In this study, imbibition process is investigated in heterogeneous hydrocarbon reservoir using the non-classical (effective viscous finger) model equations proposed by Luo et al. (SPE Res. Eval. Engineering, 20(4), 1–16 2017). Counter-current spontaneous imbibition is analyzed in different heterogeneous porous media. The heterogeneity is mainly due to the spatial variation of the porosity and absolute permeability. The proposed mathematical model is solved considering the Implicit Pressure Explicit Saturation Scheme (IMPES) via finite difference method (FDM). Effect of the viscosity ratio, growth rate exponent of the fingering function, and the maximum fingering cross section on the normalized water saturation are analyzed. The present model is verified in the limiting case of classical model equations in homogeneous medium. It is noted that rate and extent of the counter-current imbibition are significantly controlled by the distribution of heterogeneous parameters like porosity and absolute permeability of the reservoir.

中文翻译：

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空间非均质油藏自吸过程的非经典流模拟

在这项研究中，利用罗（Luo）等人提出的非经典（有效粘性指）模型方程研究了非均质油气藏的吸水过程。（SPE Res。Eval。Engineering，20（4），2017年1月16日）。在不同的异质多孔介质中分析逆流自吸。非均质性主要是由于孔隙度和绝对渗透率的空间变化引起的。考虑到隐式压力显式饱和方案（IMPES），通过有限差分法（FDM）解决了所提出的数学模型。分析了粘度比，指法函数的增长率指数和最大指法截面对归一化水饱和度的影响。在均质介质中经典模型方程的极限情况下，对本模型进行了验证。