Upscaling Transport of Adsorbing Solutes in Porous Media: Pore‐Network Modeling

Abstract

The main objec ve of this research was to enhance our understanding of and obtain quanta ve rela on between Darcy-scale adsorp on parameters and pore-scale fl ow and adsorp on parameters, using a three-dimensional mul direc onal pore-network model. This helps to scale up from a simplifi ed but reasonable representa on of microscopic physics to the scale of interest in prac cal applica ons. This upscaling is performed in two stages: (i) from local scale to the eff ec ve pore scale and (ii) from eff ec ve pore scale to the scale of a core. The fi rst stage of this upscaling from local scale to eff ec ve pore scale has been reported in an earlier manuscript. There, we found rela onships between localscale parameters (such as equilibrium adsorp on coeffi cient, k d , and Peclet number, Pe) and eff ec ve parameters (such as a achment coeffi cient, k a , and detachment coeffi cient, k det ). Here, we perform upscaling by means of a three-dimensional mul direc onal network model, which is composed of a large number of interconnected pore bodies (represented by spheres) and pore throats (represented by tubes). Upscaled transport parameters are obtained by fi ng the solu on of classical advec on -dispersion equa on with adsorp on to the average concentra on breakthrough curves at the outlet of the pore network. This procedure has resulted in rela onships for upscaled adsorp on parameters in terms of the microscale adsorp on coeffi cient and fl ow velocity.

On Laminar Flow of Non-Newtonian Fluids in Porous Media

“…In the pore network approach the porous media is represented as a 3D network of pipes. Flow rate and pressure drop in each branch is determined to find the bulk flow rate through this network [12], [1], [3] and [18].…”

Pore-scale modeling and simulation of flow, transport, and adsorptive or osmotic effects in membranes: the influence of membrane microstructure

“…To the authors knowledge there are no pore-scale simulation studies on osmotic effects in membranes. Furthermore, although numerical studies on surface reactions at the porescale do exist, these are limited to pore-network models [24,29] and, as far as we are aware, there are no software packages with the ability to solve surface reactions directly on images [14]. In contrast, our studies aim to examine the influence of the membrane morphology at the microscale directly on images obtained through techniques such as micro computerized tomography, or on virtually generated geometries when such images do not exist.…”

PoreFlow: A complex pore-network model for simulation of reactive transport in variably saturated porous media

“…and industrial (concrete, bioengi- S w , ii) the relative permeability, k r , as a function of either the saturation 9 or capillary pressure, and iii) the relationship between solute dispersivity or 10 effective diffusion and saturation in solute transport processes. 11 The relative permeability of a fluid is a measure of the conductance of the 12 porous medium for that fluid at a given saturation. Relative permeability 13 measurements on field samples are difficult and time consuming.…”

“…Also, the dependence of relative permeability on saturation is de- 9 termined by computing the resistance to flow in the connected portion of 10 a fluid. In these calculations, resistance to the flow within the pore bodies 11 is commonly ignored, assuming that conductance within the pore bodies is 12 much larger than the conductance within the pore throats. Commonly, an 13 average pressure and/or concentration is assigned to a given pore body or 14 pore throat.…”

“…For each pore, change in solute mass is described by mass bal- 15 ance equations (Lichtner, 1985). Using information on local surface area, and 16 applying an area-normalized reaction rate, a kinetic reaction is calculated for 17 each pore (Raoof and Hassanizadeh, 2010). 18 One shortcoming of a pore-network model is its idealization of the pore 19 space using simple geometries; often, pores are assumed to have uniform 20 circular or square cross-sectional shapes.…”