Effective stress coefficient for permeability (ESCK) is the key parameter to evaluate the properties of reservoir stress sensitivity. So far, little studies have clarified which ESCK is correct for a certain reservoir while rock ESCK is measured differently by different fluid media. Thus, three different fluids were taken to measure a fine sandstone sample’s ESCK, respectively. As a result, the ESCK was measured to be the smallest by injecting nitrogen, the largest by injecting water, and between the two by brine. Besides, those microcharacteristics such as rock component, clay mineral content, and pore structure were further analyzed based on some microscopic experiments. Rock elastic modulus was reduced when water-sensitive clay minerals were encountered with aqua fluid media so as to enlarge the rock ESCK value. Moreover, some clay minerals reacting with water can spall and possibly block pore throats. Compared with water, brine can soften the water sensitivity; however, gas has no water sensitivity effects. Therefore, to choose which fluid medium to measure reservoir ESCK is mainly depending on its own exploitation conditions. For gas reservoirs using gas to measure ESCK is more reliable than water or brine, while using brine is more appropriate for oil reservoirs.
The characteristics of reservoir stress sensibility for rock permeability mainly behave as follows: with the on-going exploitation of oil and gas, the pore pressure of reservoir is decreasing, while the effective stress is increasing. As a result, the pore volume of reservoir is reducing and the reservoir permeability is lowering. To reasonably evaluate the reservoir effective stress sensitivity for permeability has a major impact on analyzing productivity, adjusting proration, and scheduling recovery. Meanwhile, it can help to recognize the reservoir permeability varying rules and mechanisms [
Some studies, conducted by Warpinski and Teufel [
Other studies, conducted by Nur et al. [
And some studies, conducted by Coyner [
Moreover, there are some other studies measuring the ESCK value by using oil. In addition, Zoback and Byerlee [
According to previous studies, reservoir ESCK value is affected by multifactors such as fluid media, rock components, clay content and its distribution, mineral composition, and pore structure. The ESCK value measured by nitrogen is usually less than 1, increasing with clay mineral content increasing. The ESCK value measured by distilled water is close to 1 for granite while it is larger than 1 for sandstone and is also increasing with clay mineral content increasing up to 7.1. The ESCK value measured by brine is usually greater than 1 and between that of nitrogen and distilled water. Though many scholars adopted different fluid media to measure out different ESCK values in different range for different rock samples, no one used different fluid media to measure the same sample and discuss the difference on ESCK. A series of ESCK measurement experiments by using three different fluid media (e.g., 99.99% nitrogen, distilled water, and brine with 50000 ppm potassium chloride, KCl) to flow through a fine sandstone sample were conducted in this study. As a result, under the same condition, the value of ESCK for the same sample is smallest by injecting nitrogen, largest by injecting distilled water, and between both by injecting brine. Hence, the microscopic characteristics of the tested sample, such as mineral composition, clay content, and pore structure, were further analyzed by conducting some related microscopic experiments. The fact that the ESCK for the same rock sample is measured to be different by using different fluid media is directly dependent on the microscopic characteristics of rock. Finally, the behaviors of fluid media with rock ESCK were discussed in this study.
In order to study the influences of different media on rock ESCK and the reliability of ESCK measurement, three different fluid media, 99.99% nitrogen, distilled water, and brine with 50000 ppm KCl, were used to measure the ESCK of a fine sandstone sample.
The sandstone sample studied in this paper was drilled from a representative Chinese reservoir. And the photos of the sample appearance are shown in Figures
Fundamental properties of this sandstone sample.
Porosity |
Permeability (mD) | Depth |
Density (g/cm3) | Clay |
Length (cm) | Diameter (cm) |
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11.30 ± 1.56 | 0.53 ± 0.19 | 2428.01 ± 56.04 | 2.4 ± 0.11 | 11 ± 2.32 | 5.03 ± 0.44 | 2.47 ± 0.02 |
Photos of the sample appearance.
SEM images of this sample at different magnification times.
50 times
110 times
300 times
350 times
550 times
Cast thin section image of this sample.
Results of Mercury Injection tests of this sample.
Capillary pressure curve
Pore-throat distribution
Microscopic characteristics of this sample are described as follows.
(i) According to SEM tests and the images (shown in Figure
(ii) According to X-ray diffraction tests, most of the clay minerals are kaolinite and chlorite; next is illite-smectite interlayer, content of which is 19.6% and content ratio of which is 16%.
(iii) According to Mercury Injection tests and the images (shown in Figure
(iv) According to cast thin section tests and the image (shown in Figure
In this study, the ESCK of this sample HH50-06 was firstly measured by nitrogen, then by distilled water, and finally by brine, respectively. To measure rock ESCK by a fluid medium such as nitrogen, the sample was dried over 24 hours in an oven and kept in a desiccator. After that, the sample was placed in the core holder, vacuumed for over two hours, and saturated with nitrogen under pressure for over eight hours. When measured by distilled water or brine, it was the same to prepare sample like the above.
Based on the conception of effective stress, the effective stress of permeability can be expressed as follows:
And the steps to calculate ESCK are as follows.
The pressure diffusion across the sample can be expressed as follows [
Rock permeability was measured by using transient pulse decay method, which was proposed by Brace et al. [
Sketch of the experimental setup.
Firstly, start the ESCK measurement with nitrogen. At the beginning, aging tests were treated to the sample in order to make its physical properties more stable.
At confining pressure of 50 MPa, unload pore pressure from 25 to 5 MPa step by step with 5 MPa decrease and keep system stale over 30 min at each pore pressure. Meanwhile, sample permeability was measured and calculated at each pore pressure. Then load pore pressure from 5 to 25 MPa step by step with 5 MPa increase and proceed to the next procedures as the above unloading scenario.
After Step
After Step
All of the permeability measurements for aging tests and ESCK tests were carried out in three repetitions.
The relationship between permeability and net stress, which means the difference of confining pressure and pore pressure, in accordance with aging tests is shown in Figure
Permeability versus net stress in aging tests.
The relationships among permeability, confining pressure, and pore pressure for the sample when unloading and loading the pore pressure under nitrogen, distilled water, and brine are shown in Figures
Permeability versus pore pressure and confining pressure measured by nitrogen when unloading (a)/loading (b) the pore pressure under three different confining pressure conditions.
Unload
Load
Permeability versus pore pressure and confining pressure measured by distilled water when unloading (a)/loading (b) the pore pressure under three different confining pressure conditions.
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Load
Permeability versus pore pressure and confining pressure measured by brine when unloading (a)/loading (b) the pore pressure under three different confining pressure conditions.
Unload
Load
Comparing Figures
From Figures
Comparing Figure
From Figures
Based on response surface method, the measured ESCK data in this study can be calculated successfully. The related conversion factors (
Conversion factors and regression coefficients measuring by nitrogen, distilled water, and brine.
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HH 50-06 | Nitrogen | Unload |
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Distilled water | Unload |
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Brine | Unload |
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After that, according to (
Results of ESCK measured by three different fluid media.
Sample | Fluid media | Pore pressure | Range | Average value |
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HH50-06 | Nitrogen | Unload | (0.65, 1.04) | 0.78 ± 0.11 |
Load | (0.16, 1.18) | 0.54 ± 0.30 | ||
Distilled water | Unload | (1.13, 7.01) | 2.80 ± 1.69 | |
Load | (1.31, 6.25) | 3.25 ± 1.39 | ||
Brine | Unload | (1.30, 2.06) | 1.61 ± 0.24 | |
Load | (0.53, 3.30) | 1.63 ± 0.79 |
As a result, consider the following.
From the above experimental results, the ESCK is variable which fails to be consistent with the traditional conception of ESCK that considered it constant. Hence, an evaluation method was adopted to evaluate the ESCK values measured in this study. Based on permeability stress laws, the effective stress
Permeability versus effective pressure under nitrogen condition during pore pressure unloading (a)/loading (b) processes.
Unload
Load
According to Figures
Permeability versus effective pressure under distilled water condition during pore pressure unloading (a)/loading (b) processes.
Unload
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Permeability versus effective pressure under brine condition during pore pressure unloading (a)/loading (b) processes.
Unload
Load
In this study, all of rock permeabilities were measured under the same external experimental conditions, including temperature and loading/unloading confining pressure/pore pressure processes. Therefore, those permeabilities, corresponding to the same effective stress, display differently due to different fluid media only.
The ESCK values of fine sandstone were measured by three different fluid media, nitrogen, brine, and distilled water, based on the response surface method. As a result, the ESCK is the smallest with nitrogen, the largest, 7.01, with distill water, and the middle with brine. According to the one-one correspondence of effective stress and permeability, the ESCK values studied in this paper were approved to be valid. The elastic modulus of clay minerals decreases when the water comes into contact with clay minerals and the clay swells and spalls some particles to block pore throats. Compared with distilled water, brine, mainly the saline ions like K+, softens water sensitivity impacts on clay minerals. The ESCK values of one sample measured by different fluid media with the same effective stress are different. However, the gas like nitrogen is affected a little by the microscopic characteristics of rock sample. Hence, the reliability of the ESCK measurement is depending on the properties of rock or reservoir itself. For instance, nitrogen or gas is the best fluid medium for measuring the ESCK of gas reservoir and brine is the best for measuring oil reservoir.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is financially supported by National Natural Science Foundation of China under Grant no. 41274114 and by University-Wide Scientific and Technological Foundation of SWPU under Grant no. 2013XJ2003.