Hybrid multiscale simulation of a mixing-controlled reaction

Abstract

a b s t r a c tContinuum-scale models, which employ a porous medium conceptualization to represent properties and processes averaged over a large number of solid grains and pore spaces, are widely used to study subsurface flow and reactive transport. Recently, pore-scale models, which explicitly resolve individual soil grains and pores, have been developed to more accurately model and study pore-scale phenomena, such as mineral precipitation and dissolution reactions, microbially-mediated surface reactions, and other complex processes. However, these highly-resolved models are prohibitively expensive for modeling domains of sizes relevant to practical problems. To broaden the utility of pore-scale models for larger domains, we developed a hybrid multiscale model that initially simulates the full domain at the continuum scale and applies a pore-scale model only to areas of high reactivity. Since the location and number of pore-scale model regions in the model varies as the reactions proceed, an adaptive script defines the number and location of pore regions within each continuum iteration and initializes pore-scale simulations from macroscale information. Another script communicates information from the pore-scale simulation results back to the continuum scale. These components provide loose coupling between the pore-and continuum-scale codes into a single hybrid multiscale model implemented within the SWIFT workflow environment. In this paper, we consider an irreversible homogeneous bimolecular reaction (two solutes reacting to form a third solute) in a 2D test problem. This paper is focused on the approach used for multiscale coupling between pore-and continuumscale models, application to a realistic test problem, and implications of the results for predictive simulation of mixing-controlled reactions in porous media. Our results and analysis demonstrate that the hybrid multiscale method provides a feasible approach for increasing the accuracy of subsurface reactive transport simulations.

Intercomparison of 3D pore-scale flow and solute transport simulation methods

“…A key advantage of particle methods such as 20 SPH and LBM [33] is in their ability to advect mass with each particle, thus 21 removing the need to explicitly track phase interfaces for problems involv- were also successfully simulated to show the capability of the model. It also 6 pointed out the high computational cost of the SPH model, which could be 7 partially overcome by using parallel computing. In the more recent review of The fourth major pore-scale modeling approach considered here -pore- PDEs for the pore-network model reduces to simultaneous solution of a set of 18 analytical models for flow in each network element, the pore-network method 19 is significantly less computationally demanding than the other approaches, 20 and has been successfully applied to a broad range of problem types (e.g., Each pore-scale numerical approach mentioned above has strengths in 4 areas such as accuracy, flexibility, computational speed, or scalability.…”

“…DNS approaches include standard computational fluid dy-4 namics (CFD) [24], lattice Boltzmann method (LBM) [25][26][27], and smoothed 5 particle hydrodynamics (SPH) [28]. The second class of model represents the 6 pore space as a network connected by geometrically simplified pore bodies 7 and pore throats, and most commonly takes the form of pore-network mod-8 els (PNM) [29]. Both flow and transport processes can be represented using 9 either of these approaches.…”

“…Introduction 1 Flow and transport processes in porous media have been intensively stud-2 ied because of their importance in numerous industrial, biological, and en-3 vironmental applications [1]. Pore space geometry and topology are key 4 factors that influence flow and transport phenomena through porous me-5 dia, but the complexity and small scale of natural pore geometries renders 6 it challenging to both measure and simulate pore-scale flow and transport 7 processes. Accordingly, mathematical models have traditionally been devel-8 oped at macroscopic scales that do not explicitly consider pore geometry 9 [2].…”

“…Accordingly, mathematical models have traditionally been devel-8 oped at macroscopic scales that do not explicitly consider pore geometry 9 [2]. Recently, because of the availability of increasingly powerful comput- 10 ing resources and improved pore-scale characterization methods, pore-scale 11 modeling has become an important tool for studying complex flow and trans-12 port processes and relating them to macroscopic phenomena, and is comple- 13 mented by simplified representations of porous media, such as regular or 14 random sphere packs [3][4][5][6][7][8] and physical micromodels [9]. Pore-scale models 15 have also recently been coupled with continuum-scale models in hybrid mul-16 tiscale simulations to increase the fidelity of simulation results where needed 17 (e.g., [10][11][12][13][14]).…”

On the validity of effective formulations for transport through heterogeneous porous media

“…They deal with chemical reactivity either in a stochastic manner, representing reactivity with molecular analogies, or in classical approaches by means of concentrations Cirpka et al, 2012;Ding et al, 2013;Hayek et al, 2012;Knutson et al, 2007;Zhang et al, 2013). Extensions are both required for application purposes and attractive for capturing the consequences of anomalous transport to potential "anomalous" and enhanced reactivity (Battiato et al, 2009;Sadhukhan et al, 2014;Scheibe et al, 2015;Tartakovsky et al, 2009).…”