Abstract
Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity) idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN) models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy’s law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.
Highlights
Fluid flow in naturally fractured nanoporous reservoirs have been primarily modeled using approaches that treat the flow domain as continuum and the flow parameters as represented by their statistical averages
Several conceptual models have been developed for Naturally Fractured Reservoirs (NFR): (i) a single medium with enhanced permeability due to natural fractures, (ii) dual-porosity medium where tight rock matrix feeds into conductive natural fractures, (iii) matrix with a discrete fracture network where each fracture is individually characterized, and (iv) fractal media where properties are scaled with distance to some reference point in the domain
A modified flux law incorporating spatial and temporal heterogeneity of the velocity field has been coupled with the classic mass conservation equation to model anomalous diffusion in fractured nanoporous media
Summary
Fluid flow in naturally fractured nanoporous reservoirs have been primarily modeled using approaches that treat the flow domain as continuum and the flow parameters as represented by their statistical averages. From a fundamental fluid mechanics perspective, flow in nanoporous unconventional reservoirs takes place on an assembly of short and long flow paths — compared to the total medium — in addition to the heterogeneous distribution of these channels. Under these conditions, continuum mechanics, which is a major assumption of Darcy’s law, is inapplicable (Fig. 2).
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