A Three-Phase Non-Darcy Flow Formulation in Reservoir Simulation

Abstract

Abstract Non-Darcy flow correction is necessary in matching gas well deliverability test data as documented in the literature. There were also several research reports discussing the non-Darcy flow behavior observed in oil flow cases. However, the non-Darcy flow data from oil wells have not been rigorously analyzed in the past. This work extends the Forchheimer formulation for a three-phase system. We derived an equation to relate the non-Darcy flow coefficient of the cell-to-cell flow term in the reservoir mass balance equations to the rate-dependent skin coefficient in the well equation. This development is applicable to a 3-Phase system and allowed us to obtain the non-Darcy flow coefficient values from oil flow tests. Those values from oil well data were far greater than the values predicted by correlations derived from gas flow test data. Reservoir simulators used a so-called non-Darcy flow resistance factor to account for the non-Darcy flow effect in calculating flux terms. We derived a simple expression for the derivatives of the non-Darcy flow resistance factor. This would facilitate the implementation of the fully implicit formulation in modeling non-Darcy flow problems. For gas flows, if there was an excessive pressure drop from well-block cell center to well bore, the well equation would over-predict well deliverability. A new and simple correction factor was derived to improve gas flow prediction. Reservoir simulation runs were made using this new formulation to match field test data from both gas and oil wells.