Streamline simulation of counter-current imbibition in naturally fractured reservoirs

Describing fluid transport in naturally fractured reservoirs entails additional challenge because of the complicated physics arising from matrix–fracture interactions. In this paper, the streamline-based simulation is generalized to describe fluid transport in naturally fractured reservoirs through a dual-media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. The transfer functions that describe fluid exchange between the fracture and matrix system can be implemented easily within the framework of the current single-porosity streamline models. In particular, the streamline time of flight concept is utilized to develop a general dual-porosity, dual-permeability system of equations for water injection in naturally fractured reservoirs. The saturations equations are solved using an operator splitting approach that involves ‘convection’ along streamline followed ‘matrix–fracture’ exchange calculations on the grid. The proposed formulation reduces to the commonly used dual-porosity model when the flow in the matrix is considered negligible. For modeling matrix–fracture interactions, two different transfer functions are examined: an empirical transfer function (ETF) and a conventional transfer function (CTF). The ETF allows for analytical solution of the saturation equation for dual porosity systems and is used to validate numerical implementation. Results obtained using the CTF are compared with a commercial finite-difference simulator (ECLIPSE) for waterflooding in five-spot and nine-spot patterns. The streamline approach shows close agreement in terms of recovery histories and saturation profiles with a marked reduction in numerical dispersion and grid orientation effects. Finally, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications.