Authors : Ildar B. Badriev, Viktor V. Banderov and Morsel T. Singatullin
Abstract: The numerical simulation of the steady filtration process for highly viscous incompressible fluid following the nonlinear law of filtration in the presence of wells. It is assumed that the function determining the filtration law (dependence of filtration rate on the pressure gradient) is equal to zero if the module of the pressure gradient does not exceed a predetermined value the maximum gradient (the set of such points in the field of filtration where the flow does not occur is a stagnation zone) is continuous one, not decreasing and has exponential growth at infinity. The generalized statement of this problem is formulated in the form of an operator equation with a monotone operator in Banach space. The theorem of solvability is proved. In order to solve the operator equation a Two-Layer Iterative Method is proposed. Every step of the iterative process is reduced to the solution of the boundary issue for the Laplace equation. The convergence of the iteration process is investigated. This method was implemented numerically. The dependence of the boundaries on dead zones was investigated (sets in the field of filtration where the pressure gradient unit is less than the maximum one, the flow is absent) of the well rate. The results of numerical experiments performed for model issues the field of filtration, the number of wells, their location and rate varied the effectiveness of the proposed Iterative Method was confirmed. The proposed method can be used for the solution of problems concerning rational mining of highly viscous hydrocarbons.
Ildar B. Badriev, Viktor V. Banderov and Morsel T. Singatullin, 2015. Numerical Solution of Non-Linear Filtration Issues for High Viscous Fluids at the Presence of Wells. Research Journal of Applied Sciences, 10: 343-346.