## Investigation of the petrophysical properties of unconventional rocks using multiscale network modeling

##### Abstract

Unconventional reservoirs, specifically carbonates, tight gas sandstone and shale gas formations, provide significant potential for the growing world energy demand. However, the positive prospects of these reserves are hampered by considerable uncertainty in estimating their production. Reliable petrophysical models of these media can help reduce the uncertainty in their development. Pore-network models are cost-efficient representations of a porous medium’s pore structure that allow prediction of its macroscopic properties. In this effort, the topology and fluid physics of pores from various scales are integrated into a single-entity three-dimensional (3D) unstructured pore-network model. We start with the simplest shale matrix gas flow model that incorporates pores from nanometer and micrometer scales, but has a connectivity resembling conventional rocks. We quantify the apparent permeability of these networks with relevant, pore size-dependent physical models applied to both scales and compare the results with the continuum no slip boundary condition assumption. The discrepancy between the two can run over several orders of magnitude and grows with the fraction of nanopores and the width of the overall pore size distribution. We next attempt to create more realistic network models, closer to the true topology of the studied unconventional rocks. Workflows for integration of nanometer and micrometer pore structures are then developed for deterministic, geologically informed, process-based and image-based approaches in various unconventional scenarios. We perform a systematic forward analysis of the applicability of tracer breakthrough profiles (TBPs) in revealing the pore structure of tight gas sandstone and carbonate formations. The following features are modeled via 3D multiscale networks: microporosity within dissolved grains and pore-filling clay, cementation in the absence and presence of microporosity (each classified into uniform, pore-preferred, and throat-preferred modes), layering, and vug and microcrack inclusion. A priori knowledge of the extent and location of each process is assumed known. In general, significant qualitative perturbation of the TBPs is observed for uniform and throat-preferred cementation. Layering parallel to the fluid flow direction has a considerable impact on TBPs whereas layering perpendicular to flow does not. Microcrack orientation has a minor effect in perturbing TBPs. In most scenarios TBPs show negligible qualitative sensitivity to the fraction of micropores present. The exception is the case when macropores and pore-filling micropores have equivalent flux contributions. A quantitative parameterization of sensitivity is not conducted; an example of such is measuring the perturbations in pore-volumes associated with the breakthrough profile peaks, has not been conducted. Similar to tracer breakthrough profiles in the context of characterizing heterogeneous porous media in core scale, nitrogen sorption hysteresis is investigated for characterizing pore structure of mudrocks. Three network types are introduced to represent their multiscale pore topology; specifically: regular (Type 1), series (Type 2) and parallel (Type 3). We conclude that, in appropriate size ranges, sorption hysteresis can distinguish the three types whereas permeability hysteresis can only separate parallel from series and regular. Furthermore, the simulations show that sorption hysteresis is sensitive to compaction/cementation (closing of throats) in all network types, whereas permeability hysteresis is sensitive to the diagenesis in parallel networks only. A quantitative parameterization of the sensitivity, such as measuring the area enclosed by the hysteresis curve, was not conducted. Molecular diffusion is an important mechanism for hydrocarbon transport within matrix as well as between matrix pores and hydraulic fractures in unconventional shale production. The diffusion coefficient is also an essential parameter in two-dimensional (2D) nuclear magnetic resonance (NMR) map interpretations. However, molecular diffusion in the micro- and nanometer scale pore networks of unconventional shale rocks remain poorly understood. We attempt to link the restricted diffusion coefficient to pore-scale characteristics of shale gas media. A random walk algorithm with discrete time steps is implemented to investigate the effects of pore-throat ratio (the ratio of pore-body radius to pore-throat radius), length ratio (the ratio of throat length to pore radius), pore shape and topology. It is concluded that, at an equal surface-to-volume ratio, diffusion coefficient increases in pores with higher angularity. The effects of pore-throat radius ratio and length ratio are explicitly modeled in 3D structured regular lattices. Results indicate that, up to pore-throat radius ratios of 5, restricted diffusion is considerable in lattices with zero length throats. Furthermore, restricted diffusion decreases with the increase in length ratio. To reduce computational costs, a statistical method is developed to render simulating the effects of connectivity and pore size distribution on 3D unstructured multiscale networks feasible. Finally, we perform a preliminary assessment of the fidelity of the multiscale process-based and image-based approaches in a case study conducted on the Wilcox tight gas sandstone. A novel workflow that combines the multiscale process-based network model with petrographic analysis is developed. This methodology utilizes petrographic information (grain size distribution and sorting, cement type and thickness, microporosity types and fractions, burial sequence) to enable the prediction of the flow properties of the medium in several burial stages throughout the paragenesis of the Wilcox formation. Given the 100 -1000 times scale difference between micropores and macropores and the resultant computational costs, an upscaling scheme is proposed for the microporous clusters in the process-based algorithm. The upscaling presently does not work for the image-based modeling because of the irregularity of microporous regions. We observe discrepancy between the simulated and experimental mercury injection capillary pressure curve and use it to recommend future improvements to the workflow. In this case study, micropores are crucial in contributing to the flow path; therefore, their surface chemistry as well as physical features such as surface roughness must be quantified and taken into account to make reliable predictions of the rock flow properties.

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