Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

Abstract

Modeling multispecies reactive transport in natural systems with strong heterogeneities and complex biochemical reactions is a major challenge for assessing groundwater polluted sites with organic and inorganic contaminants. A large variety of these contaminants react according to serial-parallel reaction networks commonly simplified by a combination of first-order kinetic reactions. In this context, a random-walk particle tracking method is presented. This method is capable of efficiently simulating the motion of particles affected by first-order network reactions in three-dimensional systems, which are represented by spatially variable physical and biochemical coefficients described at high resolution. The approach is based on the development of transition probabilities that describe the likelihood that particles belonging to a given species and location at a given time will be transformed into and moved to another species and location afterward. These probabilities are derived from the solution matrix of the spatial moments governing equations. The method is fully coupled with reactions, free of numerical dispersion and overcomes the inherent numerical problems stemming from the incorporation of heterogeneities to reactive transport codes. In doing this, we demonstrate that the motion of particles follows a standard random walk with time-dependent effective retardation and dispersion parameters that depend on the initial and final chemical state of the particle. The behavior of effective parameters develops as a result of differential retardation effects among species. Moreover, explicit analytic solutions of the transition probability matrix and related particle motions are provided for serial reactions. An example of the effect of heterogeneity on the dechlorination of organic solvents in a threedimensional random porous media shows that the power-law behavior typically observed in conservative tracers breakthrough curves can be largely compromised by the effect of biochemical reactions.

A random walk solution for modeling solute transport with network reactions and multi-rate mass transfer in heterogeneous systems: Impact of biofilms

“…In subsurface hydrology, this concept has been used in the past to simulate solute transport with sorption/desorption processes (Valocchi and Quinodoz , 1989;Michalak and Kitanidis, 2000), rate-limited mass transfer processes , and kinetic network reactions (Henri and Fernàndez-Garcia, 2014). Following Michalak and Kitanidis (2000) and Henri and Fernàndez-Garcia (2014), transition probabilities can be determined from the evolution of the zeroth spatial moments of the solute plume. This is the procedure employed here.…”

“…From Henri and Fernàndez-Garcia (2014), the solution matrix that satisfies the initial condition P t (t = 0) = Id can be assimilated to a state transition probability matrix. This is easily seen by noticing that the system of equations (22) can be interpreted as the forward kolmogorov equations of a continuous-time markov chain in which the state space is formed by the N s species involved in the reaction network and the 1 + N im mobile and immobile domains.…”

“…In this context, organic chlorinated solvents are often described by first-order reaction chains schematically described by A → B → C → D, meaning that species A is transformed into species B, B into C and so on. The quantification of the risk posed by these contaminants is not a trivial problem (Benekos et al, 2006;Henri and Fernàndez-Garcia, 2014). The degradation products can constitute new noxious chemical compounds not necessarily less toxic than its parent product.…”

“…The degradation products can constitute new noxious chemical compounds not necessarily less toxic than its parent product. Even though analytical solutions (e.g., Sun et al, 1999;Zhang and Woodbury, 2002;Sun and Buscheck , 2003;Falta et al, 2007) have been routinely employed by decision makers to efficiently manage the risk posed by these contaminants, the spatial variability of aquifer properties, always observed in natural systems, have seriously questioned the application of such simple approaches (Adrian et al, 1994;Miralles-Wilhelm and Gelhar , 1996;Scholl , 2000;Cunningham and Fadel , 2007;Henri and Fernàndez-Garcia, 2014).…”

“…In this context, Particle Tracking Methods (PTMs) constitute an efficient numerical alternative to simulate reactive transport (Kitanidis, 1994;Henri and Fernàndez-Garcia, 2014). Even though a large variety of methods exist to simulate rate-limited mass transfer processes with particle tracking (Benson and Meerschaert, 2009;Delay and Bodin, 2001;Dentz and Berkowitz , 2003;Tsang and Tsang, 2001), this method is still limited in the type of chemical reactions available, which include sorption (Tompson, 1993;Valocchi and Quinodoz , 1989;Michalak and Kitanidis, 2000), radioactive decay (Wen and Gómez-Hernández , 1996;Painter et al, 2007), first-order network reactions (Burnell et al, 2014;Henri and Fernàndez-Garcia, 2014), and simple bimolecular reactions (Benson and Meerschaert, 2008;Ding et al, 2013;Edery et al, 2009Edery et al, , 2010Paster et al, 2014) among others. None of the methods available nowadays supports multi-porosity systems with network reactions in three-dimensional randomly heterogeneous porous media.…”