TABLE OF CONTENTS

Page 1 PETROLEUM RESERVOIR ROCKS ......................................... 1-1

1.1 PETROPHYSICS ............................................................................... 1-1 1.2 PETROLEUM RESERVOIR ROCKS ................................................1-2 1.3 MINERAL CONSTITUENTS OF ROCKSA REVIEW ...................1-4

1.4 ROCKS............................................................................................... 1-5 1.4.1 Igneous Rocks.................................................................... 1-5 1.4.2 Metamorphic Rocks...........................................................1-6 1.4.3 Sedimentary Rocks............................................................1-6

1.5 CLASSIFICATION OF SEDIMENTARY ROCKS ............................. 1-7 1.5.1 Clastic Sedimentary Rocks ................................................ 1-7 1.5.2 Chemical Sedimentary Rocks............................................ 1-7 1.5.3 Organic Sedimentary Rocks ..............................................1-8

1.6 DISTRIBUTION OF SEDIMENTARY ROCK TYPES .................... 1-10

1.7 SANDSTONE RESERVOIRS (CLASTIC SEDIMENTARY ROCK) ............................................................................................. 1-10 1.7.1 Pore Space ....................................................................... 1-12 1.7.2 Compaction and Cementation......................................... 1-15 1.7.3 Classification ................................................................... 1-17

1.8 CARBONATE RESERVOIRS (LIMESTONES AND DOLOMITES) .................................................................................1-20 1.8.1 Classification ................................................................... 1-21 1.8.2 Pore Space .......................................................................1-22

1.9 FRACTURED RESERVOIRS ..........................................................1-28

1.10 RESEVOIR COLUMN.....................................................................1-29

REFRENCES...................................................................................1-32

2 POROSITY AND FLUID SATURATIONS..................................2-1

2.1 DEFINITION OF POROSITY ...........................................................2-1

2.2 FACTORS AFFECTING SANDSTONE POROSITY ........................ 2-2

2.3 FACTORS AFFECTING CARBONATE POROSITY ........................ 2-4

2.4 TYPICAL RESERVOIR POROSITY VALUES.................................. 2-5

2.5 LABORATORY MEASUREMENT OF POROSITY.......................... 2-6

2.5.1 Direct Porosity Measurement by Routine Core Analysis .................................................................... 2-6 2.5.2 Indirect Porosity Measurement by CT Imaging.............. 2-11

2.6 FLUID SATURATIONS ..................................................................2-16

2.7 INDIRECT POROSITY MEASUREMENTS FROM WELL LOGS................................................................................... 2-24 2.7.1 Introduction to Well Logging......................................... 2-24 2.7.2 Mud filtrate Invasion...................................................... 2-25 2.7.3 Porosity Logs .................................................................. 2-32 Density Log .................................................................. 2-32 Sonic Log (Acoustic Log) ............................................. 2-36 Neutron Log .................................................................2-41 Combination Porosity Logs ......................................... 2-45 2.7.4 Resistivity Log ................................................................ 2-46 Electric Log ................................................................. 2-54 Induction-Electric Log................................................ 2-56 Dual Induction Laterolog ........................................... 2-58 Focused Electric Log (Guard and Laterolog) ............. 2-62 Microresistivity Logs................................................... 2-65 2.7.5 Lithology Logs ................................................................ 2-68 Spontaneous Potential Log (SP)................................. 2-68 The Gamma Ray Log (GR)...........................................2-73 2.7.6 Nuclear Magnetic Resonance (NMR) Logs.................... 2-76 Nuclear Spins in a Magnetic Field.............................. 2-76 The Effect of Radiofrequency Pulses - Resonance Absorption ............................................... 2-79 Relaxation Processes...................................................2-80 Molecular Diffusion Effect.......................................... 2-84 NMR Signal and Corresponding T2 Spectrum ........... 2-84 Pore Size Distribution................................................. 2-89 Estimation of Permeability from NMR Relaxation Times............................................... 2-95 2.7.7 NMR Imaging of Laboratory Cores................................ 2-97 The Effect of Magnetic Field Gradients...................... 2-98 Slice-Selective Excitation............................................ 2-99 Frequency Encoding ................................................. 2-100 Phase Encoding..........................................................2-101 Image Reconstruction............................................... 2-102 Three-Dimensional NMR Imaging............................2-103 Signal-to-Noise Ratio and Image Contrast............... 2-104 Example NMR Images of Laboratory Cores..............2-105 2.7.8 A Comparison of Various Porosity Measurements for Shaly Sand....................................... 2-112 2.8 RESERVE ESTIMATION PROJECT ........................................... 2-113 2.8.1 Reserve Estimation........................................................ 2-114

2.8.2 Economic Evaluation..................................................... 2-115 2.8.3 Simulation Procedure.................................................... 2-116 2.8.4 Sampling Procedure ...................................................... 2-116 2.8.5 Simulation Output.........................................................2-124

2.9 PORE VOLUME COMPRESIBILITY............................................2-126

NOMENCLATURE .......................................................................2-135

REFRENCES AND SUGGESTED READINGS.............................2-138

3 PERMEABILITY .....................................................................3-1

3.1 DEFINITION ....................................................................................3-1

3.2 DIMENSIONS AND UNIT OF PERMEABILITY ............................ 3-6

3.3 LABORATORY DETERMINATION OF PERMEABILITY...............3-7

3.4 FIELD DETERMINATION OF PERMEABILITY ..........................3-14 3.4.1 Diffusivity Equation for Slightly Compressible Liquid........................................................3-15 3.4.2 Pressure Drawdown Equation ........................................3-19 3.4.3 Pressure Buildup Equation ............................................ 3-22 3.4.4 Diagnostic Plots.............................................................. 3-24 3.4.5 Skin Factor...................................................................... 3-30 3.4.6 Homogenous Reservoir Model with Wellbore Storage and Skin............................................. 3-33 3.4.7 Type Curve Matching ......................................................3-37 3.4.8 Radius of Investigation of a Well Test ........................... 3-40 3.4.9 Field Example of Well Test Analysis .............................. 3-40 3.4.10 Welltest Model for Dry Gas Reservoir .......................... 3-52

3.5 FACTORS AFFECTING PERMEABILITY..................................... 3-56 3.5.1 Compaction..................................................................... 3-56 3.5.2 Pore Size (Grain Size) ..................................................... 3-56 3.5.3 Sorting ............................................................................ 3-60 3.5.4 Cementation ................................................................... 3-60 3.5.5 Layering .......................................................................... 3-60 3.5.6 Clay Swelling....................................................................3-61

3.6 TYPICAL RESERVOIR PERMEABILITY VALUES .......................3-61

3.7 PERMEABILITY-POROSITY CORRELATIONS............................3-61

3.8 CAPILLARY TUBE MODELS OF POROUS MEDIA..................... 3-69 3.8.1 Carman-Kozeny Equation .............................................. 3-69 3.8.2 Tortuosity ........................................................................3-75 3.8.3 Calculation of Permeability from Pore

Size Distribution............................................................. 3-79 3.9 STEADY STATE FLOW THROUGH FRACTURES....................... 3-84

3.10 AVERAGING PERMEABILITY DATA .......................................... 3-85

3.11 DARCYS LAW FOR INCLINED FLOW........................................ 3-88 3.12 VALIDITY OF DARCYS LAW....................................................... 3-99

3.13 NON-DARCY FLOW..................................................................... 3-101

3.14 DARCYS LAW FOR ANISOTROPIC POROUS MEDIA............. 3-106 3.14.1 Definition of Homogeneity and Anisotropy ................ 3-106 3.14.2 Darcys Law for Homogeneous and Anisotropic Medium.............................................3-107 3.14.3 Transformation of Permeability Tensor from One Coordinate system to Another .................... 3-114 3.14.4 Alternative Calculation of the Principal Values and the Principal Axes of the Permeability Anisotropy..............................................3-122 3.14.5 Directional Permeability...............................................3-124 3.14.6 Measurement of Transverse Permeability of a Cylindrical Core ....................................................3-137

3.15 EXAMPLE APPLICATIONS OF PERMEABILITY.......................3-140 3.15.1 Productivity of Horizontal Well ....................................3-140 Introduction............................................................... 3-141 Homogeneous and Isotropic Reservoirs ................... 3-141 Homogeneous and Anisotropic Reservoirs ...............3-145 3.15.2 Productivity of a Vertically Fractured Well..................3-152

NOMENCLATURE .......................................................................3-155

REFRENCES AND SUGGESTED READINGS.............................3-159

4 HETEROGENEITY ................................................................ 4-1

4.1 INTRODUCTION..............................................................................4-1

4.2 MEASURES OF CENTRAL TENDENCY AND VARIABILITY (HETEROGENEITY)............................................... 4-3 4.2.1 Measures of Central Tendency......................................... 4-3 Mean.............................................................................. 4-3 Geometric Mean............................................................ 4-3 Median .......................................................................... 4-3 Mode.............................................................................. 4-4 4.2.1 Measures of Variability (Heterogeneity or Spread) ............................................... 4-4 Variance ........................................................................ 4-4

Dykstra-Parsons Coefficient of Variation..................... 4-5 Lorenz Coefficient ......................................................... 4-8

4.3 MEASURES OF SPATIAL CONTINUITY ...................................... 4-11 4.3.1 Variogram........................................................................4-13 Definition .....................................................................4-13 How to Calculate the Variogram .................................4-16 Physical Meaning of the Variogram............................ 4-27 Variogram Models....................................................... 4-28 Fitting a Theoretical Variogram Model to an Experimental Variogram ....................................... 4-35 Variogram Anisotropy .................................................4-41 Example Experimental Variograms............................ 4-44 4.3.2 Covariance (Autocovariance) Function...........................4-51 Definition .....................................................................4-51 Physical Meaning of Covariance Function ................. 4-54 4.3.3 Correlation Coefficient Function (Autocorrelation Function) .............................................4-57

4.4 PROBABILITY DISTRIBUTIONS ................................................. 4-59 4.4.1 Normal (Gaussian) Distribution .................................... 4-60 4.4.2 Log Normal Distribution................................................ 4-72

4.5 ESTIMATION .................................................................................4-75 4.5.1 Introduction ....................................................................4-75 4.5.2 Ordinary Kriging Equations ........................................... 4-86 Derivation in Terms of the Covariance Function ................................................... 4-89 Derivation in Terms of the Variogram ....................... 4-94 Solution of the Kriging Equation in terms of the Covariance Function......................................... 4-98 Solution of the Kriging Equation in terms of Variogram ..............................................................4-103

4.6 CONDITIONAL SIMULATION....................................................4-132 4.6.1 Introduction ..................................................................4-132 4.6.2 Sequential Gaussian Simulation ...................................4-132 4.6.3 A Practical Application of Sequential Gaussian Simulation .....................................................4-136

NOMENCLATURE .......................................................................4-148

REFRENCES AND SUGGESTED READINGS.............................4-149

5 DISPERSION IN POROUS MEDIA ..........................................5-1

5.1 INTRODUCTION..............................................................................5-1

5.2 LABORATORY FIRST-CONTACT MISCIBLE DISPLACEMENTS........................................................................... 5-3

5.3 ORIGIN OF DISPERSION IN POROUS MEDIA.......................... 5-20 5.3.1 Molecular Diffusion.........................................................5-21 5.3.2 Mechanical Dispersion ....................................................5-21

5.4 CONVECTION-DISPERSION EQUATION................................... 5-23 5.4.1 Generalized Equation in Vector Notation...................... 5-23 5.4.2 One Dimensional Convection-Dispersion Equation ........................................................................ 5-25

5.4.2 Solution of the One-Dimensional Convection-Dispersion Equation ................................... 5-26

5.5 DISPERSION COEFFICENT AND DISPERSIVITY ..................... 5-42

5.6 MEASURMENT OF DISPERSION COEFFICENT AND DISPERSIVITY ......................................................................5-53

5.6.1 Traditional Laboratory Method with Breakthrough Curve .......................................................5-53 5.6.2 Laboratory Method of Peters et al. (1996) ..................... 5-56 5.6.3 Field Measurement of Dispersion Coefficient and Dispersivity ............................................ 5-71

5.7 FACTORS THAT COULD AFFECT DISPERSION COEFFICENT AND DISPERSIVITY ..............................................5-75

5.8 NUMERICAL MODELING OF FIRST-CONTACT MISCIBLE DISPLACEMENT .........................................................5-79 5.8.1 Introduction ....................................................................5-79 5.8.2 Mathematical Model of First-Contact Miscible Displacement ....................................................5-79 5.8.3 Numerical Modeling of Laboratory Experiments.......... 5-82 Experiment 1 ................................................................. 5-84 Experiment 2..................................................................5-91 Experiment 3................................................................. 5-99 Experiment 4................................................................5-106 Experiment 5................................................................ 5-116 Experiment 6................................................................ 5-121 NOMENCLATURE .......................................................................5-126

REFRENCES AND SUGGESTED READINGS.............................5-128 6 INTERFACIAL PHENOMENA AND WETTABILITY................ 6-1

6.1 INTRODUCTION..............................................................................6-1

6.2 SURFACE AND INTERFACIAL TENSIONS................................... 6-2 6.2.1 Surface Tension ................................................................ 6-2 6.2.2 Interfacial Tension .......................................................... 6-11

6.2.3 Measurement of Surface and Interfacial Tension......................................................... 6-20 Capillary Rise Experiment ............................................ 6-20 Sessile Drop Method ..................................................... 6-24 Pendant Drop Method .................................................. 6-26 Ring Method.................................................................. 6-27 Spinning Drop Method ................................................. 6-30

6.3 WETTABILITY................................................................................6-31 6.3.1 Definition.........................................................................6-31 6.3.2 Determination of Wettability ......................................... 6-36 Contact Angle Method ................................................. 6-37 Amott Wettability Test.................................................. 6-40 United State Bureau of Mines (USBM) Wettability Test............................................................. 6-42 6.3.3 Wettability of Petroleum Reservoirs.............................. 6-45 6.3.4 Effect of Wettability on Rock-Fluid Interactions........... 6-46 Microscopic Fluid Distribution at the Pore Scale ..................................................................... 6-47 Effect of Wettability on Irreducible Water Saturation .......................................................... 6-47 Effect of Wettability on Electrical Properties of Rocks ...................................................... 6-48 Effect of Wettability on the Efficiency of an Immiscible Displacement .............................................6-51

6.3 THERMODYMAMICS OF INTERFACES ..................................... 6-64 6.4.1 Characterization of Interfacial Tension as Specific Surface Energy.............................................. 6-64 6.4.2 Characterization of Microscopic Pore Level Fluid Displacements....................................................... 6-66 Case 1. Displacement of a Nonwetting Phase by a Wetting Phase ............................................ 6-67 Case 2. Displacement of a Wetting Phase by a Nonwetting Phase ................................................. 6-69

NOMENCLATURE .........................................................................6-71

REFRENCES AND SUGGESTED READINGS ..............................6-73 7 CAPILLARY PRESSURE .........................................................7-1

7.1 DEFINITION OF CAPILLARY PRESSURE ..................................... 7-1

7.2 CAPILLARY PRESSURE-SATURATION RELATIONSHIP FOR A POROUS MEDIUM.............................................................. 7-8 7.3 DRAINAGE CAPILLARY PRESSURE CURVE .............................. 7-17

7.4 CONVERSION OF LABORATORY CAPILLARY PRESSURE

DATA TO RESERVOIR CONDITIONS .......................................... 7-21 7.5 AVERAGING CAPILLARY PRESSURE DATA .............................. 7-21 7.6 DETERMINATION OF INITIAL STATIC RESERVOIR FLUID SATURATIONS BY USE OF DRAINAGE CAPILLARY PRESSURE CURVE.................................................. 7-28 7.7 CAPILLARY PRESSURE HYSTERESIS.........................................7-45 7.8 CAPILLARY IMBIBITION..............................................................7-54 7.9 CAPILLARY END EFFECT IN A LABORATORY CORE ...............7-57 7.9.1 Capillary End Effect.........................................................7-57 7.9.2 Mathematical Analysis of Capillary End Effect ..............7-59 7.9.3 Mathematical Model of Capillary End Effect During Steady State Relative Permeability Measurement.................................................................. 7-68 7.9.4 Experimental Evidence of Capillary End Effect...............7-70 7.10 CAPILLARY PRESSURE MEASUREMENTS ................................7-76 7.10.1 Restored State Method (Porous Plate Method)..............7-76 7.10.2 Mercury Injection Method .............................................7-77 7.10.3 Centrifuge Method..........................................................7-81 7.11 PORE SIZE DISTRIBUTION......................................................... 7-96 7.11.1 Introduction.................................................................... 7-96 7.11.2 Pore Volume Distribution .............................................. 7-98 7.11.3 Pore Size Distribution Based on Bundle of Capillary Tubes Model............................................7-103 7.11.4 Mercury Injection Porosimeter..................................... 7-115 7.12 CALCULATION OF PERMEABILITY FROM DRAINAGE CAPILLARY PRESSURE CURVE................................................. 7-118 7.12.1 Calculation of Absolute Permeability from Drainage Capillary Pressure Curve............................. 7-118 7.12.2 Calculation of Relative Permeabilities from Drainage Capillary Pressure Curve.............................7-132 7.13 EMPIRICAL CAPILLARY PRESSURE MODELS ........................ 7-133 7.13.1 Brooks-Corey Capillary Pressure Models ..................... 7-133 7.13.2 van Genuchten Capillary Pressure Model ....................7-143 7.14 CAPILLARY TRAPPING IN POROUS MEDIA........................... 7- 145 7.14.1 Pore Doublet Model of Capillary Trapping................... 7-145

7.14.2 Snap-Off Model of Capillary Trapping ......................... 7-152 7.14.3 Mobilization of Residual Non-Wetting Phase.............. 7-155 7.14.4 Oil Migration................................................................. 7-159

7.15 EFFECTS OF WETTABILITY AND INTERFACIAL TENSION ON CAPILLARY PRESSURE CURVES.......................7-162 NOMENCLATURE .......................................................................7-164

REFRENCES AND SUGGESTED READINGS ............................ 7-168 8 RELATIVE PERMEABILITY................................................... 8-1 8.1 DEFINITION OF RELATIVE PERMEABILITY...............................8-1

8.2 LABORATORY MEASUREMENT OF TWO-PHASE RELATIVE PERMEABILITY BY THE STEADY STATE METHOD ......................................................................................... 8-6 8.3 THEORY OF ONE DIMENSIONAL IMMISCIBLE DISPLACEMENT IN A POROUS MEDIUM..................................8-15 8.3.1 Mathematical Model of Two-Phase Immiscible Displacement................................................8-15 8.3.2 Buckley-Leverett Approximate Solution of the Immiscible Displacement Equation................................8-21 8.3.3 Waterflood Performance Calculations from Buckley-Leverett Theory .................................................8-31 Oil Recovery at any Time ...............................................8-31 Oil Recovery Before Water Breakthrough .....................8-31 Oil Recovery at Water Breakthrough............................ 8-32 Oil Recovery After Water Breakthrough ...................... 8-36 Water Production...........................................................8-41 8.4 LABORATORY MEASUREMENT OF TWO-PHASE RELATIVE PERMEABILITY BY THE UNSTEADY STATE METHOD ........................................................................................8-51 8.5 FACTORS AFFECTING RELATIVE PERMEABILITIES.............. 8-65 8.5.1 Fluid Saturation.............................................................. 8-65 8.5.2 Saturation History.......................................................... 8-66 8.5.3 Wettability ...................................................................... 8-67 8.5.4 Injection Rate ................................................................. 8-70 8.5.5 Viscosity Ratio ................................................................ 8-73 8.5.6 Interfacial Tension ......................................................... 8-74 8.5.7Pore Structure .................................................................. 8-75 8.5.8 Temperature ................................................................... 8-76 8.5.9 Heterogeneity ................................................................. 8-78

8.6 THREE-PHASE RELATIVE PERMEABILITIES .......................... 8-79 8.4 CALCULATION OF RELATIVE PERMEABILITIES FROM DRAINAGE CAPILLARY PRESSURE CURVE .............................8-82 NOMENCLATURE .........................................................................8-91

REFERENCES AND SUGGESTED READINGS ............................8-94 APPENDIX A: A Systematic Approach To Dimensional Analysis .. A-1

Summary.......................................................................................... A-1 Introduction..................................................................................... A-1 Algebraic Theory of Dimensional Analysis......................................A-2

Transformation of the Dimensionless pi Groups .............................A-9 Example Problem.............................................................................A-9 Procedure ....................................................................................... A-10

Transformation of the Dimensionless pi Groups for Example Problem........................................................................... A-21 Some Practical Considerations ......................................................A-28 Concluding Remarks...................................................................... A-31 Nomenclature ................................................................................ A-31 References ......................................................................................A-32

CHAPTER 1

INTRODUCTION

1.1 PETROPHYSICS

Petrophysics is the study of rock properties and their interactions

with fluids (gases, liquid hydrocarbons and aqueous solutions). Because

petroleum reservoir rocks must have porosity and permeability, we are

most interested in the properties of porous and permeable rocks. The

purpose of this text is to provide a basic understanding of the physical

properties of permeable geologic rocks and the interactions of the various

fluids with their interstitial surfaces. Particular emphasis is placed on

the transport properties of the rocks for single phase and multiphase

flow.

The petrophysical properties that are discussed in this text

include:

Porosity

Absolute permeability

Effective and relative permeabilities

Water saturation

1-1

Irreducible water saturation

Hydrocarbon saturation

Residual oil saturation

Capillary pressure

Wettability

Pore size

Pore size distribution

Pore structure

Net pay thickness

Isothermal coefficient of compressibility

Mineralogy

Specific pore surface area

Dispersivity

1.2 PETROLEUM RESERVOIR ROCKS

A petroleum reservoir rock is a porous medium that is sufficiently permeable to permit fluid flow through it. In the presence of

interconnected fluid phases of different density and viscosity, such as

water and hydrocarbons, the movement of the fluids is influenced by

gravity and capillary forces. The fluids separate, therefore, in order of

density when flow through a permeable stratum is arrested by a zone of

low permeability, and, in time, a petroleum reservoir is formed in such a

trap. Porosity and permeability are two fundamental petrophysical

properties of petroleum reservoir rocks.

1-2

Geologically, a petroleum reservoir is a complex of porous and

permeable rock that contains an accumulation of hydrocarbons under a

set of geological conditions that prevent escape by gravitational and

capillary forces. The initial fluid distribution in the reservoir rock, which

is determined by the balance of gravitational and capillary forces, is of

significant interest at the time of discovery.

A rock capable of producing oil, gas and water is called a reservoir

rock. In general, to be of commercial value, a reservoir rock must have

sufficient thickness, areal extent and pore space to contain a large

volume of hydrocarbons and must yield the contained fluids at a

satisfactory rate when the reservoir is penetrated by a well. Any buried

rock, be it sedimentary, igneous or metamorphic, that meets these

conditions may be used as a reservoir rock by migrating hydrocarbons.

However, most reservoir rocks are sedimentary rocks.

Sandstones and carbonates (limestones and dolomites) are the

most common reservoir rocks. They contain most of the worlds

petroleum reserves in about equal proportions even though carbonates

make up only about 25% of sedimentary rocks. The reservoir character

of a rock may be primary such as the intergranular porosity of a

sandstone, or secondary, resulting from chemical or physical changes

such as dolomitization, solution and fracturing. Shales frequently form

the impermeable cap rocks for petroleum traps.

The distribution of reservoirs and the trend of pore space are the

end product of numerous natural processes, some depositional and some

post-depositional. Their prediction, and the explanation and prediction of

their performance involve the recognition of the genesis of the ancient

sediments, the interpretation of which depends upon an understanding

of sedimentary and diagenetic processes. Diagenesis is the process of

1-3

physical and chemical changes in sediments after deposition that convert

them to consolidated rock such as compaction, cementation,

recrystallization and perhaps replacement as in the development of

dolomite.

1.3 MINERAL CONSTITUENTS OF ROCKS - A REVIEW

The physical and chemical properties of rocks are the consequence

of their mineral composition. A mineral is a naturally occurring

crystalline inorganic material that has specific physical and chemical

properties, which are either constant or vary within certain limits. Rock-

forming minerals of interest in petroleum engineering can be classified

into the following families: silicates, carbonates, oxides, sulfates

(sulphates), sulfides (sulphides) and chorides. These are summarized in

Table 1.1. Silicates are the most abundant rock-forming minerals in the

Earths crust.

Table 1.1 Rock - Forming Minerals

Name Chemical Formula Specific Gravity Silicates

Quartz Orthoclase Plagioclase Clay

SiO2

KAlSi2O8 NaAlSi3O8 CaAl2Si2O8

Al2Si2O5(OH)

and many more

2.65 2.57

2.62 - 2.76

2.5

Carbonates Calcite Dolomite

CaCO3

CaMg(CO3)2

2.72 2.85

Oxides Magnetite Hematite

Fe3O4 Fe2O3

5.18

4.9 - 5.3

1-4

Sulfates Anhydrite Gypsum Barite

CaSO4

CaSO4.2H2O BaSO4

2.89 - 2.98

2.32 4.5

Sulfide Pyrite

FeS2

5.02

Chloride Halite

NaCl

2.16

1.4 ROCKS

A rock is an aggregate of one or more minerals. There are three

classes of rocks: igneous, metamorphic and sedimentary rocks .

1.4.1 Igneous Rocks

These are rocks formed from molten material (called magma) that

solidified upon cooling either:

1. At the earths surface to form volcanic or extrusive rocks, e.g.,

basaltic lava flows, volcanic glass and volcanic ash.

or

2. Below the surface, usually at great depths, to form plutonic or

intrusive rocks, e.g., granites and gabbros.

Igneous rocks are the most abundant rocks on the earths crust,

making up about 64.7% of the Earths crust.

1-5

1.4.2 Metamorphic Rocks

These are rocks formed by transformation, generally in the solid

state, of pre-existing rocks beneath the surface by heat, pressure and

chemically active fluids, e.g., quartz is transformed to quartzite and

limestone plus quartz plus heat gives marble and carbon dioxide.

Metamorphic rocks are the second most abundant rocks on the

earths crust, making up 27.4% of the Earths crust.

1.4.3 Sedimentary Rocks

These are rocks formed at the surface of the earth either by

1. Accumulation and consolidation of minerals, rocks and/or

organisms and vegetation, e.g., sandstone and limestone.

or

2. Precipitation from solution such as sea water or surface water,

e.g., salt and limestone.

Sedimentary rocks are the source of petroleum and provide the

reservoir rock and trap to hold the petroleum in the earths crust.

Sedimentary rocks are the least abundant rocks on the earths crust,

making up about 7.9% of the earths crust. Because most reservoir

rocks are sedimentary rocks, they are of particular interest to us in the

study of petrophysics. Therefore, we will examine sedimentary rocks in

more detail than igneous and metamorphic rocks.

1-6

1.5 CLASSIFICATION OF SEDIMENTARY ROCKS

Sedimentary rocks may be classified by origin and composition as

clastic, chemical or organic. Tables 1.2 to 1.4 show the various rock

types for each class.

1.5.1 Clastic Sedimentary Rocks

These rocks are composed of fragments or minerals broken from

any type of pre-existing rock. Clastic sedimentary rocks are usually

classified by grain size as boulder, cobble, gravel, sand, silt and clay.

Figure 1.1 shows such a classification known as the Wentworth scale.

Table 1.2 Clastic Sedimentary Rocks

1.5.2 Chemical Sedimentary Rocks

These rocks are formed by chemical precipitation as carbonates,

e.g., limestone (CaCO3) and dolomite (CaMg(CO3)2) or as evaporties, e.g.,

gypsum (CaSO4.2H2O), anhydrite (CaSO4) and salt (NaCl).

1-7

1.5.3 Organic Sedimentary Rocks

These rocks are formed by biologic precipitation and by

accumulation of organic (plant and animal) material, e.g., peat, coal,

diatomite and limestone.

Figure 1.1 Classification of clastic rocks according to texture.

1-8

Table 1.3 Chemical Sedimentary Rocks (Precipitates)

Table 1.4 Organic Sedimentary Rocks

1-9

1.6 DISTRIBUTION OF SEDIMENTARY ROCK TYPES

Table 1.5 shows the approximate distribution of sedimentary rocks

in the earths crust. Shales make up over 50% of total sedimentary rock

volume in the earths crust.

Table 1.5 Distribution of Sedimentary Rocks Type % Earths Crust % Sedimentary Rock Shale 4.2 53

Sandstone 1.7 22 Limestone and

Dolomite 2.0 25

Total 7.9 100

1.7 SANDSTONE RESERVOIRS (CLASTIC SEDIMENTARY ROCK)

Sandstones are composed of fragmented materials, which have

been transported to the site of deposition by water currents and which

have been subjected to varying degrees of wave and current action

during transport and during deposition. Consequently, sandstone

reservoirs vary from clean, well sorted quartz sandstone with well

rounded grains (Figure 1.2a) through more angular feldspathic

sandstone containing varying amounts of clay (Figure 1.2b), to

argillaceous, very poorly sorted sandstone containing varying amounts of

rock fragments (Figure 1.2c) all of which may be affected by varying

degrees of compaction, cementation, solution and replacement.

1-10

Figure 1.2: Examples of sandstone reservoir rocks. (A) clean, well sorted sandstone, (B) angular, feldspathic sandstone and (C) argillacious, very

poorly sorted sandstone.

1-11

1.7.1 Pore Space

The basic framework of a sandstone reservoir is formed by the

sand grains between which the pore space may or may not contain

interstitial fine material and/or cement (Figure 1.3). The amount of this

intergranular pore space or porosity is controlled primarily by sorting of

the sediment and to a lesser extent by the packing of the grains. Sorting

is a measure of the spread of distribution of grain size on either side of

an average in a sediment. Theoretically, grain size has no effect on

porosity. This is true only for spherical grains of the same size.

However, the arrangement of such spheres has a large effect on the

porosity of the pack.

Figure 1.3: Framework of reservoir sand with interstitial clay and

cement.

1-12

Porosity is at its maximum for spherical grains but becomes

progressively less as the angularity of the grains increases because such

grains pack together more closely. Experimental data from artificial

sands confirm that the grain size essentially has no influence on porosity

for well sorted sand. However, porosities of wet packed sands show a

general decrease as sorting becomes poorer. This is because with a

mixture of sizes, the smaller grains partially fill the interstices between

the larger grains.

Permeability, being a measure of the ease with which a material

transmits fluids, depends primarily upon the size, shapes and extent of

the interconnections between individual pores rather than the size of the

pores themselves. However, since the interconnections are directly

related to the pore size which in turn is related to grain size, there are

relationships between these factors and permeability. Krumbein and

Monk (1942) have shown that permeability varies as the square of the

mean grain diameter and a complex function of sorting (other factors

being equal). Experimental data show a marked decrease in permeability

as grain size decreases and as sorting becomes poorer. Experience has

also shown that the permeability measured normal to the bedding is

usually less than permeability measured parallel to the bedding and that

large variations in permeability occur in different directions in the

bedding plane.

Clay in the pore space of a reservoir may affect the performance of

a reservoir very adversely. The amount and kind of clay, as well as

distribution throughout the reservoir rock, has an important bearing on

liquid permeability, whereas a small amount has little effect on porosity.

Figures 1.4 and 1.5 show how the dispersed clay morphology affects the

permeability and capillary pressure of sandstones.

1-13

Figure1.4: Three general types of dispersed clay in sandstone reservoir

rocks and their effects on permeability: (a) discrete particles of kaolinite; (b) pore lining by chlorite; (c ) pore bridging by illite (from Neasham,

1977).

1-14

Figure1.5: Three general types of dispersed clay in sandstone reservoir rocks and their effects on capillary pressure (from Neasham, 1977).

If fresh water, for example drilling fluid filtrate, invades a reservoir,

certain clays, such as montmorillonite, will swell and plug some of the

pore interconnections, drastically reducing the permeability, whereas

saline water may have no effect.

1.7.2 Compaction and Cementation

The pore space of the original unconsolidated sediment is reduced

in ancient rocks by many factors. Compaction and cementation are the

most important of these factors but they in turn are affected by

1-15

composition of the sediment, and the contained fluids and their

pressures. Compaction by the weight of the overburden commences as

soon as a sediment is deposited. It produces reduction of pore space as

a result of:

1. Closer packing of the grains which causes smaller pores and

connected passages.

2. Crushing and fracturing of grains, and dissolution at points of

contact sometimes accompanied by precipitation of silica in the

pore space nearby. Alkaline interstitial water seems to provide

conditions more conducive to dissolution than saline water.

3. Plastic deformation of the softer grains which tend to mold around

the harder grains thus destroying pore space. The softer grains

may be composed of limestone, shale, siltstone and other rock

fragments, and when the amount of such soft material exceeds 10

to 12%, the permeability may be largely destroyed even though

some porosity usually remains.

Early cementation of sand may produce a rigid framework which

will inhibit compaction until the depth of burial exceeds that at which

fracturing of the grains and cement is initiated. Abnormal fluid pressure

in sandstone reservoirs also inhibits compaction because the overburden

is partly supported by the fluid pressure.

Reduction of reservoir pressure by production of fluid can lead to

compaction of the producing zone by rearrangement of the sand grains.

This can produce serious and expensive subsidence of surface facilities

such as occurred in the Wilmington field in California, Bolivar District

fields in Venezuela and Ekofisk field in the North Sea. This form of

1-16

compaction leads to porosity and permeability reduction which is

irreversible and which may affect the producing characteristics of the

reservoir very adversely.

Cementation is the result of recrystallization from solution of silica,

carbonates and other soluble materials in the pores of clastic rocks. The

most common cementing materials in sandstone reservoirs are silica and

calcite but many others do occur. It is not uncommon to find both silica

and calcite present in the cement and in such cases, the silica in the

form of quartz has precipitated first and the calcite later. Silica cement

usually occurs in the form of quartz and grows in optical continuity with

the sand grains until finally the crystals interfere with one another and

an interlocking network results. Calcite cement is often patchy but may

completely fill the pore space.

Silica cement appears to have two origins: (1) early cementation

before the sands were compacted appreciably, and (2) deposition of silica

predissolved by pressure solution during compaction. In the Eocene

Wilcox sandstones of the Gulf Coast, the distribution of silica cement can

be related to both primary texture and depth of burial. The amount of

silica cement tends to increase in coarser and better sorted sands and, to

a lesser extent, with depth. Much of this cement appears to be early and

unrelated to the compaction process.

1.7.3 Classification

Sandstones may be classified by mineral composition (Figure 1.6).

The principal types are: (a) quartz sandstones consisting of over 95%

detrital quartz, (b) feldspathic sandstone consisting of 5 - 25% feldspar,

(c) arkosic sandstone consisting of over 25% feldspar, (d) sublithic

sandstone consisting of 5 - 25% rock fragments and (e) lithic sandstone

consisting of over 25% rock fragments.

1-17

Sandstone grain texture consists of five components: (a) size, (b)

sorting, (c) shape (sphericity), (d) roundness, and (e) packing. Figure 1.7

shows a grain size comparator where some of these qualitative terms are

presented visually. Porosity is independent of grain size for uniform

grains but decreases as sorting gets poorer. Close packing reduces

porosity and permeability. The effects of shape and roundness on

porosity are less definite. Permeability increases with increasing grain

size, but decreases with poorer sorting. Permeability generally increases

with angularity and decreasing sphericity.

Figure 1.6: Classification of sandstones by composition.

1-18

Figure 1.7: Grain size comparator chart (from Stow, 2005).

1-19

1.8 CARBONATE RESERVOIRS (LIMESTONES AND DOLOMITES)

Most carbonate rocks, like clastics, are composed of particles of clay to gravel size that were generally deposited in a marine environment.

However, they differ from terrigenous clastics in that they are deposited

as lime particles which are produced locally, whereas, sandstones are

composed of particles transported from an outside source by water

currents. They differ even more importantly from sandstones by being

subject to more post-depositional diagenesis ranging from simple

cementation of the original particles to complete recrystallization or

replacement by dolomite or chert. In addition, they are susceptible to

solution at any stage in their diagenesis. They are usually more poorly

sorted than clastics.

Components of carbonate rocks are usually (1) grains of various

kinds, (2) lime mud, and (3) carbonate cement precipitated later. There

are several kinds of grains, of which four are the most important. These

are (1) shell fragments, called bio, (2) fragments of previously deposited

limestone called intraclasts, (3) small round pellets - the excreta of

worms, and (4) ooliths - spheres formed by rolling lime particles along

the bottom. Lime mud consists of clay-sized particles of lime.

The material between the grains may be primary lime mud

deposited at the same time as the grains which would be grain-supported

rock, or the grains may be floating in lime mud which would be mud-

supported rock.

1.8.1 Classification

Carbonates are usually classified according to depositional texture

as shown in Figure 1.8. The presence or absence of lime mud and the

1-20

type and abundance of grains form the basis of the classification. A

boundstone consists of original skeletal components bound together

during deposition (Figure 1.9). Grainstones consist of packed carbonate

grains with the texture being grain-supported and very little lime mud

(Figure 1.10). Packstones are grain-supported but contain very

substantial amounts of lime mud. Wackestones have a larger amount of

lime muds, such that the grains effectively float in the mud. Mudstones

consist of essentially lime muds only. The presence of lime mud may be

most important in the development of porosity in carbonates because

under the right conditions, lime mud may be preferentially dolomitized

and may also be more readily leached out than the grains.

Good porosity in carbonate reservoirs is usually due to

dolomitization. The largest volume of carbonate petroleum reserves

comes from dolomites. Dolomitization occurs from the substitution of

magnesium for calcium in half of the sites in a carbonate crystal. A

volume loss of 12 to 13% due to dolomitization results in a corresponding

increase in porosity. Due to their larger surface area, mud-size grains

are more easily dolomitized than sand-sized grains. Thus, the best

carbonate reservoirs may have the lowest primary porosity.

Dolomitization also creates planar crystal surfaces and harder crystal

structures. Thus, dolomites retain more of their porosity during

compaction than limestones.

1-21

Figure 1.8: Classification of carbonates by texture.

1.8.2 Pore Space

The porosity, permeability and pore space distribution in carbonate

reservoir rocks are related to both the depositional environment and the

diagenesis of the sediment. They are most commonly of secondary

(diagenetic) origin although residual primary pore space does occur.

Carbonates have a large range of pore structures due to the

complex nature of carbonate constituents and diagenetic features. The

pore structures have been classified by Choquette and Pray, 1970) as

shown in Figure 1.10.

1-22

Figure 1.9: Examples of boundstone.

1-23

Figure 1.9: Examples of grainstones.

1-24

Fabric-selective porosity includes:

Interparticle porosity.

Intercrystalline porosity - typical of dolomites.

Fenestral porosity - by solution along bedding planes or joint

surfaces.

Skeletal, framework, molding, or shelter porosity - selective solution of,

within, or around fossil material.

Oomoldic porosity - selective solution of ooliths.

Non fabric-selective porosity includes:

Fracture porosity - by stress or shrinkage.

Channel porosity - widening and coalescence of fractures.

Vuggy or cavernous porosity.

Bioturbation porosity - from boring and burrowing.

Breccia porosity - in some cases, really high fracture porosity.

In carbonates, porosity and permeability are not well-correlated

with grain size or sorting. Porosity and permeability are controlled

largely by the amount of fines and by diagenesis. Correlation of

petrophysical properties with rock type is thus very difficult.

1-25

Figure 1.10: Classification of pore systems in carbonate rocks (Choquette and Pray, 1970).

1-26

Table 1.6 shows a comparison of the pore space characteristics of

clastic and carbonate rocks (Choquette and Pray, 1970).

Table 1.6. Comparison of Pore-space Properties in Clastic and Carbonate Rocks (Choquette and Pray, 1970).

1-27

1.9 FRACTURED RESERVOIRS

Natural reservoir fractures are caused by brittle failure, usually

due to such factors as (a) folding, (b) faulting, (c) fluid pressure, (d)

release of lithostatic pressure, (e) pressure solution, (f) dehydration, (g)

weathering, (h) cooling and (i) impact craters. Natural fractures can exist

in essentially any type of rock although they are particularly common in

carbonates.

Naturally fractured reservoirs are usually treated by a dual

porosity approach to deal with their properties. The matrix rock

(between fractures) usually has reasonable porosity and extremely low

permeability. Fractures range in size from hair-size to several

millimeters in aperture. Fractures that have not been filled with cement

have very high permeabilities, even though they may be fairly widely-

spaced. However, the fracture system generally contains only a small

fraction of the reservoir pore space. Thus, the matrix contains the bulk

of the reservoir pore volume while the fractures contain the bulk of the

reservoir flow capacity.

Figure 1.11 shows a naturally fractured rock together with its

idealized dual porosity approximation.

1-28

Figure 1.11: Idealization of naturally fractured reservoir (Warren and Root, 1963)

1.10 RESERVOIR COLUMN

Figure 1.12 shows a reservoir column penetrated by a well. The

total thickness of the reservoir as determined from the spontaneous

potential (SP) log, discussed in Chapter 2, is H. This reservoir contains a

hydrocarbon bearing zone and a water bearing zone at the bottom. The

gross pay thickness, which is the thickness of the hydrocarbon bearing

portion of the reservoir as determined from the resistivity log (see

Chapter 2), is . However, this thickness contains shale breaks which

will not be productive and must be discounted to determine the net pay

to be used in reserves estimation. The net pay for this example is given

by

0h

1-29

6

1Net pay

i

ii

h=

== = h (1.1)

The net to gross (NTG) pay is defined as

6

1

0 0

Net to gross (NTG)

i

ii

hhh h

=

== =

(1.2)

The net to gross is a number that is less than or equal to 1 or if

expressed as a percentage, is a number that is less than or equal to

100%. Notice that in this example, there is a gas oil contact (GOC) and

an oil water contact (OWC) in the reservoir. The thickness of the gas zone

is gash and that of the oil bearing zone is . Of course, not all petroleum

reservoirs have a gas oil contact or an oil water contact. Net pay is used

along with other petrophysical properties of the reservoir to estimate the

hydrocarbon reserve as discussed in Chapter 2.

oilh

1-30

Figure 1.12. Reservoir column showing gross and net pay.

1-31

1-32

REFERENCES

Archie, G.E. :Introduction to Petrophysics of Reservoir Rocks, AAPG Bull., Vol. 34, No. 5 (May 1950) 943-961.

Beard, D.C. and Weyl, P.K. : Influence of Texture on Porosity and Permeability of Unconsolidated Sand, AAPG Bull. (Feb. 1973) 57, 349-369.

Choquette, P.W. and Pray, L.C. : Geologic Nomenclature and Classification of Porosity in Sedimentary Carbonates, AAPG Bull., Vol. 54, No. 2 (1970) 207-250.

Krumbein, W.C. and Monk, G.D. : Permeability as a Function of the Size Parameters of Unconsolidated Sand, Amer. Int. Mining and Met. Tech. Pub. 1492, 1942.

Levorsen, A.I. : Geology of Petroleum, W.H. Freeman and Company, San Francisco, 1967.

Neasham, J.W.: "The Morphology of Dispersed Clay in Sandstone Reservoirs and Its Effect on Sandstone Shaliness, Pore Space and Fluid Flow Properties," SPE 6858, Presented at the 52nd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Denver, Oct. 9-12, 1977.

Selley, R.C. : Elements of Petroleum Geology, W.H. Freeman, New York, 1985.

Stoneley, R. : An Introduction to Petroleum Exploration for Non-Geologists, Oxford University Press, New York, 1995.

Stow, D.A.V. : Sedimentary Rocks in the Field, Elsevier Academic Press, Burlington, 2005.

2-1

CHAPTER 2

POROSITY AND FLUID SATURATIONS

2.1 DEFINITION OF POROSITY

Porosity gives an indication of the rocks ability to store fluids. It is

defined as the ratio of the pore volume to the bulk volume of the porous

medium as shown in the following equation:

p b sb b

V V VV V

= = (2.1)

Porosity may be classified as total or effective porosity. Total

porosity accounts for all the pores in the rock (interconnected and

isolated pores) whereas effective porosity only accounts for the

interconnected pores. Therefore, effective porosity will be less than or

equal to total porosity depending on the amount of isolated pores in the

rock. From a reservoir engineering standpoint, it is the effective porosity

that matters, not the total porosity.

22

Porosity may also be classified as primary or secondary. Primary

porosity is that which was formed at the time of deposition of the

sediments whereas secondary porosity was developed after deposition

and burial of the formation. Sandstone porosity is practically all primary

porosity whereas carbonate porosity tends to be secondary porosity.

2.2 FACTORS AFFECTING SANDSTONE POROSITY

Sandstone porosity is affected by packing, sorting and

cementation. Packing describes the arrangement of the sand grains

relative to one another. Figures 2.1 shows three idealized types of

packing for spherical sand grains and their theoretical porosities. The

cubic packing has a porosity of 47.6%; the hexagonal packing has a

porostiy of 39.5% and the rhombohedral packing has a porosity of

25.9%. As shown by the geometrical derivations in Figure 2.1, the

porosity of a pack of uniform spheres is independent of the grain size as

the grain diameter cancels out.

Well sorted sandstone consists of grains having approximately the

same size whereas poorly sorted sandstone consists of grains having a

wide range of different grain sizes. Poor sorting reduces the porosity of

the sandstone as may be seen in Figure 2.2 in which the small grains fit

into the pores created by the large grains, thereby reducing the porosity.

2-3

Figure 2.1. Effect of packing on porosity of uniform spheres.

Figure 2.2. Effect of sorting on porosity. (A) Irregular grains,

(B) Idealized spherical grains (from Tiab and Donaldson, 2004).

24

Table 2.1 shows experimentally measured porosities of various

artificial sandpacks. Note the general decrease of porosity with poor

sorting for all grain sizes and the approximately constant porosity of the

extremely well sorted sands for all grain sizes.

Table 2.1 Measured Porosities of Artificial Sandpacks (adapted from Beard and Weyl, 1973)

In consolidated rocks, the sand grains are cemented together

usually by quartz or carbonates. Cementation reduces the porosity of

the sand as shown in Figure 2.3.

Figure 2.3. Effect of cementation on porosity.

2-5

2.3 FACTORS AFFECTING CARBONATE POROSITY

In carbonates, secondary porosity is usually more important than

primary porosity. The major sources of secondary porosity are

fracturing, solution and chemical replacement.

Fractures are cracks in the rock. Figure 2.4 shows an idealized

fractured formation where the grains are bricks and the fractures

constitute the pore space. Although fracture porosity is generally small,

often 1-2%, the fractures are very useful in allowing fluids to flow more

easily through the rock. Therefore, they greatly enhance the flow

capacity of the rock.

Figure 2.4. Idealized fractured rock with low fracture porosity.

Solution is a chemical reaction in which water with dissolved

carbon dioxide reacts with calcium carbonate to form calcium

bicarbonate which is soluble. This reaction increases the porosity of the

limestone. The chemical reactions are

26

2 2 2 3CO H O H CO+ = (2.2)

( )2 3 3 3 2H CO CaCO Ca HCO+ = (2.3)

Chemical Replacement is a chemical reaction in which one type of

ion replaces another with a resulting shrinkage in the size of the new

compound. An example is dolomitization in which some of the calcium

ions in calcium carbonate are replaced by magnesium ions to form

calcium magnesium carbonate (dolomite). This replacement causes a

shrinkage of 12 to 13% in the grain volume, with a corresponding

increase in secondary porosity. The chemical reaction is

( )3 2 3 222CaCO MgCl CaMg CO CaCl+ = + (2.4)

2.4 TYPICAL RESERVOIR POROSITY VALUES

Sandstones have porosities that typically range from 8% to 38%,

with an average of 18%. About 95% of sandstone porosity is effective

porosity. Sandstone porosity is usually mostly intergranular porosity.

Carbonates have porosities that typically range from 3% to 15%, with an

average of about 8%. About 90% of carbonate porosity is effective

porosity. Carbonate porosities are much more difficult to characterize

and may consist of (1) intergranular, (2) intercrystalline, (3) fractures and

fissures, and (4) vugular porosities.

2-7

2.5 LABORATORY MEASUREMENT OF POROSITY

2.5.1 Direct Porosity Measurement by Routine Core Analysis

Direct measurement of porosity requires the measurements of two

of the three volumes Vb, Vs and Vp. In the laboratory, measurements

are usually performed on extracted cores, which have been cleaned and

dried.

Bulk volume can be determined by (1) caliper and (2) fluid

displacement. For well machined samples, the dimensions can be

measured with a caliper, from which the bulk volume can be calculated.

Two types of fluid displacements can be used to determine bulk

volume. In the first method, fluid that does not easily penetrate the

pores such as mercury is used. The apparatus, which is known as a

pycnometer, measures the volume of mercury displaced by the sample

(Figure 2.5a). Since mercury does not penetrate the pores at

atmospheric pressure, the volume of mercury displaced is equal to the

bulk volume of the sample.

In the second method, fluid which easily saturates the sample is

used. The sample is weighed in air, evacuated and then saturated with a

liquid (brine, kerosene, or toluene). The saturated sample is weighed in

air and then weighed fully immersed in the saturating liquid. The loss in

weight of the saturated sample when fully immersed in the saturating

liquid is proportional to the bulk volume of the sample (Archimedes

principle).

Grain volume can be determined by (1) fluid displacement and (2)

gas exapansion using Boyles law porosimeter. The loss in weight of the

28

dry sample and the sample fully immersed in a liquid is proportional to

the grain volume.

Figure 2.5b shows a schematic diagram of a Boyles law porosimeter for grain volume determination by gas expansion. The sample, which is confined in a vessel of known volume V1, is pressured

by gas (air, nitrogen or helium) to a pressure P1 (absolute units). The vessel of volume V1 is connected to a second vessel of known volume V2,

which is initially evacuated. The valve between the two vessels is opened

and the pressure in the two vessels is allowed to stabilize at P2 (absolute units). By Boyles law (PV = constant at a constant temperature),

( ) ( )1 1 1 2 2s sV V P V V V P = + (2.5)

Eq.(2.5) can be solved for the grain volume as

21 21 2

sPV V V

P P =

(2.6)

The instrument can be calibrated with steel blanks of known volume.

Calibration consists of a plot of Vs versus P2/(P1-P2), which should be

linear with a slope, -V2, and an intercept, V1. At least three steel blanks

of different sizes should be used in the calibration to ensure reliability of

the calibration. The three data points should fall on the calibration line.

Also, the slope and the intercept should be checked against the known

volumes, V2 and V1. Once the calibration line has been established, it is

used to convert the measurements from core samples to grain volume.

2-9

Figure 2.5. Schematics of equipment for measurement of core plug porosity.(a) Bulk volume pycnometer; (b) Boyles law porosimeter; (c) Bulk and pore volume porosimeter.

210

Pore volume can be determined by (1) fluid saturation and (2)

mercury injection. The difference in the weight of the saturated sample

and the dry sample is proportional to the pore volume.

Mercury injection consists of forcing mercury under relatively high

pressure into the pores of the sample using a mercury porosimeter

(Figure 2.5c). Typically, the core is evacuated before mercury injection.

Because any air left in the pores is compressed to a negligibly small

value, the volume of mercury injected is essentially equal to the

connected pore volume of the sample. This is a destructive method

because after the test, the sample is no longer suitable for other

measurements. Mercury porosimetry is also used to determine capillary

pressure and pore size distribution of the sample (see Chapter 6).

The methods so far described determine the effective porosity of

the sample. To determine the total porosity, the sample is ground into a

fine powder after bulk volume measurement. The grain volume of the

ground sample can be determined either by liquid displacement or by

assuming an average grain density.

The measurement of porosity on consolidated samples in routine

core analysis might generally be expected to yield values of the true

fractional porosity plus or minus 0.005, i.e., a true value of 27% porosity

may be measured between 26.5% and 27.5% porosity.

Core porosities may differ from in-situ porosities for the following

reasons:

The core may be altered during recovery.

2-11

The core in the laboratory is no longer subjected to the overburden and lateral stresses that it was subjected to in the reservoir.

The porosities are measured on small plugs, which may not be representative of the entire reservoir.

The volume of the core analyzed is small and may not account for the variability of the porosity in the reservoir.

Despite these limitations, core analysis provides the only direct

measurement of porosity. Frequently, the results of core analysis are

used to calibrate well logs.

Example 2.1

An experiment has been performed to determine the porosity of an

irregularly shaped core sample. The cleaned dry sample was weighed in

air. It was then evacuated and fully saturated with an oil with a density

of 0.85 gm/cc and then weighed again in air. Afterwards, the saturated

sample was weighed when it was fully immersed in the oil. Here are the

results of the experiment.

Weight of dry sample in air = 42.40 gm

Weight of the saturated sample in air = 45.49 gm

Weight of the saturated sample immersed in the oil = 28.80 gm

a. Calculate the porosity of the core.

212

b. Is there enough information from this experiment to determine the

mineralogy of the sample? If yes, what is it? Please justify your answer

with appropriate arguments.

Solution to Example 2.1

Wt of dry sample (Wdry) = 42.40 gm

Wt of saturated sample (Wsat) = 45.49 gm

Wt of sample immersed in oil (Wi) = 28.80 gm

Density of saturating oil (L) = 0.85 gm/cc

a. Required to calculate the porosity of the sample.

Pore volume (Vp) = (Wsat Wdry)/L = (45.4942.40)/0.85 = 3.64 cc

Bulk volume (Vb) = (Wsat Wi)/L = (45.4928.80)/0.85 = 19.64 cc

Porosity () = Vp/Vb = 3.64/19.64 = 0.185 or 18.5%

b. Yes. There is enough information to determine the mineralogy of

the sample through the grain density.

Grain volume (Vs) = VbVp =19.643.64 = 16.00 cc

Alternatively, Grain volume (Vs) = (WdryWi)/L = (42.4028.80)/0.85 = 16.00 cc

2-13

Grain density (s) = Wdry/Vs = 42.40/16.00 = 2.65 gms/cc

Specific gravity of mineral (m) = s /w = 2.65/1.00 = 2.65

Table 1.1 lists the specific gravities of common reservoir rock minerals.

From the table, quartz has a specific gravity of 2.65, which is the same

as the specific gravity of the sample matrix. Therefore, based on the

available information, the mineral of the sample is quartz.

2.5.2 Indirect Porosity Measurement by CT Imaging

With the availability of X-ray computed tomography (CT) imaging

systems in research laboratories, it is now possible to measure the

porosity distributions in core samples. Peters and Afzal (1992) have

made such measurements in an artificial sandpack and a Berea

sandstone approximately 60 cm long and 5 cm in diameter. CT imaging

gives rise to a very large data set, over 600,000 porosity values in some

cases. Therefore, it is convenient to present the results of the

measurements as images (Figures 2.7 and 2.8). It should be noted in

Figure 2.7 that a sandpack may not be as uniform as we always assume

it to be. The packing technique used in this test introduced significant

porosity variation into the pack. The packing history is clearly evident in

the image. The dominant feature in the porosity variation of the Berea

sandstone is layering which is clearly visible in Figure 2.8. The porosity

data also can be presented in histograms as shown Figures 2.9 and 2.10.

The porosity in each voxel (volume element) was obtained by

scanning the sample dry and then scanning it fully saturated with a

wetting fluid such as brine. The x-ray attenuation equations for the two

scans are

214

( )1m air dry + = (2.7)

( )1m brine wet + = (2.8)

Eqs.(2.7) and (2.8) can be solved simultaneously to obtain the porosity in

each voxel as

wet drybrine air

= (2.9)

The x-ray attenuation coefficient of the brine in Eq.(2.9) is obtained by

scanning a sample of the brine in a test tube and the attenuation for air

is assumed to be zero.

Figure 2.7. Porosity image of a sandpack from CT imaging. L = 54.2 cm,

2-15

d = 4.8 cm. (a) Cross-sectional slice. (b) Longitudinal vertical slice. (Peters and Afzal, 1992).

Figure 2.8. Porosity image of a Berea sandstone from CT imaging. L = 60.2 cm, d = 5.1 cm. (a) Cross-sectional slice. (b) Longitudinal vertical

slice. (Peters and Afzal, 1992).

216

Figure 2.9. Porosity histogram for a sandpack from CT imaging. L = 54.2 cm, d = 4.8 cm. Mean = 29.7%, Standard deviation = 2.5%.(Peters

and Afzal, 1992).

2-17

Figure 2.10. Porosity histogram for a Berea sandstone from CT imaging. L = 60.2 cm, d = 5.1 cm. Mean = 17.3%, Standard

deviation = 2.0%.(Peters and Afzal, 1992).

2.6 FLUID SATURATIONS

In a petroleum reservoir, there is always more than one fluid phase

occupying the pore space. In an oil reservoir, oil and water occupy the

pore space. In a gas reservoir, gas and water occupy the pore space. At a

certain point in the production of an oil reservoir, oil, water and gas

could occupy the pore space. There is a need to keep track of the

quantity of each type of fluid occupying the pore space. The

petrophysical property that describes the amount of each fluid type in

218

the pore space is the fluid saturation. It is defined as the fraction of the

pore space occupied by a fluid phase. Thus, in general,

Fluid VolumeFluid Saturation = Effective Rock Pore Volume

(2.10)

If Sw = water saturation, So = oil saturation and Sg = gas saturation,

then Sw = Vw/Vp, So = Vo/Vp, and Sg = Vg/Vp, where Vw, Vo, Vg and

Vp are the volumes of water, oil, gas and pore space, respectively. For an

oil reservoir without a free gas saturation, So + Sw = 1.0. For a gas

reservoir without a liquid hydrocarbon saturation, Sg + Sw = 1.0. For an

oil reservoir with a free gas saturation, So + Sw + Sg = 1.0. Fluid

saturation may also be expressed in %.

There are two methods of determining the in-situ fluid saturations

in a petroleum reservoir rock. The direct approach is to measure the

fluid saturations from a core cut from the reservoir. The indirect

approach is to measure some other physical property of the rock that can

be related to fluid saturation. The direct approach is discussed here.

The indirect approach such as using electric logs or capillary pressure

measurements to estimate water saturation will be discussed later.

One method of direct measurement of fluid saturations is the

retort method. In this method, a core sample is heated so as to vaporize

the water and oil, which are condensed and collected in a small,

graduated receiving vessel (Figure 2.11). The volumes of oil and water

divided by the pore volume of the core sample give the oil and water

saturations. The gas saturation is obtained indirectly by the requirement

that saturations must sum to one.

2-19

Figure 2.11. Retort distillation apparatus.

There are two disadvantages to the retort method of saturation

determination. In order to remove all the oil, it is necessary to heat the

core to temperatures in the range of 1000 to 1100 F. At these

220

temperatures, the water of crystallization (hydration) of the rock is driven

off, resulting in an estimated water saturation that is higher than the

true interstitial (connate) water saturation. The second disadvantage is

that the oil when heated to high temperatures has a tendency to crack

and coke. This cracking and coking tend to reduce the oil volume

resulting in an oil saturation that is less than the true value.

Corrections can be made to the retort measurements to make them more

accurate.

Another method of direct saturation measurement is by extraction

with a solvent. This is accomplished in a Dean-Stark distillation

apparatus (Figure 2.12). The core is placed in the apparatus in such a

way that the vapor from a solvent (e.g., toluene) rises through the core

and is condensed back over the sample. This process leaches out the oil

and water from the sample. The water and solvent are condensed and

trapped in a graduated receiver. The water settles to the bottom of the

receiver while the solvent refluxes back into the main heating vessel. The

extraction is continued until no more water is collected in the receiving

vessel. The water saturation is calculated directly from the volume of

water expelled from the sample. The oil saturation is calculated

indirectly from the weight of the saturated sample before distillation, the

weight of the dry sample after distillation and the weight of the water

expelled from the sample. Again, the gas saturation is calculated

indirectly from the requirement that the saturations must sum to one.

To ensure that all the oil has been removed from the sample, the

sample may be transferred from the Dean-Stark apparatus to a Soxhlet

extractor for further extraction (Figure 2.13). The Soxhlet extractor is

similar to the Dean-Stark apparatus except that there is no provision for

trapping the extracted liquids.

2-21

The saturations determined by direct measurements on cores

should be treated with caution because they may not represent the in-

situ fluid saturations for several reasons. If the core was cut with a

water-based drilling mud, it would have been flushed by mud filtrate

resulting in a higher water saturation than the original, undisturbed

formation water saturation. The measured oil saturation in this case

would be the residual oil saturation after waterflooding, which is less

than the original in-situ oil saturation. If the core was cut with an oil-

based mud, the water saturation obtained by direct measurement will be

essentially the correct original water saturation, if it was at irreducible

level. If the original in-situ water saturation was not at the irreducible

level, then the oil mud filtrate could potentially displace some of the

water making the laboratory measured water saturation to be too low.

Figure 2.12. Dean-Stark apparatus.

222

Figure 2.13. Soxhlet extractor.

As the core is brought from the high pressure and temperature of

the reservoir to the low pressure and temperature of the laboratory,

changes occur in the fluid saturations which can make them

considerably different from the original in-situ saturations. The free gas,

if present, will expand, expelling water and oil in the process. Solution

gas will evolve from the oil, expand and further reduce the oil and water

volumes. The evolution of solution gas causes the oil to "shrink". These

changes cause the saturations determined by core analysis to be

different from the in-situ saturations. In particular, the changes cause

gas saturation to be excessive even when there was no free gas

saturation at the original in-situ conditions.

2-23

Although the saturations determined by direct measurements on

cores may not reflect the true in-situ saturations, they do provide useful

information about the reservoir. The saturation measurements can be

used to approximately locate the gas-oil and water-oil contacts in the

reservoir if they are present.

Fluid saturations, So, Sw and Sg, only tell us the proportion of

each fluid type in the pore space. They do not tell us how the fluids are

distributed in the rock. To determine the fluid distribution, we need to

consider the interfacial forces and phenomena that arise when

immiscible fluids are confined in reservoir pores of capillary dimensions.

The important interfacial forces and phenomena include surface tension,

interfacial tension, wettability, capillarity and capillary pressure (see

Chapters 6 and 7).

Table 2.2 shows the data obtained in an example core analysis

from a hydrocarbon bearing formation from a depth of 4805.5 to 4851.5

feet. The table shows the depth, core permeability, core porosity, oil

saturation, water saturation and gas saturation as determined in the

laboratory. Although the fluid saturations are not the true in-situ

saturations, nevertheless they provide useful information. Figure 2.14

shows the saturation distributions from the core data. One can easily see

a water bearing zone at the bottom where the measured water saturation

is very high, an oil bearing zone above it, and a gas cap on top of the oil

zone. A gas oil contact exists at 4828.5 ft, and a water oil contact exists

at 4848.5 ft. Note the misleading gas saturation below the gas oil

contact. There was no free gas saturation below the gas oil contact at in-

situ conditions.

224

Table 2.2: Core Analysis Data

Depth k So Sw Sg (ft) (md

) (%) (%) (%) (%)

4805.5 0 7.5 0.0 68.0

32.0

4806.5 0 12.3

0.0 78.0

22.0

4807.5 2.5 17.0

0.0 43.0

57.0

4808.5 59 20.7

0.0 29.0

71.0

4809.5 221 19.1

0.0 31.4

68.6

4810.5 211 20.4

0.0 38.7

61.3

4811.5 275 23.3

0.0 34.7

65.3

4812.5 384 24.0

0.0 26.2

73.8

4813.5 108 23.3

0.0 30.9

69.1

4814.5 147 16.1

0.0 29.2

70.8

4815.5 290 17.2

0.0 34.3

65.7

4816.5 170 15.3

0.0 24.2

75.8

4817.5 278 15.9

0.0 26.4

73.6

4818.5 238 18.6

0.0 39.8

60.2

4819.5 167 16.2

0.0 39.5

60.5

4820.5 304 20.0

0.0 38.0

62.0

4821.5 98 16.9

0.0 34.3

65.7

4822.5 191 18.1

0.0 34.8

65.2

4823.5 266 20.3

0.0 31.1

68.9

4824.5 40 15.3

0.0 22.9

77.1

4825.5 260 15.1

0.0 13.9

86.1

4826.5 179 14.0

0.0 21.4

78.6

4827.5 312 15.6

0.0 28.8

71.2

2-25

4828.5 272 15.5

0.0 34.8

65.2

4829.5 395 19.4

6.2 25.3

68.5

4830.5 405 17.5

13.1

25.7

61.2

4831.5 275 16.4

17.7

22.5

59.8

4832.5 852 17.2

19.8

19.2

61.0

4833.5 610 15.5

21.9

21.3

56.8

4834.5 406 20.2

16.3

22.3

61.4

4835.5 535 18.3

19.7

24.6

55.7

4836.5 663 19.6

19.4

16.3

64.3

4837.5 597 17.7

17.5

19.8

62.7

4838.5 434 20.0

14.0

27.5

58.5

4839.5 339 16.8

20.8

19.7

59.5

4840.5 216 13.3

18.1

23.3

58.6

4841.5 332 18.0

15.6

15.6

68.8

4842.5 295 16.1

19.3

15.5

65.2

4843.5 882 15.1

19.2

21.2

59.6

4844.5 600 18.0

20.6

22.2

57.2

4845.5 407 15.7

15.3

13.4

71.3

4847.5 479 17.

8 20.8

14.6

64.6

4848.5 0 9.2 14.1

8.7 77.2

4849.5 139 20.5

0.0 77.1

22.9

4850.5 135 8.4 0.0 57.2

42.8

4851.5 0 1.1 0.0 63.6

36.4

226

Figure 2.14. Saturation distributions from core analysis data.

Other useful observations can be made from the core

analysis data. The low residual oil saturation of about 20% indicates a

light oil reservoir in contrast to a heavy (more viscous) oil reservoir in

which the residual oil saturation would be much higher than 20%. All of

2-27

the measured properties vary with depth, which is an indication that the

reservoir is heterogeneous in nature. The porosity and permeability

distributions are shown in Figure 2.15. Variability of reservoir properties

is pervasive. Not only do the properties vary along the well depth, they

also vary laterally away from the well. The characterization of this

variability and the estimation of the properties at unmeasured locations

are the subjects addressed by geostatistics (see Chapter 4).

2.7 INDIRECT POROSITY MEASUREMENT FROM WELL LOGS

2.7.1 Introduction to Well Logging

In-situ porosity cannot be measured directly in the field as in the

laboratory. Therefore, only indirect measurements are made through well

logging. These measurements use either sonic energy or some form of

induced or applied radiation. Most log evaluation is concerned primarily

with determining in-situ porosity and water saturation. Neither in-situ

water saturation nor hydrocarbon saturation can be measured directly in

the wellbore. However, it is possible to infer the water saturation if the

porosity is known by measuring the resistivity of the formation.

Therefore, in this section, porosity and resistivity logs are discussed.

Care should always be taken in comparing core versus log-derived

porosities, particularly in rocks that have been highly affected by

diagenesis. Logs measure average porosities over a much larger volume

than conventional laboratory core analysis. Also, a laboratory core has

been relieved of the overburden and lateral stresses and because it is an

elastic medium, it will expand. Since the minerals have very low

coefficient of expansion, the increase in volume must be due almost

solely to the increase in porosity. Thus, the porosity measured in the

228

laboratory at ambient conditions may be expected to be higher than at in

situ conditions.

Figure 2.15. Porosity and permeability distributions from core analysis

data.

2-29

2.7.2 Mud Filtrate Invasion

Well log measurements are made in the borehole after the well has

been drilled. The drilling operation alters the formation characteristics

near the wellbore where the log measurements are made. In order to

interpret the logs, it is necessary to understand the changes that have

occurred in the formation caused by the drilling mud.

Drilling mud is a complex liquid usually composed of mainly water

(for water-based muds) and suspended solids and various chemicals that

control the mud properties (viscosity, fluid loss, pH and others). Clays

(bentonite) are added to give the mud viscosity and weighting material

(barite) is added to increase the mud density above that of water.

The mud is circulated during drilling to lift the cuttings out of the

borehole. Another important function of the mud is to exert a

backpressure on the formation to prevent the well from "kicking" during

the drilling operations. In general, during drilling, the pressure in the

mud column in the borehole is higher than the formation pressure.

If we take a mud sample and place it in a mud press as is typically

done in mud testing, we can separate the mud into its two main

components: mud filtrate and mudcake. Mud filtrate is a clear liquid

whose salinity varies according to the source of the water used to mix the

mud and the chemical nature of the additives. Usually,