Reactive Transport Simulation

Each nodal block represents a distinct system, as we have defined it (Fig. 2.1). Conceptually, the properties of the entire block are projected onto a nodal point at the block s center (Fig. 20.2). A single value for any variable is carried per node in a transport or reactive transport simulation. There is one Ca++ concentration, one pH, one porosity, and so on. In other words, there is no accounting in the finite difference method for the extent to which the properties of a groundwater or the... 

Fig. 21.1. Operator splitting method for tracing a reactive transport simulation. To step forward from t = 0, the initial condition, to t = At, evaluate transport of the chemical components into and out of each nodal block, using the current distribution of mass. The net transport is the amount of component mass accumulating in a block over the time step. Once the updated component masses are known, evaluate the chemical equations to give a revised distribution of mass at each block. Repeat procedure, stepping to t = 2At, t = 3 At, and so on, until the simulation endpoint is reached.

In the previous two chapters (Chapters 26 and 27), we showed how kinetic laws describing the rates at which minerals dissolve and precipitate can be integrated into reaction path and reactive transport simulations. The purpose of this chapter is to consider how we can trace the reaction paths that arise when redox reactions proceed according to kinetic rate laws. 

Kipp, K. L., and Parkhurst, D. L., in press, Parallel processing for PHAST - A 3D reactive-transport simulator in XIV International Conference on Computational Methods in Water Resources, Delft, The Netherlands. 

We can see in Figures 10.1 (b) and (f) that the concentration fronts are now retarded because of the reactions, compared with non-reactive transport. Na+ in the column is completely displaced in about 1.5 pore volumes in the advective-reactive transport simulation versus 1.0 pore volume in the advective transport simulation. Because K+is bound to the exchanger more strongly, it is flushed out of the column later, at about 2 pore volumes. At this point, the column is saturated with Ca and the Ca front starts to appear in the effluent. Now due to ion-exchange reactions, the Ca front has traveled at about one-half of the average linear velocity of pore fluids. We can say Ca has a retardation factor of about 2 under these transport conditions. 

Figure 10.7. Kd values calculated from results of coupled reactive transport simulation. Solid line, 0 year flushing dashed line, 100 year dotted line, 200 year.

Reactive transport simulation is more realistic because of the consideration of SrSOj and BaS04 precipitation in reservoir (Bertero et al., 1988), predicting a lower scaling in the production well than the conservative transport simulation (Figure 6). This can be justified by the fact that in a reactive transport simulation part of the mineral that could cause scale in the production well has already precipitated in the reservoir. For kinetic reasons, they are called potentially precipitated minerals because the local equilibrium assumption at the production well is not necessarily valid. Produced water can be SrSO and BaS04... 

The concept and the basic steps of the reactive transport simulation approach are summarized in Fig. 3.1. At first, lithofacies types, i.e. aquifer material categories are assigned to aquifer material samples obtained from drill cores. Each facies type is characterized with respect to representative hydraulic and hydrogeochemical properties. Then, generally based on a geostatistical analysis, a spatial distribution of lithofacies types is generated. Since each lithofacies type has characteristic hydraulic and... 

A first preliminary reactive transport simulation including acid-based chemistry is set up using a ID model consisting of 10 elements with an element length of 100 m. Other parameters are selected as noted in Table 11.1. 

Xu T., Apps J.A., et al Reactive geochemical transport simulation to study mineral trapping for C02 disposal in deep arenaceous formations. 2003 Journal of Geophysical Research 108(B2) 2071-2084. 

Molecular diffusion (or self-diffusion) is the process by which molecules show a net migration, most commonly from areas of high to low concentration, as a result of their thermal vibration, or Brownian motion. The majority of reactive transport models are designed to simulate the distribution of reactions in groundwater flows and, as such, the accounting for molecular diffusion is lumped with hydrodynamic dispersion, in the definition of the dispersivity. 

A reactive transport model, as the name implies, is reaction modeling implemented within a transport simulation. It may be thought of as a reaction model distributed over a groundwater flow. In other words, we seek to trace the chemical reactions that occur at each point in space, accounting for the movement of reactants to that point, and reaction products away from it. 

Only for the intermediate cases - those with velocities in the range of about 100 m yr-1 to 1000 m yr-1 - does silica concentration and reaction rate vary greatly across the main part of the domain. Significantly, only these cases benefit from the extra effort of calculating a reactive transport model. For more rapid flows, the same result is given by a lumped parameter simulation, or box model, as we could construct in REACT. And for slower flow, a local equilibrium model suffices. 

The most sophisticated models applied to FePRBs to date combine multiple ADEs (i.e., multicomponent transport) with coupled chemical reactions [184,186,208]. These multicomponent reactive transport models were used to simulate the geochemical evolution in FePRBs for the treatment of TCE [184] and for remediating mixtures of Cr(VI) and chlorinated solvents [186,208]. The models are capable of reproducing the spatial distribution of field-observable parameters such as the concentrations of the chlorinated solvents, pH, Eh, alkalinity, Mg2 +, S042-, and N03 ... 

RT3D is an extension of MT3D, developed by researchers at Battelle Pacific Northwest Laboratories to simulate natural attenuation of chlorinated contaminants, that is capable of modeling multi-species reactive transport [19,68]. 

Like RT3D, BioRedox is a 3-D model that is capable of modeling multi-species reactive transport [70]. The public domain model can simulate coupled oxidation-reduction reactions between multiple electron acceptors and donors. Except for rate-limited sorption, it is capable of simulating all the reactions simulated by RT3D, and is more user-friendly, in that no modifications to source code are required to incorporate reaction packages [70]. 

In this work, we have approaehed the understanding of proton transport with two tasks. In the first task, deseribed above, we have sought to identify the moleeular-level stmeture of PFSA membranes and their relevant interfaees as a funetion of water content and polymer architecture. In the second task, described in this Section, we explain our efforts to model and quantify proton transport in these membranes and interfaces and their dependence on water content and polymer architecture. As in the task I, the tool employed is molecular dynamics (MD) simulation. A non-reactive algorithm is sufficient to generate the morphology of the membrane and its interfaces. It is also capable of providing some information about transport in the system such as diffusivities of water and the vehicular component of the proton diffusivity. Moreover, analysis of the hydration of hydronium ion provides indirect information about the structural component of proton diffusion, but a direct measure of the total proton diffusivity is beyond the capabilities of a non-reactive MD simulation. Therefore, in the task II, we develop and implement a reactive molecular dynamics algorithm that will lead to direct measurement of the total proton diffusivity. As the work is an active field, we report the work to date. 

Brown J. G., Bassett R. L., and Glynn P. D. (1998) Analysis and simulation of reactive transport of metal contaminants in ground water in Pinal Creek Basin, Arizona. In Special Issue—Reactive Transport Modeling of Natural Systems (eds. C. I. Steefel and P. van Cappellen). J. Hydrol. 209, 225 - 250. 

It should be noted that the flush model, other reaction path models, such as the fluid-centered reaction path model, and models with the dump option (see Wol-ery, 1992), have become less useful for their originally intended uses in simulating reactive transport. Although the extent of reactions is often monitored by the reaction progress variable (f), no temporal information is included in the model. Additionally,... 

In geochemical models, these quantities represent the smallest time period for incremental steps in a simulated titration, or the smallest distance between grid points in a finite element or finite difference grid, if LEQ is to be a valid assumption. Or, as Knapp puts it, reactive transport calculations assuming LEQ are good approximations only if teq is less than the size of the time step, and /eq is less than the distance between adjacent grid points. 

To facilitate the discussion below, we need, once again, to define the terminology first. By our definition, the isotherm-based reactive transport models are not coupled models because only one set of equations, namely partial differential equations for transport, is solved. The chemical processes are simulated according to empirical parameters rather than according to thermodynamics and chemical kinetics. 

In phreeqc, reactive transport is simulated by imagining a number of cells in a numbered sequence, containing minerals, surfaces, ion-exchangers, and an initial fluid equilibrated with these objects. The cells may all contain the same or different minerals and fluids. Another fluid is added to the first cell, equilibrated, with dispersion into the adjacent cell if desired, then that fluid is shifted or advected to the second cell, and the process is repeated until any number of shifts is performed. 

Table 10.2. phreeqc input for a reactive transport model to simulate fluid pH buffering at the Bear Creek site. This is a better alternative to the titration model in described Chapter 8. 

The coupled reactive transport model is designed to simulate the acid plume migration under this cover and attenuate reclamation plan. An 800 m strip along cross-section A-A (Figure 6.2) was discretized into 200 cells (Figure 10.4). Each cell is 4 min length. The time step is 0.08 year. 

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