响应面法和BFGS算法在试井分析中的应用

Application of response surface method and BFGS algorithm in well test analysis

试井分析是利用关井所测的井底压力随时间变化的资料来分析地层和井筒参数,是一个典型的反问题.基于响应面法提出了一种新的参数自动反求的数值试井解释方法.选定不确定参数及其范围,确定试算算例,然后利用拟合方法得到多项式逼近函数,即构造响应面模型.利用响应面模型构建计算值与实际观测值偏差的目标函数,再利用BFGS算法以及拉丁超立方抽样搜索目标函数的最小值,得到不确定参数值.算例表明该方法能有效地对井底压力以及压力导数进行拟合,因而具有很好的应用前景.

Well test analysis is a typical inverse problem that analyzes the formation and wellbore parameters using the time-varying data of the bottom hole pressure measured during shut-in. Based on the response surface method, a new method for automatically evaluating parameters was presented to solve the numerical well test interpretation. Select the uncertain parameters and their scope, the experimental examples were determined, and then the polynomial approximation function was obtained by matching method, that is, constructing the response surface model. Using the response surface model, the objective function of the deviation between the calculated value and the actual observation value was constructed. The minimum value of the objective function was obtained by using the BFGS algorithm and the Latin hypercube sampling to obtain the uncertain parameter value. The numerical examples show that the method can effectively match the bottom hole pressure and the pressure derivative, and thus has a good potential for application.