摘要
聚合物驱是一种重要的提高原油采收率的技术,它具有成本高、风险大的特点,所以研究其最优控制问题进而确定最优开发方案具有显著地现实意义。由于聚合物驱模型是由一些偏微分方程所描述的,在求解其最优控制的过程中会遇到巨大的计算量,所以研究其并行计算方法是十分必要的。本文使用SWIFT法求解了聚合物驱最优控制问题,获取了聚合物驱最优注入策略。同时,本文研究并实现了基于SWIFT法的聚合物驱最优控制的并行求解。本论文的主要内容如下:
本文介绍了求解偏微分方程的有限差分法以及并行计算的相关基础知识,同时基于实验室的现有条件,构建了一个小规模机群结构的并行计算平台,并且通过一个线性代数方程组并行求解的实例对该平台进行了测试。
本文研究了基于SWIFT法的最优控制问题求解。SWIFT法是非线性规划中一种用于求解约束优化问题的直接搜索法。它通过罚函数法的思想来处理约束条件,然后使用非线性规划中的单纯形法求解无约束优化问题。在求解过程中,本文首先使用参数最优化的方法对最优控制问题进行了转化,这种方法选用时间域内各个时间节点上的控制变量作为控制向量中的参数,其他时刻的控制变量可由它们的插值得到。只要确定了最优化控制向量,便可以得到最优控制。于是问题便转化为了求解最优控制参数的非线性规划问题。通过热传导最优控制问题的求解实例验证了SWIFT法的有效性。
结合聚合物驱实验模型,本文研究了基于SWIFT法的聚合物驱最优控制问题的求解。在最优控制模型中,性能指标为聚合物驱所获得的利润,支配方程为描述聚合物驱机理的渗流力学方程,同时选取聚合物注入浓度和注入时间作为最优控制变量,通常情况下它们会受到约束条件的限制。本文使用SWIFT法分别获得了单段塞、双段塞和三段塞情形下的聚合物驱最优注入策略,优化结果表明SWIFT法对求解该问题是有效的。
本文研究了基于SWIFT法的聚合物驱最优控制问题的并行求解,分别从算法结构的局部并行和聚合物驱模型的数值模拟两个方面进行了并行化处理。在数值模拟并行化过程中,使用基于界面修正以及移动界面的并行差分方法求解了二阶偏微分方程。最后通过比较串行求解与并行求解的结果,验证了并行计算下的最优化结果的有效性,同时获得了不错的计算性能。
Polymer flooding is an important technique for enhancing oil recovery. Because the polymer is expensive and the risk of polymer flooding is high, it is of great significance to study the optimal control problem (OCP) in order to make the optimal plan. The polymer flooding model mainly contains some partial differential equations. When solving the OCP, we should achieve huge computation work. So it is necessary to study the parallelization of optimization methods. In this thesis, the optimal injection strategies are obtained by using sequential weight increasing factor technique (SWIFT). Also, the parallelization of solving the OCPs of polymer flooding based on SWIFT is implemented. The main works of this thesis are described as follows.
In this thesis, the finite difference method which is applied to solve partial differential equations is introduced. Besides, the basic knowledge of parallel computing is demonstrated. A small-scale parallel computing platform is built based on PCs cluster and tested by using an example of parallel solving linear algebraic equations.
The solution of OCPs based on SWIFT is researched in this thesis. SWIFT is a direct search method in nonlinear programming (NLP), which is used to solve the constrained optimization problem. It is based on simplex method and penalty function method. SWIFT uses penalty function method to transform a constrained optimization problem to an unconstrained optimization problem which is solved by using simplex method. When using SWIFT to solve an OCP, it is necessary to transform the OCP into a NLP. The transformation can be achieved by parameterized optimization method. This method divides the time range into several intervals by some time nodes. The values of control variables at these nodes are chosen as parameters of the control vector. The rest values of control variables can be decided by interpolation. Once the optimal control vector is determined, the optimal control can be gained. So the NLP which is required to get the optimal control vector is established. The results of the OCPs for heat conduction show the effectivity of SWIFT.
Based on the core experiment model, the solution of OCP for polymer flooding based on SWIFT is researched. In the optimal control model, the profit of polymer flooding is chosen as the performance index. The governing equations are the flow equations which describe the mechanism of polymer flooding. The injection concentration and the injection time are selected as the control variables, which are always limited in some certain ranges. The optimal injection strategies for simple slug, double slugs and three slugs are obtained by using SWIFT. The results validate that SWIFT is an effective method to solve the OCPs for polymer flooding.
The parallel computing of the OCPs for polymer flooding based on SWIFT is studied. The parallelization is implemented by partial parallel for algorithm structure of SWIFT and parallelization of numerical simulation of polymer flooding model. In the latter, the parallel difference schemes based on interface correction and moving interface are applied to solve partial differential equation of second order. The comparisons between the serial computing results and the parallel computing results prove the validity of parallelization.
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