考虑启动压力和二次梯度的应力敏感油藏稳定渗流模型

Stable flow models for stress-sensitive reservoir taking into consideration the start-up pressure gradient and the quadratic pressure gradient

根据质量守恒原理,推导应力敏感油藏中考虑启动压力梯度和二次压力梯度非线性渗流偏微分方程,并通过变量代换,将渗流方程线性化,求得模型在不同外边界条件下解析解.结果表明:只考虑启动压力梯度、二次梯度项、应力敏感因素以及三者均不考虑所得产能公式都是文中公式的特例.

This paper derives the partial differential equation of stress-sensitive reservoir for the nonlinear flow with the start-up pressure gradient and the quadratic pressure gradient in detail based on the mass conservation principle.And then linearizing the flow equation with variable substitution,the analytic solution can be obtained under different external boundary conditions.The obtained productivity formula for only taking into consideration the start-up pressure gradient,the quadratic pressure gradient,the stress-sensitivity,or none of them,are even exceptional case of the formula(19).