Grid design and numerical modeling of multiphase flow in complex reservoirs using orthogonal collocation schemes

Abstract

An advanced grid system design was developed to capture accurately the effects of geometrically complex features such as geological features (faults, pinch outs and inclined beddings) and well-related phenomenon (multilateral wells of general orientation) in triangular coordinates. Modeling these effects can have significant impact on the accuracy of the simulation and prediction of reservoir performance as well as reservoir fluid flow using conventional grid designs. The finite difference method provides additional difficulty in capturing geological features in typical reservoir flow and grid model simulators. Hence, the orthogonal collocation method was used for simulating multiphase reservoir flow equations in triangular curvilinear coordinates [ (r), (), (z)] of domain [0,1] that were derived from Cartesian coordinates (x, y, z). This was to accommodate general three-dimensional deviated wells and complex reservoir geometry for multiphase flow of hydrocarbon in complex reservoir formations. Based on preliminary field data obtained from multinational oil and gas operator in Nigeria, the proposed model was used to predict saturation, production and petroleum productivity with time and distance in a MATLAB environment. The simulated plots revealed that pressure is parabolic at the center of the reservoir with coordinates (r) = 0.4257 , reflecting the impact of geological features in the pressure and production flow performance. Keywords Multiphase flow • Complex reservoir systems • Orthogonal grids • Triangular coordinates List of symbols A k,l Constant generated in the orthogonal collocatioñ D ij Characteristic component dispersivity, cm 2 /s ds Elementary displacement, m dt Change in time, h g Gravitational vector i Component j Phasẽ K Tensor absolute permeability, Darcy k a Absolute permeability, md k rj Relative permeability (j = oil, water) K rm Mean permeability, Darcy K i Permeability in i-direction (i = x, y, z) , Darcy n p Number of phases in porous medium