Effects of Pore Water Content on Stress Sensitivity of Tight Sandstone Oil Reservoirs: A Study of the Mahu Block (Xinjiang Province, China)

: Traditional stress sensitivity experiments are typically conducted under dry conditions, without considering the reservoir’s water content. In reality, the presence of water within pores signiﬁcantly inﬂuences the extent of stress sensitivity damage in tight sandstone oil formations, subsequently affecting the determination of stress sensitivity coefﬁcients during experimentation. By investigating sandstone samples from wells in the Mahu Block of China’s Xinjiang province, we observed that increasing water saturation reduces the stress sensitivity of tight sandstone. By conducting stress sensitivity experiments under varying water content conditions, we found that the stress sensitivity coefﬁcient is not a constant value but decreases as water saturation increases. Based on experimental comparisons, an optimized power-law model for stress-sensitive damage assessment was reﬁned. By conducting stress-sensitive damage assessment experiments under different water content conditions and integrating the concept of comprehensive compression coefﬁcient, an improved stress-sensitive power-law model was established allowing for the inﬂuence of water content. The accuracy of this improved model was increased by 46.98% compared to the original power-law model through experimental validation. The research outcomes can enhance the accuracy of permeability and productivity evaluation, providing valuable guidance for unconventional oil and gas development.


Introduction
Tight oil will be a highly significant unconventional hydrocarbon resource for increasing oil reserves and production in the future.The development of tight oil has been a major driving force behind the recent rise in crude oil production in the United States.Data based on the information provided by the U.S. Energy Information Administration shows that about 90% of the growth in oil production in the U.S. originates from six tight oil areas [1].In 2018, tight oil production reached 310 million metric tons, accounting for 60% of the total production [2].In accordance with the fourth oil and gas resource assessment conducted by PetroChina (Beijing, China), the national geological reserves of tight oil in China are Processes 2023, 11, 3153 2 of 21 about 12.5 billion metric tons, with recoverable resources of 1.3 billion metric tons and confirmed reserves of roughly 300 million metric tons [3].Tight oil has become one of the key project areas when exploring China's unconventional petroleum resources and is a major contributor to China's increased oil recoverable reserves and production.
In the case of oil and gas reservoirs, the original equilibrium involves a balancing of pressures between the overlying rock formation pressure, pore pressure, and rock framework support pressure.Nevertheless, as the fluids are extracted from the rock pores, this equilibrium is disrupted [4].Consequently, the rock framework undergoes compression, leading to a gradual reduction in pore size and a subsequent decrease in permeability [5].The greater the degree of extraction, the greater the compression of the rock pore size, resulting in a greater reduction in permeability [6].In simpler terms, the rock experiences a more signification level of stress-induced damage.Based on prior studies, if a rock is softer, indicating a weaker rock framework supporting capacity, it will experience more pronounced pore compression, resulting in a more substantial decrease in permeability when subjected to the same overlying rock formation pressure [7].Typically, soft rocks tend to display a more pronounced stress sensitivity, whereas dense rocks exhibit a less significant stress sensitivity effect.The extent of stress-induced damage is directly proportional to the rock's compressibility coefficient [8,9].Hence, rocks that are more easily compressible will experience more severe stress-induced damage.
Permeability is one of the important parameters describing reservoir properties, serving as fundamental data for reservoir evaluation, development scheme design, numerical simulation, and productivity assessment.Permeability development and evolution can both be a product of original sedimentary depositional processes and variability, as well as of post-depositional processes and modifications such as compaction, fracturing, and faulting and even of human activity [10][11][12][13][14].As fluid is extracted from reservoirs, the phenomenon of decreasing reservoir permeability due to increasing effective stress is known as stress sensitivity [15].Prior research assessed stress sensitivity by examining changes in rock fracture permeability or porosity [16].Dong et al. [9] conducted experimental studies on the stress sensitivity of tight sandstone and shale based on the changes in porosity and permeability, suggesting that shale permeability stress sensitivity is 2-3 times that of sandstone.Kassis et al. [17] derived experimental results of permeability which indicated that shale stress sensitivity is jointly influenced by factors such as effective stress loading mode, fracture characteristics, and support materials.Kang et al. [18] designed and tested experiments to investigate the influence of variable effective stress conditions and loading/unloading sustained stable time on rock sample permeability.The study determined that shale composition and multi-scale pore-fracture structures are the main causes of the differential deformation characteristics of shale pores.Geng et al. [19] conducted multiple studies which indicated that tight sandstone reservoirs generally demonstrate strong stress sensitivity during production, posing challenges for restoring permeability.Fernandes et al. [20] established a flow model considered the stress-sensitive effect and monitored its role in the permeability change to enhance oil recovery.Chang et al. [21] examined the impacts of the stress loading methods, cyclic loading, and loading rates on reservoir permeability using Ordos Basin tight sandstones; they observed a significant decrease in permeability for tight reservoirs with increasing loading time.
Mathematical models for assessing stress-sensitive damage to porosity or permeability in tight rocks are scarce [22,23], with the majority being empirical in nature.Cui et al. [24] observed that shale porosity exhibited a linear decrease with increasing effective stress, while permeability exhibited a power-law decay trend with increasing effective stress based on pressure pulse decay tests.Zhang et al. [25] investigated the applicability and physical significance of power-law formulas and their constants based on the physical meaning of the Walsh model and the intrinsic mathematical relationship between the Walsh model and power-law formulas.The researchers verified their findings through experimentation and classified stress-sensitive formulas based on five different pore types.Duan et al. [7] experimentally examined the sensitivity of matrix, micro-fracture, and artificial fracture permeability to stress.They summarized the fitting and correction results of pore-permeability power-law index model, Gangi model, and Walsh model for fracture permeability.The research findings showed that micro-fractures and unfilled artificial fractures have the strongest stress sensitivity in permeability, exhibiting exponential decay with increasing effective stress.The fitting accuracy of both the Gangi and Walsh models is above 97%.
Nevertheless, all these experiments were carried out using dry rock samples, which do not align with actual water-bearing reservoir conditions [26].Firstly, sandstone reservoirs contain a certain amount of original water.Gao et al. [27] analyzed and discovered the presence of free water in large pores, abundant capillary water in medium and small pores, and full water saturation in tiny pores within the He 8 -Shan 1 reservoir interval in the northern Tianhuan region of the Ordos Basin.Shi et al. [28] and Ma [29] identified four types of water, including bounded water, interlayer water, edge-bottom water, and isolated water, in the tight sandstone of the Sulige area.Secondly, effective production from tight sandstone oil reservoirs requires extensive hydraulic fracturing under current technological conditions.During the fracturing process, a significant amount of fracturing fluid infiltrates the sandstone reservoir, leading to a rapid increase in reservoir water saturation in the near-fracture zone [30][31][32][33][34][35], further influencing the sensitivity of sandstone permeability to stress.Prior research has shown, through numerous experiments, that the comprehensive compression coefficient of sandstone is indeed influenced by water saturation [26].Therefore, the degree of stress-sensitive damage in sandstone will also be affected by water saturation.
Based on the previous analysis, it is evident that actual reservoir rocks exist within a water-containing environment.Despite these previous analyses, and despite the major implications of better characterizing the effects of water on stress sensitivity for both oil and gas systems on land and offshore as well as emerging resource systems such as marine hydrates and geothermal reservoirs [36][37][38][39][40], there are still numerous shortcomings in the current understanding of the impact of water on the sensitivity of rocks to stress.This study aims to explore the effect of water content on stress sensitivity in tight sandstone.First, by conducting experiments to assess the extent of stress sensitivity damage under different water saturation conditions, we examine the impact of water content on stress sensitivity damage.Second, we evaluate the practicality of these models for assessing stress sensitivity damage in tight sandstone reservoirs by comparing the fitting performance of commonly used exponential models and the original power-law model.Finally, we improve the original power-law model by addressing its limitations and incorporating the comprehensive compression coefficient.Moreover, it has been determined that the stress sensitivity coefficient is not a constant value; instead, it decreases as water content increases.Building upon these experimental findings and the concept of comprehensive compression coefficient, a correction formula for the stress sensitivity coefficient under the influence of water content was established.The accuracy of this formula was validated through experimental and referenced results.The research outcomes enhance the accuracy of permeability and productivity evaluation, providing effective guidance for unconventional oil and gas development.

Geological Background
Tight sandstone samples of groups A and B were collected, each originating from wells A and B in the Mahu Block, Xinjiang Province, China, as shown in Figure 1.The Mahu Block is located on the northern slope of the western ring belt within the Mahu Depression, featuring a southwest-dipping monocline [41,42].The fault blocks exhibit dip angles of less than 10 degrees.Reservoir depths vary from 2440 m in the northernmost to 3305 m in the southernmost.The faults are predominantly reverse faults with separation distances ranging from 10 to 50 m and lengths spanning from 4 to 28.5 km [43].Baikouquan Formation 2 (T 1 b 2 ), from northeast to southwest, gradually transitions from a plain facies to a foreland facies.Baikouquan Formation 3 (T 1 b 3 ), from northeast to southwest, has the main reservoir in the foreland facies, with the southern part entering the foredeep delta.As the transition occurs from plain facies to foreland facies, the grain size of the reservoir becomes finer, evolving from medium conglomerates to fine conglomerates and conglomeratic sandstones.While grain flows in the plain facies do not yield oil, sheet-like turbidites and distributary channels in the foreland facies exhibit the most promising oil-bearing characteristics [44].The geological strata in the Madong Slope area exhibit a well-developed sequence, progressing from the bottom upwards and encompassing the Carboniferous, Permian, Triassic, Jurassic, and Cretaceous systems.Notably, there are regional unconformities present between the Permian and Triassic systems, the Triassic and Jurassic systems, as well as between the Jurassic and Cretaceous systems.
distances ranging from 10 to 50 m and lengths spanning from 4 to 28.5 km [43].Baikouquan Formation 2 (T1b2), from northeast to southwest, gradually transitions from a plain facies to a foreland facies.Baikouquan Formation 3 (T1b3), from northeast to southwest, has the main reservoir in the foreland facies, with the southern part entering the foredeep delta.As the transition occurs from plain facies to foreland facies, the grain size of the reservoir becomes finer, evolving from medium conglomerates to fine conglomerates and conglomeratic sandstones.While grain flows in the plain facies do not yield oil, sheet-like turbidites and distributary channels in the foreland facies exhibit the most promising oil-bearing characteristics [44].The geological strata in the Madong Slope area exhibit a well-developed sequence, progressing from the bottom upwards and encompassing the Carboniferous, Permian, Triassic, Jurassic, and Cretaceous systems.Notably, there are regional unconformities present between the Permian and Triassic systems, the Triassic and Jurassic systems, as well as between the Jurassic and Cretaceous systems.The target reservoir layers in wells A and B originate from the Triassic Baikouquan Formation, which can be divided into three intervals from bottom to top: Baikouquan Formation 1 (T1b1), Baikouquan Formation 2 (T1b2), and Baikouquan Formation 3 (T1b3), as shown in Figure 2 [42,44].The primary oil-bearing strata are situated within Baikouquan Formation 2. The target reservoir layers in wells A and B originate from the Triassic Baikouquan Formation, which can be divided into three intervals from bottom to top: Baikouquan Formation 1 (T 1 b 1 ), Baikouquan Formation 2 (T 1 b 2 ), and Baikouquan Formation 3 (T 1 b 3 ), as shown in Figure 2 [42,44].The primary oil-bearing strata are situated within Baikouquan Formation 2. Baikouquan Formation 1: This interval is predominantly composed of blocky gray and brown pebble conglomerates, occasionally interbedded with brown mudstone, conglomeratic mudstone, and muddy sandstone.T1b1 has a thickness ranging from 16.7 to 60.6 m, with an average of 45.2 m.
Baikouquan Formation 2: The lower portion is characterized by gray blocky mudstone with pebbles, and is relatively compact.The upper part consists of gray blocky sandy conglomerates, sandy pebble conglomerates, and conglomeratic medium to coarse sandstones, with intermittent layers of brown blocky mudstone.T1b2 has a thickness ranging from 51.7 to 67.2 m, with an average of 59.3 m.
Baikouquan Formation 3: This interval is primarily composed of brown mudstone with thin layers of gray mudstone and silty sandstone.T1b3 has a thickness ranging from 55.4 to 63.3 m, with an average of 56.8 m.
The core sampling depths for well A range from 4271 to 4277 m, while for well B, the core sampling depths are 4183 to 4186 m, 4210 to 4215 m, and 4224 to 4232 m, as shown in Figure 2. Baikouquan Formation 1: This interval is predominantly composed of blocky gray and brown pebble conglomerates, occasionally interbedded with brown mudstone, conglomeratic mudstone, and muddy sandstone.T 1 b 1 has a thickness ranging from 16.7 to 60.6 m, with an average of 45.2 m.
Baikouquan Formation 2: The lower portion is characterized by gray blocky mudstone with pebbles, and is relatively compact.The upper part consists of gray blocky sandy conglomerates, sandy pebble conglomerates, and conglomeratic medium to coarse sandstones, with intermittent layers of brown blocky mudstone.The core sampling depths for well A range from 4271 to 4277 m, while for well B, the core sampling depths are 4183 to 4186 m, 4210 to 4215 m, and 4224 to 4232 m, as shown in Figure 2.

Comparison of Stress Sensitivity Experiments in Water-Bearing and Dry Conditions for Tight Sandstone
Firstly, a section of downhole cores from wells A and B were precision-cut into standard core samples measuring 5 cm × 2.54 cm.Four samples meeting the criteria of being "intact, free of cracks, and possessing similar permeability" were chosen from each well.Samples from well A were designated as group A, and those from well B as group B. Ultimately, the initial permeability under dry conditions measured approximately 0.8 mD for group A cores and approximately 0.0024 mD for group B cores.
Secondly, the two sets of core samples were saturated with different amounts of water using the self-imbibition method [34].For group A, the samples were subjected to different conditions: dry, water saturation (S w ) of 30%, S w of 60%, and S w of 80%.Group B samples were subjected to dry conditions, S w of 25%, S w of 52%, and S w of 80%.
Thirdly, we utilized the MHY-TY3 instrument to gauge the permeability of each set of core samples under diverse confining pressures and at room temperature, while also assessing how fluctuations in water content within the cores impact stress sensitivity.The minimum confining pressure was 2.75 MPa, and it was incrementally increased to a maximum confining pressure of 15 MPa [9].The gas permeability results for both sandstone groups under different confining pressures and water saturation conditions are shown in Figure 3.

Comparison of Stress Sensitivity Experiments in Water-Bearing and Dry Conditions for Tight Sandstone
Firstly, a section of downhole cores from wells A and B were precision-cut into standard core samples measuring 5 cm × 2.54 cm.Four samples meeting the criteria of being "intact, free of cracks, and possessing similar permeability" were chosen from each well.Samples from well A were designated as group A, and those from well B as group B. Ultimately, the initial permeability under dry conditions measured approximately 0.8 mD for group A cores and approximately 0.0024 mD for group B cores.
Secondly, the two sets of core samples were saturated with different amounts of water using the self-imbibition method [34].For group A, the samples were subjected to different conditions: dry, water saturation (Sw) of 30%, Sw of 60%, and Sw of 80%.Group B samples were subjected to dry conditions, Sw of 25%, Sw of 52%, and Sw of 80%.
Thirdly, we utilized the MHY-TY3 instrument to gauge the permeability of each set of core samples under diverse confining pressures and at room temperature, while also assessing how fluctuations in water content within the cores impact stress sensitivity.The minimum confining pressure was 2.75 MPa, and it was incrementally increased to a maximum confining pressure of 15 MPa [9].The gas permeability results for both sandstone groups under different confining pressures and water saturation conditions are shown in Figure 3. From Figure 3a,b, we observed a significant decrease in gas permeability as the confining pressure gradually increases.Beyond 8 MPa, the rate of permeability reduction lev- From Figure 3a,b, we observed a significant decrease in gas permeability as the confining pressure gradually increases.Beyond 8 MPa, the rate of permeability reduction levels off.Moreover, as the water content in the samples increases, the gas permeability gradually decreases.Furthermore, as the water saturation within the rock increases, the decline rate of permeability also decreases.This phenomenon can be attributed to the rise in water content, which leads to a decrease in the overall compressibility coefficient of the rock.Consequently, the rock's resistance to compression increases.These findings align with conventional expectations and represent typical experimental outcomes.

Limitations of Traditional Stress Sensitivity Models in Fitting the Experimental Results under Water-Bearing Conditions
Currently, the type of models used for assessing stress sensitivity mainly include the exponential model [8,45] and the power-law model [9,46], as showed in Table 1.Most of the models are the improvements of the two types of assessing stress sensitivity model.These two models are the most classic models and are frequently applied in the assessment of stress-sensitive damage levels.
Table 1.The models mostly used for stress sensitivity assessment.

Type Detailed Models Equations References
Exponential model Han's model k = k 0 1 − S s lg σ eff σ eff0 3 [26] where k and k 0 are the permeability and the initial permeability, respectively, mD; P c and P are the overburden pressure and pore pressure, respectively, MPa; C k is the stress sensitivity coefficient of permeability for the exponential model, MPa −1 ; n is the fitting coefficient for the power-law model, dimensionless; C t is the compressibility factor, MPa −1 ; σ eff is the effective stress, MPa; υ is the Poisson's ratio; h and a 0 are the intersecting diameters of the pore, respectively; m is the parameter related to the pore roughness, dimensionless; λ is the model parameter, MPa; P e is the effective pressure, MPa; S s refers to stress sensitivity coefficient, dimensionless; σ eff means the effective stress, MPa; and σ eff0 is the minimum effective stress, MPa.
Using the aforementioned two equations to fit stress-sensitive experimental data of tight sandstone under dry conditions, we obtained the stress sensitivity coefficients for samples A and B under dry conditions.Specifically, the stress sensitivity coefficients obtained through the traditional exponential model (M1) were 0.162 MPa −1 and 0.1022 MPa −1 for samples A and B, respectively.Additionally, the fitting coefficients "n" obtained through the traditional power-law model (M2) were 1.1695 and 0.7195 for samples A and B, respectively.The corresponding fitting results are shown in Figure 4. Obtaining the stress sensitivity coefficients for samples under dry conditions through data fitting is a widely utilized method in both scientific research and practical production applications.It is evident that discrepancies exist between the stress sensitivity coefficients ob tained using the two methods and the actual reservoir conditions.This discrepancy arise because oil and gas reservoirs typically exist in water-bearing conditions, whereas the ex perimental results obtained from samples under dry conditions naturally deviate from the real scenario.This observation is supported by Figure 5, where we substituted th stress sensitivity coefficient Ck obtained from the exponential model under dry condition and the fitting coefficient n obtained from the power-law model under dry conditions fo fitting the experimental data under various water-containing conditions, respectively.No tably, the results calculated using the two models are difficult to fit with the experimenta results under water-containing conditions, consistently yielding values smaller than th actual experimental observations, as demonstrated in Figure 5.The observation concur rently implies that the overall compressibility coefficient under dry conditions exceed that under water-saturated conditions.In simpler terms, rocks experience greater stress induced damage under dry conditions compared to water-saturated conditions.It is evident that discrepancies exist between the stress sensitivity coefficients obtained using the two methods and the actual reservoir conditions.This discrepancy arises because oil and gas reservoirs typically exist in water-bearing conditions, whereas the experimental results obtained from samples under dry conditions naturally deviate from the real scenario.This observation is supported by Figure 5, where we substituted the stress sensitivity coefficient C k obtained from the exponential model under dry conditions and the fitting coefficient n obtained from the power-law model under dry conditions for fitting the experimental data under various water-containing conditions, respectively.Notably, the results calculated using the two models are difficult to fit with the experimental results under water-containing conditions, consistently yielding values smaller than the actual experimental observations, as demonstrated in Figure 5.The observation concurrently implies that the overall compressibility coefficient under dry conditions exceeds that under water-saturated conditions.In simpler terms, rocks experience greater stress-induced damage under dry conditions compared to water-saturated conditions.In the traditional numerical simulation process, the influence of water-containing conditions on the magnitude of stress sensitivity damage has often been overlooked, despite the ability to derive the initial permeability under such conditions from the relative permeability curves of water-gas two phases, denoted as k0 in Table 1.Furthermore, most studies have focused on addressing stress sensitivity damage, but these data are typically derived from experimental procedures conducted under dry conditions.Based on the experimental and fitting results obtained using the power-law and exponential models mentioned above, it is evident that the stress sensitivity function obtained under dry conditions is not applicable to water-containing conditions.This highlights the urgent need for corrections to existing models.

Improvement to Power-Law Function Model
By fitting the stress sensitivity data under dry conditions and different water content conditions as shown in Figures 4 and 5, we can observe that the power-law model (M2) provides significantly better fitting results when compared to the exponential function (M1).This indicates that the power-law model is more suitable for evaluating the degree In the traditional numerical simulation process, the influence of water-containing conditions on the magnitude of stress sensitivity damage has often been overlooked, despite the ability to derive the initial permeability under such conditions from the relative permeability curves of water-gas two phases, denoted as k 0 in Table 1.Furthermore, most studies have focused on addressing stress sensitivity damage, but these data are typically derived from experimental procedures conducted under dry conditions.Based on the experimental and fitting results obtained using the power-law and exponential models mentioned above, it is evident that the stress sensitivity function obtained under dry conditions is not applicable to water-containing conditions.This highlights the urgent need for corrections to existing models.

Improvement to Power-Law Function Model
By fitting the stress sensitivity data under dry conditions and different water content conditions as shown in Figures 4 and 5, we can observe that the power-law model (M2) provides significantly better fitting results when compared to the exponential function (M1).This indicates that the power-law model is more suitable for evaluating the degree of stress-sensitive damage in tight sandstone.This application pattern is further substantiated by [25], who noted that rock cores following the power-law model exhibit a rapid decrease in permeability during the initial increase in effective stress, followed by a more gradual change in permeability during the middle and later stages of effective stress increase, commonly referred to as the 'steep-then-gentle pattern.'This distinctive pattern aligns with the characteristics of low-permeability reservoirs governed by fractures, where the reservoir permeability is primarily influenced by fractures.The initial closure of fractures due to the increase in effective stress results in a sharp decrease in permeability.As the fractures are completely closed, the extremely low matrix permeability causes a gradual reduction in permeability as the effective stress continues to increase.Consequently, this paper opts to optimize the model based on the power-law formulation, given its compatibility with the observed behavior.
However, the power-law model is an empirical model, and the fitting coefficient "n" does not have a specific physical interpretation, making it difficult to modify based on concrete meanings.Nevertheless, the fitting coefficient in the power-law model is directly proportional to the sample's compressibility factor.The relationship between the fitting coefficient under dry and water content conditions and the sample's compressibility factor can be expressed using the following equations: where n and n w are the dimensionless fitting coefficients of the power-law stress-sensitive model under dry and water content conditions, respectively; C t-drying and C t-w are the total compressibility coefficients of the sandstone under dry and water content conditions, respectively, MPa −1 ; C p , C g , and C w are the compressibility coefficients of the rock, gas, and water, respectively, MPa −1 ; and S w and S g are the dimensionless water saturation and gas saturation, respectively.Therefore, a relationship is Therefore, the power-law model can be transformed into The compressibility coefficient of water is very small and can be neglected.Therefore, the above equation can be simplified to where κ is the correction coefficient of water saturation.

Verification of the Improved Stress Sensitivity Assessment Model Using Experimental Data
Under atmospheric pressure conditions, the compressibility coefficient of gas (C g ) is much greater than the rock compressibility coefficient (C p ).Thus, the correction factor C g /C t-drying in Equation ( 6) is approximately one.Consequently, the improved fitted coefficient of the power-law model becomes (1 − S w ) n.
The comparison between the corrected fitting results, original data, and uncorrected fitting results is shown in Figures 6-8.The fitting results in Figure 6 were based on Figure 3.In Figure 7, the fitting index 'n' under drying conditions is 1.4867, while in Figure 8, the fitting index under drying conditions is 1.7867.It can be observed that: (1) As the water content in the sample increases, the disparity between most of the computed results of the fitted coefficients obtained under dry conditions according to the original model and the experimental results becomes more pronounced.This result corroborates the speculation in the preceding section that an increase in water content reduces the total compressibility factor of the sample.Moreover, the larger the water content, the smaller the total compressibility factor of the sample.Certainly, this disparity does not continue to increase, primarily during the high water content stages, as shown in Figures 7 and 8. Nevertheless, on the whole, it remains evident that utilizing the stress-sensitive damage coefficient fitted under dry conditions to evaluate the extent of stress-sensitive damage under wet conditions will result in an overestimation of the degree of stress sensitivity damage.(2) The improved model, which takes into account the correction of the fitting coefficients of the power-law model for water content, exhibits improved fitting accuracy compared to the actual data, even though some disparity still remains.Comparing the fitting results of the original M2 for the sample group A, the accuracy of the improved model's fitting results has increased by 35.46%, 60.56%, and 70.94% for the samples with S w = 30%, S w = 60%, and S w = 80%, respectively.In the case of the sample group B, the accuracy of the improved model's fitting results has increased by 21.06%, 39.63%, and 54.20% for the samples with S w = 25%, S w = 52%, and S w = 80%, respectively.The average increase in accuracy for these experiments is 46.98%.As for Figure 7, the accuracy of the improved model's fitting results has increased by 6.01%, 4.18%, and −48.96% for the samples with S w = 20%, S w = 40%, and S w = 70%, respectively.As for Figure 8, the accuracy of the improved model's fitting results has increased by 9.23% and −42.90% for the samples with S w = 30% and S w = 70%, respectively.The fitting results for the improved model have decreased the errors for the samples with low water saturation, but increased the errors for the samples with S w = 70%.These comparisons highlight that the improved model performs well in assessing the degree of stress-sensitive damage in low water content samples.However, when evaluating the extent of stress-sensitive damage in high water content samples, there is some degree of error present.(3) As the water content in the sample increases, the rate of permeability decrease during the initial pressurization stage gradually slows down.This means that the type of permeability decline curve changes from a "rapid-slow" similar to an "L-shaped" decline to a more linear decline due to the fact that the increased water content in the sample counteracts the rapid compression effect of confining pressure on the pores.This phenomenon further validates the earlier speculation, indicating that as the water saturation within the rock decreases, the gas saturation increases.Therefore, under the same overlying rock formation pressure, the framework bears a greater stress load, making the rock framework more susceptible to compression.

Verification of the Improved Stress Sensitivity Assessment Model Using Referenced Data
Drawing on some experimental data from Han et al. [26], we assessed the degree of rock stress-sensitive damage under various water content conditions and further validated the accuracy of the model proposed in this paper.Although Han et al. [26] conducted stress sensitivity experiments on coal rock, which may disrupt the original structure of the coal rock during the repeated pressurization experiments, the observed phenomenon aligns broadly with this paper's approach.Therefore, their experimental results can still be used to validate the model presented in this paper.

Verification of the Improved Stress Sensitivity Assessment Model Using Referenced Data
Drawing on some experimental data from Han et al. [26], we assessed the degree of rock stress-sensitive damage under various water content conditions and further validated the accuracy of the model proposed in this paper.Although Han et al. [26] conducted stress sensitivity experiments on coal rock, which may disrupt the original structure of the coal rock during the repeated pressurization experiments, the observed phenomenon aligns broadly with this paper's approach.Therefore, their experimental results can still be used to validate the model presented in this paper.

Verification of the Improved Stress Sensitivity Assessment Model Using Referenced Data
Drawing on some experimental data from Han et al. [26], we assessed the degree of rock stress-sensitive damage under various water content conditions and further validated the accuracy of the model proposed in this paper.Although Han et al. [26] conducted stress sensitivity experiments on coal rock, which may disrupt the original structure of the coal rock during the repeated pressurization experiments, the observed phenomenon aligns broadly with this paper's approach.Therefore, their experimental results can still be used to validate the model presented in this paper.
Firstly, we utilized a power-law model to fit the stress sensitivity experimental data under dry conditions, yielding a stress-sensitive damage coefficient 'n' of 2.1167.Secondly, we separately employed the original power-law model and the improved power-law model that considers the influence of water saturation to fit the stress sensitivity experimental data under different water saturation conditions.The comparative results are depicted in Figure 9.
(1) It can be observed that using the stress-sensitive damage coefficient obtained from fitting under dry conditions to fit stress sensitivity experimental data under different water content conditions often leads to an overestimation of the degree of stresssensitive damage.In other words, the assessment results tend to be higher than the experimental results.Overall, as the water content increases, the original model exhibits a larger error in overestimating the degree of stress-sensitive damage.( 2) For low water-content samples, the improved power-law model that considers the influence of water saturation performs better than the original power-law model.However, for high water-content samples, the fitting performance of the improved power-law model considering water saturation effects is worse than that of the original power-law model.The reason for this phenomenon is that, compared to dense sandstone samples, coal rock samples exhibit plastic behavior, resulting in greater damage to permeability during the pressurization process, thus, causing errors in the experimental results for high water-content samples.
However, overall, utilizing previous experimental data to compare the original powerlaw model and the improved power-law model still demonstrates the following: (1) fitting stress sensitivity experimental data under different water content conditions with the stress-sensitive damage coefficient obtained from fitting under dry conditions often results in an overestimation of the degree of stress-sensitive damage and (2) the improved model exhibits superior fitting performance for low water content samples.
Firstly, we utilized a power-law model to fit the stress sensitivity experimental data under dry conditions, yielding a stress-sensitive damage coefficient 'n' of 2.1167.Secondly, we separately employed the original power-law model and the improved powerlaw model that considers the influence of water saturation to fit the stress sensitivity experimental data under different water saturation conditions.The comparative results are depicted in Figure 9.
(1) It can be observed that using the stress-sensitive damage coefficient obtained from fitting under dry conditions to fit stress sensitivity experimental data under different water content conditions often leads to an overestimation of the degree of stress-sensitive damage.In other words, the assessment results tend to be higher than the experimental results.Overall, as the water content increases, the original model exhibits a larger error in overestimating the degree of stress-sensitive damage.(2) For low water-content samples, the improved power-law model that considers the influence of water saturation performs better than the original power-law model.However, for high water-content samples, the fitting performance of the improved power-law model considering water saturation effects is worse than that of the original power-law model.The reason for this phenomenon is that, compared to dense sandstone samples, coal rock samples exhibit plastic behavior, resulting in greater damage to permeability during the pressurization process, thus, causing errors in the experimental results for high water-content samples.
However, overall, utilizing previous experimental data to compare the original power-law model and the improved power-law model still demonstrates the following: (1) fitting stress sensitivity experimental data under different water content conditions with the stress-sensitive damage coefficient obtained from fitting under dry conditions often results in an overestimation of the degree of stress-sensitive damage and (2) the improved model exhibits superior fitting performance for low water content samples.

Model Application and Analysis
Taking well A in the Mahu Block, Xinjiang province, China, as an example, this section presents the relevant parameters of the model, as detailed in Table 2. Additionally, the physical model is visually depicted in Figure 10.The simulation calculations were carried out using the analytical Hz oil multifrac-enhanced frac region model.The power-law model was employed in the stress sensitivity damage assessment, with the fitting exponent 'n' under different water saturation conditions using group A experimental data.Specifically, for well A, the stress sensitivity fitting exponent 'n' was 1.1695 under dry conditions, 0.8183 at 30% water saturation, 0.4678 at 60% water saturation, and 0.2339 at 80% water saturation.Apart from the differences in the water content and the stress sensitivity fitting exponent under varying water saturation conditions, we maintained consistency in other parameter values, including initial permeability.Subsequently, we evaluated the impact of stress sensitivity fitting exponent variations on permeability and productivity.The comparative results are visually presented in Figures 11 and 12

Model Application and Analysis
Taking well A in the Mahu Block, Xinjiang province, China, as an example, this section presents the relevant parameters of the model, as detailed in Table 2. Additionally, the physical model is visually depicted in Figure 10.The simulation calculations were carried out using the analytical Hz oil multifrac-enhanced frac region model.The power-law model was employed in the stress sensitivity damage assessment, with the fitting exponent 'n' under different water saturation conditions using group A experimental data.Specifically, for well A, the stress sensitivity fitting exponent 'n' was 1.1695 under dry conditions, 0.8183 at 30% water saturation, 0.4678 at 60% water saturation, and 0.2339 at 80% water saturation.Apart from the differences in the water content and the stress sensitivity fitting exponent under varying water saturation conditions, we maintained consistency in other parameter values, including initial permeability.Subsequently, we evaluated the impact of stress sensitivity fitting exponent variations on permeability and productivity.The comparative results are visually presented in Figures 11 and 12.
The primary objective of this study is to explore the repercussions of overlooking the impact of water saturation on the stress sensitivity coefficient during actual application and to gauge the magnitude of this oversight on production capacity.The simulation conditions involve relatively idealized assumptions, such as assuming the same reservoir permeability under different water saturation conditions.However, there are differences in permeability and crude oil reserves under different water saturation conditions.By employing these assumed simulation conditions, it becomes evident how much the stress-sensitive error caused by water saturation can affect production capacity, thereby capturing the attention and emphasis of reservoir engineers on the research problem addressed in this paper.The primary objective of this study is to explore the repercussions of overlooking the impact of water saturation on the stress sensitivity coefficient during actual application and to gauge the magnitude of this oversight on production capacity.The simulation conditions involve relatively idealized assumptions, such as assuming the same reservoir permeability under different water saturation conditions.However, there are differences in permeability and crude oil reserves under different water saturation conditions.By employing these assumed simulation conditions, it becomes evident how much the stresssensitive error caused by water saturation can affect production capacity, thereby capturing the attention and emphasis of reservoir engineers on the research problem addressed in this paper.
From Figure 11, we observed that the degree of stress-sensitive damage under different water content conditions is much smaller when compared to that under dry conditions.The greater the water content, the smaller the degree of stress-sensitive damage.Therefore, utilizing stress-sensitive data from dry conditions in numerical simulation of oil production can lead to an exaggerated perception of stress sensitivity impact on production.Meanwhile, as shown in Figure 12, the usage of inaccurate stress-sensitive data severely underestimates the well's production capacity.This underestimation becomes more pronounced as the actual water content increases, particularly during the early production stages.Such inaccuracies can significantly affect the assessment of production capability during the rapid decline phase.Furthermore, when fitting historical production data using production capacity simulation software, the usage of stress-sensitive data from dry conditions can affect the simulation and inversion accuracy of other engineering parameters.
To illustrate this point further, consider the application results shown in Figure 12.When the stress-sensitive fitting coefficients from dry conditions are applied to tight oil reservoirs with water saturations of 30%, 60%, and 80%, respectively, the underestimation of the ultimate recoverable reserves reaches 12.45%, 27.33%, and 38.85%, respectively.These simulation results clearly demonstrate that using stress-sensitive data from dry conditions to assess oil well production significantly underestimates the well's output.Such inaccuracies can lead to increased project investment when incorrect production values are utilized for oil well redevelopment assessments.

Signification and Limitations
Based on the experimental findings presented in Section 3.2 of this study, as well as the analysis of fitting outcomes using conventional methods, it becomes evident that traditional models for assessing stress sensitivity indices, including stress sensitivity powerlaw models, tend to disregard the influence of water content on the extent of stress-induced damage in tight sandstone [51][52][53][54][55].This oversight results in an overestimation of From Figure 11, we observed that the degree of stress-sensitive damage under different water content conditions is much smaller when compared to that under dry conditions.The greater the water content, the smaller the degree of stress-sensitive damage.Therefore, utilizing stress-sensitive data from dry conditions in numerical simulation of oil production can lead to an exaggerated perception of stress sensitivity impact on production.Meanwhile, as shown in Figure 12, the usage of inaccurate stress-sensitive data severely underestimates the well's production capacity.This underestimation becomes more pronounced as the actual water content increases, particularly during the early production stages.Such inaccuracies can significantly affect the assessment of production capability during the rapid decline phase.Furthermore, when fitting historical production data using production capacity simulation software, the usage of stress-sensitive data from dry conditions can affect the simulation and inversion accuracy of other engineering parameters.
To illustrate this point further, consider the application results shown in Figure 12.When the stress-sensitive fitting coefficients from dry conditions are applied to tight oil reservoirs with water saturations of 30%, 60%, and 80%, respectively, the underestimation of the ultimate recoverable reserves reaches 12.45%, 27.33%, and 38.85%, respectively.These simulation results clearly demonstrate that using stress-sensitive data from dry conditions to assess oil well production significantly underestimates the well's output.Such inaccuracies can lead to increased project investment when incorrect production values are utilized for oil well redevelopment assessments.

Signification and Limitations
Based on the experimental findings presented in Section 3.2 of this study, as well as the analysis of fitting outcomes using conventional methods, it becomes evident that traditional models for assessing stress sensitivity indices, including stress sensitivity power-law models, tend to disregard the influence of water content on the extent of stress-induced damage in tight sandstone [51][52][53][54][55].This oversight results in an overestimation of the stress sensitivity coefficient obtained through fitting processes.In actual reservoir conditions, rock compositions exhibit varying water-content levels [56].Consequently, evaluating the degree of stress sensitivity damage in moist tight sandstone based on an inflated stress sensitivity coefficient significantly amplifies the impact of stress sensitivity on reservoir rocks.In simpler terms, under similar pressure differential conditions, the assessments made using traditional models suggest a more pronounced pore compression and a larger decline in permeability.Moreover, as illustrated in Section 5.1 of this paper, when comparing the outcomes of production capacity simulations, an overestimated stress sensitivity coefficient leads to an underestimation of initial production rates, ultimately resulting in a lower estimation of the recoverable reserves [57].
Hence, when performing stress sensitivity assessments for reservoirs through laboratory experiments, it is crucial to preset the water content of samples according to the actual water saturation in the reservoir rocks [26].This ensures that the experimental results closely replicate reservoir conditions.Furthermore, in the production capacity simulation process, the stress sensitivity damage coefficient should be adjusted using correction factors, as illustrated in Equation (6).Only by conducting such simulations can we achieve a more precise assessment of stress sensitivity's influence on reservoir production capacity.
Based on experimental findings from downhole core samples in the Mahu Block of Xinjiang and an improved stress sensitivity power-law model, this paper first emphasizes the necessity of conducting stress sensitivity experiments under realistic reservoir water saturation conditions.Secondly, it rectifies the shortcomings of traditional models, providing guidance for production development in the Mahu Block of Xinjiang and even offering insights for the development of tight oil and gas fields.
Nevertheless, the two frequently referenced models discussed in this paper, the stress sensitivity index model and the power-law model, are both empirical in nature.While the correction coefficient is derived from the overall compressibility of the rock, the models themselves remain fundamentally empirical.For regions outside of the Mahu Block in Xinjiang, and even for other unconventional oil and gas reservoirs, future researchers may need to conduct additional refinements and precise data quantifications based on the improved model presented in this paper.Furthermore, through practical application it has been observed that the improved model still exhibits significant errors in assessing high water-content samples and highly plastic samples.Therefore, in later-stage applications, it is essential to consider the inherent characteristics of the samples and apply the improved model appropriately.

Conclusions
This paper, utilizing core samples from the Mahu Block, conducted stress sensitivity experiments on tight sandstones with differing water content levels.It refined the stress sensitivity power-law model by incorporating the comprehensive compressibility coefficient.Experimental validation and comparison confirmed the reliability of this enhanced model.These studies closely replicate actual reservoir conditions and address limitations in prior research.They have the potential to improve the precision of permeability, stress sensitivity, and production capacity assessments, thereby facilitating the efficient development of tight oil resources.
(1) The water content in sandstone samples has a discernible impact on the extent of stress sensitivity damage.Conducting stress sensitivity experiments on the sandstone samples under varying water content conditions revealed a consistent trend: higher water content leads to a reduction in the magnitude of stress sensitivity damage experienced by the samples.(2) Through a comprehensive analysis involving experimental results, fitted outcomes, and numerical simulations, a clear pattern emerged.Employing stress-sensitive fitting coefficients from dry conditions to fit stress-sensitive experimental data under wet conditions resulted in calculated data significantly lower than the experimental data.Likewise, when using these coefficients to assess the actual oil well production, the estimated production output was notably lower than the actual production of the oil well.
(3) This study has improved the power-law model used for stress sensitivity damage assessment.The model takes into account the influence of water saturation on the degree of stress sensitivity damage, enhancing the fitting accuracy of the powerlaw model.

Figure 1 .
Figure 1.The sampling location in Mahu Block, Xinjiang, China (The area of red rectangle is the study area).

Figure 1 .
Figure 1.The sampling location in Mahu Block, Xinjiang, China (The area of red rectangle is the study area).

Figure 2 .
Figure 2. Sedimentary facies diagram of the target strata in well A and well B.

Figure 2 .
Figure 2. Sedimentary facies diagram of the target strata in well A and well B.
T 1 b 2 has a thickness ranging from 51.7 to 67.2 m, with an average of 59.3 m.Baikouquan Formation 3: This interval is primarily composed of brown mudstone with thin layers of gray mudstone and silty sandstone.T 1 b 3 has a thickness ranging from 55.4 to 63.3 m, with an average of 56.8 m.

Figure 3 .
Figure 3.The experimental results of stress sensitivity for tight sandstone with different water content.(a) The experimental results of group A and (b) the experimental results of group B.

Figure 3 .
Figure 3.The experimental results of stress sensitivity for tight sandstone with different water content.(a) The experimental results of group A and (b) the experimental results of group B.

Figure 4 .
Figure 4.The experimental results in dry conditions and the fitting results of stress sensitivity usin the power-law model and the exponential model.(a) The experimental and fitting results of grou A in dry conditions and (b) the experimental and fitting results of group B in dry conditions.

Figure 4 .
Figure 4.The experimental results in dry conditions and the fitting results of stress sensitivity using the power-law model and the exponential model.(a) The experimental and fitting results of group A in dry conditions and (b) the experimental and fitting results of group B in dry conditions.

Figure 5 .
Figure 5.The experimental results with different water content and the fitting results of stress sensitivity using the power-law model and the exponential model.(a) The experimental and fitting results of group A with different water content and (b) the experimental and fitting results of group B with different water content.

Figure 5 .
Figure 5.The experimental results with different water content and the fitting results of stress sensitivity using the power-law model and the exponential model.(a) The experimental and fitting results of group A with different water content and (b) the experimental and fitting results of group B with different water content.

Figure 6 .
Figure 6.The comparison of the fitting results using the original M2 and the improved M2.(a) The comparison of the original M2 and the improved M2 with the experimental results of the sample group A and (b) the comparison of the original M2 and the improved M2 with the experimental results of the sample group A.

Figure 6 .
Figure 6.The comparison of the fitting results using the original M2 and the improved M2.(a) The comparison of the original M2 and the improved M2 with the experimental results of the sample group A and (b) the comparison of the original M2 and the improved M2 with the experimental results of the sample group A.

Figure 7 .
Figure 7.The comparison of the fitting results using the original M2 and the improved M2 for example 1.

Figure 8 .
Figure 8.The comparison of the fitting results using the original M2 and the improved M2 for example 2.

Figure 7 .
Figure 7.The comparison of the fitting results using the original M2 and the improved M2 for example 1.

Processes 2023 , 21 Figure 7 .
Figure 7.The comparison of the fitting results using the original M2 and the improved M2 for example 1.

Figure 8 .
Figure 8.The comparison of the fitting results using the original M2 and the improved M2 for example 2.

Figure 8 .
Figure 8.The comparison of the fitting results using the original M2 and the improved M2 for example 2.

Figure 9 .
Figure 9.The comparison of the fitting results with the original M2 and the improved M2.(a) The results for S w = 0 and (b) The results for S w = 20% and (c) The results for S w = 40% and (d) The results for S w = 70%.

Figure 10 .
Figure 10.The model of analytical Hz oil multifrac-enhanced frac region in harmony-RTA.

Figure 11 .
Figure 11.The relation between k/k0 and pore pressure.

Figure 10 .
Figure 10.The model of analytical Hz oil multifrac-enhanced frac region in harmony-RTA.

Figure 10 .
Figure 10.The model of analytical Hz oil multifrac-enhanced frac region in harmony-RTA.

Figure 11 .
Figure 11.The relation between k/k0 and pore pressure.

Figure 11 .
Figure 11.The relation between k/k 0 and pore pressure.

Figure 12 .
Figure 12.The effect of water content and fitting coefficient of stress sensitivity on tight oil production.

Figure 12 .
Figure 12.The effect of water content and fitting coefficient of stress sensitivity on tight oil production.

Table 2 .
Parameters for the production simulation using RTA-analytical Hz oil multifrac-enhanced frac region model.

Table 2 .
Parameters for the production simulation using RTA-analytical Hz oil multifrac-enhanced frac region model.

Table 2 .
Parameters for the production simulation using RTA-analytical Hz oil multifrac-enhanced frac region model.