Simulation of Transient Matrix-Fracture Transfers of Compressible Fluids

Abstract

The dual-medium approach is convenient for simulating flows within two interacting continua such as fractured reservoirs, because it greatly simplifies the apparent complexity of the flow problem while offering a conceptual representation of flows within and between the two continua that helps the understanding of flow responses. Considerable work has been achieved during the last decades to model the coupling term of such models, that is, matrix-fracture transfers. Whereas pseudo-steady-state transfers taking place at late times can be fairly well predicted, the simulation of transient, i.e. early-time, transfers still encounters difficulties due to intrinsically complex transfer mechanisms that the resolution of diffusion equations entails. Those difficulties are emphasized for tight porous media where transient flow behaviour persists over a durable period of time, for compressible fluids that increase inaccuracy of linear approximations of transfers, and also because of the multi-directionality of transfers. Starting from analytical solutions of diffusivity equations, the present paper proposes a methodology to account for transient effects and for non-linearities in matrix-fracture transfer formulas of dual-porosity simulators in order that they can predict the production of unconventional low-permeability hydrocarbon reservoirs. Validation of these formulas for the production of very tight fractured media is shown at the matrix block scale and at the scale of a stimulated reservoir volume.