The sensitivity of oil reservoir rocks to stress is the basis for oilfield development, which determines the production method employed in the field. Therefore, it is critical to understand the stress sensitivity behavior of oil reservoir rocks in an oilfield. In this paper, a novel method for determining the stress sensitivity of oil reservoir rocks by triaxial stress testing without fluid flooding was proposed. It measures the triaxial stress and strain of the core rock samples, and based on which, the core porosity and permeability under stress can be evaluated by theoretical model. In the model, the pores of the core were assumed to be a bundle of capillaries and the necessary relationship was derived to calculate the changes of porosity and permeability of the core samples caused by the strain. Through comparison with and analysis of experimental results obtained for various rock core samples under different stress and strain conditions, it is observed that the theoretical model match well with that of the experiments. This method provides a new approach for the stress sensitivity analysis of oil reservoirs without fluid flooding.
The variation of oil reservoir core porosity and permeability under stress is called the reservoir rock stress sensitivity, which is the basis for reservoir production mode selection. If an oil reservoir rock is relatively stress sensitive, it is necessary to take immediate actions to avoid porosity and permeability reduction. The production potential of gas hydrates mainly depends on permeability characteristics of the bearing sediments as high permeability could promote the production rate [
Therefore, in the late 1980s, scientists began to carry out research on the stress sensitivity of oil reservoirs, mainly by core flooding experiments [
However, such method faces a few problems which still need to be tackled with urgently: First, it is difficult to apply stress simultaneously in three different directions (
The changes of porosity and permeability of artificial tight core with stress were studied by Cao and Lei [
Chen et al. [
Yaser et al. [
Liu et al. [
Sui et al. [
Existing experiment.
Experiment | References |
---|---|
Porosity and permeability | Cao and Lei [ |
Stress-strain characteristics | Chen et al. [ |
Pore structure, porosity, and permeability | Yaser et al. [ |
Rock deformation and strength | Liu et al. [ |
Simulated deformation of the core with digital method | Sui et al. [ |
In order to avoid the problems discussed above, in this paper, a new testing method without fluids involved during the process was proposed. The method is to test the triaxial stress and strain of rock core samples, which eliminates the challenge of sealing between the annulus core and its holder and prevents fluids from leaking out therefrom. And to make the testing happen, a novel mathematical model is established to calculate the porosity and permeability of the oil reservoir rocks based on applied stress and strain data. Actual applications demonstrate that the method is an effective approach for stress sensitivity analysis of rocks and is simpler and more advantageous than the conventional methods.
Here, The mathematical model is established for calculating the oil reservoir rock porosity and permeability from the experimentally measured triaxial stress and strain data. And how to process and incorporate the experimental data into the model is a critical factor.
During the production stage of an oil reservoir, the formation fluid pressure decreases. This disturbs the static equilibrium of the formation and causes rock deformation under stress, which creates volumetric strain to the core rock, as illustrated in Figure
Simulation of rock stress and strain changes.
Assuming that the stresses in the
According to the laws of elastic mechanics, the relationship between volumetric strain and stress can be obtained by the general Hooke’s law. For the
Combining equations (
Under the experiment condition, Young’s Modulus (
According to the theory of elastic mechanics,
From equation (
Substituting equations (
Integrating the both sides of equation (
Similarly, for
From equations (
When
The oil reservoir rock is composed of framework and pore space. It is assumed that when the oil reservoir rock is subjected to effective stress, the core framework is not deformed, and only the pore space will be compressed, resulting in volumetric strain, as shown in Figure
Rock porosity changes under compression and strain.
According to the definition of porosity,
When external stress acts on the porous core, the porosity changes from the initial state of
At constant temperature, equation (
And substituting equations (
Then, the change in porosity at different volumetric strains can be calculated by equation (
The permeability of a rock is closely related to its strain. Here, the complex porous medium is simplified into a series of equal diameter capillary tubes [
Substituting equation (
From equation (
The rock core sample used in the verification experiment is from the Tahe Oilfield in Xinjiang Province in China. The carbonate oil reservoir is located at a depth of about 3,500 meters. A standard core rock sample was prepared for triaxial stress sensitivity experiment. The experimental setup is shown in Figure
The triaxial stress core rock experimental instrument.
In order to simplify the evaluation of stress, it was assumed that the confining and the axial pressures are equal. The experiment was done in the applied pressure range from 2 MPa to 65 MPa, and the process of loading stress was in three steps, as illustrated as follows:
The radial and axial strain data of the rock samples under different stresses were obtained by experiments, and the corresponding volumetric strain data under the conditions were calculated by equation (
Data of deformation and volumetric strain under different axial stress.
Confining stress (MPa) | Axial stress (MPa) | Radial deformation | Axial deformation | Radial strain | Axial strain | Volumetric strain |
---|---|---|---|---|---|---|
2 | 2 | -5.8080 | 1.5236 | -2.2866 | 3.7995 | 8.3705 |
4 | 4 | -9.0040 | 2.3964 | -3.5449 | 5.9761 | 1.3060 |
6 | 6 | -1.1410 | 3.1008 | -4.4921 | 7.7327 | 1.6708 |
8 | 8 | -1.3538 | 3.7248 | -5.3299 | 9.2888 | 1.9936 |
10 | 10 | -1.5528 | 4.3108 | -6.1134 | 1.0750 | 2.2960 |
13 | 13 | -1.8232 | 5.1420 | -7.1780 | 1.2823 | 2.7155 |
16 | 16 | -2.0722 | 5.9676 | -8.1583 | 1.4882 | 3.1167 |
19 | 19 | -2.2960 | 6.8996 | -9.0394 | 1.7206 | 3.5245 |
22 | 22 | -2.5042 | 7.7160 | -9.8591 | 1.9242 | 3.8912 |
25 | 25 | -2.7950 | 6.5032 | -1.1004 | 1.6217 | 3.8178 |
30 | 30 | -2.8386 | 1.1482 | -1.1176 | 2.8634 | 5.0909 |
35 | 35 | -3.0738 | 1.2770 | -1.2102 | 3.1844 | 5.5956 |
40 | 40 | -3.2838 | 1.4039 | -1.2928 | 3.5009 | 6.0759 |
45 | 45 | -3.4714 | 1.5415 | -1.3667 | 3.8441 | 6.5651 |
50 | 50 | -3.6462 | 1.6672 | -1.4355 | 4.1576 | 7.0146 |
55 | 55 | -3.8830 | 1.7214 | -1.5287 | 4.2927 | 7.3347 |
60 | 60 | -3.9602 | 1.8980 | -1.5591 | 4.7332 | 7.8343 |
65 | 65 | -4.1014 | 2.0234 | -0.001614724 | 0.005045985 | 0.008256544 |
The data in Table
Data of porosity and permeability damage rate under different confining stress.
Confining stress (MPa) | Axial stress (MPa) | Dimensionless porosity | Dimensionless permeability | Absolute value of permeability reduction (mD) | Absolute value porosity reduction | Porosity damage rate | Permeability damage rate |
---|---|---|---|---|---|---|---|
2 | 2 | 0.9811 | 0.9627 | 8.59 | 8.02 | 1.89% | 3.73% |
4 | 4 | 0.9705 | 0.9421 | 1.33 | 1.25 | 2.95% | 5.79% |
6 | 6 | 0.9623 | 0.9261 | 1.70 | 1.60 | 3.77% | 7.39% |
8 | 8 | 0.9550 | 0.9121 | 2.02 | 1.91 | 4.50% | 8.79% |
10 | 10 | 0.9482 | 0.8991 | 2.32 | 2.20 | 5.18% | 10.09% |
13 | 13 | 0.9387 | 0.8812 | 2.74 | 2.61 | 6.13% | 11.88% |
16 | 16 | 0.9296 | 0.8642 | 3.13 | 2.99 | 7.04% | 13.58% |
19 | 19 | 0.9203 | 0.8471 | 3.52 | 3.39 | 7.97% | 15.29% |
22 | 22 | 0.9120 | 0.8318 | 3.87 | 3.74 | 8.80% | 16.82% |
25 | 25 | 0.9137 | 0.8349 | 3.80 | 3.67 | 8.63% | 16.51% |
30 | 30 | 0.8847 | 0.7828 | 5.00 | 4.90 | 11.53% | 21.72% |
35 | 35 | 0.8732 | 0.7626 | 5.47 | 5.39 | 12.68% | 23.74% |
40 | 40 | 0.8623 | 0.7436 | 5.91 | 5.85 | 13.77% | 25.64% |
45 | 45 | 0.8511 | 0.7245 | 6.35 | 6.33 | 14.89% | 27.55% |
50 | 50 | 0.8408 | 0.7071 | 6.75 | 6.76 | 15.92% | 29.29% |
55 | 55 | 0.8335 | 0.6949 | 7.03 | 7.07 | 16.65% | 30.51% |
60 | 60 | 0.8221 | 0.6759 | 7.47 | 7.56 | 17.79% | 32.41% |
65 | 65 | 0.8124 | 0.6601 | 7.83 | 7.97 | 18.76% | 33.99% |
As shown in Figure
Relationship between core volumetric strain and effective stress.
Figure
Relationship between porosity and effective stress.
From Figure
Relationship between permeability and effective stress.
Figure
Relationship between dimensionless porosity and effective stress.
As shown in Figure
Relationship between dimensionless permeability and effective stress.
The results show that the oil reservoir core porosity and permeability under stress can be well evaluated using the mathematical model together with experimental stress and strain data with no need of introducing flooding fluid.
The method proposed by the paper addresses the problem of sealing and leakage of core holders in the conventional stress and flowing fluid method which provides a new approach for the stress sensitivity analysis of oil reservoirs without fluid flooding. The results of the experimental prove that the proposed method is feasible and effective. Compared with the conventional method, the proposed method measures the triaxial stress and strain of the core rock samples and based on which, the core porosity and permeability under stress can be evaluated by theoretical model. However, the enhancement of gas effective permeability with increased gas saturation weakens with higher complexity and lower discreteness of a pore network. Therefore, for the rock with higher porosity, this method is less effective and the results would have deviation errors. The future work is to continuously improve the model by adding other influence factors, to achieve higher accuracy of soft rocks or rocks with microcracks.
The experimental results showed that the triaxial stress method proposed by this investigation with applying rock mechanics method to test the stress sensitivity of reservoir rocks is feasible. The experimental method is practical and simple test while the mathematical model results are reliable. It is feasible to evaluate the mathematical model for changes in permeability and porosity with stress from experimental data of triaxial stress. The calculated results matched well with the experimental results. Comparing with the conventional method of applying stress and flowing fluid through rocks by a core flooding equipment, the proposed method by this investigation avoids the problems of sealing and leakage of core holders and has other advantages as well. However, the new method is less adaptable for soft rocks or rocks with microcracks, where the results obtained would be biased.
The data used to support the findings of the study are included within the article.
The authors declared that there is no financial and personal relationships with other people or organizations that can inappropriately influence our work, and there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in or the review of the manuscript entitled, “Determining triaxial stress sensitivity of oil reservoir rocks without fluid flooding.”