Abstract

The aim of this study is to develop a numerical method providing the possibility of computing nonisothermal compositional flows faster than traditional finite-volume methods. A plane problem of oil, water, and gas flows is considered. The oil phase is represented by two components: the light fraction and the heavy fraction, which, similarly to water, can be gasified. The study takes into account both the nonlinearity of the oil flow law and the temperature dependence of the parameters of this law. This formulation of the problem is relevant for the simulation of the development of high-viscosity oilfields. To reduce the computational complexity of the problem, the streamline method with splitting with respect to physical processes is used. It separates the convective transport directed along the flow’s propagation from processes related to the heat conduction and gravity, which directions do not coincide with the convective flow. A distinctive feature of the proposed method is the joint solution of the pressure, energy-balance, and mass-component equations both on streamlines and on the initial grid. This feature allows us to correctly calculate oil flows with a complex temperature-dependent rheology. Numerical solutions of the system of flow equations on a two-dimensional grid and on streamlines are obtained by the IMPEC method. For the presented streamline method, we propose an algorithm accounting for the thermal conductivity and transition criteria between calculations on streamlines and on a two-dimensional grid. The developed software is verified by comparison with the analytical solutions and with the results of calculations by finite-volume methods on five-point and nine-point finite-difference stencils.

中文翻译：

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粘塑性油成分非等温流动的流线模拟

摘要

这项研究的目的是开发一种数值方法，它提供了比传统的有限体积方法更快地计算非等温成分流的可能性。考虑了油，水和气体流动的平面问题。油相由两个组分表示：轻质馏分和重质馏分，类似于水，可以被气化。该研究考虑了油流定律的非线性和该定律参数的温度依赖性。该问题的提法与模拟高粘度油田的开发有关。为了降低问题的计算复杂度，使用了针对物理过程进行拆分的流线型方法。它将沿着流的传播定向的对流输运与与热传导和重力有关的过程分开，这些过程的方向与对流不重合。该方法的一个显着特征是流线和初始网格上压力，能量平衡和质量分量方程的联合解。此功能使我们能够根据复杂的温度相关流变性正确计算油流量。通过IMPEC方法获得了二维网格和流线上的流动方程系统的数值解。对于提出的流线方法，我们提出了一种算法，该算法考虑了在流线和二维网格上的计算之间的热导率和过渡标准。