The heavy-oil flow in porous media is characterized by non-Darcy law with variable threshold pressure gradient (TPG) due to the large fluid viscosity. However, available analytical and numerical models hardly consider this effect, which can lead to erroneous results. This paper is aimed at presenting an innovative approach and establishing a numerical simulator to analyze the heavy-oil flow behavior with waterflooding. The apparent viscosity of the oil phase and flow correction coefficient characterized by the TPG were applied to describe the viscosity anomaly of heavy oil. Considering the formation heterogeneity, the TPG was processed into a variable related to mobility and the directionality. The discretization and linearization of the mathematical model were conducted to establish a fully implicit numerical model; the TPG value on each grid node was obtained through oil phase mobility interpolation, and then, the Jacobi matrix was reassembled and calculated to solve pressure and saturation equations. The corresponding simulator was thus developed. The pre-/postprocessing module of the simulator is connected to ECLIPSE; then, an efficient algorithm is introduced to realize a fast solution. Results show that considering the TPG will not only reduce the waterflooding area but also reduce the oil displacement efficiency because of aggravating the nonpiston phenomenon and interlayer conflict. The numerical simulation study on the TPG of heavy oil provides theoretical and technical support for the rational development and adjustment of water-driven heavy oil.

中文翻译：

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基于变阈值压力梯度的注水稠油数值模拟研究

多孔介质中的稠油流动具有非达西定律，由于流体粘度较大，因此具有可变的阈值压力梯度（TPG）。然而，可用的分析和数值模型几乎没有考虑这种影响，这可能会导致错误的结果。本文旨在提出一种创新方法并建立一个数值模拟器来分析注水时稠油的流动行为。应用油相表观黏度和TPG表征的流动修正系数来描述稠油的黏度异常。考虑到地层的非均质性，TPG 被处理为与流动性和方向性相关的变量。对数学模型进行离散化和线性化，建立全隐式数值模型；通过油相流度插值得到各网格节点上的TPG值，然后重新组合计算雅可比矩阵，求解压力和饱和度方程。因此开发了相应的模拟器。模拟器的前/后处理模块连接到ECLIPSE；然后，引入了一种有效的算法来实现快速解决方案。结果表明，考虑TPG不仅会减少水驱面积，还会因加剧非活塞现象和层间冲突而降低驱油效率。稠油TPG数值模拟研究为水驱稠油合理开发调整提供了理论和技术支持。雅可比矩阵被重新组装和计算以求解压力和饱和度方程。因此开发了相应的模拟器。模拟器的前/后处理模块连接到ECLIPSE；然后，引入了一种有效的算法来实现快速解决方案。结果表明，考虑TPG不仅会减少水驱面积，还会因加剧非活塞现象和层间冲突而降低驱油效率。稠油TPG数值模拟研究为水驱稠油合理开发调整提供了理论和技术支持。雅可比矩阵被重新组装和计算以求解压力和饱和度方程。因此开发了相应的模拟器。模拟器的前/后处理模块连接到ECLIPSE；然后，引入了一种有效的算法来实现快速解决方案。结果表明，考虑TPG不仅会减少水驱面积，还会因加剧非活塞现象和层间冲突而降低驱油效率。稠油TPG数值模拟研究为水驱稠油合理开发调整提供了理论和技术支持。引入了一种有效的算法来实现快速解决方案。结果表明，考虑TPG不仅会减少水驱面积，还会因加剧非活塞现象和层间冲突而降低驱油效率。稠油TPG数值模拟研究为水驱稠油合理开发调整提供了理论和技术支持。引入了一种有效的算法来实现快速解决方案。结果表明，考虑TPG不仅会减少水驱面积，还会因加剧非活塞现象和层间冲突而降低驱油效率。稠油TPG数值模拟研究为水驱稠油合理开发调整提供了理论和技术支持。