A combined mixing cell/analytical model to describe two‐dimensional reactive solute transport for unidirectional groundwater flow

Schulz, Henrik; Reardon, Eric J.

doi:10.1029/wr019i002p00493

Cited by 79 publications

(23 citation statements)

References 5 publications

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“…The operator-splitting (OS) approach (Yanenko 1971;Schulz and Reardon 1983) divides the complete partial differential equation (PDE) into smaller, easier to solve sub-PDEs and adds up their changing effects. Typically, each process or group of similar processes is modeled by one sub-PDE.…”

Section: Operator-splittingmentioning

confidence: 99%

Computer simulation of deep sulfate reduction in sediments of the Amazon Fan

Adler

Hensen

Kasten

et al. 2000

International Journal of Earth Sciences

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Pore water concentration profiles of sediments at a site on the Amazon Fan were investigated and simulated with the numerical model CoTReM (column transport and reaction model) to reveal the biogeochemical processes involved. The pore water profiles for gravity core GeoB 4417-7 showed a distinct sulfate-methane transition zone in which deep sulfate reduction occurs. Only a small sulfide peak could be observed at the reaction zone. Due to high amounts of iron minerals, the produced sulfide is instantaneously precipitated in form of iron sulfides. We present a simulation which starts from a steady state system with respect to pore water profiles for methane and sulfate. Furthermore, sulfide, iron, pH, pE, calcium and total inorganic carbon (TIC) were included in the simulation. The program calculated mineral equilibria to mackinawite, iron sulfides (more stable than mackinawite), iron hydroxides and calcite via saturation indices (SI) by a module incorporating the program PHREEQC (Parkhurst 1995). The measured sulfide and iron profiles are obtained in the simulation output by using a constant SI (p0) for mackinawite and calcite, while a depth dependent SI distribution is applied for the PHREEQC phases "Pyrite" and "Fe(OH)3(a)", representing a composition and the kinetics of different iron sulfides and iron hydroxides. These SI distributions control the results of sulfide and iron pore water profiles, especially conserving the sulfide profile at the reaction zone during the simulation. The results suggest that phases of iron hydroxides are dissolved, mackinawite is precipitated within, and other iron sulfides are precipitated below the reaction zone. The chemical reactivity of iron hydroxides corresponds to the rate of sulfide production. The system H 2 O-CO 2 -CaCO 3 is generally successfully maintained during the simulation. Deviations to the measured pH profile suggest that further processes are active which are not included in the simulation yet.

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Section: Operator-splittingmentioning

confidence: 99%

Computer simulation of deep sulfate reduction in sediments of the Amazon Fan

Adler

Hensen

Kasten

et al. 2000

International Journal of Earth Sciences

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“…The program package is a one-dimensional transport and reaction model based on the mixing-cell approach of Schulz and Reardon (1983). It solves the differential equation for longitudinal transport in its combination of advection and longitudinal dispersion (with C=concentration; t=time; D l =coef®cient of longitudinal dispersion; x=coordinate in direction of¯ow; v a =¯ow velocity).…”

Section: Numerical Modelingmentioning

confidence: 99%

The influence of advective transport on redox fronts in column experiments and their numeric modeling. Part 2: modeling of the solid phase and secondary redox reactions

et al. 2001

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This study deals on the interrelation of redox processes in pore waters and solid phases. Therefore, a column experiment was carried out with sediments from an anoxic aquifer. The experiment was run for 80 weeks. Test water contained a constant concentration of the reducing agent acetate and was pumped through the column at a¯ow velocity of 0.80 m/day. Data were processed and interpreted by a combined approach of transport and reaction modeling. The primary redox processes oxygen-, nitrate-, iron-and sulfate-reduction were identi®ed to be responsible for major turnover rates. A secondary process of sul®de oxidation by ironand manganese (hydr)oxides explained a distinctive sul®de sink. Iron and manganese minerals were removed from the solid phase by reduction. While the iron released in the process completely precipitated again forming sul®des and carbonates, some manganese was removed from the system. Only one proportion of dissolved manganese precipitated to form carbonates.

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“…Often, stiff ODE solvers must be used. Schulz and Reardon (1983) used an analytical solution of the transport operator for solving ADR equations and Valocchi and Malmstead (1992) were the first to use an exact solution of a single-species first-order reaction in their OS procedure to examine the OS error from the transport operator. Geiser (2001) introduced an exact solution of sequential first-order reactions (Sun et al 1999a) into an operator-splitting procedure.…”

Section: Introductionmentioning

confidence: 99%

Modeling reactive transport using exact solutions for first-order reaction networks

Sun

Buscheck

2007

Transp Porous Med

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Operator splitting is often used for solving advection-dispersion-reaction (ADR) equations. Each operator can be solved separately using an algorithm appropriate to its mathematical behavior. Although a lot of research has been done in operator splitting for solving ADR equations, numerical approaches for the reaction operator are computationally expensive. To meet the convergence criteria of ODE (ordinary differential equation) or DAE (differential algebraic equation) solvers, a transport time step has to be subdivided into a large number of reaction time steps. Additional computation effort is also required to reduce the splitting error. In this paper, we develop exact solutions of various first-order reaction networks for the reaction operator and couple those solutions with numerical solutions of the transport operator. The reactions are treated as local phenomena and simulated using exact solutions that we develop, while advection and dispersion are treated as global processes and simulated numerically. The proposed method avoids the numerical error from the reaction operator and requires a single-step calculation to solve the reaction operator. Compared to conventional operator-splitting methods, the proposed method offers both computational efficiency and simulation accuracy.

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A combined mixing cell/analytical model to describe two‐dimensional reactive solute transport for unidirectional groundwater flow

Cited by 79 publications

References 5 publications

Computer simulation of deep sulfate reduction in sediments of the Amazon Fan

Computer simulation of deep sulfate reduction in sediments of the Amazon Fan

The influence of advective transport on redox fronts in column experiments and their numeric modeling. Part 2: modeling of the solid phase and secondary redox reactions

Modeling reactive transport using exact solutions for first-order reaction networks

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