Modeling fluid flow around horizontal wellbores

Abstract

Modeling fluid flow around horizontal wellbores with conventional reservoir simulators is somewhat inefficient due to the fact that the radial flow patterns found in the vicinity of a horizontal wellbore must be simulated with rectangular coordinate gridblocks. In this research, we present an efficient model for horizontal well simulation by incorporating radial hybrid gridblocks to simulate the approximately radial fluid flow around the wellbore and introduce the concept of spherical hybrid gridblocks to model the fluid flow around the end of the well. The spherical hybrid gridblocks consist of hemispheres corresponding to each radii in the cylindrical coordinate region which are intersected by planes that allow coupling to the reservoir region gridblocks. Transmissibilities for the irregularly shaped spherical gridblocks are calculated by the use of the integrated finite difference method. Although this technique was developed to simulate horizontal wells, it could also be used to model partially penetrating vertical wells. The linearized fluid flow equations are solved by the method of domain decomposition, which is convenient in that it allowed the use of existing band solvers to invert the associated matrix problem. Two problems from the literature were chosen to demonstrate the effectiveness of the model. The first problem is a one-phase, constant rate pressure drawdown test for which an analytical solution is available. The second problem is a water cresting problem where the results for comparison were obtained from a commercial simulator using a grid that minimized numerical dispersion.