Acta Geophysica
vol. 54, no. 3, pp. 319-332
DOI 10.2478/s11600-006-0025-8
Compressibility of Porous Rocks:
Part I. Measurements of Hungarian Reservoir Rock Samples
Ali Ahmed JALALH
Petroleum Engineering Department, Miskolc University, Miskolc, Hungary
e-mail: [email protected]
Abstract
Pore volume compressibility is one of the physical properties of a reservoir
that must be specified in many reservoir-engineering calculations. In the presented
research, the effect of compact pressure, temperature and porosity on compressibility was investigated. A total of twenty-two different cores were tested: five limestone, one friable sandstone, fourteen medium to hard sandstone, and two very
dense sandstone. Core samples were placed in the test cell and subject to compacting pressure up to 10,000 psi. Runs were made at room temperature and at 52°C for
limestone samples.
Although there were some publications concerning measurement and study of
the effect of pressure and temperature on pore volume compressibility of reservoir
rocks, nothing has been published about compressibility of Hungarian reservoir
rocks, except of the work of Tóth and Bauer (1988). The present study showed pore
volume compressibility data for different Hungarian fields. The result of the study
at high temperature (52°C) shows that pore compressibility increases with increasing temperature.
Key words: pore volume compressibility, rock compressibility, reservoir characterization, rock properties.
1. INTRODUCTION
The use of pore volume compressibility–porosity correlations in engineering calculations is well known. The correlations developed by Hall (1953) and Horne (1990) for
sandstone and limestone rocks have been widely known. Van der Knaap (1959) published a similar correlation using limestone samples from a single well and correlated
the data with net pressure.
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Such correlations were attractive because of the simple relationship established.
However, they were obtained only for well-consolidated samples: correlations for friable and strongly consolidated sandstones have not been published, except of Horne
(1990), who presented correlation for consolidated and unconsolidated sandstone and
consolidated limestone reservoir rocks.
This study compared our laboratory data and our relations with the published correlations of consolidated limestone samples as well as with values for friable and
strongly consolidated sandstones.
2. DESCRIPTION OF EQUIPMENT AND PROCESS
Experimental technique
Samples used in this study were generally plugs of 1 inch in diameter and 3 inches
long, and their condition ranged from well preserved to dry and weathered. All the
samples were subject to routine helium porosity measurements and saturation measurements. At this point, the bulk volume of the sample was determined from linear
dimensions and the sample was placed in the test cell. A hydrostatic overburden pressure of about 200 psi was exerted on the samples before starting the compressibility
test. This has been done to maintain good sealing of the sample without communicating with outer fluid used for overburden.
Measuring porosity
Porosity determination by water saturation
Initial porosities were determined by API-approved method (API RP40, 1960), which
consisted of determining the pore volume by restoration and the bulk volume by displacement or caliber measurement. Then, cleaning and drying the cores was done under vacuum in a low temperature oven, and saturating the core with salt water (mineralization on the level of 5 g/l).
Porosity determination by helium porosimeter
Porosimeter is an instrument used to measure the porosity of a sample by comparing
the bulk volume of the sample with the aggregate volume of the pore spaces between
the grains.
The Corex helium porosimeter used in this study was an analytical grade laboratory instrument used for measuring the pore volume, grain volume, porosity and grain
density of rock samples. It is supplied with sample cups for 1 and 1½ inch diameter
samples, but can also cater for a wide variety of other sample sizes using either custom
size cups, or the remote cell connection. The remote connection allows also for the
measurement of porosity at overburden pressure. The instrument was designed to be
quick and easy to use, and to give accurate, reliable and repeatable results. Optionally,
there was also available a built-in PC interface allowing automatic data acquisition via
an IBM compatible PC’s standard serial port.
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COMPRESSIBILITY OF POROUS ROCKS: PART I
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Algyo sandstone samples had a wide range of porosity: between 3 and 32%. The
other friable sandstone from Hajduszoboszlo field has a porosity value of 28.8%.
There were two consolidated samples from Foldes field of very low porosity values,
less than 0.8%. The Zsana limestone samples had almost the same values, ranging between 23 and 24.8%. The groups of samples were taken from single wells.
3. APPLYING STRESS
Confining pressure
All our data were obtained from samples under uniform hydrostatic stress. This was
accomplished by transmitting the overburden pressure to the jacketed test sample with
hydraulic fluid. The tests were conducted under varying overburden (confining) pressure.
Pore pressure
The pore pressure was controlled through the sample by rotating a scaled bar and
could be varied independently of the overburden pressure during tests. The tests were
conducted under constant pore pressure. Compressibility apparatus designed by Core
Laboratory Co. Ltd. was used for performing the measurements.
Effective stress
The ability to vary the overburden and pore pressures independently made it necessary
to expose the data at a common stress condition. This was established as a function of
Pore volume compressibility, Cpc (x10-6 1/psi)
1000
Hall curve
ZS-OO1
ZS-OO5_1
ZS-OO5_2
100
ZS-OO5_3
ZS-OO6
ZS-OO7
ZS-OO2
10
1
0
5
10
15
20
25
30
35
40
Porosity, (%)
Fig. 1. Pore volume compressibility for Zsana limestone samples versus initial porosity and
Hall’s correlation curve (after Hall 1953).
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the effective pressure, defined as the difference between the overburden (lithostatic)
and pore pressures.
Pore volume compressibility, Cpc (x10-6 1/psi)
1000
Hall curve
30.S
43.S
69.S
74.S
76.S
77.S
82.S
83.S
A985-1/2
A985-5/2
A.1.1
A.1.2
SA-5
SA-7
H-sample
F1
F2
100
10
1
0
5
10
15
20
25
30
35
40
Porosity, (%)
Fig. 2. Sandstone pore volume compressibility of Algyo, Hajduszoboszlo and Foldes samples
compared with Hall’s correlation curve (after Hall 1953).
Pore volume compressibility, Cpc (x10-6 1/psi)
100
SST
LST
Uncons
Zs-001
Zs-002
Zs-005
Zs-006
Zs-007
10
1
0
5
10
15
20
25
30
Porosity, (%)
Fig. 3. Measured pore volume compressibility of studied limestone samples compared to
widely used compressibility correlations (after Horne 1990). SST – curve for sandstone, LST –
curve for limestone, Uncons – curve for unconsolidated formations.
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COMPRESSIBILITY OF POROUS ROCKS: PART I
323
Pore volume compressibility, Cpc (x10-6 1/psi)
1000
SST
LST
Uncons
30.S
43.S
69.S
74.S
76.S
77.S
82.S
83.S
A985-1/2
A985-5/2
A.1.1
A.1.2
SA-5
SA-7
100
1
10
1
0
10
20
30
40
50
Porosity, (%)
Fig. 4. Measured compressibility of studied sandstone samples compared to widely used compressibility correlations (after Horne 1990).
Pore volume compressibility, Cpc (x10-6 1/psi)
1000
100
Carpenter, 1940
HALL, 1953
Van DER, 1959
FATT, 1958
KOHLHAASE, 1969
Von Gonten, 1969
ZS-OO1
ZS-OO5_1
ZS-OO5_2
ZS-OO5_3
ZS-OO6
ZS-OO7
ZS-OO2
H-sample
F1-Consolidate
F2-Consolidate
10
1
0
5
10
15
20
25
30
Porosity, (%)
35
40
45
50
Fig. 5. Pore volume
compressibility
of
limestone versus porosity; results from
measured
samples
and from the literature.
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Presentation of data
The values of pore volume compressibility obtained at the reservoir condition (effective pressure), plotted against the initial porosity, are shown in Figs. 1 through 4, along
with Hall’s and Horne’s correlations. Compressibility-porosity values obtained from
the literature and from this study, for both sandstone and limestone, are shown in
Figs. 5 and 6.
Pore volume compressibility, Cpc (x10-6 1/psi)
100
Jalalh, 2005
Toth and Bauer, 1988
From literature
10
1
0
5
10
15
20
25
30
35
Porosity, (%)
Fig. 6. Comparison of the pore volume compressibility of studied sandstone samples and published compressibility values of sandstone rocks from the literature.
4. CALCULATING PORE VOLUME COMPRESSIBILITY
The compressibility values of this study (see Figs. 1 through 4) were obtained by
graphically differentiating the pore volume effective pressure relationship by means of
the following relation:
C pc =
1
Vp
⎛ dV p
⎜⎜
⎝ dPeff
⎞
⎟⎟ ,
⎠ pp
where Cpc is the pore volume compressibility, vol/vol/psi , Vp is the pore volume of
the sample at a given effective pressure, dVp is the incremental change in pore volume
resulting from an incremental change in effective pressure, dPeff is the incremental
change in the effective pressure.
The above relation contains the assumption that most of the pore volume changes
result from the effective pressure difference. This approximation is valid for higher
porosity samples. Geertsma (1957) has given a more comprehensive discussion.
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5. ANALYSIS OF DATA
The pore volume compressibility values shown in this work were in most cases pressure-dependent. To compare samples that had been obtained from various depths,
which means they were subject to various effective stresses under reservoir conditions,
a common effective pressure base of 100 percent or greater of the lithostatic pressure
was used. This value was selected as the most probable average effective stress the
sample would encounter during reservoir depletion. The lithostatic pressure was assumed to be 1 psi per foot of depth.
Several highly magnified (200×) captured electron microscope pictures of selected texture of rock material have been studied and presented together with some results of other non-destructive measurements in Tables 1 and 2. A summary of the core
sample parameters used in the study is presented in Table 3.
T ab le 1
Electron microscope capture (200× magnified) of limestone textures of samples
Zs-005 and Zs-007 from Zsana field
Zs-007
Helium porosity
Water porosity
Rock type
Comments
0.2307
0.2480
Limestone
Vuggy/intercrystalline porosity
Zs-005
0.2344
0.2416
Limestone
Vuggy porosity
Limestones rocks
Zsana field samples
Five limestone samples from Zsana field were composed in more than 98% of calcium
carbonate. Results of samples Zs-001, Zs-002, Zs-005, Zs-006 and Zs-007 are presented in Fig. 7 showing gentle slope of compressibility curves and having close compressibility values, especially at high effective pressure. Five samples have close porosity values but they had different porosity type. This could be seen clearly in the pictures of samples Zs-007 and Zs-005’s in Table 1.
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T ab le 2
Electron microscope capture (200× magnified) of: (a) sandstone textures of samples 69.S and
74.S; (b) friable sandstone textures; (c) compacted sandstone textures of samples F1 and F2
(a)
69.S
Helium porosity
Water porosity
Rock type
Comments
74.S
0.317
0.0420
sandstone
presence of shale interbedding
0.1077
0.100
sandstone
(b)
H
Helium porosity
Water porosity
Rock type
Comments
0.3940
0.2922
friable sandstone
no HCl acid reaction
(c)
F2
F1
Helium porosity
Water porosity
Rock type
Comments
0.0471
0.0556
0.0193
0.0810
no permeability
no HCl react in both samples
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COMPRESSIBILITY OF POROUS ROCKS: PART I
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T ab le 3
Summary of the core sample parameters used in the study
Field name
Number
of samples
Porosity range
[%]
Rock type
14
2
1
8
4 – 35
less than 8
30
22 – 25
sandstone shales
sandstone
sandstone
limestone
Algyo
Földes
Hajduszoboszlo
Zsana
Hardness
medium to hard
very dense
friable
medium hard
Samples of Zsana
and Foldes field
-6
Pore volume compressibility, Cpc (x10 1/psi)
100
Cpc-F1
Cpc-F2
Cpc-Zs-001
Cpc-ZS-002
Cpc-ZS-005
Cpc-ZS-006
Cpc-ZS-007
10
1
0
2000
4000
6000
Effective pressure, psi
8000
10000
Fig. 7. Pore volume compressibility of consolidated limestone samples (ZS-001–ZS-007) and
very compacted samples (F1 and F2) versus effective pressure.
I should mention that the result obtained for sample Zs-005 was typical of elastic
rock (see Fig. 8), with no irreversible changes in its internal structure. The same values of compressibility in the second and third cycle runs have been observed (Jalalh
and Bódi 2004).
Limestone sample values in Fig. 5 were compared with Hall’s, Van der Knaap’s
and other published results and a wide scatter of limestones data was observed.
Sandstone rocks
To analyze further the porosity and pore volume compressibility of the sandstone
samples shown in Fig. 2, we used a qualitative rock-typing system. The samples were
grouped as friable, consolidated and very strongly consolidated, as follows:
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Pore volume compressibility, Cpc (x10-6 1/psi)
100
Cpc_ZS-OO5 (1st Run)
Cpc-ZS-OO5 (2nd Run)
Cpc_ZS-OO5 (3rd Run)
Cpc_ZS-OO5 (52C Run)
10
1
0
2500
5000
7500
Effective pressure, (psi)
Fig. 8. Pore volume compressibility of sample Zs-005 – values from different measurement cycles (runs).
1. Friable samples could be cut into cylinders, but the edges could be broken off
easily by hand.
2. Consolidated samples or “hard” rocks (thin edges could be broken off by
hand).
3. Very compacted samples or “very dense clastic rock”, very hard to cut into
cylinder (low porosity and no permeability).
Algyo field samples
Algyo field samples (30.S, 43.S, 69.S, 74.S, 76.S, 77.S, 82.S, 83.S, A985-1/2, A9855/2, A.1.1, A1.2, SA-5, SA-7) are mostly medium to fine and moderate to very hard
sandstones. The samples 74.S, 76.S and 77.S have shale interbedded layers. Samples
used in this study from Algyo field had a wide porosity range, from 4.21% to 32.28%.
These samples were mainly composed of quartz sandstone with shale interbedding, as
distinctly visible in Table 2a.
Hajduszoboszlo field sample
A Hajduszoboszlo reservoir rock has high porosity values, up to 30% (see Table 2b).
The quartzite friable sandstone was the only available sample from this underground
gas storage (H sample). Cycling the sample twice led to higher compressibility values.
This was an opposite result to the elastic behavior of limestone samples (e.g., Zs-005).
Thus, that result proved the inelastic behavior of the friable rocks as presented in
Fig. 9.
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COMPRESSIBILITY OF POROUS ROCKS: PART I
Pore volume compressibility, Cpc (x10-6 1/psi)
100
329
H-Sample (2nd Run)@ Lab. Temp.
H-Sample (1st Run) @ Lab. Temp.
H-Sample (3rd Run) @ Lab 52 deg. C. Temp.
10
1
0
1000
2000
3000
4000
5000
6000
Effective pressure, psi
Fig. 9. Inelastic compressibility behavior of the friable sandstone H from Hajduszoboszlo field.
Földes field samples
Only two samples (F1 and F2) from Földes Field were available in this study. Both
samples were very dense and well compacted, especially F1. Neither sedimentary
structures nor features could be identified to help in recognizing the rock identity.
There was also no reaction with HCl acid (1:1 % concentration). Although it appears
that in both samples the metamorphose process took place, the mineralogy and lithological description was needed.
With no information on permeability in both samples, it was hard to consider the
samples as part of potential reservoir for water or hydrocarbon.
Figure 7 and Table 2c gave additional light into physical and poroelastic parameters measured for samples F1 and F2.
Discussion
Figures 1 through 4 showed that our lower-porosity limestone and sandstone samples
follow the general trend obtained by Hall (1953): the pore volume compressibility increase with decreasing porosity. This was distinctly pronounced in Fig. 2 and the general trend obtained by Horne (1990) and presented in Figs. 3 and 4. I should mention
that Horne (1990) developed his correlations based on the extensive measurements of
Newman (1973) who run tests on 256 cores of limestone and sandstone from 40 reservoir rocks having porosities of between 1 and 35%. He also compared the results reported by other researchers. However, because Newman’s compressibility values were
computed at 75% lithostatic pressure (on the basis of the depth from which his samples were obtained), the comparison with the data from other researchers may not be
accurate.
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Eventually, the results obtained from this study are in good agreement with the
pore volume compressibility data from literature, as shown in Figs. 5 and 6.
The individual compressibility curves for the consolidated samples in Fig. 7, as
an example of limestone samples from Zsana and Folds field, showed substantially
elastic behavior. Applying more than one run in the same samples resulted in lower
compressibility value. This is due to rearrangement of the rock material. Fig. 8 explains clearly this phenomenon of elastic behavior. The opposite is true for the friable
sample from Hajduszoboszlo field (i.e. sample H). Due to loosing of cementing of the
grains, applying more than one run in the same samples will not result in lower compressibility, as represented in Fig. 9. This is due to inelastic behavior of friable rock
material (Jalalh 2005).
The samples with low porosity (F1 and F2) and very compacted tend to be of
very low compressibility, as shown in Fig. 7.
Our results of friable and very compacted samples are in poor agreement with
Hall’s correlation. The literature on compressibility covering more than 79 samples
(including Hall’s data), shown in Fig. 5, supports our result and shows about the same
scatter. Van der Knaap (1959) obtained a good correlation for 23 limestone samples
taken from the single well, but these values are also in poor agreement with Hall’s correlation but in same range as our results.
We believe that the poor agreement between our data and Hall’s data is in part
because the latter are based on only 12 samples: 7 limestone and 5 sandstone in the
porosity range of 2 to 26 percent. The huge progress in the development of laboratory
instruments since 1953 (i.e. Hall time) could also contribute to the accuracy of measurements readings. Our data based on twenty-two samples indicate the porosity range
more-or-less the same as Hall’s one but are more diversified in rock type and hardness.
The correlation developed and published by Horne (1990) on the basis of Newman’s laboratory measurement data (1973) shows poor agreement with the measured
result of this work. Zsana limestone results as presented in Fig. 3 are placed along unconsolidated compressibility rock curve. Similarly, results for the Algyo sandstones in
Fig. 4 were also not fitted to the Horne’s as well as to the Hall’s relations. In comparison to Hall’s correlation, Zsana limestone has more reliable correlation than Horne’s
curve.
The published Horne’s (1990) correlation curves display maximum porosity
value on the X-axis equal to 30% (see Fig. 3). Although Horne provided his empirical
formulas for three types of rocks, he stated that they are valid for porosity range from
0.0 to 0.1. Using the empirical formulas of Horne and extending them to higher porosity, of more than 30%, as presented in Fig. 10, we can observe the following: the curve
trend is an upward increase for porosities higher than 30%. This is opposite to Hall’s
correlation curve of Figs. 1 and 2. Basing on Fig. 10, the rocks with porosities of 50%
or 5%, have same compressibility values. Therefore, we should be careful using
Horne’s correlation for porosities higher than 30%. I had extracted pore volume compressibility for Algyo sandstone data from Tóth and Bauer (1988) and plotted against
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Pore volume compressibility, Cpc (x10-6 1/psi)
100
SST
LST
Uncons
10
1
0
10
20
30
40
50
60
Porosity, (%)
Fig. 10. Extended Horne’s correlations for pore volume compressibility versus porosity; for
porosity greater than 30%, the curves show an upward trend; this means that rocks with porosity of 50% or 5% have the same compressibility values.
our laboratory result from the same field. Our measurements show good agreement
with the extracted data from Tóth’s result, as presented in Fig. 6.
6. CONCLUSIONS
This work describes measurements, for the first time performed and published, concerning pore volume compressibility of varied rocks in a wide range of porosity, obtained from Hungarian hydrocarbon fields.
The measurement data of Hungarian limestone and sandstone rocks shows that
the correlation formulas that are available in the literature (i.e., Hall’s and Horne’s
correlations) cannot be applied to estimate the compressibility of these reservoir rocks.
The measurements performed in this work on samples of various limestone and
sandstone cores confirmed the theoretical framework of poroelasticity theory.
Compressibility for a given porosity can vary widely according to rock type.
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Attempts to correlate the data showed that friable sandstones greatly differed
from very compacted sandstones and consolidated limestones, but the available data
were too widely scattered to make correlations reliable. Well-defined trends had been
found only in the consolidated limestones.
For petroleum engineering practice it is at least necessary to measure the pore
volume changes as the inner reservoir pressure changes.
References
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Carpenter, C.B., and G.B. Spencer, 1940, Measurements of compressibility of consolidated oilbearing sandstones, RI 3540, USBM.
Fatt, I., 1958, Pore volume compressibilities of sandstone reservoir rocks, Petroleum Trans.
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Geertsma, J., 1957, The effect of fluid pressure decline on volume changes of porous rocks,
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Hall, H.N., 1953, Compressibility of reservoir rocks, Trans., AIME 198, 309-311.
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Newman, G.H., 1973, Pore-volume compressibility of consolidated, friable, and unconsolidated reservoir rocks under hydrostatic loading, Soc. Pet. Eng. J. 129-134.
Tóth, J., and K. Bauer, 1988, Deformation of porous rock structures. 2 - Pore volume deformation and pore compressibility, Oil and Natural Gas J. 65-69 (in Hungarian).
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Oct 1, 1969.
Received 5 April 2006
Accepted 1 June 2006
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