Abstract The paper presents an analytical solution of Buckley-Leverett (BL) equation in gas displacement process including viscous fingering and gravity effects at constant pressure boundary conditions for the inclined stratified heterogeneous reservoir. First, the governing equations related to the change of fluid properties, which govern viscous fingering are discussed. Then the gas flood BL-equation accounting for gravity and miscibility effects for inclined stratified heterogamous reservoir are developed and solved analytically using fractional-flow theory and MOC (method of characteristics). The analytical solution provides the guidance to predict the oil recovery through pressure and saturation distribution at any given time for horizontal, inclined, homogeneous and heterogeneous reservoirs. The results of the analytical solution (total volumetric flux, breakthrough time, front location, saturation and pressure) are compared with finite-difference numerical simulation using CMG simulator. The comparison shows that the analytical solution gives approximately similar results as finite difference numerical simulation. The results of analytical solution show that the total volumetric flux increases with increase of permeability, permeability heterogeneity, injection gas viscosity, mixing parameter and injection pressure, while it decreases with increase in gravity, reservoir inclination and normalized gas formation capacity. The breakthrough time and advance distance are found to be strong function of permeability heterogeneity, injected gas viscosity, mixing parameter and reservoir inclination angle, gravity number, normalized gas formation capacity and injection pressure. Furthermore, with increase of mixing parameter/injection pressure and decrease of permeability heterogeneity results in remarkable improvement of relative permeability and reduction of residual oil saturation led to higher oil displacement efficiency.

中文翻译：

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Buckley-Leverett方程的改进及其对倾斜层状非均质油藏恒压下粘性指法和重力作用气体驱替的解

摘要 本文提出了倾斜层状非均质油藏在恒压边界条件下的粘性指法和重力效应等气体驱替过程中Buckley-Leverett(BL)方程的解析解。首先，讨论了与控制粘性指法的流体性质变化相关的控制方程。然后，使用分数流理论和 MOC（特征方法）开发和解析解决倾斜分层杂配储层的重力和混相效应的气驱 BL 方程。对于水平、倾斜、均质和非均质油藏，解析解提供了在任何给定时间通过压力和饱和度分布预测石油采收率的指导。将解析解的结果（总体积通量、突破时间、前沿位置、饱和度和压力）与使用 CMG 模拟器的有限差分数值模拟进行比较。比较表明解析解给出的结果与有限差分数值模拟近似。解析解结果表明，总体积通量随着渗透率、渗透率非均质性、注入气粘度、混合参数和注入压力的增加而增加，而随着重力、储层倾角和归一化气层容量的增加而减少。发现突破时间和推进距离是渗透率非均质性、注入气黏度、混合参数和储层倾角、重力数、标准化的天然气形成能力和注入压力。此外，随着混合参数/注入压力的增加和渗透率非均质性的降低，相对渗透率显着提高，剩余油饱和度降低，驱油效率提高。