Commonly, dual-porosity and dual-permeability models are employed to simulate naturally fractured reservoirs (NFR). Recently, dual-porosity models have been extended to include more than one transfer function per simulation grid block. These so-called multi-rate dual-porosity models (MRDP) hence allow for more than one set of rock and fluid parameters to be present within one grid cell, which captures the natural variability in fracture, matrix, and fluid properties more accurately. Discrete fracture and matrix (DFM) based simulators have recently emerged as an alternative in NFR simulation. They use unstructured meshes to model large-scale fractures, fracture corridors, and faults explicitly but cannot represent small-scale fractures because field-simulations would become intractable, even with parallelisation.

In this paper we demonstrate a combined MRDP-DFM approach for the first time. We demonstrate how the MRDP-DFM approach can be discretised using unstructured (tetrahedral) meshes. This facilitates the partition of the geological model into regions where (1) large-scale heterogeneities such are fracture corridors are modelled by the DFM method with appropriately upscaled single-porosity properties and (2) the flow through small-scale fractures is modelled using MRDP method with a distribution of transfer function and effective fracture permeability tensors coming from classical Discrete Fracture Network models.

We use a suite of proof-of-concept simulations to demonstrate that our MRDP-DFM approach yields more realistic forecasts of oil recovery due to gravity drainage and imbibition in fractured reservoirs because it allows us to represent the multi-scale heterogeneities inherent to NFRs more realistically. It hence predicts recovery processes more accurately compared to standard dual-porosity models and more efficiently compared to standard DFM models.

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