Maarten W. Saaltink

A mathematical formulation for reactive transport that eliminates mineral concentrations

We present a concise and general mathematical formulation for reactive transport in groundwater for general applications. By means of linear algebraic manipulations of the stoichiometric coefficients of the chemical reactions we are able to reduce the number of unknowns of the equations to be solved to the number of degrees of freedom according to thermodynamic rules. We present six formulations that differ from each other by number and type of unknowns and discuss their advantages and disadvantages with respect to the two most important numerical solution methods, the Sequential Iteration Approach (SIA) and the Direct Substitution Approach (DSA). Our conclusion is that the proposed reduction of the number of variables is of special interest for the DSA. We have applied one of these formulations to an example of the flushing of saline water by fresh water.

RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media

The code RETRASO (REactive TRAnsport of SOlutes) simulates reactive transport of dissolved and gaseous species in non-isothermal saturated or unsaturated problems. Possible chemical reactions include aqueous complexation (including redox reactions), sorption, precipitation-dissolution of minerals and gas dissolution. Various models for sorption of solutes on solids are available, from experimental relationships (linear KD, Freundlich and Langmuir isotherms) to cation exchange and surface complexation models (constant capacitance, diffuse layer and triple layer models). Precipitation-dissolution and aqueous complexation can be modelled in equilibrium or according to kinetic laws. For the numerical solution of the reactive transport equations it uses the Direct Substitution Approach. The use of the code is demonstrated by three examples. The first example models various sorption processes in a smectite barrier. The second example models a complex chemical system in a two dimensional cross-section. The last example models pyrite weathering in an unsaturated medium.

On the behavior of approaches to simulate reactive transport

Two families of approaches exist to simulate reactive transport in groundwater: The Direct Substitution Approach (DSA), based on Newton-Raphson and the Picard or Sequential Iteration Approach (SIA). We applied basic versions of both methods to several test cases and compared both computational demands and quality of the solution for varying grid size. Results showed that the behavior of the two approaches is sensitive to both grid size and chemistry. As a general rule, the DSA is more robust than the SIA, in the sense that its convergence is less sensitive to time step size (any approach will converge given a sufficiently small time step). Moreover, the DSA leads to a better simulation of sharp fronts, which can only be reproduced with fine grids after many iterations when the SIA is used. As a consequence, the DSA runs faster than SIA in chemically difficult cases (i.e., highly non-linear and/or very retarded), because the SIA may require very small time steps to converge. On the other hand, the size of the system of equations is much larger for the DSA than for the SIA, so that its CPU time and memory requirements tend to be less favorable with increasing grid size. As a result, the SIA may become faster than the DSA for very large, chemically simple problems. The use of an iterative linear solver for the DSA makes its CPU time less sensitive to grid size.

Experimental and modeling investigation of multicomponent reactive transport in porous media

We present an experimental and modeling study of solute transport in porous media in the presence of mixing-induced precipitation of a solid phase. Conservative and reactive transport experiments were performed in a quasi-two-dimensional laboratory flow cell, filled with homogeneous and heterogeneous porous media. Conservative experiments were performed by injecting solutions containing sodium chloride and calcium chloride into the domain. In reactive transport experiments, inlet solutions of calcium chloride and sodium carbonate were injected in parallel, resulting in calcium carbonate precipitation where the solutions mix. Experimental results were used as a benchmark to examine the performance of a reactive transport numerical model. Good agreement between model predictions and experimental results was obtained for the conservative transport experiments. The reactive transport experiments featured the formation of a calcium carbonate mineral phase within the mixing zone between the two solutions, which controlled the spatial evolution of calcium carbonate in the domain. Numerical simulations performed on high resolution grids for both the homogeneous and heterogeneous porous systems underestimated clogging of the system. Although qualitative agreement between model results and experimental observations was obtained, accurate model predictions of the spatial evolution of calcium concentrations at sample points within the flow cell could not be achieved.

Analysis of a deep well recharge experiment by calibrating a reactive transport model with field data.

This paper describes the modeling of the hydrogeochemical effects of deep well recharge of oxic water into an anoxic pyrite-bearing aquifer. Kinetic expressions have been used for mineral dissolution-precipitation rates and organic matter oxidation. Hydrological and chemical parameters of the model were calibrated to field measurements. The results showed that oxidation of pyrite (FeS(2)) and, to a lesser extent, organic matter dominate the changes in quality of the recharged water during its passage through the aquifer. The recharge leads to the consumption of oxygen and nitrate and the formation of sulfate and ferrihydrite. Complexation reactions, cation exchange and precipitation and dissolution of calcite, siderite and rhodochrosite were also identified through the modeling. Despite problems of non-uniqueness of the calibrated parameters, the model was used successfully to depict the geochemical processes occurring in the aquifer. Non-uniqueness can be avoided by constraining the model as much as possible to measurements and/or data from literature, although they cannot be considered always as fixed values and should be considered as stochastic variables instead.

Modeling evaporation processes in a saline soil from saturation to oven dry conditions

First of all, I wish to express my sincere appreciation for the author’s courage and competence to model such a complex experimental system. However, in the current state, the numerical simulations seem to be incompletely described which makes it quite hard to understand them in detail. Furthermore, the simultaneous occurrence of a multitude of processes makes the studied system so complex that the question arises whether it is really possible to discriminate the various processes and their influence on the simulated system response. Directly related to this is the need to improve the description of parameter estimation by inverse modeling. As noted by the authors (P540 L19.21) ’all parameters influence all processes’. I would therefore acknowledge if the issues

Geochemical and environmental controls on the genesis of soluble efflorescent salts in Coastal Mine Tailings Deposits: a discussion based on reactive transport modeling.

Water-soluble efflorescent salts often form on tailings in hyperarid climates. Their high solubility together with the high risk of human exposure to heavy metals such as Cu, Ni, Zn, etc., makes this occurrence a serious environmental problem. Understanding their formation (genesis) is therefore key to designing prevention and remediation strategies. A significant amount of these efflorescences has been described on the coastal area of Chañaral (Chile). There, highly soluble salts such as halite (NaCl) and eriochalcite (CuCl(2).2H(2)O) form on 4km(2) of marine shore tailings. Natural occurrence of eriochalcite is rare: its formation requires extreme environmental and geochemical conditions such as high evaporation rate and low relative air humidity, and continuous Cl and Cu supply from groundwater, etc. Its formation was examined by means of reactive transport modeling. A scenario is proposed involving sea water and subsequently a mixture of sea water/freshwater in the groundwater composition in the formation of these efflorescences. The strong competition from other halides (i.e. halite and silvite (KCl)) for the Cl may inhibit the precipitation of eriochalcite. Therefore, the Cl/Na ratio trend >1 is a key parameter in its formation. Cation-exchange between Na(+) and other major ions such as K(+), Ca(2+), Mg(2+) and Cu(2+) in the clay fraction of tailings is proposed to account for realistic Cl/Na ratios. With regard to preventing the formation of eriochalcite, a capillary barrier on the tailings surface is proposed as a suitable alternative. Its efficiency as a barrier is also tested by means of reactive transport models.

Bacterial transformation and biodegradation processes simulation in horizontal subsurface flow constructed wetlands using CWM1-RETRASO

The performance and reliability of the CWM1-RETRASO model for simulating processes in horizontal subsurface flow constructed wetlands (HSSF CWs) and the relative contribution of different microbial reactions to organic matter (COD) removal in a HSSF CW treating urban wastewater were evaluated. Various different approaches with diverse influent configurations were simulated. According to the simulations, anaerobic processes were more widespread in the simulated wetland and contributed to a higher COD removal rate [72-79%] than anoxic [0-1%] and aerobic reactions [20-27%] did. In all the cases tested, the reaction that most contributed to COD removal was methanogenesis [58-73%]. All results provided by the model were in consonance with literature and experimental field observations, suggesting a good performance and reliability of CWM1-RETRASO. According to the good simulation predictions, CWM1-RETRASO is the first mechanistic model able to successfully simulate the processes described by the CWM1 model in HSSF CWs.

A comparison of two approaches for reactive transport modelling

Abstract We compared the numerical behaviour of two approaches for reactive transport modelling: the Sequential Iteration Approach (SIA) and the Direct Substitution Approach. Results showed that, for chemically difficult (i.e. highly non-linear) cases, the SIA often requires very small time steps leading to excessive computation times, whereas the DSA is consistently very robust and does not show this inconvenience. On the other hand, for chemically simple cases but with grids of many nodes, the DSA tends to be less favourable.

Modelling the oxidation of sulphides in an unsaturated soil

Abstract Within the framework of a study on the impact of a mine-tailing spill at Aznalćollar, SW Spain, we investigated the oxidation of pyrite and other sulphides by means of two column experiments and reactive transport modelling. The columns were filled with pyritic sludge mixed up with a sandy and a clayey soil, respectively. The columns were located outdoors for 15 months and leached 10 times. Prior to simulating reactive transport, a flow model permitted a detailed description of the behaviour of the column at a daily time-scale. The most important parameter extracted was the hydraulic saturation. This parameter controlled the amount of O2 that could diffuse into the soil, which, in its turn, affected the rate of pyrite oxidation. The sandy and clayey columns behaved very differently. In the sandy column, pH dropped due to the oxidation of pyrite. As a result, silicate minerals dissolved, providing Na and/or K that precipitate together with Fe and SO4 as jarosite. The high concentration of Zn in the leachates was consistent with the concentrations predicted from sphalerite oxidation. The low As and Pb concentrations, however, were explained by their coprecipitation in the jarosite. In the clayey column, the dissolution of dolomite kept the pH high, impeding the dissolution of silicate minerals and precipitating amorphous Fe(OH)3 in the place of jarosite. The model also permitted rate laws proposed in the literature for pyrite oxidation to be discussed. We found that the oxidation of pyrite by Fe3+ was not faster than by O2, contrary reports in the literature. Finally, the model was used to predict the behaviour of other soil types and other sludge contents. According to the predictions the dissolution of jarosite was very important to maintaining the pH at a value of approximately 2, even for gravels or low reactive sand.