求解异常高压气藏单相非线性渗流模型的一种新方法

A NEW METHOD TO SOLVE SINGLE-PHASE NON-LINEAR PERCOLATION MODEL FOR ABNORMAL HIGH-PRESSURE GAS RESERVOIRS

针对传统异常高压定参数渗流模型不能满足工程需要的现状,建立渗透率、孔隙度等参数随有效应力变化的异常高压气藏单相非线性渗流模型。为使井底附近压力分布的计算更加准确,采用对数等距网格进行网格剖分,即越靠近井底处,网格分布越密,沿径向向外,网格逐渐变稀。在求解差分方程时,创新采用自适应延拓法,克服了传统Newton法、Brown法等数值方法要求迭代初值与真解充分接近的局限性。编程计算结果表明:考虑了渗透率、孔隙度等参数随有效应力变化规律的异常高压气藏单相非线性渗流模型比常用的常系数模型更加贴近工程实际,自适应延拓法的应用对解决初值问题及奇异问题也是简单有效的。

For abnormal high- pressure gas reservoirs,the conventional invariable- parameter percolation model can not satisfy the needs of project. So,a single- phase non- linear percolation model,in which some parameters of permeability and porosity change with effective stress,is established. To more accurately calculate pressure distribution around bottomhole,a log isometric grid is adopted for grid partitioning. The closer the grid is to the bottom,the denser its distribution is; otherwise,it gets sparser. In solving difference equation,the self- adaptive continuation method is used. This method can overcome the limitation from Newton and Brown methods,which requires that iterative initial value is close enough to true solution. Calculation results show that the established single- phase non- linear percolation model is more practical than the conventional one. Moreover,the self- adaptive continuation method is simple and effective to solve the initial value and singular problems.