Multiscale Simulation of Polymer Flooding with Shear Effects
Multiscale Simulation of Polymer Flooding with Shear Effects
复制标题
剪切效应聚合物驱的多尺度模拟
作者：
Sindre T. Hilden;O. Møyner;Knut;K. Bao
多尺度方法已被开发作为一种替代方法来放大和加速油藏模拟。所有这些方法的关键思想是构造一组延拓算子，其在与保持岩石物理性质的细网格中的单元相关联的未知数和用于动态模拟的粗网格上的未知数之间进行映射。在这里，我们扩展这样一种方法-多尺度限制平滑基（MsRSB）方法-聚合物驱包括剪切变稀（和增厚）的影响，这使得高度非线性的流体模型，是具有挑战性的模拟。为此，我们首先制定了一个顺序隐式求解程序的聚合物模型与非牛顿流变学。通过处理隐式速度依赖性的粘度在一个内部的迭代循环，我们得到了一个配方，似乎是更强大和稳定的比标准的全隐式方法。然后，我们使用通用的代数多尺度框架来制定一个高效且通用的多尺度求解器。MsRSB方法的独特之处在于如何构造延拓算子。通过使用限制平滑的方式在平滑聚合多重网格方法，得到了一个强大的和灵活的方法，使粗分区和延长运营商，以半自动的方式构建，即使是高度复杂的地理细胞模型与高媒体对比度和非结构化的细胞连接。通过适当地设置迭代公差，得到的迭代多尺度求解器可以被设置为计算质量守恒近似的顺序或全隐式的解决方案，以任意精度，因此可以用来交易的效率精度。我们首先验证了顺序的解决方案的程序和多尺度求解器对一个成熟的商业模拟器上的测试用例具有简单的几何形状，高度非均匀的介质特性，和强烈的非线性流体行为。接下来，顺序精细尺度和多尺度求解器上的合成模拟模型的浅海油藏进行了验证。在这里，计算时间主要是由压力解决方案，和5-8倍的加速时，观察到的迭代多尺度方法取代精细尺度压力求解器。我们还证明了该方法的灵活性，将其应用到模型与非结构化的多面体细胞，适应良好的位置和故障。
Multiscale methods have been developed as an alternative approach to upscaling and to accelerate reservoir simulation. The key idea of all these methods is to construct a set of prolongation operators that map between unknowns associated with cells in a fine grid holding petrophysical properties and unknowns on a coarser grid used for dynamic simulation. Herein, we extend one such method—the multiscale restricted-smoothed basis (MsRSB) method—to polymer flooding including shear-thinning (and thickening) effects, which gives highly nonlinear fluid models that are challenging to simulate. To this end, we first formulate a sequentially implicit solution procedure for polymer models with non-Newtonian rheology. By treating the implicit velocity dependence of the viscosities in an inner iteration loop, we obtain a formulation that appears to be more robust and stable than the standard fully-implicit approach. We then use a general algebraic multiscale framework to formulate an efficient and versatile multiscale solver. The unique feature of the MsRSB method is how the prolongation operators are constructed. By using restricted smoothing much in the same way as in smoothed aggregation multigrid methods, one gets a robust and flexible method that enables coarse partitions and prolongation operators to be constructed in an semi-automated manner even for highly complex geo-cellular models with high media contrasts and unstructured cell connections. By setting iterative tolerances appropriately, the resulting iterative multiscale solver can be set to compute mass-conservative approximations to the sequential or fully-implicit solution to arbitrary accuracy and hence be used to trade accuracy for efficiency. We first verify the sequential solution procedure and multiscale solver against a well-established commercial simulator on a test case with simple geometry, highly heterogeneous media properties, and strongly nonlinear fluid behavior. Next, the sequential fine-scale and multiscale solvers are validated on a synthetic simulation model of a shallow-marine reservoir. Here, the computational time is dominated by the pressure solves, and 5–8 times speedup is observed when replacing the fine-scale pressure solver by the iterative multiscale method. We also demonstrate the flexibility of the method by applying it to model with unstructured polyhedral cells that adapt to well positions and faults.