考虑二次梯度项及动边界的低渗透变形介质油藏渗流规律

ANALYSES ON THE SEEPAGE FLOW RULES FOR LOW-PERMEABILITY OIL RESERVOIR WITH DEFORMED MEDIA CONSIDERING QUADRATIC GRADIENT TERM AND DYNAMIC BOUNDARY

在传统渗流试井模型中,根据弱可压缩流体的假设,非线性偏微分方程中忽略了二次梯度项,但在试井时间较长时忽略掉二次梯度项将产生一定的误差。低渗透油藏一个显著的特点就是流体的流动边界随着时间不断向外扩展。为了更好地研究低渗透变形介质油藏中流体的流动问题,综合考虑低渗透油藏启动压力梯度、动边界、二次梯度项的影响,建立了低渗透变形介质油藏渗流数学模型,并采用全隐式有限差分方法获得了有界地层定产量生产时模型的数值解,分别讨论了启动压力梯度、介质变形及动边界对压力动态曲线的影响,还分析了二次梯度项对压力数值解差异的影响。

In the traditional well-test models of seepage flow, according to the assumption of slightly compressible fluid, the quadratic gradient term in nonlinear partial differential equation is neglected, but the neglect will result in a certain errors when the test time is a little longer. One of the remarkable features of low-permeability oil reser- voirs is the flowing boundary of the fluids extends outwards continuously with the time. In order to study the flow problem of the reservoirs with deformed media much better, by means of comprehensively considering the influences of starting pressure gradient, moving boundary and quadratic gradient term, the mathematical model of the reservoir flow is established. At the same time, with the help of fully implicit finite difference method, the numerical solution of the flow model is obtained when the production is determined for the boundary reservoirs~ the effects of the start- ing pressure gradient, deformed media and moving boundary on the pressure performance curves are analyzed re- spectively ~ and then the influence of the quadratic gradient term on the numerical solution of the pressure is figured out as well.