Research papers Validity of using large-density asymptotics for studying reaction-infiltration instability in fluid-saturated rocks Chongbin Zhao a,⇑ , B.E. Hobbs b , A. Ord b a Computational Geosciences Research Centre, Central South University, Changsha 410083, China b School of Earth and Environment, The University of Western Australia, Crawley, WA 6009, Australia article info Article history: Received 25 August 2017 Received in revised form 11 February 2018 Accepted 12 February 2018 Available online 15 February 2018 This manuscript was handled by Abhijit Mukherjee, Associate Editor Keywords: Reaction-infiltration instability Chemical dissolution Large-density ratio Front instability Porous media abstract Reaction-infiltration instability, in which chemical reactions can dissolve minerals and therefore create preferential pore-fluid flow channels in fluid-saturated rocks, may play an important role in controlling groundwater quality in groundwater hydrology. Although this topic has been studied for many years, there is a recent debate, which says that the use of large-density asymptotics in the previous studies is invalid. However, there is a crucial conceptual mistake in this debate, which leads to results and conclu- sions that are inconsistent with the fundamental laws of physics. It is well known that in terms of dis- tance, time and velocity, there are only two independent variables. But they are treated as three independent variables, a procedure that is the main source of the physically unrealistic results and con- clusions in the debate. In this paper, we will discuss the results and conclusions related to the debate, with emphasis on the issues leading to the corresponding errors. In particular, we demonstrate that there is an unappreciated constraint condition between the dimensional/dimensionless distance, time and velocity in the debate. By using this constraint condition, it can be confirmed that as the ratio of the reac- tant concentration in the incoming fluid stream to the mineral concentration approaches zero, the dimen- sionless transport parameter, H, automatically approaches infinity. Therefore, it is further confirmed that the previous work conducted by Chadam and others remains valid. Ó 2018 Elsevier B.V. All rights reserved. 1. Introduction Reaction-infiltration instability, in which chemical reactions can dissolve minerals and therefore create preferential pore-fluid flow channels in fluid-saturated rocks, may play an important role in controlling groundwater quality in groundwater hydrology (Imhoff et al., 1996, 2003; Maji and Sudicky, 2008; Miller et al., 1990; Seyedabbasi et al., 2008). To solve this problem, Chadam et al. (1986) conducted a seminal study by using large-density asymptotics, in which the density ratio, c, of the reactant concen- tration in the incoming fluid stream, c in , to the mineral concentra- tion, c sol , is approaching zero. In their study, chemical dissolution fronts were considered to propagate in the infinite space, which is filled with fluid-saturated rocks. The following two main conclu- sions were drawn from their study: (1) as the density ratio (c) approaches zero, the thickness of a chemical dissolution front also approaches zero, leading to a sharp shape of the chemical dissolu- tion front; (2) for a given reaction-infiltration system with a given inflow velocity in the fluid-saturated rock, a chemical dissolution front is unstable if the wavelength of an applied small perturbation is greater than the critical wavelength of the system. Due to the theoretical importance of this seminal study, extensive theoretical analysis and computational simulations have been further fol- lowed in the past years (Ortoleva et al., 1987a,b; Ormond and Ortoleva, 2000; Chen and Liu, 2002, 2004; Chen et al., 2009; Lai et al., 2014, 2016). In particular, Imhoff and Miller extended the work of Chadam et al. (1986) to the theoretical study of non- aqueous phase liquid (NAPL) dissolution instability in fluid- saturated porous media (Imhoff and Miller, 1996), which plays an important role in removing NAPLs from contaminated ground- water resources (Imhoff et al., 1996, 2003; Maji and Sudicky, 2008; Miller et al., 1990; Seyedabbasi et al., 2008). However, there is a recent debate (Ladd and Szymczak, 2017) to question the validity of using large-density asymptotics in the work of Chadam et al. (1986). Unfortunately, there are serious mis- takes that lead to questionable conclusions in the debate paper. First, the treatment of distance, time and velocity as three indepen- dent variables violates the fundamental principle in physics. This violation leads to a constraint condition between the density ratio, c, and the dimensionless transport parameter, H. Note that this density ratio, v, is also called the mineral dissolution ratio in https://doi.org/10.1016/j.jhydrol.2018.02.030 0022-1694/Ó 2018 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: Chongbin.zhao@iinet.net.au (C. Zhao). Journal of Hydrology 559 (2018) 454–460 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol