Creep Strain and Permeability Evolution in Cracked Granite Subjected to Triaxial Stress and Reactive Flow

Fluid flow and fluid-rock interaction mainly take place in fracture network, consequently resulting in deformation and permeability variation of rock and deterioration of the wellbore performance. Mechanical-reactive flow coupling creep tests are performed on cracked granite under various confining pressures and acid and alkaline solution flows. The testing results show that the confining pressure and solution pH significantly influence the creep deformation, creep strain rate, and permeability. A primary creep stage and secondary creep stage are observed in all creep tests in this study; notably, the sample under a confining pressure of 10MPa and acid solution injection undergoes creep failure for over 2700 hours. The acid solution has a more obvious influence on the creep behavior than that of the alkaline solution. With an increase in confining pressure, the total creep strain and creep strain rate in the samples gradually decrease during the injection of either solution. The permeability of the samples injected with either solution gradually deceases during the testing process, and this deceasing rate increases with the confining pressure. The scanning electron microscopy observations on the crack surfaces after the creep tests show that the surfaces of the fractures injected with the acid solution are smooth due to the dissolution of the matrix, while those injected with the alkaline solution include voids due to the dissolution of quartz. These experimental results could improve the understanding of the long-term transport and mechanical behaviors of wellbore.


Introduction
Rock reservoir in subsurface energy resources is under triaxial stress condition, and hydraulic fracking is used to generate fluid transport path for the production of hydrocarbon and geothermal energy [1].Recent studies suggest that some additives or supercritical CO 2 could be used in enhanced geothermal systems to improve energy extraction [1,2].The reactive ions in the fluid could cause fluid-rock interaction in rock materials [3][4][5].In the long-term service period of wellbore, the rock formation is required to not only have enough bearing capacity in the early stage but also, and more importantly, meet the long-term deformation limitation as its performance deteriorates due to the coupling effect of triaxial stress and fluid-rock interaction.Previous studies [2,6] indicated that the fluid-rock interactions have a strong influence on the physical and mechanical properties (e.g., elastic modulus, strength, and permeability) of the rock.Under long-term conditions, the application of stress may aggravate the influences chemical erosion [5,[7][8][9][10].This phenomenon may cause the excessive rock deformation, result in instability of wellbore wall, and decrease the production.Therefore, it is highly needed to investigate the coupling effect of triaxial stress and fluid-rock interaction.Some scholars carried out experimental studies on the triaxial mechanical behavior of granite after chemical erosion [11][12][13][14].The effects of chemical solutions with different pH values on the strength and deformation of granite were discussed, and the corrosion mechanism of granite by chemical solution was also analyzed.Zhang et al. [15] carried out a triaxial compression test of granite treated by heating and rapid cooling.The experimental result showed that the granite strength tended to decrease with the increase in treatment temperature.Chen et al., Polak et al., and Wang et al. [16][17][18] carried out experimental studies on the effect of mechanicalhydraulic-chemical coupling on permeability and revealed the evolution of permeability with testing time.A considerable research effort has been made to investigate the effect of chemical corrosion and mechanical loading on other porous materials [11,12,14,[19][20][21][22][23] The coupling conditions, e.g., stress level, solution pH, and rock mineral compositions, have a great impact on the mechanical and transport properties of rocks.Several constitutive models were proposed to describe the mechanical response and transport evolutions of a cementbased material subjected to mechanical-reactive flow coupling [24].Mechanical damage induced by applied stress and chemical damage induced by chemical erosion were defined independently.The evolutions of the creep rate and chemical deterioration of materials were analyzed.
The previous investigations mainly studied porous materials, e.g., sandstone, cement, and chalk.However, the host rocks of extracting subsurface energy resources (e.g., enhanced geothermal systems, conventional and unconventional gas, and oil) have low porosities, and their permeability under intact conditions is also low.Therefore, fluid transportation and fluid-rock interaction mainly take place in cracks within the host rocks.The long-term mechanical-reactive flow coupling behavior of cracked rock is clearly different from that of porous rock and thus critical to study.
Granite materials are now widely used in many engineering applications due to their high mechanical strength and low permeability.Studying the creep properties of granite under mechanical-chemical coupling is of great significance for long-term work in many projects.In this paper, the long-term mechanical behavior of granite with preformed fractures in acid-alkaline environment is studied, and the influence of alkaline solution and acid solution on the physical and mechanical behavior of granite are analyzed.This paper is organized as follows.In Section 2, the physical parameters of granite and uniaxial/triaxial compression strength are tested.In Section 3, the creep test of granite with preformed fractures with injecting alkaline and acid solution into the samples during creep test, respectively, is presented.At the same time, the change of permeability of granite with preformed cracks in long-term creep test is monitored to prove the influence of chemical solutions.
Finally, the effects of confining pressure, the type of the solution, creep strain rate, and permeability are analyzed.The microstructure of fracture surfaces of the granite samples after creep test is also observed.

Test Preparations
The material used in this study is granite from an underground tunnel excavation, and all the samples are drilled from one large block without any observable joints.The density of the samples in their natural condition is 2.61 g/cm 3 .X-ray diffraction tests show that the main mineral compositions are quartz (30%), soda feldspar (21.05%), potash feldspar (45.19%), and mica (23.05%).At the microscopic level, quartz grains are scattered in a matrix of soda feldspar, potash feldspar, and mica, which act to cement the larger grains (see Figure 1).The diameter and height of the samples are 37 and 74 mm, respectively.
The intact granite samples have very low permeability, and it is difficult to achieved steady seepage in the samples.Moreover, interactions between rock and reactive solutions mainly occur in excavation damage zones, where cracks are generated in the surrounding rocks after excavation due to stress redistribution (Pepe et al., 2017).Given that tension and shear failure are the two common rock damage mechanisms observed in surrounding rocks, the samples are first subjected to triaxial compressive stress until failure, and different confining pressures, e.g., 0, 5, and 10 MPa, are applied to create different crack patterns (see Figure 2).The typical stress-strain curves of the triaxial compression tests are shown in Figure 3.The samples undergo brittle failure under the confining pressure magnitudes applied in this study.Additionally, under low confining pressure (e.g., 0 MPa), the sample failure is marked by a distinctive peak stress due to the coalescence of tensile cracks, ultimately splitting the sample.Under higher confining pressures (e.g., 5 and 10 MPa), this distinctive peak stress becomes less pronounced.The failure of the sample transitions from tensile cracking to shear cracking.A similar phenomenon has been observed in sandstone [25] and granite [8].
A thermal-hydrological-mechanical-reactive flow coupling testing system is used to perform creep tests with acid and alkaline solution injection, and the sketch diagram of this testing system is presented in Figure 4.The whole testing system is placed into a large oven to perform the tests at 2 Geofluids a predetermined temperature.The testing room is also equipped with an air conditioner and is held at a constant temperature of 20 ± 2 °C.Consequently, the temperature conditions during the tests can be controlled to a precision of ±0.2 °C.
Throughout this paper, the rock mechanics sign convention is used; compressive stresses and strains are positive.Furthermore, a fixed coordinate frame is used for the cylinder sample, and the cylinder axis is parallel to the x 1 axis.σ i and ε i (i = 1, 2, 3) denote the three principal stresses and strains in this frame, while p is the interstitial pressure.
After the triaxial compression tests are completed, the cracked samples are directly used in the subsequent creep tests.The same magnitude of confining pressure is applied to the cracked samples after triaxial compression at confining pressures of 5 and 10 MPa, whereas a confining pressure of 2 MPa is applied to the cracked samples after triaxial compression at a confining pressure of 0 MPa; this low confining pressure can avoid seepage flow between the sample and jacket.The axial stress is reloaded to the predetermined levels, which correspond to 70% of the residual strength of the cracked samples under confining pressures of 2, 5, and 10 MPa.Detailed information about the stress path of the studied samples is presented in Table 1.
Two kinds of solutions with different pH values, namely, a H 2 SO 4 solution with pH = 2 and a NaOH solution with pH = 12, are injected into the cracked samples.The pressure at the inlet is 1 MPa, and the pressure at the outlet is identical to atmosphere pressure; a pressure gradient is thus achieved to induce seepage through the samples.A metering pump with a precision of 0.01 MPa is used to apply the pressure gradient and record the seepage volume during the tests.Compared with the alkaline solution, the acid solution induces a more obvious effect on the creep behavior.Under all confining pressures, the creep strains of the samples injected with the acid solution are greater than those injected with the alkaline solution.Moreover, the time to a stable creep strain during the injection of an acid solution is greater than that of an alkaline solution, and this phenomenon becomes more significant when the confining pressure increases.The differences in creep behavior between the samples injected with acid and alkaline solutions are attributed to the different mechanisms of the solution-mineral reactions;   4 Geofluids these mechanisms will be explained in the following sections.Similar results have been observed in artificially fractured granite [26,27].The results have been shown that the feldspar and biotite are relative more sensitively reacted with the acid solution than the quartz, and the acidizing solutions change the mechanical properties of rocks.Luo et al. [26] stated that the degree of rough of crack surface decreases after 600 h chemical reaction, and the original rough crack surface gradually becomes smooth due to the chemical reaction of granite in chemical reagents.On the other hand, the degree of corrosion of granite under acidic conditions is higher than that under alkaline conditions; thus, the fracture surface in the acidic environment is strongly corroded, while the fracture surface in the alkaline environment is relatively rough.The confining pressure also has a significant effect on the creep behavior.With an increase in confining pressure, the creep strains during injection of either the acid or alkaline solution gradually decrease, and the total creep strain under a confining pressure of 10 MPa is one order of magnitude less than that under a confining pressure of 2 or 5 MPa.This phenomenon could be explained by the limitation of deformation due to confining pressure.Similar results were shown in considering the hydrologicalmechanical coupling in fractured rocks [28][29][30].

Creep Strain Rate.
To further analyze the effect of confining pressure and solution pH on the creep behavior, the creep strain rates are calculated and presented in Figure 6.The creep rate is calculated from the following relation: where ε t represents the creep rate at creep time t.ε t+1 and ε t represent the creep strains corresponding to time t + 1 and time t, respectively.Δt is the time interval between time t and t + 1.
As mentioned above, the injection of the acid solution has a more significant effect on the creep behavior than 5 Geofluids that of the alkaline solution.The curves of creep strain rate in Figure 6 confirm these results.The creep strain rates in both the axial and lateral directions with injection of the acid solution are greater and take a longer time to reach stability than those of the alkaline solution.Notably, the creep strain rate in the lateral direction under a confining pressure of 10 MPa and acid solution injection is significantly greater than that in the axial direction during the tertiary creep stage.Therefore, the sample undergoes volumetric dilation during the creep failure stage, and this volumetric dilation is attributed to the shear deformation of the compressive shear fractures (see Figure 2).

Permeability Tests.
The permeability of the samples during the mechanical-reactive flow coupling tests is measured regularly at a predetermined time interval.Given the correlation between permeability and fracture aperture, the permeability evolutions could be used to evaluate the fracture aperture and transport properties of the cracked samples.The steady-state method is applied in this study, and the permeability of a sample can be calculated by using Darcy's law by measuring the flow rate of the seepage fluid.
where k is the intrinsic permeability (m 2 ); Q is the injection flow rate (m 3 ⋅ s −1 ); μ denotes the dynamic fluid viscosity coefficient; L and A are the length and cross section of the sample, respectively; and Δp is the pressure difference between the inlet and outlet of the seepage and it is equal to 1 MPa.In Figure 7, the initial permeability of the cracked samples during the initial creep stage is highly dependent on 6 Geofluids the confining pressure.The permeability under a confining pressure of 2 MPa is two orders of magnitude greater than that under a confining pressure of 10 MPa.Consequently, the permeability of all the samples decreases as time increases and stabilizes under high confining pressures.The rate of decrease in the permeability of the samples injected with the acid solution is slightly greater than that of samples injected with the alkaline solution.Therefore, confining pressure has a greater effect on the permeability evolution than the effect of injecting a reactive solution.Similar results showed that the fracture aperture and permeability basically decrease with time under various external confinements (stresses) and solution transport for different rocks [17,31,32].According to previous hydrological-mechanicalchemical coupling models [28,30], the decrease in permeability is directly attributed to the aperture decrease caused by pressure solution.

Discussions
The results above indicate that the creep strain and permeability of the cracked samples depend on the confining pressure and the reactive solutions.The rock-solution reaction during the creep tests is discussed in the following subsection.
4.1.Rock-Solution Reaction.The abovementioned X-ray diffraction tests show that soda feldspar, potash feldspar, and mica account for 70% of the total mineral content of the samples, and quartz accounts for the remaining 30%.Under the studied acidic condition (pH = 2), the former three minerals undergo dissolution to some degree due to the acid ions [33], while quartz is nearly inactive.The reaction process can be described as follows: NaAlSi However, under the studied alkaline condition (pH = 12), the quartz undergoes slight dissolution due to the alkaline ions, while the former three minerals are nearly inactive.The reaction between the quartz and alkaline ions is described as follows: Previous studies (Lehner, 1990; Wolery, 1992) indicated that the reaction rate in (3)(4)(5) is significantly greater than that in (6); therefore, the injection of the acid solution has a greater influence on the creep behavior than that of the alkaline solution.
4.2.Fracture Surface Observations.Scanning electron microscopy (SEM) is applied to observe the fracture surface morphology of the cracked samples after the creep tests.A sheet of 1 cm 2 was taken at different positions on the fracture surface of each sample.And SEM test was performed after progress of conductive coating, and three sheets were taken for each sample.And the SEM images are shown in Figure 8.At each confining pressure, the fracture surfaces injected with acid solution are smooth, while those injected with alkaline solution are rough and include voids.According to the microscopic structure of the mineral composition, shown in Figure 1, the soda feldspar, potash feldspar, and mica grains form a rock matrix and encapsulate the quartz grains.When the acid solution comes into contact with the fracture surfaces, the rock matrix undergoes dissolution, and the dissolved ions are transported in the seepage flow.Consequently, the quartz grains debond from the fracture surface and are transported in the seepage flow once the surrounding matrix has dissolved.Therefore, the fracture surfaces in contact with the acid solution are smooth.However, when the alkaline solution comes into contact with the fracture surfaces, the quartz grains dissolve, while the surrounding matrix is nearly unaffected.Therefore, voids on the fracture surface are caused by the dissolution of quartz grains.
In addition, it can be seen from the creep curve that the sample in the acid environment under a confining pressure of 10 MPa reaches creep failure over 2700 hours.This time is much larger than the other several conditions, for example, lower confining pressure and alkaline environment.It is apparent that the rupture surface is rough after the uniaxial/triaxial compression test.Therefore, the specimen still has the ability to withstand a certain load.Since the acidic solution is highly corrosive to the fracture surface, the fracture surface is gradually smoothed.However, the fracture surface in the alkaline solution is rough.Under the action of the creep load, the fracture surface easily leads to the piercement of the test sleeve of the wrapped sample and consequently causes the end of the test.Therefore, the creep time of the sample in an acidic environment is larger than that in an alkaline environment.

Conclusions
Triaxial creep tests were performed on cracked samples injected with reactive solutions.Three different confining pressures, namely, 2, 5, and 10 MPa, and a corresponding residual strength of 70% were applied during the tests.Additionally, two solutions with different pH values, namely, a H 2 SO 4 solution with pH = 2 and a NaOH solution with pH = 12, were injected into the cracked samples during the tests.And at the same time conduct the permeability test.It can be found that the permeability of the fractured granite in the acidic solution is greater than the permeability of the fractured granite in the alkaline solution.Finally, a SEM experiment was performed on the fracture surface and can get the following conclusions: (1) The failure mode of granite samples changes from brittle failure to ductile failure with the increase of confining pressure in the triaxial compression test.And the residual strength after the peak gradually increases with the increase of confining pressure as well 7 Geofluids (2) The degree of corrosion of granite in alkaline environment is worse than that in acid environment (3) Confining pressure has a significant effect on the long-term stability of granite The study of long-term mechanical properties of granite requires more time rather than the short-term mechanical study.Therefore, the research on the creep properties of multifield coupled of granite is still rare in the world at present, especially considering the long-term performance research under the thermal-hydrological-mechanical-chemical (THMC) coupling processes.So, the next work will focus on the long-term mechanical properties of granite under multiphysics coupling conditions.

Figure 1 :
Figure 1: Microscopic structure of the mineral compositions.

3. 1 .
Creep Strain Curves.Six creep tests are performed on the cracked samples; 3 levels of confining pressure and 2 solutions, with pH = 2 and pH = 12, are studied.The variations in creep strain with time are presented in Figure 5.The creep curves of the fractured granite under mechanical-reactive flow coupling conditions show obvious creep characteristics.In the initial creep stages, the strain clearly increases with time.After a certain period, the rate of increase in the strain decreases, and the sample enters the stable stage.All the samples in this study undergo a primary creep stage and secondary creep stage, whereas sample Pc =

3
Geofluidsno.6 (confining pressure of 10 MPa with acid solution injection, Figure5(c)) undergoes a tertiary creep stage before ultimately losing its strength.

Figure 5 :
Figure 5: Creep strain evolutions of the cracked samples under different confining pressures and reactive solution injection.

Figure 6 :
Figure 6: Creep strain rate evolutions of the cracked samples under different confining pressures and reactive solution injection.

Figure 7 :
Figure 7: Permeability evolutions of the cracked samples under different confining pressures and reactive solution injection.

Figure 8 :
Figure 8: Photographs of the microstructures at the fracture surfaces of the samples after the creep tests.

Table 1 :
Detailed information of the samples used in the triaxial compression tests and creep tests.