低渗透油藏数值模拟中内边界条件的处理

低渗透油藏已经成为油田开发的重要对象,研究考虑非达西效应的数值模拟方法将有助于提高该类油藏数值模拟的准确性和可信度.低渗透油藏的数值模拟对内边界条件的处理应当考虑非达西渗流.由于井底附近压力梯度较大,流态可以认为是拟线性流动,根据拟稳态渗流理论,考虑流体在低渗透油藏流动过程中受到启动压力梯度的影响,基于三维油水两相油藏数值模拟数学方程,推导了定井底流压、定产油量和定产液量等条件下的内边界条件,并通过全隐式差分格式建立了低渗透油藏数值模拟数值模型,采用预处理共轭梯度法进行了求解.结果表明内边界条件中考虑启动压力梯度与否对井底流压影响较大,在定产量条件下,井底流压随启动压力梯度的增大而降低.

Inner boundary conditions of numerical simulation for low-permeability reservoirs

In this paper based on the pseudo stable seepage theory and mathematical model for numerical simulation of water-oil two phase reservoir, and considering the influence of start-up pressure gradient, a inner boundary conditions is derived, in which three cases were considered: fixed flow pressure, fixed oil production rate and fixed liquid production rate. Then, by means of full implicit finite difference scheme, the corresponding numerical model is established and solved by pretreatment conjugate gradient method. The simulation results show that, in inner boundary conditions, the start-up pressure gradient obviously affect flowing pressure of wells. In case of fixed oil production rate, with the increase of start-up pressure gradient, the flowing pressure becomes lower.