基于最优化原理的热流体循环数学模型求解方法  

A numerical solution method of mathematical model for circulation flow of hot fluid based on optimization principle

作　　者：杨元亮 王辉[2] 张建[2] 李清方[2] 庞会中[2] 王增林[3] 汪俊义[4] 

机构地区：[1]中石化胜利油田新春采油厂,山东东营257000 [2]胜利油田胜利勘察设计研究院,山东东营257026 [3]中石化胜利油田分公司,山东东营257000 [4]辽河油田欢喜岭采油厂,辽宁盘锦124114

出　　处：《西安石油大学学报（自然科学版）》2013年第5期75-79,2,共5页Journal of Xi’an Shiyou University（Natural Science Edition）

基　　金：中石化股份有限公司科技攻关项目"胜利西部新区污水资源化配套技术研究";中石化胜利油田重点科技攻关项目"胜利油田西部浅层稠油热采地面工程配套技术研究"

摘　　要：井筒热流体循环采油工艺的数学模型是一种具有半隐式边界条件的非线性常微分方程组边值问题,采用打靶法或共轭函数法求解时会出现数值不稳定和结果失真,基于二分原理的隐式条件显示化方法计算时又较为费时,应用有限差分方程迭代求解时虽然节省时间但精度较低.为提高运算速度和改善结果精度,依据方程组的边界条件提出一种以待求初值为设计变量,由结果误差构造目标函数并求其最小值的直接最优化算法.通过几个典型算例对本文方法和文献已有解法进行了考核,分析比较了不同方法的计算精度和CPU运算时间,结果表明本文方法是高效准确的.The mathematical model for hot fluid circulation oil recovery technology is a non-linear differential equation with semiimplicit boundary conditions. Solving it by using multi-point shooting method or conjugate function method will lead to numerical instability and result distortion,solving it by using the display of implicit conditions based on binary division principle will consume a lot of time,and solving it by using finite difference equation iteration saves time but the precision is low. For improving calculation speed and accuracy,an optimization solving algorithm is put forward. In the algorithm,the initial values of the variables are as design variables,objective function is established by result error and its minimum value is solved. This method is evaluated by several typical cases. Its accuracy and CPU operation time are compared with those of existing methods,and it is shown that the method is more accurate and efficient.

关 键 词：热流体循环 非线性常微分方程组 半隐式边界条件 最优化算法 

分 类 号：TE345[石油与天然气工程—油气田开发工程]