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首页> 外文期刊>Computational Geosciences >Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity
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Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity

机译：多孔介质中多相流的多尺度有限体积配方：重力作用下可压缩三相流的黑油配方

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摘要

Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model). Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation). The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homogeneous elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities. The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/ sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of nonlinear compressible multiphase flow in strongly heterogeneous formations.
机译：最实用的油藏模拟研究是使用所谓的黑油模型进行的，其中使用溶解度和地层体积因子表示相态。我们扩展了多尺度有限体积（MSFV）方法，以在存在重力和毛细作用力（即黑油模型）的情况下处理非线性不混溶的三相可压缩流。与MSFV框架一致，使用顺序隐式算法分别对流和传输进行区别对待。使用多尺度算子拆分策略来解决整体质量平衡（即压力方程）。黑油压力方程是非线性和抛物线的，它分解为三个部分。第一个是齐次椭圆方程，其原始MSFV方法用于计算对偶基函数和粗尺度透射率。第二个方程说明重力和毛细作用。第三个方程说明了质量积累和源/汇（井）。利用椭圆部分的基本功能，可以组装粗尺度算子。重力/毛细管压力部分由椭圆形部分和校正项组成，该校正项使用重力驱动的局部问题的解来计算。一种特定的解决方案代表堆积和井。重建的细尺度压力用于计算细尺度相通量，然后将其用于求解非线性饱和方程。为此，在原始粗网格上使用Schwarz迭代方案。使用非均质地层中非线性可压缩多相流的具有挑战性的黑油实例演示了该框架。

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