Upscaling of Discrete Fracture Characterization to Dual-Porosity Models Using an Advanced Transfer Function
Authors: Raslan Mohammed Samir , Gupta Anuj , Ates Harun , Jessen Kristian 
Published: March 2023

Abstract
Embedded discrete fracture models (EDFM's) are commonly used to study fluid flow in unconventional reservoirs. The EDFM, however, requires extensive pre-processing of non-neighboring connections. More importantly, it becomes further demanding when grid refinement is required to accurately model mass transfer between the fractures and the tight matrix rock, primarily to resolve transients in the matrix. This renders the EDFM an expensive option to model large-scale fractured reservoirs where the number of fracture segments can be substantial.
In this paper, an upscaling procedure is proposed to construct a dual-porosity model (DPM) from a discrete fracture characterization. The implicit representation of the fractures provides for an improved simulation efficiency. While the DPM's are often perceived as simple sugar-cube representations of complex fracture networks, the upscaling technique presented here, demonstrates the capability of DPM's in providing accurate and efficient solutions for a broad range of complex fractured systems.
The potential of the DPM is unlocked via application of a flexible matrix/fracture transfer function, that is similar in form to the generalized Vermeulen transfer function (gVer) introduced by Zhang et al. (2022). Unlike the traditional class of transfer functions, first introduced by Warren and Root (1963), the gVer transfer function incorporates a time-dependent correction factor to resolve the transient within the matrix without the need for sub-gridding. The use of an advanced DPM becomes key to our proposed upscaling workflow which also includes the evaluation of effective rock properties and a unique set of matrix/fracture interaction parameters.
We first examine several test cases of ultra-tight fractured systems and establish the need for advanced modeling techniques to accurately capture the matrix transient, as observed from single-porosity reference models (SPM's). In the context of EDFM, this can be accomplished by refining the mesh for the matrix grid at an increased computational cost, while the use of gVer transfer function to describe the mass transfer in the DPM is demonstrated to accomplish the same at a marginal computational cost. We then apply the approach to solve more complex problems including models with fracture networks, exhibiting arbitrary fracture orientations and geometries, in a heterogeneous nano-darcy rock. Calculations for such examples are performed using EDFM, and an equivalent upscaled DPM. We furthermore demonstrate the versatility of our approach by refining the DPM in regions of higher spatial variation to capture the details of the fractured rock as dictated by the original EDFM representation.
The proposed upscaling procedure overcomes the commonly assumed limitation of the classical DP approach and allows for modeling of unconventional reservoirs without losing the realism of a discrete fracture characterization. It is demonstrated that the proposed technique reproduces the correct response with significantly fewer grid-blocks and hence enables reduction of computational cost of advanced optimization studies in unconventional reservoirs.