Discrete Fracture Model based on Multiple Interacting Continua Proximity Function for Unconventional Reservoirs

Shale formations presents multi-scale heterogeneities, including stimulated and non-stimulated natural fractures. Besides, a hydraulic stimulation is required in order to increase production from unconventional low permeability reservoirs. However, this kind of operation increases the complexity of the fracture network and modeling a complex discrete fracture network (DFN) become crucial for simulating production from unconventional reservoirs. This paper propose a methodology, taking into account various size of fractures with different locations and orientations in a low permeability reservoir, in order to suggest a unique model as simple as possible. A typical discrete Fracture Model (DFM) rely on unstructured grids to conform the fracture geometry and location. This kind of model discretizes all types of fractures leading to a complicated and often non tractable numerical system to solve. To overcome these limitations, hierarchical methods such as Embedded Discrete Fracture Models (EDFM) are usually used to deal with this multi-scales problem. However, the matrix-fracture interaction is not properly handled with the EDFM due to the very low matrix permeability and the large matrix grid cells. In this paper, we will present a DFM based on Multiple INteracting Continua (MINC) approach to improve the EDFM. This approach rely on a triple-porosity model: matrix media, large hydraulic/propped fractures, and unpropped stimulated/non-stimulated natural fractures. Large propped fractures are explicitly discretized, natural fractures are homogenized, and their connections are based on a proximity function obtained with an integral representation. The connections between the matrix and fractures are computed with the MINC method based on a proximity function using a stochastic process. The implementation of the MINC method improves the flow exchange between the matrix and fracture media. Thus, the matrix grid cell is subdivided according to a MINC proximity function based on the distance from all sort of fractures, by using randomly sampled points. The proposed approach is particularly useful for multi-phase flow simulations in a low permeability unconventional reservoir such as a tight-oil reservoir. Several numerical examples will be presented to illustrate the accuracy of this improved DFM for a single-phase flow case and a multi-phase flow case with gas liberation from a tight-oil formation.