Correlation Between Microstructure and Flow Behavior in Porous Sandstones

Petroleum Science and Technology, 27:511–529, 2009

Copyright © Taylor & Francis Group, LLC

ISSN: 1091-6466 print/1532-2459 online

DOI: 10.1080/10916460701856666

Correlation Between Microstructure and Flow

Behavior in Porous Sandstones

S. Baraka-Lokmane,1;2 I. G. Main,3 B. T. Ngwenya,3 S. C. Elphick,3

C. Jones,4 and S. A. Hamilton1

1Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh UK2School of Environment and Technology, University of Brighton, Brighton, UK

3School of GeoSciences, University of Edinburgh, UK4Weatherford Production and Completion Systems Expandable Technology,

Aberdeen UK

Abstract: The correlation between permeability and petrographical parameters in

cored samples can be used by extrapolations to predict permeability in uncored

intervals. The core analysis described here is concerned with the study of fluid-

rock interactions in rock samples from three sandstone reservoirs, in particular the

effect of petrographical parameters on flow behavior. A positive correlation between

liquid permeability and the volume fraction of silica is clearly demonstrated. Liquid

permeability was correlated using multivariate regressions to one to five petrographical

parameters, the results of which have useful application in the estimation of reservoir

permeability where samples are not available for experimental testing.

Keywords: laboratory study, permeability, petrography, sandstone

INTRODUCTION

Reservoir engineers, petrophysicists and exploration geologists are interested

in discovering how permeability and porosity are related to petrographical

properties so they can predict permeability from petrographic data. Many

authors have tried to obtain quantitative relationships between petrographic

properties (two dimensions) and petrophysical properties (three dimensions).

They aim to predict, by extrapolating or interpolating, the petrophysical

properties of a porous medium, such as porosity, specific surface of pores,

permeability, and capillary pressure versus saturation, and electrical proper-

ties, such as formation factor and cementation exponent (Mowers and Budd,

Address correspondence to S. Baraka-Lokmane, School of Environment and

Technology, University of Brighton, Cockcroft Building, Lewes Road, Brighton, BN2

4GJ, UK. E-mail: [email protected]

511

512 S. Baraka-Lokmane et al.

1996; Anselmetti et al., 1998). Ioannidis et al. (1996) have investigated the

possibility of using statistical analysis of the porous microstructure as a

means of estimating reservoir permeability. The objective of their studies

is to examine empirically the relationship between reservoir permeability and

appropriate statistical attributes of the pore space. Ali and Chawathé (2000)

have used neural networks to predict permeability from petrographic data

from very fine-grained arkosic sandstone. This study underscored various

important aspects of using neutral networks as nonlinear estimators in a mul-

tivariate analysis. Cerepi et al. (2001) described a method of characterization

and quantification of petrophysical properties of carbonate pore systems from

petrographic image analysis on length scales spanning more than three orders

of magnitude, from submicron to millimeter scale. They compared these

results with petrophysical property values obtained by classical petrophysical

methods (3-D).

In this study, permeability measurements as well as petrographic exami-

nation of three sandstone reservoir samples (Fife and Locharbriggs sandstones

both from southwest Scotland and Slick Rock Aeolian sandstone from Utah,

United States) were used to evaluate the effect of mineralogy on permeability.

The choice of three different types of sandstones that differ in grain size,

porosity, and mineralogy will show that variations in the porous microstruc-

ture can be linked to the flow behavior of single fluids.

DESCRIPTION OF ROCK MATERIAL

Several complementary and overlapping methods have been used in this

study to characterize the material composition and texture characteristics.

This strategy allows both a full range of characteristics to be determined and

internal checking between measurements. These methods are particle size

analysis, point-counting method based on petrographic thin sections, X-Ray

Difraction (XRD), and X-Ray Fluorescence (XRF)

Particle Size Analysis

The Beckmann Coulter LS 100 Grain Size Analyzer is used for these mea-

surements. Particles in the range of 0.4 �m to 800 �m diameter are analyzed

by laser light at 750 nm. The individual analyzed grain particles have been

obtained by simple hand crashing; this was possible because of the weak

cementation of the sandstone samples. The 3-D bulk particle size analyses

were used for characterizing and classifying the samples and for determining

their heterogeneity, the percentages of the different particles (clays, silt, and

sand), the degree of sorting (So), and the mean grain size of the samples

(MGS) (Table 1). However, this information does not describe the spatial

relationships of the minerals and cements in the rock microstructure. This

Correlation between Microstructure and Flow Behavior 513

Table 1. Particle size analysis of the three groups of samples

Sample% ofclay

% ofsilt

% ofsand

d10

(mm)d50

(mm) So Uc

MGS(�m)

S2 1.77 8.94 91.06 0.07 0.14 0.26 2.36 163.4S4 0.83 6.29 93.71 0.08 0.22 0.26 2.92 225.3S5 1.46 6.17 93.83 0.08 0.25 0.26 3.25 243.1S6 1.33 5.25 94.75 0.08 0.32 0.29 2.92 233.9S7 0.97 6.08 93.92 0.08 0.18 0.29 2.36 191.2S8 1.97 12.06 87.94 0.05 0.14 0.24 3.25 170.2S9 1.08 5.87 94.13 0.08 0.20 0.26 2.62 221.6S10 1.51 6.78 93.22 0.08 0.16 0.29 2.36 183.5S11 0.89 6.96 93.04 0.08 0.20 0.29 2.62 213.8S12 1.02 7.09 92.91 0.07 0.22 0.26 3.25 230.5L1 1.6 7.68 92.32 0.07 0.18 0.29 2.92 197.2L3 1.37 13.85 86.15 0.02 0.20 0.29 10.58 193.7L4 1.16 11.78 88.22 0.03 0.20 0.29 6.89 206.1L5 1.11 15.68 84.32 0.02 0.20 0.263 10.58 198.4F2 0.00 0.00 100.0 0.20 0.31 0.32 1.53 328.4F8 0.00 0.00 100.0 0.22 0.34 0.36 1.71 368.4

d10: grain size (mm) of 10% (cumulative wt%); So: degree of sorting; Uc: coefficientof uniformity; MGS: mean grain size.

study has shown that the three groups of samples are very well sorted. The

Fife sandstone samples present the largest mean grain size (348 �m ˙ 28)

(Table 7).

Petrography

The study has been extended to the thin sections analysis, using a point-

counting technique. Forty-two thin sections were point-counted using a 400-

point density per square mm. The results are reported as percentages of

the different mineral constituents, the dominant cement, and the porosity

(Table 2). During the liquid permeability measurements, clays may absorb

brine and increase in volume. Such swelling clays may then move in the

flow field and block pore throats, thus reducing permeability. We therefore

characterized the clay content of the samples as closely as possible, both in

the bulk sample and also the separate fraction of mobile fine particles or

“fines.”

This study has shown that for the Slick Rock Aeolian sandstone samples,

the grains are rounded, well sorted, and friable. The permeability is controlled

by the porosity, varying between 20% and 23%, rather than the cement, which

varies between 7% and 13%. Quartz (77–88%), K-feldspar (3–11%), various

rock fragments (0.6–3%), and detrital mica (muscovite), which is only a minor

component (0–0.3%), are the main detrital components of the Slick Rock

Table 2. Mineralogy compositions of the three groups of samples (from 2-D thin sections analysis)

Framework Cement

Sample

Quartz

(%)

Feldspar

(%)

Mica

(%)

Rock

fragments

(%)

Clay C

Hematite

(%)

Calcite or

Pyrite

(%)

Quartz

overgrowths

(%)

Feldspar

overgrowths

(%)

Porosity

(%)

S2 77.36 11.03 0.24 3.02 5.81 1.94 0.25 0.35 22.60

S4 86.76 3.17 0.25 1.73 4.18 3.66 0.00 0.25 20.00

S5 88.63 3.30 0.00 1.25 4.57 1.23 0.25 0.77 20.70

S6 78.59 7.86 0.35 1.53 7.24 3.80 0.00 0.63 21.00

S7 82.32 6.85 0.25 1.62 4.98 3.73 0.00 0.25 20.70

S8 81.94 3.96 0.00 0.62 5.81 7.05 0.00 0.62 20.70

S9 79.47 8.50 0.25 1.48 4.95 4.33 0.25 0.77 20.20

S10 82.84 3.90 0.00 1.65 5.96 4.63 0.77 0.25 23.00

S11 82.22 2.94 0.00 2.47 4.30 6.30 0.00 1.77 21.00

S12 82.35 6.01 0.00 1.69 5.32 3.13 0.00 1.50 20.20

L1 81.22 11.41 0.00 1.61 4.51 0.72 0.33 0.20 23.00

L2 78.81 13.46 0.00 1.61 5.10 0.68 0.00 0.34 22.60

L4 83.47 8.87 0.00 0.41 5.98 0.72 0.28 0.27 20.00

L5 72.23 16.87 0.00 0.68 8.63 0.78 0.34 0.47 20.00

F2 82.85 10.16 0.00 0.63 6.35 0.00 0.00 0.00 27.00

F8 83.19 8.07 0.00 4.03 4.03 0.00 0.67 0.00 25.00

51

4


Aeolian sandstones (Figure 1). Between 7% and 18% of the sample consist

of cements, which are in the form of clay minerals (mainly illite), hematite

interspersed with illite, carbonate (calcite), and quartz and feldspar in the form

of overgrowths. Most of the microcline is largely replaced by calcite. The

samples are characterized by a large amount of clay minerals, mainly illite.

Early stages of clay cementation are visible with thin, authigenic coatings

of clays having formed around most of the detrital grains. Even such thin

coatings may serve to isolate the grains from the pore fluids and thus inhibit

alteration or cementation processes. In certain areas the illite cement forms a

thick grain coating as well as completely bridging pores in numerous places.

Fluid movements would be greatly retarded by such cementation. Hematite

cementation, when it is present, is interspersed with clays around the detrital

grains (Figure 1). The Locharbriggs sandstone samples present a red tint. The

grains are subrounded to angular and are very well sorted. The porosity varies

between 20% and 23%. Monomineralic and polycrystalline quartz (72–83%),

plagioclase and K-feldspar (9–17%), and various rock fragments (0.4–2%) are

the main detrital components of the samples (Figure 2). The cements make

up between 6% and 10% of the sample, in the form of clay minerals, quartz

and feldspar overgrowths, pyrite, and hematite (Figure 2). Hematite again

gives the red pigmentation to the sample. Authigenic clays (illite, kaolinite,

and smectite) coat most of the detrital grains. The hematite cementation is

in most cases interspersed with clays, quartz, and other detrital grains. The

pyrite crystals have been formed as a replacement in detrital grains (quartz

or feldspar). The Fife sandstones present a porosity varying between 25%

and 27%, with cement content between 5% and 6%, constituted mainly by

kaolinite (Figure 3). The main detrital components of the Fife sandstones are

Figure 1. Thin section photo of a Slick Rock Aeolian Cement containing clay (Cl)

minerals and calcite (Cal). Note clays having formed around the quartz grains and

also present in the pore space.


Figure 2. Cement containing clay minerals (Cl), hematite (H), and Pyrite (P)

(Locharbriggs sandstone)

represented by quartz (83%), microcline (8–10%), and various rock fragments

(0.6–4%) (Table 2).

X-Ray Diffraction Analyses

X-Ray diffraction (XRD) analyses were carried out both on whole rock

(Table 3) and the fine particle fraction (Table 4) to quantify the mineralogy

independently from the point-counting exercise and to estimate clay type and

Figure 3. Thin section photo of a Fife sandstone. Note the homogeneity of the rock

material (Q: quartz, Cl: clay)


Table 3. Mineralogy composition of the three groups of samples

(from XRD analyses)

Sample

Quartz

(%)

Microcline

(%)

Calcite

(%)

Muscovite

(%)

Kaolinite

(%)

S2 80 15 2 2 0

S4 91 5 1 2 0

S5 93 5 1 0 0

S6 86 9 2 2 0

S7 87 8 1 2 0

S8 93 4 1 0 0

S9 83 11 3 2 0

S10 92 5 2 0 0

S11 93 4 1 0 0

S12 91 7 1 0 0

L1 85 14 0 0 0

L3 82 17 0 0 0

L4 88 11 0 0 0

L5 79 20 0 0 0

F2 100 Trace 0 0 0

F8 97 3 Trace 0 Trace

Table 4. Mineralogy composition of the fine particles of the three groups of

samples (from XRD analyses)

Sample

Quartz

(%)

Microcline

(%)

Calcite

(%)

Illite

(%)

Hematite

(%)

Kaolinite

(%)

Smectite

(%)

S2 45 15 5 35 0 0 0

S4 85 10 5 0 0 0 0

S5 75 10 5 10 0 0 0

S6 70 10 5 15 0 0 0

S7 40 15 5 40 0 0 0

S8 90 5 5 0 0 0 0

S9 35 10 5 50 0 0 0

S10 80 10 5 5 0 0 0

S11 91 5 4 0 0 0 0

S12 60 10 5 25 0 0 0

L1 40 35 0 10 5 5 5

L3 55 25 0 6 5 4 4

L4 55 20 0 10 5 4 5

L5 50 25 0 10 5 5 5

F2 80 7 0 0 0 13 0

F8 60 10 0 0 0 30 0


its abundance. The equipment used for this type of measurement is Philips

PW1800 X-ray diffractometer with Cu target tube run at 40 kV and 50 mA.

Approximately 5 g of material were cut from each rock sample; the cut

pieces were crushed and the chips ground in a tungsten carbide barrel for 2

min. The samples are prepared by dropping the slurry of fine sediment and

water on the circular glass slides and allowing the water to evaporate at room

temperature. All samples are run from 2 to 60 degrees 2� , which covers all

the minerals. The intensity of the peaks generated gives an indication of the

amount present, and the position of the peaks identifies the minerals. When a

unique peak is chosen to characterize a particular mineral, it is obvious that

the peak has to be free of interference from the peaks of other minerals. For

the analyses of the fine particle fraction, the bulk sample had been mixed with

50 ml of distilled water and stirred. The top 30-ml suspension was removed

after 4 hours. The suspension was allowed to settle out over the next 4 days.

Nearly all the water was poured off, leaving about 2 ml for making slurry

with the sediment. The slurry was transferred to a glass slide and the water

allowed to evaporate at room temperature.

The results of the XRD analysis of the Locharbriggs sandstone samples

show that two mineral compounds (quartz and microcline) are identified.

The Slick Rock Aeolian sandstones possess calcite in addition to these two

minerals. The analysis of the fine particles of the Fife sandstone samples

shows the presence of two clay minerals (kaolinite and illite). Illite is the

only clay mineral found in the Slick Rock Aeolian sandstones. The XRD

measurements show the presence of three clay minerals in the case of the

Locharbriggs sandstones (kaolinite, smectite and illite).

X-Ray Fluorescence Analyses

Approximately 50 g of material was cut from each rock sample. The cut

pieces were crushed in a tungsten carbide barrel for 2 min. Samples were

analyzed for major elements using Philips PW 1480 automatic x-ray fluores-

cence (XRF) spectrometer with Rh-anode x-ray tube. Major-element analysis

was carried out on fused glass discs prepared by a method based on that

of Norrish and Hutton (1969) and described by Fitton et al. (1998). Rock

powders were dried in an oven overnight at 110ıC. Approximately 1 g of

each powder was ignited for 20 min in a Pt-5% Au crucible at 1100ıC

and a value for LOI (D H2O loss C CO2 loss � O2 gain) was calculated

from the weight change. The ignited powder was then fused for 20 min

at 1100ıC using a lithium borate flux (Johnson Matthey Spectroflux 105)

with a 5:1 (flux: sample) dilution. The molten material was poured from the

crucible into a graphite plate and pressed into a disc by lowering an aluminium

plunger into the globule. The casting operation was carried out on a hotplate

at 220ıC, and the glass disc was annealed at this temperature for 10 min

before cooling. Corrections for matrix effects on the intensities of major


Table 5. X-Ray fluorescence results of the three groups of samples

Sample SiO2 Al2O3 Fe2O3 MgO CaO K2O TiO2 MnO P2O5 LOI Total

S2 91.61 2.97 0.26 0.17 1.73 1.622 0.063 0.028 0.020 1.89 100.22

S4 91.06 2.90 0.35 0.16 1.20 1.640 0.082 0.040 0.024 2.19 99.65

S5 91.58 3.27 0.34 0.18 1.34 1.744 0.068 0.030 0.024 1.77 100.25

S6 91.39 2.95 0.29 0.14 1.17 1.628 0.081 0.037 0.024 2.00 99.66

S7 91.92 3.08 0.31 0.15 1.22 1.751 0.075 0.034 0.026 1.45 99.92

S8 91.10 3.04 0.32 0.18 1.77 1.731 0.080 0.038 0.024 2.00 100.15

S9 91.71 2.88 0.34 0.16 1.58 1.592 0.080 0.048 0.023 1.73 100.15

S10 90.64 2.92 0.30 0.21 2.08 1.664 0.073 0.041 0.024 2.21 100.06

S11 91.77 3.03 0.31 0.17 1.44 1.645 0.078 0.039 0.023 1.84 100.23

S12 92.13 3.04 0.32 0.14 1.19 1.707 0.087 0.034 0.024 1.40 100.28

L1 93.40 3.41 0.66 0.13 0.06 2.032 0.086 0.022 0.014 0.59 99.77

L3 93.05 3.54 0.64 0.12 0.05 2.116 0.084 0.013 0.014 0.60 99.57

L4 92.69 3.81 0.65 0.13 0.06 2.112 0.084 0.014 0.014 0.59 99.52

L5 92.63 3.89 0.64 0.13 0.06 2.101 0.083 0.012 0.017 0.58 99.55

F2 97.41 0.95 0.04 0.18 0.01 0.367 0.077 0.001 0.006 0.12 99.04

F8 97.56 1.05 0.04 0.20 0.01 0.389 0.069 0.001 0.005 0.28 99.32

element lines were made using theoretical alpha coefficients calculated using

the Philips software. The coefficients were calculated to allow for the amount

of extra flux replacing volatile components in the sample so those analytical

totals would be 100% less the measured LOI (limiting oxygen index). Average

major-elements counts were calculated from four measurements for each

element. Major-element data were screened by the total of the measured

oxides plus LOI. The analysis of samples with totals lying outside the range

99.4 to 100.4 wt% were repeated using new glass discs to confirm the total

or to obtain an analysis in the expected range. XRF analyses of the samples

were also used to determine the chemical composition of the samples using

offcuts before the flow tests, confirming the presence of iron oxide (Table 5).

XRF analyses show that Fife sandstone present the highest percentage of

SiO2 (mainly quartz), with an average around 97.5% ˙ 0.1 and Slick Rock

Aeolian sandstones present the lowest percentage of SiO2 with an average

around 91.5% ˙ 0.4 (Tables 5 and 7).

PETROPHYSICAL DESCRIPTION—PERMEABILITY

AND POROSITY

Both gas and liquid permeability were measured. The gas permeability tests

were measured using a nitrogen gas permeameter. For the liquid permeability,

the cores were mounted vertically in a core holder known as a Hoek cell,

which is normally used in rock deformation experiments. This cell provided

a means of applying confining pressure to the sample. It consisted of a steel

body (rated to 10,000 psi) within which was located a polyurethane sleeve.

Confining pressure was transmitted to the radial surface of the sample via

hydraulic oil in the annulus between the steel body and the sleeve. The vertical


or greatest principal stress was applied using an external ram, via porous

platens. During the course of an experiment brine was pumped through the

sample via the porous platens. Axial and radial strains have been measured

throughout the experiment using strain gauges. Movements of fluid through

the sample and volume measurements were made using a pumping network.

The network allows brine to be pumped in either direction through the core;

the direction can be reversed instantaneously. Expelled volume measurements

of brine were used to determine average saturation. Brine was pumped in

the inlet using a Pharmacia pump (1–499 ml/hr). Fluid flowed through the

core and was collected in a reservoir mounted on a balance. The weight

measurements were used to calculate flow rates. The balance was also used

in this configuration to measure the expelled pore fluid. Before permeability

testing, the samples were vacuum saturated with brine, which gave 90–95%

brine saturation. The samples were then saturated in a high-pressure cell at

2000 psi pore pressure for two days. The brine saturation was then confirmed

to be 100% by weight. Brine permeability was carried out at 400 psi. The

brine used in the experiment was 9% KCl brine, with a density of 1.067 g/cc

and a viscosity at 20ıC of 1.31 cp. These are measured values.

Tables 6 and 7 shows brine permeability and Klinkenberg-corrected

gas permeability values for the three groups of samples. The Slick Rock

Aeolian sandstones have the lowest liquid permeability, which is in the

range of 285 mD ˙ 71, and the lowest gas permeability, 499 mD ˙ 49.

The Fife sandstones have the highest liquid permeability, 1980 mD ˙ 388,

Table 6. Petrophysical parameters of the three groups of samples

Sample

Brine permeability,

kl (mD)

Gas permeability,

kg (mD)

Ratio

kg/kl

S2 290 447 1.54

S4 306 558 1.82

S5 280 425 1.52

S6 292 521 1.78

S7 289 470 1.63

S8 210 530 2.52

S9 280 473 1.69

S10 177 577 3.26

S11 280 521 1.86

S12 450 473 1.05

L1 894 1392 1.56

L3 664 1446 2.18

L4 784 1396 1.78

L5 480 1462 3.05

F2 1706 1411 0.83

F8 2255 1322 0.59


Table 7. Petrographical and petrophysical parameters of the three groups of samples

Sandstone Locharbriggs Slick Rock Aeolian Fife

Brine permeability, kl (mD) 706 ˙ 177 285 ˙ 71 1980 ˙ 388

Gas permeability, kg (mD)

(200 psi)

1424 ˙ 35 499 ˙ 49 1366 ˙ 63

kg/kl 2.1 ˙ 0.7 1.9 ˙ 0.6 0.7 ˙ 0.2

Porosity, ˆ (%) 26.1 ˙ 0.1 22.3 ˙ 0.5 23 ˙ 3

Mean Grain size,

MGS (�m)

199 ˙ 5 208 ˙ 28 348 ˙ 28

SiO2 content (%) 92.9 ˙ 0.4 91.5 ˙ 0.4 97.5 ˙ 0.1

Cement content (%) 7 ˙ 2 10 ˙ 2 5 ˙ 1

Type of cement illite, kaolinite,

smectite,

hematite

calcite

illite

hematite

kaolinite

Clays content (%) 6 ˙ 2 5.3 ˙ 0.9 5 ˙ 2

Type of clays illite, kaolinite,

smectite,

hematite

illite kaolinite

and gas permeability is in the range of 1366 mD ˙ 63. The Locharbriggs

sandstones have liquid permeability, 706 mD ˙ 177, and the highest gas

permeability, 1424 mD ˙ 35. These petrophysical results can be reasonably

explained by the microstructural properties, essentially by the type and the

percentage of cement and the mean grain size, as described in the following

sections.

PETROPHYSICAL CONTROLS ON FLUID FLOW

The three different types of sandstones used in this study represent a wide

range of petrophysical properties such as permeabilities and porosities and

very variable microstructural properties. These include the nature of the

constituent minerals and cement, the degree of rock cementation, and the

degree of sorting or equivalently the particle size distribution of the grains.

Table 6 summarizes the average numbers of the different parameters. The

Fife sandstones present the most homogeneous rock material. They present

the highest percentage of SiO2 content (97.5% ˙ 0.1), and the largest mean

grain size (348 �m ˙ 28). They present the lowest percentage of cement

(5% ˙ 1) constituted mainly by kaolinite. These microstrutural characteri-

zations explain the highest values of liquid permeability (1980 mD ˙ 388)

measured in these samples. Gas permeability (1366 mD ˙ 63) are equivalent

to liquid permeability, this confirms the homogeneity and the purity of this

rock material.


The Slick Rock Aeolian sandstones present the lowest permeability,

in the range of 285 mD ˙ 71 for liquid permeability and in the range

of 499 mD ˙ 49 for gas permeability. Indeed these sandstones present

the highest percentage of cement (10% ˙ 2), which are in the form of

clay minerals (mainly illite, which represents 6% of the rock material),

and hematite interspersed with illite and calcite. The ratio between the gas

permeability (kg) and liquid permeability (kl) ranges from 1 to 3 (Table 6).

During the liquid permeability measurements, swelling of the illite may be

responsible for the migration of the clay particles, which remain in the

system, and therefore liquid permeability is reduced. The Slick Rock Aeolian

sandstones present the lowest percentage of SiO2 content, with an average

equal to 91.5% ˙ 0.4. The Locharbriggs sandstone samples present the

smallest mean grain size (199 �m ˙ 5). In spite of the high values of

porosity (26.1% ˙ 0.1), these sandstones do not posses the highest values

of permeability (706 mD ˙ 177 for liquid permeability and 1424 mD ˙ 35

for gas permeability). This is explained by a relatively high percentage of

cement (7% ˙ 2), mainly in the form of clay minerals (illite, kaolinite and

smectite). These swelling clays may be responsible for the reduction of the

liquid permeability.

To study the fluid-rock interactions, liquid permeability was correlated

using multivariate regression to one to five petrographical parameters. These

parameters are: percentages of silica (SiO2) measured with x-ray fluores-

cence (XRF) analysis, cement and porosity (determined with point-counting

based on petrographic thin sections), and clay and mean grain size (MGS)

(measured with particle size analysis). This analysis was carried out to de-

termine the influence of petrographic elements on permeability. Absolute

values of correlation coefficients, which represent quality of fit, are used to

rank petrographic elements in conventional regression analysis. The results of

regression analysis are shown in Table 8 and Figures 4 to 8. Table 8 (Eqs. [a]

to [e]) and Figures 4 to 8 represent relationships between liquid permeability

Figure 4. Cross-plots of Slick Rock Aeolian, Locharbriggs and Fife sandstones, for

kl versus percentage of SiO2


Table 8. Regression results of Locharbriggs, Slick Rock Aeolian, and Fife

sandstones data, with a correlation coefficient (R2), standard deviations (SD)

and Akaike’s Information Criterion (AIC)

Variables:

petrographic elements Least squares fit R2 S.D. AIC

SiO2 a. kl D 279.27% SiO2 � 25259.20 0.95 132.44 �100.30

MGS b. kl D 9.15 �m MGS � 1439.50 0.72 319.35 �114.38

ˆ c. kl D 220.73% ˆ � 4194.40 0.60 392.63 �117.68

Cement d. kl D � 153.84% Cement C 1967.60 0.47 439.83 �119.49

Clay e. kl D � 804.79% Clay C 1511.20 0.56 402.37 �118.07

SiO2 , MGS f. kl D 254.11% SiO2 C 1.13 �m MGS � 23181.2 0.95 132.68 �99.74

SiO2 , Clay g. kl D 283.78% SiO2 C 21.88% Clay � 25701 0.94 137.20 �101.68

SiO2 , ˆ h. kl D 285.41% SiO2 � 7.86% ˆ � 25656.60 0.94 137.04 �100.25

SiO2 , Cement i. kl D 265.82% SiO2 � 15.84% Cement �

23872.60

0.95 133.35 �99.81

MGS, ˆ j. kl D 6.61 �m MGS C 113.16% ˆ � 3331.46 0.79 267.65 �110.96

MGS, Cement k. kl D 7.27 �m MGS � 77.39% Cement � 331.71 0.78 273.31 �111.29

SiO2 , MGS, Clay l. kl D 259.75% SiO2 C 2.20 �m MGS C

142.96% Clay � 24102.9

0.95 131.51 �98.96

SiO2 , MGS, Cement m. kl D 235.27% SiO2 C 1.28 �m MGS �

18.25% Cement � 21308.2

0.95 132.31 �99.05

SiO2 , Cement, Clay n. kl D 266.92% SiO2 � 15.68% Cement C 4.70%

Clay � 23981.40

0.94 138.78 �99.81

SiO2 , Clay, ˆ o. kl D 294.77% SiO2 C 34.14% Clay � 10.85%

ˆ � 26496.90

0.94 142.09 �100.19

SiO2 , MGS, ˆ p. kl D 257.14% SiO2 C 1.10 �m MGS � 3.20%

ˆ � 23386.4

0.94 138.03 �99.73

MGS, Cement, ˆ q. kl D 5.69 �m MGS � 59.35% Cement C

89.68% ˆ � 2089.31

0.83 238.75 �108.49

MGS, Clays, ˆ r. kl D 5.73 �m MGS � 97.57% Clay C 114.65%

ˆ � 3056.58

0.78 277.06 �110.88

SiO2 , MGS, Clay, ˆ s. kl D 272.01% SiO2 C 2.22 �m MGS C

158.13% Clay � 12.34% ˆ � 24992.4

0.95 136.31 �98.83

SiO2 , MGS, Cement, ˆ t. kl D 236.19% SiO2 C 1.27 �m MGS � 18.20%

Cement � 0.92% ˆ � 21371.8

0.94 138.18 �99.05

SiO2 , MGS, Cement,

Clay

u. kl D 242.86% SiO2 C 2.20 �m MGS � 15.71%

Cement C 125.82% Clay � 22379.9

0.95 132.77 �124.63

SiO2 , Cement, Clay, ˆ v. kl D 275.45% SiO2 � 15.09% Cement C

14.15% Clay � 7.79% ˆ � 24617.7

0.94 144.56 �99.77

SiO2 , MGS, Cement,

Clay, ˆ

w. kl D 252.86% SiO2 C 2.21 �m MGS � 15.00%

Cement C 138.02% Clay � 9.30% ˆ � 23127.4

0.94 138.61 �98.34


kl versus mean grain size (MGS)



kl versus percentage of porosity

Figure 7. Cross-plots of Slick Rock Aeolian, Locharbriggs and Fife sandstones for

kl versus percentage of cement


kl versus percentage of clay


(kl) and an individual petrographic element. This study shows a very good

correlation between kl and SiO2, with R2 equal to 0.95 (Eq. [a], Table 8

and Figure 4), and a quite good correlation between kl and mean grain size

(MGS), with R2 equal to 0.72 (Eq. [b], Table 8 and Figure 5), as well as

between kl and porosity, with R2 equal to 0.60 (Eq. [c], Table 8 and Figure 6).

There is an inverse correlation between liquid permeability (kl) and cement

and between kl and clay, with coefficient of correlations (R2) equal to 0.47

(Eq. [d], Table 8 and Figure 7) and R2 equal to 0.56 (Eq. [e], Table 8 and

Figure 8), respectively. Cements are composed by clay, calcite, and hematite,

as well as quartz and feldspar overgrowths. There are trends of decreasing kl

with increasing clay and therefore cement (Eqs. [d] and e], Table 8; Figures

7 and 8).

A set of multivariate regressions were performed using two to five vari-

ables of petrographic elements. To determine if what appears to be the best

model is really the best model, parameters like correlation coefficient (R2),

standard deviations (SD) and Akaike’s Information Criterion (AIC) have been

calculated (Table 8). The basic idea behind model selection is to choose from

a set of competing models the one—according to some criterion—which best

describes the data. A flexible approach to model discrimination is the Akaike

information criterion (AIC), introduced 30 years ago by H. Akaike (1973),

an information criterion for the identification of an optimal model from a

class of competing models (Main et al., 1999):

AIC3 D

�

�

hn

2

i

� LnML�

� p (1)

ML D

X

.obs � pred/2 (2)

where n is the number of data points in the regression, p is the number of

independently adjusted parameters within the model, ML is the maximum

likelihood method, and Ln is the natural log.

The first term on the right-hand side of Eq. (1) accounts for the criterion

of the goodness of fit, while the second one incorporates the doctrine of

parameter parsimony into the AIC. The best model is the one that yields the

largest AIC. Of these results, Table 8 reports only the regressions, using more

than one variable, with a correlation coefficient (R2) greater than 0.70. This

table shows that volume fraction of SiO2 alone gives a correlation coeffi-

cient of 0.95 (Eq. [a]). The most influential petrographic element controlling

permeability is therefore the volume fraction of SiO2 (silica); However the

best model is given by Eq. (s) in Table 8 (kl D 272.01% SiO2 C 2.22 �m

MGS C 158.13% Clay � 0.92% ˆ � 24992.4) by using the variables MGS

and percentages of SiO2, clay, cement, and porosity. This model presents a

correlation coefficient equal to 0.95, a standard deviation equal to 136.31,

and AIC equal to �98.83.


DISCUSSION

Reservoir quality, primarily determined by the porosity and permeability of

the relevant formations, can be a function of many controls including the

nature of the constituent minerals and cement, the degree of rock cementation,

the degree of sorting (or equivalently the grain size distribution of the grains),

and the pore-size distribution (Cade et al., 1994; Baraka-Lokmane et al.,

2001). Regression analyses have been carried out between liquid permeability

values and petrographical and petrophysical parameters such as grain size and

percentages of SiO2, clay, cement, and porosity.

Fife sandstones present systematically different petrographical and petro-

physical characteristics than Slick Rock Aeolian and Lochabriggs sandstones.

These sandstone samples present the most homogeneous rock material; the

main detrital components are represented by quartz (Tables 2 to 4), they

represent the largest percentage of SiO2 content (97.5% ˙ 0.1), the largest

mean grain size (348 �m ˙ 28), and the lowest percentage of cement

(5% ˙ 1). These microstructural characterizations explain the highest values

of permeability. Fife sandstones show good agreement between gas and liquid

permeability; this is explained by the low percentage of clays (5% ˙ 2),

represented by kaolinite. In addition, kaolinite is not prone to swelling with

changes in water content. Kaolinite, having a stable, “rigid” structure (due

to the strong book bonds) reacts with water to a minimum extent (Pajak-

Komorowska, 2003).

Slick Rock Aeolian and Lochabriggs sandstones show higher values of

the ratio between gas and liquid permeability, around (kg/kl), which is around

2. These rock materials present higher percentages of clays represented by

illite, smectite, and kaolinite (5.3% ˙ 0.9 for Slick Rock Aeolian sandstones

and 6% ˙ 2 for Lochabriggs sandstones). The impact of clay migration on

impairing reservoir permeability is a well-known problem (Baraka-Lokmane,

2002). Strongly hydrophilic minerals, particularly swelling clays, can be im-

portant in controlling the liquid permeability (Bitton and Gerba, 1984; Appelo

and Postma, 1993; Bloomfield and Williams, 1995; Baraka-Lokmane, 2002;

Pajak-Komorowska, 2003). During the liquid permeability measurements, the

swelling clays may be responsible for the migration of the clay particles,

which remain in the system, and therefore liquid permeability is reduced.

Smectite tends to swell when exposed to brine. It is very hydrophilic due

to its labile, “mobile” structure. Illite, in turn, is a mineral that reacts with

brine to a limited extent (Pajak-Komorowska, 2003). This study has shown an

excellent correlation between silica content (SiO2) and the liquid permeability

(kl), with a correlation coefficient (R2) equal to 0.95 (Eq. [a] in Table 8 and

Figure 4). This shows that the percentage of silica is the most influential

petrographic parameter controlling permeability. Silica (SiO2) is present in

the framework as well as in the cement of the sandstone rock. Quartz is

composed of silica, but other minerals like feldspar, clays, and rock fragments

also contain silica in their chemical composition. We observe a quite good


correlation between kl and MGS, with R2 equal to 0.72 (Eq. [b] in Table 8 and

Figure 5) as well as between kl and porosity, with R2 equal to 0.60 (Eq. [c]

in Table 8 and Figure 6). There is correlation between liquid permeability

(kl) and cement and between kl and clay, with R2 equal to 0.47 (Eq. [d] in

Table 8 and Figure 7) and R2 equal to 0.56 (Eq. [e] in Table 8 and Figure 8),

respectively. Cement content is composed by clay, calcite, hematite, quartz,

and feldspar overgrowths. Reduction in permeability and porosity occur via

compaction, cementation, and increasing clay content. Clay, whether having a

diagenetic or detrital origin, tends to sit between grains blocking pore throats

(see Figure 2).

The regressions results reported in Table 8 show that Eq. (f) in Table 8

presents the best model by using two variables (SiO2 and MGS), with R2

equal to 0.95, SD equal to 132.68, and an AIC equal to �99.74. This shows

that after the percentage of SiO2, the mean grain size is the most influential

petrographic parameter controlling permeability. Using three variables, the

best model is represented in Eq. (l) in Table 8, where R2 D 0.95, SD D

131.51, and AIC D �98.96. After the percentage of SiO2 and the mean

grain size, the percentage of clays is the most influential petrographic pa-

rameter controlling permeability. The regression results have shown that the

best model has been obtained by using four variables: percentages of SiO2,

porosity, and clays, as well as the mean grain size (Eq. (s) in Table 8), with

R2 D 0.95, SD D 136.31 and AIC D �98.83. The regression in Eq. (w) in

Table 8 using 5 variables (percentages of SiO2, porosity, clays, and cement, as

well as the mean grain size) does not improve the model described in Eq. (s).

This study shows that the best model according to all criteria (maximum R2,

minimum SD and maximum AIC) is described in Eq. (s). In this model four

variables have been used: percentages of SiO2, porosity and clays as well as

the mean grain size (in micrometer); however, the model described in Eq. (a)

using a single variable (SiO2) can predict the liquid permeability kl. Indeed,

comparing the models described in Eq. (1) and Eq. (s), only the value of the

maximum AIC is better in the case of Eq. (s). In this study the majority of

the rock samples are from the Slick Rock Aeolian sandstone (10 samples out

of the 16 tested samples); future work requires testing a larger number of

samples of Locharbriggs and Fife sandstones, as well as testing two or three

other sandstone samples to draw a general conclusion for the sandstone rock

samples.

CONCLUSION

Several complementary and overlapping methods have been used in this study

to characterize three groups of samples (Locharbriggs, Slick Rock Aeolian

and Fife sandstones). This strategy allows a full range of characteristics to be

determined, with internal checking between measurements. The determination

of the mineralogical composition of the samples, the type and the abundance


of the cements, and particularly the location and the abundance of hematite,

are all well characterized by several independent methods including point-

counting method and the (quantitative) XRD analysis. The characterization of

the samples has shown that the results of the point-counting method are com-

parable with those of the XRD analysis. However, point-counting has shown

the finite presence of hematite in the case of the Slick Rock Aeolian sandstone

samples. This was not detected with the XRD measurement because of its

small concentration (less than 1% of the sample). A structural method (point-

counting technique) is therefore complementary to a quantitative method

(bulk XRD analysis) to identify the different mineral species and quantify

their abundance. Regression analyses between liquid permeability values and

petrophysical or petrographical parameters such as percentages of SiO2, clay,

cement, and porosity as well as mean grain size (MGS) have been carried out.

This study has shown an excellent correlation between silica (SiO2) and liquid

permeability (kl), with a correlation factor equal to 0.95; liquid permeability

increases with the increase of the volume fraction of silica. This study has

shown that the best model according to all criteria (maximum R2, minimum

SD, and maximum AIC) is (kl D 272.01% SiO2 C 2.22 �m MGS C 158.13%

Clay � 0.92% ˆ � 24992.4). The model described in Eq. (a) using a single

variable, SiO2, can predict the liquid permeability kl (kl D 279.27% SiO2 �

25259.20), with R2 D 0.95, SD D 132.44 and AIC D �100.30.

This study shows that the permeability of sandstone cores can be pre-

dicted from the measurement of the percentages of silica (SiO2); which can

be performed with the help of XRF analyses using only 50 g of material

from rock sample. The results obtained in this study have useful application

in the estimation of reservoir permeability where samples are not available

for experimental testing.

ACKNOWLEDGMENTS

This work was funded by the Engineering and Physical Sciences Research

Council, grant: GR/M6 2150, with support from Exxon-Mobil, BP Amoco,

DTS, and RML.

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Correlation Between Microstructure and Flow Behavior in Porous Sandstones

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