New Transfer Functions for Simulation of Naturally Fractured Reservoirs with Dual Porosity Models

Abstract

Abstract This paper discusses new techniques for the modeling and simulation of naturally fractured reservoirs with dual porosity models. Most of the existing dual porosity models idealize matrix-fracture interaction by assuming orthogonal fracture systems (parallelepiped matrix blocks) and pseudo-steady state flow. More importantly, a direct generalization of single-phase flow equations is used to model multi-phase flow, which can lead to significant inaccuracies in multiphase flow behavior predictions. In this work, many of these existing limitations are removed in order to arrive at a transfer function more representative of real reservoirs. Firstly, combining the differential form of the single-phase transfer function with analytical solutions of the pressure diffusion equation, an analytical form for a shape factor for transient pressure diffusion is derived to corroborate its time dependence. Further, a pseudo-steady shape factor for rhombic fracture systems is also derived and its effect on matrix-fracture mass transfer demonstrated. Finally, a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block (i.e. non-orthogonal fractures) is proposed. This technique also accounts for both transient and pseudo-steady state pressure behavior. The results were verified against fine-grid single porosity models and were found to be in excellent agreement. Secondly, it is shown that the current form of the transfer function used in reservoir simulators does not fully account for the main mechanisms governing multiphase flow. A complete definition of the differential form of the transfer function for two-phase flow is derived and combined with the governing equations for pressure and saturation diffusion to arrive at a modified form of the transfer function for two-phase flow. The new transfer function accurately takes into account pressure diffusion (fluid expansion) and saturation diffusion (imbibition), which are the two main mechanisms driving multiphase matrix-fracture mass transfer. New shape factors for saturation diffusion are defined. It is shown that the prediction of wetting phase imbibition using the current form of the transfer function can be quite inaccurate, which might have significant consequences from the perspective of reservoir management. Fine grid single porosity models are used to verify the validity of the new transfer function. The results from single block dual porosity models and the corresponding single porosity fine grid models were in good agreement.