Combined Effects of CO2 Adsorption-Induced Swelling and Dehydration-Induced Shrinkage on Caprock Sealing Efficiency

Carbon dioxide (CO2) may infiltrate into the caprock and displace brine water in the caprock layer. This causes two effects: one is the caprock swelling induced by the CO2 adsorption and the other is the caprock dehydration and shrinkage due to CO2–brine water two-phase flow. The competition of these two effects challenges the caprock sealing efficiency. To study the evolution mechanism of the caprock properties, a numerical model is first proposed to investigate the combined effects of CO2 adsorption-induced expansion and dehydration-induced shrinkage on the caprock sealing efficiency. In this model, the caprock matrix is fully saturated by brine water in its initial state and the fracture network has only a brine water–CO2 two-phase flow. With the diffusion of CO2 from the fractures into the caprock matrix, the CO2 sorption and matrix dehydration can alter the permeability of the caprock and affect the entry capillary pressure. Second, this numerical model is validated with a breakthrough test. The effects of the two-phase flow on the water saturation, CO2 adsorption on the swelling strain, and dehydration on the shrinkage strain are studied, respectively. Third, the permeability evolution mechanism in the CO2–brine water mixed zone is investigated. The effect of dehydration on the penetration depth is also analyzed. It is found that both the shale matrix dehydration and CO2 sorption-induced swelling can significantly alter the sealing efficiency of the fractured caprock.


Introduction
The potential leakage of the stored carbon dioxide from the caprock layers is an important environmental safety issue to the CO 2 sequestration in geological formations [1,2]. The numerical simulations for the commercial-scale CO 2 sequestration projects have evaluated the migration and interaction with the storage reservoir [3,4]. These evaluations focus on the trapping mechanisms and reservoir storage capacity [5]. The trapping mechanisms of the mineral, solubility, hydrodynamics, and structure have been studied, respectively [6][7][8][9]. Further, the effective storage capacity is estimated based on the plume formation, accumulative pressure, and other factors [10,11]. The structural trapping is usually formed by many caprock layers, which are physical barriers with a low permeability to prevent the CO 2 from a further upwards migration. The CO 2 accumulates gradually from the reservoir to the bottom of the caprock layer during the sequestration process [12][13][14] and interacts with the caprock layer. When the accumulation pressure exceeds the initial entry capillary pressure, CO 2 gradually penetrates into the caprock layer [15,16] and the caprock sealing efficiency is impaired [17]. The leakage of CO 2 after the breakthrough of the caprock layer damages the safety of the storage reservoir. Therefore, the key issue to the CO 2 geological sequestration is the caprock sealing stability and efficiency. How the dehydration of the mathematically. These models together constitute a new coupled multi-physical model. It is an extension of our previous model for the efficiency of the caprock sealing [16,24]. Third, the effects of the adsorption-induced swelling and dehydration-induced shrinkage as well as the stress compaction are expressed in terms of the fracture aperture change. Through the finite element method, this fully coupled model is solved numerically and verified by a breakthrough test of a fractured sample. Finally, the effects of the adsorption-induced swelling and dehydration-induced shrinkage on the self-limiting or self-enhancement within a caprock layer are numerically investigated.

Multi-Physical Interactions in a Fractured Caprock
The disturbance mechanisms of caprock sealing induced by a two-phase flow stimulation are complex. The pressure of CO 2 at the bottom of the caprock layer continuously increases with the CO 2 accumulation from the storage reservoir. If the CO 2 pressure is lower than the sum of the reservoir pressure and entry capillary pressure [34,35], the Darcy flow does not occur. This kind of sealing is called the capillary sealing. In this sealing mode, the diffusion and flow of the dissolved gas in pore water are the main means of CO 2 migration. The Darcy flow starts once the gas pressure is over the sum of the reservoir pressure and the entry capillary pressure [35]. In two-phase Darcy flow process, the CO 2 displaces the pore water in the caprock layer.
Caprocks are a mostly fractured porous media which consist of fractures and a matrix. The fracture usually has a much lower entry capillary pressure than the shale matrix. The shale caprock of water-saturated is different from the shale gas reservoir. The pore water still remains in micropores after the CO 2 penetrates into the fractures [36]. As CO 2 in the fracture network gradually diffuses into the shale matrix, water in the shale matrix will be replaced by CO 2 and then enters the fractures. These two processes are usually diffusive and called sorption and dehydration, respectively. Figure 1 presents a detailed conceptual model of these mechanisms. In this conceptual model, the CO 2 -brine water two-phase flow is observed only in the fracture network. However, due to the interaction between the shale caprock and CO 2 , the CO 2 adsorbs into the matrix and water is then produced due to the dehydration [37]. The matrix is subjected to the two actions of both the CO 2 adsorption-induced swelling and dehydration-induced shrinkage (see Figure 2). Therefore, the multi-physical processes can be represented by this conceptual model in various time scales: (1) a CO 2 -brine water two-phase flow in the initial water-saturated fractures; (2) the propagation of gas front-induced mechanical process; (3) a CO 2 diffusion and adsorption into the caprock matrix; (4) the water dehydration of the matrix; and (5) the geochemical reactions among CO 2 , water, and caprock [38]. The first three events are short term: the mechanical deformation occurs immediately when the effective stress has any change. The CO 2 -brine water two-phase flow in the fracture network is instantly started when the entry capillary pressure is run over. The diffusion, dehydration, and geochemical reaction processes may be long term, such as the span of geological time [39].

Dehydration and Shrinkage of Shale Matrix
The CO 2 -brine water displacement mechanism in a shale matrix block is depicted in Figure 3. Shale is a sedimentary rock formed by dewatering and the cementation of clay minerals. The clay minerals are water-sensitive [40]. The shale matrix swells when water flows into the matrix (called the hydration process). Inversely, the shale matrix shrinks when the water flows out of the matrix (called the dehydration process). Figure 3a presents a shale matrix block which is surrounded by fractures. Both the fractures and the matrix were assumed to have the same initial phase pressures of a CO 2 -brine water two-phase flow. The phase pressures changed continuously with the two-phase flow process in the fracture network (see Figure 3b) and caused CO 2 to flow into the block and the water to flow out of the block.

Dehydration and Shrinkage of Shale Matrix
The CO2-brine water displacement mechanism in a shale matrix block is depicted in Figure 3. Shale is a sedimentary rock formed by dewatering and the cementation of clay minerals. The clay minerals are water-sensitive [40]. The shale matrix swells when water flows into the matrix (called the hydration process). Inversely, the shale matrix shrinks when the water flows out of the matrix (called the dehydration process). Figure 3a presents a shale matrix block which is surrounded by fractures. Both the fractures and the matrix were assumed to have the same initial phase pressures of a CO2-brine water twophase flow. The phase pressures changed continuously with the two-phase flow process in the fracture network (see Figure 3b) and caused CO2 to flow into the block and the water to flow out of the block.

Dehydration and Shrinkage of Shale Matrix
The CO2-brine water displacement mechanism in a shale matrix block is depicted in Figure 3. Shale is a sedimentary rock formed by dewatering and the cementation of clay minerals. The clay minerals are water-sensitive [40]. The shale matrix swells when water flows into the matrix (called the hydration process). Inversely, the shale matrix shrinks when the water flows out of the matrix (called the dehydration process). Figure 3a presents a shale matrix block which is surrounded by fractures. Both the fractures and the matrix were assumed to have the same initial phase pressures of a CO2-brine water twophase flow. The phase pressures changed continuously with the two-phase flow process in the fracture network (see Figure 3b) and caused CO2 to flow into the block and the water to flow out of the block.

Water Content, Saturation, and Porosity of Shale Matrix
The porosity of shale matrix is calculated by: The brine water saturation is defined as: The volumetric water content W is related to the water saturation as: The water content (by weight) is the ratio of water mass to solid mass as: Equation (4) is a relationship among the porosity, water content, and water saturation. Obviously, any change in one factor may induce a change in the other two. Further, the water loss in the shale matrix (or the dehydration process) may be not only from free water but also from some bonding water [18]. At this time, the bonding water has the following mass [41]: where m φ is the porosity of the shale, bwm S is the water saturation in the pores, V V is the pore volume, W V is the water volume, and T V is the total volume. bw M is the water  Figure 3. CO 2 -water displacement in tight caprock. The abbreviated letters P wm , P w f , P CO 2 m , P CO 2 f are short for the pressures of water in the matrix, water in the fractures, CO 2 in the matrix, and CO 2 in the fractures, respectively.

Water Content, Saturation, and Porosity of Shale Matrix
The porosity of shale matrix is calculated by: The brine water saturation is defined as: The volumetric water content W is related to the water saturation as: The water content (by weight) is the ratio of water mass to solid mass as: Equation (4) is a relationship among the porosity, water content, and water saturation. Obviously, any change in one factor may induce a change in the other two. Further, the water loss in the shale matrix (or the dehydration process) may be not only from free water but also from some bonding water [18]. At this time, the bonding water has the following mass [41]: where φ m is the porosity of the shale, S bwm is the water saturation in the pores, V V is the pore volume, V W is the water volume, and V T is the total volume. M bw is the water mass and M S is the shale mass. ρ bw is the density of the water and ρ s is the density of the shale matrix. A and α 1 are the correction factors for the total water and bonding water content contributing to a shrinkage deformation, respectively.
This bonding water is usually regarded as a part of the solid particles. If this bonding water does not contribute to a shrinkage deformation, the water content of the shale matrix is revised as: where α is the correction factor for the bonding water content not contributing to the shrinkage deformation.

Dehydration-Induced Volumetric Strain of Shale Matrix
This matrix shrinkage is measured by the volumetric strain ε vbw through a moistureadsorption test. A quadric function is here used for the moisture-swelling relationship as: where K 1 and K 2 are the expansion coefficients. A typical hydration-induced swelling of the Mancos shale [42] is presented in Figure 4, where K 1 = 0.212 and K 2 = 33.24. Obviously, the swelling strain of this shale is big and Equation (7) is able to describe this relationship.
water content contributing to a shrinkage deformation, respectively. This bonding water is usually regarded as a part of the solid particles. If this bonding water does not contribute to a shrinkage deformation, the water content of the shale matrix is revised as: where α is the correction factor for the bonding water content not contributing to the shrinkage deformation.

Dehydration-Induced Volumetric Strain of Shale Matrix
This matrix shrinkage is measured by the volumetric strain vbw ε through a moisture-adsorption test. A quadric function is here used for the moisture-swelling relationship as: where 1 K and 2 K are the expansion coefficients. A typical hydration-induced swelling of the Mancos shale [42] is presented in Figure 4, where 1 =0.212 K Obviously, the swelling strain of this shale is big and Equation (7) is able to describe this relationship.

Porosity Evolution in Homogeneous Shale Matrix
The porosity ratio is obtained as: where R = α/φ 0 . S 0 and S are the effective volumetric strains in the initial and current state, respectively. They are defined as follows where ε v and ε v0 are the current and initial volumetric strain, respectively, and ε s0 and ε s are the initial and current volumetric strain induced by the sorption. ε D0 and ε D are the initial and current hydration-induced volumetric strain, respectively. φ 0 is the initial porosity and p 0 is the initial pore pressure.

Local Fracture Strain
Both the fractures and matrix contribute to the total deformation of the fractured shale (see Figure 5).
where v ε and 0 v ε are the current and initial volumetric strain, respectively, and 0 s ε and s ε are the initial and current volumetric strain induced by the sorption. p is the initial pore pressure.

Local Fracture Strain
Both the fractures and matrix contribute to the total deformation of the fractured shale (see Figure 5). The change in the fracture aperture is: Equation (10) can be reformulated as: The local fracture strain is derived as: where s is the fracture spacing and φ f 0 is the initial fracture porosity. b i /s = φ f 0 /n are in an n-dimension case. ε e is the average effective strain and ∆ε e is its increment in a fixed representative length (∆ε e = (S 0 − S)/(1 + S)). ε em is the effective strain, and ∆ε em is the increment of ε em . R m = ∆ε em /∆ε e is the increment strain ratio of the average effective strain to effective strain.

Evolution of Permeability
The initial permeability of the fracture is expressed as the following cubic law: If fracture aperture b i changes due to the compaction, swelling, dehydration or their combinations, the permeability k will change as follows: where ∆b is the change in the fracture aperture.
Combining Equation (14) with Equation (13) yields the permeability ratio of the fracture as: In two-dimensional space, this permeability ratio is:

Change in Entry Capillary Pressure with Fracture Deformation
The caprock is initially water saturated. The entry capillary pressure (Appendix A) limits the CO 2 containment capacity of the caprock and depends on both the pore geometry in the matrix and the CO 2 /brine water/rock wettability [43]. The entry capillary pressure is calculated by where r is the pore radius. σ is the interfacial tension of water, CO 2 , and caprock. θ is the contact angle to express the hydrophilic interactions. The current aperture of a fracture is: It is equivalent between the aperture of a fracture and the representative radius of a pore in this paper. In the calculation of the entry capillary pressure in a fracture, r = b. The entry capillary pressure of the fracture at the initial state is: Here, the subscript 'i' denotes the initial state. The interfacial tension and wettability are influenced by the pressure, temperature, or chemical reactions during CO 2 -brine waterrock contacting process [36]. If these physical variables do not change with the deformation, the CO 2 entry pressure is concluded as: This is our new entry pressure of CO 2 after considering the effective strain.

Mass Transfer of CO 2 between Fractures and Shale Matrix
The sorption rate of CO 2 is denoted by: where Q m is the source term of mass and the minus sign '-' represents the mass transfer from the shale matrix to the fractures. m b is the residual content of CO 2 in the matrix at pressure p. dm b /dt is the exchange rate of CO 2 between the fractures and the shale matrix and is expressed as: where τ is the diffusion time, m e is the gas content at the equilibrium state, and p is the pressure of the fractures. The diffusion time is defined as: where a is a shape factor and D is the diffusion coefficient of CO 2 in the matrix.

Dehydration due to Water Transfer between Fractures and Shale Matrix
The dehydration of the shale matrix is still assumed to follow a diffusion process [42]. In this paper, this process is described by a simplified diffusion equation as: where m bw is the mass of the water phase in the shale matrix, and m bwe is the water content at the equilibrium state with the water saturation s bw in the fractures. The diffusion time of water in the shale matrix is denoted as: where C is the water diffusion coefficient in the matrix [42]. The CO 2 -brine water two-phase flow displacement is complicated in a porous media [44], but can be described by following the diffusion process over spherical pellets [45]: where D bw is the diffusion coefficient and R bw is the characteristic radius of spherical pellets. It is obvious that both Equation (26) and (24) have the same form.

Mass Conservation Laws for CO 2 -Brine Water Two-Phase Flow in Fractures
The CO 2 -brine water two-phase flow occurs in the fractures. CO 2 is considered as the non-wetting phase, and the brine water is considered as the wetting phase. According to the mass conservation law, the governing equations of CO 2 and brine water are obtained as follows.
For the brine water phase: ∂(φρ bw s bw + ρ bw m bw ) ∂t Being different from the brine water, the CO 2 has two unique features: (1) a strong compressibility in both free and supercritical states and (2) the existence of both free and absorbed phases in the fractures. Furthermore, the CO 2 diffuses from the fractures into the matrix and displaces the pore water in the shale matrix. The mass of CO 2 , m nw , can be derived as Equation (28) shows that the storage states of the CO 2 phase include a free-phase form (the first term), an absorbed form in the fracture network (the second term), and the mass exchange from the matrix (the third term).
For the CO 2 phase: where ρ bw is the density of the brine water. k is the absolute permeability of the shale. k rbw and k rnw are the relative permeabilities (Appendix B) of the brine water and CO 2 in the fracture network, respectively. The viscosity at in situ conditions is µ w for water and µ nw for CO 2 . φ is the porosity of the fracture network. The source term is f w for water and f nw for CO 2 . p bw and p nw are the pore pressures of the brine water and CO 2 in the fractures. s bw and s nw are the saturations of the brine water and CO 2 , respectively. H is the height in the vertical direction. ρ nwa and ρ c are the densities of the CO 2 and the shale caprock under the standard conditions, respectively. g is the gravity acceleration. The equation of the state gives the CO 2 density, ρ nw , as: where M nw and Z nw are the molecular weight and compressibility factor of CO 2 , respectively. R denotes the universal gas constant and T nw is the temperature of CO 2 . β is a constant of a range for the CO 2 pressure and temperature. The pressure of CO 2 , p * nw , in the fractures is: Introducing the relationship between the capillary pressure and saturation yields the final form of two-phase flow governing equations in the fractures.
For the brine water flow: For the CO 2 flow: The sorption modified porosity is: where ∂φ ∂t is the change in the porosity with time under the action of a compaction, swelling/dehydration, sorption, and chemical reaction. −p a ρ c dm b dt is the source term of CO 2 . It is provided by the diffusion processes of free gas and absorption/adsorption process of adsorbed gas in the shale matrix (Appendix C). Similarly, −ρ bw dm bw dt is the water term. It is supplied by the dehydration of the matrix. p a corresponds to the atmospheric pressure. f bw = ρ bw f bw and f nw = β f nw .

Navier Equation for Shale Deformation
For the elastic shale saturated by the CO 2 and brine water, the Navier equation for the deformation of the porous medium is [16]: where G is the shear modulus. u i,jj is the second-order derivative in the jth direction of the displacement in the ith direction u i . ν is the Poisson's ratio. p ,i is the derivative of the pore pressure in the ith direction and calculated by p = S w p w + S nw P nw . α is the Biot coefficient. Equation (36) shows that there are four sources of the body force: the body force induced by dehydration-swelling (Kε D,i ), the body force induced by sorption-swelling (Kε s,i ), the friction force induced by the two-phase flow (drag force or αp ,i ), and the body force induced by gravity ( f i ). The resistance is decided by the Biot's coefficient, and the body force induced by the swelling of the skeleton is correlated with the bulk modulus.

Verification of This fully Coupled Multi-Physical Model
The British Geological Survey has carried out a gas breakthrough test on the argillite in the Callovo-Oxfordian formation [46]. Figure 6 shows the sample for this breakthrough test whose dimension was 5.39 cm high and 2.72 cm wide. For the flow field, there was no flow at the two side walls. For the deformation field, the two walls were also fixed. Helium was slowly injected from the bottom of the caprock with the pressure increasing from 6.5 to 10.5 MPa in a series of increments. A constant backpressure of 4.5 MPa was applied at the top of the caprock, and a confining stress of 12.5 MPa was maintained through the experiment. Before the gas injection, the caprock was fully saturated by water. Water and helium were allowed to flow out from the top boundary at a constant pressure. Gerard et al. [46] completed the hydro-mechanical modeling with a preferential gas pathway. They proposed a continuous finite element matrix embedding a single fracture to describe this problem. This study uses their computational parameters except the capillary-saturation relationship. We also use our log-log relationship instead of their Van Genuchten relationship for the relative permeabilities. Those parameters which were not given by Gerard et al. [46] are taken from other publications or our estimation. Tables 1 and 2 summarize all the parameters in our computations. Because helium was used, no sorption and hydration were considered. In this proposed multi-physical model, the helium flow was only along the fracture network, thus no additional single fracture was required for the simulations. The flow rate of helium gas from the top boundary was calculated and compared with the experimental measurements. Our simulations considered two cases: the first case was a constant entry pressure of 2.1 MPa and the second case was a variable gas entry pressure which was evolving with the effective strain. The initial gas entry pressure was taken as p ei = 2.1 MPa. Figure 6. Geometry of breakthrough test problem.   Comparison between the experimental data and numerical simulations is shown in Figure 7. It is found that there are the same flow rates before the gas breakthrough in either the constant or variable entry pressure cases. These flow rates before the gas breakthrough are very low and depend on the absolute permeability and the initial gas saturation. With the gas-water front moving to the top boundary, the sample deforms and the fracture aperture thus changes, particularly near the mixing zone of helium and water. This deformation changes the gas entry pressure. The case of variable gas entry pressure is observed to have an earlier gas breakthrough time and the rapid increase in the flow rate after the gas breakthrough. The case of a constant gas entry pressure has a much later gas breakthrough time and a much lower flow rate after the gas breakthrough. It is also shown that a variable gas entry pressure can better reproduce the experimental data. A good agreement is observed between the numerical results by the variable gas entry pressure in Equation (20) and the experimental observations. There is a single fracture in the computational domain of their model. However, only the flow in fracture network is described in our model, thus a single fracture is not required. This treatment largely extends the capacity of our model to handle large-scale problems for the evaluation of the caprock sealing efficiency. Comparison between the experimental data and numerical simulations is shown in Figure 7. It is found that there are the same flow rates before the gas breakthrough in either the constant or variable entry pressure cases. These flow rates before the gas breakthrough are very low and depend on the absolute permeability and the initial gas saturation. With the gas-water front moving to the top boundary, the sample deforms and the fracture aperture thus changes, particularly near the mixing zone of helium and water. This deformation changes the gas entry pressure. The case of variable gas entry pressure is observed to have an earlier gas breakthrough time and the rapid increase in the flow rate after the gas breakthrough. The case of a constant gas entry pressure has a much later gas breakthrough time and a much lower flow rate after the gas breakthrough. It is also shown that a variable gas entry pressure can better reproduce the experimental data. A good agreement is observed between the numerical results by the variable gas entry pressure in Equation 20 and the experimental observations. There is a single fracture in the computational domain of their model. However, only the flow in fracture network is described in our model, thus a single fracture is not required. This treatment largely extends the capacity of our model to handle large-scale problems for the evaluation of the caprock sealing efficiency. Figure 7. Comparison of gas outflux between experimental data [46] and our numerical simulations.

Model and Parameters
As shown in Figure 8

Model and Parameters
As shown in Figure 8, a typical geometric model of 10 m × 10 m was established for a one-dimensional penetration problem. For the flow field, there was no flow at the two side walls. However, CO 2 and brine water can flow out from the top boundary. For the deformation field, the two walls and bottom were constrained. The CO 2 was injected from the bottom with a given injection pressure. It increased from the reservoir pressure to 27 MPa in an exponential form and then remains constant for 1000 years. The diffusion time for both the CO 2 and brine water was taken as 1d. The computational parameters are shown in Table 3. The caprock contains 54.1% quartz, 25.6% kaolinite, 13.5% illite and mica, and 2.5% K-feldspar by weight. The dehydration-induced swelling is still described by Equation (7). In this example, the short-term interaction mechanism was studied in the CO 2 -brine two-phase flow process. Furthermore, the impacts of the two-phase flow, the CO 2 sorption, and dehydration/swelling on the caprock sealing efficiency were comprehensively analyzed in the two-phase flow process.
for both the CO2 and brine water was taken as 1d. The computational parameters are shown in Table 3. The caprock contains 54.1% quartz, 25.6% kaolinite, 13.5% illite and mica, and 2.5% K-feldspar by weight. The dehydration-induced swelling is still described by Equation (7). In this example, the short-term interaction mechanism was studied in the CO2-brine two-phase flow process. Furthermore, the impacts of the two-phase flow, the CO2 sorption, and dehydration/swelling on the caprock sealing efficiency were comprehensively analyzed in the two-phase flow process.    The impacts of dehydration-induced shrinkage on the CO 2 -water displacement are studied here. The two initial states of the shale matrix were assumed: a fully saturated with the dehydration (called dehydration) state and a fully saturated without the dehydration (called the base case) state. The time of the numerical calculation was 317 years (10 10 s). Figure 9 presents the effect of the matrix dehydration on the water saturation in the fracture network when the injection time is 317 years. It is noted that the shrinkage strain due to the dehydration is only specified as 15 % of the swelling strain. This figure shows that the dehydration of the shale matrix has a slight impact on the water saturation distribution in the vertical direction. In the CO 2 -brine water two-phase flow process, two competitive factors result in the swelling or shrinkage of the shale matrix. Figure 10a presents the increase in the swelling strain induced by the CO 2 sorption with time. The observation point is located at 0.1 m away from the lower face. The CO 2 diffusion causes the swelling of the shale matrix. At the same time, the dehydration process makes the shale matrix shrink, as shown in Figure 10b. It is noted that the magnitude of the shrinkage strain is much smaller than the sorption-induced swelling strain in this example. The combination of the CO 2 sorption-induced swelling and the dehydration-induced shrinkage makes the permeability ratio slightly increase, then decrease, and finally reach a low value. Figure 11 presents the permeability evolution at the observation point. The dehydration process contributes a little to the increase in the early stage but significantly reduces the extent of self-limiting in the fracture network. This reduction in self-limiting is also observed from the vertical distribution of the permeability ratio at time of 3.17 years in Figure 12. The minimum permeability ratio is bigger due to dehydration. This implies that the dehydration increases the fracture apertures and thus alleviates the reduction in the permeability of the fracture network due to swelling. The impact of the dehydration on the penetration depth is shown in Figure 13. In this sense, the penetration depth with the dehydration is much higher than without the dehydration. Therefore, the risk of a gas breakthrough is increased due to the dehydration.

Self-Limiting Mechanism Analysis
The self-limiting mechanism of caprock is complicated. This mechanism comes from the two competitions of the shale matrix swellings: the CO2 sorption-induced swelling and the dehydration-induced shrinkage. As the flow paths narrow down and even close under the action of the swelling, the permeability in the fractures will decrease and the penetration speed of the CO2-water front will slow down [47]. If the action of the swelling becomes stronger along the flow direction, the efficiency of the caprock sealing can be enhanced. For the initially water-saturated shale matrix, the CO2 diffusion can induce the shale matrix dehydration [48]. This dehydration changes the water content and induces the shrinkage of the shale matrix. The fracture apertures get wider due to the shrinkage of the shale matrix during the CO2 diffusion. The worst case is to reopen the flow channels which are closing due to a full swelling of the shale matrix under in situ conditions. Such an increase in the apertures increases the permeability and penetration depth [35]. This condition reduces the efficiency of the caprock sealing and there is a potential leakage risk of CO2. Figure 12 shows that the permeability fluctuates and is different in the two-phase flow region or the sweeping zone which moves with the CO2-water front. After the twophase flow, the permeability decreases by about 10% along the flow direction for the base case and approximately 6% from the contribution of dehydration. In this regard, the dehydration process has an effect on the swelling strain. In addition, the self-limiting/enhancing capacity has also been influenced. On this sense, it can be concluded that the strong dehydration within the caprock can significantly influence the caprock sealing. For the water-saturated caprock, the CO2 infiltration may cause the matrix dehydration [49]. Therefore, the caprock dehydration should be carefully considered in the evaluation of the caprock sealing.

Conclusions
A multi-physical coupling model was proposed to investigate the effects of dehydration and sorption on the efficiency of the caprock sealing. This model was further validated by a gas breakthrough test. The combined effects of CO2 adsorption-induced swelling and dehydration-induced shrinkage on the permeability and entry capillary pressure of the fracture network were studied through this model. Particularly, the impact of the dehydration-induced shrinkage on the penetration depth was particularly studied. The following conclusions can be drawn from these investigations: First, this multi-physical coupling model is a sound tool for the assessment of the sealing efficiency of caprock. It includes the capacity of our previous model in illustrating the physical and mechanical properties of caprock, such as the compaction deformation, gas flow, and sorption. It also expands its capacity, including the dehydration of the shale matrix and the porosity and permeability evolution in the fracture network due to the dehydration shrinkage and compaction.
Second, the evolution mechanisms of the porosity and permeability are complicated and complex, particularly in the CO2-brine two-phase flow region and the gas sweeping region. These evolutions are the interaction results among the CO2 diffusion, mechanical compaction, two-phase flow, CO2 sorption-induced swelling, and dehydration-induced shrinkage. These interactions cause the effects of self-enhancing/limiting in these regions due to a swelling/shrinkage of the shale matrix.
Finally, the sorption-induced swelling and dehydration-induced shrinkage in the saturated shale caprock are two competitive factors to alter the efficiency of caprock sealing. A CO2 infiltration may cause the matrix's dehydration from the water-saturated caprock. This matrix dehydration can induce the re-opening of some fractures, enhance the permeability, and reduce the efficiency of caprock sealing, thus being a potential risk for CO2 geological sequestration. Caprock dehydration is worthy of being carefully considered in the evaluation of the caprock sealing efficiency.

Self-Limiting Mechanism Analysis
The self-limiting mechanism of caprock is complicated. This mechanism comes from the two competitions of the shale matrix swellings: the CO 2 sorption-induced swelling and the dehydration-induced shrinkage. As the flow paths narrow down and even close under the action of the swelling, the permeability in the fractures will decrease and the penetration speed of the CO 2 -water front will slow down [47]. If the action of the swelling becomes stronger along the flow direction, the efficiency of the caprock sealing can be enhanced. For the initially water-saturated shale matrix, the CO 2 diffusion can induce the shale matrix dehydration [48]. This dehydration changes the water content and induces the shrinkage of the shale matrix. The fracture apertures get wider due to the shrinkage of the shale matrix during the CO 2 diffusion. The worst case is to reopen the flow channels which are closing due to a full swelling of the shale matrix under in situ conditions. Such an increase in the apertures increases the permeability and penetration depth [35]. This condition reduces the efficiency of the caprock sealing and there is a potential leakage risk of CO 2 . Figure 12 shows that the permeability fluctuates and is different in the two-phase flow region or the sweeping zone which moves with the CO 2 -water front. After the two-phase flow, the permeability decreases by about 10% along the flow direction for the base case and approximately 6% from the contribution of dehydration. In this regard, the dehydration process has an effect on the swelling strain. In addition, the self-limiting/enhancing capacity has also been influenced. On this sense, it can be concluded that the strong dehydration within the caprock can significantly influence the caprock sealing. For the water-saturated caprock, the CO 2 infiltration may cause the matrix dehydration [49]. Therefore, the caprock dehydration should be carefully considered in the evaluation of the caprock sealing.

Conclusions
A multi-physical coupling model was proposed to investigate the effects of dehydration and sorption on the efficiency of the caprock sealing. This model was further validated by a gas breakthrough test. The combined effects of CO 2 adsorption-induced swelling and dehydration-induced shrinkage on the permeability and entry capillary pressure of the fracture network were studied through this model. Particularly, the impact of the dehydration-induced shrinkage on the penetration depth was particularly studied. The following conclusions can be drawn from these investigations: First, this multi-physical coupling model is a sound tool for the assessment of the sealing efficiency of caprock. It includes the capacity of our previous model in illustrating the physical and mechanical properties of caprock, such as the compaction deformation, gas flow, and sorption. It also expands its capacity, including the dehydration of the shale matrix and the porosity and permeability evolution in the fracture network due to the dehydration shrinkage and compaction.
Second, the evolution mechanisms of the porosity and permeability are complicated and complex, particularly in the CO 2 -brine two-phase flow region and the gas sweeping region. These evolutions are the interaction results among the CO 2 diffusion, mechanical compaction, two-phase flow, CO 2 sorption-induced swelling, and dehydration-induced shrinkage. These interactions cause the effects of self-enhancing/limiting in these regions due to a swelling/shrinkage of the shale matrix.
Finally, the sorption-induced swelling and dehydration-induced shrinkage in the saturated shale caprock are two competitive factors to alter the efficiency of caprock sealing. A CO 2 infiltration may cause the matrix's dehydration from the water-saturated caprock. This matrix dehydration can induce the re-opening of some fractures, enhance the permeability, and reduce the efficiency of caprock sealing, thus being a potential risk for CO 2 geological sequestration. Caprock dehydration is worthy of being carefully considered in the evaluation of the caprock sealing efficiency.