Thermalhydromechanical (THM) coupling process is a key issue in geotechnical engineering emphasized by many scholars. Most existing studies are conducted at macroscale or mesoscale. This paper presents a porescale THM coupling study of the immiscible twophase flow in the perfectplastic rock. Assembled rock matrix and pore space models are reconstructed using microCT image. The rock deformation and fluid flow are simulated using ANSYS and CFX software, respectively, in which process the coupled physical parameters will be exchanged by ANSYS multiphysics platform at the end of each iteration. Effects of stress and temperature on the rock porosity, permeability, microstructure, and the displacing mechanism of water flooding process are analyzed and revealed.
Thermalhydromechanical (THM) coupling processes in geotechnical media play an important role in a wide range of engineering applications. Many significant issues, such as resources mining (e.g., coal, geothermal energy, natural gas, and oil) [
Many scientific efforts have been exerted to reveal the THM interaction mechanism in the geotechnical systems. Since most geotechnical applications are characterized by longterm operating (several tens or hundreds of years) and large scales in size (several hundreds or thousands of meters in length, width, and depth), it is impossible to conduct in situ physical experiments. Therefore, mathematical models and simulation codes are emphasized by scholars. The THM coupling model originates from the isothermal hydromechanical (HM) coupling mechanism (also named fluidsolid interaction). The first HM coupled theory is the 1D consolidation theory of soil proposed by Terzaghi, followed by Biot’s 3D consolidation theory with isothermal and elastic consolidation [
Theoretically, multiphase models based on NavierStokes equations in porous media are applied for THM coupling analysis in geotechnical materials, which covers the immiscible or miscible multiphase flow of Newtonian fluid or nonNewtonian fluid [
Experiments on rock at micro or mesoscale are more feasible in consideration of the size of the test sample. The mesoscopic THM coupled study refers to the fluid flow test on rock core under the condition of pressure and temperature obtained from experiments or numerical simulation. Nowadays, the uniaxial/triaxial test of rock at HTHP (High Temperature, High Pressure) is widely used in the laboratory to acquire mechanical properties [
The developments of the imaging technologies, such as nano or microCT technology and SEM, make it possible to investigate the rock structure and minerals distribution at the resolution of micron or nanometer [
This paper presents a fully THM coupled process in the rock using the reconstructed and assembled porescale models of rock matrix and pore space. Then the effects of stress and temperature on the pore structure, petrophysical properties, and water flooding efficiency are analyzed.
The porescale models of both pore space and rock matrix are generated using the algorithm proposed in our previous paper [
Rock sample image information.
Number  Rock type  Image resolution 
Size/pixel  Porosity  Number of computational elements  

Matrix  Pore  
B1  Berea sandstone  5.345  400^{3}  19.65%  6428360  1571640 
C1  Carbonate  3.314  400^{3}  17.12%  6630176  1369824 
MS1  Synthetic sandstone  2.055  300^{3}  34.86%  2198473  1176527 
S5  Sandstone from Shengli Oilfield, China  2.51  400^{3}  12.11%  7031198  968802 
S6  Sandstone from Shengli Oilfield, China  5.01  200^{3}  40.34%  4772656  3227344 
Pore radius distribution of images used in this paper.
As is shown in Figure
Reconstructed model and boundary conditions of sample MS1.
Assembled rock matrix and pore space model
Boundary condition of pore space
Boundary condition of rock matrix
Rock matrix is assumed as isotropic, homogenous, and ideal elasticplastic, thus only a limited range of stress and temperature values are simulated in this study. The rock properties used in the simulation are presented in Table
Rock properties of different sample.
Sample number  Property  

Density 
Elastic modulus 
Poisson’s Ratio  Yielding strength 
Thermal expansion/×10^{5°}C^{−1}  
B1  2100  18.43  0.225  92.9  3.5 
C1  2700  76.26  0.24  250  6 
MS1  2300  14.19  0.31  81  5 
S5  2675  20.13  0.28  73  6 
S6  2500  9.35  0.29  67  6 
Fluid properties used in the simulation at the temperature of 273 K.
Fluid  Density 
Viscosity 
Interfacial tension 
Contact angle 


Drainage  Water flooding  
Water  890  48  1 


Oil  1200  1 
The mathematical model of multiphase flow in deformable rock contains two parts: governing equations of fluid flow and solid deformation.
VOF (volume of fraction) model in CFX software is used to simulate the immiscible water and oil in the reservoir. The continuity equation for the
The properties in the transport equations are determined by the volume fraction of the component phases in each cell:
NavierStokes equation is used as the conservation of momentum for the fluid flow [
The energy equation is shared by all the phases in the control volume and can be described as [
The interfacial tension between two immiscible phases is unneglectable in the micropores of rock, which would lead to high capillary force. Here, the continuum surface force (CSF) model proposed by Brackbill et al. in 1992 [
In the CSF model, the phase interface curvature can be calculated by the local gradients of phase interface normal, which is determined by the volume fraction gradient of
By the divergence theorem, the force on the interface can be transferred into the volume force. It has the following form:
Considering the wall adhesion effect, the contact angle between the solid surface and the fluid is adopted to modify the unit normal (
Using CFX software, the outlet flow rate can be acquired. Then the absolute permeability is calculated in the following term [
Then the relative permeability is given by [
The threedimensional equilibrium differential equation is
The threedimensional geometric equations of the rock matrix are
The elastic physical equations are
Based on the rock mesh model, the THM coupling mechanism in rock and its influence on water flooding process in the petroleum industry are analyzed using both ANSYS and CFX software. The fluid used in the singlephase flow simulation is water, and both oil and water are used for twophase flow. In the CFX solver, a laminar flow is assumed. A transient model is used with the secondorder backward Euler scheme. Automatic timestep and a convergence criterion of 10^{−6} are used. In the ANSYS solver, a transient structural solver is used to apply the boundary conditions of solid part and the default solver control is used. The mechanical input file will be generated and used as input to the ANSYS multifield solver.
Based on the structured mesh models of samples B1, C1, MS1, and S6, the evolution mechanism of effective pressure is analyzed. Taking sample MS1 as an example, under the condition of
THM simulation of model MS1 under the condition that the confining pressure is 20 MPa and the pore pressure is 1000 Pa.
Deformation displacement of matrix
Deformation displacement of pore space
Distribution of fluid pressure (Pa)
Distribution of fluid velocity (m/s)
As is shown in Figure
Variation of porosity and permeability with the rising of confining pressure and constant pore pressure.
In addition, comparative analysis on the variation of permeability with the porosity under the same load is shown in Figure
Permeability variation versus porosity variation.
In this section, the effects of temperature on the porosity and permeability under the condition of constant confining pressure (20 MPa) and pore pressure (5 MPa) are analyzed. The rock is assumed to be elastic under the temperature, and only the thermal expansion of rock in the temperature range of
Thermal strain distribution of model MS1 under the temperature of 100°C.
As is shown in Figure
Variation of porosity and permeability with temperature.
Based on the simulation, the permeability variation of model MS1 with the effective pressure and temperature along
Permeability variation of model MS1 with effective pressure and temperature along
Permeability versus effective pressure and temperature along
Permeability versus effective pressure and temperature along
Permeability versus effective pressure and temperature along
Considering that the oil solubility in water is small enough to neglect, the VOF (volume of fraction) model is used to simulate the immiscible displacement process between water and oil in the reservoir. The core sample is initially saturated with water to represent the original stratum without oil. Then the firstcycle oil flooding is proceeded to represent the formation of oil, in which process the core sample becomes more oilwet. After that, water injection is simulated to represent the water flooding development of the reservoir. The oil distribution of MS1 after the first cycle of oil flooding process and the second cycle of water flooding process is shown in Figure
Oil volume fraction of MS1 after oil flooding and water flooding process; the red parts represent the oil phase.
After first cycle of oil flooding process
After second cycle of water flooding process
The effects of confining pressure on water flooding efficiency under the condition of constant pore pressure (1000 Pa) and temperature (20°C) are analyzed. The variations of relative permeability curves of model S5 and MS1 are presented in Figure
Effects of stress on the relative permeability.
Relative permeability curves of S5 for different confining pressure
Relative permeability curves of MS1 for different confining pressure
As is shown in Figure
Effects of temperature on the relative permeability.
Relative permeability curves of S5 for different temperature
Relative permeability curves of MS1 for different temperature
In this paper, a porescale study on the thermalhydromechanical coupling simulation of porous rock is conducted. Based on the structured mesh models of rock matrix and pore space, the effects of stress and temperature on the microstructure, porosity, permeability, and relative permeability in the linear elastic and linear thermalexpanding process are analyzed. The results indicate that the rising of effective pressure or temperature would lead to the decline of the porosity and permeability, and the drop ratio of permeability is larger than that of porosity. The relative permeability of oil and water decreases with the increasing of the effective pressure, so it is with the oil recovery. However, the relative permeability of the two phases and oil recovery increase as a result of the fluid mobility improvement by the rising of temperature. Thus, high temperature and high pressure of induced water are beneficial to enhance oil recovery, especially for heavy oil with high viscosity. Though the petroleum industry is the main concern in this paper, the outcomes can be applied to other kinds of THM coupling process of porous media.
The authors declare that they have no conflicts of interest.
This paper is financially supported by National Science and Technology Major Project of China under Grant no. 2017ZX05013001002.