低渗透气藏整体压裂流-固耦合渗流数学模拟

整体压裂会导致低渗透储集层发生固体应变,进而导致对气体渗流的影响。假设气藏开发生产过程为等温、单相气体渗流,并假设储集层为小变形弹性多孔介质,考虑岩石变形、地应力变化、人工裂缝、流体渗流与岩石应变耦合、储集层渗流与裂缝渗流耦合、非达西效应等因素,建立低渗透气藏整体压裂流固耦合渗流数学模型。首先推导出考虑固体应力应变的气藏整体压裂渗流模型控制方程;然后基于线弹性理论和有效应力概念,建立了孔隙含有气体的岩石的应力应变控制方程。由于这两组非线性控制方程互含应力、应变和压力项,因此用有限差分、块中心网格剖分方法,将方程组离散为主对角占优的七对角矩阵,采用隐式迭代方法求解,数值稳定性较好。通过示例分析,揭示了应力、应变、孔隙度和渗透率等参数的动态变化规律,而且模拟结果比其它模型更接近实际情况。图4参11(范学平摘)

Mathematical simulation of coupled fluid flow and geomechanical behavior for full low permeability gas reservoir fracturing

Full reservoir fracturing will change the stress in the low permeability gas reservoir and induce the strain of rock, so it will influence the gas percolation. We suppose the temperature is constant in production, and there is one phase of gas, and that the porous reservoir will deform elastically, and also suppose the following other factors, such as rock deformation, changes of stress, induced fracture, coupled fluid flow and geomechanical behavior, coupled flow in fracture and that in matrix, and non Darcy flow exist, the coupled fluid flow and geomechanics mathematical model is set up for full low permeability reservoir fracturing. In this paper, firstly, the gas percolation governing equation comprised the strain stress of reservoir rock is deduced. Then, based on the linear elastic theory and effective stress concept, the governing equation on stress strain of the rock containing gas is derived. Because both of the two nonlinear partial equations comprise pressure and stress strain, the equations are discretized and arranged as seven point stencils form by using the methods of finite difference and block centered grid. Its numerical solution is developed with implicit iterative sequence for better numerical stability. Analyzing the example, parameters of stress, strain, porosity and permeability change with time and space are revealed. It is shown that this model is more close to the practical results by comparing with other models.