A new mathematical flow model is derived for characterizing the multiphase fluid flow phenomenon in naturally fractured reservoirs. This model treats the reservoir as a double porosity medium consisting of a heterogeneous, isotropic primary rock matrix and an anisotropic, heterogeneous fracture. The statistical distribution in space and orientation of the fracture is manifest in terms of the fracture permeability tensor. The model permits flow through the rock matrix and the fractures to be described simultaneously. The fluid interaction terms coupling flow between the rock matrix and fractures, the gravity effects, the capillary forces and the fracture velocity of fluids are all taken into consideration.

The simulator is run and tested with data from a field example. The results show that the phase pressures respond to each other more spontaneously in the fractures than they do to the phase pressures in the rock matrix, and vice versa. Furthermore, the velocity of the fluids in the fractures have negligible effect on the results. The results suggest that the conventional way of assuming that fluids first flow from the rock matrix into the fractures and then flow through the fractures toward the wellbore may not be an adequate description of the flow phenomenon in a naturally fractured reservoir.

According to this model, the numerical simulation program is developed in FORTRAN IV computer code using the finite difference approximation technique, the fully implicit approach, and the Point Successive Over-Relaxation method. Extension of the simulator capability to incorporate the Monte Carlo technique for randomly generating fracture locations is also discussed.