摘要
基于低渗透多孔介质边界层理论，建立了描述低渗透多孔介质渗流特征的非线性渗流模型，并通过实验数据的拟合．验证了非线性渗流模型的有效性。以该渗流模型为基础，获得了视渗透率连续变化函数，揭示了视渗透率形成原因；应用表征视渗透率效应的流动模型，建立了反映低渗透多孔介质渗流特征的径向不稳定渗流数学模型，并用全隐式格式离散方法求得流动方程的数值解。数值结果表明：在等产量条件下，在视渗透率效应和流动渗流阻力的影响下，随时间的变化低渗透多孔介质井底压力先快速上升后缓慢下降，存在上升最大值。最小启动压力梯度越大，井底压力上升的最大值越小，后期井底压力下降的幅度越大；相对静态边界层厚度越大，井底压力上升的最大值越小，后期井底压力下降的幅度越大；非线性系数对井底压力的影响主要体现在后期，且非线性系数越大，后期井底压力下降的速度越缓慢．井底压力上升的最大值越大。
Based on the boundary layer theory of low permeability porous media, the nonlinear percolation model describing the char- acteristics of flow in low permeability porous media is established in the paper. The validity of the nonlinear seepage model is verified by fitting the experimental data. A continuous changing function of the apparent permeability is obtained on the basis of the percola- tion model, revealing the reasons of the formation of apparent permeability. A mathematical model of radial unsteady percolation that reflects the percolation characteristics of the low permeability porous media is established by application of a flow model that charac- terizes apparent permeability effect. The numerical solution of the flow equations is obtained with a fully implicit discretization method. The results show that, under the isoquant of production conditions, and influenced by the apparent permeability effect, the bottomhole pressure rises rapidly then declines slowly over time through low permeability porous media. There is a maximum increase of the bottomhole pressure. The greater the minimum starting pressure gradient, and the smaller the maximum bottomhole pressure rise, the greater the later bottomhole pressure decreases; the greater the thickness of the relatively static boundary layers, and the smaller the maximum bottomhole pressure rise, the greater the later bottomhole pressure decreases too. The influence of nonlinear co- efficients on the bottomhole pressure is mainly reflected in the later stage. The greater the nonlinear coefficient, and the slower the later bottomhole pressure decline, the greater the maximum bottomhole pressure rises.
基金
基金项目：国土资源部“矿产资源节约与综合利用示范基地项目”子项目“胜利油田低渗透油藏综合利用示范基地建设”（编号：SLZB-PY-KF[2013]0150）.
关键词
边界层理论
非线性渗流
视渗透率效应
井底压力
低渗透多孔介质
boundary layer theory
nonlinear percolation
apparent permeability effect
bottomhole pressure
low permeability porous media
