In this paper, a comprehensive numerical simulation model is introduced to resolve the problem of non-Darcy flow in porous media. As represented by this model, both pressure gradient and velocity profile predicted are based on the two viscous terms of Darcy and Brinkman, Forchheimer's inertial term and Navier-Stoke's convective term. At the point of departure from the Darcian domain to the non-Darcian domain it has been found that this model predicted the dimensionless term " Be" to be zero which agrees with Forchheimers model prediction. At 5% deviation from the Darcian flow the proposed model predicts " Be" to be 0.0756 as compared to 0.0526 predicted by Forchheimers model. The difference is due to higher flow velocity prediction by the proposed comprehensive model.
The proposed model is expected to have wide applications in the field of reservoir simulation and fluid flow in porous media in both gas and oil reservoirs. Replacing the traditional model used to predict pressure gradient at any point of space and time by the proposed model would resolve the problem of inaccurate predictions associated with non-Darcy flow. This model predicts the correct pressure gradient and flow velocity regardless of the source of deviation. The model is continuous in Darcian regime as well as non-Darcian regime.
The right expression of the non-Darcy flow behaviour in porous media remains an unsolved problem. The way that many researchers and specialists look to the solution of the problem had reflected their belief and understanding of the phenomena of Non-Darcy behaviour. Some believe that the inertial term presented in Forchheimer's equation is enough to correct the extra pressure drop caused by high spatial velocity, others use Brinkman's viscous term in addition to Darcy's term to describe a solution in such circumstances.
Numerical simulation of petroleum reservoirs is aimed at predicting production so that optional development plans for the reservoir can be envisaged and the suitable production strategy can be selected. The more accurately the models represent the physics of the reservoir, the more useful the prediction made from the models can be. Most developments in the numerical reservoir simulation have revolved around accurate modelling of fluid properties and interactions and accurate representation of the storage and transmissibility properties of the porous rock material.