the diffuse opal-CT peaks of those two samples, the integrated

peak height method plots those data on the calibration trend as well.

The right plot in Figure 2.12 superimposes on the calibration curve pyrolysis data

analyzed for composition using the Rietveld method. Though the Rietveld method

produces a similarly shaped trend line, it consistently overestimates the amount of

quartz in the samples compared to the peak-height method. This is because the

pattern-matching algorithm can account for tridymite and cristobalite spectral peaks

but cannot account for the diffraction due to intergrowth of the crystals. If the


Table 2.4: XRD results for recovered pyrolyzed materials.

temp timeRietveld analysis peak height fraction

opal-CT quartz dolomite calcite opal-CT quartz of rxn

(◦C) (hrs) (%) (%) (%) (%) (%) (%) complete

– (raw MF) – 52.5 1.9 45.6 0.0 95.4 4.6 0.00

310◦C

96 60.4 4.8 0.0 34.8 94.1 5.9 0.02168 59.3 5.4 0.0 35.3 93.7 6.3 0.03270 51.7 11.3 0.0 37.0 86.4 13.6 0.10408 37.9 28.9 0.0 33.2 69.9 30.2 0.28576 0.9 70.9 0.0 28.2 10.0 90.1 0.90

333◦C

24 53.2 5.3 21.8 19.7 93.2 6.8 0.0348 59.2 9.2 0.0 31.5 88.3 11.7 0.0872 52.2 13.3 0.0 34.4 84.7 15.3 0.1296 34.4 31.4 0.0 34.2 65.6 34.4 0.32120 20.7 46.7 0.0 32.6 48.3 51.7 0.50144 2.2 68.8 0.0 29.0 12.8 87.2 0.87168 0.3 67.6 0.0 32.1 8.5 91.5 0.91

360◦C24 49.2 9.2 32.4 9.2 85.8 14.2 0.1148 32.6 27.7 18.9 20.8 68.1 31.9 0.2976 0.0 71.7 0.0 28.3 6.4 93.6 0.93

algorithm considered not just the heights of the opal-CT peaks but also the contribu-

tion of the diffracted rays, then the estimated opal-CT content would likely increase,

reducing the estimated weight percent of quartz.

The Rietveld analysis overestimates the quartz content by as much as 20% in

the mid-range. This can be seen more clearly in Figure 2.13, which compares the

estimated weight percent of quartz in the pyrolyzed samples as determined by the

Rietveld method and by using the calibration curve and Equation 2.2.

Because the results of the Rietveld analysis were not completely consistent with

those of the integrated peak-height ratio analysis, they were used only for the general

composition estimates shown in the ternary diagrams in Figure 2.10. Quartz fractions

determined from integrated peak-height ratios were used for all subsequent kinetics

analyses. Table 2.4 summarizes both the Rietveld analysis results and the results of

integrated peak height ratio analysis.

It should be noted that the sample composition was also measured using Fourier

transform infrared spectroscopy (FTIR) at the Schlumberger-Doll Research Center in

2.3. EXPERIMENTS 31

Cambridge, Massachusetts. FTIR can provide an extremely detailed analysis of the

precise minerals in a sample, including trace minerals. Because it is so precise, its

spectra-matching algorithms are very sensitive to the spectra of the constituents. Be-

cause opal-CT is a fairly broad designation that includes variable amounts of tridymite

and cristobalite, a spectrum considered to be pure opal-CT can vary depending on

the source of the opal-CT. This makes quantitative FTIR analysis of opal-CT frac-

tions susceptible to interpretation errors. Though the acquisition of FTIR spectra

was completed successfully, the initial decomposition of the FTIR spectra yielded

physically unrealistic component minerals, so they were not used in determining the

kinetics of this reaction.


15 20 25 30 35 40 45 50 55 60 65 70(2θ)

17 days, 28% complete

11 days, 10% complete

4 days, 3% complete

unaltered

opal-CT

qtz

calcite

dolomite

Figure 2.9: XRD spectra for the 310◦C pyrolysis samples. The primary peak for each com-ponent is labeled. The bottom spectrum (gray) corresponds to the unaltered MontereyFormation sample before pyrolysis. The second spectrum (blue) shows the sample af-ter four days of pyrolysis and 3% conversion. Note that the dolomite peak completelydisappeared, replaced by a strong calcite peak. In addition, the broad opal-CT peakshowed increased crystallinity. The third (green) and fourth (orange) spectra corre-spond to 10% and 28% opal-CT conversion, respectively. The opal-CT peak decreasedin amplitude as the quartz peak grew.

2.3. EXPERIMENTS 33

0

0

0

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.5

0.50.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1

1

1

Opal-CT

Quar

tz

Carbonate

0 64 128 192 256 320 384 448 512 576

pyrolysis time (hours)

0

0

0

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.5

0.50.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1

1

1

Opal-CT

Quar

tz

Carbonate

0 19 37 56 75 93 112 131 149 168


transformation if carbonate concentration is constant

actual transformation

carbonateloss

310°C 360°C

333°C

0

0

0

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.5

0.50.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1

1

1

Opal-CT

Quar

tz

Carbonate

0 8 17 25 34 42 51 59 68 76


Figure 2.10: Ternary diagrams showing compositions of the pyrolyzed samples as deter-mined by the Rietveld method (Rietveld, 1969) for pyrolysis temperatures of 310◦C,333◦C, and 360◦C. If the fraction of carbonate had remained constant, the silica phasetransformation would have progressed along the orange pathway. An overall decreaseof carbonate is evident.


18 19 20 21 22 23 24 25 26 27 28 292θ

HCl washed333°C, 2 days333°C, 6 days

calcitequartz

Figure 2.11: Representative XRD spectra showing the regions (gray boxes) used forintegrated peak heights. The two left boxes were summed to represent opal-CT. Theright box contains the primary quartz peak.

2.3. EXPERIMENTS 35

Figure 2.12: Calibration plots for XRD analysis of opal-CT and quartz abundance. (left)Calibration data for this study compared to Ernst and Calvert (1969). (right) Cali-bration data compared to whole-pattern matching results. Data are from the pyrolysisexperiments where the peak-height ratios were measured and the percent quartz wasdetermined using the Rietveld method. MF = Monterey Formation


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

percent quartz from Rietveld method

perc

ent q

uartz

from

cal

ibra

tion

curv

e

310°C data333°C data360°C data

Figure 2.13: Percent quartz determined using the Rietveld method compared to valuesobtained using integrated peak-height ratios and the calibration curve (Figure 2.12).The Rietveld method consistently overestimates the amount of quartz by as much as20%. The diagonal 1:1 line is shown for visual reference.

2.4. KINETICS ANALYSIS 37

2.4 Kinetics Analysis

Chemical kinetics describe how experimental conditions affect reaction rate and, in

ideal cases, shed light on the reaction mechanism. Kinetics determination involves

experimentation to measure reaction rates for given environmental parameters and

models to relate changes in each parameter to changes in rate. For example, the

rate of a first-order reaction depends on the concentration of the reactant (see Equa-

tion 2.6). By mapping the reaction rate at various concentrations, a rate constant

can be determined. If this is repeated at a variety of temperatures, rate constants can

be used to model the temperature dependence of the reaction (Brown et al., 2006).

For any reaction, the primary parameters of interest are concentration, temper-

ature, pressure (typically only a factor at very high pressures), diffusion, and the

presence of catalysts. For the experiments shown here, concentration is measured,

temperature is controlled, and pressure is known to be low and likely to have negligi-

ble effect on the reaction rate. Catalysts were purposely included by using a buffered

aqueous solution and including natural dolomite in the reaction vessels. These cata-

lysts are considered controlled for the purposes of this analysis and generally reflect

realistic natural conditions for this reaction.

In this work, kinetic parameters were determined in three steps. First, a rate law

was chosen to represent the reaction. Second, a rate constant was calculated from

the data for each pyrolysis temperature. Finally, the rate constants determined using

data combined from experiments at various temperatures were used to calculate the

kinetic parameters. These kinetic parameters allow prediction of the reaction rate at

any temperature. Section 2.4.1 gives an overview of the equations and methods used

in this analysis, while §2.4.2 and §2.4.3 show the resulting rate constants and kinetic

parameter calculations, respectively.

2.4.1 Chemical analysis methods

The process of converting microcrystalline opal-CT to quartz in the presence of an

aqueous solution likely comprises several reactions with many potential species being

formed. To simplify the analysis, the rate contributions of those secondary reactions


are absorbed into the rate determination of the overarching reaction,

(SiO2)(opal-CT,aq) −→ (SiO2)(qtz,aq) abbreviated Op −→ Qtz . (2.3)

This reaction is associated with a rate law that describes how the reaction pro-

gresses as a function of the concentrations of reactant and product. Note that for this

reaction, the relevant concentration is not that of silica in aqueous solution but rather

the fractional proportions of opal-CT and quartz relative to the‘ 1 total solid silica.

Therefore, the concentration of opal-CT ([Op]) will be a number between 0 and 1, and

the concentration of quartz ([Qtz]) will also range from 0 to 1 with [Qtz] = 1− [Op].

Three different rate laws were considered in this analysis: a zero-order reaction, a

first-order reaction, and a combined nucleation and growth reaction.

Zero-order reaction

A zero-order reaction has the simplest rate law; the reaction progresses independently

of the concentrations of the species involved. The reaction rate r is equal to the rate

constant k. In differential form, the zero-order rate law is written

r = −∂[Op]

∂t

∣∣∣∣P,T

= kT . (2.4)

Here, the rate constant is given a subscript T to indicate it is associated with a single

temperature. The integral form of this rate law is

[Op] = [Op]0 − kT t , (2.5)

where [Op]0 is the initial concentration of opal-CT. Because the sum of opal-CT

and quartz concentrations equal unity, for a zero-order rate law, a plot of quartz

concentration versus time will yield a line with a slope of kT .


First-order reaction

In a first-order reaction, the reaction rate depends on the concentration of reactant.

The differential form of the rate law is

r = −∂[Op]

∂t

∣∣∣∣P,T

= kT [Op] , (2.6)

and the integral form is

[Op] = [Op]0e−kT t . (2.7)

For a first-order reaction, a plot of ln[Op] versus time will yield a line with a slope of

−kT .

Nucleation and growth reaction

The nucleation and growth reaction kinetics are typically modeled using the Avrami

equation (Avrami, 1939) which can be written as (Christian, 1975; Stein and Kirk-

patrick, 1976)

f = 1− exp{−κIY n−1tn

}, (2.8)

where f is the product fraction, κ is a geometric factor, I is the nucleation rate, and

Y is the growth rate. The exponent n is interpreted to correlate with the dimension

of growth. In this formulation, n = 2 corresponds to 1D growth (needles), n = 3 is 2D

growth (platelets), and n = 4 is 3D growth (cubes and spheres). When heterogeneous

nucleation sites become saturated, the nucleation rate may decrease causing n to take

on non-integer values (Avrami, 1940).

If the nucleation and growth rates are combined with the geometric factor and

represented as a single reaction rate, Equation 2.8 can be written as (e.g., Huang,

2003)

f = 1− exp {−kT tn} . (2.9)

The integral form of this equation is

ln [ln (1/(1− f))] = n ln t+ ln kT . (2.10)


For this reaction, a plot of ln [ln (1/(1− f))] versus ln t will yield a line with a slope

of n. If initial product fraction is non-zero, as is the case here with detrital quartz

present in the starting material, the equation must be rewritten as

ln [ln (α/(α− f ′))] = n ln t+ ln kT , (2.11)

where α is the initial reactant fraction and f ′ is the product fraction minus the initial

product fraction.

As stated before, any dissolution and precipitation reaction will be influenced

by a variety of factors, many of them involving the solvent, including dissolution

rate, diffusion, and reactions involving intermediate species. Even the nucleation and

growth equations presented here are a simplified representation of these processes.

Comparing rate laws

A cartoon depicting the various reaction curve shapes is shown in Figure 2.14. The

cartoon approximates a plot of the quartz fraction versus time. Rate constants are

arbitrarily scaled for easy comparison of the curves. The zero-order reaction, which

progresses at a constant rate regardless of concentration, plots as a straight line (blue).

The first-order reaction (green curve) progresses quickly at the beginning when the

quartz content is low, but it slows as the quartz content grows. The nucleation and

growth reaction (purple dashed curves) plots as a series of sigmoids with varying n

values. For n = 1, the curve is coincident with the first-order reaction curve. For

n = 1 through 4, the “S” shape grows increasingly clear. These reactions start out

slowly, speed up for intermediate quartz concentrations, and then trail off again as

the reaction nears completion.

Arrhenius equation

The rate constants for a reaction at varying temperatures are related through the

Arrhenius equation (e.g., Brown et al., 2006)

kT = A0 exp {−Ea/(RT )} , (2.12)


time

reac

tion

prog

ress

ion

zero orderfirst orderAvrami n = 1.0Avrami n = 2.0Avrami n = 3.0Avrami n = 4.0

start

finish

Figure 2.14: Cartoon showing the reaction progressions for zero-order, first-order, andnucleation and growth reactions (Equations 2.5, 2.7, and 2.10, respectively). Reactionrates are arbitrarily scaled to aid in visualization. Note that the Avrami equation takesthe same shape as a first-order reaction when n = 1.

where A0 is the pre-exponential factor, Ea is the activation energy, and R is the ideal

gas constant. The activation energy can be thought of as the potential energy barrier

that the reaction must overcome to proceed. The pre-exponential factor is a measure

of how frequently molecules collide in the reactive system. When these two parameters

are determined experimentally, the rate of the reaction at any temperature can be

predicted.

2.4.2 Determining reaction rates

The reaction rate at each temperature was calculated assuming zero-order, first-order,

and nucleation and growth reactions. The data from Ernst and Calvert (1969) are

shown with this study’s data for comparison.

Note that a pyrolysis time corresponding to 100% quartz concentration provides an


upper bound on the time to full conversion but will not necessarily fit the conversion

trend for that temperature run. Therefore, the analysis shown here excludes the 100%

quartz times from the Ernst and Calvert data.

Zero-order reaction

If the opal-CT to quartz phase transition is a zero-order reaction, a plot of fractional

quartz concentration versus time will yield a line with a slope equal to the reaction

rate k and an intercept equal to the initial quartz concentration [Qtz]0. During this

analysis, an initial detrital quartz concentration was assumed to be 3.5% and was

removed from the data by rescaling. A linear fit to the data was found using a least-

squares method and the constraint that [Qtz]0 = 0. The data and resulting linear fits

are shown in Figure 2.15.

0 500 10000

0.2

0.4

0.6

0.8

1.0

R2 = 0.69

0 50 100 150 2000

0.2

0.4

0.6

0.8

1.0

R2 = 0.82

0 50 1000

0.2

0.4

0.6

0.8

1.0

R2 = 0.78

310°C 333°C 360°C

this study

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1.0

R2 = 0.94

0 100 200 300 4000

0.2

0.4

0.6

0.8

1.0

R2 = 0.94

0 10 20 300

0.2

0.4

0.6

0.8

1.0

R2 = 0.94

300°C 400°C 500°C

Ernst & Calvert

time (hrs)

frac

tion

of re

actio

n co

mpl

eted

([Q

tz])

Figure 2.15: Plots of experimental data and the linear fit of the form of Equation 2.5.The R2 values for each line are shown on the plots.

The axes in Figure 2.15 match those in Figure 2.14, so the shape of the data

trends can be compared to three reaction types. The Ernst and Calvert (1969) data


(top panels) appear linear with a possible exception of the 300◦C experiments. It is

not surprising, then, that these data were initially interpreted to represent a zero-

order reaction. In contrast, the data from this study (bottom panels) do not follow

linear trends. The reactions appear to start slowly and gradually increase in rate

at approximately 20% quartz concentration. This is more indicative of a nucleation

and growth reaction than of a zero-order reaction. The R2 values associated with

linear fits to these data are lower than those of the Ernst and Calvert data, further

supporting the observation that the curves are shaped differently.

Note that the outlier in the Ernst and Calvert data, the curved trend for the 300◦C

experiments, is their only run conducted below the critical point of water. This lends

additional support to the decision in this study to conduct all three pyrolysis runs

below 374◦C.

The rate constants calculated for all six pyrolysis runs are given in the top section

of Table 2.5. The units of kT for a zero-order reaction are concentration per time,

typically mol/L/hr. Because fractional concentrations are used here, the units of k

simplify to inverse time, 1/hr.

First-order reaction

If the opal-CT to quartz phase transition is a first-order reaction, a plot of the natural

logarithm of fractional opal-CT concentration versus time will yield a line with a slope

whose magnitude is the reaction rate k and an intercept equal to the logarithm of the

initial opal-CT concentration [Op]0. Again, an initial detrital quartz concentration

was assumed to be 3.5% and was removed from the data by rescaling. A linear fit to

the data was found using a least-squares method and the constraint that [Qtz]0 = 0,

that is, that ln[Op]0 = ln 1 = 0. The data and resulting linear fits are shown in

Figure 2.16.

Neither the Ernst and Calvert (1969) data nor the data from this study are fit

well by a line in this domain. The R2 values for lines fitting all six pyrolysis series

are lower than for the corresponding zero-order fits.

The first-order rate constants calculated for all six pyrolysis series are given in the

lower half of Table 2.5. The units of kT for a first-order reaction are inverse time;


0 1000 2000 3000 4000-1.0

-0.8

-0.6

-0.4

-0.2

0

R2 = 0.87

0 100 200 300 400-2.0

-1.5

-1.0

-0.5

0

R2 = 0.85

0 10 20 30-5.0

-4.0

-3.0

-2.0

-1.0

0

R2 = 0.62

0 500 1000-2.5

-2.0

-1.5

-1.0

-0.5

0

R2 = 0.55

ln (f

ract

ion

of re

actio

n co

mpl

eted

)

0 50 100 150 200-2.5

-2.0

-1.5

-1.0

-0.5

0

R2 = 0.66

0 50 100-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

R2 = 0.61

310°C 333°C 360°C

300°C 400°C 500°C

time (hrs)

this study

Ernst & Calvert

Figure 2.16: Plots of experimental data and the linear fit of the form of Equation 2.7.The R2 values for each line are shown on the plots.

this is true regardless of the units of concentration. Although the zero and first-order

rate constants have the same units in this formulation, they reflect fundamentally

different relationships between concentration and time and should not be confused.

Nucleation and growth reaction

If the opal-CT to quartz phase transition is a nucleation and growth reaction de-

scribed by Avrami’s equation, a plot of the left hand side of Equation 2.11 versus the

logarithm of time will yield a line with a slope of n and an intercept of ln kT . In this

case, the initial detrital quartz concentration was not removed by rescaling. Instead,

α was set to 0.965 and f ′ = f − 0.035. A linear fit to the data was found using a

least-squares method with no applied constraints. The data and resulting linear fits

are shown in Figure 2.17.

The fits to the Ernst and Calvert data have R2 values comparable to those deter-

mined using a zero-order reaction. However, the fits for data in the present study are


Table 2.5: Rate constants for all six pyrolysis series calculated assuming zero-order andfirst-order reactions. Initial quartz concentrations were constrained to zero.

reaction Ernst & Calvert this study

type temp kT (hr−1) temp kT (hr−1)

zero-order300◦C 0.0001748 310◦C 0.001092400◦C 0.002697 333◦C 0.004742500◦C 0.03528 360◦C 0.01013

first-order300◦C 0.0002433 310◦C 0.002428400◦C 0.002465 333◦C 0.01033500◦C 0.1116 360◦C 0.02603

significantly better than the zero-order fits.

The top section of Table 2.6 shows the n values (indicating dimension of crystal

growth) and rate constants corresponding to Equation 2.11 determined for the six

pyrolysis series. The results for the Ernst and Calvert data shown here are consistent

with those of Stein and Kirkpatrick (1976). However, they assumed an initial quartz

concentration of 8%, which affects the slopes of the best fit lines, particularly for the

300◦C series, which has several points with quartz concentrations near the assumed

detrital values. Their analysis included visual inspection of the pyrolysis products to

determine the morphology of the quartz growth. They found primarily quartz needles

which were consistent with their slopes of 1.99, 1.11, and 2.16 (n = 2 corresponding

to one-dimensional growth). No explanation for the low n value of the 400◦C data

was offered, but they pointed out that exclusion of the early time data for that run

would yield a fit line (shown in gray in Figure 2.17) whose slope is consistent with

the other two temperatures.

Because of the different assumed initial quartz concentration, the n values calcu-

lated here for the Ernst and Calvert data were lower than that of Stein and Kirkpatrick

(1976). There was also a wide scatter in n values for those pyrolysis series. However,

the data from this study produced a fairly focused group of n values between 2 and 3.

This indicates 1D growth (needles) to 2D growth (platelets), consistent across all

three temperatures.

In the analysis so far, each set of temperature experiments has a slightly different


1 2 3 4 5 6 7 8 9-5

-4

-3

-2

-1

0

1

2this study

ln (time [hrs])

310°C(R2 = 0.88)333°C

(R2 = 0.92)

360°C(R2 = 0.92)

1 2 3 4 5 6 7 8 9-5

-4

-3

-2

-1

0

1

2

? Ernst & Calvert

ln ln

(α/(α

-f’)

)

300°C(R2 = 0.91)

400°C(R2 = 0.88)500°C

(R2 = 0.91)

Figure 2.17: Plot of experimental data and the linear fit of the form of Equation 2.11.The R2 values for each line are shown on the plot. The gray line superimposed on the400◦C data reflects the subset of data used by Stein and Kirkpatrick (1976) to matchthe observed quartz morphology (see text).

value of n with a corresponding rate constant that depends on n. These rate constants

cannot be compared on a standard Arrhenius plot because of the differing n values.

Therefore, another set of fit lines was generated using the averages of n, a fixed value

of 1.30 for the Ernst and Calvert data and 2.45 for this study’s data. The effect was a

series of lines with a single, fixed slope. Only the intercept, related to kT , was allowed

to vary. The resulting rate constants are listed in the lower portion of Table 2.6. The

new fits are compared to the previous fits in Figure 2.18. Note that the Ernst and

Calvert data, which had a larger spread in n, show different trends with a fixed n.


The data from this study are fit well by their fixed-n lines. In fact, the R2 values of

the new fits are almost unchanged for these data while the R2 values for the fixed-n

lines of the Ernst and Calvert data are significantly reduced from the unconstrained

fits.

fit with n = 2.45

fit with n = 1.30

1 2 3 4 5 6 7 8 9-5

-4

-3

-2

-1

0

1

2this study

ln (time [hrs])

310°C(R2 = 0.88)333°C

(R2 = 0.92)

360°C(R2 = 0.91)

1 2 3 4 5 6 7 8 9-5

-4

-3

-2

-1

0

1

2Ernst & Calvert

ln ln

(α/(α

-f’)

)

300°C(R2 = 0.88)

400°C(R2 = 0.77)500°C

(R2 = 0.83)

Figure 2.18: Plot of experimental data and the linear fit of the form of Equation 2.11.Thin solid lines are the fits shown in Figure 2.17. The dashed lines show the fit withn values (slope) fixed at 1.30 for the Ernst and Calvert data and 2.45 for this study’sdata. The R2 values for each new fit are shown on the plot.

2.4.3 Determining kinetic parameters

Using the rate constants found in the previous section, the pre-exponential factor A0

and activation energy Ea were determined using Equation 2.12. They were calculated


Table 2.6: Nucleation and growth reaction rates for the six hydrous pyrolysis runs. Initialquartz concentrations were not scaled a priori ; instead, Equation 2.11 was used toaccount for the initial quartz concentration. The top section of the table containsvalues calculated from the unconstrained fit to the data. The lower section fixes n andfinds the best fit value of kT .

Ernst & Calvert this study

temp n kT (hr−n) temp n kT (hr−n)

300◦C 1.09 0.00009483 310◦C 2.47 0.0000001687400◦C 0.961 0.004310 333◦C 2.25 0.00001722500◦C 1.83 0.006301 360◦C 2.63 0.00002207

300◦C 1.30 0.00002355 310◦C 2.45 0.0000001861400◦C 1.30 0.0009688 333◦C 2.45 0.000007148500◦C 1.30 0.02503 360◦C 2.45 0.00004408

from an unconstrained least-squares linear fit to the data plotted as ln kT versus 1/T .

The resulting plots including fits and their R2 values are shown in Figure 2.19.

The pyrolysis series from this study all transformed faster than expected based

on the Ernst and Calvert zero-order kinetics. This is reflected by the rate constants

from this study, which are larger than those of Ernst and Calvert at high laboratory

temperatures. However, the rate at which kT changes with temperature is the predic-

tor of low temperature behavior. For both the zero- and first-order reaction analyses,

the Arrhenius plot shows steeper slopes for this study’s data than those of the Ernst

and Calvert data. This means there is a temperature at which the two data series

predict the same rate constant; and at temperatures below that, the data from this

study predict slower reaction rates than those of Ernst and Calvert. These cross-over

temperatures are indicated on the plots; it is approximately 208◦C for the zero-order

reaction and 170◦C for the first-order reaction. Thus, in natural systems where this

phase transition occurs, the data from this study predict slower transitions than those

of Ernst and Calvert.

The nucleation and growth plot (right panel in Figure 2.19) shows the extreme

temperature dependence of the data from this study. The implied transition time

cannot be directly compared to that of the Ernst and Calvert nucleation and growth


curve, though, because the rate constants are related to concentration through dif-

ferent values of n.

Extrapolation of the laboratory-derived Arrhenius plots to typical basin condi-

tions involves significant uncertainty because the temperatures used to define the

rate constant are much closer to each other than they are to basin temperatures. Un-

fortunately, little can be done to reduce that uncertainty because lower temperature

experiments would involve reactions far too slow to be measured in the laboratory.

1 1.5 2 2.5 3 3.5-30

-25

-20

-15

-10

-5

0

5

log(

k)

zero order

R2 = 0.995

R2 = 0.96

1 1.5 2 2.5 3 3.5-30

-25

-20

-15

-10

-5

0

5

1000/temp (1/K)

first order

R2 = 0.98

R2 = 0.98

1 1.5 2 2.5 3 3.5-30

-25

-20

-15

-10

-5

0

5nucleation and growth*

R2 = 0.998

Ernst & Calvert

this study

R2 = 0.96

Ernst & Calvertthis study

Ernst & Calvertthis study

* n = 2.45

* n = 1.30208°C

170°C

Figure 2.19: Arrhenius plots (Equation 2.12)for zero-order, first-order, and nucleation andgrowth reactions. The R2 values for the linear fits are shown on the plots. The cross-over temperature (the highest temperature at which this study’s data predict fastertransformation than Ernst and Calvert data) is marked for the zero- and first-orderreactions. The two nucleation and growth fits are not directly comparable becausethey assume different values of n.

The pre-exponential factors and activation energies calculated for the zero-order,

first-order, and nucleation and growth reactions are shown in Table 2.7. The acti-

vation energies for this study’s zero- and first-order reactions are higher than those

from Ernst and Calvert. The pre-exponential factor is higher as well.

2.4.4 Implications for transformation rates

Comparing kinetic parameters across differing reaction types may not be intuitive,

but included here are two simple ways to assess the implications of these parameters

on transformation rates. The first example computes the half life of the reaction


Table 2.7: Pre-exponential factors and activation energies for the zero-order, first-order,and nucleation and growth reactions.

Ernst & Calvert this study

reaction A0 Ea A0 Eatype (1/hr)* (kcal/mol) (1/hr)* (kcal/mol)

zero-order 1.157×105 23.22 1.960×109 32.52

first-order 3.063×106 26.68 2.709×1010 34.67

nucleation & growthn = 1.30 9.762×106 30.54 – –n = 2.45 – – 2.215×1023 79.79

*unit of A0 for nucleation and growth is 1/hr−n

for each set of parameters at selected temperatures. The second example shows the

reaction progress predicted by each set of kinetic parameters compared to measured

data.

Reaction half life

The half life of a reaction is the time required to reach 50% completion. For the

opal-CT to quartz transition, this is the time required to convert 50% of the initial

opal-CT into quartz. The transition time depends on the kinetic parameters as well

as the reaction type (Equations 2.5, 2.7, or 2.11). Table 2.8 shows the rate constant

and corresponding half life predicted by the Ernst and Calvert (1969) data and this

study’s data for three temperatures. The selected temperatures, 30◦C, 60◦C, and

120◦C, were chosen to represent typical basin temperatures.

At the selected temperatures, the Ernst and Calvert kinetic parameters for the

zero-order reaction predict the fastest phase transitions. Even at only 30◦C, the

reaction is predicted to take less than 30 Ma. At low temperatures, this study predicts

longer opal-CT to quartz transitions times by two orders of magnitude or more.

One interesting feature illustrated in the half life table concerns the comparison

between the zero-order and nucleation and growth reactions. The difference between

the predicted reaction half lives of those two reaction types is less than 20% for the

Ernst and Calvert data and about 10% for this study’s data. This demonstrates why


Table 2.8: Predicted rate constants and reaction half lives at low temperatures. Recallthat the nucleation and growth equations use n = 1.30 for the Ernst and Calvert dataand n = 2.45 for this study.

reaction Ernst & Calvert this study

type temp kT half life (Ma) kT half life (Ma)

zero-order30◦C 2.062×10−12 27.66 6.842×10−15 8337.60◦C 6.645×10−11 0.8583 8.861×10−13 64.37

120◦C 1.408×10−8 0.004052 1.603×10−9 0.03558

first-order30◦C 1.733×10−13 456.2 2.605×10−15 29835.60◦C 9.377×10−12 8.433 4.736×10−13 167.0

120◦C 4.415×10−9 0.01791 1.408×10−9 0.05618

nucleation 30◦C 9.097×10−16 33.28 6.110×10−35 9254.and 60◦C 8.765×10−14 0.9912 9.316×10−30 70.91

growth 120◦C 1.005×10−10 0.004393 9.174×10−22 0.03874

zero-order reaction kinetics have been relatively successful at predicting silica phase

transition depths even though the morphological data show that it is not a simple

zero-order reaction (Stein and Kirkpatrick, 1976).

Reaction progress

Visualization of the full reaction progression can be helpful in understanding the

differences between the various kinetics parameters. The reaction progressions pre-

dicted by the six combinations of reaction types and calculated kinetics parameters

are shown in Figure 2.20. Note that each plot can be compared to those in Figures 2.14

and 2.15.

Each plot in Figure 2.20 contains data for a single temperature. The 300◦C

pyrolysis series from Ernst and Calvert (1969) is in the upper left; the other three

plots contain data from this study. At each temperature, the data are compared

to the predicted reaction progression for zero-order, first-order, and nucleation and

growth reactions using parameters determined from both studies.

Not surprisingly, the data are fit best using the kinetic parameters they produced;

that is, the data from this study are best fit by the kinetic parameters derived from


them. The kinetic parameters from this study greatly underestimate the transfor-

mation time for the Ernst and Calvert data, and the Ernst and Calvert parameters

greatly overestimate the transition times for the data in this study.

At the four temperatures shown in Figure 2.20, the Ernst and Calvert parameters

for all three reaction types show fairly linear progressions. The sigmoid shape of

the nucleation and growth reaction is not pronounced because of the small n value

obtained in this analysis.

The kinetic parameters derived from the data in this study show much more dis-

tinctive reaction progressions. The sigmoid of the nucleation and growth reaction

approximates the sigmoid shape of the pyrolysis data. Although the zero-order re-

action line misses the curvature in the phase transition data, it predicts the time to

total phase transition well. This is another indicator that zero-order kinetics may be

an adequate substitute for full nucleation and growth kinetics as long as the time to

total (or half) transition is of primary importance. The zero-order reaction approxi-

mation will be less reliable when intermediate states (say, 25% quartz concentration)

are considered.

2.5 Additional Samples

In addition to the Monterey Formation samples discussed in §2.3.1, the characteriza-

tion and hydrous pyrolysis experiments here were also carried out using an opal-CT-

rich porcelanite from the Neogene Wakkanai Formation, an agrillaceous sedimentary

formation in northeastern Horonobe, Hokkaido, Japan. The region is tectonically

active, and the test site is located 15 km from the coast of the Japan Sea and 3 km

from regional hydrothermal hot springs. The opal-CT-rich Wakkanai Formation,

along with the overlying opal-A-rich Koetoi Formation, were studied extensively by

the Horonobe Underground Research Laboratory in conjunction with the Japan Nu-

clear Cycle Development Institute (e.g., Morioka, 2004; Amo et al., 2007; Hama et al.,

2007; Amo et al., 2008; Kurikami et al., 2008). The Wakkanai Formation is a known

source rock for regional oil and gas fields, although many are no longer in production

(Wasada et al., 1996; Hama et al., 2007).

2.5. ADDITIONAL SAMPLES 53

0 1000 2000 3000 40000

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1.0

0 50 100 150 2000

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1.0

time (hr)

frac

tion

of re

actio

n co

mpl

eted

([Q

tz])

300°C 310°C

333°C 360°C

Ernst & Calvertdatazero order

first ordernucleation & growth

this studydatazero order

first ordernucleation & growth

Figure 2.20: Hydrous pyrolysis data compared to the predicted reaction progress usingzero-order, first-order, and nucleation and growth reactions determined by data fromthis study and Ernst and Calvert (1969).

The Wakkanai Formation samples studied here, provided by JOGMEC, came

from well HDB-2 at a depth of 141 m (personal communication, Kunihiro Tsuchida,

2009), approximately 100 m below the first significant appearance of opal-CT in the

well (Ota et al., 2007). Analogous samples from the region contain approximately

1% TOC (Amo et al., 2007). XRD analysis indicates that the material used in this

study was roughly 51% opal-CT, 26% quartz, 17% albite, and 6% muscovite. Unlike

the Monterey Formation porcelanite, the Wakkanai Formation porcelanite contains

no natural carbonate as a magnesium source. However, it does contain clay which

is observed to correspond with accelerated opal-CT to quartz transition (Keller and

Isaacs, 1985).

The core was prepared by drilling plugs parallel and perpendicular to the bedding.


Figure 2.21 shows one of these plugs. The millimeter-scale lamination that was vis-

ible in the Monterey Formation samples is not apparent in the Wakkanai Formation

samples. The plugs were more homogeneous in appearance and darker in color due

to clays and organic material that were lacking in the weathered Monterey Formation

samples. The remaining material was ground for pyrolysis experiments and prepared

in the same way as the Monterey Formation samples.

Figure 2.21: Photograph of representative core plug from the Wakkanai Formation porce-lanite. No lamination can be seen in this sample. The dark color arises from thepresence of clay and a non-zero TOC.

Results of the geophysical characterization of the samples are shown in Table 2.9.

The Wakkanai Formation samples have significantly higher porosity than the Mon-

terey Formation porcelanite. The average grain densities are similar, but for different

reasons. The Monterey Formation porcelanite comprises opal-CT and dolomite, but

the Wakkanai Formation samples contain more high-density quartz and low-density

clay. Only compressional benchtop velocities could be measured for the Wakkanai

Formation samples. The resulting values were approximately half of those of the

Monterey Formation porcelanite, consistent with other geophysical studies (Ota et al.,

2007). Because the shear wave speed was not measured, Poisson’s ratio could not be

calculated, but published values suggest it averages 0.11 (Morioka, 2004). The single

Thomsen parameter ε was determined to be

ε ≈ Vp(90)− Vp(0)

V p(0)= 0.147 .

The Wakkanai Formation material underwent hydrous pyrolysis using the same

conditions described in §2.3.2.1. Five grams of the ground and sieved material was

2.5. ADDITIONAL SAMPLES 55

Table 2.9: Sample characterization for Wakkanai Formation plugs.

quantity units ⊥ to bedding ‖ to bedding

bulk density [g/cc] 1.58± 0.07 1.57± 0.06grain density [g/cc] 2.406± 0.004 2.450± 0.006

porosity [–] 0.35± 0.03 0.36± 0.02Vp [km/s] 2.299± 0.005 2.636± 0.005Vs [km/s] – –ν [–] – –

combined with 13.3 g, 12.25 g, or 10.5 g of pH 7 buffered solution and heated to

310◦C, 333◦C, or 360◦C, respectively.

The pH of the recovered fluid, which ranged from 7.0 to 7.4, was slightly lower on

average than that of the Monterey Formation samples. These values are consistent

with the measured pH of the natural, circulating pore fluids in the formation at depth

(Hama et al., 2007).

The Wakkanai Formation solids recovered after pyrolysis were quite different in

character than the Monterey Formation solids. When the vessels were opened, there

was a strong odor of sulfur and hydrocarbons. Instead of a light-colored scale forming

on the interior of the pyrolysis vessels, there was often a dark-colored scale flecked

with shiny gold-colored bits, likely pyrite.

After drying, the recovered solid Wakkanai Formation samples were analyzed using

powder XRD to determine the extent of the opal-CT to quartz phase transition. Even

at the highest pyrolysis temperature (360◦C), samples heated for 17 days showed no

discernible phase transformation. The opal-CT peak sharpened, indicating improved

crystallinity, but the quartz concentration did not change. Recall that the Monterey

Formation material transformed completely in only three days at that temperature.

The cause of the severe retardation of the reaction rate for the Wakkanai samples

remains undetermined. The pH values of the pore fluids for the two sample types were

similar, so pH is not likely to be the key factor. The Wakkanai Formation samples do

have a non-zero amount of organic material, in contrast to the Monterey Formation

samples. It is possible that the rock matrix is oil wet; a fine coating of residual oil,

immiscible with water, could provide a physical barrier to dissolution. This could


be tested by chemically removing the organic material from the ground sample and

attempting pyrolysis again. Residual oil may also be observable in thin section.

The other important question that these experiments raise concerns the role of

clay. Field observations indicate that clay is a catalyst for the opal-CT to quartz

phase transition (Keller and Isaacs, 1985). However, those observations were made at

significantly lower temperatures than these experiments. Figure 2.19 demonstrated

that the dependence of rate on temperature, not the absolute rate, is crucial to pre-

dict phase transitions under varying conditions. Clay may be a catalyst for the phase

transition at low temperatures, but behavior at high temperatures could be very dif-

ferent. This is illustrated in Figure 2.22. The kinetics predicted by the Monterey

Formation samples is shown in purple (no clay). Dashed line 1 represents a shift to

faster reaction rates at all temperatures. Dashed line 2 represents a suppressed depen-

dence on temperature. At the observed reaction rate at basin temperatures indicated

in the figure, both dashed lines predict that clay accelerates the phase transition.

At laboratory conditions, though, the two dashed lines predict very different behav-

ior. It is possible, therefore, that clay itself may be the cause of the slow Wakkanai

Formation transformation at laboratory temperatures while also being the cause of

improved transformation conditions at low temperatures.

2.6 Conclusions

The reaction pathway from opal-A to opal-CT to quartz is observed in siliceous de-

posits throughout the world. Despite extensive investigation, the chemical kinetics

describing the transitions remain poorly determined. This study focused on assessing

the kinetics of the opal-CT to quartz transition under geologically realistic conditions

that included buffered pH similar to that in subsurface reservoirs.

Hydrous pyrolysis experiments on weathered Monterey Formation porcelanite in-

dicate that the opal-CT to quartz phase transition is well described by a nucleation

and growth model with one dimensional (needle) to two dimensional (platelet) growth.

A zero-order reaction model provides an acceptable approximation to the full nucle-

ation and growth model; the time to total conversion differs only by about 10%.

2.6. CONCLUSIONS 57

1 1.5 2 2.5 3 3.5-30

-25

-20

-15

-10

-5

0

5

log(

k)

zero order

1000/temp (1/K)

no clay

observed rate

clay

2 ?

1 ?

Figure 2.22: Two possible ways clay could affect kinetic plots (see Figure 2.19). If clayacts as a catalyst at all temperatures, the kinetics could be represented by dashed line1. If clay also affects the temperature dependence of the reaction, dashed line 2 mightbe more accurate. The reaction rate at a single observed temperature could be thesame under either scenario while laboratory experiments at high temperatures wouldsee very different rates.

The new kinetics data derived here differ significantly from prior studies that

involved similar source material but used distilled water. In this study, the naturally-

occurring carbonates and buffered aqueous solution resulted in a 10 kcal/mol increase

in activation energy for the zero-order reaction assumption.

Parallel experiments on clay-rich Wakkanai Formation porcelanites exhibited sig-

nificantly reduced reaction rates to the extent that no phase transition occurred dur-

ing pyrolysis. The mechanism behind the reaction retardation is still unknown, but

further experiments could elucidate this problem.

It is hoped that the phase transition kinetics determined here will prove useful for

basin-scale petroleum system modeling because the experimental conditions under

which they were derived more closely match geologic conditions than those from

previous studies.


Acknowledgements

This work would not have been possible without significant contributions of expertise

and resources by Michael D. Lewan at the U.S. Geological Survey. Kenneth Peters

(Schlumberger) consulted extensively on the project. Monterey Formation samples

were provided by John Roulston (World Minerals Inc.). Initial XRD spectra were

acquired by Bill Benzel (USGS). FTIR data were acquired at the Schlumberger-

Doll Research Center with Michael Herron. Bob Jones provided XRD training at

Stanford. Additional thanks to Stephanie Vialle for many discussions of geochemistry

and physico-chemical processes.

59

Chapter 3

Incorporating silica phase

transition kinetics into a basin and

petroleum system model of the San

Joaquin Basin, California

3.1 Abstract

Basin and petroleum system models are useful to predict the volume and composition

of hydrocarbon accumulations. They contain information on both the present day

structure and the evolution of that structure over geologic time and the associated

generation, migration, and accumulation of fluids.

In basins containing siliceous facies, amorphous opal-A undergoes a phase transfor-

mation to microcrystalline opal-CT, which subsequently can transform to crystalline

quartz. These mineralogical changes are accompanied by changes in porosity and

permeability that affect the migration and trapping of fluids. Silica phase changes

can result in diagenetic traps where no structural traps exist. The rate and timing

of the phase transformations is therefore important to consider when modeling the

evolution of basins that contain siliceous deposits.

This chapter compares the ability of different phase transformation descriptors to

60 CHAPTER 3. SAN JOAQUIN BASIN MODEL

accurately predict the transition depth from opal-CT to quartz in known oil fields.

Two- and three-dimensional (2D and 3D) basin models were run using PetroMod R©software along a seismic section in the southern San Joaquin Basin, California. Pre-

dictions from these models were compared to the observed transition depth in the

nearby Rose and North Shafter oil fields. The phase change was predicted using

chemical kinetics determined by Ernst and Calvert (1969) and kinetics derived ex-

perimentally in this volume (Chapter 2). The transition was also predicted using a

regional nomogram based on detritus content developed by Keller and Isaacs (1985).

Results show that the known opal-CT to quartz transition depth for the Monterey

Formation in the southern San Joaquin Basin is best predicted from the Keller and

Isaacs nomogram by assuming a clay content of approximately 20%, although a priori

knowledge of the clay content is not generally available. The Ernst and Calvert

kinetics underestimate the transition depth by nearly 3000 ft. The kinetics derived

here improve on the Ernst and Calvert prediction but overestimate the transition

depth by roughly 800 ft.

Density and acoustic velocity predictions from the 2D basin model were extracted

to create a synthetic seismic section through the Monterey Formation. The modeled

seismic response of the opal-CT/quartz boundary mimics the response of an oil/water

fluid interface in a homogeneous layer, demonstrating why this transition is difficult

to interpret during exploration using seismic data alone.

3.2 Introduction

Expansive deposits of siliceous rocks occur throughout the world, particularly around

the Pacific Rim from Sakhalin and Japan to central California. They originate from

marine diatoms that undergo diagenetic conversion. Their silica content is converted

from amorphous opal-A to microcrystalline opal-CT and eventually to fully crystalline

quartz. The opal-A-rich diatomites that are initially formed are characterized by high

porosity but very low permeability. A standard burial trend predicts monotonically

decreasing porosity and permeability with depth; however, the subsequent phase tran-

sitions affect the storage and transport properties of the rock. During the conversion


from opal-A to opal-CT, porosity and permeability are relatively unaltered. However,

during the conversion from opal-CT to quartz, preferential dissolution pathways can

develop, leading to an increase in permeability in the quartzose chert phase. In addi-

tion, water is expelled as the denser quartz crystals form, and further burial causes

the development of fracture networks. This results in a low-porosity, quartzose chert

that retains significant permeability (e.g., Williams and Crerar, 1985; Nobes et al.,

1992; Chaika and Williams, 2001; Reid and McIntyre, 2001). These property changes

are summarized in Figure 3.1.

intermediate quartz

medium porosity

quartz

low porosity

low matrix perm

Burial

high fracture perm

opal-A

high porosity

low perm

opal-CT

high porosity

low perm

oil-filled pores

medium perm

Figure 3.1: Schematic transition of a siliceous layer from porcelanite to medium and lowporosity quartz phases ending in chert. Porosity generally decreases with burial; perme-ability increases in the intermediate region before decreasing again. The permeabilityin the quartz region is due almost entirely to fractures.

The complex evolution of porosity and permeability in siliceous deposits is impor-

tant in oil and gas exploration. Significant chert permeability allows the quartz-rich

sections to act as conduits for hydrocarbons. The decrease in permeability at the

(shallower) opal-CT/quartz boundary can act as a seal causing a diagenetic trap for

hydrocarbons even in dipping layers that contain no structural or other stratigraphic

traps (e.g., Kidney et al., 2003; Grau et al., 2003). Figure 3.1 shows a schematic of

how this trapping mechanism works.


In some locations, such as southern California and northern Japan, the siliceous

rocks that undergo phase transitions also contain organic material. The hetero-

geneities resulting from silica phase changes can cause a single geologic layer to com-

prise three of the four essential elements of a petroleum system (source rock, reservoir

rock, seal rock, and overburden rock). This is illustrated in Figure 3.2. Siliceous rocks

can also be affected by both processes of the petroleum system (trap formation and

petroleum generation-migration-accumulation) (Magoon and Dow, 1994).high fra

cture perm

1

2

34

1 source rock2 reservoir rock3 seal rock4 overburden rock

Figure 3.2: Schematic shows how a single depositional layer can comprise multiplepetroleum system elements.

In efforts to successfully predict the volumes and locations of hydrocarbon ac-

cumulations, timing is as important as geometry. A structural anticline fails to act

as a structural hydrocarbon trap if the anticline forms after hydrocarbons migrate

through the region. That is why dynamic basin and petroleum system modeling has

become a critical tool in oil and gas exploration. A basin and petroleum system model

integrates all available geological and geophysical data for a basin (including outcrop

data, well picks, and seismic sections) to create as complete a picture as possible of

the basin in the present day. Paleosections may also be used for constraining past ge-

ometries. Geochemical data on the organic material in the source rock and generated

hydrocarbons is incorporated as well. The present-day model of the basin becomes a

boundary condition for the dynamic model. Evidence concerning depositional history

and erosion are incorporated to infer historical basin conditions. Models also include


estimates of compaction, uplift, basal heat flow, global temperature and sea water

changes, petroleum generation, and petroleum migration. Iterative forward modeling

of the model area from the time of deposition produces predictions of present-day

conditions that can be calibrated to observational data (Hantschel and Kauerauf,

2009, and references therein). With a well-calibrated thermal history, silica phase

transition depths can be calculated as long as a reliable description of what triggers

the reaction is available.

Chapter 2 discussed the difficulty in identifying the triggers of silica phase transi-

tions. Generally, heat and time are required for the reactions. Because the transitions

from opal-A to opal-CT and from opal-CT to quartz are dissolution and precipitation

(nucleation and growth) reactions, the chemistry of the pore fluid can profoundly

affect the rates at which the reactions occur.

There are two practical approaches to predict silica transition depths in the sub-

surface. The first approach is to map the transition depths along with any relevant

chemistry to create a nomogram that can be used to infer the transition depth in

unexplored regions in each basin based on temperature (see Keller and Isaacs, 1985).

This empirical method has the advantage of being grounded in measured transition

depths, but the relevant recorded chemistry in one basin may not apply in other

basins. For instance, clay may promote quartz formation in one location while mag-

nesium controls the reaction rate in another. For this reason, the results of mapped

transition depths are not generally applicable in basins having different geochemical

and geothermal histories. The second approach is to determine the kinetics of the

reaction in the laboratory (Ernst and Calvert, 1969, and this volume, Chapter 2)

for a set of known chemical conditions. While the relevant chemical conditions may

be difficult to identify, they are at least separated and controlled. The results are

in theory applicable to any siliceous deposit, although fully mapping the chemical

parameter space is quite time-consuming.

In this chapter, silica diagenesis predictions are incorporated into a fully-calibrated

4D basin and petroleum system model of the San Joaquin Basin, California (Peters

et al., 2007; Menotti, 2010). Both kinetics-based and nomogram-based methods are

used to predict the opal-CT to quartz phase transition depth across the SJ-6 seismic


line in the east central portion of the basin. The predicted depths are compared to

measured depths in nearby oil fields.

To emphasize the importance of geochemical predictions of transition depths, a

1D extraction is used to create normal incidence synthetic seismic sections through

the siliceous layers. Several fluid- and mineral-substitution techniques demonstrate

that a fluid interface within a pure opal-CT unit has nearly the same seismic signature

as the opal-CT/quartz interface.

3.3 San Joaquin Basin Model

The San Joaquin Basin is a forearc basin in central California. It is bound by the

Sierran magmatic arc complex to the east, the San Andreas Fault to the west, the

Stockton Arch to the north, and the Tehachapi-San Emigdio Mountains to the south

(see Figure 3.3). It forms an asymmetrical trough with a basin axis parallel to its

western boundary. Sediments in the basin are 10 km thick in some places and are

largely Mesozoic and Cenozoic in age. The basin history is complex due to wrench

tectonism associated with the San Andreas Fault and thermal variations associated

with movement of the Mendocino Triple Junction. A detailed discussion of the region

can be found in Graham and Williams (1985).

The Monterey Formation extends throughout most of central and coastal Cali-

fornia, including the San Joaquin Basin. It broadly comprises thick deposits of fine-

grained siliceous rocks of Miocene age. These predominantly biogenic sediments were

frequently contaminated with terrigenous detritus but to varying degrees depending

on location. Kerogen types vary accordingly, with marine and terrigenous kerogens

in the western portion of the San Joaquin Basin to mostly terrigenous kerogen in the

east (Graham and Williams, 1985; Lillis and Magoon, 2007).

The Monterey formation has proven to be an important source of petroleum. It

is the primary source rock in the San Joaquin Basin which has more than 100,000

oil and gas wells (Hosford Scheirer, 2007). In fact, the U.S. Department of Energy

recently estimated the technically-recoverable shale oil in the Monterey Formation at

more than 15 billion barrels, more than half of the shale oil in the contiguous states

3.3. SAN JOAQUIN BASIN MODEL 65

SJ-6 Rose Field

North Shafter Field

Figure 3.3: San Joaquin Basin map (from Peters et al., 2007) showing the approximatelocations of the SJ-6 seismic line (Bloch, 1991) and the nearby Rose and North Shafteroil fields.

and twice as much as the Bakken and Eagle Ford shales combined (Brown, 2012).

Predicting the locations of oil and gas accumulations in the Monterey Formation

is challenging, though, due to the complex tectonic history and spatial heterogeneity

of the San Joaquin Basin. To facilitate these predictions, a complete 4D basin and

petroleum system model of the San Joaquin Basin was developed through collabo-

ration between the U.S. Geological Survey and Integrated Exploration Systems, Inc.

(now a subsidiary of Schlumberger).


The foundation of the 4D model is a detailed, present-day 3D model of subsurface

units in the basin, details of which can be found in Hosford Scheirer (2007). Geological

and geophysical data spanning the entire basin, including information from published

cross sections, fault maps, regional seismic surveys, and more than 3200 well-top

picks, were compiled, digitized, and sorted into a consistent geological framework.

The resulting internally-consistent model contains 15 chronostratigraphic horizons

extending from the Mesozoic crystalline basement to the topographical surface. There

are no gaps in the model; values for incomplete or missing data were inferred by

interpolation.

The 4D model extends the present-day 3D model by incorporating reconstructions

of the basin burial history. Iterative forward modeling of the basin evolution provided

predictions of various properties such as heat flow, surface temperatures, and physical

properties of various lithologies. In this case, the model was calibrated to match

present-day measurements of vitrinite reflectance and Horner-corrected bottom-hole

temperatures. Details of the 4D model and its calibration data can be found in Peters

et al. (2007).

The simulations shown in this chapter involve an extracted cross section of the

calibrated 4D model. The extraction is along the SJ-6 seismic line (Bloch, 1991),

which runs along the northern edge of Kern County, California, north of the Bakers-

field arch, from the eastern rim of the basin to the basin axis (see Figure 3.3). Just

south of the SJ-6 line are two oil fields, Rose and North Shafter, where the opal-CT

to quartz phase transition is known to be an important element of the trap.

The central San Joaquin Basin is characterized by relatively simple, homoclinal

geology consisting of an alternating series of marine sandstones and shales (see Fig-

ure 3.5). Rocks are preserved from the granitic Sierran basement, through the Creta-

ceous sequence, grading into Paleocene and Eocene rocks, and finally into Oligocene

and Miocene sequences. Structural traps are rare.

Figure 3.4 shows the model of the present day SJ-6 cross section. The Reef Ridge

Shale and Devilwater Shale form the top and bottom members, respectively, of the

Monterey Formation. Between them are the Antelope Shale and McDonald Shale

members, both of which undergo silica diagenesis. Note the lack of obvious structural

3.4. SILICA PHASE TRANSITION DESCRIPTORS 67

traps in the region.

Figure 3.4: SJB cross section along the SJ-6 seismic line.

3.4 Silica Phase Transition Descriptors

To predict when and where silica phase changes occur in the subsurface, basin mod-

eling software must be able to evaluate a transition criterion. The current version of

PetroMod R© software includes two options for determining the transition, one based

on a nomogram developed by Keller and Isaacs (1985), and the other utilizing kinetics

of the opal-CT to quartz transition.

3.4.1 Transition temperature nomogram

Attempts to correlate observed silica transition depths in the Monterey Formation

with temperature resulted in wide and overlapping temperature ranges even though

the silica phases appeared to stay within coherent zones. Keller and Isaacs (1985)

accounted for this variation by linking the observed conversion temperature to the

relative amount of terrigenous detritus (clay) in the measured samples. The result

is a nomogram, reproduced in Figure 3.6, which allows transition temperatures to


.5

6

0.7

12

11

14

16

17

17.5

19

21

Oceanic sand

T umey formation

Antelope shStevens sd

Fruitvaleshale

Nozu sd

Rio Bra vo sd

Fam

oso

sand

Alluvium

Basement rocks

Santos

Wygal Ss Mbr

Cymric ShaleMbr

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er S

and

CarnerosSs Mbr

Kreyenhagen Formation

PLEIS.

PLIO.

ZEM

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San Joaquin Fm

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FreemanSilt

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OlceseSand

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Devilwater ShMbr/Gould Sh

Mbr, undiff

B=Buttonbed Ss Mbr

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SYSTEM SERIES STAGE

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DEL.

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SAUC

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NM

OHNI

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MaMega-

sequences(2nd order)

Monterey Fm

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tion

and

Lara

mid

eor

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basin axis

unna

med

unna

med

unna

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unnamedCanoas Slts Mbr

PH=Pyramid Hill Sd MbrKR=Kern River Fm

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ker F

m

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br

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120 Ma160 Ma

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le ju

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n

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undifferentiatedCretaceous

SantaMargaritaSs

0

5

10

15

20

25

35

40

30

45

50

65

80

75

70

60

55

85

90

95

100

105

110

SAN JOAQUIN BASIN PROVINCE

~~

~~

Gas reservoir rock

Potential marine reservoir rock

Potential nonmarine reservoir rock

Oil-prone sourcerock/

Gas-prone sourcerock

Nonmarine coarse grained

rockMarine coarse grained rock

Coast Range ophiolite/Granitic basement

Clay/shale/mudstone/

biosiliceousHiatus or loss by erosion

Oil reservoir rock

Paci�cOcean

North

Central

South

WWF

SIERRA NEVADA

SAN ANDREAS FAULT

San Joaquin Basin Province

basin axis

Bakersf

ield Arch

0 25

miles

121˚W 120˚W 119˚W

36˚N

35˚N

37˚N

38˚N

DDPH

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SAN EMIG

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Figure 3.5: Stratigraphic column of the southern San Joaquin Basin Province, from Hos-ford Scheirer and Magoon (2007).


be read if the amount of detrital material is known. For example, in a unit with

20% terrigenous detritus and 80% biogenic silica, they predict the transition from

opal-A to opal-CT will occur at 44◦C, and the transition from opal-CT to quartz will

occur at 85◦C. Note that the nomogram reflects the observed retarding effect of clay

(i.e., higher transition temperatures) on the opal-A to opal-CT reaction as well as its

catalysis (lower transition temperatures) of the opal-CT to quartz reaction (Williams

and Crerar, 1985).

Once the transition temperatures are known, careful mapping of the maximum

temperature reached at each point in a basin can be used to relate the temperature

at conversion to the silica phase at depth.VOL. 5, NO. 1, 1985

expressions for oxygen-isotope fractionation in the opal-CT- Water and quartz-water systems [3,4]; and 6) unknown ox- Ygen-isotope ratios of pore water at the depth and diagenetic environment where phases are transformed [3,4]. In addition, many isotopic estimates of the temperature of formation of quartz are based on quartz in clay-poor carbonate-bearing beds [4] in which volumetrically minor amounts of quartz form at anomalously low temperatures [5],

The results from these temperature studies, as summarized by Pisciotto [4], suggest that the two phase transformations of silica can occur over broad and overlapping temperature ranges--18 ° to 56 ° C for opal-A to opal-CT and 31 ° to 110 ° C for opal.CT to quartz. In fact, available oxygen-isotope data might suggest even broader ranges, taking into account the Uncertainty in fractionation relations and the large range of geologically reasonable values for the equilibrating pore fluid (Fig. 2).

In contrast, stratigraphic and diagenetic relations in nu- .~erous individual Monterey sequences [2,5] indicate that silica phases in the Monterey Formation transform over a much narrower temperature range. Silica phases in the Monterey FOrmation, with rare exception [5], co-exist only in two non- OVerlapping transition zones that persist over a limited depth/ temperature range. Accordingly, we conclude that the wide and Overlapping range of temperatures of phase transfor- rnations of silica from previous studies [4 and references therein] is mainly a product of the many unknown parameters and uncertainties inherent in the different methods used to estimate temperature, and that silica phases did not actually transform throughout this range.

APProach to a Reliable Temperature Scale for Silica biagenesis

R e range of uncertainty in individual temperatures based either on oxygen-isotope ratios or on estimated maximum burial depth is large relative to the temperature differences that lshed b a silica eothermometer are potentially distingu" y " ' g rhus, a reliable temperature scale needs to take advantage of the constraints on temperature imposed by superposition in individual sequences of diatomaceous/siliceous strata.

Our approach to a temperature scale for silica diagenesis (]Fig. 3) combines an empirical silica-phase zonation with temperature calibration from two points of phase transformation in diatomaceous/siliceous strata presently at maximum temperature and depth of burial. The empirical silica- Phase zonation (modified from Isaacs [5]) is a relative scale that represents the effects of increasing temperature on rocks having various compositions (abundances of terrigenous detritus); it is based on a synthesis of relations between silica Phase, rock composition, and opal-CT d-spacing at outcrops In the Santa Barbara coastal area and the western Ventura

R e l a t i v e d e t r i t u s in w e i g h t %

70 60 50 40 30 20

33

(/)

O Z

< a.

I C~

4 5 °

5 0 ° 0 0

5 5 ° L -

6 0 ° = L-

6 5 ° ~>

7 0 ° E ! -

7 5 °

8 0 °

30 40 50 60 70 80

R e l a t i v e b i o g e n i c s i l ica in w e i g h t %

Figure 3. A preliminary temperature scale for silica diagenesis in the Monterey Formation, representing the combined effects of temperature and rock composition. The temperatures of two points of silica-phase transformation (black dots) in the Point Conception COST well were used to cal- ibrate temperature for this empirical silica-phase zonation (modified from Isaacs [5]).

basin [5,7]. Inasmuch as empirical data from the Monterey Formation indicate that calcite affects rates of silica diagenesis only in extremely clay-poor rocks (<10% relative de- tri[nbtus) ]5], the zonation can be used in carbonate-bearing as well as carbonate-free strata.

Our temperature calibration is based on the Point Concep- tion COST well (OCS-CAL 78-164 No. 1) because Neogene strata in this well probably have not been uplifted or eroded and are, thus, at maximum depth of burial [14]. Moreover, several independent indicators of temperature and maturity in this well, including other diagenetic reactions and thermal metamorphism of organic matter, suggest that Neogene temperatures in the well did not exceed the present adjusted average temperature gradient [14,15]. Although temperatures were not measured at equilibrium in the well, disequilibrium values were empirically adjusted, yielding an average geothermal gradient of 48 ° C / k m [ 15].

Figure 3.6: Nomogram for predicting the temperatures at which the opal-A to opal-CTand opal-CT to quartz phase transitions occur based on the relative amount of detritus(from Keller and Isaacs, 1985). The circles indicate calibration data.

It is important to emphasize that this nomogram is based on observations specific

to the Monterey Formation and may not reflect phase transition behavior in other


siliceous deposits. The depth-temperature correlation also obfuscates the importance

of time in this reaction. The opal-CT to quartz conversion is slower at lower temper-

atures, but it does not stop. Using the kinetics determined in Chapter 2, for example,

we expect that full conversion of opal-CT to quartz will take 4 Ma at 85◦C. It will

still occur at 80◦C, but it will take 8 Ma. If opal-CT sits at 80◦C for only 4 Ma, it will

not be unconverted but rather 52% converted. The temperatures Keller and Isaacs

(1985) relate to full conversion are inherently tied to the average length of time rocks

in this particular formation spent at various temperatures. The nomogram is really

only known to be valid in the Santa Barbara coastal region and the western Ventura

Basin. It is likely useful in analogous basins containing the Monterey Formation;

but its use outside of southern California, or for formations other than the Monterey

Formation, is not wise since the depositional and thermal histories of basins may vary

widely.

The Keller and Isaacs (1985) silica phase transition criterion is simple to imple-

ment in a basin model; the current version of PetroMod R© includes a module for

using the nomogram. For all simulations, the PetroMod R© software predicts temper-

atures throughout the model area based on estimates of basal heat flow and thermal

conductivity. If silica phase transitions are to be modeled using the nomogram, then

the clay content of the siliceous layer must be specified by the user. The software

automatically calculates the temperature at which the conversions will occur based on

the nomogram. When a grid cell reaches the calculated silica conversion temperature,

the software records the lithology change.

3.4.2 Transition kinetics

The timing of the phase transitions of silica can be calculated independent of basin

location if the kinetic parameters of the transition are known. While the actual opal-

CT to quartz reaction type is likely governed by the Avrami nucleation and growth

equation (Avrami, 1939), the time to full conversion can be approximated using a

simple zero-order reaction rate law (see Chapter 2 for details).

In this formulation, the known kinetic parameters are the preexponential factor


A0 and the activation energy Ea. Together with temperature, they define the rate

constant kT through the equation

kT = A0 exp {−Ea/(RT )} , (3.1)

where R is the ideal gas constant and T is the temperature.

The rate constant can be used to calculate the time to total conversion through

the rate law. For a zero-order reaction, the integral form of the rate law is

[Op] = [Op]0 − kT t , (3.2)

where [Op] is the solid opal-CT concentration (between 0 and 1), [Op]0 is the initial

concentration of opal-CT, kT is the temperature-dependent rate constant, and t is

the time.

The current version of PetroMod includes kinetics-based silica phase transition

options. Because Ernst and Calvert (1969) only determined kinetic parameters for

the opal-CT to quartz conversion, PetroMod only accepts kinetic parameters for that

reaction. The opal-A to opal-CT reaction is determined by a user-supplied transition

temperature which can, but does not necessarily, come from the Keller and Isaacs

(1985) nomogram.

3.4.3 Modeled parameters

Table 3.1 gives the parameters used to generate the model results in §3.5.

Custom parameters were used for the two kinetics-based models. Because Petro-

Mod allows the user to input only a temperature criterion for the opal-A to opal-CT

transition, a transition temperature of 45◦C was chosen because it was the approx-

imate midpoint of the temperatures predicted by the nomogram for reasonable clay

fractions. For the opal-CT to quartz transition, the kinetic parameters used were

those determined by Ernst and Calvert (1969) and by Dralus (this volume, Chap-

ter 2). Note that PetroMod accepts the pre-exponential factor with units of 1025/Ma

instead of 1/hr; the table contains both values.


Table 3.1: PetroMod input parameters used to model the opal-A to opal-CT to quartzphase changes in this study. When using the Keller and Isaacs (1985) nomogram,clay content is the input parameter. The transition temperatures, shown in gray, arederived based on the specified clay content.

opal-A to CT opal-CT to quartz

temp A0 A0 Ea(◦C) (1/hr) (1025/Ma) (kcal/mol)

Ernst & Calvert 45 1.27×105 1.11×10−10 23.2this study (ch. 2) 45 1.96×109 1.72×10−6 32.5

temp tempKeller & Isaacs (20% clay) 44.0 85.2Keller & Isaacs (45% clay) 46.5 74.2

Two nomogram-based models were also considered, one with 20% detrital ma-

terial and one with 45%. The nomogram defines the transition temperatures based

on detrital (clay) content, so clay content is the input parameter. Transition tem-

perature, which is the phase transition criterion for the nomogram-based models, is

derived from the specified clay content and the nomogram. However, the transition

temperatures associated with the modeled clay contents are included in the table

(gray font) for reference.

3.5 Basin Modeling Results

The modeling results shown here reflect the fully-calibrated SJ-6 cross section model

(run using PetroMod R© version 2012.2) of the San Joaquin Basin with a single set of

modifications: the siliceous material for three source rocks (the Kreyenhagen Forma-

tion, and the McDonald Shale and Antelope Shale members of the Monterey Forma-

tion) was replaced by a transition from diatomite to a lean opal-CT to chert. The

transitions were determined by either kinetic parameters or the built-in nomogram

using the parameters in Table 3.1.

Figure 3.7 shows the predicted temperatures throughout the cross section. Note

3.5. BASIN MODELING RESULTS 73

that the Antelope, McDonald, and Kreyenhagen source rocks are all predicted to be

above 44◦C at all depths, so opal-A has fully converted to opal-CT in all source rock

layers with modeled silica diagenesis. While no opal-A is remains in this model, the

criterion for the opal-A to opal-CT transition remains important. The phase change

includes changes in porosity, permeability, and thermal properties that affect heat

flow. However, the effect should be small compared to other heat flow trends, so a

consistent transition criterion is adequate for these comparisons.

Model results of silica phase are shown in Figures 3.8 through 3.11. Each figure

shows the modeled cross section with only source rocks colored. Two source rocks

(Tumey and Moreno formations) were not subjected to modeled silica diagenesis;

those layers are shown in blue (no transition). For the layers that experienced silica

phase transitions, opal-CT is shown in light brown and quartz is shown in dark brown.

Figure 3.8 shows the silica phases predicted by the Ernst and Calvert (1969) kinet-

ics. The Kreyenhagen Formation and the Antelope Shale are completely transformed

to quartz. Only the McDonald Shale maintains an opal-CT/quartz interface, which

occurs at 5022 ft depth as measured at the midpoint of the model layer.

Figure 3.9 shows the silica phases predicted by the kinetics determined in this

study (Chapter 2). The opal-CT to quartz transition is suppressed and is still present

in all three layers. It occurs at 8800 ft, 8926 ft, and 9047 ft in the Antelope Shale,

McDonald Shale, and Kreyenhagen Formation, respectively.

Figures 3.10 and 3.11 show the silica phases predicted by the Keller and Isaacs

(1985) nomogram using 20% clay and 45% clay, respectively. The 20% clay predic-

tion has transition depths similar to those predicted by kinetics from this study but

approximately 700 ft shallower. For the 45% clay prediction, the Antelope Shale

has transitioned to quartz at all depths, but the McDonald Shale contains an opal-

CT/quartz interface at 6838 ft depth. The Kreyenhagen Formation maintains a small

region of opal-CT; its transition is at 7289 ft.

The primary data of interest in the models are the predicted opal-CT to quartz

transition locations, which include both the depths and the distances along the strike

of the cross section. Table 3.2 shows these transition distances and depths for each


Figure 3.7: Modeled temperature profile for the present-day San Joaquin Basin, SJ-6 crosssection, using this study’s zero-order kinetics. Only the source rocks are colored.

of the three source rocks modeled with silica diagenesis for the four transition crite-

ria. Also reported are the modeled present-day temperatures at the opal-CT/quartz

interfaces.

The observed opal-CT to quartz transition depth in the San Joaquin Basin varies

across the region. In the Elk Hills oil field, which is near the Bakersfield Arch but

closer to the basin axis than this cross section, the transition depth in the Monterey

Formation is about 4500 ft (Zumberge et al., 2005). At the Rose and North Shafter

fields, which are much closer to the cross section shown here and exhibit diagenetic

trapping, the pay zone along the transition is closer to 7800 ft depth (Grau et al.,

2003). Figure 3.12 compares the predicted transition depths from basin modeling

to the observed transition depths at Rose and North Shafter fields. Positive values

indicate the prediction is too shallow. The Ernst and Calvert (1969) kinetics predict

transition depths that are approximately 3000 ft too shallow. The kinetics from this

study produce transition depths that are too deep, although they are generally within

1000 ft of the observed transition depth. The Keller and Isaacs (1985) nomogram best

matches the observed transition depth if a clay content of 20% is used. If the clay

content is estimated at 45%, then nomogram fares no better than the kinetics from

this study.

Although the transition depths are the most important predictions arising from

3.5. BASIN MODELING RESULTS 75

Table 3.2: Opal-CT to quartz phase transition depths for the Antelope Shale, McDonaldShale, and Kreyenhagen Formation predicted using PetroMod simulations. Distance ismeasured along the strike of the cross section. “All qtz” means the layer is predictedto be fully converted to quartz at present day.

Ernst & Dralus Keller & Keller &Calvert (1969) (Chapter 2) Isaacs (1985) Isaacs (1985)

(zero-order) (zero-order) (20% clay) (45% clay)

Ante

lop

e dist (mi) N/A 16.40 18.89 N/A

depth (ft) all qtz 8800 8036 all qtz

temp (◦C) N/A 93 85 N/A

McD

onal

d dist (mi) 27 17.74 20.07 22.59

depth (ft) 5022 8926 8161 6838

temp (◦C) 60 92 85 74

Kre

yenhag

en dist (mi) N/A 24.43 25.25 29.12

depth (ft) all qtz 9047 8672 7289

temp (◦C) N/A 88 85 74


Figure 3.8: Silica phase map for the present-day SJ-6 cross section in the San JoaquinBasin using Ernst and Calvert (1969) zero-order kinetics. Only the source rocks arecolored.

these models, the location along the strike of the cross section is also relevant. Because

of the gentle dip of the Monterey Formation, the lateral variations in its modeled

transition distance span at least 9 mi from east to west.

The present-day temperatures at the opal-CT/quartz interfaces should also be

noted in Table 3.2. The nomogram method fixes a transition temperature, so it is not

surprising that the temperatures at the interface are equal to the input temperatures.

However, the kinetics-based models are tied to both temperature and time. This

allows for lower transition temperatures if the time spent at that temperature is

longer. The present-day temperatures at the opal-CT/quartz interfaces using the

kinetics of this study show the Kreyenhagen Formation transitioning at a much lower

temperature than the Monterey Formation (88◦C compared to 92◦C). This trade-off

between temperature and time is not reflected in the nomogram.

3.6. SYNTHETIC SEISMIC SECTION 77

Figure 3.9: Silica phase map for the present-day SJ-6 cross section in the San JoaquinBasin using this study’s zero-order kinetics. Only the source rocks are colored.

3.6 Synthetic Seismic Section Across the Opal-CT

to Quartz Boundary

In a siliceous rock, during the phase transition from opal-CT to quartz, the mineral

density increases slightly (from 2.33 g/cc to 2.66 g/cc), the porosity and permeability

evolve, and fractures develop. These processes cause subtle but measurable differences

in bulk density and acoustic velocities. If the transition zone is sharp, then the

resulting impedance contrast can be observed in seismic data. Unfortunately, the

seismic response of the phase change mimics a fluid effect, which is demonstrated in

the following synthetic seismic profiles.

The synthetic sections created here are simple, normal incidence seismic sections.

To create them, the simulated material properties (density, porosity, compressional

and shear velocities, and pore pressure) from PetroMod were exported along a vertical

profile at 19.58 mi, shown in Figure 3.13. This extraction crosses the Monterey

Formation in the approximate location of the expected opal-CT/quartz transition.

The vertical resolution of the extracted PetroMod data varies with the layer thick-

ness, but it is generally on the order of 50 m. Therefore, the extracted properties were


Figure 3.10: Silica phase map for the present-day SJ-6 cross section in the San JoaquinBasin using the Keller and Isaacs (1985) nomogram with 20% detrital material (clay).Only the source rocks are colored.

downsampled to 10 m spacing, a resolution suitable for seismic modeling. A simple in-

terpolation between exported values would smooth the discontinuities between facies

and cause a reduction in the modeled seismic reflections. To preserve the discontinu-

ities, the downsampled values were interpolations of the basin-scale values only when

neighboring data points represented the same facies. When neighboring PetroMod

data points represented two different facies, the downsampled values between them

were not interpolations but rather direct copies of the nearest exported value. For

example, suppose there is an interface between facies A and B at a depth of 200 m,

and suppose that there are basin-scale exported values of porosity at 50 m intervals.

If the 100 m porosity is 0.40 and the 150 m porosity is 0.30, then the downsampled

data between those points would be interpolated (0.38, 0.36, 0.34, and 0.32 at 110 m,

120 m, 130 m, and 140 m, respectively). Because the 200 m datum marks a facies

change, the downsampled data between 150 m and 200 m would be repeated values

of the 150 m data (0.30 porosity at 160 m, 170 m, 180 m, and 190 m).

Once the exported data were downsampled to 10 m resolution, pseudologs were

created. They are shown in Figure 3.14. The first subplot shows bulk density; the

second, compressional and shear wave velocities; the third, porosity; and the fourth,

3.6. SYNTHETIC SEISMIC SECTION 79

Figure 3.11: Silica phase map for the present-day SJ-6 cross section in the San JoaquinBasin using the Keller and Isaacs (1985) nomogram with 45% detrital material (clay).Only the source rocks are colored.

the calculated compressional impedance. Values for the Antelope Shale and the Mc-

Donald Shale are indicated by the dashed lines. Both are in the opal-CT phase in

this extraction, so the contrast between them is minimal.

Strong seismic reflections occur at large impedance contrasts, such as at the top

of the Antelope Shale and base of the McDonald Shale. These reflections can be

seen in Figure 3.15, which contains the synthetic seismic section through the basin

from surface to basement assuming a bin size of 25 m, vertical sampling resolution

of 10 m, frequency of 50 Hz, and signal-to-noise ratio of 1. The Monterey Formation

reflections are featured in the enlarged subset on the right half of the figure. The

single vertical trace produced by the 1D extraction is repeated horizontally to aid

in visualization. The actual 2D geometry of the facies, which would be modeled

using multiple extractions along the cross section, is not reconstructed in this simple

representation.

A single trace from the synthetic seismic is the base case in Figure 3.16, which

contrasts the effects of mineral and fluid changes on seismic response. Subplot (a)

is a single trace from Figure 3.15 in which both the Antelope Shale and McDonald

Shale are brine-saturated opal-CT samples with porosities of 0.08. For subplot (b),


Figure 3.12: Deviations of the predicted opal-CT to quartz transition depths compared tothe observed transition depths. Positive values indicate predicted depths are shallowerthan the observed depths. The Keller and Isaacs (1985) nomogram with an assumedclay content of 20% yields the best prediction in this case. The kinetics from this studyshow significantly improved predictions over the Ernst and Calvert kinetics.

Gassmann fluid substitution was used to predict the rock properties when the Ante-

lope Shale is saturated with a typical live oil at the predicted pore pressure of 30 MPa

(Gassmann, 1951; Mavko et al., 2003). This case, which shows a fluid interface in

a homogeneous layer, is the response expected for a structural trap. Subplot (c)

shows the response of brine-saturated opal-CT over a brine-saturated quartz layer

with similar porosity (0.10). This is the response for a mineral interface with no

fluid contrast. Finally, subplot (d) shows a brine-saturated opal-CT layer over an oil-

saturated quartz layer, which is the type of stratigraphic trap the opal-CT to quartz

phase transition can produce. The three scenarios that produce reflections within the

Monterey Formation are nearly indistinguishable.

Figure 3.16 demonstrates why the diagenetic opal-CT/quartz boundary can be so

misleading in exploration geophysics. There is no good way to differentiate between

the seismic response of the fluid interface and the mineral interface. A reflection within

a siliceous layer could lead to a diagenetic trap saturated with oil or to a dry hole.

A full basin model incorporating phase transition criteria provides an independent

prediction of the location of the mineral phase boundary and indicates which scenario

3.7. CONCLUSIONS 81

Figure 3.13: Sythetic seismic sections were based an extraction at 19.58 mi along the SJ-6seismic line.

is more likely.

3.7 Conclusions

Predicting the depth of transition from opal-CT to quartz in a siliceous deposit is

important for oil exploration, particularly in locations where the phase change can

cause the formation of diagenetic traps. This is particularly relevant in the eastern

portion of the San Joaquin Basin where the Monterey Formation may contain large

reserves of oil in structural and diagenetic traps. The location of the opal-CT to quartz

phase change can be predicted by utilizing time-dependent basin modeling software

(such as PetroMod) in conjunction with information on the conditions under which

the phase transformation will occur.

Chemical kinetics parameters from two series of hydrous pyrolysis experiments

were used to predict the opal-CT to quartz transition depth along the SJ-6 seismic

line. The kinetics derived in this study did a better job of predicting the observed

transition depth than did the older Ernst and Calvert (1969) kinetics.


Antelope Shale

McDonald Shale

1500 2000 2500 3000

0

500

1000

1500

2000

2500

3000

3500

4000

4500

density (kg/m )3

dept

h (m

)

0 2000 4000 6000

velocity (m/s)0 0.2 0.4 0.6

porosity0 5 10 15

x 106

impedance (kg/m s)2

VpVs

Figure 3.14: Downsampled pseudologs for the extraction shown in Figure 3.13. The loca-tions of the Antelope Shale and McDonald Shale, which are members of the MontereyFormation, are indicated. In this log, both are in the opal-CT phase. Values areresampled at 10 m intervals.

A regional nomogram was also used to predict the transition. An assumed clay

content of 20% provided an excellent match to the observed transition depth, although

other assumed clay contents can yield inaccurate predictions. A priori knowledge of

the clay content is imperative to the success of silica phase transition modeling using

the nomogram. While the nomogram was relatively successful in the San Joaquin

Basin, it assumes that only clay content and temperature determine the transition

depth. This obfuscates the importance of time, which is inherent in the burial history

of the basin. For example, a basin model for Sakhalin or Hokkaido would involve burial

rates, basal heat flows, clay types, and circulating fluids that differ from those of the

San Joaquin Basin. There is no reason to expect the nomogram to work outside of

southern California.

Geological and geochemical predictions of the opal-CT to quartz transition are

important supplements to geophysical data in oil and gas exploration. The seismic

response of an oil/brine fluid interface mimics the response of the opal-CT/quartz

3.7. CONCLUSIONS 83

time

distance50 100 150 200 250 300 350 400 450

0.5

1.0

1.5

2.0

2.5

Antelope Shale

McDonald Shale

Figure 3.15: Synthetic seismiogram for the pseudologs in Figure 3.14. The central Mon-terey Formation reflections are indicated on the plot.

boundary. Independent predictions of transition depth are the only way to differen-

tiate between these two cases aside from direct observation.


Reef Ridge Shale

Antelope Shale

McDonald Shale

Devilwater Shale

CTCT

CTCT

CTQtz

CTQtz

amplitude (same scales)

time

(a) (b) (c) (d)

Figure 3.16: Synthetic seismic response through the Monterey Formation. Droplets in-dicate the saturating fluid: black for live oil, blue for brine (both at pressure). Theoil/water interface in (b) has the same seismic characteristics as the opal-CT/quartzinterface in the (c). Therefore, the fluid effect and mineral effects are difficult todistinguish.

3.7. CONCLUSIONS 85

Acknowledgements

Thanks are due to Kenneth Peters, Allegra Hosford Scheirer, Oliver Schenk, and

Carolyn Lampe for their valuable discussions of the San Joaquin Basin model and

PetroMod R© software.


87

Chapter 4

Anomalous strain behavior in

CO2-saturated zeolitic tuffs

4.1 Abstract

Zeolites are aluminosilicate minerals with open, cage-like structures and negatively

charged frames. Some naturally-occurring zeolites are stabile at geothermal tem-

peratures and have cage structures large enough that small molecules can traverse

the intracrystalline cage network easily. This, in addition to their negatively-charged

frames, makes these zeolites strong adsorbents (and potentially absorbents) of carbon

dioxide.

This chapter describes a series of experiments to determine what effects on geo-

physical parameters result from carbon dioxide interaction with zeolitic samples.

Seven samples were exposed to carbon dioxide while their lengths and acoustic veloc-

ities were monitored to achieve three goals. First, a Fontainebleau Sandstone sample

was measured to establish a baseline for non-reactive interaction. Next, two zeolitic

tuffs and one compacted zeolite powder were tested under a variety of stress regimes

to determine which parameters, if any, were sensitive to fluid type. Finally, three

tuffs, one without zeolite and two with different types of zeolite, were tested under

the same conditions to systematically determine how property changes under CO2

saturation were related to zeolite content.

88 CHAPTER 4. ZEOLITE STRAIN

All samples were were tested in a hydrostatic pressure vessel, some subjected

to confining pressures of 30 MPa or more. Strains and ultrasonic acoustic velocities

were measured under dry conditions as well as during fluid (helium or carbon dioxide)

injection.

Results show that acoustic velocities for all samples depend only on differential

pressure and not on pore fluid type. Samples containing zeolite show decreased strain

with gaseous carbon dioxide in the pore space. For samples saturated with helium and

then carbon dioxide at pressure, the decreased strain (swelling) under CO2 saturation

represented an 8% to 16% deviation from the strain under He saturation. Samples

without zeolite showed no difference in strain based on fluid type. This indicates that

it is the interaction between zeolite minerals and CO2 causing the anomalous strain

readings.

4.2 Introduction

Fluid movement in geologic formations is often monitored using seismic methods

with relations, such as Gassmann fluid substitution and effective stress, providing the

basis for quantitatively interpreting subsurface fluid saturation and state from seismic

data. Almost all commonly used relations assume the rock matrix is chemically inert

irrespective of the pore fluid introduced. Coupling between the rock and pore fluid is

treated as purely mechanical; neither the rock matrix properties nor its microstructure

changes. For many systems, this is a useful first approximation. For others, even small

changes in pore fluid chemistry can induce dissolution, precipitation, or adsorption,

any of which may potentially alter the rock’s porosity, permeability, and stiffness.

This necessitates the inclusion of robust fluid-optimized physico-chemical models in

the rock physics toolkit.

Zeolites are framework aluminosilicates comprising cages and channels that are,

in many cases, large enough to house a variety of small molecules including water,

carbon dioxide, and methane. The frame consists of corner-sharing SiO4 tetrahedra.

Without aluminum substitution, the frame is inert; but when an aluminum atom is

substituted for a silicon atom, the tetrahedral unit takes on a negative net charge


that is subsequently balanced by the addition of a cation. Zeolite’s charged frames

have proven useful in wide range of applications; for example, zeolites are used as ion

exchangers in water softening systems. Used as a catalyst, the size and shape of the

cages can limit the types of reactions that can occur or which products and reactants

can traverse the material. These nanoporous structures are also used as molecular

sieves, filtering residential pool water and industrial flue gases (Chue et al., 1995).

Zeolitization is a relatively rapid process under specific conditions. Many types of

zeolites are naturally occurring and abundant. Commercially viable amounts of zeolite

are found throughout the southwestern United States from the Amargosa Valley into

central Arizona (Hay et al., 1986; Sheppard and Gude, 1968). Another prominent

region of zeolite-rich tuffs is found in southern Italy in the Campi Flegrei volcanic

complex. Approximately ten cubic kilometers of Neapolitan Yellow Tuff was erupted

there 12,000 B.P. (Barberi et al., 1991). Along with volcanic and seismic activity, the

area has experienced anomalous uplift throughout its history. Seismic monitoring of

the region is increasingly important since the area is densely populated. However,

interpretation of seismic data is difficult (Zamora et al., 1994; Vanorio et al., 2002).

The mechanical changes due to large ground deformations are complicated, and the

data become even harder to understand when transient fluid flow and the possibility

of volcanic gases interacting with zeolitic tuffs are included in the analysis.

While zeolites in volcanic regions may represent the most pressing concerns, de-

posits have occasionally been identified as oil reservoirs (Vernik, 1990). As enhanced

oil recovery and carbon sequestration projects become more common, even small ze-

olite deposits could present challenges for oil and gas projects that introduce new

pore fluids to the subsurface. The goal of this study is to understand the interaction

of certain zeolites and zeolite-rich tuffs with their pore fluids. A fluid of particular

interest is carbon dioxide because it is often a volcanic gas and extensively used in

the oil and gas industry.

This chapter details a series of experiments designed to test whether the introduc-

tion of carbon dioxide to a zeolitic tuff causes measurable effects on acoustic velocities

or strain behavior in the laboratory. Initial tests of non-reactive Fontainebleau Sand-

stone establish a baseline for comparison of the potentially reactive zeolitic materials.


Next, tests of three zeolitic samples demonstrate a swelling of chabazite-rich tuffs

under CO2 injection. The final series of experiments compares the behavior of three

naturally-occurring tuffs, one containing chabazite, one containing clinoptilolite, and

one that has not undergone zeolitization, under similar experimental conditions.

4.3 Methods

The experiments shown here were designed with three goals: (1) establish a baseline

for non-reactive fluid-rock interactions, (2) explore what, if any, changes occur in the

physical properties of zeolitic rocks due to interaction with carbon dioxide under a

variety of conditions, and (3) systematically determine how any observed changes are

related to zeolite content.

A variety of rock samples were used to explore the influence of CO2 on zeolite prop-

erties. All samples were characterized, primarily through measurements of porosity,

permeability, and acoustic velocities under both dry and fluid-saturated conditions.

All experiments were conducted in the rock physics laboratory at Stanford University.

4.3.1 Sample Selection and Preparation

A total of seven samples provided results for the three listed goals. To establish a

baseline for non-reactive interaction between a siliceous rock and carbon dioxide, ex-

periments were conducted on an Oligocene Fontainebleau Sandstone sample composed

primarily of cemented quartz grains and collected from outcrop in the Ile-de-France

region near Paris (from the same collection as the samples used in Chapter 6).

To explore the effects of CO2 saturation on zeolites, experiments were conducted

on three samples. The first two were cut from outcrop samples of the Neapolitan Yel-

low Tuff (NYT), a naturally occurring zeolite-rich rock from the Compania Region

of Southern Italy in the Campi Flegrei volcanic complex. They are composed of ap-

proximately 60% zeolite, half of that in the form of calcium and potassium chabazite,

which has the general formula

(Ca2,Na4,K4)Al4Si8O24 · 12H2O .

4.3. METHODS 91

The chabazite frame contains channels with apertures of 3.8 A by 3.8 A, large enough

for a CO2 molecule to traverse (IZA Commission on Natural Zeolites, 2012a). The

other half of the zeolitic material comprises mostly phillipsite and analcime; however,

they are not presumed to factor into CO2 adsorption. No clay has been observed in

these samples (Pande and Fabiani, 1989; de’Gennaro et al., 1990)

The third sample used in the second set of experiments was made in the labora-

tory by compacting zeolite powder derived from the NYT. Its zeolitic composition is

therefore similar to the tuffs listed above, but its microstructure is different.

All three samples used in the second set of experiments had been studied previ-

ously and were subjected to high pressures in the laboratory prior to the experiments

shown here (e.g., Vanorio et al., 2002).

Finally, to determine how changes in properties are related to zeolite content,

experiments were performed on three new tuff samples. The first (referred to here

as “gray tuff”) was a tuff from the Campi Flegrei volcanic complex that had not

undergone zeolitization. The second (“yellow tuff”) was from the same formation

as the first but from a region that had undergone zeolitization, the NYT. The third

sample (“green tuff”) was from a nearly-pure sodium and potassium clinoptilolite

deposit from the Lake Tecopa basin in Inyo County, California, USA (KMI Zeolite,

2012; Sheppard and Gude, 1968). Clinoptilolite has the general formula

(Na,K,Ca)2−3Al3(Al, Si)2Si13O36 · 12H2O .

The clinoptilolite frame contains sets of intersecting channels with apertures of 3.0 A

by 7.6 A and 3.3 A by 4.6 A, both large enough for a CO2 molecule to traverse (IZA

Commission on Natural Zeolites, 2012b).

All three samples from the third set of experiments were freshly-cored from outcrop

samples and had not been pressure-cycled in the laboratory.

The seven samples described here were all cylindrical, approximately one inch in

diameter and anywhere from one half to two inches in length. They were dried and

stored in a cool oven (around 70◦C) for at least 48 hours before any measurements

were taken.


4.3.2 Sample Characterization

When possible, the samples were initially characterized by measuring their mass,

length, diameter, porosity, and permeability. Before characterization, samples were

stored in a cool, humidity-controlled oven. Note that the low heat and low humidity

controlled water saturation in the intercrystalline pore space but was not intended

to mobilize or desorb any water or gaseous molecules in the intracrystalline pore

structure.

For each sample, the initial length and diameter were measured repeatedly with

a digital caliper at varying orientations; averages were recorded.

The grain density of the samples was measured using a helium pycnometer, and

porosity was calculated from those measurements. For the compacted powder sample,

care was taken to keep the pressure in the pycnometer below 35 psi to minimize the

chance of inducing cracks.

Permeability of the tuff samples was measured using a constant-head nitrogen

permeameter; measurements were Klinkengerg-corrected when possible. The perme-

ability of the compacted powder sample was not measured because the pressures in

the permeameter were large enough to cause the samples to disintegrate.

In all cases, it was assumed that neither the helium nor the nitrogen used during

characterization reacted significantly with the sample matrices.

4.3.3 Velocity Measurements

Acoustic velocities of the samples were measured using the pulse-transmission tech-

nique (Birch, 1960) using a hydrostatic pressure vessel. A cartoon of the apparatus

is shown in Figure 4.1. The sample endcaps contained P- and S-wave transducers

operating at 1 MHz and 0.7 MHz, respectively. Acoustic signals were displayed on an

oscilloscope where the arrival times were chosen manually and then digitally recorded.

Each jacketed sample was surrounded by three linear potentiometers that provided

measurements of the changing axial length of the sample. Volumetric changes were

calculated assuming the material deformation was isotropic.

The hydrostatic pressure vessel allowed for separate control of confining pressure

4.3. METHODS 93

gas booster

helium orCO2

oscilloscope

confining fluid

ultrasonic P- and S-wave

transducers

linearpotentiometers

Figure 4.1: Cartoon of the hydrostatic pressure vessel apparatus for measuring strain andultrasonic acoustic velocities at pressure. Each one inch diameter sample was jacketedand subjected to a confining pressure. The pore pressure was controlled independentlyfrom the confining pressure.

and pore fluid pressure. Confining pressures for the sandstone and previously-studied

tuff samples were increased to 30 MPa or more. For the fresh tuff samples, the

confining pressures were kept relatively low, at or under 12 MPa, to preserve as much

of the fragile tuff pore structure as possible. The stress cycles varied between most

of the experiments and are described in the appropriate results sections.

The pore network of each sample could be either left open to the atmosphere for

dry measurements or connected to a pore fluid system for saturated measurements.

The pore fluid system was a closed circuit connected to a gas source (either helium

or carbon dioxide), a gas booster, and pressure gauges at both ends of the sample.

Pressures were monitored at both ends of the sample to ensure that the saturating

fluid was able to penetrate the sample; that is, to ensure that the permeability of the

sample did not decrease to zero during the injection process. Confining pressure and

pore fluid pressure were measured and recorded manually.

While pressures were monitored inside and outside the sample, the temperature


Table 4.1: Sample characterization for the seven samples described in this chapter.

B102 GA VRtgn Zeo3

zeolite none chabazite chabazite chabazitelocation Fontainebleau, Campi Flegrei, Campi Flegrei, Campi Flegrei,

France Italy Italy Italy

bulk density (g/cc) 2.37 1.38 1.43 1.34grain density (g/cc) 2.639 2.21 2.254 2.178

porosity (–) 0.101 0.3764 0.3658 0.3845permeability (mD) 157 10.99 4.14 –

Vp (m/s) 3920 2290 1480 750Vs (m/s) 2430 1680 1000 460

Gray Yellow Green

zeolite non-zeolitized chabazite clinoptilolitelocation Campi Flegrei, Campi Flegrei, Inyo Co., CA,

Italy Italy USA

bulk density (g/cc) 1.05 1.1 1.55grain density (g/cc) 2.528 2.265 2.184

porosity (–) 0.58 0.52 0.29permeability (mD) 1170 ∼ 100 ∼ 1

Vp∗ (m/s) 1523 2409 3203Vs∗ (m/s) 853 1325 2007

∗ measured in the pressure vessel, after pressure cycling, fully relaxed

was not. It was assumed that the pore fluid and sample equilibrated to room tem-

perature rapidly compared to the experimental time.

4.4 Results

The results of sample characterization for all seven plugs are shown in Table 4.1.

4.4.1 Establishing a Baseline

Measurements (acquired by Tiziana Vanorio) of the Fontainebleau Sandstone sample

B102 provided a base case representing a purely mechanical coupling between a rock

4.4. RESULTS 95

matrix and pore fluid. The sample was measured under dry (drained) conditions for

both increasing and decreasing differential pressures up to 40 MPa. The confining

pressure was then set at 5 MPa; CO2 was subsequently introduced into the pore space

at a pressure of 4.5 MPa. A measurement was taken, and the confining pressure was

increased multiple times (the “CO2 saturated, pore pressure 4.5” data). The pressures

were lowered and the process repeated maintaining pore pressures of 7.5 MPa.

Figure 4.2 shows the results of these tests. On the left are P- and S-wave velocities

as a function of differential pressure. On the right are the corresponding strains;

increasing strain is compaction. The velocity curves are generally quite smooth, in

part a result of the clean signals typically seen in sandstones. There is no apparent

change in velocity with the introduction of CO2. Similarly, the sample length depends

on differential pressure, but it does not exhibit dependence on pore fluid, nor does

it show hysteresis. This is the classical pressure behavior for non-reactive fluids and

rocks.

0 5 10 15 20 25 30 35 402.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

differential pressure (MPa)

velo

city

(km

/s)

FB Sandstone, velocities

P-wave

S-wave

dry increasing dry decreasingCO2 saturated, pore pressure 4.5 MPaCO2 saturated, pore pressure 7.5 MPa

0 5 10 15 20 25 30 35 400.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040


stra

in

FB Sandstone, strains

dry increasing dry decreasingCO2 saturated, pore pressure 4.5 MPaCO2 saturated, pore pressure 7.5 MPa

Figure 4.2: Experimental data for the non-reactive Fontainebleau Sandstone. P- andS-wave velocities are shown on the left; strains are on the right. Both plots showthe classical dependence on differential pressure with no variation resulting from CO2

injection. Data acquired by Tiziana Vanorio.


4.4.2 Exploring Fluid/Rock Interaction

Three experiments were conducted to explore the effects of CO2 saturation on zeolitic

material, each with its own stress path. In the first experiment, a tuff was exposed

to CO2 at varying pore pressures and differential pressures. In the second, the CO2

and confining pressures were raised in parallel to maintain the differential pressure.

In the third, a compacted zeolite powder was saturated repeatedly with CO2 to check

for changes due to exposure time.

Test 1: sample GA

The first experiment monitored strain and velocity as a function of varying differential

pressure. To begin with, the zeolitic tuff GA was measured under dry (drained)

conditions. The confining pressure was incremented to 30 MPa then decremented to

2 MPa. The confining pressure was then set to 8 MPa, and the pore-fluid circuit was

flooded with carbon dioxide and closed at 1.1 MPa pore fluid pressure. The confining

pressure was held constant at 8 MPa while the pore pressure was gradually increased

to nearly 8 MPa. The pore fluid was ultimately released, and an additional series of

dry (drained) strain measurements were taken for decreasing confining pressure.

Figure 4.3 shows the acoustic velocities for this stress path as a function of differ-

ential pressure. The sample velocities demonstrate a strong sensitivity to the differ-

ential pressure, increasing by more than 25% for Vp and 40% for Vs over the 30 MPa

range. The CO2-saturated measurements, displayed as blue diamonds, are nearly in-

distinguishable from the dry measurements. A standard Gassmann fluid substitution

was performed using the dry velocity measurements and the average properties of

carbon dioxide in the gas phase. The gray triangles in the plot show the Gassmann-

predicted velocities using the dry increasing and dry decreasing data. For Vp, the

measured CO2-saturated data fall in the predicted Gassmann range. For Vs, the

CO2-saturated data appear somewhat lower than predicted by Gassmann, but they

are well within uncertainty. Therefore, CO2 appears to have no effect on the velocities

of the zeolitic tuff aside from the classical mechanical interaction.

4.4. RESULTS 97

0 5 10 15 20 25 30 351.5

2.0

2.5

3.0

velo

city

(km

/s)

dry decreasingCO2 saturated

dry increasing

Gassmann predicted


P-wave

S-wave

Figure 4.3: Acoustic velocities for GA at varying differential pressures and pore fluids.Dry data are represented by red circles; CO2-saturated data are represented by bluediamonds. Also shown are velocities predicted by Gassmann fluid substitution (graytriangles). The dry and saturated velocities are nearly indistinguishable.

Figure 4.4 contains the strain data corresponding to the velocities shown in Fig-

ure 4.3. The maximum strain measured was 2.5% for the dry sample at 30 MPa

confining pressure. The strain curves are different for increasing differential pressure

(loading) and decreasing differential pressure (unloading); though when the sample

was left to relax overnight with no confining pressure, it returned to its original length.

Because the CO2-saturated measurements were taken with increasing pore pres-

sure (decreasing differential pressure), the CO2-saturated data was compared to the

dry decreasing (unloading) trend. The dashed lined in the figure represents a least-

squares fit to the dry decreasing data both before and after CO2 injection. The

saturated strains were of smaller magnitude than the dry decreasing strains, indicat-

ing some sort of overall swelling that occurred when the pore space was filled with

CO2. It is assumed that swelling was due to an interaction between carbon dioxide

and chabazite.

Figure 4.5 quantifies the amount of swelling that occurred in the tuff. It shows


0 5 10 15 20 25 300.000

0.005

0.010

0.015

0.020

0.025

0.030


stra

in

dry increasingdry decreasing

dry decreasingfit to dry decreasing

CO2 saturated

compaction

Figure 4.4: Strain as a function of differential pressure for sample GA. After the CO2

was released from the pore space, additional strain data were taken as the confiningpressure was decreased. The CO2-saturated data were expected to follow the drydecreasing (unloading) curve. CO2-saturated pores show decreased strain for the samedifferential pressures, interpreted as swelling.

the difference between the dry strains as described by the fitted curve and the CO2-

saturated data. The uncertainties displayed for the strain measurements were calcu-

lated assuming a 1% uncertainty in the voltage reading on each linear potentiometer.

The difference in strain appears to be statistically significant with a magnitude of

approximately 0.4%. The swelling appears to be relatively constant across the entire

range of differential pressures.

Test 2: sample VRtgn5

Sample VRtgn5 was used to test the tuff under constant differential pressure by

varying the pore pressure and confining pressure in parallel. It was tested under dry

(drained) conditions with increasing confining pressure up to 7 MPa and decreasing

confining pressure down to 1 MPa. The sample was then injected with CO2, and the

pore pressure was raised to 0.9 MPa. Successive measurements increased both the

4.4. RESULTS 99

0 1 2 3 4 5 6 7


∆st

rain

0.005

0.004

0.003

0.002

0.001

0.000

Figure 4.5: Difference between dry strain and CO2-saturated strain as a function of dif-ferential pressure for sample GA. The dry strain was interpolated using the fit to thedry decreasing data shown in Figure 4.4. The error bars were estimated assuminga 1% uncertainty in the voltage across each linear potentiometer. The strain differ-ence is statistically significant and approximately constant through the entire range ofdifferential pressures, which correspond to pore pressures from 1 to 7 MPa.

confining pressure and the pore pressure so that the differential pressure remained at

0.1 MPa.

The velocity behavior of this sample was similar to that of the GA sample; the

CO2 did not affect the acoustic velocities.

The strains resulting from this pressure cycling are shown in Figure 4.6. The sam-

ple again exhibited similar behavior to sample GA. The strains for the CO2-saturated

rock were significantly lower than those of the dry sample at similar differential pres-

sures.

Figure 4.7 is a more useful display of the strain data. The horizontal axis is

pore pressure instead of differential pressure. The uncertainties in the CO2-saturated

strains (blue diamonds) were again estimated using a 1% uncertainty in the voltage

on the linear potentiometers. The horizontal red line represents the dry strain asso-

ciated with 0.1 MPa differential pressure. The horizontal light red band represents

the uncertainty in the dry strain estimate, which is dominated by the uncertainty

associated with the least-squares fit to the dry strain data.


0 1 2 3 4 5 6 7 80.000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016


stra

in

dry increasingdry decreasing

fit to dry decreasingCO2 saturated

Figure 4.6: Strain as a function of differential pressure for sample VRtgn5. Dry datawere taken for increasing and decreasing confining pressure. At a confining pressureof 1 MPa, the sample was saturated with 0.9 MPa CO2; the strain was measured.Both the confining and pore pressures were increased by 1 MPa, and the measurementwas repeated. The strains under CO2-saturated conditions are less than under dryconditions, again indicating swelling.

Again, we see a statistically significant difference in strain between the dry and

saturated conditions. For pore pressures less than about 5 MPa, this difference in

strain was nearly constant and approximately 0.4%, consistent with the value found

for sample GA. There was an increase in strain (that is, a reduction in apparent

swelling) for higher pore pressure. Though the reason for the increased strain is

not clear, it is possible that it is related to a phase change of carbon dioxide at

that point. For CO2 at room temperature, the transition from gas to liquid phases

occurs at approximately 6 MPa, which corresponds to the pore pressure at which the

increased strain occurs.

Test 3: sample Zeo3

Sample Zeo3 was used to test property changes due to increased carbon dioxide

exposure time. This was done by setting the confining pressure to 0.3 MPa, injecting

the sample with CO2 at 0.2 MPa pore pressure, allowing the system to sit in that

4.4. RESULTS 101

0 1 2 3 4 5 6 70.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

pore pressure (MPa)

stra

in

CO2 saturateddry

Figure 4.7: Strain as a function of pore pressure for sample VRtgn5. The red line de-notes the dry strain at 0.1 MPa differential pressure as predicted by the fit to the drydecreasing data shown in Figure 4.6. The light red bar is the estimated uncertainty.CO2-saturated strains are statistically significantly less than those of the dry system,and they are essentially independent of pore pressure for pressures under 6 MPa, thatis, for gaseous CO2.

charged state for a period of time, taking a strain measurement, releasing the CO2,

taking a dry measurement, and then recharging system with CO2 for the next cycle.

Figure 4.8 shows the result of a series of injections, displaying strain as a function of

CO2 exposure time under two different conditions. The red series denotes a differential

pressure of 0.30 MPa, which is the dry state. The blue series denotes a differential

pressure of 0.09 MPa for pores saturated with CO2 at 0.21 MPa. The initial dry

strain measurement at 0.3 MPa confining pressure is indicated in the plot. When the

pressurized CO2 was first injected into the zeolite powder, it was done with the outlet

open to the atmosphere. The pressure at the injection point dropped to zero almost

instantaneously, indicating the sample had good permeability. The pulse of CO2 did

cause a jump in strain, most likely due to grain rearrangement in the unconsolidated

sample. The dry (red) series shows a general trend of decreasing strain with increasing

CO2 exposure time, though the strain values are within uncertainty of each other

after the initial grain rearrangement. The saturated (blue) series appears to stay

constant through time. The two curves trend to similar values at long exposure times,


though the dry measurements should show greater strains than the CO2-saturated

measurements because of the greater differential pressure.

0 20 40 60 80 100 120 140 160 180 2000.015

0.016

0.017

0.018

0.019

0.020

0.021

0.022

0.023

0.024

0.025

CO2 exposure time (min)

stra

in

differential pressure = 0.30 MPa (dry pores)differential pressure = 0.09 MPa (CO2 saturated pores)

initial dry strain

dry strain after CO2 pulse

Figure 4.8: Strain for the compacted zeolite powder as a function of CO2 exposure time.The initial large strains were most likely a result of grain rearrangement in the com-pressed powder. Strain does not exhibit a clear dependence on exposure time at thisscale but may over much shorter times.

Overall, the compacted zeolite powder sample was inconclusive. Grain rearrange-

ment and plastic deformation were the likely sources of any strain changes associated

with fluid pulses.

4.4.3 Relating Strain to Zeolite Content

The third and final series of experiments was designed to systematically determine

how the observed changes in strain are related to zeolite content. To that end, three

freshly-cut tuff plugs were subjected to identical stress cycles. Two plugs were from

the same formation, one having undergone zeolitization and the other not. They

enabled the comparison of a zeolite-rich sample to one without zeolite but having

similar pore structures. The third plug was from a different formation and contained

4.4. RESULTS 103

clinoptilolite instead of the chabazite found in the second plug. This allowed the

comparison of different types of zeolite.

Recall from Table 4.1 that the physical properties of the gray and yellow tuffs were

similar. They had high porosities (> 50%) and relatively high permeabilities. The

yellow tuff had significantly higher acoustic velocities than the gray tuff, but their

Vp/Vs ratios were both approximately 1.8. The green tuff, however, had very different

properties than the Campi Flegrei tuffs. Its grain density was significantly lower but

its bulk density was higher due to greatly reduced porosity. The permeability of the

green tuff was barely measurable in the nitrogen permeameter, only around 1 mD.

The permeability was sufficient for these experiments, though; the pore fluid in the

pressure vessel was able to equilibrate within seconds of fluid injection.

All three samples experienced the stress cycling shown as a cartoon in Figure 4.9.

First, the confining pressure was raised to 12 MPa and lowered with the pore net-

work open to atmospheric conditions (dry or drained measurements, listed as “dry1”).

Dry measurements were repeated to test for hysteresis (“dry2”). Then the confining

pressure was raised to 6 MPa and fixed, after which helium was injected into the

pore space at increasing and decreasing pressures (“He-saturated”). The helium was

released and CO2 was injected into the pore space at increasing and decreasing pres-

sures (“CO2-saturated”). The confining pressure was raised again to 12 MPa and the

pore pressure of the CO2 increased to the liquid CO2 range above 8 MPa. Finally,

the CO2 was released and additional dry measurements were taken (“dry3”).

Figure 4.10 shows the ultrasonic P-wave velocities of the three colored samples.

All five pressure cycles are shown. The additional dashed red lines denote the dry

sample velocity in the fully relaxed state at the end of the pressure cycling. The

highly porous Campi Flegrei samples (yellow and gray) show lower velocities than

the denser green tuff, as expected. The yellow and gray tuffs also show very little

pressure sensitivity in this range. As in the previous experiments, the velocities show

no change with saturating fluid; He-saturated and CO2-saturated symbols overlie the

dry measurements. The S-wave velocity behavior was similar.

Figure 4.11 shows the full strain data for the gray tuff (which contains no zeolite).


σconfining

σpore

σdifferential

dry 1

dry 2

He-saturated

CO2-saturated

dry 3

confining pressure: 0-12 MPapore pressure: 0 MPapore fluid: atmosphereconfining pressure: 0-12 MPapore pressure: 0 MPapore fluid: atmosphereconfining pressure: 6 MPapore pressure: 0-5 MPapore fluid: heliumconfining pressure: 6 MPapore pressure: 0-5 MPapore fluid: carbon dioxide

confining pressure: 0-12 MPapore pressure: 0 MPapore fluid: atmosphere

exposure to high pressure CO2

Figure 4.9: Description of the stress cycling to which each colored sample was subjected.Upper black lines are confining pressure, lower lines are pore pressure (colored by fluidtype), and the difference between the upper and lower lines is the differential pressure.

The data include an initial period of plastic deformation followed by a series of re-

peatable strain measurements under injection of helium and gaseous CO2. There is

a slight increase in compaction during and after injection of liquid CO2, perhaps due

to thermal damage from rapid CO2 depressurization. However, there is no evidence

of decreased strain (swelling) under saturation with any fluid.

Figure 4.16 shows a subset of the data from Figure 4.11. Only the stress paths

showing decreasing differential pressures are plotted. This removes from view the

initial plastic deformation and allows easier comparison of related strain curves. In

this view, it is quite clear that the strains under dry (2), He-saturated, and gaseous

CO2-saturated conditions are identical.

Figures 4.13 and 4.14 show strain as a function of differential pressure for the

yellow tuff (chabazite), which is a zeolitized version of the gray tuff. Like the data

for the gray tuff, the yellow tuff displays an initial plastic deformation followed by

dry and He-saturated conditions with identical strains. However, upon injection of

gaseous CO2, the strain in the yellow tuff decreases significantly at all differential

pressures. This amounts to a 10-15% decrease in compaction while gas CO2-saturated

compared to the He-saturated case. After the pressure of the CO2 is increased to the

liquid phase, continued compaction is observed just as in the gray tuff case.

4.4. RESULTS 105

0 2 4 6 8 10 12 140

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


P-w

ave

velo

city

(km

/s)

dry 1 He-saturated dry 3

dry 2 CO2-saturated fully relaxed after stress cycling

Green tuff(clinoptilolite)

Yellow tuff(chabazite)

Gray tuff(no zeolite)

Figure 4.10: P-wave velocities for the green, yellow, and gray tuff samples. Velocitiesof the highly porous Campi Flegrei tuffs (yellow and gray) show very little pressuresensitivity in this range. The denser green tuff is pressure sensitive. For all threesamples, the velocities appear to depend only on differential pressure; they show nochange with saturating fluid.

Figures 4.15 and 4.16 show strain measurements for the green tuff (clinoptilolite).

Recall that this tuff is denser than the other two with a much lower porosity. The

initial plastic deformation is much less pronounced. The dry unloading curve is

identical to the subsequent dry and He-saturated curves. Again, there is a decreased

strain upon injection of gaseous CO2. In this case, the swelling represents 9-16% of

the strain in the He-saturated case. When the pore space of the green tuff is filled with

supercritical CO2, an additional swelling occurs. It represents 25-33% of the helium-

saturated strain; it approximately doubles the swelling observed during gaseous CO2

saturation. Upon release of the CO2, the sample compacts again, though it does not

reach its maximally-compacted state.


0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.10


stra

in

He-saturated

dry 3

dry 2

CO2-saturated

dry 1

fully relaxed after stress cycling

gray (no zeolite)

Figure 4.11: Full strain behavior for the gray (non-zeolitized) tuff including 95% confi-dence intervals. The dashed red line indicates the sample length once the sample wasfully relaxed after the experiments. After an initial plastic deformation, strains wereconsistent for dry and fluid-saturated cases.

4.5 Discussion

Microstructure in tuffs can be quite fragile, particularly in high-porosity samples.

Pumice, glassy inclusions, and weak welds break at a variety of pressures making

sample seasoning difficult. It is hard to tell from these data if the additional com-

paction seen under the final dry cycles in the gray and yellow tuffs is from interaction

with the liquid CO2, a result of thermal shock from rapid venting of the CO2, or just

an indication that the sample was not fully seasoned upon fluid injection. However,

the near-perfect correlation between dry and helium-saturated cycles suggests the

effect is not solely related to seasoning.

Data from the three colored samples do indicate, however, that CO2 interacts

with large-channel zeolites in tuffs. The tuff without zeolite experienced the classical

behavior that strain is a function of differential pressure only and does not depend

4.5. DISCUSSION 107

gray (no zeolite)

0 2 4 6 8 10 120.060

0.065

0.070

0.075

0.080

0.085

0.090


stra

in

He-saturated

dry 3

dry 2

CO2-saturated

Figure 4.12: Strain behavior for the gray (non-zeolitized) tuff, decreasing differentialpressure curves only, including 95% confidence intervals. Strains for the gray tuffshowed no dependence on pore fluid type, only on differential pressure. In this seriesof unloading curves, the non-zeolitized tuff shows a classical stress dependence ondifferential pressure. The CO2 curve overlies the helium and dry curves. The final drycurve reflects additional deformation that may be the result of thermal damage afterhigh pressure CO2 exposure.

on the type of pore fluid. Neither zeolite-rich tuff samples showed any interaction

with helium, but they experienced a decreased strain of 20% on average when CO2

saturated the pore space. Strain, therefore, depended on both the differential pressure

and the saturating pore fluid type.

The magnitude of the strain difference between He-saturated and CO2-saturated

conditions were the same in the two colored zeolitic tuffs, as summarized in Table 4.2.

The green tuff experienced less than half of the plastic deformation the yellow tuff

did, but they experienced similar swelling under CO2 saturation. The magnitudes

of the strain differences were similar, as were their differences relative to the helium

strain based on the original length. If the strains are rescaled based on the final dry

measurements (removing the plastic deformation), the soft yellow tuff shows a larger

fractional strain difference. In fact, the CO2-saturated sample under pressure was

longer than the final unconfined dry sample.

These data suggests the CO2 is interacting with the zeolite minerals in particular,


0 2 4 6 8 10 120.000

0.005

0.010

0.015

0.020

0.025

0.030


stra

in

He-saturated

dry 3

dry 2

CO2-saturated

dry 1


yellow (chabazite)

Figure 4.13: Full strain behavior for the yellow (chabazite-rich) tuff including 95% con-fidence intervals. The dashed red line indicates the sample length once the samplewas fully relaxed after the experiments. After an initial plastic deformation, dry andHe-saturated measurements of strain are similar. Injection of gaseous CO2 causes adecrease in strain (swelling).

causing samples to swell. This is seen for two different types of naturally occurring

zeolites, both of which have cage structures large enough that CO2 could be adsorbing

on the pore wall surfaces or absorbing into the crystalline structure.

Strains vary based on pore fluid type, but acoustic velocities do not. Assuming

the bulk density decreases slightly during CO2 swelling, the bulk and shear moduli of

the rock matrix must adjust to compensate. Again, the CO2 appears to change the

zeolite matrix properties resulting in no net velocity change.

4.5. DISCUSSION 109

yellow (chabazite)

0 2 4 6 8 10 120.0140.0160.0180.0200.0220.0240.0260.0280.030


stra

in

He-saturated

dry 3

dry 2

CO2-saturated


Figure 4.14: Strain behavior for the yellow (chabazite-rich) tuff, including 95% confidenceintervals, decreasing differential pressure curves only. The helium curve overlies theinitial dry curve, but the CO2 curve shows reduced strain at the same differentialpressures. It is less strain than the final unconfined dry measurement. The final drycurve reflects a small additional deformation from high pressure CO2 exposure.

Table 4.2: Relative strains experienced by the yellow and green tuff samples under CO2

saturation.

yellow tuff green tuff

zeolite content ∼ 60% ∼ 100%He-CO2 strain difference (εHe − εCO2) 0.0019 to 0.0028 0.0013 to 0.0024relative strain difference (εHe − εCO2) /εHe 8% to 15% 9% to 16%rescaled relative strain

(ε′He − ε

′CO2

)/ε

′He 46% to 938% 5% to 33%


0 2 4 6 8 10 120

0.005

0.010

0.015

0.020

0.025


stra

in He-saturated

dry 3

dry 2

CO2-saturated

dry 1


green (clinoptilolite)

Figure 4.15: Full strain behavior for the green (clinoptilolite-rich) tuff including 95%confidence intervals. The dashed red line indicates the sample length once the samplewas fully relaxed after the experiments. After an initial plastic deformation, dry andHe-saturated measurements of strain are similar. Injection of gaseous CO2 causes adecrease in strain (swelling). Increasing the CO2 pressure to the liquid phase causes asharp decrease in strain that is largely reversed upon release of the CO2.

4.5. DISCUSSION 111

green (clinoptilolite)

0 2 4 6 8 10 120.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022


stra

in

He-saturated

dry 3

dry 2

CO2-saturated

Figure 4.16: Strain behavior for the green (clinoptilolite-rich) tuff, including 95% con-fidence intervals, decreasing differential pressure curves only. After the initial drypressure curve, strains are identical for dry and He-saturated conditions. Injection ofgaseous CO2 causes a decrease in strain (swelling) that is doubled under liquid CO2

injection. Upon release of the CO2, the sample does not return to its maximally-compacted state. The green tuff did not appear to be damaged by high pressure CO2

exposure.


4.6 Conclusions

Zeolites are interesting materials for testing rock-fluid interactions. The open cage

structures of many naturally-occurring zeolites, along with their electrically charged

framework, make them strong adsorbents of many common molecules. Unfortunately,

naturally-occurring zeolitic tuffs often have fragile and complicated pore structures

that make separating mechanical deformation of samples difficult to separate from

chemical effects.

It has been shown here that zeolite-rich tuffs demonstrate statistically significant

swelling when saturated with gaseous CO2. This effect is not seen under saturation

with helium, nor is it seen in a tuff containing no zeolite. The swelling does not

appear to affect acoustic velocities as long as the length change is monitored.

Acknowledgements

Tiziana Vanorio supervised this project in the laboratory and acquired the sand-

stone data. Additional laboratory support from Stephanie Vialle and Yael Ebert was

appreciated. KMI Zeolite provided the green (clinoptilolite) tuff from their quarry.

113

Chapter 5

Density Functional Theory study

of CO2 adsorption in chabazite

5.1 Abstract

Density functional theory (DFT) has become an increasingly important tool in under-

standing electronic interactions of materials, particularly crystalline structures and

surfaces. In this chapter, electronic DFT is applied to the problem of zeolite swelling

during saturation with CO2.

The zeolite chabazite was simulated, and the bulk modulus of its crystalline struc-

ture was calculated using changes in electronic energy as a function of unit cell volume.

A bulk modulus of 54 GPa was obtained. Adsorption of a carbon dioxide molecule

was simulated by introducing it to the interior of the crystalline structure and al-

lowing it to relax to its equilibrium position. Though the carbon dioxide molecule

was repelled by the charged chabazite cage, inclusion of a coordinated calcium cation

provided a binding site for the carbon dioxide molecule. Adsorption of CO2 by the

calcium chabazite structure was successfully simulated.

114 CHAPTER 5. DFT IN CHABAZITE

5.2 Introduction

Zeolites are framework aluminosilicates comprising complex cages and channels that

provide significant intracrystalline porosity. For many naturally occurring zeolite

types, the channels are large enough to accommodate passage of small molecules

such as carbon dioxide and methane. If no aluminum were present in the zeolite

frame, the cages would be a charge-neutral and inert form of silica. The substitution

of an aluminum atom for a silicon atom creates a negative charge on the zeolite frame.

The combination of a charged frame and a very open structure causes zeolites to be

important adsorbents and catalysts.

Natural zeolites are often found in altered volcanic tuffs and near hydrothermal

vents. Important deposits include the Neapolitan yellow tuff in the Compania Region

of Southern Italy near Campi Flegrei, where anomalous ground deformation has been

observed; and the Bowie Formation in Arizona, USA, which is extensively mined

for industrial use. Some deposits, such as the ones found in the oil fields of eastern

Georgia (country), have even served as oil reservoirs (Vernik, 1990).

Many common pore fluids may experience strong interactions with a zeolite ma-

trix. For example, laboratory measurements indicate zeolitic tuffs experience swelling

when saturated with carbon dioxide (see Chapter 4). Carbon dioxide can also travel

through the intracrystalline channels of the zeolite and bind to the interior cage sur-

faces. The extent to which these interactions can affect reservoir-scale projects, such

as seismic monitoring or enhanced oil recovery, is still undetermined. If these inter-

actions are to be thoroughly understood, though, they must be studied at the atomic

scale.

Electronic Density Functional Theory (DFT) is a basis for atomic-scale modeling

that allows the calculation of physical and chemical properties of molecular structures.

While it is used extensively in surface chemistry, it has not yet had much exposure

in geophysics. This may change, though, as more geochemical analysis is used in

rock physics. For example, DFT can be used to calculate compliance tensors for

crystalline structures, giving geophysicists estimates of moduli for minerals that are

rarely found as large, homogeneous structures suitable for laboratory characterization.

5.3. OVERVIEW OF DFT 115

Furthermore, it can be used to predict changes to moduli when a mineral is exposed

to a reactive fluid.

This chapter describes efforts to explore zeolite interaction with carbon dioxide

using DFT in an attempt to understand the interactions between zeolites and carbon

dioxide observed in Chapter 4. The structure of the zeolite chabazite was simulated

both as a frame and with carbon dioxide in the cages. Completed calculations of its

system properties are reported with some interpretations. The calculations are pre-

ceded by a brief introduction to DFT with a qualitative description of its derivation.

5.3 Overview of DFT

An excellent overview of DFT and its applications is given in Sholl and Steckel (2009),

which is a substantial resource for applying DFT to engineering problems. The fol-

lowing overview of DFT is largely summarized from that work.

A natural way of describing a collection of atoms is to look at its ground-state

energy and analyze how it changes as electrons and nuclei are moved. Quantum me-

chanics provides a way to do this by describing the system using a wave function.

Solutions to Schrodinger’s equation can be approximated by assigning each electron

its own wave function that is a function of spatial coordinates. If there are N elec-

trons in the system, then there are 3N variables to solve for in the time-independent

Schrodinger equation. The problem can be reduced to solving for only 3 variables

if instead of considering individual electrons, electron density is used. The electron

density is essentially a total probability that any electron is located at a particular

point in space.

Information on electron density is related to information on the macrosystem

through two important theorems from Hohenberg and Kohn. The first theorem proves

that the ground-state energy from the Schrodinger equation is a unique functional of

the electron density. This means that there is a unique mapping from the electron

density (a function of space) to the total energy of the system (a number). The

second theorem proves that the electron density that minimizes the total energy of

the system is in fact the real electron density found by solving Schrodinger’s equation.


The electron-density functional is not known generally, so it must be approxi-

mated. This is done by breaking it into two parts, one that is the known functional of

the individual electron wave functions, and another that handles the interactions be-

tween electrons (exchange-correlation functional). The simplest approximation uses

the exchange-correlation functional for a uniform electron gas, which is known ex-

plicitly. This approximation considers only the local electron density, so it is called

the local density approximation (LDA). When local density information is combined

with information on the electron density gradient, it is called a generalized gradient

approximation (GGA). There are many types of GGA functionals, and each may

yield a different total system energy. That is why the most useful DFT calculations

compare states and report changes in energy, not absolute energy. It is also important

to use functionals consistently when comparing or combining systems. For example,

to look at the binding energy of a carbon dioxide molecule to a surface, one needs to

calculate the energy of the carbon dioxide molecule alone, the energy of the surface

alone, and the energy of the combined system. The same functional should be used

for all three calculations.

If the system in question is periodic in space, like an infinite crystal, then Bloch’s

theorem asserts that solutions to the Schrodinger equation can be written as a sum-

mation of k terms, each of which must take the form of a periodic function of the

spatial coordinate r times a plane wave of the form exp(ik · r). This method is called

plane-wave DFT. It is often easier to solve the Schrodinger equation in terms of k

than r, so formulations are made in k space, a reciprocal space to the real space r.

Solution of the Schrodinger equation in reciprocal space involves an infinite sum

for each point in k space. For computational purposes, the summation must stop at

some defined upper bound. The plane waves exp(ik · r) in the summation correspond

to solutions with a specific kinetic energy of E = (hk)2/m, so putting a bound on the

summation index essentially discards solutions with very high energies. The lower-

energy solutions are the more physically meaningful ones, so the truncated summation

converges to the real solution as more terms are included. The upper bound on the

summation index is described in terms of the maximum energy solution included in

the sum, the energy cutoff. Appropriate energy cutoffs vary between systems, so

5.4. DFT CALCULATIONS 117

the value must be calibrated. Comparisons of energies should only be made between

systems that have been evaluated using the same energy cutoff. For example, the

energy of a lone carbon dioxide molecule might be adequately described with an

energy cutoff of 300 eV; but if its energy will be used to determine the adsorption

energy on a surface that requires an energy cutoff of 450 eV, then 450 eV must be

used consistently for all calculations.

5.4 DFT Calculations

This section reports results of DFT calculations on a chabazite framework. While

some computational details will be given, the main purpose is to describe the process

with emphasis on the types of information needed to perform the calculations and

the types of information returned by the software.

The following plane wave DFT calculations were performed with the Vienna ab

initio Simulation Package (VASP) (Kresse and Furthmuller, 1996). The exchange

correlation was treated using the local density approximation (LDA) with the Perdew-

Burke-Enzerhof (PBE) generalized gradient approximation (Perdew et al., 1996).

The electron-ion interactions were described using Blochl’s all-electron projector-

augmented wave (PAW) method. Brillouin-zone integrations employed a 4 × 4 × 4

Monkhorst-Pack grid of k-points.

5.4.1 System calibration

The mineral of interest in this study is chabazite, a zeolite with the formula

(Ca,Na2,K2,Mg)Al2Si4O12 · 6H2O .

It is a framework silicate composed of linked rings of SiO4 tetrahedra with a compli-

cated ice-like water structure in the center holding the cations in place. An example

of the unit cell for calcium chabazite in three orientations is shown in Figure 1. The

hydrated form is shown in the left column, while the dehydrated framework is shown

on the right. Although hand samples of chabazite are in the hydrated form, the water


and cations are easily displaced by other molecules. The ease with which the water

molecules are displaced, combined with their electrically charged frames, makes many

types of zeolites excellent adsorbents, causing them to be the focus of many studies.

The all-silica form of chabazite has a rhombohedral unit cell and space group

symmetry R-3m. When dehydrated, the unit cell contains 12 silicon atoms and 24

oxygen atoms. Natural chabazite has aluminum atoms in place of some silicon atoms;

for the Neapolitan yellow tuff studied in Chapter 4, the ratio is approximately 1Al:3Si

(de’Gennaro et al., 1990). The initial atomic coordinates used in this study come from

the experimental determination of Gualtieri (2000), as reported in the American

Mineralogist Crystal Structure Database. The experimental crystal structure was

found to be

a = b = c = 9.3969 A and α = β = γ = 93.866◦ .

The experimental data were for calcium chabazite with 71% silicon and 29% alu-

minum. For the simulations shown here, sites for the aluminum atoms in 1Al:11Si,

2Al:10Si, and 3Al:9Si ratios were specified explicitly; naturally-occurring chabazite

exhibits semi-random placement of the aluminum atoms. An example of the initial

configuration of a unit ring with a single aluminum atom is shown in the right column

of Figure 5.1. The diameter of that ring is approximately 11 A, which is large enough

to allow easy passage of a carbon dioxide molecule, which is shorter than 3 A. Ad-

ditional rings are formed in the chabazite framework when the unit cell is repeated

periodically. The smallest of those rings is approximately 3.8 A in diameter, also

large enough to accommodate carbon dioxide.

Initial calibration of the system typically begins by determining the minimum

number of k-points and the minimum energy cutoff that give results sufficiently close

to the true solutions. This is done by calculating the energy of the system for a series

of values and evaluating how rapidly the energy converges. Figure 5.2 is an example

the energy cutoff calibration for the chabazite system containing one aluminum atom

per unit cell. In this exapmple, the system appears to converge for an energy cutoff

of 450 eV, though 400 eV may be adequate if computation time is an issue. In this


Figure 5.1: The unit cell for a calcium chabazite molecule. (yellow = aluminum, cyan =silicon, dark gray = oxygen, red = calcium, light blue = water) The hydrated moleculeis shown on the left; note the ring of coordinated calcium atoms and the tight clusterof water molecules. The zeolite framework, which contains only aluminum, silicon, andoxygen, is shown on the right. The top row is the view along the 111 axis. Subsequentrows are rotated up 45◦ and then 35◦.

study, a reasonable energy cutoff of 350 eV was chosen to keep computation time low.

This energy cutoff is high enough to make meaningful comparisons between systems


200 250 300 350 400 450 500 550 600

energy cutoff (eV)

Syst

em E

nerg

y E

tot

(eV

)

Figure 5.2: Energy cutoff calibration for chabazite with one aluminum. As higher energystates are included, the solution converges on the “true” system energy. An energycutoff of 450 eV would be appropriate for this example.

but it likely too low for claims of absolute energies.

5.4.2 Lattice parameter

The shape of the tessellated unit crystal cell is described by three vectors. The

vector lengths are scaled by lattice parameter, a number that can be varied to change

the volume of the unit cell without changing its shape. In many chemical studies,

the lattice parameter is treated as another input parameter to be calibrated for the

system. For mechanical studies, varying the lattice parameter yields important elastic

information, which is summarized below.

The vectors of the three crystal axes of the unit cell are specified to describe the

locations of the atoms in space. These were reported for chabazite in the previous

section; they define a rhombohedron. The atomic positions are reported as fractions

of those basis vectors. The actual size of the cell in angstroms is specified by the lattice

parameter, which is a scalar that premultiplies all three basis vectors. Changing the

lattice parameter alters the volume of the cell, analogous to imposing a bulk strain on


the crystal structure. The bulk modulus of the crystal can be calculated by plotting

the total energy Etot as a function of the lattice parameter a0. If the total energy is

expanded as a function of the lattice parameter a0 using a Taylor series, it can be

written as

Etot (a) ≈ Etot (a0) + α (a− a0) + β (a− a0)2 , (5.1)

where α and β are fitting parameters. If a0 is chosen so that it is the optimal lattice

parameter predicted by DFT calculations, that is, the one that gives the minimum

total energy, then α is zero. The parameter β is related to the second derivative

change in energy with lattice parameter. The equilibrium bulk modulus K of the

crystal is related to the second derivative change in energy with volume. The bulk

modulus can be found from β using the relation

K =2

9

(1

a0

)β . (5.2)

Figure 5.3 shows the result of this calculation for two chabazite frames, one contain-

ing no aluminum atoms and the other containing a single aluminum atom per unit

cell. The equilibrium lattice parameters was determined to be 9.367 A and 9.427 A,

respectively; the experimental value from Gualtieri (2000) was 9.3969 A. The curve

fit to the data yielded a β values of 19.15 and 13.11, which correspond to bulk mod-

uli of 73 GPa and 39 GPa, respectively. These values are similar to values in other

DFT studies (e.g., Astala et al., 2004), though again the energy cutoff in this study

is somewhat low. The smaller lattice parameter and lower total energy of the no-

aluminum configuration indicate it is a more energetically favorable system than the

one-aluminum case.

The analysis above changes the volume of the cell uniformly to describe a bulk

modulus. Because the scaling of the cell volume reflects an imposed strain and not

a true imposed pressure, the modulus calculated is really an isotropic approximation

to the real bulk modulus. Anisotropy can be explored if the lattice vectors are scaled

independently (Astala et al., 2004). This is analogous to imposing strain in one

direction at a time. Newer versions of VASP have this functionality built in.

It is important to note that the bulk modulus found using this method is the bulk


9.15 9.2 9.25 9.3 9.35 9.4 9.45 9.5 9.55 9.6-281.5

-281.0

-280.5

-280.0

9.15 9.2 9.25 9.3 9.35 9.4 9.45 9.5 9.55 9.6-285.0

-284.5

-284.0

-283.5

lattice parameter (Å)

Eto

t (eV

)

K = 73 GPa

a0 = 9.367 Å β = 19.15

a0 = 9.427 Å

K = 49 GPa β = 13.11

1 Al : 11 Si

0 Al : 12 Si

Figure 5.3: Plots of total energy of the dehydrated chabazite framework as a function of thelattice parameter for frames containing no aluminum atoms (blue) and one aluminumatom (red) per unit cell. Dashed lines are the best fit to each data set. The estimatedminimum-energy lattice parameter a0, the resulting value of the fitting parameter β,and the bulk modulus calculated from them are shown on the plot for each case. Thesingle-aluminum case has a larger cell size (larger a0) and a less favorable energy statethan the no-aluminum case.

modulus of the dehydrated crystalline structure. It does not provide any information

about the bulk modulus of a rock matrix composed of complicated crystalline grains

and pore structures, nor does it represent the bulk modulus of a naturally-occurring

chabazite crystal whose cages are filled with water and coordinating cations. The

values of compressibility may still be useful, though, in effective media modeling that

requires a mineral modulus.


Figure 5.4: Example of Bader charge mapping from Henkelman et al. (2006). (a) Eachpoint traces a path of steepest ascent in charge density until a local maximum isreached. (b) Points that terminate at the same maximum are assigned to the sameBader region.

5.4.3 Bader charge analysis

It is common to describe materials in terms of their charges and how electrons are

transferred during bonding. This sort of description is nontrivial for DFT calcula-

tions because electron density is not a discrete quantity. There are algorithms for

partitioning the electron density so that electronic charge is associated with particu-

lar atoms. One algorithm for this purpose, Bader decomposition, is shown here. For

each point in space, the algorithm calculates the charge density gradient and steps in

the direction of steepest ascent. It traces a path to a local charge maximum. Points

that terminate at the same maximum are assigned to the same Bader region. This is

illustrated in Figure 4 (from Henkelman et al., 2006).

Table 5.1 shows the result of a Bader charge decomposition for the 36 atoms in

a chabazite frame containing one aluminum atom per unit cell. The table lists each

atom, its nominal number of valence electrons, and the number of electrons assigned

to it in the Bader charge decomposition. Note that the aluminum atom loses nearly

2.5 of its 3 valence electrons. The silicon atoms donate approximately 3 out of 4

valence electrons each, though it varies by position. The oxygen atoms all gain about

1.5 electrons. The simulated patterns of electron donation are as expected for this


Table 5.1: Result of Bader charge analysis for the chabazite framework with one alu-minum atom per unit cell. Shown are each atom, the number of valence electrons theisolated ion would have, and the number of valence electrons assigned to it using Baderdecomposition. As expected, aluminum and silicon lose electrons, and oxygen gainsthem.

Al 3 0.5272 O 6 7.584 O 6 7.5789Si 4 0.8144 O 6 7.5714 O 6 7.5649Si 4 0.8068 O 6 7.5662 O 6 7.5685Si 4 0.8184 O 6 7.5894 O 6 7.5874Si 4 0.7995 O 6 7.5958 O 6 7.4896Si 4 0.8052 O 6 7.4772 O 6 7.5903Si 4 0.8159 O 6 7.4933 O 6 7.5832Si 4 0.8066 O 6 7.5848 O 6 7.5902Si 4 0.8101 O 6 7.5657 O 6 7.5968Si 4 0.8069 O 6 7.5811 O 6 7.576Si 4 0.8039 O 6 7.5769 O 6 7.5984Si 4 0.8145 O 6 7.5669 O 6 7.4937

system.

5.4.4 DOS/LDOS

For many analyses, it is not enough to know the approximate number of electrons

associated with a particular atom. Detailed information on the electronic structure

of the entire system is needed. For these cases, the electronic density of states (DOS)

is considered. The density of states is essentially a measure of the occupied energy

levels in the system (see Hoffman, 1988, for an intuitive development of DOS from

molecular orbital theory). For instance, Figure 5.5 shows a DOS plot for the chabazite

frame with one aluminum atom per unit cell. The horizontal axis shows the energy

associated with the state. The plot has been scaled so that zero energy corresponds

to the Fermi energy, the energy of the highest occupied electronic state. States to the

left of the Fermi energy are occupied states and are in the valence band. The states

to the right of the Fermi energy are part of the conduction band. The nearly 5 eV

range between these bands where the density of states is zero is called the band gap.

A large band gap qualitatively means that it is not easy to excite valence electrons


-30 -20 -10 0 10

Den

sity

(sta

tes/e

V)

Energy (eV)

conduction bandvalence band

band gap

20

Figure 5.5: Example of a density of states (DOS) plot for chabazite with one aluminumatom per unit cell. The energy has been translated so that the Fermi level is at 0 eV.

into the conduction band where they can conduct electricity. The very large band

gap of the chabazite crystal indicates it is a strong insulator.

Figure 5.6 shows a plot of the local density of states (LDOS) for the same crystal.

The LDOS is similar to the Bader analysis in that it finds the electron energy states

in a region around each atom. Unlike the Bader analysis, the size of the region is

defined and the states inside the region are summed. Improper region sizing can lead

to either under-counting states or counting states that actually belong to a different

atom. The LDOS in Figure 5.6 is separated into atoms, but it can be decomposed

further into specific orbitals. If this is done, it becomes clear that the s orbitals have

the lowest energies and form the peak near -18 eV; the p orbitals are the primary

components of the -4 ev peak.

The DOS and LDOS are sensitive to the number of k points used in the simula-

tions. Because the sampling used here is relatively coarse, the values shown above

should not be over-analyzed.


-30 -20 -10 0 10 20

Den

sity

(sta

tes/e

V)

Energy (eV)

Oxygen

Silicon

Aluminum

mostly s

mostly p

Figure 5.6: Example of a local density of states (LDOS) plot for the three types of atomsin the chabazite frame containing one aluminum atom per unit cell. Lower energystates are typically associated with s orbitals while the higher states are primarilyassociated with p orbitals.


5.4.5 Joined systems

A key point of interest in this study is how a carbon dioxide molecule interacts with

a charged chabazite frame. The first step is to simulate the chabazite frame and the

carbon dioxide molecule separately. Once they are each calibrated, they can be com-

bined in a single system and allowed to react. Information can be obtained concerning

the preferred bonding sites, preferred orientations, and the energy of adsorption.

If the bonding sites and orientations are known approximately, it is a relatively

simple matter to place a carbon dioxide molecule in the appropriate position and allow

the system to relax to its equilibrium position of minimum energy. For the dehydrated

chabazite frame shown here, the bonding configuration is unknown, so the energy of

the system must be mapped in some way. To begin this process, the carbon dioxide

molecule was placed in the center of the chabazite ring. All of the atoms were fixed

except the two oxygens belonging to the carbon dioxide molecule. Once a minimum

energy configuration was achieved, the entire carbon dioxide molecule was translated

toward the aluminum atom. The process was repeated as the oxygen atoms were

allowed to rotate into stable positions. An example of this progression is shown in

Figure 5.7. The series of images looks down on the chabazite frame obliquely; the

carbon dioxide molecule is aligned perpendicular to the plane of the ring. When near

the center of the ring, the carbon dioxide molecule maintains its linear shape. As it

approaches the aluminum atom, the oxygen atoms begin to bend. The O-C-O bond

angles shown are, clockwise from the upper left, 180◦, 178◦, and 143◦.

The strength of the bond between the carbon dioxide and the chabazite frame

is measured by the adsorption energy. If the equilibrium energies of the adsorbate

(carbon dioxide) and the adsorbent (chabazite frame) are known, then the adsorption

energy is simply

Eads = Eframe+CO2 − ECO2 − Eframe . (5.3)

For adsorption to be favorable, the adsorption energy should be less than zero. If

its absolute value is less than approximately 0.5 eV per atom, the adsorbate is

physisorbed; greater values imply it is chemisorbed. In our current calculations,

the adsorption energy is positive, indicating that the carbon dioxide molecule does


Figure 5.7: The combined carbon dioxide and chabazite framework system. (yellow =aluminum, cyan = silicon, dark gray = frame oxygen, green and black = carbondioxide molecule) From the left, the carbon dioxide molecule was brought closer tothe aluminum atom. The oxygen atoms attached to the carbon were allowed to relaxat each stage; the oxygens bend away from the aluminum as they approach it. CO2 isrepulsed by the frame and is does not adsorb.

not adsorb directly to the dehydrated chabazite frame. This was expected because

naturally-occurring chabazite crystals have coordinating cations participating in the

adsorption.

Additional simulations were run to show the effect of a coordinating cation in the

bonding process. Figure 5.8 shows the minimum energy configuration for a carbon

dioxide molecule interacting with chabazite by way of a calcium ion. In this case, the

CO2 molecule is chemisorbed to the calcium chabazite structure.

5.5 Discussion

This project has focused on developing a general understanding of the chabazite sys-

tem and its interactions with a single carbon dioxide molecule. More generally, it has

also involved developing a greater facility in running and analyzing DFT calculations

using VASP. To this extent, a great deal of progress was made. Converging chabazite

framework structures with aluminum substitutions yielded reasonable electronic en-

ergies. Simulation times were relatively short; most systems converged within a day

using current resources at the Stanford Center for Computational Earth and Envi-

ronmental Science (CEES).

5.5. DISCUSSION 129

Figure 5.8: CO2 adsorbed to a coordinated calcium ion. (yellow = aluminum, cyan =silicon, dark gray = frame oxygen, red = calcium, green and black = carbon dioxidemolecule)

To truly simulate the mechanical properties of natural chabazite, more informa-

tion on the configuration of water molecules must be obtained. The experimental

structural data locates water molecules but does not specify the orientations of the

molecules or even the approximate locations of the hydrogen atoms involved. The

addition of a more complete water and cation network will likely have a large effect on

the equilibrium position of the carbon dioxide molecule within the chabazite frame.

Only when the complete system is simulated can a representative map of the system

energy be made.

If the preferred orientations and binding sites can be located, the effects of carbon

dioxide loading on the system can be explored. It can be used to determine how many

carbon dioxide molecules can be housed in a single chabazite cage. Of particular

interest in rock physics is whether DFT predicts any changes in cell volume or bulk

modulus as a result of carbon dioxide loading in the cage. If so, the simulations may

help explain the swelling observed experimentally in Chapter 4.

Information on binding energies and mechanisms may not have immediate appli-

cability in large-scale geophysical surveys. However, modeling of this sort may shed


some light on how well carbon dioxide can be chemically held in a zeolite structure

as well as what other molecules are likely to displace the carbon dioxide. The same

methods presented here can also be applied to other materials, such as shales and

clays. They are also used in modeling surfaces as opposed to the bulk structures

shown here.

5.6 Conclusions

Density functional theory provides a powerful method of describing the electronic

interactions of atoms. This chapter demonstrates that it is feasible to apply this the-

ory to materials measured in the rock-physics laboratory. It can be used to estimate

chemical interactions such as adsorption; but it also provides information on changing

mechanical properties that result from the chemical interactions, such as modification

of the mineral bulk modulus and strain resulting from gas loading. This information

may be useful in understanding laboratory observations like swelling, and it provides

input parameters to other mesoscopic models.

Acknowledgements

Thanks to Jennifer Wilcox and Shela Aboud for their guidance in DFT. Computa-

tional equipment was provided by the Stanford Center for Computational Earth and

Environmental Science (CEES) and by TeraGrid.

131

Chapter 6

Anthropogenic salt deposition in

sandstones

6.1 Abstract

Ionic salt precipitation in oil and gas reservoirs is common and can lead to forma-

tion damage and impermeable zones. To successfully predict the locations of salt

deposition and monitor its progress, we must understand how and to what extent

interaction with brine can alter the rock matrix.

The purpose of the experiments in this chapter is to test the feasibility of monitor-

ing changes in rock properties that result from temperature-driven brine evaporation

in sandstone plugs. Porosity, permeability, and acoustic velocities were measured on

three dry Fontainebleau Sandstone samples before and after NaCl precipitation.

All measured properties showed detectable changes resulting from salt deposition.

Results indicate that porosity and permeability evolve along the natural diagenetic

trend of porosity versus permeability for these sandstones. Acoustic velocities, par-

ticularly shear wave velocities, increase after the deposition of salt. The effect is most

pronounced in lower porosity samples.

132 CHAPTER 6. SALT DEPOSITION

6.2 Introduction

Before production, oil and gas reservoirs in the deep subsurface are in equilibrium

with the brines they contain. The dissolved ions are in equilibrium with each other,

and the aqueous solution is in equilibrium with the rock matrix around it. During

production, this equilibrium is perturbed; reservoirs are often subjected to enhanced

recovery techniques, receiving floods of water, gas, or polymers.

A common side effect of chemical disequilibrium is the formation of ionic salt

scales; in reservoirs, these are most often calcium carbonate, calcium sulfate, stron-

tium sulfate, and barium sulfate (Merdhah and Yassin, 2009). This has been recog-

nized as a source of formation damage, but it can also be utilized as a production

tool. For example, the volumetric sweep efficiency from gas flooding can be increased

by inducing salt precipitation. To do this, the reservoir is flooded with brine that

preferentially saturates the more permeable zones. Salt precipitates predominantly in

the larger pores thus reducing the heterogeneity of the formation. Salt precipitation

can also be used to block the gas pay zones in reservoirs experiencing gas coning

thereby reducing the undesired production of gas (Koncz et al., 2004).

There are three main mechanisms for salt deposition: a pressure decrease or tem-

perature increase that reduces the solubility of an ionic component, mixing of incom-

patible brines, and brine evaporation (Mackay and Jordan, 2005). These have been

studied from an engineering standpoint, but less is known about their effect on rock

physics properties. For example, it is unknown whether the different depositional

mechanisms produce different acoustic signatures from alteration of the rock matrix.

Understanding this is particularly important for reservoir monitoring.

The purpose of this study is to expand existing rock physics tools to include

information on storage, transport, and acoustic properties of rocks undergoing an-

thropogenic diagenesis. Specifically, these experiments aim to determine whether

clear changes in porosity, permeability, and acoustic velocities can be detected as

a result of salt deposition in the laboratory. Also of interest is whether the initial

microstructure of a rock sample influences salt deposition and whether these anthro-

pogenic alterations of the rock matrix mimic natural diagenetic trends. The results

6.3. METHODS 133

will help elucidate the mechanism involved in altering the rock matrix as well as

provide empirical trend information.

This work includes brine injection experiments using Oligocene Fontainebleau

Sandstone samples collected from outcrop in the Ile-de-France region near Paris. Use

of a high-salinity NaCl brine in nearly pure quartz sandstone ensured that only salt

deposition, and not grain dissolution, occurred. Porosity, permeability, and acoustic

velocities of the dry samples before and after salt deposition were measured so that

changes to the rock matrix could be quantified.

6.3 Methods

The three samples used in this study were cylindrical plugs from the Fontainebleau

Sandstone rock catalog at Stanford University. The samples were chosen so that

their initial porosities spanned the range of values in the catalog. CT scans of the

three samples, shown in Figure 6.1, provide a qualitative comparison of the variation

in grain size, pore size, and connectivity. Previous characterization determined that

porosity and permeability for this family of samples is well described by a Kozeny-

Carman relation with a tortuosity of 2.5, critical porosity of 0.02, and a mean grain

diameter of 250 microns (Gomez, 2009, chap. 3).

(a) GW23 φ = 0.18 (b) A117 φ = 0.10 (c) A33 φ = 0.06

Figure 6.1: CT scans of the three Fontainebleau Sandstone samples before induced saltprecipitation. Sample IDs and pycnometer porosities are listed below each image.Permeabilities range from (a) 1050 mD to (c) 11 mD. Courtesy of Ingrain.


The samples were characterized by measuring their dimensions, mass, porosity,

permeability, and P- and S-wave velocities. They were dried in an 80◦C oven contain-

ing Drierite for a minimum of 48 hours before measurements were taken. Dimensions

were taken at least ten times with digital calipers and averaged. The grain density of

the samples was measured using a helium pycnometer, and porosity φ was calculated

from those measurements. The permeability k was measured with a Klinkenberg-

corrected constant-head nitrogen permeameter.

The acoustic velocities Vp and Vs of the samples were measured using a benchtop

pulse transmission apparatus (Birch, 1960). A Panametrics 5052 PR pulse generator

provided the signal to Panametric transducers (either V103 for 1 MHz P-waves or

V154 for 0.7 MHz S-waves). The signal was recorded using a Tektronix TDS 420A

digital oscilloscope. Samples were unconfined, but an axial stress of approximately

3 psi was applied to facilitate coupling between the transducers and the sample sur-

face. Uncertainty in measured velocities due to instrument precision was estimated

to be 1%.

The aqueous solution used to saturate the samples was prepared by mixing 360 g

NaCl in 1 L distilled water. The solution was stirred on maximum speed for a

minimum of one hour to ensure full dissolution of the salt. This yielded an aqueous

solution that was approximately fully saturated with respect to NaCl, about ten times

the salinity of seawater. This high salt concentration brine was chosen to ensure that

the samples experienced maximal salt precipitation.

The sandstone samples were saturated under vacuum and allowed to equilibrate

in the solution overnight. They were then placed in an 80◦C oven for temperature-

induced evaporative drying. During the first six hours, the samples were rotated

frequently to help ensure even distribution of any precipitated salts. After approxi-

mately 24 hours, the sample mass no longer changed as a function of time; the samples

were deemed dry. They were lightly sanded to remove any surface coating of salt that

could skew permeability readings. All properties were then remeasured.

6.4. RESULTS 135

Table 6.1: Data summary for salt precipitation experiments. Dimensions were measuredonce. Other properties were measured before and after induced salt precipitation.

quantity units GW23 A117 A33

length cm 3.3879 3.8173 3.7532diameter cm 2.5135 2.504 2.4894

sample volume cc 16.81 18.80 18.27

mass (before) g 36.63 44.59 45.22porosity (before) - 0.175 0.102 0.063

permeability (before) mD 1057.2 71.2 11.2pore space volume (before) cc 2.94 1.92 1.15

Vp (before) m/s 4142 4716 4893Vs (before) m/s 2641 2951 3224

mass (after) g 37.23 44.79 45.41porosity (after) - 0.160 0.096 0.057

permeability (after) mD 911.9 46.8 2.2pore space volume (after) cc 2.68 1.81 1.05

Vp (after) m/s 4235 5107 5226Vs (after) m/s 2708 3401 3580

6.4 Results

Mass, porosity, permeability, and acoustic velocities were measured for each sample

before and after salt precipitation. Those measurements are reported in Table 6.1.

In this analysis, a property P has an absolute property change ∆P defined as

∆P = Pfinal − Pinitial , (6.1)

and a relative property change ∆%P calculated as

∆%P =Pfinal − Pinitial

Pinitial

× 100% , (6.2)

reported as a percentage.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510-1

100

101

102

103

104

porosity [fraction]

perm

eabi

lity

[log(

mD

)]

Bourbie and Zinszner (1985)

Gomez (2009)

Before salt precipitation

After salt precipitation

GW23

A117

A33

Figure 6.2: Permeability as a function of porosity for Fontainebleau Sandstone samples.Light gray data are from Bourbie and Zinszner (1985); dark gray data are from Gomez(2009). Colored data are samples measured in this study before (open circles) andafter (closed circles) induced salt precipitation.

6.4.1 Porosity – Permeability Trend

Perhaps the most interesting result of this study is shown in Figure 6.2. It compares

the porosity-permeability relationship of the data before and after salt deposition

with the observed diagenetic trend for clean Fontainebleau Sandstone (Bourbie and

Zinszner, 1985; Gomez, 2009). As expected, both porosity and permeability decrease

as a result of salt precipitation.

The relative changes in porosity and permeability are such that the salt-filled

6.4. RESULTS 137

samples still fall along the natural diagenetic trend. This need not be the case be-

cause the mechanical and chemical processes involved in rock diagenesis can be quite

varied. The Fontainebleau Sandstone is an unusual case, though. Only 50-80 m thick

and having been buried no more than 100 m, these rocks did not undergo burial di-

agenesis. They were silicified recently through hydrological processes occurring near

the water table at the interface between the regional groundwater system and the

local recharge water (Thiry and Marechal, 2001). This cementation through aqueous

silica precipitation is closely related to the salt precipitation conditions in these ex-

periments. It is perhaps not surprising, then, that the porosity-permeability trends

are the same, although this may not be true for sandstones that were consolidated

during burial diagenesis.

6.4.2 Mass, Porosity, Salt Volume, and Permeability Changes

The plots in Figure 6.3 summarize the changes in mass, porosity, and permeability

as functions of either initial porosity or porosity change.

Figure 6.3a shows that the magnitude of the porosity change due to salt deposition

depends on the initial porosity of the rock. The sample with the largest initial porosity

experienced the largest porosity change; the lower initial porosity samples experienced

progressively less porosity reduction. Figure 6.3b recasts these data to show the

relative porosity change as a function of initial porosity. The samples with highest

and lowest initial porosities both experienced approximately 9% porosity loss due to

salt precipitation. The sample with a mid-range initial porosity experienced less than

a 6% porosity loss. The trend, if there is one, dictating the relative porosity change

as a function of initial porosity is not clear with only three data points.

Figures 6.3c and 6.3d show data for the change in mass of the samples after salt

deposition. In Figure 6.3c, samples with higher initial porosity experience greater

mass changes. In Figure 6.3d, greater porosity changes correlate to greater relative

mass changes. This is the expected result for a system where the salt affects the total

porosity and effective porosity by the same amount; that is, a small volume of salt

does not cause a disproportionally sharp decrease in effective porosity.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-0.025

-0.02

-0.015

-0.01

-0.005

0

ϕ initial [fraction]

Δϕ [f

ract

ion]

GW23

A33 A117

(a)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-10

-8

-6

-4

-2

0


Δ%

ϕ [%

]

GW23A33

A117

(b)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


Δm

ass [

g]

GW23

A33 A117

(c)

-0.025 -0.02 -0.015 -0.01 -0.005 00

0.5

1

1.5

2

Δϕ [fraction]

Δ %

mas

s [%

]

GW23

A33

A117

(d)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.05

0.1

0.15

0.2

0.25

0.3

Vsalt (pycnometer) [cc]

Vsa

lt (m

ass d

iffer

ence

) [cc

]

0.35

GW23

A33 A117

(e)

-0.025 -0.02 -0.015 -0.01 -0.005 0-103

-102

-101

-100

Δϕ [fraction]

Δk

[log

(mD

)]

GW23

A33

A117

(f)

Figure 6.3: Property changes resulting from salt deposition. (6.3a) Absolute porositychange versus initial porosity. (6.3b) Relative porosity change versus initial porosity.(6.3c) Absolute mass change versus initial porosity. (6.3d) Relative mass change versusabsolute porosity change. (6.3e) Volume of salt precipitated estimated by mass differ-ence and by pycnometer measurements. (6.3f) Absolute permeability change comparedto absolute porosity change.

6.4. RESULTS 139

Figure 6.3e supports the mass change plots by displaying volume of salt deposited

in the plugs using two methods of estimation. The salt volume plotted on the abscissa

was calculated using the helium pycnometer which is sensitive to effective porosity.

The salt volume on the ordinate is calculated from the sample mass change assuming

a known salt density. All three points lie close to the 1:1 line.

Finally, Figure 6.3f shows the magnitude of permeability change as a function

of porosity change. As expected, larger porosity losses lead to larger permeability

losses. Moreover, samples with lower initial porosity experienced the greatest relative

permeability reduction: the φ = 0.18, 0.10, and 0.06 samples experienced relative

permeability reductions of 14%, 34%, and 81%, respectively.

6.4.3 Elastic Property Changes

The plots in Figure 6.4 summarize the changes in velocity as functions of either initial

porosity or porosity change.

Figure 6.4a shows the P- and S-wave velocities before and after salt deposition as

a function of porosity. Both Vp and Vs increase as a result of salt deposition. The

sample with the highest initial porosity experienced the lowest increase in acoustic

velocities, while the lower initial porosity samples experienced sharper increases in

velocities.

Figure 6.4b, which shows the magnitude of the change in velocity as a function

of porosity change, has three notable features. First, the sample with the greatest

porosity change (and the highest initial porosity) shows the least change in acoustic

velocities; the lower porosity samples show nearly four times the velocity change.

However, for the two low porosity samples, the one with the greater porosity change

experiences the greater velocity changes. Second, in the higher porosity sample, Vp

shows a greater absolute increase than does Vs. In the lower porosity samples, Vs

experiences the greater magnitude change. Third, for any sample, the increases in

Vp and Vs are similar in magnitude. Because the compressional wave velocities are

nearly twice the shear wave velocities for each sample, this means that Vs is relatively

more sensitive to salt deposition than is Vp.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.352

2.5

3

3.5

4

4.5

5

5.5

6

ϕ [fraction]

velo

city

[km

/s]

GW23

A33A117

Vp before salt precipitation

Vp after salt precipitation

Vs before salt precipitation

Vs after salt precipitation

(a)

-0.025 -0.02 -0.015 -0.01 -0.005 00

0.1

0.2

0.3

0.4

0.5

Δϕ [fraction]

Δve

loci

ty [k

m/s

]

GW23

A33

A117Vp change

Vs change

(b)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.351.4

1.45

1.5

1.55

1.6

1.65

1.7

ϕ [fraction]

Vp/

Vs [

--] GW23

A33

A117

before salt precipitation

after salt precipitation

(c)

-0.025 -0.02 -0.015 -0.01 -0.005 0-0.1

-0.08

-0.06

-0.04

-0.02

0

Δϕ [fraction]

ΔV

p/V

s [--

]

GW23

A33

A117

(d)

Figure 6.4: Elastic property changes resulting from salt deposition. (6.4a) Acoustic veloc-ity versus porosity. (6.4b) Absolute velocity change versus absolute porosity change.(6.4c) Vp/Vs ratio versus porosity. (6.4d) Absolute Vp/Vs ratio change versus absoluteporosity change.

These three features combined suggest that there may be different response regimes

for salt deposition. The low porosity data appear to fit a regime where any deposited

salt is near grain contacts, stiffening the rock matrix significantly. The shear waves

are affected more acutely than compressional waves, and the magnitudes of velocity

changes are directly proportional to the change in porosity. The high porosity datum

appears to fit a regime where large volumes of deposited salt do little to affect the

acoustic velocities. Perhaps the increases in matrix moduli are offset by the density

change. Additional experiments in the φ = 0.10− 0.18 range may show complicated

6.4. RESULTS 141

transition behavior if the mode of salt deposition changes between regimes.

Figure 6.4c shows how the Vp/Vs ratio evolves with salt deposition. Because the

relative change in Vs is greater than that of Vp in all three samples, the Vp/Vs ratio

decreases for all three samples. The effect is minimal for the high porosity sample.

Figure 6.4d shows the change in Vp/Vs ratio as a function of porosity change.

Again, two regimes may be represented. The high porosity sample shows very little

change in Vp/Vs ratio despite a large porosity change. The Vp/Vs ratio is more strongly

affected in the two low porosity samples where a larger magnitude porosity change

correlates to a larger Vp/Vs deviation.

The plots contained in Figure 6.5 summarize the changes in elastic properties (cal-

culated from the acoustic velocities) as functions of either initial porosity or porosity

change.

Figures 6.5a and 6.5b show the relationship between Poisson’s ratio and porosity

before and after salt deposition. They show the same features as the Vp/Vs ratio

plots (Figures 6.4c and 6.4d). The Poisson’s ratio is within the expected range for all

samples both before and after salt deposition.

Figure 6.5c shows the bulk modulus K (circles) and shear modulus µ (squares) for

each sample before and after salt deposition. Both bulk and shear moduli increase

after salt deposition for all three samples. The bulk modulus is only slightly increased

(a 6% change or less). The high porosity sample shows only a slight increase in shear

modulus (7%) as well, but the two lower porosity samples show large increases in

shear modulus (24% and 33%).

Figure 6.5b displays the change in moduli with the change in porosity. The bulk

modulus changes are only 1 GPa or less, while the shear modulus changes range from

1 GPa to 7 GPa. The low porosity samples experience significant increases in shear

moduli with minimal increases in bulk moduli.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.1

0.2

0.3

0.4

0.5

ϕ [fraction]

ν [-

-]

GW23

A33

A117

before salt precipitation

after salt precipitation

(a)

-0.025 -0.02 -0.015 -0.01 -0.005 0-0.1

-0.08

-0.06

-0.04

-0.02

0

Δϕ [fraction]

Δν [-

-]

GW23

A33

A117

(b)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3515

20

25

30

35

ϕ [fraction]

mod

uli [

GPa

]

GW23

A33

A117

Κ before salt precipitation

Κ after salt precipitation

μ before salt precipitation

μ after salt precipitation

(c)

-0.025 -0.02 -0.015 -0.01 -0.005 00

1

2

3

4

5

6

7

8

Δϕ [fraction]

Δm

odul

i [G

Pa]

GW23

A33

A117

Κ change

μ change

(d)

Figure 6.5: Elastic parameter changes resulting from salt deposition. (6.5a) Poisson’sratio versus porosity. (6.5b) Absolute Poisson’s ratio change versus absolute porositychange. (6.5c) Bulk and shear moduli versus porosity. (6.5d) Absolute modulus changeversus absolute porosity change.

6.5 Conclusions

Three Fontainebleau Sandstone samples were injected with a saturated brine and

dried to induce salt precipitation whose effects could be measured reliably using exist-

ing laboratory equipment. The data shown here confirm that this technique produces

enough salt within the samples to be measured both in mass and porosity changes.

Furthermore, permeability is noticeably altered as are compressional and shear wave

velocities. Additional experiments on Fontainebleau Sandstone samples, including

6.5. CONCLUSIONS 143

those using a brine comparable in salinity to seawater, should yield useful data.

The observed porosity-permeability trend due to salt deposition follows the natural

diagenetic trend for Fontainebleau Sandstone, possibly because the natural cementa-

tion of this sandstone occurred by quartz overgrowth in an active hydrological system

and not during burial diagenesis. It should not be expected that anthropogenic salt

deposition mimics diagenesis in all sandstones.

The limited data here indicate that the samples may span two separate regimes

for salt precipitation. Lower porosity samples are strongly affected by small amounts

of salt. The magnitude of the shear modulus increase suggests the salt predominantly

stiffens grain contacts. Higher porosity samples do not experience the large increases

in shear modulus that their lower porosity counterparts do, despite significantly more

salt deposition. This suggests that less salt is involved in stiffening grain contacts;

the rest may be crystals free in the pore space or coating grain walls. Comparing

moduli changes with SEM imaging will likely elucidate this problem.

Acknowledgements

Thanks to Tiziana Vanorio for her guidance in the rock physics laboratory.


REFERENCES 145

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