TY - JOUR

T1 - First-principles derivation of reactive transport modeling parameters for particle tracking and PDE approaches

AU - Hansen, Scott K.

AU - Scher, Harvey

AU - Berkowitz, Brian

N1 - Funding Information:
Scott Hansen gratefully acknowledges the support of a postdoctoral fellowship from the Azrieli Foundation and Brian Berkowitz gratefully acknowledges the support of a research grant from the Weizmann – UK Joint Research Program. Brian Berkowitz holds the Sam Zuckerberg Professorial Chair in Hydrology.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Both Eulerian and Lagrangian reactive transport simulations in natural media require selection of a parameter that controls the "promiscuity" of the reacting particles. In Eulerian models, measurement of this parameter may be difficult because its value will generally differ between natural (diffusion-limited) systems and batch experiments, even though both are modeled by reaction terms of the same form. And in Lagrangian models, there previously has been no a priori way to compute this parameter. In both cases, then, selection is typically done by calibration, or ad hoc. This paper addresses the parameter selection problem for Fickian transport by deriving, from first principles and D (the diffusion constant) the reaction-rate-controlling parameters for particle tracking (PT) codes and for the diffusion-reaction equation (DRE). Using continuous time random walk analysis, exact reaction probabilities are derived for pairs of potentially reactive particles based on D and their probability of reaction provided that they collocate. Simultaneously, a second PT scheme directly employing collocation probabilities is derived. One-to-one correspondence between each of D, the reaction radius specified for a PT scheme, and the DRE decay constant are then developed. These results serve to ground reactive transport simulations in their underlying thermodynamics, and are confirmed by simulations.

AB - Both Eulerian and Lagrangian reactive transport simulations in natural media require selection of a parameter that controls the "promiscuity" of the reacting particles. In Eulerian models, measurement of this parameter may be difficult because its value will generally differ between natural (diffusion-limited) systems and batch experiments, even though both are modeled by reaction terms of the same form. And in Lagrangian models, there previously has been no a priori way to compute this parameter. In both cases, then, selection is typically done by calibration, or ad hoc. This paper addresses the parameter selection problem for Fickian transport by deriving, from first principles and D (the diffusion constant) the reaction-rate-controlling parameters for particle tracking (PT) codes and for the diffusion-reaction equation (DRE). Using continuous time random walk analysis, exact reaction probabilities are derived for pairs of potentially reactive particles based on D and their probability of reaction provided that they collocate. Simultaneously, a second PT scheme directly employing collocation probabilities is derived. One-to-one correspondence between each of D, the reaction radius specified for a PT scheme, and the DRE decay constant are then developed. These results serve to ground reactive transport simulations in their underlying thermodynamics, and are confirmed by simulations.

KW - Continuous time random walk

KW - Fickian diffusion

KW - Langevin equation

KW - Model calibration

KW - Particle tracking

KW - Reactive transport

UR - http://www.scopus.com/inward/record.url?scp=84899879492&partnerID=8YFLogxK

U2 - 10.1016/j.advwatres.2014.04.007

DO - 10.1016/j.advwatres.2014.04.007

M3 - Article

AN - SCOPUS:84899879492

SN - 0309-1708

VL - 69

SP - 146

EP - 158

JO - Advances in Water Resources

JF - Advances in Water Resources

ER -