NUMERICAL SIMULATION OF AN IN-SITU COMBUSTION MODEL FORMULATED AS MIXED COMPLEMENTARITY PROBLEM

Abstract. The difficulty of the extraction of medium and heavy oil is its hight viscosity. One form of decreasing it consists in applying the thermal methods as steam injection or in-situ combustion. In the present work one simple model for in-situ combustion is presented. It consists of two nonlinear partial differential equations. As obtaining the analytical solutions for this type of equation is near impossible, it is necessary to make computational simulations. In fact, the solutions for in-situ combustion problem involves shock waves, which increases the difficulty of the numerical simulations. A possible way to avoid this problem is to rewrite the differential equations as one mixed nonlinear complementarity problem. In this work numerical simulations are performed using the finite difference method and a feasible directions algorithm for mixed nonlinear complementarity problem to obtain approximate solutions of the proposed model. The results are compared with ones obtained by using the Newton’s method that was used in other references. Keywords: In situ combustion, Conservation laws, Mixed complementarity problem.