油藏渗流与应力耦合分析中的有限元等效结点力的计算方法

在岩土力学与渗流力学相结合的基础上，建立了油藏渗流与应力耦合作用的数学模型，给出了耦合分析的数值模型和数值求解的思路和步骤。要实现这一耦合分析过程，建立了单元平衡方程，给出了单元等效结点力的计算表达式，对表达式中的自重载荷、孔隙压力载荷、表面力载荷分别进行了分析，并对初应力载荷进行了计算。根据这些计算方法，在建立了单元刚度矩阵、计算了单元等效结点力、形成单元平衡方程之后，将这些方程集合起来，形成总体平衡方程。通过对总体平衡方程求解，即得各结点的位移值及应变、应力场分布。根据有限元的基本理论，建立了油藏渗流与应力耦合分析中的有限元等效结点力的计算方法，为实现油藏渗流与应力耦合分析提供了有效的途径。

Calculating Method for the Force at the Effect Node in Finite Element in the Couple Analysis of Porous Flow and Stress in Reservoir

Based on the correlation of rock mechanics and porous flow mechanics,the mathematical model considering the porous flow and stress effect in the reservoir was build up. The numerical model and solving method and steps were also given. In order to execute couple analysis process, element equivalence equation and calculation formation for the force at every effect node in the element were made. The analysis of the effect factors in the formation such as sole weight load,pore pressure load,surface force load were analyzed. The initial stress load was also calculated. According to these methods,after making up the element stiffness matrix,calculating the force at the effect node of the element and making up the element equivalence equation,integrating all the equations,the total equivalence equation was build up. Then the value of movement,strain and distribution of the stress field were got. According to the basic thesis of the finite element,the calculation method for the force at the effect node in finite element in the couple analysis of porous flow and stress in reservoir was build up. That is an effect method to execute the couple analysis of porous flow and stress effect.