Numerical Identification of Hydrodynamic Parameters of a Reservoir under Elastic-Water-Drive Development Mode

The process of oil reservoir development in the elastic-water-drive mode is considered. It is assumed that the displacement of oil by the edge water occurs completely and a clear boundary between two liquids is formed in the reservoir, which moves according to a previously unknown law. Within the framework of a one-dimensional model of the elastic-water-drive development regime, the task is set to identify the main hydrodynamic parameters of the reservoir, i.e. the pressure at the interface between liquids, the pressure distribution in the reservoir and the position of the interface between liquids, only on the basis of information obtained from the gallery of production wells. The problem set belongs to the class of boundary inverse problems. By applying the methods of front straightening and difference approximation, the problem is reduced to solving a system of difference equations. A special representation is proposed to solve the system of difference equations, having previously written it down as a variational problem with local regularization. As a result, an explicit formula is obtained for determining the approximate value of the pressure at the interface of liquids and recurrent formulas for determining the distribution of pressure and the position of the interface of liquids in the reservoir at each time layer. Based on the proposed computational algorithm, numerical experiments were carried out for a model oil reservoir.