论文标题
将加速的固定点算法应用于流体动力良好的裂纹耦合
Application of accelerated fixed-point algorithms to hydrodynamic well-fracture coupling
论文作者
论文摘要
井，液压裂缝和储层之间动态相互作用的耦合模拟在石油储层工程的某些地区具有重要意义。过去几年中，整个系统的这些部分的数值模型之间的耦合问题已经解决了几种方法。在本工作中研究了允许将问题提出为定点问题的可能的方法之一。加速了Anderson和Aitken的定点算法，应用于耦合问题。将加速算法与代表性测试案例集的传统PICARD迭代进行了比较，其中包括耦合的问题。测量相对性能，并测试算法的鲁棒性。在某些情况下，在简单的PICARD迭代失败的情况下，加速算法在某些情况下可以提高（最多两个数量级）的性能（最多两个数量级）的性能。基于分析，我们根据问题的预期复杂性，为选择特定算法和可调放松参数提供建议。
The coupled simulations of dynamic interactions between the well, hydraulic fractures and reservoir have significant importance in some areas of petroleum reservoir engineering. Several approaches to the problem of coupling between the numerical models of these parts of the full system have been developed in the industry in past years. One of the possible approaches allowing formulation of the problem as a fixed-point problem is studied in the present work. Accelerated Anderson's and Aitken's fixed-point algorithms are applied to the coupling problem. Accelerated algorithms are compared with traditional Picard iterations on the representative set of test cases including ones remarkably problematic for coupling. Relative performance is measured, and the robustness of the algorithms is tested. Accelerated algorithms enable a significant (up to two orders of magnitude) performance boost in some cases and convergent solutions in the cases where simple Picard iterations fail. Based on the analysis, we provide recommendations for the choice of the particular algorithm and tunable relaxation parameter depending on anticipated complexity of the problem.
