History Matching for Reservoirs of Complex Structure

Any adequate reservoir model must include permeability parameters of blocks and faults and parameters that define the reservoir interaction with its outer environment. Our proposal is to determine outer contour properties of the reservoir using a procedure of History Matching. We consider both permeabilities of blocks and faults and transparency coefficients for various segments of the outer contour as variable parameters. To solve History Matching problems, we developed two C++ software programs: a reservoir simulator and an inverse solver. The simulator is based on the finite element method and the method of direct integration with an automatically-selected step in the time domain. The inverse solver is based on a number of methods of non-linear programming (gradient methods, the methods of deformed polygon and coordinate descent). We obtained three different History Matching solutions for a model representation of a complex reservoir (531360 nodes, 31 producers, 29 injectors). In the process of solving the History Matching problem, 150 variable parameters defined lateral and vertical permeability of 5 reservoir layers, 21 parameters defined permeability of 5 faults, and 16 parameters described transparency coefficients of the reservoir outer contour. Outer-contour transparency coefficients found closely match the reference model for all solutions.