Identification of Permeability Field under Three-Phase Filtration Conditions Using Spline Surfaces with Unknown Number and Location of Interpolation Nodes

The problem of determining the permeability fields of a layered three-phase reservoir in the form of spline surfaces is considered. Measurements of the liquid flow rate and bottom hole pressure at the wells that penetrate the reservoir are used as initial information. The coordinates of the interpolation nodes of the spline surfaces and the permeability values in them are considered unknown. An algorithm is proposed to solve the problem based on methods for solving inverse coefficient problems. The location of the interpolation nodes is determined using the gradient of the objective function. The algorithm’s performance is tested on model identification tasks.