Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods
Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods
复制标题
通过多点、模拟和混合方法对故障进行精确建模
作者：
H. Nilsen;J. R. Natvig;Knut
在行业标准流量模拟器中，对故障进行建模的主要方式是在底层两点离散化中引入所谓的传输率乘数。虽然这种方法在许多实际情况下提供了足够的精度，但两点离散化仅对K正交网格是一致的，并且可能对严重偏离K正交的网格引入显著的离散化误差。这种网格畸变误差可以通过对偏离断层进行横向或垂直阶梯式处理来避免，但代价是在几何断层描述中出现误差。换句话说，建模者可以选择通过使断层适应几乎K正交的网格来产生（几何）误差，或者如果网格适应偏离断层，则由于缺乏K正交性而引入离散化误差。
我们提出了一种基于混合或模拟离散化的求解器故障精确描述方法，其中也包括MPFA-O方法。其核心思想是将故障表示为内部边界，并直接计算故障传输率，而不是使用乘数来修改与电网相关的传输率。由此产生的方法是地质驱动的和一致的单元与平面表面，从而避免了网格误差固有的两点法。我们还提出了一种方法来转换故障传输率乘数故障传输。这使得我们的方法很容易适用于包含故障乘数的油藏模型。
The predominant way of modeling faults in industry-standard flow simulators is to introduce so-called transmissibility multipliers in the underlying two-point discretization. Although this approach provides adequate accuracy in many practical cases, two-point discretizations are only consistent for K-orthogonal grids and may introduce significant discretization errors for grids that severely depart from being K-orthogonal. Such grid-distortion errors can be avoided by lateral or vertical stair-stepping of deviated faults at the expense of errors in the geometrical fault description. In other words, modelers have the choice of either making (geometrical) errors by adapting faults to a grid that is almost K-orthogonal, or introducing discretization errors because of the lack of K-orthogonality if the grid is adapted to deviated faults.
We propose a method for accurate description of faults in solvers based on a hybridized mixed or mimetic discretization, which also includes the MPFA-O method. The key idea is to represent faults as internal boundaries and calculate fault transmissibilities directly instead of using multipliers to modify grid-dependent transmissibilities. The resulting method is geology-driven and consistent for cells with planar surfaces and thereby avoids the grid errors inherent in the two-point method. We also propose a method to translate fault transmissibility multipliers into fault transmissibilities. This makes our method readily applicable to reservoir models that contain fault multipliers.