A Study of Imbibition Mechanisms in theNaturally Fractured Spraberry Trend Area

by

YANFIDRA

THESIS

Submitted in Partial Fulfillment

of the Requirements for Degree of

Master of Science in Petroleum Engineering

New Mexico Institute of Mining and TechnologySocorro, New Mexico

November, 1998

This thesis is accepted on behalfof thefaculty

ofthe institute bythe following committee:

Advisor

Ncv£M6I?^Date

ABSTRACT

The importance of characterizing the imbibition mechanism foranalysis of reservoir performance during waterflooding in the naturallyfractured Spraberry Trend Area has been studied. Analyzing reservoirperformance during waterflooding is obviously useful before other EORmethods such as CO2 injection are applied. When waterflooding is performedin this type of reservoir, the intent is to fill the fractiu'es with water toinitiate spontaneous counter-current imbibition. Using the action of capillaryforces, oil from the interior of matrix blocks is displaced to surroundingfractures. Once the oil is in the fractures, the water displaces the oil to theproducing well by viscous forces, depending on the volume of water injected.Thus, the imbibition mechanism plays a very important role iii recovering ofoil from this reservoir.

The purposes of this study are (i) to investigate the wettability of lowpermeability Spraberry reservoir rock, oil and brine that affect recoverymechanisms in the Spraberry Trend Area reservoir; Hi) to upscale thelaboratory imbibition results to field-scale dimensions, (Hi) to predict the oilrecovery from the imbibition mechanisms, and (iv) to determine the criticalwater injection rate at laboratory and field dimensions.

Two types of imbibition experiments were performed, i.e., the staticimbibition test and the d3aiamic imbibition test. The static imbibitionexperiments followed by waterflooding were carried out at ambient, mixedand reservoir conditions to investigate the rock wettability. Theseexperiments demonstrate that Spraberry rock and oil is a very weaMy water-wet system. The static imbibition data were also upscaled to field dimensionsin order to determine the contribution of spontaneous imbibition mechanismto oil recovery and to investigate degree ofheterogeneity in the matrix andnatural fracture systems. Dynamic imbibition experiments were performedusing artificially fractured cores at reservoir conditions to illustrate theactual waterflooding process in naturally fractured reservoirs. The results ofthese experiments were used to generate capillary pressure and to determinethe critical injection rate. Knowledge of the injection rate is helpful to solvethe problem of early water breakthrough, one of common problems ofwaterflooding in naturally fractured reservoirs.

With these two sets ofexperiments, understanding static and dynamicimbibition mechanisms in naturally fractured, low permeability matrix isuseful as a guideline for field development. The results serve as a tool toupscale and predict oil recovery from the imbibition mechanism in naturallyfract\ired reservoirs.

-1'

ACKNOWLEDGEMENT

I would like to express my deep gratitude to my research adviser, Dr.

David S. Schechter, Head of the Integrated Naturally Fractured Reservoir

Study Group, Petroleimi Recovery Research Center (PRRC), for all of his

invaluable gmdance, suggestions, patience, and encouragement throughoutthe course of this study. I also express my appreciation to my academic

advisor. Dr. Robert L. Lee, and my other thesis committee members. Dr. H.Y.

Chen and Dr. Donald Weinkauf, for all of their valuable comments and

suggestions.

I wish to express my gratitude to the Petroleum Recovery Research

Center (PRRC) for the financial support through research assistantship

grant. Appreciation is also extended to the Department of Petroleum and

Chemical Engineering ofthe New Mexico Institute ofMining £ind Technology

for the partial financial support provided during the first semester of the

study.

I also wish to thank Erwin Putra, Dr. Boyun Guo, Hujun Li, Cletus

Scharle, Mary Downes, Bob Svec and Mary Watson for their assistance and

helpful discussions during this study, Ucok Siagian and Liz Bustamante for

their help in correction of the thesis manuscript, Drs. Pudji Permadi, Doddy

Abdassah and Leksono Mucharam for their recommendation to go to this

school, and many thanks are also extended to the entire staff of the PRRC for

their kindness and assistance.

Above all, I dedicate this work to my wife, Ribelti, my son, Febrian, my

parents and my other family members for their love, understanding, moral

support and encouragement during this study.

- II •

TABLE OF CONTENTS

ABSTRACT i

ACKNOWLEDGMENT H

TABLE OF CONTENTS Hi

LIST OF TABLES vi

LIST OF FIGURES vii

CHAPTER 1 INTODUCTION 1

CHAPTER 2 LITERATURES REVIEW 6

2.1 Wettability of Rocks 6

2.2 Imbibition 8

2.2.1 Static Imbibition Experiments 13

2.2.2 D3mamic Imbibition Experiments 14

2.2.3 Effect of Temperature and Pressure on SpontaneousImbibition 16

2.2.4 Scaling of Imbibition Data 18

CHAPTER 3 EXPERIMENTAL DESCRIPTION 20

3.1 Materials 20

3.1.1 Rock Preparation and Properties 20

3.1.2 Brine Compositions 24

3.1.3 Oil Sample 24

3.2 Experimental Procedures 33

3.2.1 Cleaning Process 33

• Hi-

3.2.2 Saturating the Core with Brine 34

3.2.3 Establishing Initial Water Saturation 34

3.2.4 Aging Procedures 35

3.2.5 Spontaneous Imbibition Tests 36

3.2.6 Brine Displacement 45

3.2.7 D3aiamic Imbibition Tests in ArtificiallyFractured System 46

CHAPTER 4 PRESENTATION AND DISCUSSION OF EXPERIMENTALRESUTLS 51

4.1 Static Imbibition 52

4.1.1 Experiment using Berea Cores 52

4.1.1.1 Effect ofTemperature 52

4.1.1.2 Effect ofpressure 60

4.1.1.3 Effect ofInitial Water Saturation 67

4.1.1.4 Effect ofRock Permeability 72

4.1.2 Experiment using Reservoir Cores 74

4.1.2.1 Effect ofAging Time 74

4.1.2.2 Effect of Temperature 79

4.1.2.3 Wettability Index 85

4.1.2.4 Heterogeneity in Rock Properties 88

4.1.2.5 Numerical Analysis ofSpontaneousImbibition 92

4.2 Dynamic Imbibition 96

4.2.1 Experiment using Berea Cores 98

4.2.2 Experiment using Reservoir Cores 104

4.2.3 Critical Injection Rate 112

•IV '

CHAPTER 5 RESERVOIR PERFORMANCE ANALYSIS 115

5.1 Scaling of Imbibition Data 115

5.1.1 Imbibition Recovery Model 116

5.1.2 Production Decline Model 120

5.2 Analysis of Recovery Mechanisms 122

5.2.1 Recovery Based on Scaling of Imbibition Data 122

5.2.2 Recovery Field Performance 132

5.2.3 Sensitivity Study of Imbibition Model 138

5.3 Upscaling of Djmamic Imbibition Data 147

5.3.1 Critical Fracture Capillary Number 147

CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 153

REFERENCES 158

APPENDIXES

- V •

LIST OF TABLES

Table 2-1 : Summary of experimental studies of water imbibition 11

Table 3-la : The physical properties of Berea core samples for static imbibitionexperiments 22

Table 3-lb : The physical properties of Berea core samples for d3niamicimbibition experiments 22

Table 3-2a : The physical properties of the reservoir core samples for staticimbibition experiments 23

Table 3-2b : The physical properties of the reservoir core samples for dynamicimbibition experiments 23

Table 3-3 : Synthetic Reservoir Brine 25

Table 3-4 : Properties of Spaberry Crude Oil 25

Table 3-5 : Spraberry Crude Oil Composition 25

Table 5-1 : The average absolute permeability and porosity for both sand units(lU and 5U) in Spraberry Trend Area Reservoir 131

Table 5-2 : Evaluation ofWater Saturation and Current Oil Saturation 134

Table 5-3 : Evaluation of Displacement Efficiency and Volumetric Efficiency onbasis of Cores from Different Wells 138

Table 5-4. : Reservoir parameters as input data 140

Table 5-5 : Fracture Spacing 140

Table 5-6 : Upscaling of dynamic imbibition experiments to determine criticalinjection rate 150

Table 5-7 : Estimated critical injection rates for wells in E.T. O'Daniel pilotarea 151

' VI •

LIST OF FIGURES

. Scliema.tic process ofimbibition flooding in Spraberry Trend Area3

Fig. 3-1 : Variation in viscosity ofsynthetic Spraberry brine with temperature26

Fig. 3-2 : Variation in density ofsynthetic Spraberry brine with temperature27

Fig. 3-3 : Variation in viscosity of Spraberry oil with temperature 28

Fig. 3-4 : Variation in densityof Spraberry oil with temperature 29

Fig. 3-5 : Interfacial tension ofSpraberry oil —brineat elevated pressure 30

Fig. 3-6 : Interfacial tension ofSpraberry oil - brineat elevated temperature31

Fig. 3-7 : Thermal expansion of Spraberry oil 32

Fig. 3-8 : A good correlation was obtained by making comparison ofcorepermeabilities determined &om Minipermeameter and Hassler-sleeve measurements 39

Fig. 3-9 : Spontaneous imbibition glass 40

Fig. 3-10 : High pressure and high temperature of Spontaneous imbibitionapparatus

Fig. 3-11 : Reproducibility of spontaneous imbibition for Crude Oil-Brine andBerea Rocks using glass imbibition cell at reservoir temperaturewith no initial water saturation 42

Fig. 3-12 : Reproducibility of spontaneous imbibition for Crude Oil-Brine andSpraberry Rocks using glass imbibition cell at reservoir temperature

43

Fig. 3-13 : Reproducibility of spontaneous imbibition for Crude Oil-Brine andBerea using glass imbibition cell at reservoir temperature andpressure 44

- Vll '

Fig. 3-14 : Flooding Apparatus

Fig. 3-15 : Experimental apparatus for dynamic imbibition test 49

Fig. 3-16 : Reproducibility of the d3aiamic imbibition flooding result 50

Fig.4-1 : Effect of temperature on the imbibition mechanism for a Spraberryoil, brine, and Berea sandstone system 55

Fig. 4-2 : Effectof temperature on the imbibitionmechanism in terms ofdimensionless time 57

Fig.4-3 : Effect ofchange in temperature on oil recovery by imbibition forcores without an initial water saturation 58

Fig. 4-4 : Effect ofchange in temperatureonoil recovery byimbibition forcores with 42% initial water saturation 59

Fig.4-5 : Effect of confining pressure on imbibition mechanism for cores with35% average initial water saturation. Reference curve is from staticimbibition performed at reservoir condition using refine oil for avery strongly water-wet system 63

Fig.4-6 : Effect of confining pressiire on imbibition mechanism for cores with25% average initial water saturation. Reference curve is from staticimbibition performedat reservoir conditionusing refine oil for avery strongly water-wet system 64

Fig.4-7 : Effect of confining pressure on imbibition mechanism for coreswithout initial water saturation. Reference curve is from staticimbibition performed at reservoir condition using refine oil for avery strongly water-wet system 65

Fig.4-8 : Effect ofpresent ofinitial water saturation for cores were agedforseven days and the imbibition experiments were performed at 138oFand 1000 psi confining pressure. Reference curve is from staticimbibition performed at reservoir condition using refine oil for avery strongly water-wet system 69

Fig.4-9 : Effect ofpresent of initial water saturation for coreswere aged forseven days and the imbibition experiments were performed at 138oFand atmospheric pressure. Reference curve is from static imbibitionperformed at reservoir condition using refine oil for a very stronglywater-wet system 70

- Vlll -

Fig.4-10 : Effect of present of initial water saturation for cores were withoutaging in oil and the imbibition experiments were performed at138oF and atmospheric pressure. Reference curve is from staticimbibition performed at reservoir condition using refine oil for aveiy strongly water-wet system 71

Fig.4-11 : Effect of rock permeability on the imbibition mechanism 73

Fig. 4-12 : Schematic of experimental program using low permeabilitySpraberry cores 75

Fig. 4-13 : Complete oil recovery curves obtained from imbibition experimentperformed at reservoir and room temperature 76

Fig. 4-14 : Effect of aging time on recovery by imbibition 77

Fig. 4-15 : Total recovery (recovery from imbibition and recovery from brinedisplacement) versus aging time to exclude the effects of aging timeon the recovery mechanism 78

Fig. 4-16 ; Effect of temperature in imbibition tests 82

Fig. 4-17 : Effect of change in temperature on oil recovery by imbibition due tochange in mobility of fluid, expansion of oil and reduce in interfacialtension 83

Fig. 4-18 : Effect of aging time on total recovery at elevated temperatures . 84

Fig. 4-19 : Wettability index to water versus aging time for the differentexperiment temperatures 87

Fig. 4-20 : Effect of initial water saturation on recovery by imbibition 90

Fig. 4-21 : Effect of initial water saturation on total recovery 90

Fig. 4-22 : Effect of permeability on recovery by imbibition 91

Fig. 4-23 : Effect of permeability on total recovery 91

Fig.4-24 : Matching between spontaneous imbibition experiment results andnumericsd solution 93

Fig. 4-25 : Water distribution at different imbibition time from x-plane view94

Fig.4-26 : Imbibition capillary pressure obtained from matching ofspontaneous imbibition data 95

- ix •

Fig.4-27 : Schematic representation of the displacement process in fracturedporous media

Fig.4-28 : Results of dynamic imbibition experiment for Spraberry oil, brineand fractured Berea cores 100

Fig.4-29 : Effect of the injection rate on oil recovery versus total fluid producedfor Spraberry oil, brine and fractured Berea cores 101

Fig.4-30 : Water-cut produced during the dynamic imbibition experiment forSpraberry oil, brine and fractured Berea core 102

Fig. 4-31 : The effect of initial water saturation on the dynamic imbibitionprocess at the same injection rate (4 cc/hr) 103

Fig.4-32 : Comparison of recovery for dynamic imbibition experiments usingfractured and unfractured Spraberry core 105

Fig.4-33 : Water-cut during the djmamic imbibition experiment for Sprabenyfractiu'ed and unfractured cores during the dynamic imbibitionprocess 106

Fig.4-34a : Match of oil recovery and water produced for Berea Sandstone .. 108

Fig. 4-34b : Match of oil recovery and water produced for Spraberry reservoirrocks 109

Fig.4-35 : Capillary pressure curves obtained as a result of matchingexperimental data 110

Fig. 4-36 : Effective capillary pressure obtained from simulation, compared tocapillary pressure obtained in the static equilibriimi experimentmethod Ill

Fig. 4-37 : Injection rate versus oil-cut curve for Berea and Spraberry cores 114

Fig.5-1 : Oil recovery curves performed at reservoir condition plotted usingdimensionless variables and compared with oil recoveries curvesperformed at ambient condition 118

Fig.5-2 : Averaging ofimbibitioncurves using Aranofsky equation to fit theimbibition experimental data by adjusting empirical constant X 121

Fig.5-3 : Porosity and absolute permeability ofUpper Spraberry lU Unitversus depth (data taken from Well Shackleford 1-38A) 124

- X -

Fig.5-4 : Porosity and absolute permeability of Upper SpraberrySU Unitversus depth (data taken from Well E.T.O'Daniel 37) 125

Fig.5-5 : Calculated imbibition oil recoveryfor 5 years waterflood from UpperSpraberry lU formation based on scaling of experimental data andfracture spacing of 3.79 feet 126

Fig.5-6 : Calculated imbibition oil recovery for 5 years waterflood from UpperSpraberry 5U formation based on scaling of experimental data andfracture spacing of 3.79 feet 127

Fig.5-7 : History of waterflood recovery profiles from Upper Spraberry lUformation based on scaling of experimental data and fracturespacing of 3.79 feet 128

Fig.5-8 : History of waterflood recovery profiles from Upper Spraberry 5Uformation based on scaling of experimental data and fracturespacing of 3.79 feet 129

Fig.5-9 : Calculated imbibition oil recovery for 40 years waterflood fromSpraberry lU and 5U formations based on scaling of imbibition dataand using the same fracture spacing of 3.79 feet for both sand units

131

Fig.5-10 : Initial water saturation in Spraberry reservoir 134

Fig. 5-11 : Evaluated water saturations after wells have been waterflooded inSpraberry reservoir (data from Guo, 1995) 135

Fig. 5-12 : Effect ofmatrix permeability on imbibition recovery 143

Fig. 5-13 : Effect of matrix permeability on calculation of production rates . 144

Fig. 5-14 : Effect of fracture spacing on imbibition waterflooding 145

Fig. 5-15 : Effect of matrix permeability and fracture spacing to decline ratesconstant 146

Fig. 5-16 : Fracture capillary number versus oil-cut for Berea and Spraberrycores 149

- XI -

Chapter 1

Introduction

In the naturally fractured Spraberry Trend Area of West Texas, the

reservoirs behave considerably differently from conventional reservoirs, due to

the existence of two interconnecting paths i.e. fractures and matrix with

completely different properties. The fractures constitute a continuous path for

fluid flow in the reservoir, while the low permeability matrix blocks are

discontinuous and provide the main storage for oil and gas.

The Spraberry Trend Area originally contained about 10 Bbbls lOIP, of

which less than 10% has been recovered by primary production under solution

gas drive (Elkins, 1953; Schechter, 1996(a) & (b)). The concept of displacement

of the oil from the matrix by capillary imbibition led to implementation of

large-scale waterflooding in the Spraberry Trend. However, after more than 40

years of waterflooding, the current oil recovery in most areas is still less than

15% (Dimon, 1991; Baker, 1996(b), Guo, et al 1998).

-1-

-2-

This study addresses the importance of characterizing the imbibition

mechanism for analysis ofreservoir performance during waterflooding in the

naturally fractured Spraberry Trend Area. Analyzing reservoir performance

during waterflooding is obviously useful before other EOR methods such as

CO2 injection are applied. When waterflooding is performed in this type of

reservoir, the intent is to fill the fractures with water to initiate spontaneous

counter-current imbibition. Using the action of capillary forces, oil from the

interior of matrix blocks is displaced to surroimding fractures. Once the oil is

in the fractures, the water displaces the oil to the producing well by viscous

forces, depending on the volimie of water injected, as illustrated in Fig. 1-2.

Therefore, the imbibition mechanism plays a very important role in recovering

of oil from this reservoir.

Numerous laboratory studies have been conducted regarding this

subject, as can be seen in Chapter 2. However, most of those experiments were

performed using certain types of oil and brine with homogeneous high

permeability rocks (Berea sandstone) as the porous medium, and mostly

conducted at ambient conditions. Thus, the imbibition mechanism based on

those experiments cannot be upscaled to reservoir dimensions since high

permeability rock at ambient conditions may not be representative of low

permeability matrix at reservoir pressure and temperature.

Counter-current exchangemechanism

Invaded Zone

Matrix

Matrix

Fracture

Oil + Water

^ Fracture

Fig.1-1 : Schematic process of imbibition flooding in Spraberry TrendArea.

The purposes of this study are (i) to investigate the interaction between

low permeability Spraberry reservoir rock, oil and brine that affect recovery

mechanisms in the Spraberry Trend Area reservoir; (ii) to upscale the

laboratory imbibition results to field-scale dimensions, (Hi) to predict the oil

recovery from the imbibition mechanisms, and (iv) to determine the critical

water injection rate at laboratory and field dimensions.

-4-

In order to achieve these objectives, two types ofimbibition experiments

were performed, i.e., the static imbibition test and the dynamic imbibition test.

The static imbibition experiment were carried out at ambient and reservoir

conditions to determine the rock wettability. These data were also upscaled to

field dimensions in order to determine the contribution of spontaneous

imbibition mechanism to oil recovery. While, dynamic imbibition experiments

were performed using artificially firactured cores at reservoir conditions to

illustrate the actual waterflooding process in naturally fractured reservoirs.

The results of these experiments were used to generate capillaiy pressure and

to determine the critical injection rate. Quantification of capillary pressure is

vital in imderstanding the imbibition process, where this capillary pressure

can also be used to indicate rock wettability. Knowledge of the injection rate is

helpful to solve the problem of early water breakthrough, one of common

problems ofwaterflooding in natiirally firactured reservoirs.

Chapter 3 describes materials and experimental procedures for the

static and dynamic imbibition experiments conducted in this study. Two types

of porous media were used; Berea sandstone and Sprabeny reservoir rocks.

The Berea sandstone was used to verify the effects of temperature, pressure,

and initial water saturation on the behavior of static and d3aiamic imbibition

mechanisms using Sprabeny oil and brine in a porous medium. The results

show that pressure has less effect on recovery. Thus, the reservoir cores taken

from low-permeability Sprabeny reservoir were used in order to investigate

-5-

static and dynamic imbibition at reservoir temperature and atmospheric

pressure. With these two experiments, understanding static and dynamic

imbibition mechanisms in naturally fractured, low permeability matrix is

useful as a guideline for field development. The results serve as a tool to

upscale and predict the oil recovery from the imbibition mechanism in

naturally fractured reservoirs.

The experimental results of static and d3niamic imbibitions are

presented and discussed in Chapter 4. The rates of imbibition and recovery

mechanisms from both types of experiments were analyzed. The experimental

results were also simulated using a numerical analysis to determine the

matrix capillary pressure curves. Finally, the scaling of experimental results

from static and dynamic imbibition experiments were discussed in Chapter 5

to determine contribution of capillary imbibition mechanisms and critical

water injection rates during full-scale waterflooding in a naturally fractured

reservoir.

The final chapter of this thesis (Chapter 6) concludes the thesis and

proposes recommendation for future studies regarding this subject.

Chapter 2

Literature Review

In this chapter a literature review regarding wettabihty and imbibition

is presented, and the efforts to perform the experiments under representative

conditions are described.

2.1 Wettability of Rocks

The term of wettability is commonly used to describe the ability of a

fluid to wet a solid surface in the presence of a second fluid. Amott (1959)

defined wettability as the relative preference of a particular surface to be

covered by one of the fluids under consideration. The wettability of reservoir

rock is a critical factor in determining the displacement effectiveness and

ultimate oil recovery by driving fluids, such as water in waterflooding.

Quantitatively, the wettability index can be determined after

establishing the initial water saturation using Amott test method, which

-6-

-7-

consists of two parts. The first part is spontaneous imbibition in water and

the second part is followed by forced displacement by water. The amount

fluid expelled by spontaneous displacement is recorded. Numerical value of

this is called index for water, which expressed as:

(2.1)^iw ^ ^dw

where Viw is oil produced from imbibition process and Vdw is oil produced from

displacement process.

Wettability in porous media is generally classified as either

homogeneous or heterogeneous. For the homogeneous case the entire rock

surface has a uniform molecular affinity for either water or oil. Conversely,

heterogeneous wettability indicates distinct surface regions that exhibit

different affinities for oil or water. Three classifications of homogeneous

wetability exist; strongly water-wet, strongly-oil wet, and intermediate-wet.

Two t3rpes of homogeneous wettability are generally recognized. Mixed

wettability refers to distinct and separates water-wet and oil wet surfaces,

which coexist a porous medium. Speckled or spotted wettability refers to

continuous water wet surface enclosing regions of discontinuous oil-wet

surfaces or vice-versa.

Before 1940's, it was widely believed that most oil reservoirs were

strongly water wet because the reservoirs were deposited in a water

-8-

enviromnent and buried for a very long geologic time before oil migrated and

occupied part of the rock pore spaces. This idea was disputed in the early

1940's because some crude oil samples showed an ability to wet sand grains

(Bartell and Miller, 1928) or silica (Benner and Bartell, 1941). Later, the

terms intermediate (Marsden and Nikias, 1962), fractional (Fatt and Klikoff,

1959; Iwankow, 1960) or heterogeneous (Browns and Fatt, 1956), mixed

wettability (Salathiel, 1973) and speckled (Morrow et al., 1986; Cuiec, 1991))

were introduced to indicate types of wetting conditions which are not simply

either strongly water wet or oil wet. In general, quantification of wettability

depends upon the methods adopted in the evaluation. The most common

methods used today are contact angle (Treiber et. al., 1972; Morrow, 1976),

spontaneous imbibition and forced displacements (Amott, 1959; Boneau and

Clampitt, 1977; Cuiec, 1984) and capillary pressure curves (Donaldson et al.,

1969).

2.2 Imbibition

The transfer of fluids by imbibition mechanism can play a very

important role in the oil recovery from most reservoirs during waterflooding.

In naturally fractured reservoirs, the imbibition process may be the dominant

recovery mechanism during water injection. Therefore, understanding the

imbibition process and the key parameters that control the imbibition process

are crucial. The imbibition mechanism can be characterized by its rate and by

-9-

the total amount of fluid displaced, which depends on the wettability. The

imbibition mechanisms have been studied extensively both theoretically and

experimentally in the past. Nimierous publications dealing with these

subjects have appeared in the literature.

In Table 2-1, a selection of published work on imbibition is presented

together with a list of the main parameters that was investigated. As

presented in this table, most of the early experimental studies of imbibition

were made with strongly water-wet system and constant fluid properties [1-

lll*>. Several investigators have introduced changes in fluid properties, rock

properties and boundary conditions [12-20,25-27]. Other experimental

parameters such as exposure of rock to oil, aging temperature, temperature

effect on imbibition mechanism, handling of the crude oil, and all of which

affect wetting properties were taken into account [22,23,26]. A detailed study of

oil recovery from crude oil/brine/rock systems including measurements of

spontaneous imbibition rates has been investigated [19,24]. Lately, the

imbibition studies were focused on fluid exchange mechanism in fractured

porous medium [21,25,27] and upscaling of laboratory to field dimensions [28].

*) Listing number on Table 2-1

-10-

Detennination ofthe imbibition mechanism provides knowledge about

capillary forces and displacement behavior that related to changes in wetting

behavior of system. In laboratory, the imbibition experiments can be

performed under two conditions, which are static and/or dynamic conditions.

In static imbibition experiments, capillary forces only govern the drive

mechanism. While in d3aiamic imbibition process, both capillary and viscous

forces involve during displacement of fluid mechanisms.

-11-

Table 2-1: Summary ofExperimental Studies ofWater Imbibition

No. Author Porous

MediumGeometry Partly open (S)

All open (0)

Forces Type ofFluids

Fluidproperties

S.,

(%)

Wettebility ExperimentalConditions

1. Brownscombe& Dyes(1952)

Spraberrysandstone

CylindersPlates

S + 0 Imbibition WaterX-rayopaque

phenyl

Constant 5.6-

63.3

Stronglywater-wet

Ambient

2. Graham&

Richardson(1959)

Fused quartz Triangular S ImbibitionPressure

Distilledwater

Constant 24 Stronglywater-wet

Ambient

3. Handy (1960) SandstoneLimestone

Cylinders 0 ImbibitionGravity

WaterAir

Constant 0 Stronglywater-wet

Elevated P&T

4. Mettax &Kyle (1962)

AlundumSandstone

CylindersCubes

S-t-0 ImbibitionGravity

Water(^1

Constant 0 Variable Ambient

S. Parsons &Chaney(1966)

Dolomite Cubes S + 0 ImbibitionGravi^

Distilledwater

White

Constant 0 Stronglywater-wet

Ambient

6. Kyte(1970) Sandstone Cylinders 0 ImbibitionGravity

WaterOil

Constant -0 SlighUy Ambient

7. IfHy, et al.(1972)

Siltstone Cylinders S*0 ImbibitionGravity

WaterNapthetnicoil

Constant 11-43 Variable Ambient

8. KleppeAMorse

(1974)

Berea

sandstoneCylinders 0 Imbibition

GravityWater

KeroseneConstant -0 Strongly

water-wet

AmbientElevated

9. Kazemi &

Menu(1977)

Berea

sandstoneCylindersBlocks

s ImbibitionGravity

WaterDiesel

Constant 0 &43 Stronglywater-wet

AmbientElevated

10. Lefebvre duPrey(1978)

Fontaine-bleau

sandstone

CylindersBlocks

s>0 ImbibitionGravityPressure

DistiUedwater

5(V50BayolParaffin/

Constant -0 Stronglywater-wet

AmbientElevated

pressure

11. Torsaeter(1984)

Chaik Cylinders 0 ImbibitionGravity

WaterCrude oil

Constant 2-56 WettabilityindecesfromOto 1

Ambient

12. TorsaeterASilseth(1986)

SandstoneChalk

BlocksCylindersPrism

IneKular

S>0 ImbibitionGravity

WaterPnrnflRn

Variables 0-32 Stronglywater-wet

Ambient

13. Hamon &Vidal(1986)

AlundumSilicate

Sandstone

Cylinders Si-O ImbibitionGravity

Water

Refined oilVariables 8-35 Strongly

water-wet

Ambient

14. Bourbiaux &Kalaydjian(1988)

Sandstone Blocks s ImbibitionGravity

WaterSoltiol 130

Variables 40 Stronglywater-wet

Ambient(68*F and atm

15. Cuiec, et al(1990)

Chalk Blocks

Cylinderss Imbibition

GravityWaterPara£Rn

Variables -3031-48

Stronglywater-wet

Ambient

16. Keijzef&De Vries(1990)

Bereasandstone

Cylinders s ImbibitionGravity

WaterSurfactantn-

hexadeeanen-dodecane

Variables 24 Ambient

17. Ghedan&

Poettmann(1990)

Berea

sandstoneCylinders s + 0 Imbibition

GravityPressure

VariousbrinesPolymersVarious oil

Variables•

Stronglywater-wet

Elevatedpressure

-12-

Table 2.1 (continued)

18. Schechter,et al. (1991)

LimestoneSandstone

Cylinders 0 ImbibitionGravity

Brine

isoctane

isopropanol

Variables 0 Ambient

19. JadhiinandanSt Morrow

U991)

Berea

landstoneCylinders 0 Imbibition

GravityBrineRefine oil

Variables 21-40 Neutral toStrongly

Ambient

20. Peres, et al.(1992)

Sandstonelimestone

Cylinders S ImbibitionGravity

Carbonatewater

Kerosene

Variables Variab

leAmbient

21. Babadagli &Ershaghi(1992)

Berea

sandstoneCylinders S Imbibition

PressureBrine

KeroseneConstant 0 Strongly

water-wet

Ambient

22. Zhou &Morrow

(1993)

Berea

sandstoneCyUnders 0 Imbibition

GravityBrineCrude oil

Constant -25 Stronglywater-wet

Aging atelevatedtempertureImbibition at

23. Babadagli(1994)

BereaSandstone

CylindersGlass beadmodels

S ImbibitionPressure

BrineKerosene

Constant 0 Stronglywater-wet

Ambient

24. Morrow, etal.(1994)

Berea

sandstoneCylinders 0 Imbibition

GravityBrine

Refined oUKerosene

Constant -25 Neutral toStronglywater-wet

Ambient

25. Babadagli(1996)

Berea

sandstoneCylinders 0 Imbibition Brine

KeroseneVariable 0 Strongly

water-wet

Elevatedtemperature

26. Tang,etal.(1996)

Berea

sandstoneCylinders 0 Imbibition

GravityBrine

3 types ofVariable 21-25 Strongly

water-wet

Elevatedtemperature

27. Babadagli(1997)

Bereasandstone

Cylinders S^OImbibitionGravity

Brine

Kerosene Variable 0 Strongly Elevated

28. Guo St

Schechter(1998)

Sprabenysandstone

Cylinder 0 ImbibitionGravity

BrineCrude oil

Constant 30-40 WeaUywater-wet

Ambient

-13-

2.2.1 Static Imbibition Experiments

Spontaneous imbibition or static imbibition is defined as the

displacement of non-wetting flmd by wetting fluid through the action of

capillary forces alone. The process occurs when a porous medium saturated

with non-wetting fluid is brought into contact with wetting fluid. The

magnitude of the capillary force is proportional to the geometry and pore

structure of the porous medium, the interfacial tension between the two

fluids and the cosine of the contact angle.

In term of parameters that affect static imbibition process, several

studies have been performed by different authors and can be classified as

follows:

- size of the rocks sample (Mattax and Kjrte, 1962; Torsaeter, 1985)

- rock characteristics such as porosity, permeability, and local

variations of these parameters (Mattax and Kjrte, 1962; Torsaeter,

1984; Thomas 1984; Hemion and Vidal, 1988)

- low permeability of Chsdk reservoirs (Torsaeter, 1984; Bourbiaux

and Kalaydjian, 1990; Cuiec et al., 1990)

- boundary conditions (Ififly et al., 1972; Hamon and Vidal, 1988;

Bourbiaux and Kalaydjian, 1990)

- wettability (Thomas, 1984; Hjelmeland, 1986; Zhou et al., 1995)

-14-

- fluid properties such as viscosity, density, interfacial tension and

chemical composition of water (Iffly et al., 1972; Cuiec et al., 1990;

Keijzer and De Vries, 1990; Ghedan and Poetmann, 1990;

Schechter et al., 1991; Babadagli, 1995; Al-Lawati and Saleh, 1996)

- aging time and temperature (Zhou et al., 1993)

- initial water saturations (Jadhunandan and Morrow, 1991; Zhou et

al., 1995)

2.2.2 Dynamic Imbibition Experiments

In the fractured porous media, viscous displacement occurs in the

fracture network due to its higher conductivity compared to the matrix, while

an exchange of fluids occurs between these two media. This means that

imbibition process occurs due to continuous flow in fracture.

Brownscombe and Dyesf^l (1952) introduced a concept of the process,

which is called dynamic imbibition, for the Spraberry Trend Area. The

process was visualized in terms of a single fracture in which water is injected

at one end and production is collected at the other end. As the injected water

flows toward the producing end, it imbibes into the matrix and releases the

oil. If the rate of natural imbibition into the matrix is greater than the

injection rate, all of the water will soak into the matrix and only oil will reach

the producing end of the fractures. Any water injected above the rate of

natural imbibition will increase the water oil ratio. The water oil ratio is a

-15-

function of both injection rate and imbibition rate. However, to verify this

concept, instead of dynamic conditions, they conducted a laboratory

imbibition experiment under static conditions on the rate of natural

imbibition for very low matrix permeability, by assuming that the matrix

rock was water wet.

Graham and Richardson^21 (1960) presented the results of theoretical

and experimental studies of dynamic water imbibition. They investigated the

effect of fracture flow rate on the matrix imbibition. They found that

imbibition is rate sensitive and proportional to the square root of matrix

permeability, interfacial tension, contact angle, and viscosity ratio. At high

rates, it is necessary to inject more water to produce the same amount of oil.

Kleppe and Morse^®! (1974) numerically studied the effect of injection rate on

the recovery of oil and experimentally verified the results. Similar study was

performed by Kazemi and MerrilU^l (1977) for high permeability matrix

element (Berea Sandstone) and nimierically verified the results.

Babadagli and Ershaghi^^H (1992) performed laboratory experiments

on tighter matrix elements to define pseudo relative permeability curves for

fractured system. Babadaglit23) (1994) continued this type of laboratory

experiments to examine the influence of the injection rate on capillary

imbibition behavior and saturation distribution in the matrix. They observed

that the limiting value of the injection rate (critical rate) was a function of

maximum matrix capillaiy pressure and matrix permeability.

-16-

2.2.3 Effect of Temperature and Pressure on Spontaneous Imbibition

It is well known that there are numerous possible factors that causes

the difference between the reservoir and the laboratory that can affect

fluids/rock interaction and capillary imbibition transfer, such as

thermodjniamic conditions, i.e., temperature and pressure.

Numerous studies were conducted to investigate the effect of

temperature on imbibition transfer. The results show that there is a tendency

to increase the affinity to water as temperature increases. Hjelmeland (1986)

demonstrated that a strongly oil wet system at room temperature becomes

water wet at higher temperatiwe (60oC). Anderson (1986) observed that

changing the temperature tends to make the core more water-wet at higher

temperatures. Two different effects occur during this change; first, an

increase in temperature tends to increase the solubility of the wettability-

altering compounds. Some of these compounds will even desorb from the

surface as the temperature increases. Second, the IFT and the contact angle

measured through the water will decrease as the temperature increases.

However, other experiment results show the opposite tendency. The

water wettability diminishes when temperature increases. In recent studies,

Jadhunandan and Morrow (1990 & 1995) have demonstrated that Berea

sandstone aged with various crude oils becomes more oil-wet when the aging

temperature of the rock/fluids system increases. They realize that this result

-17-

is difficult to interpret, as the adsorption of polar compounds of oils should

decrease with an increase in temperature. To explain the result, reference is

made to the potential for change in the stability, the solubility or the

dispersal of asphalthenes in the oil phase, as well as to the influence of

temperature on the stability ofwater films.

Regarding the imbibition mechanism, increasing temperature

substantially increases the spontaneous imbibition rate as demonstrated

numerically by Briggs et al. (1988). If the matrix contains heavy-oil, the only

way to increase the efficiency of spontaneous imbibition is to reduce the oil

viscosity by injecting steam or hot water into the reservoir. Zhou et al. (1993)

conducted static imbibition experiments at room temperature on samples

saturated and aged with crude oil at high temperatures. They found that

increasing the aging time and temperature decreased the early time rate of

imbibition ofwater.

Hjelmeland et al. (1986) foimd little difference in contact angles

measured using stock-tank versus live crude at the reservoir temperature

(190oF) and pressure (3800 psi). Mugan (1972) measured water advancing

contact angle of 87° using live reservoir crude oil and S3nithetic formation

brine at reservoir temperature (138oF) and pressure (1200 psi). The water-

advancing contact angle was almost identical (85°), using degassed crude and

brine at ambient pressure and reservoir temperature. In general, pressure

has the little effect on fluid-rock interaction

-18-

2.2.4 Scaling of Imbibition Data

In composite systems, the mechanisms of matrix-fracture counter-

current imbibition have mostly concentrated on the behavior of a single

matrix block. Mattax and K3rtef' J (1962) studied the effect of matrix block size

on the recovery for reservoir scaling purposes. They proposed the scaling

equation based on the theoretical work of Rapoport (1955).

t[) = Ctkm CT 1

(2.1)0 tiw

They showed that the imbibition time required to recover a given

fraction of oil from a single matrix block is proportional to the square of the

distance between fractures. Using this relationship, and by neglecting gravity

and capillary forces, recovery behavior for large reservoir matrix block was

predicted from an imbibition test on a small core sample. The prediction was

then extended to analyze the recovery behavior of fracture-matrix, water-

drive reservoirs in which imbibition is the dominant oil-producing

mechanism.

Later, Lefebvre Du Preyt^oi (1978) presented another reference time for

scaling of capillary imbibition as follows;

tD=' (2.2)

-19-

He investigated the effect of gravity and capillary forces in recovery

processes from matrix blocks (using Fontainebleau sandstone). He compared

centrifugal and conventional imbibition results for various ratios between

capillary and gravity forces. The results indicated that a great discrepancy

exists among the scaled recovery curves corresponding to different block

sizes. The failure of scaling rules was due to the effect of boundary condition,

local heterogeneities, and instabilities in the water sweep.

Cuec et allisi (1990) proposed a modified form of Mattax and Kyte's

dimensionless group for low permeability Chalk, by replacing the water

viscosity with oil viscosity. Zhang et al (1996), on the other hand, combined

the oil and water viscosities as the geometric mean of the viscosity of both

phases. While in terms of rock properties Ma et al (1995) was modified the

dimensionless group by defining the characteristic length as:

4 =

1

(2.3)

Guo and Schechterl^si (1998) applied combination Ma and Zhang's

scaling equation and modified Gupta and Civan*s (1996) analytical equations

to evaluate Spraberry waterflood performances fi'om small core plugs to field

dimensions. However, they performed the static imbibition experiment under

ambient conditions, in stead of at reservoir conditions.

Chapter 3

Experimental Description

This chapter describes the spontaneous and d3niainic imbibition

experiments conducted in this study. Two types of porous medium, i.e. Berea

and reservoir rocks, liquids and chemicals employed in this study are

described. Experimental procedures, including core treatments, spontaneous

imbibition and followed by dynamic imbibition tests are explained in detail.

3.1 Materials

Materials used in this study consisted of Berea outcrop and reservoir

rock samples, S3nithetic brine and crude oil from the Sprabeny Trend Area.

3.1.1 Rock Preparation and Properties.

Two porous media, i.e. Berea sandstone and reservoir rock were used

in this study. Berea sandstone was selected because it is widely used as a

standard porous rock for experimental work in the petroleum industry. These

-20-

-21 -

porous rocks were utilized to study the temperature and pressure effects on

the behavior of Spraberry crude oil in porous medium. The reservoir rock

taken from low permeability Spraberry reservoir formation was used to

measure, model and upscale to reservoir conditions. Restored state core

analysis for this rockwas performed during this experiment.

Berea cores. The core samples were cut from 0.5 blocks of Berea

sandstone. The diameter of all samples was 3.75 cm. The length of the cores

varied between 6.4 to 7.4 cm long. Each dimension is an average value of3 to

4 measurements using a vernier caliper. Before being used, the core samples

were dried at ambient temperature. The samples were then dried in an oven

at 110 °C for at least 3 days and cooled in a vacuum chamber until gas

permeability measurements were conducted. The physical properties of core

samples are listed in Table 3-la and 3-lb for static and d)mamic imbibtion

experiments, respectively.

Reservoir cores. The reservoir cores used in this study were

prepared from 4-inch diameter cores taken from the Spraberry Shackelford

Unit 1-38. The cores were cut to 3.80 cm in diameter and about 5.10 cm long.

The air permeabilities of some cores were measured which varied from 0.1 to

1.5 mD. All cores have porosity ranging from 9.5 to 12 percent, and the

absolute permeabilities to brine ranged from 0.10 to 0.51 mD. The physical

properties of the reservoir core samples are presented in Table 3'2a and 3'

2b for static and dynamic imbibtion experiments, respectively.

•22-

Table, 3-la. The physical properties ofBerea core samples

Core Diameter, Length, kbm. ko. Pore Volume, Porosity, Swi,No. (cm) (cm) (mD) (mD) (cc) (%) (%)

B-1 3.620 4.920 74.70 - 8.05 15.90 41.63B-2 3.620 4.610 - 67.87 8.34 17.60 0.00B-3 3.620 4.940 86.13 - 8.10 15.90 41.96B-4 3.620 4.605 - 70.51 8.30 17.50 0.00B-5 3.785 6.769 11.24*> - 9.95 13.10 0.00B-6 3.800 6.167 237.61 - 13.44 19.20 25.60B-7 3.805 6.193 237.99 - 14.76 21.00 35.60B-8 3.810 6.421 245.40 - 15.16 20.70 35.30B-9 3.800 6.477 294.01 - 13.61 18.50 38.30B-10 . 3.800 6.477 - 220.61 13.85 18.90 0.00B-11 3.810 6.525 - 216.75 14.89 20.00 0.00B-12 3.769 5.918 266.79 - 13.46 20.40 25.00B-13 3.602 7.049 - 216.94 13.65 19.00 0.00B-14 3.777 7.264 - 51.17 12.47 15.33 0.00B-15 3.777 7.330 - 37.17 12.19 14.85 0.00B-16 3.787 6.871 78.17 - 13.35 17.26 42.00B-17 3.787 6.894 - 54.70 13.32 17.16 0.00

Note : *)Air permeability

Table. 3-lb. Thephysical properties ofBerea coresamples

Core d L Qiiy kmatrix. kfracture, Wf PV 0 Swi,No. (cm) (cm) (cc/hr) (mD) (mD) (cm) (cc) (%) (%)

B-14 3.603 7.198 8.0 66.74 4876 0.0090 12.47 16.99 0.00

B-15 3.607 7.145 8.0 63.56 5072 0.0093 12.24 16.78 0.00

B-16 3.787 7.264 4.0 64.13 4977 0.0092 12.47 16.82 0.00

B-17 3.607 7.193 2.0 60.44 5456 0.0097 12.75 17.36 0.00

B-18 3.607 7.216 16.0 64.19 5201 0.0094 11.60 15.74 0.00

B-19 3.607 7.391 40.0 63.12 5168 0.0094 11.42 15.14 0.00

B-20 3.787 6.871 4.0 78.17 4003 0.0083 13.35 17.26 42.00

B-21 3.607 6.432 1.0 61.69 5231 0.0094 11.70 17.09 0.00

-23-

Table. 3-2a. The physical properties ofSpraberry reservoir core samples forstatic imbibition experiments

Core Diameter, Length, kbrine. PoreVolume, Porosity, SwiNo. (cm) (cm) (md) (cc) (%) (%)

SPR-IHR 3.608 6.579 0.22 6.55 9.74 34.36

SPR-2HR 3.607 6.579 0.34 7.11 10.58 43.72

SPR-3HR 3.607 5.842 0.51 7.08 11.86 40.66

SPR-4HR 3.607 5.669 0.30 6.93 11.97 33.62

SPR-5HR 3.607 5.702 0.24 6.94 11.92 36.59

SPR-6HR 3.607 5.563 0.21 5.65 9.94 38.03

SPR-7HR 3.607 5.433 0.14 5.61 10.11 32.22

SPR-8H 3.608 6.487 0.17 7.28 10.98 34.04

SPR-9H 3.607 6.502 0.33 6.81 10.26 41.29

SPR-IOH 3.607 5.804 0.12 6.66 11.24 39.96

SPR-llH 3.607 5.842 0.10 6.39 10.71 40.55

SPR-12H 3.607 5.685 0.38 6.42 11.05 34.54

SPR-13R 3.594 5.829 0.10 6.16 10.42 35.03

SPR-14R 3.594 5.723 0.13 6.03 10.38 33.62

SPR-15R 3.594 6.111 0.22 5.13 8.28 41.53

SPR-16WF 3.608 6.487 0.23 6.04 9.11 30.45

Table. 3-2b. The physical properties ofSpraberry reservoir core samplesfor dynamicimbibition experiments

Core d L Quv kmatrix. kfractiire, Wf PV <1) Swi,No. (cm) (cm) (cc/hr) (mD) (mD) (cm) (cc) (%) (%)

SPR-17F 3.607 5.842 1.0 0.50 335 0.0024 6.47 10.84 37.17

SPR-18F 3.607 7.145 0.2 0.08 178 0.0017 6.12 10.47 34.60

SPR-19F 3.787 7.264 0.5 0.18 194 0.0018 5.87 10.38 31.87

•24-

3.1.2 Brine composition

Synthetic Spraberry brine was used in the experiments. It was

prepared by dissolving NaCl and CaCl2.2H20 in distilled water. The brine

compositions are shown in Table 3-5. The viscosity and density of the

synthetic brine at elevated temperature are presented in Fig. 3-1 and Fig, 3-

2, respectively.

3.1.3 Oil samples

Sprabeny dead oil is used in the investigation. Table 3-4 sximmarizes

the physical and chemical properties of the oil samples. The composition of

the sample, determined from gas chromatography analysis, is listed in Table

3-5. The viscosity of Sprabeny oil was determined using Cannon-Fenske

Routine Viscometer and the density was determined using Digital Density

Meter. The plots of oil viscosity and density at elevated temperature are

shown in Fig, 3-3 and Fig, 3-4, respectively. The interfacial tensions (IFT) of

oil/brine systems were also measured using a Pendant Drop instrument and

de Nouy Ring. Fig, 3-5 shows the interfacial tensions of Spraberry oil/brine

at different pressures determined using Pendent Drop. The plot of IFT at

elevated temperature is presented in Fig, 3-6. Both methods show that the

results of IFT measurement at room and reservoir temperature are in

-25

agreement. In addition, the volumetric expansion due to increase in

temperature was also measured and it is shown in Fig» 3'7.

Table- 3-3. Synthetic Reservoir Brine

Salts Content Concentrations (mg/L)

NaCl 122,699CaCl2.2H20 7,497Total Dissolved Solids 130,196

Table, 3-4. Properties ofSpaberry Crude Oil*)

API Gravity @ 60oF 31

Acid Number (mg KOH/ff oil) 0.085 ± 0.022

Base Number (mg KOH/g oil) 2.65 ± 0.040

Density @ 25oC (g/ml) 0.8635

Refractive index @ 20oC 1.47824 ± 0.00007

PRI with n-C7 n/a

Asphalthene ppt with n-Cs (wt %) 0.39

Asphalthene ppt with n-C? (wt %) 0.16

Molecular Weight 180

*) Chang, v., and Buckley, J.S., (1997)

Table, 3-5. Spraberry Crude Oil Composition**)

Components Mole fractions

Ci 0.0211

C2 0.0172

C3 0.0351

C4 0.0212

Cs - Clo 0.5137

Cii - C20 0.2151

C21 - C30 0.0710

C30 - C36 0.0302

0CO

+

0.0740

Total 1.0000

**) Siagian, W.R., (1997)

1.4

1.2-

1.0 •

&-0.8 +

CQO

^0.6 +

0.4-

0.2-

•26.

Reservoirten5)erature

50 70 90 110 130 150

Teccperature, °F

170 190

Fig. 3-1. Variation in viscosity ofsynthetic Spraberry brine withtemperature.

1.090

1.088-

1.086-

1.084 ••oo

&1.082

§g 1.080-1<D

Q1.078 •;

1.076-1

1.074-1

1.072 +

-27-

Beservoir ten^rature

50 70 90 110 130 150

' • I •

170

Tenoperature, °F

Fig, 3-2. Variation in density ofsynthetic Spraberry brine withtemperature:

190

30

25-

Oho

•3 15o

CO

5-

-28-

0 I I I '• I ' I I I I t I I I I I I t I I

0 20 40 60 80 1CX) 120 140 160 180

Temperature, °F

Beservoir temperature

I I I I I I • • • •

Fig. 3-3 : Variation in viscosity of Spraberry oil with temperature.

0.880

0.870 • •

0.860 ••uo

&^ 0.850 ••*w

§o

0.840 +

0.830-•

-29-

Reservoir temperature

0.820-H-•-'--H-*-'-'-H• I • • ' • I '

0 20 40 60 80 100 120 140 160 180

Temperature, °F

Fig. 3-4: Variation in density of Spraberry oil withtemperature.

40

35 ••

30--

g25.:

Si5-:

-30

10.! # IFT at Room Temperature

• IFT at Reservoir Temperature

500 1000 1500 2000 2500 3000

Pressure, psig

Fig. 3-5. Interfacial tension ofSpraberry oil - brine at elevatedpressure.

40

38-

g364

la.fl32

I 300

13 28-f•fH

,cd^126

1A 24

22 +

20

-31-

IFr@room teix^ierature = 30.35 dyne/cmIFr@^:«senroirtenq)erature = 26.22 dyne/cm

Equation:y=35.523e-®"®^

Reservoir teirperature

20 40 60 80

• I • •

100

Tenqjerature, °F

120 140 160

Fig. 3-6 Interfacial tension ofSpraberry oil - brine at elevatedtemperature.

180

-32-

H-*-

80 100 120

Temperature,(°F)

Reservoir temperature

Fig. 3-7. Thermal expansion ofSpraherry oil.

200

-33-

3.2 Experimental Procedures

3.2.1 Cleaning Process

The cleaning process was performed particularly carefully for reservoir

cores. The objective of core cleaning is to remove all organic compounds

without altering the basic pore structure of the rock. The process is the early

step in performing re-established reservoir wettability condition. In order to

clean very tight core samples from the Spraberry formation, traditional

toluene Dean-Stark extraction, which removes water and light components

by boiUng was used. To insure the core sample was really clean, the process

was then followed by injecting chloroform into the core sample under 200 psi

injection pressure until the color of produced fluid was clear. These clean

cores were then dried in an oven at 110 for at least 5 days.

To determine the permeability homogeneity of reservoir rock samples,

the permeability distribution of several reservoir cores were measured using

a Scanning Minipermeameter (SMP). The measurements were performed on

each face of the core samples. Each face of the core samples has nine points of

measurement with 0.5 in x 0.5 in area of measurement. Nine values of

permeability were gathered from one side of core face. Then, these values

were compared with values from the other side of core face. As shown in

-34-

Fig,3-8j core permeabilities determined from minipermeameter compare well

with those determined using Hassler-sleeve apparatus.

3.2.1 Saturating the Core with Brine

Dry core samples were weighed on a balance after measurement of the

air permeability. The core sample was then saturated with deaerated brine

using a vacuum pump for at least 12 hours. After saturating the core samples

with brine, a period of about 3 days was allowed for the brine to achieve ionic

equiUbrium with the rock. The porosity and pore volvmie of the core were

determined from the dry and saturated weights of core sample, bulk volume,

and brine density. The core sample was then inserted into a Hassler core

holder using a confining pressure of 500 psig to measure the core absolute

permeability to brine.

3.2.2 Establishing Initial Water Saturation

The core sample was saturated with oil by injecting oil through the

core confined in a Hassler core holder with a confining pressure of 500 psig to

establish initial water saturation in core.

Berea cores. The oil flooding pressure applied varied from a few psi to

50 psig with oil throughput ranging from 2 to 10 pore volimies, depending on

the initial water saturation desired. In establishing initial water saturation,

the direction of flooding was reversed halfway through the oilflooding cycle to

-35-

minimize unevenness in saturation distribution. The lowest initial water

saturation achieved was 30%.

For lower initial water saturations, high viscosity paraffin oil was

injected into the core sample until initial water saturation was achieved.

About 10 pore-volimies of Spraberry oil then was injected into the core to

displace paraffin oil. The initial water saturation achieved using this method

was about 25%.

Reservoir cores. To establish initial water saturation, oil was

injected into a brine-saturated core. The injection was ceased aiter 2 to 5 pore

volumes oil was produced from the core. The lowest initial saturation

achieved was 32 %.

3.2.3 Aging Procedure

In an oil reservoir the adsorption equilibrium between the rock surface

and the oil is established over the geologic time of the rock-oil system. In an

effort to restore adsorption equilibrium, prior to each of the imbibition tests,

the core samples were aged by immersing the core samples in an oil bath at

the reservoir temperature (60oC) for a certain period of time. To investigate

the effect of adsorption eqmlibrium level on the imbibition process, the aging

period was varied between 3 to 30 days. The Berea core samples were aged

-36-

for seven days while the reservoir cores were aged for 3, 7, 14, 21 and 30

days. As comparison, some ofthe cores were not aged.

3.2.4 Spontaneous Imbibition Tests

To investigate the effect of thermodynamic parameters on the

imbibition mechanism, the imbibition tests were carried out under two

different conditions i.e. Low Pressure High Temperature (LPHT) and High

Pressure High Temperature (HPHT). The temperature of the tests was set

constant at the temperature of the reservoir under consideration which is

about 138 op.

Low Pressure High Temperature (LPHT). The LPHT imbibition

tests were performed using a low pressure imbibition apparatus

schematically shown in Fig. 3-9. As can be seen from the figure, the

apparatus is a simple glass container eqtdpped with a graduated glass cap.

To perform an imbibition test, a core sample was immersed in the glass

container filled with preheated brine solution. The container was then

covered with the graduated cap. Afler fully filling the cap with brine solution,

the container was then stored in an air bath that had been set at a constant

temperature of 138 F. Due to capillary imbibition action, oil was displaced

from the core sample by the imbibing brine. The displaced oil accumulated in

the graduated cap by gravity segregation. During the experiment, the volume

of produced oil was recorded against time. Before taking the oil volimie

-37-

reading, the glass container was gently shaken to expel oil drops adhered at

the core surface and the lower part of the cap so that all of the produced oil

accumulated in the graduated portion of the glass cap. At the early stage of

the test the oil volume was recorded every 1/2 hour while near the end of the

test the oil volume reading was recorded every 24 hoiu*s. Excluding the core

preparation, one test was usually completed within 21 days.

High Pressure High Temperature (HPHT). To simulate the

elevated pressure in the reservoir, an imbibition test at elevated pressure

was designed. The test was performed using an apparatus schematically

shown in Fig. 3-10. The apparatus consisted of a high-pressure imbibition

cell, a brine storage tank, a high-pressure nitrogen gas bottle and a

graduated glass cylinder to collect the produced fluids. Excluding the gas

bottle and the glass cylinder the apparatus was enclosed in a temperature-

controlled air bath.

The imbibition cell, which is the main part of the apparatus, is four

inches in diameter and 6 inches long mounted steel pipe designed to expose a

core to pressurized brine solution. The inlet and outlet ports of the cell were

located at the bottom and the top ends of the cell, respectively. As shown in

the enlarged cross section of the cell in Figure 3-10, the top part of the cell

was equipped with a metal cap specially designed to confine and direct the oil

produced during the imbibition test to flow into the cell outlet port. Also

shown in the cross section is the lower part of the cell was equipped with a

-38-

secondary inlet port which was used to create tangential flow of brine

injected into the cell to help lift and accumulate the produced oil at the top

cap of the cell.

To perform the experiment, the vessel was first filled with preheated

brine solution. A treated corewas then immersed in the cell. After connecting

the top cap with the graduated cylinder and closing the outlet valve, the inlet

port of the cell was then connected to the brine storage tank and pressurized

to the desired pressure. The pressure of the brine solution was created and

maintained by connecting the brine tank to a high-pressure nitrogen bottle.

The oil produced during the imbibition test was collected and recorded

periodically by carefully opening the outlet valve of the cell. The

measurement of produced oil was made eveiy 12 hours. The test was usually

completed within 21 days.

To investigate the reproducibility of the experimental methods used in

this study, each experiment was repeated using cores of similar properties.

The results for low pressure - high temperature tests are presented in Fig, 3-

11 for Berea cores and Fig. 3-12 for reservoir cores. Figure 3-13 shows the

results of tests for Berea cores at HPHT. As shown in the figures, the

reproducibility of the experimental method is satisfactory.

0) 0.5

-39-

=0.9848

0.5 1.0

Mmipermeameter Permeabilities, (mD)

Fig. 3-8.A good correlation was obtained by making comparison of corepermeabilities determined from minipermeameter and Hassler-sleeve measurements.

-40.

Air Bath

Oil recovered

Oil bubble

Glass funnel

Core plug

Fig. 3-9. Spontaneous imbibition cell

AGraduated

Cylinder

N2 tank(2000 psi)

NB = Ball Valve

NV = Needle Valve

PR = Pressure Regulator

-41 -

Air Bath

Side View

Inlet for creatingUttccntiBl Oow

Fig. 3-10. High pressure, high temperature imbibition apparatus.

7:3 20

A-Core B-10, Swi = 0 %

-*-Core B-13, Swi = 0%

Expprimfint Tbmppratairp;

138°F at atmospheric pressure

42-

0.10 1.00 10.00

limB, hours100.00 1,000.00

Fig. 3-11. Reproducibility ofspontaneous imbibition for Crude Oil-Brine and Berea Rocks using a glass imbibition cell atreservoir temperature with no initial water saturation.

25

20--

PhHH

o

5 15t:0)

1^'

5-

0.1

-O-CoreSPR-lHR

-0-CoreSPR-12H

-43-

Experiment Temperature:

138°Fat atmos{dierLC pressure

I I I

10

Time, Hours

100 1000

Fig. 3-12. Reproducibility ofspontaneous imbibition for Crude Oil-Brine and Spraberry Rocks using a glass imbibition cell atreservoir temperature.

A5

40-

35-

Core B-8, Swi = 35.33%

-A-Core B-9, Swi = 38.29%

.44.

T<!xpprimp!rit TV^i iniMm<.nra •

138^at 1(XX) psiocmfinmgpressure

10

TLme,hours

100 1000

Fig. 3-13. Reproducibility ofspontaneous imbibition for Crude Oil-Brine and Berea using a glass imbibition cell at reservoirtemperature and reservoir pressure.

-45-

3.2.5 Brine displacement

To determine the wettability index for water (Iw) quantitatively, after

the core had attained an oil production plateau in spontaneous imbibition,

the core was then transferred to a Hassler Sleeve for brine displacement. The

pressure gradient varied from 4 to 8 psi/inch for Berea core samples and from

60 to 100 psi/inch for reservoir cores, depending on the wetting condition. The

injections were performed under ambient and reservoir temperature. The

flooding apparatus was used for this experimental process as shown in Fig,

3-14.

Eh

Brine

Pump

W

OU

Pump

Ol ti nk Bri

Air Bath

;e mk

Confiningpressure gauge

Core

Fig. 3-14 : Flooding Apparatus,

Graduated

cylinder

•46-

3.2.6 Dynamic Imbibition Tests

In fractured porous media, viscous displacement occurs in the fracture

network due to its higher conductivity compared to matrix. In addition to

that, an exchange of fluids occurs between these two media.. The

displacement process as water is injected into the fractured medium thereby

displacing by the imbibition mechanism is called dynamic imbibition or

forced imbibition.

In order to understand imbibition processes in fractured core, dynamic

imbibition experiments using a low injection rate core flood experiment were

performed. A single fracture on the core sample was generated along the axis

of a cylinderical core by using a hydraulic cutter as shown in Fig.3'15. The

cut section was reassembled without polishing the cut surfaces and without

spacers. Sjmthetic Spraberry brine and oil was used respectively as wetting

and non-wetting phases. In detail, the experimental procedure is described as

follows:

1) After the core dimensions and weight were determined, the core sample

was saturated with brine. The core saturation was performed in a

Hassler-type core holder using a confining pressure of 500 psi. About 2-5

pore volimies of synthetic Spraberry brine were injected into the core

sample using a constant pressure of 30 psi for Berea cores and of 200 psi

for reservoir cores. By measuring brine rate and differential pressure, the

-47-

absolute matrix permeability to brine was calculated. The brine-saturated

core was then weighed to determine pore volume and porosity.

2) The initial water saturation was established by injecting oil into the

brine-saturated core. Once the initial water saturation was established,

the oil permeability at initial water saturation was determined. Then, the

oil-saturated core was taken out from the core holder. To prevent air from

penetrating into the core sample, aluminum foil was used to cover the

core. Then, the core was cut in half to generate artificial fracture

horizontally along the axis of the core using hydraulic cutter.

3) The fractured core was then inserted back into the Hassler-t3rpe core

holder. The effective permeability of the core was then determined by

injecting oil into the core and measuring the differential pressure across

the core and flow rate. The fracture permeability (Guo and Svec, 1998)

was calculated based on the following relations by assuming the fracture

porosity is 1%:

ke=k^+<l>fl^f (3.1)

where ke, km, kf and <fff are the effective reservoir permeability, matrix

permeability, fracture permeability and fracture porosity, respectively.

The fracture width (wf^ in cm) was calculated based on modification of

correlation developed by Seright et al (1996):

-48-

Wf =0.000m^ (3.2)

4) The oil-saturated, artificially fractured core again was taken out from the

core holder to remove oils adhering on the core surfaces. Then, the core

was inserted back into the core holder. The djniamic imbibition test was

performed by injecting brine into the core. In order to allow the injected

brine to flow only through the fracture, the matrix surface was sealed off

at the injection end using a plastic sheet and aluminimi foil. The

experiment was performed at a constant temperature of 138°F. The brine

injection rate was held constant at either of 4.0 and 8.0 cc/hour for Berea

cores and 1.0 cc/hour for Spraberry core. The schematic diagram of the

dynamic imbibition test is presented in Fig, 3-15.

5) During the experiment, the produced oil and brine volumes were recorded

against time. The experiment was terminated when the oil production

ceased. Each test usually was completed within 48 hours.

6) The experiment for cores with zero initial water saturation was basically

the same as that for cores with initial water saturations, except that Step-

1 (brine saturation) was omitted. Brine saturation as described in Step-1

on the procedure is replaced by saturating the core by oil directly. Then,

the procedure is continued from Step-2 to Step-5. The core porosity was

determined by the weight of the oil-saturated core.

-49-

To determine the reproducibility of the imbibition procedure, two series of

tests with different cores at the same experimental conditions were

performed. As shown in Fig.3-16, the reproducibility of the procedure used in

this study is satisfactory for dynamic imbibition tests.

NjTank(2000 psi)

Ruska

Pump Fracture

Air Bath

Brine tank

Confining pressuregauge

Artificiallyfractured core

Matrix

Fig. 3-15, Experimental apparatus for dynamic imbibition tests.

Graduated

cylinder

0.01

First Run

-5K-SecondRun(repeated)1st Run

2ndRun(rq]eated)

j = 8cc/hr=0%

= 138f^

0.1

-50-

QQ curves

1 10

Hme^bours

100

Fig. 3-16. Reproducibility ofthe dynamic imbibition floodingresult *

1000

Chapter 4

Presentation and Discussion of

Experimental Results

In order to understand the interaction between reservoir rock, oil, and

brine in the Spraberry Trend Area reservoir, water imbibition experiments

using Spraberry oil, S3mthetic reservoir brine, and porous media under

reservoir temperature (138 oF) were performed. Two porous media were used

in this study; Berea sandstone and Spraberry reservoir rock. The Berea

sandstone was used to study the effects of temperature, pressure, and initial

water saturation pn the behavior of Spraberry oil and brine in a porous

medium. The reservoir rocks taken from the low-permeability Spraberry

reservoir were used in order to represent reservoir conditions in the

spontaneous and dynamic imbibition experiments.

-51-

-52-

In this chapter, the experimental results of static imbibition and

dynamic imbibition are presented and discussed. Based on study performed

by Putra, et al., (1998), the rate of imbibition and recovery mechanisms in

both types of experiments were also investigated, mathematically modeled,

and nimierically simulated using a commercial simulator.

4.1 STATIC IMBIBITION

4.1.1 EXPERIMENT USING BEREA CORES

The following section presents the experimental results and discussion

on the effect of experiment temperature and pressure on brine imbibition in

Berea sandstone cores. The results of the experimental study on the effect of

initial water saturation and rock permeability on the imbibition process are

also presented and discussed.

4.1.1.1 Effect of Temperature

In considering the effect of temperature, it is necessaiy to distinguish

between the aging temperature (Ta), the imbibition temperature (Timb), and

the displacement temperature (Td). The aging temperature is the

temperature condition applied when core is aged in oil. The imbibition

temperature is the temperature condition when spontaneous imbibition

-53-

experiments are performed. Finally, the displacement temperature is applied

during brine displacement after the imbibition test has been completed.

To investigate the effect of temperature on the spontaneous imbibition

mechanism, two series of experiments have been performed. The first series

was performed at room and reservoir temperature using cores with zero

initial water saturation. The second series was performed at the same

temperature, but using cores with 42% initial water saturation. The brine

displacement temperature depends upon the imbibition temperature of each

test. All preparations before a test were conducted at room temperature and

all cores were prepared without any aging in oil. Based on fluid properties, by

changing the experimental temperature, the viscosity of oil and brine and

interfacial tension between oil and brine are altered (see Fig»3-2 to Fig.3'8).

As is demonstrated in these figures, the values of oil viscosity are 20.6 cp at

room temperature and 5.92 cp at reservoir temperature. The viscosity of

water changes fi:om 1.21 cp at room temperature to 0.68 cp at reservoir

temperature. The interfacial tension decreases fi*om 30.35 dynelcm to 26.22

d3nie/cm when the temperature is increased. All of these parameters are

expected to influence the imbibition process.

The effect of temperature on the rate of brine imbibition is presented

in Fig.4'lf where the recovery of oil produced fi*om the core sample as a

function of time for different imbibition temperatures and initial water

saturations are plotted. The results demonstrate that the rock imbibes water

60

50--

gj400

b30

1d 20 4

10-

0.01 0.1

-55-

Swi s 0%, Reservoir ConditiQn

Swi = 42%, Resezvoir Condition

B-2, Swi = 0%, Room Condition

Swi = 42%, Room Condition

Reference

10 100

Tiiiie» hours

1000 10000

Fig.4-1: Effect oftemperature on the imbibition mechanism for aSpraberry oil, brine, and Berea sandstone system. Referencecurve is from imbibition test using refine oil for a very stronglywater-wet system.

-56-

These results agree with previous studies (Handy, 1960; Anderson

(1986); Reis (1990); Babadagli, 1995; Tang, G.Q., et aL, 1996). If the contact

angle is not affected by changes in temperature, the rate of imbibition

increase with an increase in temperature is can be attributed to changes in

water and oil viscosity, or interfacial tension between oil and water. In

addition, based on known concepts in surface physical chemistry (Anderson,

1986), an increase in temperature tends to increase the solubility of

wettability-altering compounds in the brine. A decrease in the viscosity ratio

of oil and water due to increasing temperature results in oil being recovered

easily and improved ultimate recovery. Figure 4-2 shows the plot of

imbibition curves in terms of dimensionless time, where the effect of viscosity

and interfacial tension are normalized.

To test the sensitivity of the imbibition mechanism to temperature,

after oil recovery ceased at the end of the imbibition test performed at

ambient temperature, the experimental temperature was increased to

reservoir temperature. Figures 4-3 and 4-4 presents respectively the effect of

temperature changing on oil recovery for cores with 0% and 42% initial water

saturation. It can be seen that changing the temperature from ambient to

reservoir results in a dramatic increase in the rate of spontaneous imbibition.

The increase in imbibition rate is related to improvement in recovery, as it is

almost the same as the ultimate recovery for imbibition at reservoir

conditions.

-57-

According to Tang (1996), in contrast to the large change in imbibition

recovery for crude oil, increasing temperature during the course of imbibition

has essentially no effect on refined oil. Therefore, the crude oil^rine/rock

interactions are responsible for the dramatic increase in oil recovery with

temperature increase. Comparable behavior has also been reported for chalk

core samples (Dangerfield, et al, 1985).

§

II

60

; -A-B-2,Swi =0%, Room Temperature

B-3, Swi =42%,Room Tenq)eratuTe 0 Q-O 0—0 00-0- B-4, Swi = 0%, Reservoir Temperature

• -^B-l,Swi = 42%, Reservoir Temperature

Rwm Tgmwrafare;^e =20.6q>yu 3 1.21 q)

IFT s 30.35 dyne/cm

Reservoir Temoerature:

Me s:5.92q>

(iw sO.eSq)

IFT a 26.22 dyne/cm

20-

10-

10 100 1000 10000

Dimensionless Time

100000 1000000

Fig. 4-2: Effect oftemperature on the imbibition mechanism in terms ofdimensionless time.

-58-

60

50^ee© ^

t5s A

J?30

II 20

:o-

0 J

-100 0 100 200 300 400 500 600 700 800 900 1000 1100

lime, hours

()

-A-

Extended to

temperature 138°F

-Ar B-2, Swi = 0%, Room Condition

B-4, Swi = 0%, Reservoir Condition

I ' ' I I I i ' • ' ' 1

Fig.4-3: Effect ofchange in temperature on oil recovery by imbibition forBerea cores without an initial water saturation.

45

40

35

2 SO-f

f? 25

I .S 20 4

15 -

10 •

5 -

-100

H

-59-

r-h A

\Extended to

temperature 138 °F

-A- B-3, Swi = 42%, Room Condition

B-1, Swi = 42%, Reservoir Condition

100 200 300 400 500 600 700 800 900 1000 1100

Timey hours

Fig. 4-4 : Effect ofchange in temperature on oil recovery by imbibition forBerea cores with 42% initial water saturation.

-60-

4.1.1.2 Effect of Pressure

To investigate the effect of confining pressure on spontaneous

imbibition, three pairs of imbibition experiments were performed using six

Spraberry oil and/or brine-saturated Berea cores. Each pair was designed for

0%, 25% and 35% initial water saturation. All of these saturated cores were

tested at constant temperature of 138 °F and at variable confining pressure of

atmospheric pressure (13.5 psig) and 1000 psig. For experiments at

atmospheric confining pressure, the LPHT apparatus was used, while HPHT

apparatus was used for 1000 psi confining pressure experiments. To examine

the reproducibility of tests, two additional tests were performed at 1000 psig

confining pressure with 35% initial water saturation and at atmospheric

pressure with 0% initial water saturation. All cores were aged in oil. The

resvilts of these experiments are presented inFig8.4'5 to Fig.4'7.

From Fig.4'5, one can see that all runs have a similar trend in

unbibition curves. In each run, the initial water saturation of core was about

35%. Imbibition Curve-A represents a test result performed at atmospheric

confining pressure and Curve-B is a test result at 1000 psig confining

pressiire. To determine the repeatability of the test, an additional test was

performed using similar material properties with Curve-B. The repeatabihty

of test is satisfactory, as presented in Curve-C. From the figure, it can be

seen that imbibition started at about the same time for all cases. However,

-61 -

increased oil recovery at atmospheric pressure is faster than that at higher

pressure after 0.5 hour of imbibition until no more oil is produced. At high

confining pressure, the rock imbibed brine slowly to expel oil from core;

therefore, the recovery rate at high confining pressure is slightly slower than

that at atmospheric conditions.

Figure 4-6 shows the initial water saturation was reduced to 25%.

From the figure one can see that the early imbibition for the test performed

at 1000 psig confining pressure (Curve B) is slower than that of the test

performed at atmospheric confining pressure (Curve A). It was observed that

the imbibition rate for high confining pressure increased rapidly in middle of

the experiment. Curve B crossed over Curve A after eight hours of imbibition

time. However, the final recoveries for both tests are almost the same.

Furthermore, when the experiments at zero initial water saturation were

performed, as shown in Fi^.4-7, changes in pressure give a slight effect on

imbibition curves at the beginning of imbibition time.

It is shown in Fig»4'5 to Fig,4-7 that when imbibition tests were

conducted at high confining pressure for variations of initial water

saturations of 35%, 25% and 0%, the initial rate of imbibition was slower

than that at atmospheric confining pressure. It was also observed that the

ultimate recoveries of each experiment run were almost the same. However,

for 25% Swi, due to unknown reasons, the imbibition rate increased rapidly in

the middle of imbibition time until the same final recoveries were achieved.

-62-

A method to establish the initial water saturation for cores that have

initial water saturation of 25% was different from that used with the other

cores. The low viscosity of Spraberry oil results in difficulty in estabhshing

initial water saturation below 30%. As mentioned in the experimental

procedure, paraffin oil was used to displace brine until 25% brine remained in

the core. Spraberry oil was then injected for about 3 to 4 PV to flush out all of

the paraffin oil. The different method of establishing initial water saturation

causes imbibition curves for this type of test to be distinguished from the

other two t3rpes of tests.

60

0.01 0.1

-63

SWW

Curve A

Curve C

Curves

Experiment Temperature: 138T

B-7, Swi = 35.73%, P = 13.5 psi

<— Swi = 35.33%, P = 1000 psiA— B-9, Swi = 38.29%, P = 1000 psi

Reference

I I I I 111 ^ —I I 111 lll

1 10

Time, hours

100 1000

Fig.4-5: Effect ofconfining pressure on imbibition mechanism for Bereacores with 35% average initial water saturation. Reference curveis from static imbibition performed at reservoir condition usingrefine oil for a very strongly water-wet system.

60t

50-

£j40o

b30

20-

10-

0.01

sww ..

/

0.1

/•

-64-

\Curve A

ExperimentTenqwrature: 138°F

A B-6, Swi = 25%, P = 13.5 psi

-^B-12, Swi = 25%, P = 1000 psi

Reference

1 10

Tinie, hours

100 1000

Fig.4-6: Effect ofconfining pressure on imbibition mechanism for Bereacores with 25% average initial water saturation. Reference curveis from static imbibition performed at reservoir condition usingrefine oil for a very strongly water-wet system.

70

60-

50

O

^.40

>

§ 30

O 20

10-

0.01

-*~B-13,P=13.5psi"A-B-10,P=13.5psi—^B-ll,P=1000psi

Reference

SWW

/'

/'

-65-

Ejqjeriment Temperature: 138TFInitial water saturation : 0 %

I ii]|

0.1

-M-

1 10

Tiiiie» hours100 1000

Fig.4'7: Effect ofconfining pressure on imbibition mechanism for Bereacores without initial water saturation. Reference curve is fromstatic imbibition performed at reservoir condition using refineoil for a very strongly water-wet system.

-66-

With similar variable conditions in experiments, according to Handy

(1960), the final water saturation increased due to a decrease in confining

pressure during a gas-water imbibition test. However, there are three

examples in the literature indicating that pressure is much less important

than temperature. Mugan (1972) found an identical value ofwater-advancing

contact angle at different pressures. Hjelmeland (1986) found little difference

in contact angles measured at 190°? and 3800 psi compared to measurement

of those at ambient conditions. Recently, Cuiec (1995) concluded fi-om

experimental results that each reservoir is unique and it is currently

impossible to predict the influence of a change in temperature, pressure and

type of oil on the wettability of a rock/fluid system.

In this study, it can be concluded that in terms of ultimate recovery

firom d3aiamic imbibition tests, there is no significant effect in changing

confining pressure. However, in terms of the rate of imbibition, the initial

imbibition rate is slightly slower at high confining pressure than it is at

atmospheric confining pressure. The reason for this might because, the use of

dead oil at ambient temperature and reservoir pressure may change the

wettability because the properties of the crude oil are altered. Light ends are

lost fi:om the crude oil, while the heavy eiids are less soluble, which may

render the core less water-wet.

-67-

4.1.1.3 Effect of Initial Water Saturation

Initial water saturation is an important parameter of the imbibition

process in porous media that does not enter the more basic measures of

wettability, which are made in the absence of the rock. The effects of initial

saturation have been included in previous experiments. Testing of initial

water saturation of 0, 25 and 35% at reservoir temperature with varied

pressure condition of atmospheric and 1000 psig confining pressure indicated

that the initial rate of imbibition decreased with an increase in initial water

saturation. It is also seen that experiments performed at higher initial water

saturation showed of oil recovery by spontaneous imbibition. The results are

shown in Fig8.4-8, 4-9, and 4-10. In those three figures, effects of initial

water saturation on the imbibition mechanism were obtained under different

experimental conditions. In Fig.4'8 and Fig.4'9, the experiments were

performed with seven days aging time at reservoir temperature and

imbibition tests conducted at low and high confining pressures, respectively.

On the other hand, no aging was performed for results shown in Fig,4'10.

The core permeabilities used for experiments presented in Fig,4-8 and Fig,4-

9 were higher than those in Fig.4'10. However, all these experiments were

carried out at the same temperature (138oF).

The efifect of an increase in initial water saturation on the imbibition

rate is related to change in imbibition capillary pressure, decrease in

-68-

volumetric displacement, and water/oil mobility ratio for countercurrent flow.

An increase in initial water saturation and the subsequent increase in water

saturation by imbibition will decrease the capillary imbibition pressure,

which drives the imbibition process. At the beginning of imbibition, relative

permeability to water is very low, while relative permeability to oil is very

high. The water mobility increases more readily during imbibition with an

increase in initial water saturation. Thus as initial water saturation

increases during imbibition there are opposing effects which determine the

imbibition rate; the mobility of the water phase increases while the capillary

pressure, which drives imbibition, decreases. Jadhunandan and Morrow

(1991) explained that the configuration of coexisting water and oil within the

space of the rock during aging also affects this imbibition behavior. If the

initial water saturation is low, the fraction ofdrained surface exposed to oil is

relatively high, then partially emptied pores with a higher water content

tend to have higher oil-water interfacial areas. Imbibition curvatures also

tend to be higher than in equivalent pores with low water saturation, because

the oil-water interfaces associated with water held in the pore comers are

equivalent to a completely water-wet surface.

The effect of increase in initisd water saturation on ultimate recovery is

also related to the capillary pressure in the system. Increase in initial water

saturation will decrease capillary pressure, which results in a decrease of the

ultimate oil recovery.

^40 +

> 30-

-69-

&8,Swi = 35'%\k=:245iid

A-B-12, Swi=2595% k=267 nd

B-11,Swi=0%^ k=217 md

Refeaienoe

Tdavsagjpg

I I I 1111A

Texperiiffint =138PF^xnfining = 1000psi

SWW

1 10

Hme, hours100

FigA-8: Effect of initial water saturation for cores aged for 7 days andimbibition experiments performed at 138°F and 1000 psiconfining pressure. Reference curve is from static imbibitionperformed at reservoir condition using refine oil for a verystrongly water-wet system.

1000

70

60--

50 +CU

o

>30 +

20-

10-'

-70-

-a-B-7, Swi = 35%, k = 238 md

—^ B-6, Swi = 25%, k = 238 md

-5K-B.13, Swi =10%, k = 217 md

Refe-ence

7 days agiDg

/' T«cperiiiient=138* '^confining ~ 13«5 psi

SWW

Fig.4-9 : Effect ofinitial water saturation for cores aged for 7 days andimbibition experiments performed under 138°F and atmosphericpressure. Reference curve is from static imbibition performed atreservoir condition using refine oil for a very strongly water-wetsystem.

TO

60--

50-

PU

0

540

1> 30O

&

10-

0.01

Texperi»ent=138'FPowifining = 13.5 psi

0.1

-TI

SWW

No flffinpr

•e—&4,Swi = 0%

-^B-l,Swi = 42%

Reference

100 1000 10000

Fig.4-10: Effect of initial water saturation for cores without aging in oiland imbibition experiments performed at 138°F andatmospheric pressure. Reference curve is from static imbibitionperformed at reservoir condition using refine oil for a verystrongly water-wet system.

-72-

4.1.1.4 E^ect of Permeability

The core permeabihties were also considered in this study. As a

comparison, two different permeability rocks from Berea cores (which have

201 md and 11 md of absolute air permeability) and one low permeability

rock from Spraberry core (k = 0.6 mD for air) were used to investigate the

effect of rock permeability on the imbibition mechanism. There was no aging

performed for any of these cores before the imbibition test started. The result

of the effect of core permeability on the imbibition process is presented in

Fig.4-11.

The result shows that both the rates of imbibition and ultimate

recoveries of imbibition increase with an increase in absolute permeability of

the rock. This is expected, because; it is easy for brine to imbibe into higher

permeability porous medium.

-73-

60

50-

Bereacore, Air penneability = 201md

-A- Bereacore. Air penneability= 11.24md ,

-0-Sprabenycore. Airpermeabilily =0.60 md

A A—A

' 4 / /

!• wrTxui 1^ 1'Mill 1—1 111lll| -j—' I'll"!

0 0

£S 40O

^30

(S20

10-

0.01 0.1 1 10

Time, hours

100

FigA-11: Effect ofrock permeability on the imbibition mechanism.

1000

-74-

4.1.2 EXPERIMENT USING RESERVOIR CORES

The following section presents the experimental results and

discussions on the effect of aging time, experimental temperature during

brine imbibition and brine displacement, and rock wettability using low

permeability Spraberry cores. During the preparation of cores for the

experiments, the heterogeneity in rock properties was also considered, such

as initial water saturation and rock permeability. The spontaneous

imbibition results using Spraberry oil, S3mthetic reservoir brine and a

Spraberry rock system performed at reservoir temperature can be scaled

from the laboratory model to reservoir scale. A schematic of the experimental

program is presented in Fig, 4^12.

4.1.2.1 Effect ofAging Time

The effect of aging time with crude oil before brine imbibition was

investigated using eleven cores aged in oil at 138 ^F. The aging time varied

from seven to 30 days and for a comparison two cores were not aged in oil. Oil

recovery from spontaneous imbibition tests plotted against time in hours

shows that the rate of imbibition for cores without aging is faster than that

with aging (see Fig, 4-13). Slightly different imbibition rates at the beginning

of the imbibition test are observed for cores aged from seven to 30 days.

However, oil recovery after 21 days of imbibition decreased systematically

-75-

from 15% to 10% lOIP with an increase in aging time from no aging to 30

days aging {Fig, 4-14). A more representative condition is obtained when

Spraberry core is aged before the imbibition test at reservoir temperature.

Aging core samples in oil

time (days)

14 21

Imbibition tests(21 days) ] Imbibition tests (21 days)'.]at reservoir temperature at reservoir temperature -}

Brine displaconentat room temperature

Brine displacement' at reservoir t^peratnre

Results

Ibnbibition tests (2 months)at ambient condition

Brine displacementat Twm temperature

Fig. 4-12 : Schematic of experimental program using low permeabilitySpraberry cores.

20 -r

18 -J

16

£)l4.i2 ;^12":

^ 10|.s «•:

4.:

2 ••

0.01

-0-Core SPR-IHR

-©-Core SPR.8H-A-CoreSPR-9H

-*-CoreSPR.12H

-♦-CoreSPR-lOH

-•-Core SPR-2HR

*CoreSPR-6HR

—•—Core SPR-5HR

H-CoreSPR-7HR

—^Core SPR-3HR

CoreSPR-llH

-^SPRrl3R

-»«-SPR.14R

-»-SPR.15R

-76-

Time, Hours

Noaging

7 days aging

X ^ 14 days aging

21 days aging

30 days

70 T

100 1000 10000

Fig. 4-13: Complete oil recovery curves obtained from imbibitionexperiments performed at reservoir and room temperature.

-77-

25

20-

g Reservoir Ten^wrature

§ 00 i

•L. V

§0

0

\RoomTemperature

&1S

I§ 10

a

g

-1 14 19

AgingHme, days

24 29

4-i4 ; Effect ofaging time on recovery hy imbibition.

34

-78-

The effects of aging become less important for the recovery mechanism

if force imbibition or brine displacement takes place after spontaneous

imbibition. Figure 4-15 shows a plot of total recovery (i.e., recovery after

imbibition plus recovery after brine displacement) versus aging time. The

total oil recoveries appear to remain constant for cores aged more than seven

days. For the Spraberry, a reasonable time to start the brine imbibition and

displacement test is after the core has aged in oil at reservoir conditions for

at least seven days.

> 30

I • • ' • I

9 14 19 24

Aging Time, ta (days)

Fig. 4-15: Total recovery(recovery from imbibition and recovery frombrine displacement) versus aging time to exclude the effectsofaging time on the recovery mechanism.

-79-

4.1.2.2 Effect of Temperature

Previous experiments using Berea cores show that there is a sUght

effect of pressure on fluid-rock interactions. Some of the literature also

reports that the effect of pressure is much less important than the effect of

temperature. In the spontaneous imbibition experiment using low

permeability Spraberry cores, the temperature effect was taken into

consideration more than the pressure effect. Thus, all experiments for low

permeability Spraberry cores were performed at reservoir temperature and

atmospheric pressure using a glass imbibition apparatus described in

Section 4.1,1.2,

Temperature Effect on Spontaneous Imbibition. A series of

experiments were performed to investigate the effect of temperature on

spontaneous imbibition using a volumetric method. Four Spraberry cores

were used to investigate the effect of temperature during imbibition tests.

Two of these cores were prepared for spontaneous imbibition at reservoir

temperature (138 ^F). The other two cores were prepared for spontaneous

imbibition under ambient conditions (70 ^F). All cores were reduced to almost

the same initial water saturation of about 34%. The preparations to establish

initial water saturation were made at room temperature and there was no

aging of cores in oil performed for this test.

-80-

The effect of temperature on the rate of brine imbibition in low

permeability Spraberry cores is presented in Fig, 4-16. The recovery of oil

produced from the core sample as a function of time for different imbibition

temperatures is plotted. Two measurements were carried out for each

temperature and good reproducibility is indicated in Fig, 4-16. The results

demonstrate that during the process of brine imbibition into low permeability

core, the water is imbibed by rock faster at reservoir temperature than at

room temperature. The ultimate recovery is also affected by the temperature.

Higher ultimate recovery can be expected as the temperature increase with

all other parameter remaining constant.

Similar to the experiments described with Berea cores with Berea

cores, a sensitivity test of the imbibition mechanism to temperature was

performed. After oil recovery ceased at the end of the imbibition test

performed under ambient temperature, the experimental temperature was

changed to reservoir temperature (see Fig, 4'17). As indicated in Fig, 4'17,

changing the temperature from ambient to reservoir results in a dramatic

increase in the rate of spontaneous imbibition, due to change in fluid

mobility, oil expansion and decrease in interfacial tension.

Temperature Effect on Brine Displacement. After imbibition

tests, all core plugs were waterflooded with brine. As shown in the

experimental program presented in Fig, 4-12, brine displacements were

performed under two different temperatures (i.e. room and reservoir

-81-

temperature). Figure 4-18 shows total recovery (recovery after imbibition

plus recovery after brine displacement) versus aging time at elevated

temperatures during the displacement process. The total recoveries for cores

aged more than seven days and flooded by brine at room temperature after

imbibition was performed at reservoir temperature remained constant at an

average of about 35% lOIP. When brine displacement was performed at

reservoir temperature, the total oil recoveries improve to 65% lOIP for

Spraberry cores with and without aging in oil. Increase in temperature

during the brine displacement process appears to increase the displacement

recovery, thus significantly increasing total recovery. It is also shown in Fig,

4-18 that the total recovery was 44% after both brine imbibition and

displacement at room temperature.

0.1

-82-

-0-Core SPR-1HR, Reservoir Temperature

©-Core SPR-12H, Reservoir Temperature

-O-CJore SPR-13R, Room Temperature

-^Core SPR-14R, Room Temperature

10 100

Time, Hours

1000

Fig. 4-16: Effect oftemperature for imbibition tests.

10000

-83-

-0- Core SPR-1HR, Reservoir Temperature

-e-Core SPR-12H, Reservoir Temperature

-A-Core SPR-15R, RoomTemperature

=0

AAA A

/A A—A

I • • ' • I '

\extended to

reservoir temperature

-100 100 300 500 700 900 1100 1300 1500 1700 1900 2100

Time, Hours

Fig. 4-17: Effect ofchange in temperature on oil recovery by imbibitiondue to change in mobility offluid, expansion ofoil andreduce in interfacial tension.

100-r

go-

so-

1 70-

60-

&> 50-0u

& 40-

50 30-

H

20-

10-

0-

-84-

O Brine Imbibition and Displacement at Reservoir Temperature

A Brine Imbibition and Displacement at Room Temperatime

• Brine Imbibition at Reservoir Temperature and Displacement at Reservoir Temperature

i

9 14 19 24

Aging Time, (days)29 34

Fig. 4-18: Effect ofaging time on total recovery at elevated temperature.

-83-

4.1.2.3 Wettability Index

The wettability index is determined on the basis of oil recovery by

imbibition and subsequent brine displacement. The relationship is expressed

as:

WI =^wi ^wf

(4.1)

where Rwi is oil recovery by water imbibition andRwf is oil recovery by water

displacement.

A plot of the brine wettability index, versus aging time for brine

displacement at different temperatures is shown in Fig. 4-19. This figure

shows that the wettability index is about 0.35 for brine imbibition at

reservoir temperatures with brine displacement at room temperature. The

wettability index is 0.24 for both brine imbibition and displacement at

reservoir temperature. This result can be explained as an effect of a low

viscosity ratio between oil and brine at high temperatures. As the

temperatvire rises, the viscosity ratio of oil to brine decreases. The decrease in

viscosity is much greater for oil than for brine. Thus, an increase in

temperature can result in asubstantial decrease in the viscosity ratio of oil to

brine.

-86-

When brine is injected to displace oil at high temperature, a decrease

in the viscosity ratio ofoil and water due to increasing temperature results in

oil being recovered more easily from the core and improvement in ultimate

recovery, due to the higher temperature brine displacement.

As observed previously, oil recovery after brine imbibition decreased

corresponding to aging time. If oil recovery for brine displacement performed

at reservoir temperature is higher than recovery with brine at room

temperature, then based on the wettability index equation (Eq. 4.1), the

wettability index must be lower.

As a comparison, Fig. 4-19 also shows the plot of the wettability index

versus aging time for both brine imbibition and displacement at room

temperatxire. The wettability index is 0.22. This low value is due to low oil

recovery obtained with brine imbibition. This result is close to the wettability

index for both brine imbibition and displacement at reservoir temperatures.

The wettability results shows that performing imbibition tests at

reservoir temperature and displacement tests at room temperature results in

a WI that is approximately 0.3 to 0.4. However, performing both imbibition

and displacement tests at the same temperature (i.e., reservoir temperatiire

or at room temperature) lowers the WI in range of 0.20 to 0.25; thus, the

temperature during the experimental sequence significantly affects

wettability index determination. In conclusion, comprehensive experimental

-87-

data clearly demonstrates that Spraberry reservoir rock is a very weakly

water-wet system.

s

I

1I

0.9

0.8

0.7

0.6

0.5

OA':

0.3':

0.2 ':

0.1 -

O Brine Imbibitionand Displacementat ReservoirTemperature

A Brine Imbibitionand Displacementat Room Temperature

• Brine Imbibitionat Reservoir Temperatureand Displacement at Room Temperature

& 0

0.0

-1

I • ' • ' I ' • • • I • • • • I

9 14 19 24

Aging Time, ta (days)

29 34

Fig. 4-19: Wettability index to water versus aging time for the differentexperimental temperatures.

•88.

4.1.2.4 Heterogeneity in Rock Properties

The initial water saturation and permeability of different low

permeability Spraberry cores were not the same. An imderstanding of the

effects of initial water saturation and core permeability on the recovery

mechanisms is also necessary to resolve scading issues. In this study,

variation of initisil water saturation and permeability using Spraberry cores

are presented in Appendix-F.

Initial water saturations were found to vary from 32% to 43%. Thus,

there is difficulty establishing constant values for initial water saturation in

low permeability matrix. The initial water saturations established in these

cores do not provide a great enough variability to conclusively state that the

initial water saturation does not have an effect on the recovery. However, the

initial water saturation data in this experiment does indicate that for the

range under discussion, both imbibition and total recovery are affected only

slightly, if at all, by the initial water saturations in these cores (see Fig, 4-20

and 4'21), If the initial water saturations have a wide variability, as expected

in the capillary pressure curve where the initial water saturation is related to

the capillary pressure in the system, increase in initial water saturation will

decrease capillary pressure, which results in decrease of ultimate oil

recovery.

-89-

Cores used in this study have variable permeabilities, which ranged

from 0.1 to 0.5 md. To investigate the effect of core penneability on the

recovery mechanism, oil recoveries from imbibition were plotted against

permeability as shown in Fig, 4-22. The results show that the imbibition

recoveries were not significantly affected by core heterogeneity. Total

recovery values indicate no effect from heterogeneity {Fig. 4-23). In

summary, the results show that aging time has a large influence on

imbibition recovery with permeability affecting the imbibition recovery only

slightly.

40

7

35

&230

h2

5

S«2

0

01

5

saS10

15

+

-9

0-

•B

rineIm

bibitionat

ReservoirT

emperature

andD

isplacementat

Room

Tem

perature

AB

rineIm

bibitionand

Displacem

entat

Room

Tem

perature

OB

rineIm

bibitionand

Displacem

entatR

eservoirTem

perature

jfje"

02

04

06

08

0

Initia

lW

ate

rS

atu

ratio

n(S

^i),%P

V

Fig.

4-2

0:E

ffectofin

itialw

atersatu

ration

on

recoveryby

imbibition.

10

0

90

•

370-

i60-

I§5

0-

&§-

330-

^.0-1

0•

0-

•B

rine

Imb

ibitio

nat

Reserv

oir

Tem

peratu

rean

dD

isplacem

enta

tR

oomT

emp

erature

AB

rine

Imbibition

and

Disp

lacemen

tat

Room

Tem

peratu

re

OB

rine

Imbibition

and

Disp

lacemen

tat

Reservoir

Tem

peratu

re

8Sa

"

10

0

20

40

60

Initia

lW

ate

rS

atu

ratio

n(S

^i),

80

10

0

PV

Fig.

4-2

1:E

ffectofin

itialw

atersatu

ration

onto

talrecovery.

-91-

fiu

O

25 -

O Brine Imbibition and Displacement at ReservoirTemperature

A Brine Imbibition and Displacement at Room Temperature

• BrineImbibition Reservoir at Temperature and Displacement at Room Temperature

^ 20

>O

1'^o

:-210A•p4

a5

o •

A A

OO

0.00 0.10 0.20 0.30 0.40

Permeability, md

Fig. 4-22: Effect ofpermeability on recovery by imbibition.

0.50 0.60

euM

o

100

fu

&

I

O Brine Imbibition and Displacement at Reservoir Temperature

A Brine Imbibition and Displacement at Room Temperature

• Brine ImbibitionReservoirat Temperature and Displacementat Room Temperature

i ° 0>o o

o

^ A •A•

•

• • ••

0.00 0.10 0.20 0.30 0.40

Permeability, md

0.50 0.60

Fig. 4-23 : Effect ofpermeability on total recovery.

-92-

4.1.2.5 Numerical Analysis of Spontaneous Imbibition

The imbibition process was also simulated numerically, based on

spontaneous imbibition data, to investigate the effect of key variables on the

static imbibition rate. A fully finite-difference implicit scheme was developed

to solve non-Unear diffusion of the spontaneous imbibition equation

(Schechter, 1998). The numerical results matched satisfactorily with the four

spontaneous imbibition experiments as presented in Fig,4-24. The distance

of water imbibed into the core plug is demonstrated by the water satiu-ation

profile as shown in Fig, 4-25. As time increases, more water is imbibed into

the core plug and in turn, more oil is recovered. The ability of water to soak

into the rock is weak, only 0.6 cm into the core plug after 200 hours with the

oil volume recovered less than 14% lOIP. This mechanism is caused by low

capillary pressure diiring displacement of oil by water. The effective capillary

pressure during the displacement process is presented in Fig. 4-26.

0.8 1

0.7 -

^0.6-w

0.5 -

O© 0.4 is

5 0.3 -o

>0.2 -

0.1 -

0 ^

1

-93-

—Numerical Solution

o SPR-8H

• SPR-9H

♦ SPR-7HR

• SPR-11H

100 10000

Time (Sec)

• •

1000000 100000000

Fig.4-24 : Matching between spontaneous imbibition experiments resultsand numerical solution.

-=^0.80

o

2 0.60LL

W 0.40

0.00-1

0.5

1hr-o-20hr

-94-

1.5 2

x-Plane(cnf^

50 hr-o-100 hr150 hr

2.5

200 hr

Fig. 4-25: Water distribution at different imbibition time from x-plane view.

0.025

^ 0.020 +•pN

ft

9 0.015 +

I>» 0.010

&0.005-

0.000

-95-

0.4 0.5 0.6 0.7

Water Saturation, (%FV)

Fig.4-26: Imbibition capillary pressure for Spraberry reservoir rockobtained from matching ofspontaneous imbibition data.

-96-

4.2 DYNAMIC IMBIBITION

A series of dynamic imbibition experiments were performed using

Berea sandstone and Spraberry reservoir rocks to investigate fluid

interaction between matrix and fracture. During the dynamic process, viscous

displacement and imbibition mechanisms are involved. In this type of

experiment, a viscous pressure gradient is created by injecting the wetting

flmd through the fracture continuously. Wetting fluid (brine) flowing in the

fracture is imbibed by the matrix element thereby displacing non-wetting

fluid (oil) into the fracture. The schematic representation of this process is

presented in Fig, 4-27. The displacement of oil in the fracture is due to the

applied viscous gradient, whereas the displacement of oil in the matrix is

achieved only by capillary pressure.

Water Oil + Water

Oil saturated matrixOi Imbibed water

Capillary imbibition Viscous flow

Oil produced

Fig.4-27: Schematic representation of the displacement process infractured porous media .

-98-

4.2.1 EXPERIMENT USING BEREA CORES

An artificially fractured core was designed and water injection

experiments were conducted at different rates {i.e., 1, 2, 4, 8,16 and 40 cc/hr).

Foreach experiment, the core was stored in a core holder at 500 psi confining

pressure. All the oil was stored in the matrix, and there was no oil in the

fracture. The initial water saturation for all cores in this set of experiments

was zero. During the experiment, brine was injected at a constant rate and

recovery was monitored versus time.

The oil recovery curves versus time for continuous flow in the fracture,

obtained by varying the brine injection rate of 1, 2, 4, 8, 16 and 40 cc/hr are

presented in Fig. 4-28. In the experiment, it was observed that increasing

injection rate caused faster recovery. However, the ultimate recovery for all

cases is almost the same. Figure 4-29 shows a plot of oil recovery versus

total amount of produced fluid. The recovery curves seen in this figure imply

that once capillary imbibition is initiated (i.e., the first drop of water

penetrates the matrix), imbibition is continuous until the recoverable amount

of the oil in the matrix is displaced by capillary imbibition. However, the oil

recovery rate of this process is different at each injection rate. As the

injection rate is increased, the brine tends to flow in the fracture because of

the high fracture-matrix permeability ratio, which results in slower oil

recovery until ultimate recovery is approached. Because faster injection rates

-99-

allow water a shorter time to contact the matrix, the result is weaker

capillary imbibition. In Fig»4'30, the water-cuts at different injection rates

were also plotted against time. The plot indicates that an increase in the

injection rate causes higher water-cut, which results in significantly faster

water breakthrough.

Figure 4-31 shows the effect of initial water saturation on the

dynamic imbibition process at the same injection rate (4 cc/hr). The initial

water saturation for djniamic imbibition is a similar to that for static

imbibition. When initial water saturation is not present in the core, the rate

of oil recovery is slower than it is for a core with initial water saturation.

However, ultimate oil recovery for core without initial water satviration is

higher than it is for core with initial water saturation due to the capillary

pressure effect.

O 20-

0.01

Qinj = Icc/hr

-A-Qinj =2cc/hr

-O-Qiiq =4cc/hr

Qu\j = 8 cc/hr

Qiiy = 8 cc/hr (repeated)Qily = 16 cc/hr

Qinj = 40 cc/hr

0.1

-100-

10

Time, hours

Fig.4-28: Results ofdynamic imbibition experiment for Spraberry oil,brine and fractured Berea cores.

100

0.01

Qiiy = Icc/hr

-A-Qiiy =2cc/hr

-O-Qiiy =4cc/hr

-Q-Qinj = 8cc/hr

-5K-Qinj = 8 cc/hr (repeated)

Qinj s 16 cc/hr

•;>- Qinj = 40 cc/hr

0.1

-101-

10 100

Total Production, PV

Fig.4'29: Effect of injection rate on oil recovery versus total fluidproduced for Spraberry oil, brine and fractured Berea cores.

^0.6

-•-Qinj = lcc/hr= 2a^

-O-Qinj =4o(yhr-©-^j sScolir-5K-Qnj = 8 cc/hr(repeated)-♦-C^j =16oc/hr

=40cc/hr

0.01 0.1

-102-

10 100

Tune, hours

Fig.4-30Water-cut produced during the dynamic imbibition experimentfor Spraberry oil, brine and fractured Berea core.

70

60 ••

50 •

I40 •

t30 • •

20 •

10 •

0.01

-O- Qiiy = 4 cc/hr, Swi = 0%

-dr- Qiiy = 4 cc/hr, Swi = 42%

-103-

Time, hours

100

Fig. 4-31: The effect of initial water saturation on the dynamic imbibitionprocess at the same injection rate (4 cdhr).

-104-

4.2.2 EXPERIMENT USING RESERVOIR CORES

An extension of the dynamic imbibition experiment was performed

using low-permeability Spraberry rock as a porous medium. Four Spraberry

cores were used in this experiment. Three cores were designated as fractured

core with djoiamic imbibition investigated at different injection rates. The

other core was designated as an unfractured core. The experiments were

carried out for 70 hours. The results are presented in Fig.4-32, If unfractured

core is compared with fractured core at the same injection rate of 0.2 cc/hr,

brine displaces oil in a piston-like process in the unfractured core with an

ultimate recovery of about 55% lOIP at the production end. The ultimate

recovery of the fractured core was lower than it was for unfractured core (30%

lOIP). Obviously, this is due to a difference in displacement mechanisms. The

experiment using unfractured core is piston-like displacement, while

countercurrent imbibition and viscous displacement were involved in the

fractured core.

For fractured cores with different injection rates (i.e., 0.2, 0.5 and 1.0

cc/hr), the behavior was similar to that of fractured Berea cores. Faster

injection rates resulted in a slower rate of oil recovery, while the ultimate

recovery approached the same value (see Fig. 4-32). The reason is that

increasing injection rate decreases contact time with the matrix in the

wetting phase resulting in weaker capillary imbibition transfer. This effect

-105-

can also be observed experimentally by plotting time versus water-cut, as

presented in Fig. 4-53, where an increase in the injection rate results in

higher water fraction, and simultaneously, faster water breakthrough.

0.50

Unfractuied core, Qii\j = 0.2 cc/hr

-O-Fractured core, Qiiy = 0.2 cc/hr

Fractured core, Qiiy = 0.5 cc/hr

-^Fractured core, Qiiy s 1.0 cc/hr

1.00 1.50 2.00 2.50

Total Production, PV3.50

Fig.4-32: Comparison ofrecovery for dynamic imbibition experimentsusing fractured and unfractured Spraberry core.

-106-

A A A

Ibfiractured one, Qinj = 0.2 cc^

HD-FVactured core, Qinj = 0.2

Fractured core,Qiifl= 0.5 oc/hr

FVacturedOOTe, Qig s 1 colir

30 40 50

Tiliie, hours

Fig.4-33: Water-cut during the dynamic imbibition experiment forSpraberry fractured and unfractured cores during thedynamic imbibition process.

-107-

The experimental data from fractured Berea and Spraberry core

experiments were then matched by numerical modeling using an ECLIPSEtm

simulator (Putra, 1998). The experiment data were taken from the recovery

curves with four cc/hr and one cc/hr injection for Berea and Spraberry cores.

In the ntunerical modeling of the imbibition flooding process, the matrix

capillary pressure controlling the imbibition mechanism was the primary

parameter, adjusted to match the experimental data. Meanwhile, the fracture

capillary pressure was set to zero. The oil recovery and produced water were

used as parameter for matching between observed experimental data with

the numerical model. The final matches can be seen in Fig8.4-34a and 4'34b

for Berea and Spraberry, respectively. The effective capillary pressure for

Berea and Spraberry cores which match the experimental study are shown in

Fig8.4'35. The matrix capillary pressure from dynamic imbibition

experiments indicates that wettability of Berea core is more water-wet than

Spraberry core. Thus, the imbibition capillaiy pressure is more dominant in

Berea core than Spraberry core. Figure 4-36 shows the plot of the capillary

pressure determined from matching of dynamic imbibition experimental data

from Spraberry core. This capillary pressure curve is compared with the

capillaiy pressure curve determined experimentally using a static

equilibrivmi method from a previous study (Schechter, 1997).

- 108.

WO = ^ =ROCUC£i:? VS 'IVIE M3io got vs ~ VE obs

CUMM. Oii_ PRODUCTION <CC)

^ o .. p.. 0 -

V'"Id'

30.0TIME (HOURS)

Figure 4. 18/06/98 at 17:13:25

1BO.O

1 60.0

1 AO.O

120.0

lOO.O

ao.o

60.0

♦o.o

20.0

O.O

O O QWT VS TIME OBSWWPT PRODUCER VS TIME IMBI

CUMM. WATER PRODUCTION (CO)

,<s

20.0 30.0TIME (HOURS)

Figure 2 18/06/98 ot 17:10:51

O O 0

,0

a'

Fig.4-34a : Match ofoil recovery and water produced for BereaSandstone.

-109-

WOPT f=RODoC£R VS TIME IM3lO QOT VS Time OBS

CUMM. OIL PRODUCTION (CC)

A.O r—

Qinj = l.Occ/hrSwi = 36.6%Wf =0.0024 cmkf =335 md

<90

o.o.1 o.o 20.0 30.0

time (HOURS)

Figure 4- 18/06/98 ot 17:13:25

1 60.0

1 60.0

1 ■♦O.O

1 20.0

1 OO.O

ao.o

60.0

AO.O

20.0

O.O

O QWT VS time OBS-- WWPT PRODUCER VS TIME IMBI

CUMM. WATER PRODUCTION (CC)

Qinj = 1.0 cc/hrSwi—36,6%Wf = 0.0024 cmkf =335md

rOW

-OO'O'

TIME (HOURS)

Figure 2 18/06/98 at 17:10:51

.''0

Fig.4-34b : Match ofoil recovery and water produced for Spraberry reservoirrocks.

-110-

0.3 0.4 0.5 0.6

Water Saturation, (%PV)

Fig. 4-35: Capillary pressure curves obtained as a result ofmatchingexperiment data.

30

25--

t6

« 20a

Imbibition

-Ill-

•Pc deteminedexperimentally at roomtemperatiire

' Pc determined bynimierically at reservoir temperatiire

Drainage

0.4 0.5 0.6 0.7

Water Saturation (PV)

1.0

Fig.4-36: Effective capillary pressure obtained from simulation, comparedto capillary pressure obtained in the static equilibriumexperiment method.

-112-

4.2.3. CRITICAL INJECTION RATE

According to Babadagli (1994), when the injection rate increases and

reaches a certain value, there is no capillary imbibition because the contact

time with the matrix was not long enough. Based on this mechanism, the

limiting value of injection rate can be defined for an efficient capillary

imbibition transfer, which is defined as a critical injection rate.

The critical injection rate is the rate at which the injected fluid does

not contact the matrix long enough to initiate capillary imbibition. Thus,

water flows only in the fracture displacing the oil and no matrix interaction

occurs.

The critical injection rate is related to the oil production from the

matrix and the injected amount of wetting phase to recover oil in the matrix.

It can be defined as oil-cut which means the ratio of oil produced from the

matrix (OPFM) by capillary imbibition to the total amount of injected water

(TIW) to recover that much oil. If only the oil in the fracture is recovered, this

ratio becomes zero, which means there is no matrix interaction with fluids.

In this study, injection rate versus oil cut (OPFM/TIW) plots for Berea

sandstone and Spraberry reservoir rock samples are shown in Fig, 4'37.

According to the experimental observation, the curves will intersect the x-

axis because the oil-cut approaches zero at a certain rate. Based on

-113-

exponential correlation to fit experimental data using Berea cores, increasing

the injection rate results in constant of ratio of oil produced form matrix and

total injected water. The limiting injection rate value is the point where the

curves bend and beyond this point the curves are essentially constant. The

limiting values were defined as the critical rate for djoiamic imbibition in

fractured Sprabeny and Berea cores and are marked by arrows in Fig. 4-37.

An exponential correlation is used to fit the experimental data. Then, the

injection rate beyond experimental points can be approximated. The critical

rate for dynamic dynamic imbibition performed with Spraberry reservoir rock

was found to be 5 cc/hr. These vedues can be upscaled to reservoir dimensions

by introducing a dimensionless variable which we refer to as the Fractured

Capillary Number (FCN).

1.00

0.90

q. ^ 0.80 -

I 'O 0.70 -

0.50-

'3 0.40S3 0.30

^ 0.20

0.10

0.00

-114-

O Experimental data from Berea cores

♦ Experimental data fit)m Spraberry cores

c,max for Berea = 1.2 psifor Spraberry = 7.0 psi

Critical Injection ratefor Berea cores, 20 cc/hr

Critical Injection ratefor Spraberry cores, 10 cc/hr Injection Rate, cc/hr

Fig. 4-37: Injection rate versus oil-cut for Berea and Spraberry cores

Chapter 5

Scaling of Static and Dynamic Imbibition

Mechanisms

In this chapter, the static and dynamic imbibition results are upscaled

to field dimensions. The contribution of spontaneous imbibition on oil

recovery mechanism in the West Texas Spraberry reservoir is evaluated on

basis of static imbibition experimental data. The critical water injection

injection rate during the waterflood process is determined based on djniamic

experimental data.

5.1 SCALING OF STATIC IMBIBITION DATA

The anal3rtical model for describing oil recovery by water imbibition

was developed by Aronofsky et al (1958). This recovery model can be applied

using small reservoir core samples to scale the laboratory imbibition data to

field dimensions. All laboratory parameters are converted into dimensionless

forms (Mattax and Kyte, 1962). :he following conditions must be met for

-115 -

-116-

scaling imbibition: (t) the gravity effects are negligible, (ii) the rock type used

in the laboratory must be identical to that of the matrix block of the

reservoir, {Hi) the wettability and relative permeability represents the matrix

block, (iv) the capillary pressure functions for the matrix block and the

laboratory model must be related by direct proportionality through Leverett's

dimensionless J-function, (y) the viscosity ratio of oil to water must be

duplicated.

5.1.1 Imbibition Recovery Model

In order to apply the experimental imbibition data to field scale

imbibition waterflooding, the dimensionless time (to) initially proposed by

Mattax and Kyte (1962) and then modified by Ma et al. (1995) is used:

tp = Ctkm <7 cos(g) (51)

where t is imbibition time, C is a constant, km is permeability, 0 is porosity, a

is interfacial tension, Hg is the geometric mean of viscosity, and d is the

contact angle. The characteristic length, Lc, of the matrix block is given in

another relation defined by Ma et al (1995):

(5.2)" A

/=I "^Ai

-117-

In the above equation V is the volume of a matrix block where there are n

fracture faces exposed to imbibition, Ai is the surface area of face i and xai is

the distance from the fracture face to the center of the matrix block.

Aronofsky (1958) showed that for the capillary imbibition mechanism,

the recovery versus time curve could be approximated by the following

exponential decline equation:

(5.3)

Then, the recovery equation is normalized as:

(5.4)

where is ultimate recovery and A, is a curve fitting parameter and it can

take any value to yield matching effort.

Based on laboratory imbibition experiments conducted at reservoir

temperature using Spraberry cores and oil, recoverable oil by water

imbibition can be up to 13% of lOIP. In analysis of the imbibition data from

Spraberry cores, all of the imbibition experimental data presented in

Chapter-4 (Fig,4'13) are plotted in Fig.5-1 using dimensionless time, which

is defined in Eq.(5.1). As a comparison, the experimental data from

imbibition tests imder ambient condition were also plotted in Fig,5'l, In

these experiments, the rate of imbibition at reservoir temperature is greater

than the rate of imbibition at ambient condition.

1.0

0.9

0.8

I*0.7-;%I as,10.5-;•S^ 0.43

I"-®-:0.2 •:

0.1-

0.01

—Core SPRr3HR

-O-Core SrarSHR

-•-CoreSPEWHR

-A-CoreSPRr7HR

-•-CoreSPIWH

-0-CareSPR-9H

-3)6-Core SPRrlOH

-o-CoreSPRrllH

-t-CoreSPR-lSR

-•-CoreSPR-14R

—Core SFR-15R

0.1

-H8-

Reservoir Condition

Ambient Condition

10 100

Diineiisioiiless Tune

1000 10000 100000

Fig.5'1 : Oil recovery curves performed at reservoir temperature plottedusing dimensionless variables and compared with oil recoveriescurves performed at ambient condition

- 119-

A composite imbibition curve is shown in Fig.5-2. A composite

imbibition curve obtained for very strongly water-wet Berea sandstone with

zero initial water saturation is also shown for reference. Ma and Morrow

(1997) derived a correlation for this curve as:

I-(l+0.04r„rj

(5.5)

where R„ is the ultimate recovery by spontaneous imbibition data and to is

dimensionless time. The composite imbibition curves obtained from Berea

sandstone were then used to compjire the imbibition cxirves obtained from

Spraberry rock as shown in Fig»5'2. To achieve the best match of the

experimental data from Spraberry cores, an average recovery curve was

established using Eq.(5.4) by adjusting the value of X, A curve fit of Eq.(5.4)

for the experimental data as shown in Fig»5'2 is obtained when the following

relation is used for Spraberry cores as :

Af = 0.0053 (5-®)

Substituting Eq.(5.6) into Eq.(5.4), the recovery curve fit presented inFig,5'2

can be expressed as

D ?__i_g-0.0053(, (5.7)

Using the dimensionless time to defined by Eq. (5.1), the decline rate

or the rate coefficient which has unit 1/days can be expressed as :

-120-

A = 0.0053 Ckfn G COs{d)

0 Z-c(5.8)

The experimental data was then normalized and fit to an empirical

model using Eq. (5.1) and substituting into Eq. (5.7). Then, recovery can be

expressed as:

<7COS(0)-0.0053 a ' "n —— —2

M.L. (5.9)Aoo

The characteristic length (Lc) for a matrix block in the reservoir is assumed to

be half of the fracture spacing (Ls). Equation (5.9) can be used for analysis of

the recovery mechanism in a naturally fractured reservoir during

waterflooding

5.1.2 Production Decline Model

Guo and Schechter (1997) modified an analytical model for decline

curve analysis based on imbibition theory. It was developed on the basis of

the rate law that governs mass transfer (Gupta and Civan, 1996). Decline of

oil production rate is expressed as:

a cos(e)q. =0.0053CV., g ^Kf, i-. (5.10)M P tig

121-

where Vo is the original oil in place recoverable by imbibition. The above

equations are valid when consistent units are used. The derivation of Eq.

(5.10) is presented in Appendix-A.

iI

VN

I

1.00

0.90 +

0.80 AranofskyEg: swwBereaCore ,Rn=1-&(p('XtD) (' erenceci^) /

0.70

0.60-;

0.50 ••

0.40 •;

0.30

0.20-;

0.10 • •

0.00 4-0000 •

0.01 0.1

Spraberry Cores

XaaooBs

Sprabeny Coresat Airhitwt P/tivtiHnn

Xaaoois

H 1 I initil • • I

10 100 1000 10000

Diniensioiiless Hme

100000

Fig.5-2 : Averaging of imbibition curves using Aranofsky equation tofit the experimental imbibition data by adjusting theempirical constant X.

-122-

5.2 ANALYSIS OF RECOVERY MECHANISMS

5.2.1 Recovery Based on Scaling of Imbibition Data

The oil recovery in the lU Unit (data from Well Shackleford 138) and

5U Unit (data from Well E.T. O'Daniel 37) of the Spraberry reservoir were

calculated based on the imbibition model developed and log-derived porosity

and permeability (Banik and Schechter, 1996) as shown in Fig.5-3 and 5-4.

In Figs. 5-5 and 5'6 show the plot of oil recovery together with pore size of

rocks versus well depth. The pore size is the square root of ratio of

fkpermeability and porosity , which is proportional to a macroscopic

11I0J

radius in porous medium. The characteristic length (Lc) for a matrix block in

the reservoir core which is half of the maximum fracture spacing of 3.79 ft, as

determined from horizontal core analysis (Lorenz, 1996), was used in the

scaling equation (Eq.(5.1)). The calculations of imbibition recovery were

performed using Eq.(5.9) on the basis of 13% ultimate oil recovery from static

imbibition data. In analysis of five years waterflooding performance, pore size

of lU and 5U Units is plotted versus well depth as presented in Fig,5-5 and

5-6, respectively. The oil recoveries are then plotted in the same figures,

respectively. As shown in these figures, the integration of recovery profiles

along the depth of the pay zone resulted in an estimation of average oil

-123-

recovery at about 9% 10IP for lU sand and 11% lOIP for 5U sand. This data

is consistent with waterflood recoveries in the Spraberry Trend Area.

The effect of time on recovery profiles was investigated. Several

scenarios were performed at 1, 5, 10, 20 and 40 years waterflood. The

recovery calculations based on imbibition model are plotted against well

depth for Upper Spraberry lU and 5Usands as presented in Fig,5-7 and 5-8,

respectively. Within 10years ofwaterflood initiation, the average recovery is

11% to 13% for oil recovered from lU Sand and 5U sand, respectively. When

waterflooding is extended up to 20 years, the recovery improves to 12.5% for

the lU sand. At 20 years there is no more oil recovered from the 5U sand

indicating that the 5Usandhas reached the ultimate recovery. After 40 years

of waterflooding, there is no increase in oil recovery from both lU and 5U

sands. Thus, the scaling from coreflood geometry to reservoir matrix block

geometry in the lU and 5U Units of the Upper Spraberry zone resulted in oil

recovery ofonly13% lOIP after 40years ofwaterflooding.

-124-

0.160

0.--... / \ / \/ .O..® \J '® \ /\ * p-' \ ^

—A— Porosity \ /

••o ••Absolute Penneability ®,.o.

• .0'' \

0*' 0

RoufBcdng pay zone Non-pay muddy zone

0.140

0.120

a.2 0.100u

I0.080

10 0.060

04

0.040

0.020

0.000

7080 7082 7084 7086 7088 7090 7092 7094 7096

Depth in Shackelford 1-38A, feet

10.00

B1.00 s;

.0eo

£•w

o.,o I

0.01

7098

Fig.5-3 : Porosity and absolute permeability of Upper Spraberry lUUnit versus depth (data taken from Well Shackleford 1-38A)

0.160

0.140

0.120

J 0.100ts

I0.080

O 0.060cu

0.040

0.020

0.000

7215

-A—Porosity

•o •• Absolute Permeability

-125-

Ftourendng pay zone

7220 7225 7230 7235

Depth in WellE.T.O'Daniel 37, feet

10

1

jaC9

Is9

0.1 "o01

0.01

7240

Fig.5-4 : Porosity and absolute permeability of Upper Spraberry 5UUnit versus depth (data taken from Well E.T.O Daniel 37)

a

'•S•Mi

rS

I

16

14

12

I1& 10(SS

81 ®

o

1s

•a

2

7082

-126-

'-^Calculated Imbibition Oil Recoveiy

•Pore size

5 years waterfloodAverage Recovery = 9%Fracture Spacing = 3.79 ft

7083 7084 7085 7086 7087 7088 7069

Depth in Well l^iackelford l-SaA, feet

7090 7091

4.0

3.5

3.0

1.0

0.5

0.0

7092

Fig.5-5 : Calculated imbibition oil recovery for 5 years waterflood fromUpper Spraberry lUformation based on scaling ofexperimental data and measured fracture spacing of3.79 feet.

§

I§1 a.al

III

I

7220

-127-

5 years waterfloodAverage Recovery=11%Fracture Spacing = 3.79 ft

•Calculated Imbibition Oil Recovery

•Pore size

7225 7230 7235

D^th in WenE.T.ODaniel 37, feet

7240

6.00

5.00

4.00 ^

fW

3.00

cn

S(22.00 ^

1.00

0.00

7245

Fig.5-6: Calculated imbibition oil recovery for 5years waterflood fromUpper Spraberry 5Uformation based on scaling ofexperimental data and measured fracture spacing of3.79 feet.

7080

4>7a82--

7084-•

g 7086

pSs 7088MQQ

« 7090

.aja 7092

ft

® 7094 +

7096

•128-

C^ciilated Recoveiy Based on Lnbibitiaa Model, %lOlP2 3

-1—I—y-

4 5 6

I . I • I

' 1 year iminbition-floodiiig

' 10years imbibitiaQ-floodiiig

' 20 years imbibition-fioodiiig

10 11 12 13 14 15

H—.—I—I—I—1—I—.—I—.

-5 years imMbition-flooding

-15 yeais imbibitioi>floodiiig

-40 years imbilntian-floQiiig

Fig.5-7: History ofwaterflood recovery profiles from Upper SpraberrylU formation based on scaling of experimental data andmeasured fracture spacing of3.79 feet.

7210

7215-

«

<5

I> 7220-CO

3*i 7225QbH 7230

^ 7235.9^ 7240A

7245

7250

-129-

C^culated Recovery Based on Imbibition Model, %[OIP

1 year imbilntian-flooding

10years imbibition-flooding

-20years imbibition-flooding

10 11 12 13 14 15

H r—t-

e-5 years imbilntion-flooding

15years imbibition-flooding

40years imbibition-flooding

Fig.5-8: History ofwaterflood recovery profiles from Upper Spraberry5U formation based on scaling of experimental data andmeasured fracture spacing of3.79 feet.

-130-

For further analysis, the calculated recovery of lU and 5U sands were

plotted versus time. The average permeability and porosity for both sand

units (lU and 5U) as input data in the calculation was tabulated in Table 5-

1, Because waterflooding in this field has been ongoing for 40 years, the

recovery analysis is performed on the basis ofthis time period. Equation (5.9)

was then utilized to analyze 40 years of waterflood performance in the

Spraberry Trend Area reservoir. The result is plotted in Fig. 5-9. This figure

indicates that the time reqxiired to recover oil on the basis of the contribution

of imbibition mechanism fi-om 5U Unit sands is almost double that of the

permeability of the lU unit sands. Based on Table 5'1, the average porosity

for both sand units are almost the same. However, the average permeability

in 5U Unit is higher than that in lU Unit. Figure 5-9 shows that the matrix

permeability is one of the key factors affecting this oil recovery mechanism.

As expected, higher permeability results in faster recovery of oil until an

ultimate recovery of about 13% lOIP is reached. For the Spraberry, this was

achieved after 11 years of waterflooding. This implies that no more oil can be

produced by the imbibition process after the field undergoes 11 years of

waterflooding. This also confirms that the calculated imbibition oil recoveries

are in agreement with the observed 8 to 15% lOIP for 40 years of waterflood

experience in the Upper Spraberry sand. The ultimate recovery for each zone

is indicated to be the same for each zone by Fig. 5-9.

do

14

12-

10-

-131-

Table 5-1. The average absolute permeability and porosityfor both sand units (lU and 5U) in SpraberryTrend Area Reservoir

Sand Units Absolute Permeability(mD)

Porosity(%)

lU Sand 0.34 10.10

5U Sand 0.70 9.93

rs-

a 0o|2

Q

8-

Porosity = 10.10%, Permeability = 0.34mD —

-A-Porosity =9.93%, Permeability=0.7 mD T

/ Of 40years

5U Unit Sand

/ lUIMtSand

P&rameters for 40 vears waterfloodinfir:TmhihitinnEfficiencys 13%

Fracture Spadngs 3.79 ftBrine Viscosity s 0.68 q>Oil Viscosity s 5.92 q)Inter&cial Tension = 26.22 dyn^cm

6-

4-

2-

10 100

Tune, Years

Fig.5-9 : Calculated imbibition oil recovery for 40 years waterflood fromSpraberry lU and 5U formation based on scaling ofexperimental data and using the same fracture spacing of3.79feet for both units.

-132-

5.2.2 Recovery Field Performance

Evaluation of the fluid saturation of the Spraberry field is an

important parameter to be determined. The initial water saturation (Swi) and

current oil saturation (Sor) are crucial data for estimating waterflood

performance, i.e., displacement efficiency and volumetric sweep efficiency.

These data can be used to explain the low recovery in Spraberry Trend Area

reservoir.

Fluid saturation. Water saturations have been evaluated on the

basis of permeability cutoff criteria to determine the oil saturation of the

Spraberry field. In 1953, Elkin used a cutoff of Swi = 60%, which roughly

corresponds to a permeability of 0.1 mD. Baker (1996a) determined the

average water saturation of cores taken fi-om four wells in the Spraberry

field. He used air permeabilities cutoff value of 0.3 and 0.8 mD for these

cores. The average water saturation was determined to be 49.3% and 52.6%

for cutoff of 0.3 mD and 0.8 mD, repectively. These values corresponded to

50.7% and 47.4% oil saturation (assuming no gas saturation to be present).

By reviewing all methods of analysis to estimate initial water saturation.

Baker concluded that the initial water saturation in the Spraberry rock is

about 30 to 40%. The water saturation data and reservoir oil recovery by

waterflood were then used to determine the displacement ef&ciency and

volumetric sweep efficiency. Initial water saturation was established based

on cores taken fi-om 46 wells drilled prior to waterfiooding before 1954

-133-

(Schechter 1996b). In this study, the initial water saturations based on data

from Guo (1995) were re-plotted against the absolute permeability ofcores, as

presented in Fig,5'10. The correlation of the average initial water saturation

was then determined to be:

Swi = 0.20 + 0.13 e-o-6(k-o.i) (5 ID

where Swi is the initial water saturation and k is absolute permeability of the

core in millidarcies. From the plot, the high water saturations in the higher

permeability rock are probably associated with a microporosity system in

which both the oil and the water are immobile (Baker, 1996a).

The current water saturations (Sw) were then analyzed using cores

taken from wells that were waterflooded. The plot of absolute permeability

versus water saturation is shown in Fig. 5-11. By assimiing there is no gas

saturation, the current oil saturation can be determined. The results of this

analysis are presented in Table 5-2. These data will be used later to

determine the displacement ef&ciency and volumetric sweep efficiency.

0.50

0.45

0.40

ofa a®0

2 0.30

1M 0.25

I^ 0.20•C 0.15•fN

A

0.10

0.05

0.00

-134-

Table 5-2. Evaluation of Water Saturation and Current Oil Saturation

Source of Data Year kairc *b) Sw Sor

(mD) (%) (%) (%)

Tippett 5 1963 0.76-1.31 26-29 37-40 63-60

Nannie Parish 7 1974 0.13-0.40 31-33 43-50 50-57

Judidn A5 1987 0.15-0.70 29-33 40-50 50-60

Pembrook 9407 1990 0.06-0.80 29-33 42- 50 50-58

Notes: (a) from Guo (1995)

(b) using Eq. (5.11)

• 44 wdls oared befiH« 1961

• •

A SbowdenNd 1(1951)

X PtentowkNd 2(1954)

Average rfInitial WaterSatuFation

XX

AA

A

A

: •••

"t •

•A

AverageafS^:

A

^ A ^AaA"®

A

Sui =0.2+ 0.13 e'0.6(k-ai)

• ' • I 1 • • ' • 1 • • ' • 1 ' ' • •

0.0 0.5 1.0 1.5 2.0 25

AbsolutePermeability, mD

3.0 3.5 4.0

Fig.5'10. Initial water saturation in the Spraberry reservoir.

0.7

0.6

ta

i

I

0.5-

10.4-

§

u

IGO

I

0.3-

0.2-

0.1-

0.0-h-*

0.0

-135-

^—Average Initial Water Saturation

• TlppettSdSeS)

A P&rish-7(1974)

• Judkins-5(1987)

X Pfeiiibrook.9407(1990)

•H—'—'—'—'—I—'—'—'—'—I—'—^

0.5 1.0 1.5

Absoliite Permeability, md

2.0 2.5

Fig. 5-11: Evaluated water saturations after wells have been waterflooded

in the Spraberry reservoir (data from Guo, 1995).

-136-

Displacement Efficiency (EdispO* The displacement efficiency is the

ratio between the amount of oil displaced and amounts of oil contacted by

displacing fluid (Lake, 1989). The displacement efficiency can be determined

by initial water saturation and current water saturation of the rock.

Assuming that the oil and gas are produced during waterflooding (no gas

saturation in the rock after waterflooding), the displacement efficiency can

then be determined using the following equation:

l-5^w/ -Spr _ (5.12)^dispL-

where Swi is initial water saturation, Sor is current oil saturation of residual

oilsaturation, and Sy^ is current water saturation.

Volumetric Sweep Efficiency (Evoi). The volumetric sweep efficiency

is defined as the ratio between the volume of oil contacted by the displacmg

fluid and the volume of oil originally in place (Lake, 1989), It can be

calculated using the correlation between oil recovery (Er) and displacement

efficiency. The equation canbe rendered as :

Er —Efjispl. ^ Eygj^ical ^ ^areal

if

Eyoi = ^vrrtica/ ^ ^areal

therefore.

- 137-

Er^vol=-^ (5.14)

^displ.

Oil recovery in the Spraberry field after more than 40 years of

waterflooding is estimated in the range of 8 to 15% lOIP. Thus, the

displacement and volimietric sweep efficiency in the Sprabeny can be

determined using the water saturation data presented in Table 5-2 and the

estimated oil recovery fi-om waterflooding. The results are presented in

Table 5-3.

The results show that the volumetric sweep efficiency in the Spraberry

reservoir ranges firom 47 to 83%, which is much higher than the displacement

efficiency (15 to 26%). The high volumetric sweep ef&ciencies £ire also

supported by infill drilling and pressure interference testing data. The infill

drilling programs in Spraberry tend to produce wells with high water cuts

indicating that water has contacted a large portion of the reservoir fi-acture

system (Baker, 1996a), and pressure interference test dtiring waterflooding

showed conclusively that pressure commimication was very good (Elkin,

1960). Low displacement efficiency is indicated by low recovery imbibition

experiments. The results show that the waterflood was less successful than

t3rpical waterfloods primarily becatise of low imbibition displacement

efficiency, not because of poor volumetric sweep efficiency. However, the

maximum recovery by imbibition, as indicated previously, is about 13%.

-138-

Table5-3. Evaluation ofDisplacement Efficiency (Ed) and VolumetricEfficiency on basis of Cores from Different Wells

Source of Data Year Swi(%)

Sw(%)

Edis/'(%)

c (d)Cvol

(%)

Tippeti 5 1963 26-29 37-40 15-16 76-83

Nannie Parish 7 1974 31-33 43-50 18-26 47-68

Judkin A5 1987 29-33 40-50 15-26 47-78

Pembrook 9407 1990 29-33 42- 50 19-25 48-64

Note: • (c)usingEq. (5.12) • (d) usingEq. (5.14)

• Average ofreservoir oil recovery is 12% lOIP

5.2.3 Sensitivity Study of Imbibition Model

Previously, several key parameters involved in the analysis of the oil

recoveiy mechanism based on the imbibition model have been described.

Understanding the individual parameters of the recoveiy mechanism helps

define the effects, interaction, and range of these key parameters. Matrix

permeability and fracture spacing are used in this study to define and limit

the uncertainty of the reservoir model. The contribution of the imbibition

process is a dominant effect on oil production. It is analyzed here by

performing sensitivity studies in the Humble Pilot Waterflood.

A pilot waterflood program was inaugurated on Humble's L.H.

Shackelford B lease in the west central portion of the Spraberry Trend Area

in March 1955. The pilot consisted of four injection wells with a center

-139-

producer, creating a confined 80-acre five-spot pattern. Oil production firom

the center well increased within six months of initiating water injection. The

water injection was then stopped. Although injection had stopped, the center

well still produced oil at a higher rate above primary.

The reservoir performance in this pilot study demonstrated non-

conventional waterflood characteristics according to observed Sraberry area

response. It appears that during the first injection, the injected water

displaced oil fi-om the firactures and simultaneously imbibed into the matrix.

When injection was stopped, the water continuously imbibed into the matrix

rock to expel oil fi-om the matrix, which resulted in improvement of oil

production. The imbibition mechanism is believed to have strongly affected

the waterflood recovery mechanism.

The Humble pilot was considered a successful Spraberry waterflood.

Subsequently, fiill-scale waterflood was initiated. However, the performance

did not emulate the results ofthe Humblepilot. Understanding the difference

between this pilot and field-wide waterflooding is vitally important for

improving waterflood performance in theSpraberry Trend Area.

Reservoir Parameters. The initial oil in place(lOIP) in the pilot area

was estimated to be about 724,181 reservoir barrels. The mechanism of

primary oil production in the Spraberry Trend Area is believed to be

dominated by solution gas drive (Elkin, 1953). The gas saturation after

reservoir repressurization by waterflooding was assumed to be zero. The

-140-

reservoir parameters used in the calculation of oil recovery based on the

imbibition model are summarized in Table 5-4. A recent horizontal core

study by Lorenz (1996) showed three distinct fracture sets. The fracture sets

present in cores from the lU and 5U reservoirs trend NNE, NE and ENE.

Table 5-5 presents the spacing of these sets. As shown in the table, the

arithmetic average of the fractures spacing is 2.86 fl. All data were then used

as the input for performing the sensitivity analysis ofoil recovery for 15 years

of waterflooding experience.

Table 5-4. Reservoir parameters as input data

Area 80 acreNet Pay 20 feetBulk Volume 69,696,000 cuftPorosity 10.02 %Pore Volume 6,983,539.20 cuftWater saturation 31.53 - 33.72%Gas Saturation (assumed after waterflood initiated) 9.0 - 9.3%Oil Saturation 57.3-59.2%Initial Oil In Place 712,404 - 735,957 rbImbibition Efficiency 13%

Recoverable Oil 92,613 - 95,674 rbOil Formation Volume Factor 1.294 rb/STBInterfacial Tension 26.22 dyne/cmViscosity 2.01 cp

Table 5-5. Fracture Spacing

Fracture Set Spacing Range (ft) Average Spacing (ft)

NNE 0.05 - 4.50 1.62

NE 0.73 - 5.75 3.17

ENE 0.04-13.00 3.79

Average 2.86

-141-

Matrix Permeability. Matrix permeability is an important parameter

in modeling imbibition data, because when water comes in contact with the

oil zone, water may imbibe into the matrix block to displace oil. Higher

permeability results in less time required for the water to imbibe into the

matrix block.

In this study, to investigate the effect of matrix permeability on field

recovery mechanism, four values of permeability (i.e., 0.01, 0.03, 0.10 and

0.30 md) were used. Based on the experimental imbibition results from core

plugs, the imbibition efficiency is 13% and the constant rate of imbibition (A.)

is 0.0053. Using initial water saturation as a function of absolute

permeability (Eq.ll), an average fracture spacing of 2.86 ft, and an average

porosity from logs of 10.02%, the oil recovery using the imbibition model for

15 years of waterflooding is simulated and the result is presented in Fig.5-

12. From figure 5-12, the recovery rates of this pilot field, as expected, are

dependent on the matrix permeabiUty. An increase in the matrix

permeability results in an increase in the rate of recovery. For the reservoir

with the highest matrix permeability to reach the ultimate recovery of 13%

takes approximately six years. The production rate drops from 185 Bpd to

below 10 Bpd within six years of production (see Fig.5-13). For reservoirs

with lower matrix permeability, afi;er 15 years of waterflooding the recoveries

still increase with time.

-142-

Fracture Spacing. Fracture permeability is a function of fracture

spacing. A decrease in fracture spacing results in an increase in fracture

density and therefore an increase in the fracture permeability. To investigate

the effect of fracture spacing on the recovery after 15 years of waterflooding,

the four sets of fracture spacing shown in Table 5-5 were used in a

sensitivity study. The calculated matrix permeability was 0.1 mD while the

other parameters were the same as the previous calculation in the sensitivity

of matrix permeability. The model assumes that all fractures are evenly

spaced, perpendicular and extend the full length of the zone. The result

presented in Fig»5'14 shows that recovery is sensitive to fracture spacing.

Increasing the fracture spacing jdelds improvement in recovery. For example,

the ultimate recovery is achieved within five years for the shortest fracture

spacing, while the ultimate recovery is not reached yet for the longest one

after 15 years of waterflooding. When the average fracture spacing is 2.86 ft,

the ultimate recovery will be reached after 15 years of waterflooding.

Production Decline. The sensitivity sinalysis for the production

decline parameters is presented in Fig, 5-15, Figure 5-15 shows that the

decline rate constant increases with matrix permeability and also increases

with decreasing fracture spacing. The figure shows that for the lowest

fracture spacing (1.62 ft), the decline rate constant increases rapidly with

small increases in permeability. Thus it appears that both the matrix

permeability and the fracture spacing affect these parameters.

-143-

k=:0.01mD

k=0.03mD

k=0.1inD

k=0.3mD

Tiiiie, Years

Psirainetera:

IOIP=712,404 - 735,957 ri)

IU = 13%Porosity = 10.02%Bb = L294riySrB

Fracture spadng, 1^= 2.86ft

Srt=0.2+0.13e^'^"

Fig. 5-12 : Effect ofMatrix Permeability on Imbibition Recovery.

250

>»200-

150-

100-

-144-

lOIP = 712,404- 735,957ibIU = 13%Porosity = 10.02%

Bb= 1.294 riySTB

Fracture spacing, L, s 2.86 ft

S«i =0.2+0.13e-®®^-^"

Apta

10

Tiine, years

k = 0.01mD

k = 0.03niD

— - 'ksO-lniD

k=:0.3inD

12 14 16

Fig.5-13 : Effect of matrix permeability on calculation of productionrates.

-145-

U = 1.62ft

lOIP=712,404 - 735,957 rb

IU = 13%Porosity = 10.02%Bb = 1.294 riySIBMatrixpermeability =0.1mD8^=0.2 +0.136^®''"*^"

— - •!£ = 2.86ft (averagefracture spadn^

l£ = 3.17ft

Ls=3.79ft

Time, Years

Fig.5'14 :Effect ofFracture Spacing on Imbibition Waterflooding.

0.006

0.005-

Q 0.004

§O 0.003

= 0.002

0.000-

146-

-e-Ls = 162ft

Ls=2.86ft (aweragB fiadiirespacing)

-6-l£ = ai7ft

0.05 0.10 0.15 0.20 0.25

lVfe±ixK Permeeliilily, noD

ax 0.35

Fig.5-15: Effect ofMatrix Permeability and Fracture Spacing on theDecline Rate Constant

-147-

5.3 UPSCALING OF DYNAMIC IMBIBITION DATA

5.3.1 Critical Fracture Capillary Number

There are two processes involved during waterflooding of a fractured

core, spontaneous imbibition (capillary forces) and displacement (viscous

forces). The efficiency of these processes can be defined in terms of a

dimensionless group we will refer to as the fracture capillary number (Nf,ca).

The fracture capillary number is a ratio of the viscous forces that are effective

in the fractures to the capillary forces that are effective in the matrix. This

dimensionless term can be used for upscaling parameters of laboratory

dimensions to reservoir dimensions.

The viscous force is defined as fimctions of water velocity, water

viscosity and fracture cross sectional area and it is assimied that the forces

occur only in the fr^icture. While the capillary forces, which occur only in the

matrix, is defined as functions of interfacial tension, contact angle and matrix

volume. Thus, the equation can be written as follows:

Viscous Forces vfj^ Af .eNf = = (.5.15)

Capillary Forces CTCOS0

where v is the velocity of the injected fluid into the fracture, ^iw is water

viscosity, Afis the fracture cross section area, c is the interfacial tension, h is

the contact angle. Am is the matrix volume.

-148-

In lab units unit the equation can be rewritten as follows:

^ 0.0127 (cc /hr)ii^ {cp)

A^icm ),

In a similar manner, the lab units can be written to field units as :

0.0905 qinj (STB / day)]U^ (cp)N

krnimd)

/a2x

AS^i) ^km(md)

0,m

(5.16)

(5.17)

The derivation ofthis equation is presented in Appendix-B.

Higher firacture capillary number (higher rate, water viscosity or

fracture permeability) results in stronger tendencies of water to flow in the

firactures. Whereas, the lower values of the fi-acture capillary number, which

is provided by the slower rate (weaker viscous forces), cause stronger

capillary imbibition.

In order to upscale laboratory experiment to field dimensions,

equation 5.16 was used to produce plots as presented in Fig, 5-15, This

figure shows the correlation of the firacture capillary number with oil-cut

(OPFM/TIW). As shown in Fig,4'36, the laboratorjr's critical injection rate is

20 cc/hr and 10 cc/hr for Berea and Spraberry cores, respectively. If these

values are converted into dimensionless terms, the fi-acture capillary

nvunbers are 0.00028 for Berea cores and 0.0001 for Spraberry cores. It

-149-

means, the limiting capillary number in these experiments was to be 0.00028

and 0.0001 for Berea and Spraberry cores, respectively, which beyond a

limiting capillary fracture number, the capillary imbibition dominated

displacement in artificially fractured porous media can be considered as an

inefficient process.

0.45 -

0.40 -

0.35 -

0.30 ^

0.25 -

0.15 •

0.05 •0.0001

O Experimental data from Berea cores

^ Experimental data from Spraberry

Viscous forces

Capillary forces

^ 0.0127 qinj{cclhr)n^(cp)

0.00028

Berea cores

Spraberry cores

0.0001 0.0002 0.0003 0.0004 0.0005

Fracture Capillary Number, Nf,ca

Fig. 5-16: Fracture capillary number versus oil-cut for Berea andSpraberry cores.

0.0006

-150-

Once the fracture capillary number is found, the laboratory data can

be upscaled to reservoir dimensions. The critical rate of water injection for

field dimensions can be calculated using a rearranged of Eq, 5-17. The

upscahng of laboratory data to field dimensions is tabulated in Table 5-6,

and Berea sandstone is used as comparison. For the Spraberry waterflood

case, the waterflood pilot consistes of four injection wells with a center

producer for creating a confined 80-acre five-spot pattern, 0.1 matrix

permeability, 10% porosity and 10 ft pay zone, the critical injection rate is

about 751 bbl/day water.

Table 5-6: Upscaling ofdynamic imbibition experiments to determinecritical injection rate.

Porous

mediumBerea sandstone Sprab(^rry

Dimension Core size Field scale Core size Field scale

Nf.ca 0.00028 0,000110

Area - 80 acre -80 acre

|Xwater 0.68 cp 0.68 cp 0.68 cp 0.68 cp

Linj-prod 7.12 cm 1320 ft 6.8 cm 1320 ft

h 3.63 cm 10 ft 3.7 cm 10 ft

Ani 25.81 cm2 13200 ft2 24.8 cm2 13200 ft2

k 63.41 md 63.41 md 0.1 md 0.1 md

<!> 16.6 % 16.6 % 10% 10%

Pcmax 1.2 psi 1.2 psi 7 psi 7 psi

J (Swi) 0.99 0,99 0.2 0.2

Critical Water 20 cc/hr 1435 bbl/day 10 cc/hr 751 bbl/day

-151-

The fracture capillary number concept can be applied to the O'Daniel

Pilot Area to determine the critical water injection rates. This pilot area

consists ofsix water injection wells (two injection wells are perpendicular to

fracture orientation), four CO2 injection wells, three oil production wells, and

two loging-observation wells. Well location is shown in Fig* 5'16. Before C02

flooding, this pilot area will be waterflooded. The ciirrent oil reserve in this

area is estimated to be about 38,500 STB. The distance between center

production well (Well-39) and the four water injection wells (Well-25, 47, 45,

and 48) that are parallel to fracture orientation is presented in Table 5-7.

Using the fracture capillary number concept, the critical injection rate for

OT)aniel Pilot Area can be estimated, and the results are tabulated in Table

5-7.

Table 5-7: Estimated Critical Injection Rates for Wells in 0*DanielPilot Area.

InjectionWell

Distance to well-39

(ft)

Critical waterinjection rate

(STB/D)

W.45 1420 807

W-47 1450 824

W-48 1460 830

W-25 1450 824

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52

-

Chapter 6

Conclusions and Recommendations

6.1 CONCLUSIONS

This study suggests the following conclusions:

1. Imbibition tests using Spraberry oil, brine, and Berea sandstone show

that

• Effect of pressure is much less importeint than the effect of

temperature on imbibition rate and recovery.

• Performing the imbibition tests at higher temperature results in faster

imbibition rate and higher recovery due to change in mobility of fluids.

• The effect of an increase in initial water saturation on the imbibition

recovery is related to decrease in imbibition capillary pressure, which

results in a decrease in ultimate oil recovery.

153-

-154-

2. Imbibition tests using Spraberry oil, brine, and Spraberry reservoir rocks

performed at reservoir temperature show that

• The final recovery due to imbibition varies from 10% to 15% of lOIP,

depending on aging time.

• Based on numerical analysis of the static imbibition process, the

ability ofwater to imbibe the matrix rock is weak, only 0.6 cm into the

core plug after 200 hours with the oil recovery less than 14% lOIP.

This result is due to very low capillary pressure during displacement

oil by water during the imbibition cycle.

• Change in mobility of fluids at higher temperature (i.e., reservoir

temperature) results in faster oil recovery with a greater ultimate

recovery compared to imbibition at ambient temperature.

3. Wettability determination conducted using Spraberry oil, synthetic brine

and Spraberry reservoir rock suggest that:

• Performing the imbibition tests at reservoir temperature and

displacement tests at room temperature indicate that WI is 0.3 to 0.4.

• Performing both imbibition and displacement tests at the same

temperature (i.e., reservoir temperature or at room temperature)

lowers the WI in range of 0.20 to 0.25; thus, temperature during the

experimental sequence affects wettability index determination.

• Comprehensive experimental data clearly demonstrates that

Spraberry reservoir rock is very weakly water-wet.

-155-

4. Performing the imbibition experiment under dynamic condition using

both Berea sandstone and Spraberry reservoir rocks as porous media

show that:

• Injection rate is an important parameter on the dynamic imbibition

process in fracture systems, as the flow rate increases, contact time

between matrix and fluid in fracture decreases causing less effective

capillary imbibition.

Increase in injection rate causes higher water-cut which results in

significantly faster water breakthrough.

The initial water satiu*ation for dynamic imbibition is similar to that

for static. When initial water saturation is not present in the core, the

rate of oil recovery is slower than for a core with an initial water

saturation. However ultimate oil recovery for core without initial water

saturation is higher than it is for core with initial water saturation due

to the capillary pressure effect.

• An effective capillary pressure curve can be obtained from dynamic

imbibition experiments by matching the recovery curves from

experimental data and numerical simulation.

The capillary ctirve obtained from dynamic imbibition experiments ishigher that it is from static imbibition experiments due to viscousforces during the dynamic imbibition process that are not present inthe static imbibition case.

-156-

• The limiting value of fracture capillary number for an efficient

displacement process in this study was found to be 0.0001 and 0.00028

for Berea and Spraberry cores, respectively. Beyond this range, the

displacement process is inefficient due to high water-cut.

5. Analysis of field fluid saturation indicates that the volvunetric sweep

efficiency in the Spraberry reservoir is much higher than the

displacement efficiency. This indicates that the waterflood in the

Spraberry trend was less successful than tjrpical waterfloods primarily

because of very poor imbibition displacement efficiency. The results from

this work support this observation.

6. Scaling of imbibition data under reservoir conditions indicates that the

contribution of the imbibition mechanism to oil recovery is up to 13%

lOIP, depending on rock properties and wettability.

7. Degree of heterogeneity in the matrix and natural firacture systems

controls the efficiency ofSpraberry waterflood performance.

-157-

6.2 RECOMMENDATIONS

1. Since the dynamic imbibition is more representatives of reservoir

conditions, it is necessary to correlate the static and dynamic tests in

order to achieve proper upscaling.

2. The capillary pressure curve obtained from dynamic imbibition

experiments using artificially fractured core can be used as input data in

naturally fractured reservoir simulations instead of using mercury

injection capillary pressure curves or difficult to measure imbibition

capillary pressure curves.

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APPENDIX-A

Mathematical Models to Scaling-up

the Experimental Imbibition Data

The imbibition process may be mathematically modeled using the followingrate law governing mass transfer (Guo, et al. 1998):

dV^=-AV« (A-l)

where V is the volume of oil in place recoverable by imbibition, t is time, Ais aproportionality coef&cient, and a is an empirical exponent. Equation (A-l) iswidely used in chemical engineering and frequently employed by petroleumresearchers such sis Gupta and Civan (1994) for analyzing mass transfer innaturally fractured reservoirs.

If an initial condition of V=Vo at ^=0 is used, where Vo is the volume ofrecoverable oil by imbibition, the following two solutions to Eq. (A-l) can beobtained:

V=V^e'^ (A-2)

for a = 1, and

1

V=[v/"-A(l(A-3)

for a not equal to unity.

1. Recovery Equations.

Dimensionless oil recovery due to imbibition is defined as

V -V(A-4)

" o

Substitutions of Eqs. (A-2) and (A-3) into Eq. (A-4) result in

(A.5)

A-l

APPENDIX-A

for a = 1, and

1-X{\-a)t

\-a

\-a

(A-6)

for oc not equal to unity.

2. Production Decline Equations.

The volume of produced oil (cumulative oil production due to imbibition) isexpressed as:

y,=yo-v (A-7)

Substitution of Eq. (A-2) into Eq. (A-7) yields:

(A-8)

An expression for oil production rate is obtained by taking the derivative ofEq. (A-8) with respect to time:

dV(A-9)

Eq. (A-9) represents an exponential decline model.

Other decline models can be derived from Eqs. (A-3) and (A-7). Substitutionof Eq. (A-3) into Eq. (A-7) yields:

l-a

Taking derivative ofEq. (A-10) with respect to time gives:

dV,dt

1 +

l-a

Xat

V'""(^—)Of

o-l

A-2

(A-10)

(A-11)