Horizontal well simulation with local grid refinement

Abstract

Horizontal wells are more and more important because they offer solutions to the problem of producing oil and gas in resevoir where conventional technology may fail. Some examples are thin reservoirs, reservoirs with gas or water coning problems, reservoirs with natural fractures, reservoirs with low permeability and high anisotropy, and servoirs with poor sweep efficiency. The specific requirement of simulating horizontal wells is to have more detail (fine gridblocks) in the vicinity of horizontal wellbores of regiions of interest. Though it can be done by simulators with conventional gridding technique, unnecessary gridblocks must be introduced because the technique requires the gridlines to be extended all the way to external boundaries of the reservoir. This problem can be avoided by local grid refinement is not banded. A special mathematical technique, called domain decomposition must be introduced to solve this non-banded matrix. In this research, a fully implicit, three-dimensional, three-phase black-oil reservoir simulator has been developed. It can be used for simulating both vertical and horizontal wells. The cartesian local grid refinement has been developed and incorporated into the simulator. Three domain decomposition techniques for reservoir level domain decomposition have been proposed. These techniques are (1) solution extrapolation; (2) Dirichlet-Neuman boundary conditions and (3) preconditioned generalized conjugate gradient approach. The simulator developed for this research has been validated by numerous test cases. The simulation results indicate that the simulator is highly competitive with most commercial simulators in terms of accuracy, speed and efficiency. The simulation results also indicate that: (1) Solution extrapolation improves the initial estimate of Newton-Raphson method. It not only reduces number of Newton iterations and number of timesteps, but number of domain iterations as well. (2) Dirichlet-Neuman boundary conditions reduce the overall material balance by at least two orders of magnitude compared with Dirichlet-Dirichlet boundary conditions. (3) The preconditioned generalized conjugate gradient approach reduces number of domain iterations in most cases. However, it is sensitive to the difficulty of the simulated problem.