双重介质分形油藏非线性流动分析

NON-LINEAR FLOW FRACTAL ANALYSIS ON RESERVOIR WITH DOUBLE-MEDIA

在非线性偏微分方程中 ,根据弱可压缩液体的假设 ,忽略了二次梯度项 ,这在混气石油和低渗透储层的计算中将产生误差。对于双重分形介质流动系统及其物质平衡方程 ,在保留非线性偏微分方程中所有项的前提下建立了新的双孔模型。采用Douglas Jones方法 ,获得了定产生产和定压生产时分形介质双孔模型的数值解。结果表明 ,对于定产生产 ,油藏参数cLD对非线性影响更敏感 ,线性解和非线性解的偏差约为 10 %。对于定压生产 ,cLD的影响可忽略不计。讨论了液体压缩系数和双重分形介质参数变化时的压力变化规律 ,给出了典型压力曲线。

According to assumption of slightly compressible fluid, the quadratic gradient term in non linear partial differential equation was usually neglected, which is easy to result in some errors in calculation for live oil and low permeability reservoirs. The traditional well test models for fluid flow were not consistent with the material balance equation. A fractal double porosity model consistent with the material balance equation for double media fractal reservoir was developed, while all terms in nonlinear partial differential equation were retained. The numerical solutions of fractal double porosity models for the constant rate and constant pressure production of an infinitely large system were obtained by Douglas Jones predictor corrector method. Reservoirs with high values of parameter were found to be more sensitive to non linear solution. The difference between the non linear solution and the linear solution may be around 10 percent for the constant rate production. The effects may be neglected in the constant pressure production.