Coupled THM (thermalhydromechanical) processes have become increasingly important in studying the issues affecting subsurface flow systems. CO_{2} permeability of the fracture in caprock is a key factor that affects sealing efficiency of caprock. A new model associated with coupled THM processes that shows a good reliability was derived. Then, based on the COMSOL multiphysics software, a series of numerical calculations were performed on caprock models with a single fracture subject to coupled THM effects. Transmissivity of the fracture as a function of fracture angle, overburden pressure, fluid pressure difference, injected CO_{2} temperature, and the initial fracture aperture was elucidated, respectively. Average transmissivity of the fracture undergoes an increase by 1.74 times with the fracture angle (45°–90°), 23 orders of magnitude with the fluid pressure difference (5–30 MPa), and 45 orders of magnitude with the initial fracture aperture (0.05–0.5 mm), while it decreases by 34 orders of magnitude as overburden pressure increases from 30 to 80 MPa. Injected CO_{2} temperature has a small impact on the fracture permeability. This work provides an alternative tool to enrich the numerical modeling for the assessment of CO_{2} caprock sealing efficiency.
To address the increasing concerns regarding carbon dioxide emission and its impact on climate change, CO_{2} geological sequestration has become a promising approach [
Schematic of CO_{2} injection in the presence of fractures within the caprock layer.
Research on subsurface CO_{2} flow systems involves thermal (T), hydrodynamic (H), and mechanical (M) processes. In fact, these processes are interrelated and affect each other and are referred to as “coupled THM effects” [
Numerical simulations have been widely used to evaluate CO_{2} multiphase flow, diffusion, geomechanics, and chemical reactions during CO_{2} injection and storage. In the multiphase flow research field, TOUGH2 codes, which consider the crosscoupling of TH and THC processes for multiphase flow, were developed [
This paper is organized as follows. A new coupled thermalhydromechanical model for CO_{2} flow through a single fracture in caprock was first derived. The governing equations were linked with COMSOL multiphysics software, and the reliability of the model was verified using a sample problem. Finally, several numerical calculations on caprock models with a single fracture subject to coupled THM effects were performed, and CO_{2} permeability of the fracture with respect to different fracture angle, overburden pressure, fluid pressure difference, injected CO_{2} temperature, and initial aperture was, respectively, evaluated. In this study, these models were calculated under simplified conditions of singlephase flow and heat conduction alone in thermal field for brevity.
In the following, a set of field equations are defined which govern the deformation of caprock matrix, the fluid flow through the fracture, and the heat conduction process. These derivations are obtained based on the following assumptions. (i) Caprock matrix is a kind of homogeneous, isotropic, and elastic continuum. (ii) Strains are much smaller than the length scale. (iii) No crack propagation happens to the caprock matrix and no dislocation occurs between the matrix blocks. (iv) The matrix is impermeable, and CO_{2} flows through the fracture alone. The fluid flow behavior can be described using Darcy’s law. (v) Heat effect induced by fluid flow through the fracture is negligible, and heat conduction within the matrix follows Fourier’s law. (vi) Density and viscosity of the supercritical CO_{2} vary with the temperature and pressure.
To elucidate the mechanical response of caprock containing fractures under coupled THM effects and to evaluate the permeability of fractures within the caprock, a typical mechanical model is built and shown in Figure
Mechanical model of caprock containing fractures.
Then, the constitutive relation for the deformed caprock matrix becomes
Equation (
Natural fractures are often subjected to field stresses or mechanical displacements, which have a direct influence on the fracture aperture and hence the permeability of the fractured rock. The fracture aperture may increase due to shear dilation [
Figure
Mechanical model of the fracture.
According to the definition of effective stress in porous media, the effective stress in the fracture can be written as
By using the distinct element code of UDEC, a simple description of the relation between
Fracture aperture as a function of the effective normal stress.
From Figure
In this study, for
According to (
For the two dimensional model described in Figure
Hydraulic model of fluid flow through a fracture.
In terms of the local coordinate system of a fracture, for continuously saturated fluid flow, the mass conservation equation regardless of the source sink can be written as
According to Darcy’s law,
By neglecting the velocity head, the relationship between total head
Taking a derivative of (
Substituting (
During the fracture deformation process (closure/opening), the length of
Assuming that the variation of fluid concentration is negligible, compression coefficient and the expansion coefficient of the fluid can be, respectively, written as [
The compression coefficient of the fracture can be written as
Since the fracture length does not vary with
When the external load is ensured, the total stress of the fracture will keep constant. The relationship between the effective normal stress and fluid pressure can be written as
Substituting (
Combination of (
Assuming that
The transmissivity can be written as
The injection of CO_{2} could result in variation of the temperature in caprock, which would then produce thermal stress [
Property parameters of the supercritical CO_{2} injected in the storage layer vary with the pressure and temperature. In this study, the density and dynamic viscosity of the supercritical CO_{2} are, respectively, determined according to the empirical models put forward by Span and Wagner [
Variations of (a) density [
A 2D single fracture model, which has been studied before by Bower and Zyvoloski [
Input parameters of the validation model [
Parameter  Value  Note 

Length, m  25  Model 
Width, m  1  


Density, kg/m^{3}  2716  Matrix 
Young’s modulus, MPa  1000  
Poisson’s ratio  0.0  


Normal stiffness, MPa/m  1 × 10^{6}  Fracture 
Porosity  1.0  
Initial aperture, m  1 × 10^{−5}  
Residual aperture, m  1 × 10^{−30}  
Maximum aperture, m  0.002  


Density, kg/m^{3}  1000  Fluid 
Dynamic viscosity, Pa⋅s  0.001  
Compression coefficient, 1/Pa  0.0 
Validation model [
An initial stress field of
For this case, numerical and analytic solutions of aperture variation along the fracture length at
Comparison of analytic, numerical (FEHM) aperture [
By using (
To quantitatively analyze permeability of the single fracture in caprock, a conceptual model is set up, as shown in Figure
Parameters used in 2D THM coupled model.
Parameter  Value  Note 

Density, kg/m^{3}  2500  Rock matrix 
Young’s modulus, GPa  100  
Poisson’s ratio  0.3  
Heat conductivity, W/(m × K)  2.57  
Specific heat capacity, J/(m × K)  710  
Thermal expansion, 1/K  6.0 × 10^{−7}  


Initial normal stiffness of fracture closure, GPa/m  60  Fracture 
Normal stiffness of fracture opening, GPa/m  100  
Initial aperture, m 
 
Residual aperture, m  1 × 10^{−6}  
Maximum aperture, m  0.002  
Fluid pressure at the lower side, MPa 
 
Fluid pressure at the upper side, MPa 
 


Density, kg/m^{3}  Figure 
Supercritical CO_{2} 
Dynamic viscosity, Pa⋅s  Figure 

Compression coefficient, 1/Pa  Calculated with Figure 

Thermal expansion, 1/K  Calculated with Figure 
2D conceptual model of a single fracture in caprock subjected to coupled THM effects, in which
First, variation of
Boundary and initial conditions are as follows:
At initial time, CO_{2} was continuously injected in the fracture through the lower fracture side with a constant
Temperature distribution along the fracture at different times.
During the heat conduction process, thermal expansion happens to the rock. Since both lateral boundaries (left and right) of the model are displacement constraint, the thermal expansion of rock leads to variation of normal stress in the fracture. Figures
Distribution of (a) total normal stress, (b) fluid pressure, and (c) effective normal stress along the fracture at different times.
Fluid pressure
Variation of
Distribution of
Variation of (a) density and (b) viscosity of supercritical CO_{2} along the fracture at different times.
Density
Viscosity
Under the coupled THM effects and taking variation of property parameters of CO_{2} with different temperature and pressure into account, the transmissivity
Transmissivity distribution along the fracture at different times.
Due to complicated geological conditions of the caprock, included angle between fracture and the horizontal direction is various. Thus, it is of great significance to study the effect of
Effect of (a) included angle
Included angle
Overburden pressure
Fluid pressure difference
Temperature
Initial aperture
When the storage layer of CO_{2} is in different buried depths, the overburden pressure
For CO_{2} sequestration in the storage layer, it is easier for CO_{2} to diffuse with a larger inlet fluid pressure. However, a large inlet pressure would produce a large
Temperature
From (
In this study, a new coupled CO_{2} flow, caprock deformation, and heat conduction finite element model is developed. A series of numerical calculations using COMSOL multiphysics software on caprock models with a single fracture subject to coupled THM effects were conducted. The main purpose is to elucidate the effect of fracture angle, overburden pressure, fluid pressure difference, injected CO_{2} temperature, and the initial aperture on single fracture permeability in caprock. The conclusions can be drawn as follows.
A 2D single fracture FE model has been applied to verify the performance of the new model under hydromechanical coupled effects. Variation of fracture aperture along the fracture length shows a good agreement compared with the numerical and analytic results of Bower and Zyvoloski [
For a vertical fracture under coupled THM effects, with the increase of time, heat in fracture achieves a stable state at
For all tested cases, with the increase of time, transmissivity
The authors declare that they have no competing interests regarding the publication of this paper.
The financial supports from the State Key Development Program for Basic Research of China (no. 2013CB036003), the Chinese Natural Science Foundation (no. 51374198), and the College Graduate Research and Innovation Projects of Jiangsu Province (