论齐成伟幂比方程作为致密油藏渗流本构方程

摘要

岩心渗流测试显示致密油藏渗流是低速非线性渗流,而描写低速非线性渗流本构关系的数学模型已有很多.对已有低速非线性渗流数学模型中引用率较高的姜瑞忠方程、黄延章方程和最新出现的幂比方程进行对比分析,发现:幂比方程为整体可微函数方程,优于两分段可微函数方程形式的姜瑞忠方程和黄延章方程;幂比方程令启动压力梯度似有实无,巧妙地调和了存在启动压力梯度和不存在启动压力梯度两种对立观点,使致密油藏渗流研究不再纠缠于有无启动压力梯度,而姜瑞忠方程和黄延章方程中存在备受争议的启动压力梯度项;幂比方程首次从岩心渗流测试所得数据点的平滑线上拐点的存在,揭示出中速近线性渗流的存在并成功对其描述,而姜瑞忠方程和黄延章方程不具备描述中速近线性渗流的能力.因此,齐成伟幂比方程可作为致密油藏渗流本构方程.%To realize efficient development of tight reservoirs, mechanics of fluids in tight reservoirs should be established. In order to establish it, constitutive equation for fluid flowing through tight reservoirs must be available first. Core flow test suggests that fluid flowing through tight reservoirs belongs to low-velocity nonlinear flow in porous media, and there exist many mathematical models which describe the constitutive relation of low-velocity nonlinear flow in porous media, so constitutive equation for fluid flowing through tight reservoirs should be selected properly among all. Compare frequently referenced Ruizhong Jiang's equation and Yanzhang Huang's equation with newly appeared Power-Quotient Equation among those mathematical models, discovering that: Power-Quotient Equationis global differentiable functional equation, which is simpler than two-piecewise differentiable functional equations such as Ruizhong Jiang's equation and Yanzhang Huang's equation; Power-Quotient Equation makes starting pressure gradient seem to exist but actually not, and reconciles two contrasting views about whether starting pressure gradient exist or not, then leads the research of fluid flowing through tight reservoirs will not intertwine in whether starting pressure gradient exist or not any more, however there exists controversial starting pressure gradient term in Ruizhong Jiang's equation and Yanzhang Huang's equation; Power-Quotient Equation first reveals that near-linear flow at medium velocities in porous media exists and describes it successfully according to the existent inflection point on a smooth curve of the data points from core flow test, while Ruizhong Jiang's equation and Yanzhang Huang's equation failed to describe the near-linear flow at medium velocities in porous media. Thus, Chengwei Qi's Power-Quotient Equation can be used as constitutive equation for fluid flowing through tight reservoirs.