Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy's velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.
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.
In order to study the meso-mechanism of deformation, crack evolution, and energy conversion of gas-containing coal under loads, considering the gas pressure and adsorption expansion, the gas-solid coupling calculation program of MatDEM software was developed, and the triaxial compression process of gas-containing coal under different gas pressures was numerically simulated. The results show that the strength and stiffness of gas-containing coal decrease with the increase of gas pressure. During the loading process, the permeability of the coal sample decreases first and then increases, while the initial permeability, minimum permeability, and maximum permeability all decrease with the increase of gas pressure. There are far more shear cracks in coal samples than tension cracks, and the number of cracks increases simultaneously with the peak stress drop. With the increase of gas pressure, the macroscopic cracks in coal samples gradually change from large-angle shear cracks to multiple intersecting small-angle ones, and the coal sample gradually changes from brittle failure to ductile. There is an initial accumulation of elastic energy inside the gas-bearing coal, and the dissipated damping heat presents a stage change. As the loading stress level increases, the gas pressure gradually produces a degrading effect. The rockburst tendency of gas-bearing coal changes from weak to none with the increase of gas pressure, which is related to the evolution of the accumulated elastic energy and dissipated damping energy in the coal.
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