聚合物驱提高原油采收率的动态规划方法研究
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摘要
聚合物驱作为一种重要的三次采油技术,因其技术简便,适应性好,是我国工业化应用最成功的三次采油技术。但聚合物价格昂贵,且注入时间长,见效期相对滞后,因此制定一种科学合理的聚合物注入策略,以提高经济效益,是十分必要的。本文基于动态规划方法研究了聚合物驱的注采方案的优化设计。
在聚合物驱动态规划问题中,以原油开采获得的净现值最大为性能指标,以描述聚合物驱替动态过程的渗流力学方程为支配方程,并根据生产实际需要考虑聚合物最大用量约束和聚合物注入浓度的上下限约束。因此聚合物驱动态规划问题可具体描述为一个带有状态和控制不等式约束的聚合物驱分布参数系统动态规划问题。
针对固定终端时间,且带有不等式约束的动态规划问题,提出了一种基于迭代动态规划的数值求解算法,将聚合物驱注采过程从时间和空间两个角度进行离散,利用迭代的方式补偿离散化带来的误差,有效地避免了复杂的伴随方程的求解。计算实例表明了迭代动态规划求解聚合物驱动态规划问题的有效性。
针对终端时间自由,以及优化注入浓度及段塞大小的聚合物驱动态规划问题,提出了一种级长可变的迭代动态规划数值求解算法,能够同时优化控制量和分级长度,给出了最优聚合物驱注入浓度、段塞大小以及终端时间的动态规划算例。
针对聚合物驱油过程中油价变化波动较大的问题,建立了动态规划模型。采用自回归模型对原油价格进行预测,并给出了油价变化下的二次聚合物驱方案优化的迭代动态规划数值求解算法。
对于聚合物驱大规模动态优化问题,采用迭代动态规划计算量较大,为提高计算效率,构建了基于Windows的并行计算平台,以MPI函数的消息传递机制为基础,构建了基于PC机群的迭代动态规划粗粒度主从式并行算法。采用该平台,研究了聚合物驱迭代动态规划算法的并行化问题,计算实例表明并行求解结果与串行一致,而且可以大大提高计算效率。
以胜利油田利21区块的聚合物驱动态规划问题为例,进行实例研究,以验证所提出的迭代动态规划方法的有效性。针对各井相同单段塞方案、各井相同三段塞方案及各井不同三段塞方案,分别采用所提出的迭代动态规划方法求解,获得了净现值、增油量及采油率,并对不同方案的优化结果进行了比较。
Polymer flooding is an important tertiary oil recovery technology. Because of its convenient and wide adaptability, it has become the most successful enhance oil recovery technology in the industrial applications of our country. But the polymer flooding technology also has drawbacks: high polymer price, long inject time, and lagged effective period. So it is necessary to formulate a reasonable polymer flooding inject strategy. In this paper, based on the dynamic programming method, the optimal polymer inject strategy is researched.
In the polymer flooding dynamic programming problem, the maximum of net present value (NPV) is selected as the performance index. The fluid flow equations of polymer flooding act as governing equations. According to the requirement of industrial applications, the maximum polymer usage and bound constraints of polymer injecting concentrations are considered. Thus the researched problem can be described as a dynamic programming problem governed by a polymer flooding distributed parameter system with state and control constrains.
An iterative dynamic programming based numerical algorithm is illustrated to deal with dynamic programming problems with fixed terminal time and inequality constraints. The discretization of the polymer flooding process is done from time and spaces domains. And the error of the discretization is compensated by the iterative approach, thus the solving of the complicated adjoint equations can be avoided. Several numerical examples show the effectiveness of iterative dynamic programming algorithm for solving dynamic programming problems.
An iterative dynamic programming with variable stages based numerical algorithm is presented to deal with dynamic programming problems with free terminal time. The controlled variables and the stage lengths can be optimized at the same time. Several dynamic programming examples for polymer flooding are given, in which polymer injection concentration, slug size and terminal time are optimized simultaneously.
Considering the stochastic process of the oil price, a dynamic programming model is established related to an autoregressive model for predicting the oil price in future. And an iterative dynamic programming based numerical algorithm is given to solve the optimization problem of secondary polymer flooding.
For large-scale dynamic optimization problem of polymer flooding, when iterative dynamic programming algorithm is used, there will be a high computation cost. In order to improve the computing efficiency, a parallel computing platform based on Windows is developed. A coarse-grained master-slave parallel iterative dynamic programming algorithm based on Message Passing Interface (MPI) and Cluster of PC is realized. Using this, the parallelization of iterative dynamic programming algorithm for polymer flooding is completed. Several numerical examples show the effectiveness of parallel algorithm.
To show the effectiveness of the dynamic programming approach, the polymer flooding optimization problem of the Li21 block of the Shengli Oil Field is studied. The dynamic programming based injection strategies are made for one same slug case, three same slugs case, and three different slugs case respectively. Corresponding to each strategy, the net price value, the cumulative oil production and the recovery ratio are also obtained. The comparisons of the results with different strategies are also given.
在聚合物驱动态规划问题中,以原油开采获得的净现值最大为性能指标,以描述聚合物驱替动态过程的渗流力学方程为支配方程,并根据生产实际需要考虑聚合物最大用量约束和聚合物注入浓度的上下限约束。因此聚合物驱动态规划问题可具体描述为一个带有状态和控制不等式约束的聚合物驱分布参数系统动态规划问题。
针对固定终端时间,且带有不等式约束的动态规划问题,提出了一种基于迭代动态规划的数值求解算法,将聚合物驱注采过程从时间和空间两个角度进行离散,利用迭代的方式补偿离散化带来的误差,有效地避免了复杂的伴随方程的求解。计算实例表明了迭代动态规划求解聚合物驱动态规划问题的有效性。
针对终端时间自由,以及优化注入浓度及段塞大小的聚合物驱动态规划问题,提出了一种级长可变的迭代动态规划数值求解算法,能够同时优化控制量和分级长度,给出了最优聚合物驱注入浓度、段塞大小以及终端时间的动态规划算例。
针对聚合物驱油过程中油价变化波动较大的问题,建立了动态规划模型。采用自回归模型对原油价格进行预测,并给出了油价变化下的二次聚合物驱方案优化的迭代动态规划数值求解算法。
对于聚合物驱大规模动态优化问题,采用迭代动态规划计算量较大,为提高计算效率,构建了基于Windows的并行计算平台,以MPI函数的消息传递机制为基础,构建了基于PC机群的迭代动态规划粗粒度主从式并行算法。采用该平台,研究了聚合物驱迭代动态规划算法的并行化问题,计算实例表明并行求解结果与串行一致,而且可以大大提高计算效率。
以胜利油田利21区块的聚合物驱动态规划问题为例,进行实例研究,以验证所提出的迭代动态规划方法的有效性。针对各井相同单段塞方案、各井相同三段塞方案及各井不同三段塞方案,分别采用所提出的迭代动态规划方法求解,获得了净现值、增油量及采油率,并对不同方案的优化结果进行了比较。
Polymer flooding is an important tertiary oil recovery technology. Because of its convenient and wide adaptability, it has become the most successful enhance oil recovery technology in the industrial applications of our country. But the polymer flooding technology also has drawbacks: high polymer price, long inject time, and lagged effective period. So it is necessary to formulate a reasonable polymer flooding inject strategy. In this paper, based on the dynamic programming method, the optimal polymer inject strategy is researched.
In the polymer flooding dynamic programming problem, the maximum of net present value (NPV) is selected as the performance index. The fluid flow equations of polymer flooding act as governing equations. According to the requirement of industrial applications, the maximum polymer usage and bound constraints of polymer injecting concentrations are considered. Thus the researched problem can be described as a dynamic programming problem governed by a polymer flooding distributed parameter system with state and control constrains.
An iterative dynamic programming based numerical algorithm is illustrated to deal with dynamic programming problems with fixed terminal time and inequality constraints. The discretization of the polymer flooding process is done from time and spaces domains. And the error of the discretization is compensated by the iterative approach, thus the solving of the complicated adjoint equations can be avoided. Several numerical examples show the effectiveness of iterative dynamic programming algorithm for solving dynamic programming problems.
An iterative dynamic programming with variable stages based numerical algorithm is presented to deal with dynamic programming problems with free terminal time. The controlled variables and the stage lengths can be optimized at the same time. Several dynamic programming examples for polymer flooding are given, in which polymer injection concentration, slug size and terminal time are optimized simultaneously.
Considering the stochastic process of the oil price, a dynamic programming model is established related to an autoregressive model for predicting the oil price in future. And an iterative dynamic programming based numerical algorithm is given to solve the optimization problem of secondary polymer flooding.
For large-scale dynamic optimization problem of polymer flooding, when iterative dynamic programming algorithm is used, there will be a high computation cost. In order to improve the computing efficiency, a parallel computing platform based on Windows is developed. A coarse-grained master-slave parallel iterative dynamic programming algorithm based on Message Passing Interface (MPI) and Cluster of PC is realized. Using this, the parallelization of iterative dynamic programming algorithm for polymer flooding is completed. Several numerical examples show the effectiveness of parallel algorithm.
To show the effectiveness of the dynamic programming approach, the polymer flooding optimization problem of the Li21 block of the Shengli Oil Field is studied. The dynamic programming based injection strategies are made for one same slug case, three same slugs case, and three different slugs case respectively. Corresponding to each strategy, the net price value, the cumulative oil production and the recovery ratio are also obtained. The comparisons of the results with different strategies are also given.
引文
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