自动识别油藏边界水侵量微分方程反演算法

Inversion algorithm of differential equation for automatically identifying water influx of reservoir boundary

针对水驱油数值模拟,提出一种基于微分方程反演的自动历史拟合算法,解决了单相微可压缩流体渗流中油藏边界水侵量自动识别问题。利用生产井的动态观测资料识别油藏边界上的水侵量,在数学上称为边界控制反问题。基于微分方程反演理论,将其转化为一个非线性优化问题,利用共轭梯度法求解。共轭梯度法是通过引入相应的伴随问题和敏感性问题,分别确定每次迭代的搜索方向和搜索步长,解决了时空域中一般反演方法的不稳定性、收敛速度慢和依赖于初值等一系列问题。理论模型和实际资料检验表明,该方法不仅丰富了微分方程反演理论,而且具有生产实用价值。

An automatic history matching method for identifying boundary water influx in a reservoir containing a single-phase fluid of incompressibility was developed on the basis of numerical simulation of water-displacing oil. This method is mathematically called boundary control inverse problem to identify water fluxes in a reservoir by using the dynamic observation data of production wells. Based on the differential equation inversion theory, this problem can be transformed to a nonlinear optimization problem that can be solved by conjugate gradient method （CGM）. The search direction and step-length at each step were determined by corresponding adjoint problem and sensitivity problem, respectively. Some problems such as instability, slow convergence and dependence on initial value for general inversion methods in time-space domain can be avoided. The numerical results of theoretical model and practical application show that this method not only richens the differential equation inversion theory but also has applicable value in practice.