s Krit Pum Petro Reservoir

8/16/2019 s Krit Pum Petro Reservoir

1/65


2/65

2

CHAPTER 9 NMR MEASUREMENTS ........................................................................... 58

9.1

FUNDAMENTALS ........................................................................................................... 58

9.2 APPLICATIONS............................................................................................................... 59

9.3

NMR DATA PROCESSING .............................................................................................. 60

9.4

PERMEABILITY FROM NMR .......................................................................................... 61 9.5

SUMMARY ..................................................................................................................... 62

CHAPTER 10 SUMMARY .................................................................................................. 63

CHAPTER 11 REFERENCES ............................................................................................. 64


3/65

3

CHAPTER 1 INTRODUCTION

Fundamental Problems

Oil and/ or gas reserves ? ... Production ?

Geometry of the reservoir

Reservoir properties

- porosity

- saturation

- permeability , cap . pressure

Change of reservoir properties

( saturation = f(t), monitoring )


4/65

4

The growing interest in petrophysics results from the need to extract more informationfrom geophysical measurements concerning the accuracy, reliability and representativevalidity of the results from:

the increasing importance of reservoir rock characterisation with respect to their

fundamental properties like porosity, permeability, rock composition, the particular interest in reservoir fluids, their motion and distribution also as a

function of time the "broadening" of the spectrum of rock types, which are of interest, ranging

from granular pore reservoirs to fractured rocks, the dramatic development concerning "input data" by the modern equipment, the development of integrated techniques and methods, particularly seismic and

well logging.

Petrophysics is a key in the network of applied geosciences and related engineeringdisciplines - it must connect the various properties of rocks. The optimal use of allrelevant information is the crux of a modern interpretation.In this way, petrophysics

is integrated into the general techniques, strategies, algorithms, and thecomplete process of exploration, and simultaneously it

is an integrating part of this process, because rock physics couples andconnects the different disciplines.

"Petrophysics" is suggested as the term pertaining to the physics of particular rocktypes. ... This subject is a study of the physical properties of rock which are related tothe pore and fluid distribution ..." [G.E. Archie (1950), a pioneer in the application andquantification of rock physical relations to geosciences and petroleum engineering.]


5/65

5

Seismic and geological data

on extent

Reservoir pore volume

Water and hydrocarbon

saturation

Fluid flow characteristics

Reservoir engineering models

Oil recovery predictions

Laboratory tests

Porosity (overburden

corrected)

Core resistivities (m,

n, Pc, ... )

Absolute and relative

permeability

Field tests

Shale indicators,

Porosity tools, NMR

Resistivity tools

and NMR

Well flow tests

and NMR

Figure 1 Reservoir Engineering - Data Sources (modified after Glover,)

Information is derived from: Geology, lithology, sedimentology, maps, profiles, seismicstructure, reservoir architecture, hydrocarbon indications, wells, cores, cuttings, logs,tests – therefore cooperation between different disciplines is essential.


6/65


7/65

7

CHAPTER 2 RESERVOIR ROCKS AND KEY PROPERTIES

2.1 ROCKS AND THEIR CLASSIFICATION

Geological classification Igneous rocks (magmatites, eruptiva) Metamorphic rocks (metamorphites) Sedimentary rocks (sediments)

Igneous rocks are crystallized from molten fluid/magma:a) plutonic rocks: Intrusion into pre-existing rocks, crystallize below surfaceb) volcanic rocks: crystallize on the surface as lava.

granite gabbro basalt

Figure 2: Igneous Rocks – Examples (Source: http://geology.about.com/library)

Sedimentary rocks are deposited on the ground or ocean bottoma) Clastic sediments (weathered rock particles)

b) Organic sediments (e.g. seashells, diatomeen)c) Chemical sediments (precipitated salts)

conglomerate sandstone limestone shale

Figure 3: Sedimentary Rocks –Example (http://geology.about.com/library)

Metamorphic rocks (for example gneiss) are recrystallized under high temperature,

pressure and long time.

Rocks are heterogeneous and structured systems.

Figure 4: Rocks Demonstrating theHeterogeneity and Internal Structure/Texture

http://geology.about.com/libraryhttp://geology.about.com/libraryhttp://geology.about.com/libraryhttp://geology.about.com/library


8/65

8

In terms of physics we define two pairs of general properties:Isotropy and Anisotropy Homogeneity and Inhomogeneity

isotropic-inhomogeneousisotropic-homogeneous

anisotropic-homogeneous anisotropic-inhomogeneous

isotropic-inhomogeneousisotropic-homogeneous

anisotropic-homogeneous anisotropic-inhomogeneous

Figure 5 Isotropy – Anisotropy and Homogeneity – Inhomogeneity

2.2 RESERVOIR ROCKS

Hydrocarbons are accumulated in the pore space of the reservoir rock. In this sectionwe discuss reservoir rock properties with respect to the following questions:

Porosity: how much space is in the rock?Saturation: how much is occupied by oil, gas, water?Permeability: at what rate I can produce?

Determination and derivation of reservoir propertiesDirect: Measurements on samples (cores) in core laboratories. Limited volume, “point-information” Indirect: from logs (well log measurements, formation analysis). Continuousinformation as a curve. But a “calibration” is necessary (comparison with laboratorydata or tests).

The two major reservoir rock types

Clastic rocks (Sandstone) Carbonatic rocks (Limestone, Dolomite)

have different pore properties, different abundance, and importance for world’sproduction.

2.2.1 Clastic Rocks

Clastic rocks are formed by erosion: reworking, transportation deposition/sedimentation compaction, diagenesis

Typical members are sandstone, siltstone, claystone, shale.Classification principle of clastic rocks is the grain sizesandstone

siltstone

claystone

decreasinggrain size


9/65

9

Pelites PsephitesPsammites

Clay GravelSandSilt Boulder

f cm f cm f cm

0.002 0.02 0.20 2.0 20

0.0063 0.063 0. 63 6.3 63

size

mm

Pelites PsephitesPsammitesPelites PsephitesPsammites

Clay GravelSandSilt Boulder

f cm f cm f cm

Clay GravelSandSilt Boulder Clay GravelSandSilt Boulder

f cm f cm f cm

0.002 0.02 0.20 2.0 20

0.0063 0.063 0. 63 6.3 630.0063 0.063 0. 63 6.3 63

size

mm

phi-scale:

ph i = - l og 2 d

where d is the grain diameter in mm

Figure 6 Grain Size Nomenclature for Clastic Rocks

Grain size analysis (distribution): Determination at disaggregated samples: Sieve analysis: Mesh size of sieve; Sand and gravel fraction Sedimentation analysis: Stokes law; Silt and clay fraction

Laser Particle Size Analysis; Scatter of a laser beam.

100 10 1 0.1 0.01 0.001Grain size in mm

0

20

40

60

80

100

Percentfiner

100

80

60

40

20

0

Percentcoarser

boulder gravel sand silt clay

well sorted poorly sorted

Figure 7 Grain size distribution curve for two sediments.

Clay has a strong influence on all properties: it decreases the pore space it reduces permeability

A source of confusion: clay - clay minerals – shale

Clay - is defined as a particle size ( < 0.002 mm) Clay minerals - are a group of phyllosilicates with specific properties (CEC,

double layer) Shale is a rock type (high amount of clay minerals, but also fine grained

feldspars, quartz, … Shale

consists of clay minerals and other fine particles. The clay fraction in shale about 40 .... 90 %. shales are low energy clastic sediments.

Types of clay distribution:

Laminar clay - thin clay layers alternating with sand Dispersed clay - clay in the pores (also authigenic clay, diagenetic clay) with a

strong influence on reservoir properties (decrease of effective porosity and

permeability) Structural clay - clay forms grains and is a rock building component.


10/65

10

Figure 8 Types of Clay Distribution in Sedimentary Rocks

Clay minerals and mineral structures have a large active surface area can bind large volume of water at surface and between layers have negative surface charge - attract and exchange cations contain K, U, Th in different form.

2.2.2 Carbonate and Evaporite Rocks

Carbonate and evaporite rocks are formed by chemical or biochemical precipitation. -Carbonates mineralogy is usually simple. Principal minerals are calcite, dolomite,(minor clay); secondary minerals are anhydrite, chert, and quartz; Accessory minerals are: phosphates, glauconite, ankerite, siderite, feldspars, clayminerals, pyrite, etc. But pore space is complicated!

We distinguish two main reservoir rock types: Limestone is composed of more than 50 % carbonates, of which more than

half is calcite CaCO3 Dolomite is composed of more than 50 % carbonates, of which more than half

is dolomite CaMg(CO3)2

Figure 9: Some Pore Types of Carbonate Rocks


11/65

11

Petrophysical Classification Carbonate Pore Types (Lucia, 1999)

Compare the two groups: Clastic rocks Carbonatic rocks

difficult mineralogical composition, but asimple pore geometry,

simple mineralogy, but a complicatedpore geometry

2.3 LABORATORY DETERMINATION OF PROPERTIES – CORE

ANALYSISCores are used for a direct determination/ measurement of reservoir properties(porosity, permeability etc.). They are also used for determination/measurement ofother physical properties (electrical resistivity) in order to derive relationships for loginterpretation (log measurements deliver an indirect reservoir characterization).

Petrophysicist’s Reasons for Coring: Porosity and Permeability (this was primary reason for coring until the advent of

quality gamma-gamma density tools) Source of critical petrophysical parameters (a, m, and n), Capillary Pressure,

Relative Permeability data, Wettability, … Geological Information Reserves/Saturation

Two techniques:

Conventional (or rotary) cores: 1 ¾ in (4.5 cm) … 5 ¼ in (13.5 cm)Note: Loss of core can indicate good reservoir rock. Sidewall core (percussion and rotary sidewall coring); 1in.


12/65

12

In most cases core is acquired using a metal sleeve. At the end of coring the core isrecovered from the barrel and taken in (3-ft) boxes.

Initial inspection and core description on site

homogeneity of the cored section type of porosity and permeability, cementation mineral content presence of fractures (open, filled, natural, drilling induced) presence of hydrocarbons

Plugs

Conventional Core Analysis:Cores are normally slabbed, cut in parts for measurements (plugs etc.), and cleaned(using a solvent)Determination ofporosity (helium porosimeter)- permeability- grain density

Special Core Analysis: Porosity and permeability at overburden conditions (equivalent stress field) Archie parameters (m, n)Capillary pressure measurementsFor homogeneity a CAT (Computed Axial Tomography) is powerful.

„Scaling“ Problem


13/65

13

CHAPTER 3 DENSITY, POROSITY, AND SATURATION

Rock density (bulk density) is controlled by- Density of components (minerals, fluids)

- Volume fractions (mineral content, porosity, saturation).

For reservoir characterization is importantPorosity: how much space is available for fluid storage?Saturation: which percentage of pore space is filled with different fluids (water, gas/oil)?

3.1 DENSITY

Definition

Density=mass/volumeUnit: g/cm3 or kg/m3

Distinguish between:- rock density, bulk density (i.e. sandstone)- density of the solid matrix material (i.e quartz)- density of the pore fluid(s) (i.e. water)

0 1 2 3 g/cm3

ores

gas oil,water rock forming minerals

Rock density decreases with

increasing porosity

Porous rock density increases

with increasing water saturation

(compared to dry rock) Figure.10: Density of Rock Constituents

Table: Density of RockConstituents

Note: density quartz < density calcite < density dolomite2.65 2.71 2.87

high density of anhydrite 2.96

Minerals density Minerals density

in g/cm3 in g/cm3

Quartz 2.65 Halite 2.16

Orthoclase 2.57 Anhydrite 2.96

Muscovite 2.83 Illite 2.64

Biotite 2.90 Chlorite 2.88

Calcite 2.71 Montmorillonite 2.61

Dolomite 2.87 Kaolinite 2.59

Fluids:

Fresh water 1.000 g cm-3

Formation water 120,0000 ppm NaCl 1.086 g cm-3

Oil (medium gravity 0.80 g cm-3

Gas (160°F, 5,000 psia) 0.20 g cm-3

Depending on

composition,

temperature,

pressure


14/65

14

1.00 1.50 2.00 2.50 3.00 3.50

Igneous rocks - intrusiva

Granite

Syenite

Diorite

Gabbro

Dunite

Peridotite

Pyroxenite

Igneous rocks - extrusiva

Rhyolite

Porphyrite

Diabase

Basalte

Tuffs

Metamorphic rocks

Quartzite

Marble

Phyllite

Schist

Gneiss

Amphibolite

Eclogite

Density in 103kg m-3

1.00 1.50 2.00 2.50 3.00

Sedimentary rocks - consolidated

Anhydrite

Dolomite

Limestone

Sandstone

Shale

Marl

Gypsum

Salt

Sedimentary rocks - unconsolidated

Sand, gravel

Loam

Clay

Lignite

Density in 103 kg m

-3

Figure 11: Overview densities for different rock types (Schoen, 2011)

As a result of the distinct differences between the mean matrix density range, there is astrong correlation between density and porosity.

3.2 POROSITY

Porosity gives a measure of the non-solid space in a rock. This volume fraction may beoccupied by fluids (gas, oil, water).Thus, porosity gives an answer to the question: “How much fluid could be in thereservoir?”

Definition

sample

pores

V

V

sampleof volumetotal

poresof volume porosity

sample

pores

V

V

sampleof volumetotal

poresof volume porosity

V m

V pV p

Pore p

1 -

Matrix m

Porosity Types (Tiab and Donaldson):“Engineering Classification”:

Total porosity Effective porosity

“Geological Classification”:

- Primary porosity- Secondary porosity


15/65

15

„ ... Amount of internal space or voids in a given volume of rock is a measure ofthe amount of fluid in a rock will hold ... Is called total porosity.

The amount of void space that is interconnected, and thus able to transmitfluids, is called effective porosity.

Isolated pores and pore volume occupied by adsorbed water are excluded froma definition of effective porosity but are included in the definition of totalporosity.”(Asquith & Krygowski, 2004)

Table Mean porosity for selected clastic rocks, data from Schopper, 1982Rock type Minimum porosity Maximum porositySt. Peter sandstone 3.6 14.1Berea sandstone (439 .. 458 m) 4.7 17.1Bunter sandstone 7.7 26.4Fontainebleau sandstone 6.8 22.4Shale, Venezueladepth 89 … 281 m

619 … 913 m 919 … 1211 m 1526 … 1677 m 2362 … 2437 m

31.3

22.917.812.810.3

35.8

28.925.614.610.4

Tendencies:

.

decreasingporosity

high porosity marine sedimentsunconsolidated sedimentssandstonescarbonates (limestone - dolomite)anhydrite, fractured igneous andother initially "dense" rock types

Porosity is controlled by- sedimentation process- rock type- grain size distribution- depth and compaction- cementation and chemical processes.

Primary and secondary porosity:

Primary: grain size, grain size distributiongrain packingparticle shape

Secondary: mechanical processes (compaction, plastic and brittle deformation,fracture evaluation, ...), geochemical processes (dissolution, prereciptation, volumereductions - mineralogical changes ...)

Clastic Sediments: Porosity versus Depth – The Compaction CurveWith increasing depth porosity decreases.The porosity-depth function is a nonlinear function, controlled by the mechanicalproperties of the sediment.In addition to compaction also chemical processes (cementation,

recrystallization, pressure solution etc.) can change the porosity.


16/65

16

Figure 12 Semilogarithmic Presentation

of Porosity vs. Depth Function, Experimental

Data for Sandstone; (Nagumo, 1965)We can describe this correlation by anempirical equation (Athy 1930, Nagumo1965):

)exp()( 0 z b z where0

is the initial

porosity (at depth 0 z ).

Porosity versus depth relationships for sandstone and shale from the Northern NorthSea (after Liu & Roaldset 1994; References: B - Baldwin & Butler 1985, S - Sclater &Christie 1985, L - Liu & Roaldset 1994):

Sandstone = 0.49•exp(-2.7 10-4 • z) S, BSandstone = 0.728-2.719 10-4 • z+2.604 10-8 • z2 LShale = 0.803 • exp(-5.1 10-4 • z) SShale = 0.803-4.3 10-2 • ln(z+1)-5.4 10-3 • ln(z+1)2 BShale = 0.803-2.34 10-4 • z+2.604 10-8 • z2 Lz in meter, as fraction

Compare Sandstone = 0.49 •exp(-2.7 10-4 • z) Shale = 0.803 • exp(-5.1 10-4 • z)

Initialporosity

Rock skeletoncompressibility

Carbonate Pore Space: Problems and difficulties of porosity and pore spacecharacterization of carbonates result from:

the variety of pore and fracture sizes variety of “pore- and fracture shape” connected and isolated pore volumes.

An important process is dolomitisation: Geochemical process, where Mg-ions replace Ca-ions, forming dolomite from

calcite Replacement of calcite by dolomite increases porosity and creates important

reservoir space Dolomitisation creates new intercrystalline pores that improved the connectivity

of the pore network.

2 CaCO3 + Mg2+ CaMg(CO3)2 + Ca

2+ 12.5 % shrinking by volume

4000

3000

2000

1000

depthinm

0.1 10.2 0.5

porosity


17/65

17

argillacious limestone

clean limestone

dolomitic limestone

dolomite

0.1 1.0 10 porosity%

4000

6000

8000

10000

1.5

2.0

2.5

3.0

depth kmdepth ft

Figure 13 Image Logs can help to

detect and to characterize pore types

and fractured zones

Figure 11 Porosity vs. Depth for

Carbonates

Compare the Pore Space of Clastic and Carbonate Rocks:

3.3 DETERMINATION OF DENSITY AND POROSITY IN THE CORELAB

- Gravimetric measurements (Archimedes principle)- Volumetric measurements(Gas pycnometer)- Directly (length, mass and diameter


18/65

18

3.4 SATURATION - FLUIDS IN THE PORE SPACE

Simplest case: One fluid (water) occupies the whole pore space (Sw = 100 %) General case: pore space is filled with two (Gas/Water, Gas/Oil; Oil/Water) or

three (Gas/Oil/Water) fluids. They are spatial distributed following wettability,interface forces, and pore geometry).

Saturation gives a measure of the volume-fraction or percentage of a particular fluid(gas, oil, water) in the available pore space.Saturation is defined as the volume fraction of a fluid divided by the pore volume.

volumepore

ifluidvolumesaturation

i

volumepore

ifluidvolumesaturation

i

Water saturation Sw - fraction of pore volume occupied by water Irreducible water saturation Sw,irr - fraction of pore volume occupied byimmobile capillary-bound water

Clay Bound Water Saturation - water bound to negatively charged claymineral surface

Oil saturation Soil - fraction of pore volume occupied by oil Gas saturation Sgas - fraction of pore volume occupied by gas.

Sw + Soil + Sgas = 1

The term “bulk volume fluid” refers to the total rock volume (the term “saturation”refers to the pore volume):

bulk volume fluid i = porosity x saturation fluid I

BVW Bulk Volume Water: fraction of pore volume occupied by water BVI Bulk Volume Irreducible: fraction of pore volume occupied by immobile

capillary-bound water CBW Clay Bound Water: water bound to clay mineral surface

Figure 15 VolumetricModel for Clastics and

Carbonates

matrix dry

clay

clay-

bound

water

mobile

water

capillary

bound

water

hydrocarbon

BVMBVI

PHI eff

total

CBW

clastics

matrix dry

clay

clay-

bound

water

mobile

water

capillary

bound

water

hydro-

carbon

BVMBVI

PHI eff total

CBW

carbonate

vug


19/65

19

CHAPTER 4 PERMEABILITY AND CAPILLARYPRESSURE

4.1 FUNDAMENTALS – DARCY’S LAW Porosity – how much pore space is available for fluids? Saturation – what is the fractional composition of the pore fluids (e.g. what is

the oil saturation)? Permeability – how much fluid moves in the pore space under the influence of

the pressure gradient? Relative permeability – what is the fractional flow of a particular fluid component

(e.g. oil) under the influence of a pressure gradient?

Definition: Permeability is the ability of a rock to transmit a fluid, controlled by the connected passages of the pore space (pore throats!)

Three types:Absolute permeability describes the laminar flow of a single non-reactive fluid.Effective permeability refers to the flow of one fluid in the presence of another fluid,when the fluids are immiscible.Relative permeability is the ratio of effective and absolute permeability

Darcy’s law (1856) for laminar flow

Figure 16: Permeability – Principle of Determination

Units:

Oil industry: Darcy (d) and millidarcy (md): A permeability of 1 d allows the flow of 1cm3 per second of water with 1 centipoise, cP, viscosity, through a cross sectional areaof 1 cm2, when a pressure gradient of 1 atmosphere pressure per centimetre is applied.S.I. unit: m2 Conversion: 1 d ~ 10-12 m-2


20/65

20

Laboratory Techniques and Correct ions

Figure 17 Permeameter (VINCI Technologies)

Permeameters (gas, fluids) – two effects corrections Klinkenberg Effect: at low gas pressures mean free path of gas molecules >

pore dimensions causes overestimated permeability correction Forchheimer Effect: at high flow rates the difference of flow velocity between

pore throats and pore bodies causes turbulence - but Darcy‘s law requireslaminar flow correction.

Methods for permeability determination (Georgi, 1997): Well and drillstem tests, Wireline formation testers Cores: conventional cores, core plugs, sidewall cores Wireline logs: NMR, Stoneley waves.

4.2 PERMEABILITY – CONTROLLING FACTORS AND INFLUENCES

The next two figures give an overview of the main influences and the extreme range ofpermeability values over decades:

Figure 18: Permeability – Mean Range of the Magnitude


21/65

21

4.2.1 Sandstone and shaleSmall Flat GrainsLarge Flat Grains

Large Rounded Grains Very Small Irregular Grains

Horiz Perm 2000 mdVert Perm 800 md




Figure 19: Sedimentary Rocks – Internal Texture and Structure Influences

Permeability (same porosity assumed); after Bigelow

First we note the strong correlation between permeability and porosity, but additionallythere is a strong influence of

pore or grain size grain shape and arrangement connectivity of pores

The following figures describe the controlling factors in more detail.

10-5

10-6

10-8

10-9

10-10

10-7

kinm2

10-1

100

101

102

103

104

kinmd

0 0.20.1 0.30 0.20.1 0.3

1

2

3

Figure 20 Poro-Perm-Plot: Core Samples are from Three Sandstone

Reservoirs (from Timur 1968)

Practical application of Permeability-Porosity Plots:

1. Laboratory measurements of core plugs from wells in a formation/field

deliver the regression Permeability vs. Porosity

2. Borehole measurements in new wells (without core) deliver Porosity.

3. Porosity can be transformed into a permeability for the same formation.

This is one way to estimate permeability in wells, because there are no other logging

methods (except Nuclear Magnetic Resonance).

Gulf Coast FieldColorado FieldCalifornia Field


22/65

22

Permeability

vs. grain size d

(Bentheim Sandstone,

Scherhorn oilfield,

Germany);

from Engelhardt 1960,

Schopper 1982

104

5

102

2

5

2

103

104

5

102

2

5

2

103

5 10 2 2 5d in m

k

inmd

k d 2.2

log k =2.2 log d - 2.101

k in md d in µm

Figure 21 Permeability vs. mean grain size (Engelhardt, 1960)

We derive the empirical relationship:

101.2log2.2log d k with k in md and d in µm

Empiric al Equations:

In general permeability increases with porosity, pore (throat) size, connectivity.The main problem of derivation empirical equations is to implement pore size anddistribution properties in the relationship.

k = 5.1 · 10-6 ·5.1 · d 2 ·exp (-1.385 · )

k in Darcy, in percent

d median grain diameter in mm

sorting term in phi units

BERG, 1970

k = 5.1 · 10-6 ·5.1 · d 2 ·exp (-1.385 · )




BERG, 1970k = 5.1 · 10-6 ·5.1 · d 2 ·exp (-1.385 · )




BERG, 1970

Shale Influ ence

Best and Katsube, 1995: "shales have some of the lowest permeability values (10-7-10-3 md ) ..."

Therefore shale – in general – reduces the permeability. The effect depends on The shale content The shale type (mainly the clay minerals) The shale/clay distribution (laminated, dispersed)


23/65

23

Shale disperse distributed

Shale laminar between sand layers

increasing shale content

increasing shale content

permeability decreases

laminated shale

permeability anisotropy

Figure 22 Shale effect upon permeability for dispersed and laminated

shale distribution

10

100

1000

10000

0.00 0.05 0.10 0.15 0.20 0.25

Vsh

kinmd

Figure 12 Decrease of permeability with increasing shale content (dispersed),

Data from Vernik, 2000Laminated sediments show a directional dependence of permeability (anisotropy). Theknowledge of kh and kv is important particularly for horizontal wells.

kv < kh

Figure 24 Permeability kv vs. kh, North Sea sediments, Bang et al. 2000


24/65

24

porosity - linear scale

permeability

logarithmicscale

c e m e n t ,

c l a y

c o a r s e n i n g

f i n i n g

g r a v e l f r a c t i o n

s o r t i n g

Figure 25: Summary Sketch: Impact of Grain Size, Sorting, Clay, and

Interstitial Cements - Upon Permeability Porosity Trends, (after a Figure

from Nelson, 1994)

4.2.2 Carbonates

What causes additional problems in permeability for carbonates ?- non uniform pore size- complicated pore geometry- non connected pore space

The complex pore structure and diversity of carbonates results in problems to deriveand correlate permeability. With respect to the pore space and its hydraulic connectivitywhich contributes to permeability we distinguish two types:

non-vuggy rocks with permeability and porosity controlled by intercrystalline

type pore; they are similar to siliciclastic sediments. rocks with (non touching) vugs with porosity controlled by vugs and non-

uggy pores but permeability controlled by non vuggy and connected pores.

A systematic analyse of carbonate rock pore properties is published in papers fromLucia, particularly the textbook Carbonate Reservoir Characterization (Lucia,1999. Wefollow strong his detailed description.


25/65

25

Figure 13 Two examples demonstrating the effect of connected and non

connected pore space upon permeability; from: Lucia, 1983

Fracturing Compaction and Cementation Leaching

0 10 20 30

porosity

1000

k in mD

100

10

1

0.1

0.01

L e a c h

e d

c h

a n n e l s

i n

r e e f a l

r o c k

s

P a r t i c l e

d i a

m e t e r ~

5 0 0

µ m

P a r t i c l e

d i a

m e t e r ~ 3 0

0 µ m

P a r t i c l e d i a m

e t e r

~ 1 0 0

µ m

g r a i n

s t o n e

moldic grainstone

v u g g

y d o l o

m i t e

w a c k e s t o

n e

p a c k e s

t o n e

s ,

l i m e m u d

c o c c o l i

t h c h a l k

p o r e d i a m e t e r


26/65

26

4.3 PERMEABILITY MODELS

OverviewThere are different model concepts to describe permeability. In the following section

the capillary-tube model will be discussed more in detail; it will be shown that thissimple model gives a description of some main controlling influences helps to formulate the background and content of empirical modifications creates a link to log-derived parameters (Sw,irr , NMR).

The capillary tube model (Kozeny-Carman) - the fundamental equationThe model concept is applied mainly for clastic sediments. The rock with connectedpores is represented in the simple case by an impermeable cube (side length L ) with acapillary tube:

r

l

LL

L r l

LL

L

porosity tortuosityspecific surface

L

l T

r

2

l r

l r 2S

L

l r 2 por 3

2


L

l T

r

2

l r

l r 2S

L

l r 2 por 3

2


L

l T

r

2

l r

l r 2S

L

l r 2 por 3

2

Figure 15 The simple capillary tube model

The element with the length L has the cross section A = L2.We consider the model under two views/aspects:Macroscopic view: we describe the fluid flow using Darcy’s law

p grad k

A

q

the flowing fluid volume/time is

L p Ak p grad Ak q

Microscopic view: we describe the pore space properties by the capillary length l, thecapillary radius r and define as

tortuosity the ratio

L

l

the porosity is

A

r

AL

l r

22


27/65

27

The basic equation for the fluid flow is Hagen-Poiseulle’s law for a tube

l

pr q

41

8

Comparision of the two expressions for volume flow results in

p grad r p grad Ak

q

11

8

4

Solved for permeability and implementation of porosity gives

2

2

8

1

r

k

The equation shows and explains permeability as a function ofporosity; the resulting linear dependence is not in confidence with a stronger

dependence derived from experiments,- pore radius; the dependence on the square of the radius fits very well the

general correlation found by experiments with a dependence of permeability onthe square of mean grain size,

- the tortuosity; this property stands in the model for the real complicated path ofthe pore channel and covers a part of the textural influences.

Implementat ion of Specif ic Surface

We transform the fundamental problem of the influence of pore radius into a problem ofinfluence of specific internal surface. With this fundamental step a permeability

estimate from logs becomes possible.We express the pore radius by the specific internal surface.The specific internal surface

describes the surface of the pores is related to the grain size (increases with decreasing grain size) and influenced

by the “grain morphology” opens a way for a permeability estimate using measurements controlled by

specific internal surface (Nuclear Magnetic Resonance).

For the model the pore surface to pore volume is

r r

r Spor

22

2

Thus, we can replace in equation the pore radius by

Spor

r 2

S por

Stotal

=

=

Pore volume

Surface area of the pores

Total volume

Surface area of the pores

Stotal = S por •


28/65

28

Insertion results in the permeability

222

211

2

1

8

1

por S

r k

Replacement of radius by specific surface gives

opportunity of permeability estimate from logs

2

22

1

por S k

Describes the influence of

Pore space geometry

Porosity

Internal pore surface

Spor r

2

There are two ways, to implement – in addition to porosity – the effect of specificinternal surface:

Way 1: Understand Irreducible water saturationirr w

S ,

as a measure of po r S :

In an oil- or gas bearing formation: irreducible water covers the grain surface with a thin

film. Thus, the water content gives a measure of the grain surface ( irr w por S S , ).

Timur’s empirical equation (Timur, 1968).

2

,

5.44

2

,

25.21

10100

irr wirr w S S

k

Note: only works only under condition of a reservoir section with irr wS , .

Way 2: Derive po r S from NMR measurement:

The Coates equation for NMR derived permeability is24

BVI

BVM

C k

whereBVM bulk volume moveable fluids BVI bulk volume irreducible fluidsC empirical constant

Thus, the ratio BVM BVI is a measure for the specific internal surface pvS

But note: pores are not tubes! Permeability controlled by pore throat radius (area) Surface area strong influenced by pore body radius (area)

Figure 16 Pore Throat and Pore Body


29/65

29

4.4 MULTIPHASE FLOW (RELATIVE PERMEABILITY) AND CAPILLARY

PRESSURE

Permeability in Darcy’s law is defined for a single fluid - this is the absolutepermeabilty.

If the reservoir contains two or even three non miscible fluids (water, oil, gas) then theflow of the individual fluids interfere and the effective permeabilities of the individualfluids are less than the absolute permeability.

Multiphase fluid and fluid flow in the reservoir are controlled and described by threeproperties:

Wettability Relative permeability Capillary pressure

4.4.1 Wettability

Wettability is defined as the tendency for one fluid to adhere to a rock surface in the

presence of another immiscible fluid. described by an contact angle and is related to interfacial tension.

Figure 30: Wettability Types, Cosentino, 2001

Figure 31 Wettability and Interfacial Tension Terms


30/65

30

Figure 32: Water Wet and Oil Wet

Types: Water wet: The whole rock surface is coated with water, while oil and gas

occupy the central position of the largest pores. Oil wet: The relative positions of oil and water are reversed with respect to the

water wet state – the oil coating the rock surface and the water residing in thecentre of the largest pores.

Intermediate wettability: This term applies to reservoir rocks where there issome tendency for both oil and water to adhere to the pore surface. (AfterCosentino, 2001).

4.4.2 Absolute and Relative Permeability

Permeability in Darcy’s law is defined for a single fluid - this is the absolutepermeability

The reservoir can contain two or even three fluids (water, oil, gas) the flow ofthe individual fluids interfere and the effective permeabilities are less than the

absolute permeability. Thus, effective permeability describes the flow of a fluid through a rock in the

presence of other pore fluids. It depends on the saturations. Relative permeability is the ratio of effective permeability and absolute

permeability; it varies between 0 and 1.

Figure 33: Relative permeability for waterrW

k and hydrocarbonrHY

k (oil or

gas) as function of saturation W S or HY S


31/65

31

4.4.3 Capillary Pressure

Capillary pressure describes the fluid saturation distribution in a reservoir,depending on pore size distribution and wettability of the fluid components.

Capillary pressure can be determined/investigated in the laboratory. Then theapplied fluid pressure represents the equivalent height above the free waterlevel.

Capillary pressure curves give an insight into the fluid distribution (transition) ina reservoir.

Capillary pressure:

r P c

cos2 equilibrium with the weight of the water column

(height)

- interfacial tension- meniscus contact angle

r - radius of the tube - density of water g - gravity acceleration

h

r g

g

P

g r h c

cos

2

Figure 34 Capillary Pressure

The finer the capillary tube, the higher the water will rise.

Pc

Sw

Pd

0 Sw,irr 1

above

transition

transition

water zone

Production:

water cut = 0

clean oil

water cut > 0

water + oil

Sw = 1

water only

Figure 17: Capillary Pressure Controls Fluid Distribution in a Reservoir


32/65

32

Figure 36 Capillary Pressure Curves, Amyx, 1960

Rules: large pore throat diameter high permeability low cap. pressure small pore throat diameter low permeability high cap. Pressure

Capillary pressure – description by an equation: Leverett, 1941: Capillary curves from a specific formation are reduced to a

single J-function versus saturation curve Thomeer et al. 1960: Log-log plot of capillary pressure is approximated by a

hyperbola; introduction of a “Pore geometrical factor” as curve parameter Swanson, 1981: Analysis of the Pc vs. Sw curve and definition of a “point A” in

order to find a correlation to permeability.

Conversion from laboratory capillary curves to fluid distribution in a reservoir


33/65

33

Figure 37 From laboratory capillary pressure measurement to thesaturation vs. depth estimate for the reservoir.

4.5 SUMMARY - PORE SPACE PROPERTIES

Porosity, pore fluid distribution, permeability, and specific internal surface are mostimportant reservoir (pore space) parameters.

They show a more or less strong correlation, but express different physical properties:Porosity characterizes the volume of pore space; it is a scalar property.Specific internal surface characterizes the surface of pore space; it is a scalar property.Permeability expresses the ability of fluid flow and is a tensorial property.

Porosity shows a strong correlation to density (and other properties measured bynuclear, acoustic, or electrical methods).

Permeability correlates with porosity, but is strongly influenced by pore diameter (orgrain size). This circumstance causes the difficulties in permeability determination.

Specific internal surface links porosity and permeability. Therefore “surface - sensitive”properties, such as Sw,irr or NMR, give a possibility of permeability derivation.

Porosity, fluid saturation, and permeability are criteria for net pay definition: Net/Grossratio „ ... aims at representing the portion of reservoir rock which is considered tocontribute to production.These properties are determined directly at samples (cores, plugs); this is the job of“Core Analysis” (conventional and special core analysis).


34/65

34

CHAPTER 5 RESERVOIR ROCKS – PROPERTIESDERIVED FROM GEOPHYSICAL MEASUREMENTS – OR “THE INDIRECT” WA Y

5.1 INTRODUCTION AND MOTIVATION

Core analysis delivers directly the key parameters for a reservoir characterization. Coredetermined parameters

are relatively expensive (because coring is expensive) represent only a very small part of the whole profile.

Therefore we are interested in additional methods in order to derive a continuousprofile of properties like porosity, saturation, permeability, but also for example rockcomposition (particularly shale).In the following section we will discuss only some typical methods to solve this problemmainly using Well Logging (Borehole Geophysics).We will see that the derivation is an “indirect” way, and the question therefore is not “ Core or Well Logs ? – because we will see the solution is “Core plus Well Logs”.

Please note: This refers only to some selected methods and their petrophysicalbackground – a more detailed presentation is given later in special classes to this topic.

5.2 WELL LOGGING AND FORMATION EVALUATION - OVERVIEW

In this section we discuss some selected methods of well logging mainly under theaspects of:

their physical fundamentals the petrophysical information and response the expected information as part of a logging program.

The general purpose of log measurements is Lithologic profile, the exact depth of formation/rock boundaries Rock properties

reservoir properties (porosity, saturation, permeability) rock composition, mechanical properties Change of properties, particularly fluid content/saturation (monitoring, time

lapse measurements)

The logging equipment conists of a set of probes, the cable with winch, a depthsensor, and the measuring and control unit.

The result is the “log”: each trace shows the variation of a physical parameter as afunction of depth.


35/65

35

Figure 38: The log (each trace shows the variation of a physical parameter as a

function of depth the „Art of Formation Analysis“ is the extraction of

Reservoir Properties from a set of logs; Baker Atlas, 2002)

Note: We will discuss the petrophysical background, in order to explain why we canuse for example a density measurement for porosity determination or a resistivity

measurement for water saturation. We will not discuss the tools and instruments (this issubject of courses in well logging and seismic).


36/65

36

CHAPTER 6 THE QUESTION FOR LITHOLOGICPROFILE AND SHALE CONTENT – MEASUREMENT OFGAMMA ACTIVITY

Gammalog measures the natural radioactivity in a well. It is a member of the family ofnuclear methods and it can also be measrued in the laboratory with agammaspectrometer. Nuclear measurements are possible in open hole and casedhole. All nuclear measurements show a characteristic statistical fluctuation.Natural radioactivity is spontaneous decay of a certain isotope into another isotope,characterized by emission of radiation ( ,, ):

, are particle radiation with a very shallow penetration/high absorption

is an electromagnetic wave, high penetration, the Energy is in the order of keV toMeV

6.1 NATURAL GAMMA ACTIVITY OF MINERALSNatural gamma activity of minerals and rocks is originated by

URANIUM decay series THORIUM decay series POTASSIUM monoenergetic radiation

The abundance of these elements or isotopes controls the intensity of naturalradioactivity. The result is a spectrum of radiation.

U Uranium series

spectrum with typical

energy 1.76 MeV (214Bi)

Th Thor ium series

spectrum with typical

energy 2.61 MeV (208Th)

40K Potassium isotope

monoenergetic 1.46 MeV

Figure 18: Spectrum of Natural Gamma Radiation Sources

6.2 NATURAL GAMMA ACTIVITY OF ROCKSU, Th, and K content of the minerals and mineral abundance control the naturalradioactivity of rocks

Rock type

Igneous rocks

Sedimentary rocks

Increasing radiation

K - evaporites

basic

acid

shaly

clean

Figure 40 Radioactivity of Rocks – General Tendency (Schoen, 1989)


37/65

37

6.3 TYPES OF MEASUREMENT

The spectral character of decay results in different types and techniques ofmeasurement

Integral measurement Spectral measurement Selective measurement

detector

K U Th

1,3 ... 1,6 ... 2,4 ... 2,8 MeV

E (MeV)

nspectral

selective

integral

all impulses above

a treashold of energy

channels

Figure 41: Gamma Measurements – Principles

Integral Gamma MeasurementIntegral activity is effect of 3 contributionsI = k (a K + U + b Th)Unit: API-unit: API facility is constructed of concrete with an admixture of radium toprovide 238U decay series, monazite ore as a source of thorium, and mica as a sourceof potassium.

Table Mean API values for gamma activity (S - data from Schlumberger 2000)

material Gamma in APIQuartz, calcite, dolomite (clean)Plagioclase (albite, anorthite)

Alcali feldspar (orthoclase, anorthoclase, microcline)MuscoviteBiotiteShale (mean)KaoliniteIlliteChloriteMontmorilloniteSylviteCarnallite

00 220 270 275

80 …130 250 …300 180 … 250 150 … 200 500 + 220


38/65

38

6.4 APPLICATIONS

Application 1: Sand-shale separation in the profile

Figure 42 Sand-Shale Separation (1. Plot Sand Line (Minimum); 2. PlotShale Line (Maximum); 3. Design Lithologic Profile; Note: Consider the Caliper)

Application 2: Shale content calculation Basis: correlation between shale content and gamma activity Assumption: only shale and clay are radioactive components in rock, no other

radioactive minerals

log response in

zone of interest

log response in a

zone considered

clean (shale free)

log response in a

shale zone sh

cn

GR

GR

GR

cn sh

cn

GRGRGR

GRGR I

GR

Figure 19 Calculation of the “Gamma Ray Shale Index”

Figure 44 Determination of the shale content from shale Index using an

empirical relationship


39/65

39

Attention high gamma radiation: Sandstone with high content of feldspar, mica, glauconite („green sand“), Carbonates in reducing environment, stylotithes, phosphates.

In carbonate series, the integral gamma intensity is very often a poor clay indicator,because the measured value is not related to clay content, but to the presence ofuranium. Typical cases are

Pure carbonate (chemical origin) which has a thorium and potassium level nearzero. If uranium is zero too, this carbonate was precipitated in an oxidizingenvironment.

If there is a variable uranium content, the carbonate can either have beendeposited in a reducing environment, or it corresponds to a carbonate withstylolithes or to phosphate-bearing layers.

If thorium and potassium are present with uranium, this indicates clay content ofthe carbonate

If potassium is present with or without uranium it can correspond to a carbonate

of algal origin or a carbonate with glauconite (Schlumberger, 1982).

6.5 NATURAL RADIOACTIVITY – SUMMARY

Natural Gamma-activity is controlled by U-, K- and Th content of the rocks Two techniques:

- integral measurement- spectral measurement

Gammalog is a typical „lithology log“ based on the measurement of the naturalgamma-radioactivity of a formation.

high gamma reading.

Shale-free („clean“) rocks (sandstones and carbonates) usually have lowgamma intensity.

Gammalog can be applied for lithologic profile design, shale content estimate,and well-to-well-correlation.


40/65

40

CHAPTER 7 THE QUESTION FOR POROSITY

There are several petrophysical properties with a strong correlation to porosity: Density Velocity of elastic waves Neutron interactions

We will discuss two properties: Density and Elastic wave velocity.

7.1 POROSITY FROM DENSITY MEASUREMENT (GAMMA-GAMMA-

LOG)

Interaction of incident radiation (source) with

electrons

- gives information about density porosity

- gives information about lithology

source

detector

7.1.1 Gamma Ray Interactions with Rocks

For our study we need some fundamentals regarding the atomic structure:

Materials (rocks)

consist of atoms of

various elements

Atom consists of the nucleus of mass Ma number Z oforbiting electrons

3 effects of interaction result in an energy loss: Photoelectric effect Compton effect Pair production

The probability of interaction depends on the energy of radiation and the atomicnumber of target material.


41/65

41

Cs Co

Rock

forming

elements

Rock

forming

elements

In the energy range between 0.5 and 5 MeV

for most abundant elements the COMPTON-effect dominates.

Figure 20: Gamma Ray Absorption Effects

Interactions result in attenuation (absorption) of radiation, described by absorptioncoefficient

x I x I exp0 The absorption coefficient is

connected with the absorption cross section related to the effect of interaction, thus we have a coefficient for the

photoelectric effect and a different for the Compton effect.

C - absorption coefficient for Compton effect

Pe - absorption coefficient for Photoelectric effect (Pe)

Photoelectric Effect:

For many elements the photoelectric cross section shows the proportionality to atomicnumber 6.3 Z

Pe 3.6 on this basis a effective photoelectric index Pe (average

photoelectric cross section per electron) is defined:Pe = (Z/10) 3.6

Pe - unit: b/e barns per electronPe depends on elemental composition (lithology) - see table.

Table: Mean Values for Density , Electron Density , ratio Z/A, and Photoelectric Absorption Index Pe, Baker Atlas Document

Substance (g/cm3) e (g/cm3) Z/A Pe (b/e)

quartz 2.654 2.650 0.499 1.806calcite 2.710 2.708 0.500 5.084

dolomite 2.870 2.864 0.499 3.142

halite 2.165 2.074 0.479 4.65

gypsum 2.320 2.372 0.511 3.420

anhydrite 2.97 2.96 0.499 5.05

kaolinite 2.44 2.44 0.50 1.83

illite 2.64 2.63 0.499 3.45

barite 4.48 4.09 0.446 266.8

water (fresh) 1.000 1.110 0.555 0.358

oil 0.850 0.948 0.558 0.125


42/65

42

Note: Pe can help to discriminate between Quartz, Calcite, and Dolomite, Pe is one component in mineralogy-porosity crossplt technique Pe is extremely sensitive with respect to barite (mud!)

Compton effect density

There is a difference between bulk density and electron density in general:

Electron density is related to the number of electrons per molecule (Z), and bulkdensity is related to the total atomic mass per molecule (A).For most common Earth minerals, the ratio is constant

5.0 A

Z

and thus

eeb A

Z

2

Gamma Ray Interactions - Summary For practical log applications are important Compton effect and Photoelectric

effect Density determination by nuclear measurements applies Compton effect; the

correlation between density and electron density bases on a nearly constantZ/A.

Determination of Pe applies Photoelectric effect and gives an information aboutmineral composition by the strong correlation to atomic number Z.

7.1.2 Porosity from Gamma-Gamma-Density Log

The way: We determine density (Gamma - Gamma - Log) We transform density into porosity (remember the definition of porosity).

Vm

VpVp

1 -

fluid matrix

matrix

fluid matrix

1

Relationship between

porosity and density

For porosity calculation from Gamma-Gamma-Density we need

matrix density fluid density

+

+ + +

+

-

-

-

-

-

Number of orbiting electronse control probability of

Compton effect

Number of orbiting electronse control probability of

Compton effect

But bulk density

is controlled by

A = Z + N

But bulk density

is controlled by

A = Z + N

e = Z

Z/A 0.5

Compton effect controlled by bulk densityCompton effect controlled by bulk density


43/65


44/65

44

Soniclog/Acousticlog measures travel time of the waves tool geometry controls way (distances) thus, time and distance gives velocity v

= distance/time in m/s or ft/s slowness t = time/distance in µs/m or µs/ft.

Slowness and velocity - what can they tell us about rocks ? Porosity Determination:

- Slowness depends on porosity, shale content, .… Wyllie’s famousequation allows a porosity estimate,

- Porosity and lithology determination (combination with neutron andgamma-gamma-densitylog (cross plots etc.)

but the seismic signal (waveform, modes) carries much more information aboutthe rock mechanical proper ties, stress field, fracturing, …

Figure 21: Soniclog/Acousticlog – Principle


45/65

45

7.2.2 Elastic PropertiesDescription of the elastic properties of an isotropic material by two properties: E Youngs modulus, defined as ratio of stress to strain in an uniaxial stress state M Compressional (P) wave modulus, defined as ratio of stress to strain in an uniaxial

strain statek Bulk compressional modulus, defined as ratio of hydrostatic stress to volumetricstrain Shear modulus, defined as ratio of shear stress to shear strain

Poisson’s ratio, defined as the (negative) ratio of lateral strain to axial strain in anuniaxial stress state.

Wave velocities can be expressed in terms of the elastic moduli and the density:

Compressional wave

3

4

211

1 k

E M V p

Shear wave

12

1 E V s

Units and conversions:Elastic moduli (E, µ, … ): SI-unit Pa (Pascal)

1 GPa = 109 Pa 1 MPa = 106 Pa1 Pa = 1.0197 · 10-5 kp cm-2 = 1.4504 ·10-4 psi

Poissons ratio: dimensionlessVelocity: SI-unit m s-1

1 m s

-1

= 3.2808 ft s

-1

1 ft s

-1

= 0.3048 m s

-1

Interval transit time/slowness: SI-unit µs m-11 µs m-1 = 0.3048 µs ft-1 1 µs ft-1 =3.2808 µs m-1

7.2.3 Elastic Properties of Rocks – Some Experimental Results

Mean values & overview

vP tp vs tsm/s µs/ft m/s µs/ftMinerals:

Quartz

Calcite

Dolomite

Pore fluids

Water

Oil

Gas

6000 51 4100 74

6600 46 3400 90

7300 42 4000 76

1450 … 1700 210…180

1000 … 1400 305…220

300 … 400 1010…760

gas oil water minerals

0 2000 4000 6000 m s-1

Figure 22: Velocities of Rock Components – Overview

The following examples and figures demonstrate the dependence of wave velocity on Rock type (mineralogy, lithology) Porosity Pore fluid Pressure


46/65

46

Figure 23: Velocity of Compressional and Shear Wave as a Function of

Porosity (and Clay Content); after Han et al., 1986

microporosity

interparticle

crystalline porosity

densely cemented

low porous

8 MPa effective pressure

0 10 20 30 40 50 60

porosity

7000

vp in m/s

6000

5000

4000

3000

2000

1000

moldic porositymoldic porosity

Figure 24: Carbonates: Velocity vs. porosity, Different pore types cluster in

the Porosity-Velocity Field, indicating that scattering at equal porosity is

caused by the specific pore type and their resultant elastic property. Data

from: Eberli et al., 2003

Pressure influence: velocity increases with increasing pressure velocity vs. pressure function is non-linear the effective pressure p has the controlling influence

Total and effective pressure:

Pressure

- reduces porosity

- changes grain to grain contact

elasticity

Total external

pressure Ptotal

Pore

pressure

Ppore

Change of elasticity (porosity

and grain to grain elasticity) is

pressure effect acting on rock

skeleton (effective pressure):

Peff = P = Ptotal - Ppore

Peff = P = Ptotal - n Ppore

Figure 50: Total and Effective Pressure

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4

porosity

vp,vs

inkm/ 0.00

0.01...0.09

0.10...0.19

0.20...0.50

0.00

0.01...0.09

0.10...0.19

0.20...0.50

clay contentclay content

75 sandstone samples

Confining pressure 40 MPa

Pore pressure 1 MPa

(Han et al., 1986)


47/65

47

v p

increases from

air --> oil --> water

v s

decreases from

air --> oil --> water

Figure 51: Pressure dependence of vP and vS, Influence of different pore fluids;

Boise Sandstone (King 1966)

)21)(1(

)1(v p

E E strong increases

moderate increases

µ non influenced

moderate increases

s v

vp/vs ratio is a pore fluid and lithology indicator.

7.2.4 Theories and Models – the Wyllie Equation (time average

relationship)

For porosity calculation

Figure 52: Explanation of Wyllie’s equation “Time Average Relationship”

(Wyllie et al. 1956)

1 1

matrix

fluid

length = 1

medium distance velocity travel time

matrix

fluid

rock, model

(Wyllie et al. 1956)

1 -

1

1 matrixmatrix t v

1 fluid fluid t v

1 t v

matrixt 1

fluid t

t

The “Time Average Relationship”


48/65

48

Addition of the partial

travel times results in:

fluid matrix t t t 1 fluid matrix t t t 1

from Wyllie’s original publication, reprinted by Ellis 1987

Time Average ft/sec (m/s)Matrix 19500 (5944)

Fluid 5000 (1524)

10

15

35

20

25

30

5

0

10

15

35

20

25

30

5

0

Porosity(pu)

120 80 70 60 50100 90110120 80 70 60 50100 90110

matrix fluid

matrix

fluid matrix

t t

t t

t t t

1

Summary - Wyllie’s Time-Average-Relationship gives good average porosity value for consolidated sediments; does not consider influence of pressure differential; needs corrections for unconsolidated sands : “compaction correction”;

needs correction for shale influence (laminated or dispersed shale correction)

7.2.5 Summary Acousticlog/Soniclog

measures wave propagation in a formation via mud works in the ultrasonic frequency range (kHz) gives information about porosity, lithology, … supports seismic exploration (velocity vs. depth function)

Note: Gamma-Gamma-Density-Log, Neutronlog, and Acoustic-/Soniclog are

„porositylogs“. But for the porosity calculation we need the matrix (and fluid) properties.


49/65


50/65

50

Figure 54 Example seimsic and interpretation

7.3.2 Vp /vs information

0 0.1 0.2 0.3 0.4 0.5

Poisson's ratio

crystalline rocks

consolidated sediments

sandstone, water sat. clay and shale

dry, gas sat. sand water sat. sand

Vp/Vs 1.5 1.6 1.7 2.0 2.5 3.0

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

2000 3000 4000 5000 6000 7000 8000 9000 10000

Acoustic Impedance in (g cm

-3

)(m s

-1

)

Vp/Vs

ratio

40 %

40 %

30 %

30 %

20 %

20 %

10 %

10 %

Porosity

Porosity

clean sand

Sw = 100 %

shale

clean sand

gas bearing gas

saturation

10 %

100 %

increasing shalyness

decreasing effective pressure

increasing porosity

increasing

gas

saturation

increasing

cementation

ell sorted and compacted quartz sand


51/65


52/65

52

8.1.1 Electrical Properties of Rocks

Rocks mostly have two properties relevant to an electrical field: Electric conduction, described by conductivity or inverse - specific resistivity Dielectric polarization, described by relative permittivity (dielectric number)

Most rock forming minerals - insulators*

Pore content “gas” - insulator

Pore content “oil” - insulator

Pore content “water” - conductor

Clay, Shale - conductor

* exceptions, for example, ores, metallicsulphide, graphite

Conclusion: Electrical conductivity of porous rocks is

due to electrolytic conductivity of pore water and

conductivity of clay or shale.

Figure 25: Electrical Resistivity of Rock Forming Constituents

8.2 CLEAN POROUS ROCK – ARCHIE EQUATIONS

there is no clay or another conductor than pore water.

Rock conductivity (or resistivity) is proportional to water conductivity (or resistivity). controlled only by water conductivity, its amount and the distribution or

geometry of “conductor water.”


53/65

53

We assume a water saturated porous rock 1W

S :

o R resistivity of water-saturated rock

w R resistivity of pore water

wo

R R

Introduction of formation resistivity factor F results in:

wo R F R

F express the “resistivity magnification” by non conducting matrix (formation) anddepends on porosity:

m F

1

m cementation exponent (empirical); m ≈ 2

Figure 56: Archie’s Equations – the Principle


54/65


55/65

55

Figure 27: Resistivity Index I vs. Water Saturation, Sandstone (Cosentino,

2001)

Archie’s fundamental equation for water saturation calculation:

n

won

w

o

t S R

S

R R

n

t

o

w R

RS

1

Mean value for saturation exponent 2n

Saturation exponent is: controlled by conducting brine distribution in pore space depends on rock texture, wetting properties, saturation technique Table Saturation Exponent n (Worthington et. al. 1989)

Rock type n ReferenceSandstones 1.42…2.55 Wyllie, Spangler 1952

1.12…2.52 Pierce, Loewe 1958

1.69…2.08 Walther, 1968

1.65…2.44 Wilson, Hensel 19821.42…2.24 Hunt et al. 1985

Limestones 2.30 …2.38 Walther 1968

1.10…1.90 Sharma et al. 1980

1.65…2.22 Swanson 1980

8.3 RESISTIVITY OF SHALY SANDS

Shale in the formation: results in a decrease of reservoir quality (porosity, permeability)

„disturbes“ traditional interpretation algorithms and techniques (for example Sw determination using Archie equation) influences various logs (for example Resistivity, Neutron Log) can be indicated by logs/ log combinations (SP, Gamma, Neutron/Density).

Shale ConductivityIn a historical experiment Winsauer and McCardell, 1953 detected an “excessconductivity” in addition to the electrolytic conductivity (water) in shaly rocks. The Effectof the “Excess Conductivity” of clay depends on

clay type (clay mineral and its cation exchange capacity) clay content (volume fraction) distribution of clay in the formation

frequentlywe use

2n


56/65


57/65

57

B

A

B

A

B B

N

M

Ao

A1'

A1

single conventional focussed micrologelectrode 4-electrode electrolog

Conventional Resistivity Tools consist of 2 current electrodes (A, B); and 2 potential(voltage) electrodes (M, N)

Modern tools measure the individual potentials (and gradients inversion gives asolution in terms of true resitivity distribution.

8.5 SUMMARY

The specific electric resistivity of porous rocks depends on the specific electrical resistivity of the water on the porosity and water saturation.

This is expressed by Archie‘s equation and is the basis of a water saturation calculationfrom log measurements. Archie‘s equation is valid for „clean“ rocks (rocks without other conductive componentsthan water – e.g. shale).

Neglecting the shale content results in an overestimate of water saturation.


58/65

58

CHAPTER 9 NMR MEASUREMENTS

9.1 FUNDAMENTALS

NMR stands for (Nuclear) Magnetic Resonance. - NMRmeasurements use the property of hydrogen nuclei – having amagnetic moment and an angular momentum – to interact in amagnetic field like a little bar magnet + gyroscope combination.

Spinning magnetic nuclei interact with external magnetic fields precessing motion with a typical frequency (Larmor frequency).

Hydrogen nuclei we find in fluid molecules of water and

hydrocarbons.Note: The response of this type of measurements comes only from

the hydrogen nuclei and their physical constitution in the pore space; there is no “matrixeffect”.

Two informations are extracted from the spin echo sequence Initial signal amplitude: the initial signal amplitude is controlled by the number of

hydrogen nuclei associated with the pore fluids in the measurement volume – thus, it gives the porosity.

Signal amplitude decay: Amplitude decays exponentially with time. The decayalso reflects the specific internal surface or the distribution of the pore size. This

gives also a link to permeability.

The precession motion and Larmor frequency:

The precession motion is characterized by its frequency, the so-called Larmorfrequency:

002

B

where

0 B is the external magnetic field and is the gyromagnetic ratio.

Table: Gyromagnetic Properties

nucleus 2 in MHz/Tesla1 H13 C23 Na

42.5810.711.28

Larmor frequency is proportional to gyromagnetic ratio of the nucleus: different species can be differentiated or

separated on the basis of frequencies, magnitude of the static magnetic field: strength is a local function for a

nucleus species (1H) the sensitive volume is determined.

Tuning the NMR tool to the resonant frequency maximizes the signal amplitude.

B 0

0= B

0


59/65


60/65

60

0

20

40

60

80

100

0 100 200 300 400 500

Time (ms)

IncrementalPorosity%

Small Pore Size = Rapid Decay Rate

Large Pore Size = Slow Decay Rate

T2-1

S/V)

Baker Atlas, 2005

0

20

40

60

80

100

0 100 200 300 400 500

Time (ms)

IncrementalPorosity%



T2-1

S/V)



T2-1

S/V)

Baker Atlas, 2005

Figure 30: Pore Size and T2

9.3 NMR DATA PROCESSING

We measure a sum of relaxation contributions from the clay bound water from the capillary bound water from the free movable water

and can describe it as a sum of exponential terms with different relaxation time andmagnitude

The processing extracts from the decay curve a distribution of T2 (Echo DataInversion):

Figure 31: NMR Echo Data Inversion – Principle; T2 Spectrum with

Contributions from Clay Bound Water, Capillary Water and Free

Moveable Fluid

A m p l i t u d e

time (ms)

T2 decay curve

Acquisition time domain T2 Relaxation time domain Acquisition time domain T2 Relaxation time domain

T2 spectrum

0

5

10

15

20

0.1 1 10 100 10000.1 1 10 100 1000 T2 (ms)

cutoff

CBW BVI

BVM

part.

matrix clay clay capillary mobile

dry bound bound water and

water water hydrocarbon


61/65

61

Note: The cutoff depends on specific internal surface and surface relaxation.CBW/BVI: about 1 ... 5 ms (clay minerals)BVI/BVM: faster decaying clastics about 33 ms - slower decaying carbonatesabout 92 ms. Carbonate surface is characterized by a weaker surface relaxivity thanquartz surface.

CBW BVI BVMGR

0.00

1.00

2.00

3.00

4.00

0.1 1 10 100 1000 10000

BVI BVM

4.00

0.00

1.00

2.00

3.00

IncrementalPorosity(pu)

CBW

T2 Decay (ms)

T2 Cutoffs

Default T2 Cutoff Values:

3 ms for CBW - Effective Porosity

33 ms for BVI - BVM (Clastics)

92 ms for BVI - BVM (Carbonates)

CBW BVI BVMGR CBW BVI BVMGR

0.00

1.00

2.00

3.00

4.00

0.1 1 10 100 1000 10000

BVI BVM

4.00

0.00

1.00

2.00

3.00

IncrementalPorosity(pu)

CBW

T2 Decay (ms)

T2 Cutoffs

Default T2 Cutoff Values:

3 ms for CBW - Effective Porosity

33 ms for BVI - BVM (Clastics)

92 ms for BVI - BVM (Carbonates)

Figure 32: Example: Pore Volumetric Partitioning of T2 Spectra/Baker Atlas

Figure 66 NMR Rock Core Analyzer; (Magritek, Laboratory Instrument)

9.4 PERMEABILITY FROM NMR

e remember: Kozeny-Carman equation for k

r

l

LL

L r l

LL

L

22

1

2 por

S T k


62/65

62

Now we express specific internal surface with BVI and get the “Coates equation”:

24

BVI

BVM

C k

24

BVI

BVM

C k

BVM - bulk volume moveable fluids

BVI - bulk volume irreducible fluids

porosity effect Spor effect

C calibration parameter (empirically)

9.5 SUMMARY

NMR delivers: Mineralogy independent porosity, no interpretation constants required effective and total porosity and BVI and BVM, partitioning of pore fluids NMR echo decay is related to S/V (Pore surface/Pore volume): pore-size distributions grain-size distribution Specific internal surface S/V is related to permeability

But, T2 relates to pore body radius and permeability is controlled by pore throatradius! NMR derived permeability does not consider directional dependence.


63/65

63

CHAPTER 10 SUMMARY

Study and understanding physical rock properties are a fundament for application andcombined interpretation of geophysical data produced by

laboratory measurements borehole measurements surface geophysical measurements

Petrophysics today- Is integrated in geoscience & petroleum engineering- has an integrating function, connecting various disciplines.

Development includes theoretical studies and experimental work. Combination of bothmethods develop models and theoretical considerations to

derive fundamental relations and understand physical background apply experimental results to modify and specify theoretical equations andinvolve geological real world.


64/65

64

CHAPTER 11 REFERENCES

A part of the figures was taken from our course material “Introduction to Petrophysicsand Formation Evaluation” (Baker Atlas); I thank the colleagues from Baker Atlas,

particularly Dan Georgi and Allen Gilchrist.

For a detailed study textbooks and manuals are recommended, for example Amyx, J.W., Bass, D.M., Jr., Whiting, R.L., 1960, Petroleum reservoir engineering:McGraw-Hill Book Co. Asquith, G., Krygowski, D., 2004: Basic Well Log Analysis (second edition), AAPGMethods in Exploration Series, No. 16, TulsaBassiouni, Z., 1994 Theory, Measurement, and Interpretation of Well Logs, H.L.Doherty Memorial Fund of AIME, SPEHyne, N. J., 2001: Nontechnical Guide to Petroleum Geology, Exploration, Drilling, andProduction, PennWell Corp., TulsaLucia, F.J.: Carbonate Reservoir Characterization, Springer Berlin Heidelberg 1999Mavko, G., Mukerji, T., Dvorkin, J., 1998, The Rock Physics Handbook, CambridgeUniv. PressRider, M.H. (1996): The Geological Interpretation of Well Logs (second edition).-Whittles PublishingSchön, J. H.: Physical properties of rocks: Fundamentals and Principles ofPetrophysics (Handbook of Geophysical Exploration Series, 583 p.) - PergamonPress, 1-st ed. 1996, last reprint 2004Schön, J.H., 2011, Physical Properties of Rocks – a Workbook (Elsevier Publ.)http://www.elsevierdirect.com/companion.jsp?ISBN=9780444537966 Darling, T., 2005, Well logging and Formation Evaluation, Gulf Profess.Publish./Elsevier Inc.

Tiab, D., Donaldson, E.C., 1996, Petrophysics; Gulf Publishing Company,Houston

Documentations/manuals:Baker Atlas: (2000, 2002) Introduction to Wireline Log Analysis,(2003) Log Interpretation ChartsSchlumberger: (1989) Log Interpretation Charts, (1989) Log InterpretationPrinciples/ Applications

References and recommended papers in alphabetic order Akbar, M., Petricola, M. Watfa, W. et al., 1995, Classic Interpretation Problems:Evaluating Carbonates, Oilfield Review, Jan 1995, 38-56

Archie, G.E. (1942): The electrical resistivity log as an aid in determining somereservoir characteristics.- Trans. AIME, 146, S. 54 –62 (also in: Trans. SPE, 1941, 146) Arps, J.J. (1953): The effect of temperature on the density and electrical resistivity ofsodium chloride solutions.- Journ. Petrol. Technol. Techn. Note 175, 17-20 Athy, L. F. (1930), Density, porosity and compaction of sedimentary rocks: Bull. Am. Ass. Petrol. Geol., 14, 1.Bang, J., Solstad, A, Mjaaland (2000), Formation Electrical Anisotropy Derived FromInduction Log Measurements in a Horizontal Well, SPE 62908, paper presented at the2000 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 1-4October 2000.Best, M. E., Katsube, T.J. (1995) Shale permeability and its significance in hydrocarbonexploration, The Leading Edge, March 1995, 165-170

http://www.elsevierdirect.com/companion.jsp?ISBN=9780444537966http://www.elsevierdirect.com/companion.jsp?ISBN=9780444537966http://www.elsevierdirect.com/companion.jsp?ISBN=9780444537966


65/65

Castagna, J.P., Batzle, M.L., Kan, T.K., 1993, Rock Physics - The Link between RockProperties and AVO response; in: Offset-Dependent Reflectivity - Theory and Practiceof AVO Analysis; J.P. Castagna M.L. Backus (eds.), Investigations in Geophysics, No.8 SEG, Tulsa, 135-171Choquette, P. W., L. C. Pray (1970), Geologic Nomenclature and Classification ofPorosity in Sedimentary Carbonates: Bull. Am. Ass. Petr. Geol., 54, 207-250.Coates, G.R, Xiao, L., Prammer, M. (1999) NMR Principles and Applications,Halliburton Energy Services Publ. H02308Darcy, H .(1856), Les fontaines publiques de la Ville de Dijon: V. Dalmont, Paris.Dewan, J.,T., Holdtich (1992): Radial response functions for borehole logging tools.-Gas Research Institute Report, Jan. 1992 ChikagoEberli, G.P., Baechle, G.T., Anselmetti, F.S., 2003, Factors controlling elasticproperties in carbonate sediments and rocks, The Leading Edge, July 2003, 654-660Engelhardt, W. V. (1960), Der Porenraum der Sedimente: Springer-Verlag Berlin,Göttingen, Heidelberg.Fatt, I. (1953), The Effect of Overburden Pressure on Relative Permeability: Petr.

Trans., AIME, 198, 325 -326.Fertl, W.H. (1979): Gamma ray spectral data assists in complex formation evaluation.-Trans 6th Europ. Symp. SPWLA, London, Paper QGassmann, F. (1951), Über die Elastizität poröser Medien: Vierteljahresschr. d.Naturforsch. Ges. Zürich, 96, 1-22.Georgi, D. T., S. K. Menger (1994), Reservoir quality, porosity and permeabilityrelationships: Trans. 14. Mintrop-Seminar (Beilage), DGMK und Ruhr-UniversitätBochum 163/1 - 163/35.Han, D.A, Nur, A., Morgan, D. (1986): Effects of porosity and clay content on wavevelocities in sandstones.- Geophysics, 51, 11, 2093-2107Katsube, T.J., 2000, Shale Permeability and pore-structure evolution characteristics,Geological Survey of Canada, Current Research, 2000-E15

Kenyon, W.E. (1997): Petrophysical principles of applications of NMR Logging.- TheLog Analyst, 38, 2, S.21-43Kumar,D., 2006, A tutorial on Gassmann Fluid substitution: Formulation, Algorithm, andMathlab code, Geohorizons, Jan. 2006/4-12Leverett, M.C., 1941, Capillary behaviour in porous solids, Trans. AIME 142, 152-168Lucia, F.J., 1983, Petrophysical Parameters Estimated From Visual Descriptions ofCarbonate Rocks: A Field Classification of Carbonate Pore Space, SPE 1983, 88-96,paper presented at the 1981 SPE Ann. Conf. And Exhib. San Antonio 1981 (SPE10073)Nelson, P.H., 1994, Permeability-Porosity Relationships in Sedimentary Rocks: TheLog Analyst, May-June 1994, 38-61.Nelson, Ph., 2005, Permeability, Porosity, and Pore-Throat Size - A Tree-Dimensional

Perspective, Petrophysics, December 2005, 452-455Thomeer, J. H. M., Introduction of a pore geometrical factor defined by the capillarypressure curve, Journ. Petr. Technol., March 1960, 73-77Timur, A., 1968, An investigation of permeability, porosity, and residual watersaturation relationships for sandstone reservoirs: The Log Analyst, v. 9, n. 4, p. 8-17.Vernik, L. (2000) Permeability Prediction in Poorly Consolidated Siliciclastics Based onPorosity and Clay Volume Logs Petrophysics March-April 2000 138-147

Documents

s Krit Pum Petro Reservoir