油藏中渗流与水平井筒内流动的耦合数学模型

Mathematical Model Coupling Seepage in the Reservoir with Flow in the Horizontal Wellbore

通过引入势的理论研究了油气两相稳定渗流问题.在描述无界地层三维稳态势基础上,结合水平井上射孔孔眼在无界地层中产生的势分布,建立了把油层中的渗流与水平井筒内的流动耦合的数学模型,该模型可以同时描述油藏-水平井筒内油、气两相流和原油单相流时的情况,给出了求解的方法.并且结合实例研究了水平井水平段的流量分布和压力分布.结果表明:水平井水平段的流量分布成明显的"凹"型曲线,其压力分布变化较为平缓.该模型为水平井的产能预测及水平井长度的优化等提供了理论依据.

The two-phase stable flow in porous media was analyzed using potential theory. Based on the description of infinite stratum three-dimensional stable potential and potential distribution of perforation borehole in horizontal wellbore, a mathematical model coupling the flow in porous media with flow in horizontal wellbore was established. The model can describe oil-gas two-phase and single-phase flow in reservoir-horizontal wellbore simultaneously. The solution process of the model was also presented, and with an example the distribution of the flux and pressure were analysed. The result shows that the flux distribution curve of the horizontal well is concave and the change of the pressure is small. The model provides a basis for horizontal wells production forecast and length optimization.