Finite element modelling of multi-phase flow through deformable fractured porous media

• Main Author: Ghafouri, H. R.
• Published: Swansea University 1997
• Subjects: 620.106
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637047

Based on the theory of 'Double-Porosity', three-phase fluid flow in a fractured porous media has been formulated using continuity and equilibrium equations where displacement is also a primary unknown. Unlike previous models used for fractured media, the pressure of each fluid phase within the fracture network and porous rock has been considered to be coupled with the deformation of porous media. Also coupling between the fracture network and the porous rock is carried out using 'Transfer Function' or 'Leakage Term'. The derived equations are then discretised using 'Finite Element Method' where the displacements as well as pressure of fluids within matrix and fracture are primary unknowns. The resulting set of equations, is an implicit, fully coupled formulation which is capable of modelling three phase (Oil, Gas and Water) flow in a fractured reservoir where the deformation and consequent surface subsidence is of particular interest i.e. a case frequently encountered in petroleum engineering. In its extreme case, the presented formulation turns to the conventional one-phase models for heterogeneous porous media and by further simplification, the governing equations for ordinary single porosity models could be obtained. A computer code based on the mathematical model is developed and validated. Important aspects of the developed code, based on the double porosity theory, are presented together with several example problems. The model is also employed to solve a field scale example where the results are compared to those of ten other uncoupled models. As a genuine application of the present model, it is employed to solve the real field problem of the subsidence at the Ekofisk oil field in the Norwegian sector of the North Sea. The impact of various parameters of the model are verified by conducting sensitivity analyses. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.