A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract

A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36Cl−) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90Sr++) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

A New Modeling Framework for Multi-Scale Simulation of Hydraulic Fracturing and Production from Unconventional Reservoirs

“…A second set of simulations makes use of a dual continuum model that accounts separately for "bulk water porosity", where the porewater is assumed electrically neutral, and "diffuse layer porosity", where the pore water has a net positive charge that balances the fixed negative charge of the clays in the shale (Figure 18B). This approach, captured in the code CrunchClay [9,10], combines a Nernst-Planck treatment of diffusion in the pore water with the dual porosity approach in which cations accumulate in the diffuse layer while anions are suppressed. The dissolution and precipitation of iron hydroxide (goethite) results in a focused clogging of the pore space at about 0.15 mm from the low concentration end of the 1 mm shale sample, resulting in a cessation of diffusion at about 10 days.…”

“…At the reservoirscale, the framework is built upon integration of two existing high-performance simulators for reservoir-scale behavior: the GEOS code for hydromechanical evolution during stimulation [4] and the TOUGH+ code for multi-phase flow and chemical evolution during production [5]. At the micro-scale, we deploy sophisticated imaging and testing methods (e.g., [6][7][8]), combined with reactive transport simulations [9,10], to develop a fundamental understanding of the mechanical and chemical processes within the propped fractures and across the fracture-rock interfaces. Constitutive upscaling relationships built upon this fundamental understanding are then incorporated in the reservoir-scale simulators.…”

Integrating Process‐Based Reactive Transport Modeling and Machine Learning for Electrokinetic Remediation of Contaminated Groundwater

“…The flux of charged species in a porous medium can be described with the Nernst‐Planck equation (Alt‐Epping et al., 2015; Rasouli et al., 2015; Rolle et al., 2018; Steefel & Tournassat, 2020; Tournassat & Steefel, 2019; Wu et al., 2020), which accounts for the contribution of diffusion, migration, and electroosmosis: where is the accessible porosity, is the pore diffusion/dispersion coefficient in which is the aqueous diffusion coefficient of the species , is the tortuosity, the molar concentration, is the concentration gradient, is the charge, is the Faraday constant, is the gas constant, is the temperature, is the electric potential gradient, and is the average velocity resulting from electroosmotic flow, calculated as …”

An Integrated Multiscale Modeling Framework for Unconventional Stimulation and Production (Final Report)

“…At the reservoir-scale, the framework is built upon integration of two existing high-performance simulators for reservoir-scale behavior: the GEOS code for hydromechanical evolution during stimulation (Settgast et al, 2017) and the TOUGH+ code for multi-phase flow and chemical evolution during production (Moridis & Pruess, 2014). At the micro-scale, we deploy sophisticated imaging and testing methods (Voltolini and Ajo-Franklin, 2020;Hakala et al, 2017;Li et al, 2019), combined with reactive transport simulations (Tournassat & Steefel, 2019;Steefel & Tournassat, 2021) to develop a fundamental understanding of the mechanical and chemical processes within the propped fractures and across the fracture-rock interfaces. Constitutive upscaling relationships built upon this fundamental understanding are then incorporated in the reservoir-scale simulators.…”

“…CrunchClay was used for the simulation of the diffusion experiment, representing an evolving branch of the code CrunchTope/CrunchFlow (Steefel et al, 2015) that considers electrostatic effects associated on transport (Tournassat & Steefel, 2019a;Tournassat & Steefel, 2019b;Tournassat et al, 2020;Steefel & Tournassat, 2021). A flexible representation of the pore space can be provided using a dual continuum approach (Tournassat & Steefel, 2019a).…”