Research article
Chemically reactive multicomponent transport simulation in soil and groundwater: 1. Model development and evaluation H. Gao á A. Butler á H. Wheater á V. Vesovic including DYNAMIX, HYDROGEOCHEM, MINTRAN, RT3D, etc. DYNAMIX (Narasimhan and others 1986) is a dynamic mixing cell model, based on a transport model TRUST and a geochemical speciation model PHREEQE, capable of handling several element problems (Narasimhan and others 1986). HYDROGEOCHEM (Yeh and Tripathi 1991) is a coupled chemically reactive transport model based on the previous model FEMWATER, a ¯ow and transport model on both saturated and unsaturated conditions, and EQMOD, a geochemical model for aqueous complexation, precipitation±dissolution, adsorption±desorption, oxidation±reduction, ion exchange and acid-base reactions. Walter and others (1994) developed a model, MINTRAN, for multiple component reactive transport in groundwater. This model resulted from a ®nite element transport model (PLUME2D) and a geochemical speciation model (MINTEQA2). RT3D (Clement and others Keywords Geochemical á Reaction á Transport á 1998) is based on MT3D (Zheng 1990), which requires Modeling USGS groundwater ¯ow model MODFLOW to obtain groundwater ¯ow heads. It is claimed that the present version of RT3D is suf®ciently ¯exible for simulating various types of chemical reactions, microbial metabolisms, and microbial transport kinetics. However, primary Introduction applications studied so far are mostly related to natural attenuation of certain organic species. Restricted by The methods for the simulation of chemically reactive multiple component transport have attracted much inter- MODFLOW, this model is applicable to saturated porous media only. These models are undoubtedly very useful to est from hydrogeologists and/or hydrogeochemists for solve a wide range of reactive groundwater problems. years. So far, quite a few models have been developed, However, in real environmental applications, those methods seem inadequate in terms of solving some speci®c environmental problems. For example, the problem of heat Received: 21 February 2001 / Accepted: 17 July 2001 contamination and the in¯uence of heat distribution on Published online: 31 August 2001 ã Springer-Verlag 2001 the behavior and fate of contaminants were not considered. In fact, those scenarios, which involve more complex environmental problems, are common. To take acid mine H. Gao (&) drainage contamination as an example, the heat transport Franz Environmental Inc., 18 King Street East Unit E-9, and the disturbed temperature ®eld may be of concern, Bolton, ON L7E 1E8, Canada given the evidence that the temperature in sulphide-conE-mail:
[email protected] taining waste rock tailings could be as high as 45 °C Tel.: +1-905-9514334 Fax: +1-905-9518661 (Cathes and Apps 1975), even up to 80 °C (Fell and others 1993). A high temperature source may cause an uneven A. Butler á H. Wheater distribution of groundwater temperature in the nearby Department of Civil & Environmental Engineering, tailings area. The distributed rather than a constant temImperial College, London, SW3 2BU, UK perature in groundwater may result in a quite different V. Vesovic situation because chemical reactions are in¯uenced by the Huxley School of Environment, ambient temperature (Freeze and Cherry 1979; Stumm and Earth Sciences and Engineering, Morgan 1996). The effect of temperature on chemical Imperial College, London, SW7 2BP, UK Abstract The model, REACTRAN2D, is for simulating the transport of chemically reactive components in conjunction with energy transport in groundwater systems. It is coded on the basis of two well-known models, SUTRA and MINTEQA2. On the assumption that local equilibria exist, this coupled geochemical and heat transport model is solved by a parallel and sequential iteration approach. It has been compared with HYDROGEOCHEM and limited ®eld data. Very close matches were achieved. This model can deal with chemically reactive transport involving solid phase, aqueous phase and gas phase, therefore, having a great potential to simulate the full range of geochemical problems covered by MINTEQA2.
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Environmental Geology (2001) 41:274±279
DOI. 10.1007/s002540100412
Research article
reactions makes the already complicated processes for chemically reactive multi-component transports even more complex. As a requirement from engineering of groundwater remediation, a more ¯exible and functional tool to simulate the behavior and fate of multiple pollutants in groundwater systems is needed.
in mol m±3, Rj is the accumulation rate of component j due to different chemical reactions, in mol m±3ás±1, Qs is the existing source or sink, in volumetric ¯uid per unit time, s±1. Sw is the saturation index in a ¯ow domain, Nc is the number of components, and L denotes the advection-dispersion spatial operator, which is described by, L
/Sw Cj r
/Sw D r Cj /Sw VC j :
2
Model development For a contaminated groundwater system, the ¯owing water body will carry contaminants through the transport medium, while the contaminants react with both groundwater body and possible minerals in the transport matrix. This complex procedure includes physical transport and some geochemical reactions. For the sake of numerical solution to the fully coupled equations, some assumptions have to be given. First, chemical reactions are assumed to be suf®ciently fast, relative to hydrological processes, for the local equilibria to be established throughout the solute transport domain (Rubin 1983; Yeh and Tripathi 1989; Walter and others 1994). This assumption may not be applicable to some very slow reactions such as the acid buffering reactions with non-carbonate minerals and redox reactions without acceleration, i.e. Fe2+/Fe3+ transfer without bacterial acceleration. Secondly, for a multi-component system, the transport of individual components or species is considered to occur independently (Rubin 1983). In other words, all individual components have identical physical transport behaviors. Finally, the energy change caused by various exothermic and endothermic chemical reactions in the groundwater environment is suf®ciently small not to cause observable temperature variations in the huge groundwater and rock body. In stead, the groundwater temperature changes may only be caused by energy transport originating from a heat source (a tailings dam for example). Multiple component reactive transport model The chemically reactive multi-component transport includes both physical and chemical processes. The physical processes cover solute advection and dispersion. The chemical processes may include the potential chemical reactions of complexation, ion exchange, oxidation± reduction (redox), precipitation-dissolution, acid-base reaction and adsorption-desorption. When chemical reactions take place during the transport, the easiest way to introduce them into the advection-dispersion equation is by way of accumulation rates Rj (j=1, 2, ..., Nc) for all components. Then the chemically reactive multi-component transport equation can be written, for each component j, as follows (Gao 1998): @ /Sw Cj L /Sw Cj /Sw Rj Qs Cjs ; j 1; :::; Nc
1 @t
Chemical reaction term: derivation of the accumulation rate RJ All possible chemical reactions cause a change of the concentration of component j during the transport. This rate is a sum of the mass accumulation from all chemical reactions expressed as: p
rd ab Rj Raj Rsj Rj Rex j Rj Rj :
3
where Raj is the rate of accumulation of the j substance due to the aqueous complexation, Rsj is the rate of accumulation p of the j substance due to adsorption-desorption, Rj is the rate of accumulation of the j substance due to precipitation-dissolution, Rex j is the rate of accumulation of the j substance due to ion exchange reaction, Rrd j is the rate of accumulation of the j substance due to redox reaction, and Rab j is the rate of accumulation of the j substance due to acid-base reaction. Since the rate of accumulation of component j due to ionexchange reaction, redox reaction and acid-base reaction can be described mathematically in terms of accumulation of component j due to aqueous complexation, adsorption/ desorption and precipitation/dissolution reactions (Yeh and Tripathi 1989; Gao 1998), Eq. (3) can be simply re-written as: p
Rj Raj Rsj Rj :
4
They can be further extended in the following expressions: Raj p
Rj
" # " # Nx Ns X @ X @ ax Xi ; Rsj as SX ; @t i1 ij @t i1 ij i "N # p @ X p X a P ; j 1; :::; Nc @t i1 ij i
5
where axij is the stoichiometric coef®cient for the total aqueous concentration of component j in complex Xi , and Nx is the number complex for component j; asij is the stoichiometric coef®cient for the total adsorbed concentration of component j in adsorbed site SXi , and Ns is the p number of sorbed complexes for component j; while aij is the stoichiometric coef®cient for the total precipitated concentration of component j in precipitate PXi , and Np is the number precipitates for component j.While, the concentrations, Xi, SXi , and PX are related to the concentration ±3 where, Cj is the concentration of component j, in mol m , of aqueous component j by means of the following ways, Cjs is the concentration of component j in the source ¯ux, respectively: Environmental Geology (2001) 41:274±279
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Research article
Nc aXij KX Y Xi xi cj Cc ci j1
@ Sw C tot / @t j
i 1; . . . ; Nx ; !
!
Nx P x /L Sw Cj aij Xi Qs Cjs i1
j 1; . . . ; Nc
9 i 1;:::; Ns ; and The term of the left-hand side represents the change of j1 total concentration of component j. The ®rst term in the p N c right-hand side stands for transport processes for aqueous Y p aij p c j Cj i 1; . . . ; Np : Ki components and complexes. The second term represents j1 for the existing source. The adsorption term may include
6 ion-exchange, acid base reactions. The complexation term may include redox reaction and ion exchange reaction as well. x where ci is the activity coef®cient of complex i; cj is the This equation indicates that the expression of the basic activity coef®cient of the j component, and kxi is equilibrium concept of reactive hydrogeochemical transport, namely, constant of the i complexed species; KiS is the equilibrium the concentration change of each component over time in constant of the ith adsorbed species, cSi is the activity co- solution, on surface, and in solid form, depends on the ef®cient of the ith sorbed species, cci is the activity coef®- transport of that component and its aqueous complexes cient of the jth adsorbate component, and csj is the activity (by advection and dispersion), and on the amount prop coef®cient of the jth adsorbent, equal to unit; Ki is the vided by a source. solubility product equilibrium constant for the precipitate. This general form of equation for chemically reactive The concentration of PXi , PXi , does not appear in the above multiple component transport is applicable in subsurface expression because it is assumed that the activity of a solid groundwater systems under saturated conditions (when is unity. The inequality of this equilibration equation in- S =1.) and unsaturated conditions (when S
