Numerical Analysis of the Effects of Apparent-Permeability Modeling and Secondary-Fracture Distribution for Hydraulic-Fractured Shale-Gas Production Analysis
Authors: Zhong Chuanyao , Leung Juliana Y. 
Published: May 2020

Summary
Complex flow mechanisms, such as Knudsen diffusion, are encountered in the shale matrix because of the presence of nanopores. Numerous apparent-permeability models have been proposed to capture the ensuing non-Darcy flow behavior. However, these models are not readily available in most commercial reservoir simulators, and ignoring these mechanisms can potentially underestimate the overall matrix conductivity. This work implements an explicit coupling strategy for integrating a pressure-dependent apparent-permeability model in reservoir simulation. The numerical models are subsequently used to study the effects of apparent-permeability modeling and natural-fracture distribution on gas production and water loss during flowback. The effects of multiphase-flow functions on fluid retention are also assessed.
A set of 3D reservoir models are constructed using field data obtained from the Horn River shale-gas reservoir. First, stochastic 3D discrete-fracture-network (DFN) models are scaled up into equivalent continuum dual-porosity/dual-permeability models. An apparent-permeability (Kapp) model accounting for contributions of slip flow, Knudsen diffusion, and surface pore roughness is applied at each gridblock. A novel coupling scheme is formulated to facilitate the updating of Kapp after a certain specified time interval, capturing the pressure dependency of the Kapp. The sensitivity of the updating frequency is analyzed.
The results reveal that incorporating these additional flow mechanisms by means of the apparent-permeability formulation could potentially increase the overall gas-production prediction by up to 11%, depending on the average pore radius, reservoir pressure, and several other matrix or fluid properties. The implications of Kapp modeling in water-loss mechanisms are further examined through a set of sensitivity analyses, where the effects of multiphase-flow functions and DFN distributions are systematically investigated. The following interesting findings are observed:
Ignoring Kapp modeling could overestimate water recovery. Fracturing-fluid propagation and long-term water recovery are strongly affected by the secondary-fracture intensity; increase in secondary-fracture intensity would enhance water loss during flowback. Gas production is highly affected by the amount of water in the near-well region. In a gas/water system, compressibility of the in-situ fluids renders the effects of countercurrent imbibition and water retention to be more complex from those observed in similar water/oil systems.
This work offers a novel, yet practical, scheme for representing the pressure-dependent matrix apparent permeability in the flow simulation of shale reservoirs. The proposed method captures the non-Darcy flow behavior caused by the complex transport mechanisms occurring in nanosized pores. Most importantly, this coupling procedure can be implemented in existing commercial reservoir-simulation packages. The results have revealed a few interesting insights regarding the potential implications in fracturing design and estimation of stimulated reservoir volume.