黏弹性流体分形多孔介质渗流数学模型及计算方法

为了研究黏弹性流体在多孔介质中的渗流规律，将分形理论应用于黏弹性流体的渗流模拟中，通过推导黏弹性流体有效黏度关系式，得到了多孔介质的分形孔隙度和分形渗透率表达式，进一步建立了黏弹性流体分形多孔介质渗流数学模型。使用有限差分方法对黏弹性流体分形多孔介质渗流数学模型进行了数值求解，并利用拉格朗日插值法求得了稳定流状态不同压力下的流量。通过对大庆油田采油四厂5口复合驱井进行实例计算的结果表明，黏弹性流体分形多孔介质渗流数学模型计算所得产液量与实测产液量之间的平均相对误差较小，该模型具有一定的实用价值。

Mathematical model and numerical calculation for viscoelastic fluid flow through fractal porous media

To investigate the flow pattern of viscoelastic fluids in porous media, this study applies the fractal theory to simulation of the porous flow of viscoelastic fluids. The relational expression of effective viscosity of viscoelastic fluids is derived to obtain the mathematical expressions of fractal porosity and fractal permeability of porous media and further establish the mathematic model of viscoelastic fluids flow through fractal porous media. The numerical solution of the proposed mathematical model is obtained using the finite difference method, and the rate of flow in a stable state under different pressures is calculated using the Lagrange interpolation method. The proposed model is validated by an example study in five wells of No.4 Oil Production Plant in Daqing oilfield. There are relatively small average relative errors between the calculated and measured data of fluid production, suggesting that the mathematical model has practical value for simulating the flow of viscoelastic fluids flow through fractal porous media.