# Investigation of the Effect of Confining Pressure on the Mechanics-Permeability Behavior of Mudstone under Triaxial Compression

Authors: Lu Shi; Zhijiao Zeng; Zhiming Fang; Xiaochun Li
Journal: Geofluids
 (2019)

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## Abstract

Injecting CO2 into a reservoir disturbs the geostress field, which leads to variations in the permeability of caprock and affects its sealing performance. In this paper, the evolution characteristics of the permeability of Yingcheng mudstone were experimentally studied during deviatoric compression under different confining pressures. As the confining pressure increased, the strength of the mudstone increased bilinearly, the angle between the fault and the maximum principle stress increased, and the fault became flatter. During compression, the permeability of mudstone first decreased and then increased and the turning point of the permeability was between the onset of dilatancy and the turning point of volumetric strain; when the fault formed, the permeability increased sharply and the fault-induced increment was reduced exponentially with increasing confining pressure. In addition, the mudstone transformed to the ductile failure mode when the effective confining pressure was greater than 35 MPa, which means that the permeability did not jump within a small strain. Finally, a practical strain-based model of permeability evolution that separately considers compaction and dilatancy was proposed, and the predicted permeability values were in good agreement with the experimental results. This study revealed the effect of confining pressure on permeability evolution during compression and can help evaluate the sealing ability of mudstone caprock.


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## Body

## 1. Introduction

Mudstone, the most common material in sedimentary basins, has extremely low permeability and high capillary entry pressure [1], which means that geofluids take a very long time to saturate and pass through a mudstone formation [2]. Therefore, mudstone formations are an effective barrier to geofluid accumulation and play an important role in petroleum systems and in deep energy and waste disposals. Although not always the case, the permeability of mudstones in a well-compacted and undisturbed state is less than 1 μD (≈10-18 m2) based on laboratory measurements of intact mudstone samples [3–9]; the reason for this result is that mudstone is rich in fine-grained and clay sediments and usually has a mean pore radius of less than 100 nm [4, 10, 11], which is more than several orders of magnitude smaller than that of coarser-grained rocks such as sandstone that retains geofluids [12, 13]. Since the clay grains are platy shaped, mudstone has higher compressibility than other sedimentary rocks and its permeability, which is related to porosity, decreases greatly with increasing diagenesis depth or consolidation pressure [14–18]. Therefore, many researchers have carried out experiments on the influence of effective hydrostatic pressure or consolidation pressure on mudstone permeability to understand the stress sensitivity of mudstone permeability [2, 19–21].In CO2 capture and storage (CCS) projects, mudstone usually serves as the caprock formation to seal CO2 safely in the crust for a long time [22–25]; therefore, its permeability is the essential factor affecting its sealing performance. However, when CO2 is injected into deep saline aquifers or depleted hydrocarbon fields, the fluid pressure of the reservoirs will inevitably change, which influences the stress field of the caprock. Stress changes during injection may cause deformation and damage to the caprock and even result in failure of the caprock when the stress state approaches the failure envelope [9]. Since the pore structure of caprock can be altered due to these behaviors, its permeability will also change during CO2 injection, which can affect the sealing performance of the caprock. Therefore, a comprehensive understanding of the response of mudstone permeability to stress is crucial when accessing the leakage risk of CCS sites. However, reports on the evolution of mudstone permeability under general stress variations, such as conventional triaxial compression (CTC) with constant confining pressure, are very limited.Hydrostatic or confined compression usually makes the mudstone more compact and less permeable. However, many CTC tests on sandstone [26–33], granite [34–36], limestone [33, 37, 38], etc. have revealed that the permeability of the sample gradually increases until failure after the initial reduction during compression, and the formation of faults leads to a jump in the permeability magnitude; the variation in mudstone permeability shows the same trend during compression with a relatively low effective confining pressure [28, 39, 40]. For CCS projects, the caprock studied is usually at a depth of over 1 km below the ground and the lithostatic pressure is greater than 25 MPa [19]. However, there is a severe lack of data concerning the permeability variation in mudstone corresponding to compression under a high confining pressure, which is the objective of this study. More importantly, to better understand the relationship between the permeability and the deformation of mudstone, experiments were carried out to measure permeability changes during deviatoric compression with different confining pressures. Therefore, the results of this paper are very helpful in assessing the leakage risk from CO2 injection sites.


## 2. Specimen, Apparatus, and Experimental Procedure

The brown mudstone cores for investigation were drilled in the Paleogene Formation at a depth of 30~40 m from Yingcheng, China. The mudstone belongs to the lower part of the Paleogene Gypsum-Salt Formation of the Yunying Sag in the northeast of the Jianghan Basin and has a diagenesis depth of more than 1500 m. Therefore, the preconsolidation pressure should be greater than 30 MPa. The mudstone was composed of 14% feldspar, 23% quartz, 15% calcite, 3% hematite, 6% dolomite, 9.75% illite, 5.85% chlorite, and 23.4% montmorillonite. The skeleton particles of the mudstone were composed mainly of quartz, calcite, and feldspar, and the particles were cemented by clay minerals. Most of the mudstone composition, except for the clay minerals, was silt-sized particles. The pore radius distribution of the mudstone was unimodal, with the peak located at approximately 16 nm, and pores with radii less than 100 nm accounted for more than 95%. Moreover, the porosity of the mudstone is as high as 21.83%.We have already used the same cores to study the influence of the intermediate principal stress (σ2) on the permeability evolution during true triaxial compression [41]. Although this paper emphasizes the effect of confining pressure (Pc) on the strain-permeability behavior of mudstone, which can be tested by a conventional triaxial apparatus with a cylindrical specimen, the true triaxial apparatus for rocks [41–45] at the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, which can exert three stresses independently, was still employed in this study because the specimen usually failed with a relatively flat fault parallel to σ2 [42, 46–48]; the flow in the σ2 direction can still be regarded as a one-dimensional flow. In contrast, the fault of the specimen in the CTC is not only very rough but also oblique to the flow direction [40, 49] and the fluid flow inside the specimen near or after failure cannot be approximated as a one-dimensional flow; therefore, the cores in this study were also processed into cuboid specimens of 5 cm square by 10 cm long (Figure 1) and the permeability in the σ2 direction was monitored during deviatoric loading. The permeability of the mudstone was measured using the transient pulse method (TPM) [50–53] with nitrogen as the fluid medium. The apparatus and its reliability, the principles of TPM, and the experimental procedure were detailed in Shi et al. [41].Figure 1
Cuboid specimen of mudstone with dimensions of50×50×100mm.Six specimens (P4 to P9) were compressed at confining pressures of 8, 15, 22, 30, 40, and 50 MPa to study the influence of confining pressure on the permeability evolution and the corresponding mechanical behaviors of mudstone during compression. The deviatoric stress in theσ2 direction for all specimens was 2 MPa, which is the minimum value for normal operation of the true triaxial apparatus. In addition, the pore pressure was maintained at 5 MPa. The specific loading process was as follows: first, pressures of 4 MPa and 2 MPa were provided to clamp the specimen assembly in the maximum principal stress (σ1) and σ2 directions, respectively; then the confining pressure was raised to a predetermined value; the permeability measurement system was evacuated, and a pore pressure of 5 MPa was exerted in sequence; finally, deviatoric compression in the direction was implemented. During the loading process of σ1, the permeability of each specimen was measured approximately 9 times at different stress-strain states. The mudstone has obvious creep characteristics, and the specimen undergoes large deformation during permeability measurement, which takes over a half hour to complete; therefore, in the permeability measurement, strains, rather than stresses, were kept unchanged. Notice that the increasing Pc is consistent with the simultaneously increasing minimum principal stress (σ3) and σ2; therefore, the effect of Pc is not equivalent to the influence of σ3.


## 3. Test Results and Interpretation

The major test results related to the permeability and deformation behaviors of each specimen are summarized in Table1. The deformation mechanisms of rocks under hydrostatic compression and deviatoric compression are significantly different. In addition, the specimen cannot be regard as a homogeneous body due to the formation of faults, which dramatically affects deformation behavior and permeability. Therefore, the influence of confining pressure on permeability and mechanical behavior will be described in three sections of hydrostatic compression and deviatoric compressions before and after the peak.Table 1
Strength, deformation parameters, and permeability of mudstone specimens.
No.
Pc (MPa)
Eu (GPa)
σf (MPa)
σr (MPa)
ϵ1f (%)
ϵ3f (%)
ϵd (%)
k2a (μD)
k2min (μD)
k2max (μD)
k2maxk2a
P4
8
8.923
52.81
43.73
3.366
-1.208
2.864
1.64
0.93
763.47
465
P5
15
7.593
92.29
68.67
3.978
-1.512
2.960
1.77
1.01
11.74
6.6
P6
22
7.932
109.07
81.63
4.653
-1.591
3.555
0.91
0.46
4.12
4.5
P7
30
8.181
131.46
111.45
6.387
-2.547
5.147
0.61
0.29
0.91
1.5
P8
40
8.930
157.91
/
/
/
>7.83
0.51
0.24
0.66
1.3
P9
50
9.719
187.52
/
/
/
>7.99
0.34
0.07
0.34
1
Eu is the unloading modulus; σf is the strength; σr is the residual strength; ϵ1f and ϵ3f are the strains at the peaks in the σ1 and σ3 directions, respectively; ϵd is the degree of ductility; k2a, k2min, and k2max are the initial, minimum, and maximum permeability values, respectively, in the σ2 direction during deviatoric loading.


### 3.1. Hydrostatic Compression

We did not test the permeability at different hydrostatic pressures on a single specimen, but the effect of the confining pressure on permeability in this section can still be illustrated according to initial permeability (k2a) before the deviatoric loading of different specimens. In general, the permeability of the mudstone decreases nonlinearly with confining pressure during hydrostatic compression and the power function [54] or exponential function [21, 55] was usually used to fit the relationship between effective confining pressure (Pce) and permeability, where the superscript e represents effective stress. The results of fitting the k2a−Pce relationship using an exponential function k2a=k0e−bPce are shown in Figure 2; here, k0 and b are two parameters used to represent the permeability at Pce=0 and the sensitivity of permeability variation to confining pressure. The R-squared value for the exponential function with k2a=2.051μD and b=−0.0403MPa−1 used to fit the values of all six specimens was 0.877. When the k2a of specimen P5 that was greater than that of specimen P4 under higher confining pressure was removed, the goodness of fit was improved to 0.991; however, the parameters from the fit varied very little, i.e., k2a=1.829μD and b=−0.0398MPa−1.Figure 2
Variation in mudstone permeability with effective confining pressure under hydrostatic condition.Compared with the reported permeability of mudstones [2, 21, 40, 54], the permeability under hydrostatic compression has two characteristics: (1) the permeability k0≈2μD is low and (2) the permeability is less sensitive to changes in confining pressure. The permeability of mudstone under a certain hydrostatic pressure is closely related to the preconsolidation pressure of the mudstone; experiments revealed that mudstone permeability during pressurized steps is significantly higher than that during depressurized steps [2, 21, 40], which is because the closure of the microcracks and pore throat and the rearrangement of the platy clay grains are irreversible. Therefore, there may be two reasons for the relatively low value of k0. First, the preconsolidation pressure is high and the near-surface coring without significant stress release did not cause the formation of microcracks and damages in the samples. Second, the confining pressure was applied prior to the pore pressure, which means that the effective hydrostatic pressure first increased and then decreased; thus, permeability evolution in the low Pce section, where the permeability drops sharply with increasing Pce, may not be captured. Moreover, when Pce increased from 3 MPa (P4) to 45 MPa (P9), the permeability only decreased by approximately 5 times and the sensitivity of the mudstone permeability to Pce is comparable to those of the mudstones reported by McKernan et al. [2], Zeng et al. [21], and Zhang [40] in depressurized steps.


### 3.2. Deviatoric Compression before the Peak

After applying the confining pressure, the mudstone specimens were deviatorically loaded while permeability was monitored. Figures3–5 show the stress-strain relationship of Yingcheng mudstone under different confining pressures in the σ1, σ2, and σ3 directions, respectively. Here, ϵ1, ϵ2, and ϵ3 represent the strains in the σ1, σ2, and σ3 directions, respectively. The strains in the deviatoric loading stage start from zero, and those induced by hydrostatic compression were omitted. From the stress-strain curves, the permeability measurement points, where significant stress relaxation occurs, can be clearly identified. Notice that stress is constant during the first three permeability measurements of specimen P4.Figure 3
Curves of deviatoric stressσ1−σ3 vs. strain ϵ1 for different confining pressure.Figure 4
Curves of deviatoric stressσ1−σ3 vs. strain ϵ2 for different confining pressure.Figure 5
Curves of deviatoric stressσ1−σ3 vs. strain ϵ3 for different confining pressure.


#### 3.2.1. Strength and Strains at the Peak

As shown in Figure6, the failure strength σf of the specimen increased with the confining pressure. Note that the uniaxial compressive strength σc of the mudstone that was tested using a cylindrical specimen (Φ50×100mm) is 35 MPa. Moreover, due to the limitation of the strain range (9%) in the σ1 direction, the failure of specimens P8 and P9 did not occur and their strengths were approximated. The variational trend of the strength can be represented by a bilinear model with slope K equal to 5.302 and 2.725 at lower and higher confining pressures, respectively. That is, the sensitivity of strength to confining pressure with lower Pc is stronger than that with higher Pc, which is consistent with the results of other researchers [56, 57], because the low confining pressure does not induce the closure of all microcracks before triaxial loading and the remaining microcracks cause a decrease in the strength of the specimen. If the σf-Pc relationship is piecewise fitted by the Mohr-Coulomb criterion, the friction angles ϕ of the low- and high-Pc zones are approximately 43° and 28°, respectively, and the corresponding shear failure angles oblique to the σ3 direction are 66.5° and 59°.Figure 6
Yingcheng mudstone strength as a function of confining pressure.With the increase inPc, the corresponding strain in each direction increased when the mudstone specimen reached its peak. When Pc exceeds 30 MPa, the increase became very significant due to the brittle-ductile transition of the mudstone. The ductility of the specimen can be quantified by the degree of ductility ϵd, which is defined as follows [58]:
(1)ϵd=ϵ1f−σ1−σ3fEu,where the subscript f represents the quantities at failure and Eu is the unloading modulus. In fact, ϵd is the permanent strain in the σ1 direction. From the data of ϵd in Table 1, it can be concluded that the ductility of the mudstone increases remarkably with increasing confining pressure. The failure mode of specimens P4 and P5 can be classified as brittle failure (ϵd<3%), and the failure mode of P6 is semibrittle, with ϵd in the range from 3% to 5%. The failure mode of P7 to P9 is ductile, with ϵd greater than 5%. Obviously, the mudstone has completed the brittle-ductile transition when Pce has increased to 25 MPa. The high ductility of the mudstone helps maintain its sealing performance because the large deformation of caprock causes a decrease in the fluid pressure in the reservoir. In addition, ductile deformation does not bring about new seepage channels as brittle deformation does; therefore, it has little effect on permeability.


#### 3.2.2. Stress-Strain Behavior and Permeability Evolution

Unlike the stress-strain curve of hard rock, mudstone does not have a distinct linear elastic section at the beginning of loading; therefore, the yield point on each stress-strain curve is difficult to determine. The irreversible deformation induced by consolidation is always accompanied by compression, including hydrostatic precompaction [21, 33], before deviatoric loading. However, the onset of plastic deformation induced by the initialization, opening, and propagation of microcracks can be determined using the curve of ϵ1 against volumetric strain ϵv, which has a distinct linear section, as shown in Figure 7. The latter deformation is directly related to the dilatancy of the specimen, and a larger confining pressure delays the onset of dilatation, where deviatoric stress is approximately 45 to 50% of the peak. Another characteristic point is the turning point at which the specimen volume changes from compressive to dilatate, and the deviatoric stress at this point is approximately 80 to 85% of the peak. Notably, strains ϵ1 and ϵ2 were obtained by measuring the relative displacements of one side of the end spacers in the σ1 and σ3 directions, and the spacers were adjusted due to specimen preparation error, which brought a certain deviation to the measurement of these two strains under low load compression. In addition, the specimens were ground manually to avoid exposure to water; therefore, the preparation precision was relatively low and the ϵ2 may be measured inaccurately under extremely low deviatoric stress (2 MPa) in the σ2 direction.Figure 7
Volumetric strain as functions of strainϵ1. The numbers for each curve are the confining pressure in MPa. For a clearer illustration, the curves at 15, 22, 30, 40, and 50 MPa are translated by 1, 2, 3, 4, and 5 along the longitudinal axis, respectively.The two points of the onset of dilatancy and the turn of volumetric strain can divide the prepeak deformation into three stages, which will be introduced in conjunction with the relative changes in the permeability (Figure8) as follows:
(1)
Nondilatant Stage. Before the stress of the specimen reaches the onset of dilatancy, the sizes of the pores and throats decrease and the original microcracks close under initial deviatoric loading, resulting in a decline in mudstone permeability. The magnitude of the decline is directly related to the degree of compaction in hydrostatic compression and therefore decreases with increasing confining pressure
(2)
Gentle-Dilatant Stage. Further increasing the stress after reaching the onset of dilation results in the initialization, reopening, and propagation of microcracks, which undoubtedly increases the permeability of the specimen. However, when the stress has not yet reached the turning point of ϵv, the microcracks are still independent and do not fully connect with their neighbors to form an effective pathway. Moreover, the compaction process continues. Therefore, the permeability decreases first and then increases and the variation amplitude is relatively small. That is, the turning point of k2 is located between the onset point of dilatancy and the turning point of ϵv
(3)
Accelerated-Dilatant Stage. When the deviatoric stress exceeds the turning point of ϵv, the microcracks grow much faster and coalesce with neighbors to form macrofractures with further loading. Therefore, the increase in permeability in this stage is noticeable. The ratios of the permeability at the peak to k2a of the six specimens are 2.33, 1.26, 1.22, 1.00, 1.30, and 0.62, respectively, which means that, in general, the increment in permeability in this stage is negatively correlated with the confining pressureFigure 8
Relative change in permeability as functions of strainϵ1 at different confining pressures.It can be concluded that the evolution of mudstone permeability during deviatoric loading is the result of a combination of compaction and dilatation and is dependent on the confining pressure.When the specimens are unloaded, the volumetric strain of the specimens will decrease, mainly because the openings of the cracks became smaller, which leads to the decrease in mudstone permeability. After complete unloading of deviatoric stress, the reduction in permeability is negatively correlated with confining pressure: the corresponding permeability decreases of specimens P5 to P9 are 44%, 32%, 17%, 15%, and 11%, respectively.


#### 3.2.3. Prediction of Permeability Variation

Many models based on the power law or exponential law have been proposed to predict the permeability evolution during deviatoric compression in terms of stress and damage [41, 49, 59–61]. These models have been experimentally proven to have good predictive ability under hydrostatic compression but poor prediction ability under deviatoric compression [41, 49]. As mentioned above, compaction and dilatancy are two coupled processes that increase and decrease permeability, respectively. Therefore, Shi et al. [41] proposed a permeability-strain relationship that separately considers the contribution of compaction and dilatancy to permeability without using the indirect variable of damage. However, the model is not appropriate for applications where plastic deformation is large because the dilatant deformation weight rd and predicted permeability are still increasing with deformation such as the rearrangement of clay grains, which can cause a decrease in permeability.Figure9 shows that ϵ3 at the peak increases remarkably with increasing confining pressure. In contrast, tangent Poisson’s ratio υ, defined as the magnitude of the slope of a tangent to the curve of ϵ3 versus ϵ1, decreases slightly with increasing confining pressure, which is consistent with the variation in the relative change in the permeability at failure with confining pressure (Figure 8). Therefore, this study attempts to employ the tangent Poisson’s ratio to reflect the effect of dilatancy on the permeability, and the permeability evolution can be written as follows:
(2)k2k2a=e−αϵ1+eβυ−υ0−1,where υ0 is the initial tangent Poisson’s ratio at the nondilatant section and α and β are parameters that are set to 0.6372 and 0.9702, respectively, by fitting the testing results with an R-squared value of 0.89. For comparison, the permeability evolution is also fitted by our previously proposed model [41] and the two parameters and the R-squared value are 0.5314, 2.182, and 0.81, respectively. The comparison of permeability values from the model prediction and the experiments plotted in Figure 10 shows that the proposed model can describe the permeability-strain relationship well before failure. Note that the permeability of specimen P4 at the peak does not contribute to the fit because strain localization has already started. Obviously, the prediction results of the model proposed in the study are superior to those by the model in Reference [41]. Moreover, the combination of permeability evolution functions under hydrostatic and deviatoric compressions can be easily applied in practical problems.Figure 9
Strainϵ3 as function of strain ϵ1 for different confining pressures together with the calculation of tangent Poisson’s ratio.Figure 10
Comparison between the permeability obtained by model prediction (curve) and the testing results (mark). Note that the ordinate value of the starting point of each data set is 1.The permeability evolution after the peak, which is dominated by the formation and slippage of the fault, is not within the prediction range of the above model. Although the model can better match the permeability data of Yingcheng mudstone, it is based on experience and lacks theoretical background; therefore, the model needs further experimental verification.


#### 3.2.4. Effect of Confining Pressure on Deformation Mechanism and Permeability Evolution

Mudstone is an extremely fine-grained sediment with very small pores. The pore throat is smaller than the pore, and its aspect ratio, defined as the ratio of the breadth to the length of the section of the throat, is very small as a result of the platy nature of clay minerals [10]. When compressed, the narrow throats of mudstone are closed as easily as plate-shaped microcracks [54, 62]; many published data have shown that compaction-induced permeability reduction in mudstone is more sensitive than that in sandstone [41, 55, 63].The pressure that induces grain crushing is negatively correlated with grain size; thus, for mudstone with very fine grains [27, 64], grain crushing is less likely to occur within the studied pressure range. Therefore, there are two main types of plastic deformation of mudstone under deviatoric compression: pore compression and microcrack evolution. The entire loading process is accompanied by these two deformations. Undoubtedly, the latter increases the permeability, while the former reduces the permeability.At the initial stage of deviatoric loading, pore compression and microcrack closure make the secant modulus (approximately 2.15 to 3.15 GPa) of the mudstone significantly lower than the unloading modulus. As the confining pressure increases, more pore and microcrack compressions occur during the exertion of the confining pressure; therefore, the irreversible strain in this stage decreases and the secant modulus increases slightly with the increase in the confining pressure. The rate of change of the permeability withϵ1 is negatively correlated with the secant modulus of this stage, which can be illustrated by the highest rate of permeability change of specimen P4 (Figure 8), which has the lowest secant modulus (2.15 GPa).The strength of the mudstone is determined mainly by the evolution of microcracks. When the coalescence of growing microcracks progresses to a certain extent during deviatoric loading, the strain begins to localize, at which point the specimen begins to lose its load-carrying capacity. However, according to micromechanical theory, confining pressure can make the growth of microcracks more difficult [65, 66], which improves the specimen strength.Mudstone is highly compressible because it is rich in platy clay particles whose microstructures vary from a card or book house structure to a perfect stack with considerable porosity loss. Therefore, crack propagation under higher confining pressures requires a greater deviatoric stress, leading to grain rearrangement and significant deformation.Figure11 illustrates two SEM photomicrographs (magnification 800) of specimens P5 and P9 after compressive testing, and their vertical and horizontal directions are coincident with the σ1 and σ3 directions, respectively. A large number of angular silt and sand grains (>10 μm) can be observed in Figure 11(a), and these silt grains are in close proximity to each other. Pores larger than 5 μm are visible everywhere, but the channels connecting them are either invisible or very narrow. In addition, the grains are randomly arranged and a very uneven crack with an average aperture of 25 μm can be observed. The situation of specimen P9 under a high confining pressure in Figure 11(b) is almost opposite to that of specimen P5; namely, the grains are arranged in an orderly and compact manner, the slit grains are floating on the clay matrix, and a flat and closed crack can be found in line with the grain-arranged direction, which is oblique to the σ1 direction. Regarding pores and cracks, the permeability of specimen P9 is obviously much lower than that of specimen P5, which verifies the microscopic mechanism explanation of the influence of confining pressure on the deformation and permeability of mudstone. Moreover, k2a of specimen P5 is relatively high possibly due to the high content of silt and sand grains.Figure 11
SEM photomicrographs of specimens after compressive tests: (a) specimen P5 under a confining pressure of 15 MPa; (b) specimen P9 under a confining pressure of 50 MPa.
(a)
(b)


### 3.3. Deviatoric Compression after the Peak

When deviatoric compression exceeded the peak, the load-carrying capacity of the specimen dropped sharply with the formation of the fault. In addition, the residual strengthσr of the mudstone, which is directly related to the friction of the fault, increases with increasing confining pressure. Although the deviatoric stress in the σ2 direction is very low, the specimen still failed with a flat fault parallel to the σ2 direction, as in the normal true triaxial test, as shown in Figure 12. As σ3 increases from 8 to 30 MPa, the angle between the failure surface and the σ2 direction decreases gradually from 76° to 61°. The failure angles of specimens P5 and P7, whose confining pressures are in the middle of the low-Pc and high-Pc regions, respectively, are close to the predicted failure angles of the Mohr-Coulomb criterion mentioned in Section 3.2.1. There is no fault on specimens P8 and P9 because failure has not occurred due to their high ductility. The fault is generated by the propagation and coalescence of a large number of microcracks. With increasing σ1, the microcracks parallel to σ1 grow in the form of axis split, while those that are oblique to σ1 are more prone to shear propagation. The numbers of microcracks with split and shear growth are inversely related; i.e., the confining pressure can inhibit a splitting of microcracks. Therefore, when the number of shear propagation microcracks increases with increasing confining pressure, the fault is gentler when the σ1 direction is vertical. In addition, the increased splitting failure of microcracks makes the fault rougher, which can be verified by the comparison of the faults of specimens P4 and P7. In general, the failure and aforementioned deformation are related to microcrack evolution.Figure 12
Failure pattern of specimens under different confining pressures. Note that the photos in the first row were taken after the test was completed in 2015. However, the faults of specimens P5 and P6 cannot be observed due to the tight compaction. Therefore, recent photos of the specimen are included in the second row. Most of specimens P5 and P6 were cut for analysis of mineral composition, porosity, and microstructure; specimens P8 and P9 were lost. The change in color is due to the loss of water from limonite to hematite.In this compression section, the formation of fault results in a shape increase in permeability. At a low confining pressure of 8 MPa, the permeability is increased by two to three orders of magnitude. As the confining pressure increases from 15 to 30 MPa, the multitude of increases in the permeability relative tok2a decreases from 6.6 to 1.5. Therefore, at a higher confining pressure, σ3>30MPa and the permeability does not change much with the formation of the fault. After the fault is sufficiently developed, deformation and permeability evolution are dominated by fault slippage.Since the fault plane is parallel to the flow direction, the one-dimensional flow assumption after failure is still valid. Therefore, based on a sudden increase in permeability, the permeability of the local fault zonekf can be estimated according to Figure 13. It is assumed here that (1) the fault is a shear zone with a certain width Df, (2) the shear zone is homogeneous, and (3) the permeability of the bulk kb is the permeability at the peak and remains unchanged after failure. Therefore, kf is given by kf=ΔkbA/Af, where A=LW is the cross-sectional area of the specimen and Af=DfLsecθf is the cross-sectional area of the fault zone. With the width of the fault zone set to 2 mm according to the results of Uehara and Takahashi [39], the local permeability kf of specimens P4 to P7 is approximately 18.6 mD, 224.7 μD, 68.1 μD, and 5.7 μD, respectively. Thus, the local permeability of the fault decreases exponentially with increasing confining pressure.Figure 13
Schematic illustration of fault-contained cross-section perpendicular to theσ2 direction.


## 3.1. Hydrostatic Compression

We did not test the permeability at different hydrostatic pressures on a single specimen, but the effect of the confining pressure on permeability in this section can still be illustrated according to initial permeability (k2a) before the deviatoric loading of different specimens. In general, the permeability of the mudstone decreases nonlinearly with confining pressure during hydrostatic compression and the power function [54] or exponential function [21, 55] was usually used to fit the relationship between effective confining pressure (Pce) and permeability, where the superscript e represents effective stress. The results of fitting the k2a−Pce relationship using an exponential function k2a=k0e−bPce are shown in Figure 2; here, k0 and b are two parameters used to represent the permeability at Pce=0 and the sensitivity of permeability variation to confining pressure. The R-squared value for the exponential function with k2a=2.051μD and b=−0.0403MPa−1 used to fit the values of all six specimens was 0.877. When the k2a of specimen P5 that was greater than that of specimen P4 under higher confining pressure was removed, the goodness of fit was improved to 0.991; however, the parameters from the fit varied very little, i.e., k2a=1.829μD and b=−0.0398MPa−1.Figure 2
Variation in mudstone permeability with effective confining pressure under hydrostatic condition.Compared with the reported permeability of mudstones [2, 21, 40, 54], the permeability under hydrostatic compression has two characteristics: (1) the permeability k0≈2μD is low and (2) the permeability is less sensitive to changes in confining pressure. The permeability of mudstone under a certain hydrostatic pressure is closely related to the preconsolidation pressure of the mudstone; experiments revealed that mudstone permeability during pressurized steps is significantly higher than that during depressurized steps [2, 21, 40], which is because the closure of the microcracks and pore throat and the rearrangement of the platy clay grains are irreversible. Therefore, there may be two reasons for the relatively low value of k0. First, the preconsolidation pressure is high and the near-surface coring without significant stress release did not cause the formation of microcracks and damages in the samples. Second, the confining pressure was applied prior to the pore pressure, which means that the effective hydrostatic pressure first increased and then decreased; thus, permeability evolution in the low Pce section, where the permeability drops sharply with increasing Pce, may not be captured. Moreover, when Pce increased from 3 MPa (P4) to 45 MPa (P9), the permeability only decreased by approximately 5 times and the sensitivity of the mudstone permeability to Pce is comparable to those of the mudstones reported by McKernan et al. [2], Zeng et al. [21], and Zhang [40] in depressurized steps.


## 3.2. Deviatoric Compression before the Peak

After applying the confining pressure, the mudstone specimens were deviatorically loaded while permeability was monitored. Figures3–5 show the stress-strain relationship of Yingcheng mudstone under different confining pressures in the σ1, σ2, and σ3 directions, respectively. Here, ϵ1, ϵ2, and ϵ3 represent the strains in the σ1, σ2, and σ3 directions, respectively. The strains in the deviatoric loading stage start from zero, and those induced by hydrostatic compression were omitted. From the stress-strain curves, the permeability measurement points, where significant stress relaxation occurs, can be clearly identified. Notice that stress is constant during the first three permeability measurements of specimen P4.Figure 3
Curves of deviatoric stressσ1−σ3 vs. strain ϵ1 for different confining pressure.Figure 4
Curves of deviatoric stressσ1−σ3 vs. strain ϵ2 for different confining pressure.Figure 5
Curves of deviatoric stressσ1−σ3 vs. strain ϵ3 for different confining pressure.


### 3.2.1. Strength and Strains at the Peak

As shown in Figure6, the failure strength σf of the specimen increased with the confining pressure. Note that the uniaxial compressive strength σc of the mudstone that was tested using a cylindrical specimen (Φ50×100mm) is 35 MPa. Moreover, due to the limitation of the strain range (9%) in the σ1 direction, the failure of specimens P8 and P9 did not occur and their strengths were approximated. The variational trend of the strength can be represented by a bilinear model with slope K equal to 5.302 and 2.725 at lower and higher confining pressures, respectively. That is, the sensitivity of strength to confining pressure with lower Pc is stronger than that with higher Pc, which is consistent with the results of other researchers [56, 57], because the low confining pressure does not induce the closure of all microcracks before triaxial loading and the remaining microcracks cause a decrease in the strength of the specimen. If the σf-Pc relationship is piecewise fitted by the Mohr-Coulomb criterion, the friction angles ϕ of the low- and high-Pc zones are approximately 43° and 28°, respectively, and the corresponding shear failure angles oblique to the σ3 direction are 66.5° and 59°.Figure 6
Yingcheng mudstone strength as a function of confining pressure.With the increase inPc, the corresponding strain in each direction increased when the mudstone specimen reached its peak. When Pc exceeds 30 MPa, the increase became very significant due to the brittle-ductile transition of the mudstone. The ductility of the specimen can be quantified by the degree of ductility ϵd, which is defined as follows [58]:
(1)ϵd=ϵ1f−σ1−σ3fEu,where the subscript f represents the quantities at failure and Eu is the unloading modulus. In fact, ϵd is the permanent strain in the σ1 direction. From the data of ϵd in Table 1, it can be concluded that the ductility of the mudstone increases remarkably with increasing confining pressure. The failure mode of specimens P4 and P5 can be classified as brittle failure (ϵd<3%), and the failure mode of P6 is semibrittle, with ϵd in the range from 3% to 5%. The failure mode of P7 to P9 is ductile, with ϵd greater than 5%. Obviously, the mudstone has completed the brittle-ductile transition when Pce has increased to 25 MPa. The high ductility of the mudstone helps maintain its sealing performance because the large deformation of caprock causes a decrease in the fluid pressure in the reservoir. In addition, ductile deformation does not bring about new seepage channels as brittle deformation does; therefore, it has little effect on permeability.


### 3.2.2. Stress-Strain Behavior and Permeability Evolution

Unlike the stress-strain curve of hard rock, mudstone does not have a distinct linear elastic section at the beginning of loading; therefore, the yield point on each stress-strain curve is difficult to determine. The irreversible deformation induced by consolidation is always accompanied by compression, including hydrostatic precompaction [21, 33], before deviatoric loading. However, the onset of plastic deformation induced by the initialization, opening, and propagation of microcracks can be determined using the curve of ϵ1 against volumetric strain ϵv, which has a distinct linear section, as shown in Figure 7. The latter deformation is directly related to the dilatancy of the specimen, and a larger confining pressure delays the onset of dilatation, where deviatoric stress is approximately 45 to 50% of the peak. Another characteristic point is the turning point at which the specimen volume changes from compressive to dilatate, and the deviatoric stress at this point is approximately 80 to 85% of the peak. Notably, strains ϵ1 and ϵ2 were obtained by measuring the relative displacements of one side of the end spacers in the σ1 and σ3 directions, and the spacers were adjusted due to specimen preparation error, which brought a certain deviation to the measurement of these two strains under low load compression. In addition, the specimens were ground manually to avoid exposure to water; therefore, the preparation precision was relatively low and the ϵ2 may be measured inaccurately under extremely low deviatoric stress (2 MPa) in the σ2 direction.Figure 7
Volumetric strain as functions of strainϵ1. The numbers for each curve are the confining pressure in MPa. For a clearer illustration, the curves at 15, 22, 30, 40, and 50 MPa are translated by 1, 2, 3, 4, and 5 along the longitudinal axis, respectively.The two points of the onset of dilatancy and the turn of volumetric strain can divide the prepeak deformation into three stages, which will be introduced in conjunction with the relative changes in the permeability (Figure8) as follows:
(1)
Nondilatant Stage. Before the stress of the specimen reaches the onset of dilatancy, the sizes of the pores and throats decrease and the original microcracks close under initial deviatoric loading, resulting in a decline in mudstone permeability. The magnitude of the decline is directly related to the degree of compaction in hydrostatic compression and therefore decreases with increasing confining pressure
(2)
Gentle-Dilatant Stage. Further increasing the stress after reaching the onset of dilation results in the initialization, reopening, and propagation of microcracks, which undoubtedly increases the permeability of the specimen. However, when the stress has not yet reached the turning point of ϵv, the microcracks are still independent and do not fully connect with their neighbors to form an effective pathway. Moreover, the compaction process continues. Therefore, the permeability decreases first and then increases and the variation amplitude is relatively small. That is, the turning point of k2 is located between the onset point of dilatancy and the turning point of ϵv
(3)
Accelerated-Dilatant Stage. When the deviatoric stress exceeds the turning point of ϵv, the microcracks grow much faster and coalesce with neighbors to form macrofractures with further loading. Therefore, the increase in permeability in this stage is noticeable. The ratios of the permeability at the peak to k2a of the six specimens are 2.33, 1.26, 1.22, 1.00, 1.30, and 0.62, respectively, which means that, in general, the increment in permeability in this stage is negatively correlated with the confining pressureFigure 8
Relative change in permeability as functions of strainϵ1 at different confining pressures.It can be concluded that the evolution of mudstone permeability during deviatoric loading is the result of a combination of compaction and dilatation and is dependent on the confining pressure.When the specimens are unloaded, the volumetric strain of the specimens will decrease, mainly because the openings of the cracks became smaller, which leads to the decrease in mudstone permeability. After complete unloading of deviatoric stress, the reduction in permeability is negatively correlated with confining pressure: the corresponding permeability decreases of specimens P5 to P9 are 44%, 32%, 17%, 15%, and 11%, respectively.


### 3.2.3. Prediction of Permeability Variation

Many models based on the power law or exponential law have been proposed to predict the permeability evolution during deviatoric compression in terms of stress and damage [41, 49, 59–61]. These models have been experimentally proven to have good predictive ability under hydrostatic compression but poor prediction ability under deviatoric compression [41, 49]. As mentioned above, compaction and dilatancy are two coupled processes that increase and decrease permeability, respectively. Therefore, Shi et al. [41] proposed a permeability-strain relationship that separately considers the contribution of compaction and dilatancy to permeability without using the indirect variable of damage. However, the model is not appropriate for applications where plastic deformation is large because the dilatant deformation weight rd and predicted permeability are still increasing with deformation such as the rearrangement of clay grains, which can cause a decrease in permeability.Figure9 shows that ϵ3 at the peak increases remarkably with increasing confining pressure. In contrast, tangent Poisson’s ratio υ, defined as the magnitude of the slope of a tangent to the curve of ϵ3 versus ϵ1, decreases slightly with increasing confining pressure, which is consistent with the variation in the relative change in the permeability at failure with confining pressure (Figure 8). Therefore, this study attempts to employ the tangent Poisson’s ratio to reflect the effect of dilatancy on the permeability, and the permeability evolution can be written as follows:
(2)k2k2a=e−αϵ1+eβυ−υ0−1,where υ0 is the initial tangent Poisson’s ratio at the nondilatant section and α and β are parameters that are set to 0.6372 and 0.9702, respectively, by fitting the testing results with an R-squared value of 0.89. For comparison, the permeability evolution is also fitted by our previously proposed model [41] and the two parameters and the R-squared value are 0.5314, 2.182, and 0.81, respectively. The comparison of permeability values from the model prediction and the experiments plotted in Figure 10 shows that the proposed model can describe the permeability-strain relationship well before failure. Note that the permeability of specimen P4 at the peak does not contribute to the fit because strain localization has already started. Obviously, the prediction results of the model proposed in the study are superior to those by the model in Reference [41]. Moreover, the combination of permeability evolution functions under hydrostatic and deviatoric compressions can be easily applied in practical problems.Figure 9
Strainϵ3 as function of strain ϵ1 for different confining pressures together with the calculation of tangent Poisson’s ratio.Figure 10
Comparison between the permeability obtained by model prediction (curve) and the testing results (mark). Note that the ordinate value of the starting point of each data set is 1.The permeability evolution after the peak, which is dominated by the formation and slippage of the fault, is not within the prediction range of the above model. Although the model can better match the permeability data of Yingcheng mudstone, it is based on experience and lacks theoretical background; therefore, the model needs further experimental verification.


### 3.2.4. Effect of Confining Pressure on Deformation Mechanism and Permeability Evolution

Mudstone is an extremely fine-grained sediment with very small pores. The pore throat is smaller than the pore, and its aspect ratio, defined as the ratio of the breadth to the length of the section of the throat, is very small as a result of the platy nature of clay minerals [10]. When compressed, the narrow throats of mudstone are closed as easily as plate-shaped microcracks [54, 62]; many published data have shown that compaction-induced permeability reduction in mudstone is more sensitive than that in sandstone [41, 55, 63].The pressure that induces grain crushing is negatively correlated with grain size; thus, for mudstone with very fine grains [27, 64], grain crushing is less likely to occur within the studied pressure range. Therefore, there are two main types of plastic deformation of mudstone under deviatoric compression: pore compression and microcrack evolution. The entire loading process is accompanied by these two deformations. Undoubtedly, the latter increases the permeability, while the former reduces the permeability.At the initial stage of deviatoric loading, pore compression and microcrack closure make the secant modulus (approximately 2.15 to 3.15 GPa) of the mudstone significantly lower than the unloading modulus. As the confining pressure increases, more pore and microcrack compressions occur during the exertion of the confining pressure; therefore, the irreversible strain in this stage decreases and the secant modulus increases slightly with the increase in the confining pressure. The rate of change of the permeability withϵ1 is negatively correlated with the secant modulus of this stage, which can be illustrated by the highest rate of permeability change of specimen P4 (Figure 8), which has the lowest secant modulus (2.15 GPa).The strength of the mudstone is determined mainly by the evolution of microcracks. When the coalescence of growing microcracks progresses to a certain extent during deviatoric loading, the strain begins to localize, at which point the specimen begins to lose its load-carrying capacity. However, according to micromechanical theory, confining pressure can make the growth of microcracks more difficult [65, 66], which improves the specimen strength.Mudstone is highly compressible because it is rich in platy clay particles whose microstructures vary from a card or book house structure to a perfect stack with considerable porosity loss. Therefore, crack propagation under higher confining pressures requires a greater deviatoric stress, leading to grain rearrangement and significant deformation.Figure11 illustrates two SEM photomicrographs (magnification 800) of specimens P5 and P9 after compressive testing, and their vertical and horizontal directions are coincident with the σ1 and σ3 directions, respectively. A large number of angular silt and sand grains (>10 μm) can be observed in Figure 11(a), and these silt grains are in close proximity to each other. Pores larger than 5 μm are visible everywhere, but the channels connecting them are either invisible or very narrow. In addition, the grains are randomly arranged and a very uneven crack with an average aperture of 25 μm can be observed. The situation of specimen P9 under a high confining pressure in Figure 11(b) is almost opposite to that of specimen P5; namely, the grains are arranged in an orderly and compact manner, the slit grains are floating on the clay matrix, and a flat and closed crack can be found in line with the grain-arranged direction, which is oblique to the σ1 direction. Regarding pores and cracks, the permeability of specimen P9 is obviously much lower than that of specimen P5, which verifies the microscopic mechanism explanation of the influence of confining pressure on the deformation and permeability of mudstone. Moreover, k2a of specimen P5 is relatively high possibly due to the high content of silt and sand grains.Figure 11
SEM photomicrographs of specimens after compressive tests: (a) specimen P5 under a confining pressure of 15 MPa; (b) specimen P9 under a confining pressure of 50 MPa.
(a)
(b)


## 3.2.1. Strength and Strains at the Peak

As shown in Figure6, the failure strength σf of the specimen increased with the confining pressure. Note that the uniaxial compressive strength σc of the mudstone that was tested using a cylindrical specimen (Φ50×100mm) is 35 MPa. Moreover, due to the limitation of the strain range (9%) in the σ1 direction, the failure of specimens P8 and P9 did not occur and their strengths were approximated. The variational trend of the strength can be represented by a bilinear model with slope K equal to 5.302 and 2.725 at lower and higher confining pressures, respectively. That is, the sensitivity of strength to confining pressure with lower Pc is stronger than that with higher Pc, which is consistent with the results of other researchers [56, 57], because the low confining pressure does not induce the closure of all microcracks before triaxial loading and the remaining microcracks cause a decrease in the strength of the specimen. If the σf-Pc relationship is piecewise fitted by the Mohr-Coulomb criterion, the friction angles ϕ of the low- and high-Pc zones are approximately 43° and 28°, respectively, and the corresponding shear failure angles oblique to the σ3 direction are 66.5° and 59°.Figure 6
Yingcheng mudstone strength as a function of confining pressure.With the increase inPc, the corresponding strain in each direction increased when the mudstone specimen reached its peak. When Pc exceeds 30 MPa, the increase became very significant due to the brittle-ductile transition of the mudstone. The ductility of the specimen can be quantified by the degree of ductility ϵd, which is defined as follows [58]:
(1)ϵd=ϵ1f−σ1−σ3fEu,where the subscript f represents the quantities at failure and Eu is the unloading modulus. In fact, ϵd is the permanent strain in the σ1 direction. From the data of ϵd in Table 1, it can be concluded that the ductility of the mudstone increases remarkably with increasing confining pressure. The failure mode of specimens P4 and P5 can be classified as brittle failure (ϵd<3%), and the failure mode of P6 is semibrittle, with ϵd in the range from 3% to 5%. The failure mode of P7 to P9 is ductile, with ϵd greater than 5%. Obviously, the mudstone has completed the brittle-ductile transition when Pce has increased to 25 MPa. The high ductility of the mudstone helps maintain its sealing performance because the large deformation of caprock causes a decrease in the fluid pressure in the reservoir. In addition, ductile deformation does not bring about new seepage channels as brittle deformation does; therefore, it has little effect on permeability.


## 3.2.2. Stress-Strain Behavior and Permeability Evolution

Unlike the stress-strain curve of hard rock, mudstone does not have a distinct linear elastic section at the beginning of loading; therefore, the yield point on each stress-strain curve is difficult to determine. The irreversible deformation induced by consolidation is always accompanied by compression, including hydrostatic precompaction [21, 33], before deviatoric loading. However, the onset of plastic deformation induced by the initialization, opening, and propagation of microcracks can be determined using the curve of ϵ1 against volumetric strain ϵv, which has a distinct linear section, as shown in Figure 7. The latter deformation is directly related to the dilatancy of the specimen, and a larger confining pressure delays the onset of dilatation, where deviatoric stress is approximately 45 to 50% of the peak. Another characteristic point is the turning point at which the specimen volume changes from compressive to dilatate, and the deviatoric stress at this point is approximately 80 to 85% of the peak. Notably, strains ϵ1 and ϵ2 were obtained by measuring the relative displacements of one side of the end spacers in the σ1 and σ3 directions, and the spacers were adjusted due to specimen preparation error, which brought a certain deviation to the measurement of these two strains under low load compression. In addition, the specimens were ground manually to avoid exposure to water; therefore, the preparation precision was relatively low and the ϵ2 may be measured inaccurately under extremely low deviatoric stress (2 MPa) in the σ2 direction.Figure 7
Volumetric strain as functions of strainϵ1. The numbers for each curve are the confining pressure in MPa. For a clearer illustration, the curves at 15, 22, 30, 40, and 50 MPa are translated by 1, 2, 3, 4, and 5 along the longitudinal axis, respectively.The two points of the onset of dilatancy and the turn of volumetric strain can divide the prepeak deformation into three stages, which will be introduced in conjunction with the relative changes in the permeability (Figure8) as follows:
(1)
Nondilatant Stage. Before the stress of the specimen reaches the onset of dilatancy, the sizes of the pores and throats decrease and the original microcracks close under initial deviatoric loading, resulting in a decline in mudstone permeability. The magnitude of the decline is directly related to the degree of compaction in hydrostatic compression and therefore decreases with increasing confining pressure
(2)
Gentle-Dilatant Stage. Further increasing the stress after reaching the onset of dilation results in the initialization, reopening, and propagation of microcracks, which undoubtedly increases the permeability of the specimen. However, when the stress has not yet reached the turning point of ϵv, the microcracks are still independent and do not fully connect with their neighbors to form an effective pathway. Moreover, the compaction process continues. Therefore, the permeability decreases first and then increases and the variation amplitude is relatively small. That is, the turning point of k2 is located between the onset point of dilatancy and the turning point of ϵv
(3)
Accelerated-Dilatant Stage. When the deviatoric stress exceeds the turning point of ϵv, the microcracks grow much faster and coalesce with neighbors to form macrofractures with further loading. Therefore, the increase in permeability in this stage is noticeable. The ratios of the permeability at the peak to k2a of the six specimens are 2.33, 1.26, 1.22, 1.00, 1.30, and 0.62, respectively, which means that, in general, the increment in permeability in this stage is negatively correlated with the confining pressureFigure 8
Relative change in permeability as functions of strainϵ1 at different confining pressures.It can be concluded that the evolution of mudstone permeability during deviatoric loading is the result of a combination of compaction and dilatation and is dependent on the confining pressure.When the specimens are unloaded, the volumetric strain of the specimens will decrease, mainly because the openings of the cracks became smaller, which leads to the decrease in mudstone permeability. After complete unloading of deviatoric stress, the reduction in permeability is negatively correlated with confining pressure: the corresponding permeability decreases of specimens P5 to P9 are 44%, 32%, 17%, 15%, and 11%, respectively.


## 3.2.3. Prediction of Permeability Variation

Many models based on the power law or exponential law have been proposed to predict the permeability evolution during deviatoric compression in terms of stress and damage [41, 49, 59–61]. These models have been experimentally proven to have good predictive ability under hydrostatic compression but poor prediction ability under deviatoric compression [41, 49]. As mentioned above, compaction and dilatancy are two coupled processes that increase and decrease permeability, respectively. Therefore, Shi et al. [41] proposed a permeability-strain relationship that separately considers the contribution of compaction and dilatancy to permeability without using the indirect variable of damage. However, the model is not appropriate for applications where plastic deformation is large because the dilatant deformation weight rd and predicted permeability are still increasing with deformation such as the rearrangement of clay grains, which can cause a decrease in permeability.Figure9 shows that ϵ3 at the peak increases remarkably with increasing confining pressure. In contrast, tangent Poisson’s ratio υ, defined as the magnitude of the slope of a tangent to the curve of ϵ3 versus ϵ1, decreases slightly with increasing confining pressure, which is consistent with the variation in the relative change in the permeability at failure with confining pressure (Figure 8). Therefore, this study attempts to employ the tangent Poisson’s ratio to reflect the effect of dilatancy on the permeability, and the permeability evolution can be written as follows:
(2)k2k2a=e−αϵ1+eβυ−υ0−1,where υ0 is the initial tangent Poisson’s ratio at the nondilatant section and α and β are parameters that are set to 0.6372 and 0.9702, respectively, by fitting the testing results with an R-squared value of 0.89. For comparison, the permeability evolution is also fitted by our previously proposed model [41] and the two parameters and the R-squared value are 0.5314, 2.182, and 0.81, respectively. The comparison of permeability values from the model prediction and the experiments plotted in Figure 10 shows that the proposed model can describe the permeability-strain relationship well before failure. Note that the permeability of specimen P4 at the peak does not contribute to the fit because strain localization has already started. Obviously, the prediction results of the model proposed in the study are superior to those by the model in Reference [41]. Moreover, the combination of permeability evolution functions under hydrostatic and deviatoric compressions can be easily applied in practical problems.Figure 9
Strainϵ3 as function of strain ϵ1 for different confining pressures together with the calculation of tangent Poisson’s ratio.Figure 10
Comparison between the permeability obtained by model prediction (curve) and the testing results (mark). Note that the ordinate value of the starting point of each data set is 1.The permeability evolution after the peak, which is dominated by the formation and slippage of the fault, is not within the prediction range of the above model. Although the model can better match the permeability data of Yingcheng mudstone, it is based on experience and lacks theoretical background; therefore, the model needs further experimental verification.


## 3.2.4. Effect of Confining Pressure on Deformation Mechanism and Permeability Evolution

Mudstone is an extremely fine-grained sediment with very small pores. The pore throat is smaller than the pore, and its aspect ratio, defined as the ratio of the breadth to the length of the section of the throat, is very small as a result of the platy nature of clay minerals [10]. When compressed, the narrow throats of mudstone are closed as easily as plate-shaped microcracks [54, 62]; many published data have shown that compaction-induced permeability reduction in mudstone is more sensitive than that in sandstone [41, 55, 63].The pressure that induces grain crushing is negatively correlated with grain size; thus, for mudstone with very fine grains [27, 64], grain crushing is less likely to occur within the studied pressure range. Therefore, there are two main types of plastic deformation of mudstone under deviatoric compression: pore compression and microcrack evolution. The entire loading process is accompanied by these two deformations. Undoubtedly, the latter increases the permeability, while the former reduces the permeability.At the initial stage of deviatoric loading, pore compression and microcrack closure make the secant modulus (approximately 2.15 to 3.15 GPa) of the mudstone significantly lower than the unloading modulus. As the confining pressure increases, more pore and microcrack compressions occur during the exertion of the confining pressure; therefore, the irreversible strain in this stage decreases and the secant modulus increases slightly with the increase in the confining pressure. The rate of change of the permeability withϵ1 is negatively correlated with the secant modulus of this stage, which can be illustrated by the highest rate of permeability change of specimen P4 (Figure 8), which has the lowest secant modulus (2.15 GPa).The strength of the mudstone is determined mainly by the evolution of microcracks. When the coalescence of growing microcracks progresses to a certain extent during deviatoric loading, the strain begins to localize, at which point the specimen begins to lose its load-carrying capacity. However, according to micromechanical theory, confining pressure can make the growth of microcracks more difficult [65, 66], which improves the specimen strength.Mudstone is highly compressible because it is rich in platy clay particles whose microstructures vary from a card or book house structure to a perfect stack with considerable porosity loss. Therefore, crack propagation under higher confining pressures requires a greater deviatoric stress, leading to grain rearrangement and significant deformation.Figure11 illustrates two SEM photomicrographs (magnification 800) of specimens P5 and P9 after compressive testing, and their vertical and horizontal directions are coincident with the σ1 and σ3 directions, respectively. A large number of angular silt and sand grains (>10 μm) can be observed in Figure 11(a), and these silt grains are in close proximity to each other. Pores larger than 5 μm are visible everywhere, but the channels connecting them are either invisible or very narrow. In addition, the grains are randomly arranged and a very uneven crack with an average aperture of 25 μm can be observed. The situation of specimen P9 under a high confining pressure in Figure 11(b) is almost opposite to that of specimen P5; namely, the grains are arranged in an orderly and compact manner, the slit grains are floating on the clay matrix, and a flat and closed crack can be found in line with the grain-arranged direction, which is oblique to the σ1 direction. Regarding pores and cracks, the permeability of specimen P9 is obviously much lower than that of specimen P5, which verifies the microscopic mechanism explanation of the influence of confining pressure on the deformation and permeability of mudstone. Moreover, k2a of specimen P5 is relatively high possibly due to the high content of silt and sand grains.Figure 11
SEM photomicrographs of specimens after compressive tests: (a) specimen P5 under a confining pressure of 15 MPa; (b) specimen P9 under a confining pressure of 50 MPa.
(a)
(b)


## 3.3. Deviatoric Compression after the Peak

When deviatoric compression exceeded the peak, the load-carrying capacity of the specimen dropped sharply with the formation of the fault. In addition, the residual strengthσr of the mudstone, which is directly related to the friction of the fault, increases with increasing confining pressure. Although the deviatoric stress in the σ2 direction is very low, the specimen still failed with a flat fault parallel to the σ2 direction, as in the normal true triaxial test, as shown in Figure 12. As σ3 increases from 8 to 30 MPa, the angle between the failure surface and the σ2 direction decreases gradually from 76° to 61°. The failure angles of specimens P5 and P7, whose confining pressures are in the middle of the low-Pc and high-Pc regions, respectively, are close to the predicted failure angles of the Mohr-Coulomb criterion mentioned in Section 3.2.1. There is no fault on specimens P8 and P9 because failure has not occurred due to their high ductility. The fault is generated by the propagation and coalescence of a large number of microcracks. With increasing σ1, the microcracks parallel to σ1 grow in the form of axis split, while those that are oblique to σ1 are more prone to shear propagation. The numbers of microcracks with split and shear growth are inversely related; i.e., the confining pressure can inhibit a splitting of microcracks. Therefore, when the number of shear propagation microcracks increases with increasing confining pressure, the fault is gentler when the σ1 direction is vertical. In addition, the increased splitting failure of microcracks makes the fault rougher, which can be verified by the comparison of the faults of specimens P4 and P7. In general, the failure and aforementioned deformation are related to microcrack evolution.Figure 12
Failure pattern of specimens under different confining pressures. Note that the photos in the first row were taken after the test was completed in 2015. However, the faults of specimens P5 and P6 cannot be observed due to the tight compaction. Therefore, recent photos of the specimen are included in the second row. Most of specimens P5 and P6 were cut for analysis of mineral composition, porosity, and microstructure; specimens P8 and P9 were lost. The change in color is due to the loss of water from limonite to hematite.In this compression section, the formation of fault results in a shape increase in permeability. At a low confining pressure of 8 MPa, the permeability is increased by two to three orders of magnitude. As the confining pressure increases from 15 to 30 MPa, the multitude of increases in the permeability relative tok2a decreases from 6.6 to 1.5. Therefore, at a higher confining pressure, σ3>30MPa and the permeability does not change much with the formation of the fault. After the fault is sufficiently developed, deformation and permeability evolution are dominated by fault slippage.Since the fault plane is parallel to the flow direction, the one-dimensional flow assumption after failure is still valid. Therefore, based on a sudden increase in permeability, the permeability of the local fault zonekf can be estimated according to Figure 13. It is assumed here that (1) the fault is a shear zone with a certain width Df, (2) the shear zone is homogeneous, and (3) the permeability of the bulk kb is the permeability at the peak and remains unchanged after failure. Therefore, kf is given by kf=ΔkbA/Af, where A=LW is the cross-sectional area of the specimen and Af=DfLsecθf is the cross-sectional area of the fault zone. With the width of the fault zone set to 2 mm according to the results of Uehara and Takahashi [39], the local permeability kf of specimens P4 to P7 is approximately 18.6 mD, 224.7 μD, 68.1 μD, and 5.7 μD, respectively. Thus, the local permeability of the fault decreases exponentially with increasing confining pressure.Figure 13
Schematic illustration of fault-contained cross-section perpendicular to theσ2 direction.


## 4. Discussion

In the CCS projects, CO2 is structurally trapped within deep geological formations over long periods of time (103–104 years). Therefore, low permeability is a prerequisite for the effectiveness of the caprock. Low permeability means that it takes a long time for CO2 to penetrate the caprock and that the capillary pressure of the caprock is very high. Actually, permeability is a comprehensive representation of the rock pore-crack structure characteristics. Laboratory tests on 141 samples from different tectonic units of South China have shown that the relationship between capillary pressure and permeability can be expressed by a pow function with a negative exponent [67]. Chen et al. [68] pointed out that effective caprock in petroleum engineering should have a permeability of no more than 5×10−19m2 (approximately 0.5 μD).In the field of petroleum engineering, the evaluation of caprock sealing properties helps locate oil-gas accumulations but the evolution of caprock sealability after exploitation is less of a concern. After CO2 is injected into the reservoir, the fluid pressure of the reservoir is significantly increased and the pressure increment is gradually attenuated from the injection well to other areas [69]. The reduction of effective stress in the reservoir will inevitably lead to uneven uplift of the overburden [70] and deformation in the caprock. From the above study, the permeability of mudstone caprock can be markedly increased by more than 5 times without failure, which cannot be neglected in the evaluation of caprock sealing performance; even for ductile deformed specimens P8 and P9, dilatancy occurred under deviatoric compression. In addition, the brittle-ductile property of caprock is considered to be the key factor controlling the integrity of the caprock, as brittle caprock is more susceptible to cracking after the uplift of the formation [1, 71]. However, it can be inferred that, if the effective confining pressure exceeds 25 MPa, the increase in permeability of Yingcheng mudstone due to failure is insignificant.In short, it is not enough to evaluate the sealing of the caprock of CCS simply by using indicators such as the overconsolidation ratio, density, and brittleness index, and special attention should be paid to the dynamic evolution of sealability after injection of CO2. Therefore, we should study the mechanical and permeability properties of caprock to obtain the constitutive equation and permeability evolution equation of caprock, establish a numerical model, and evaluate caprock sealing after injection according to the actual injection conditions.


## 5. Conclusions

This paper investigated the influence of confining pressure on mechanics-permeability behavior of Yingcheng mudstone based on true triaxial compressive experiments. The pore pressure and deviatoric stress in theσ2 direction for all specimens are set to 5 MPa and 2 MPa, respectively. Several main conclusions can be drawn as follows:
(1)
The sensitivity of the mudstone strength to the confining pressure under low confining pressure is higher than that under high confining pressure, and the relationship between strength and confining pressure can be represented by a bilinear model
(2)
As the confining pressure increases, the fractural angle, i.e., the angle between the normal of the fault and theσ1 direction, is smaller and the fault is flatter
(3)
Increased confining pressure can greatly improve the ductility of mudstone; the failure mode of mudstone transforms from brittle to ductile under an effective confining pressure of 35 MPa
(4)
Mudstone permeability is reduced by approximately 5 times under hydrostatic pressure when the effective confining pressure is increased from 3 to 45 MPa
(5)
Mudstone permeability under deviatoric compression before failure first decreases and then increases as a result of the combination of compaction and dilatancy induced by the evolution of microcracks. The strain corresponding to the turning point of permeability is between the strains corresponding to the onset of dilatancy and the turning point of volumetric strain
(6)
A strain-based permeability evolution predictive model, whose prediction is consistent with the experimental data, is proposed with two variables of strain in theσ1 direction and tangent Poisson’s ratio to reflect the effects of compaction and dilatancy on permeability, respectively
(7)
The jump in mudstone permeability induced by fault formation decreases exponentially with an increase in confining pressure; when the effective confining pressure reaches 25 MPa, the change in permeability caused by the fault is negligibleIn summary, the increase in confining pressure has great advantages for the sealing performance of mudstone: it improves the strength and ductility of mudstone while effectively reducing permeability, especially after the peak.



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*Source: 1796380-2019-06-04.xml*