Development of a Local Grid-Refinement Technique for Accurate Representation of Cavity-Completed Wells in Reservoir Simulators

Abstract

Summary In this paper the development of a three-dimensional, single-, and two-phase fluid flow model to study flow performances of cavity-completed wells is presented. A static local grid refinement (LGR) is embedded into the model in order to adequately capture the flow behavior around cavity completions using a reasonable number of grid cells. The model adopts an approach that is significantly different from the current practice in which cavity-completed wells are incorporated into computations by assigning large wellbore radii and/or large negative skin values to a conventional wellbore model. The model utilizes the residual equation rather than a wellbore equation to determine the flow into cavity-completed wells. Cavity-completed wells are described as a collection of fine rectangular grid blocks. This representation is referred to as the cavity approach. The constructed fine grid lines are terminated at the coarse/fine grid block interfaces by implementing the LGR technique developed. The technique subdivides selected coarse grid blocks into fine rectangular grid blocks in all three dimensions that are known as window blocks. The flow equations generated for window and coarse grid cells are then solved simultaneously by using the preconditioned biconjugate gradient stabilized iterative method. First, a radial-cylindrical wellbore is approximated using the cavity representation. The model results from single phase, slightly compressible fluid flow simulation with the cavity approach are, then, compared against the analytical solutions. In these comparisons, very good matches are obtained for both flow rate and sandface pressure specifications at the wellbore. The model is further extended to single phase, compressible, and two-phase fluid flow conditions in both conventional and coalbed reservoirs. The model results are, in this case, compared with the existing numerical models that utilize Peaceman's wellbore model. Again, close agreement in flow response is obtained for a series of comparisons. Finally, the cavity approach is tested by modeling flow performances of irregularly shaped, cavity-completed wells in conventional and coalbed reservoirs. During the creation of cavity completions in coal seams, it is hypothesized that fracture networks in certain directions are generated around cavities. The effects of fractures are usually incorporated into a simulation study by modifying the permeability values around the wellbore. The cavity approach presented in this paper provides not only a better approximation to the shape of the cavity but also a better representation of the altered permeability values around the cavity since fine grid cells are already in place around cavity completions.