Amao, A: MATHEMATICAL MODEL FOR DARCY FORCHHEIMER FLOW

This work reviewed several scenario where non-Darcyor non-linearity in flow exists in the reservoir.Itshowed the inadequacies inherent in Darcy's law as amodeling equation for flow in porous media.Laboratory experiments were conducted to determinethe criteria for and the onset of non-linear flow incore samples.It was discovered that non-Darcy flowwill occur in a porous media as long as the pressuregradients in the porous media is sufficient. The maindetermining property for non-linearity is thepermeability of the porous media.A mathematical equation was developed to modelnon-Darcy flow, following standard scientificprocedures. The mathematical model developed was usedto simulate reservoir behavior while consideringDarcy andnon-Darcy flow in the reservoir. COMSOL Multiphysics,a software used for solving partial differentialequations (PDE) was used for the simulations. Theresults were presented, discussed and analyzed forseveral reservoir geometries.The results of this work is useful for reservoirengineers and production engineers who need tooptimize flow rate and well performance. It will alsobe applicable in well diagnosis for remedial actionor work over.