关键词: 水驱油藏, 数值模拟, 水侵量, 自动历史拟合算法, 微分方程反演, 共轭梯度法

Abstract: 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.

Key words: water-flooding reservoir, numerical simulation, water influx, automatic history matching method, differential equation inversion, conjugate gradient method