Biot theory research has been extended to the multi-scale heterogeneity in actual rocks. Focused on laboratory frequency bandwidth studies, we discuss the relationships between double-porosity and BISQ wave equations,...Biot theory research has been extended to the multi-scale heterogeneity in actual rocks. Focused on laboratory frequency bandwidth studies, we discuss the relationships between double-porosity and BISQ wave equations, analytically derive the degeneration method for double-porosity＇s return to BISQ, and give three necessary conditions which the degeneration must satisfy. By introducing dynamic permeability and tortuosity theory, a full set of dynamic double-porosity wave equations are derived. A narrow band approximation is made to simplify the numerical simulation for dynamic double-porosity wavefields. Finally, the pseudo-spectral method is used for wave simulation within the laboratory frequency band （50 kHz）. Numerical results have proved the feasibility for dynamic double-porosity＇s description of squirt flow and the validity of the quasi-static approximation method.展开更多
Hydraulic fracture （HF） in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method （XFEM） coupling wit...Hydraulic fracture （HF） in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method （XFEM） coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures （NFs）. In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex frac^xre network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk （KGD） model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.展开更多
Rocks in earth＇s crust usually contain both pores and cracks. This phenomenon significantly affects the propagation of elastic waves in earth. This study describes a unified elastic wave theory for porous rock media ...Rocks in earth＇s crust usually contain both pores and cracks. This phenomenon significantly affects the propagation of elastic waves in earth. This study describes a unified elastic wave theory for porous rock media containing cracks. The new theory extends the classic Biot＇s poroelastic wave theory to include the effects of cracks. The effect of cracks on rock＇s elastic prop- erty is introduced using a crack-dependent dry bulk modulus. Another important frequency-dependent effect is the ＂squirt flow＂ phenomenon in the cracked porous rock. The analytical results of the new theory demonstrate not only reduction of elas- tic moduli due to cracks but also significant elastic wave attenuation and dispersion due to squirt flow. The theory shows that the effects of cracks are controlled by two most important parameters of a cracked solid： crack density and aspect ratio. An appealing feature of the new theory is its maintenance of the main characteristics of Biot＇s theory, predicting the characteristics of Blot＇s slow wave and the effects of permeability on elastic wave propagation. As an application example, the theory cor- rectly simulates the change of elastic wave velocity with gas saturation in a field data set. Compared to Biot theory, the new theory has a broader application scope in the measurement of rock properties of earth＇s shallow crust using seismic/acoustic waves.展开更多
基金supported by the National Basic Research Program of China (973 Program, 2007CB209505)the International Cooperative Project of the Ministry of Science and Technology of China (2006DFB62030)
文摘Biot theory research has been extended to the multi-scale heterogeneity in actual rocks. Focused on laboratory frequency bandwidth studies, we discuss the relationships between double-porosity and BISQ wave equations, analytically derive the degeneration method for double-porosity＇s return to BISQ, and give three necessary conditions which the degeneration must satisfy. By introducing dynamic permeability and tortuosity theory, a full set of dynamic double-porosity wave equations are derived. A narrow band approximation is made to simplify the numerical simulation for dynamic double-porosity wavefields. Finally, the pseudo-spectral method is used for wave simulation within the laboratory frequency band （50 kHz）. Numerical results have proved the feasibility for dynamic double-porosity＇s description of squirt flow and the validity of the quasi-static approximation method.
基金supported by the National Natural Science Foundation of China(Grant Nos.11532008,and 11372157)
文摘Hydraulic fracture （HF） in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method （XFEM） coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures （NFs）. In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex frac^xre network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk （KGD） model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.
文摘Rocks in earth＇s crust usually contain both pores and cracks. This phenomenon significantly affects the propagation of elastic waves in earth. This study describes a unified elastic wave theory for porous rock media containing cracks. The new theory extends the classic Biot＇s poroelastic wave theory to include the effects of cracks. The effect of cracks on rock＇s elastic prop- erty is introduced using a crack-dependent dry bulk modulus. Another important frequency-dependent effect is the ＂squirt flow＂ phenomenon in the cracked porous rock. The analytical results of the new theory demonstrate not only reduction of elas- tic moduli due to cracks but also significant elastic wave attenuation and dispersion due to squirt flow. The theory shows that the effects of cracks are controlled by two most important parameters of a cracked solid： crack density and aspect ratio. An appealing feature of the new theory is its maintenance of the main characteristics of Biot＇s theory, predicting the characteristics of Blot＇s slow wave and the effects of permeability on elastic wave propagation. As an application example, the theory cor- rectly simulates the change of elastic wave velocity with gas saturation in a field data set. Compared to Biot theory, the new theory has a broader application scope in the measurement of rock properties of earth＇s shallow crust using seismic/acoustic waves.
