A knowledge-based reactive transport approach for the simulation of biogeochemical dynamics in Earth systems

A knowledge-based reactive transport approach for thesimulation of biogeochemical dynamics in Earth systems

D. R. Aguilera, P. Jourabchi, C. Spiteri, and P. RegnierDepartment of Earth Sciences—Geochemistry, Faculty of Geosciences, University of Utrecht, P.O. Box 80.021, NL-3508TA Utrecht, Netherlands ([email protected])

[1] A Knowledge-Based Reactive Transport Model (KB-RTM) for simulation of coupled transport andbiogeochemical transformations in surface and subsurface flow environments is presented (http://www.geo.uu.nl/�kbrtm). The scalable Web-distributed Knowledge Base (KB), which combinesInformation Technology (IT), an automatic code generator, and database management, facilitates theautomated construction of complex reaction networks from comprehensive information stored at the levelof biogeochemical processes. The reaction-centric approach of the KB-RTM system offers full flexibilityin the choice of model components and biogeochemical reactions. The procedure coupling the reactionnetworks to a generalized transport module into RTMs is also presented. The workings of our KB-RTMsimulation environment are illustrated by means of two examples of redox and acid-base chemistry in atypical shelf sediment and an aquifer contaminated by landfill plumes.

Components: 9832 words, 9 figures, 5 tables.

Keywords: biogeochemistry; information technology; Knowledge Base; numerical methods; reactive transport.

Index Terms: 1009 Geochemistry: Geochemical modeling (3610, 8410).

Received 16 December 2004; Revised 10 March 2005; Accepted 4 May 2005; Published 27 July 2005.

Aguilera, D. R., P. Jourabchi, C. Spiteri, and P. Regnier (2005), A knowledge-based reactive transport approach for the

simulation of biogeochemical dynamics in Earth systems, 6, Q07012, doi:10.1029/2004GC000899.

1. Introduction

[2] Reactive transport models (RTMs) are power-ful tools for capturing the dynamic interplay be-tween fluid flow, constituent transport, andbiogeochemical transformations [Steefel and VanCappellen, 1998]. They have been used to simu-late, among others, rock weathering and soil for-mation [e.g., Ayora et al., 1998; Soler and Lasaga,1998; Steefel and Lichtner, 1998a, 1998b; Thyne etal., 2001; Soler, 2003; De Windt et al., 2004],nutrient dynamics in river drainage basins andestuaries [e.g., Soetaert and Herman, 1995; Billenet al., 1994; Regnier et al., 1997; Regnier andSteefel, 1999; Vanderborght et al., 2002], reactivetransport in groundwater, like contamination ofaquifers [e.g., Engesgaard and Traberg, 1996;Brown et al., 1998; Hunter et al., 1998; Xu et al.,

1999; Murphy and Ginn, 2000; Barry et al., 2002;Brun and Engesgaard, 2002; Thullner et al., 2004;van Breukelen et al., 2004], early diagenetic trans-formations in sediments [e.g., Soetaert et al., 1996;Boudreau, 1996; Van Cappellen and Wang,1996; Dhakar and Burdige, 1996; Berg et al.,2003; Jourabchi et al., 2005], benthic-pelagic cou-pling in ocean systems [e.g., Soetaert et al., 2000;Archer et al., 2002; Lee et al., 2002] and hydrocar-bon migration and maturation in sedimentary basins[e.g., Person and Garven, 1994]. By integratingexperimental, observational and theoretical knowl-edge about geochemical, biological and transportprocesses into mathematical formulations, RTMsprovide the grounds for prognosis, while diagnosticcomparison between model simulations and mea-surements can help identify gaps in the conceptualunderstanding of a specific system or uncertainties

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27 July 2005

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ISSN: 1525-2027

Copyright 2005 by the American Geophysical Union 1 of 18

in proper parameterization of biogeochemical pro-cesses [Berg et al., 2003; Jourabchi et al., 2005].

[3] RTMs have traditionally been developed andused to investigate the fate and transport of aselected set of chemical constituents within agiven compartment of the Earth system (e.g., theearly diagenetic models by Soetaert et al. [1996],Boudreau [1996], Van Cappellen and Wang [1996],Dhakar and Burdige [1996], and references citedabove). As a result, they have tended to be envi-ronment and application specific with regards tothe flow regime and the biogeochemical reactionnetwork.

[4] Although the first attempts to develop interac-tive software systems for automatic solution ofmodels based on ordinary and partial differentialequations date back to the creation of digital com-puters [e.g., Young and Juncosa, 1959; Lawrenceand Groner, 1973; Mikhailov and Aladjem, 1981,and references therein], such developments have sofar received little attention in the field of reactive-transport modeling. Literature review shows thatRTM codes allowing for more flexible definition ofstate variables and processes without requiring in-depth knowledge of programming or numericalsolution techniques have been developed over thelast decade [e.g., Reichert, 1994; Chilakapati,1995; Regnier et al., 1997; Chilakapati et al.,2000; MacQuarrie et al., 2001; Meysman etal., 2003a, 2003b; Van der Lee et al., 2003].Database tools, such as that developed by Katsevet al. [2004], have also been presented recently tothe reactive transport community. Model flexibilityis a critical feature since a major challenge in thefield of reactive transport modeling is the realisticrepresentation of the highly complex reaction net-works (RN) that characterize the biogeochemicaldynamics of natural environments [e.g., Mayer etal., 2002; Berg et al., 2003; Quezada et al., 2004].At the same time, many field- and laboratory-basedexperiments are also being conducted to identifynovel reaction pathways, quantify reaction ratesand microbial activity levels, describe ecologicalcommunity structures, and elucidate interactionsbetween biotic and abiotic processes. This rapidlygrowing knowledge about biogeochemical trans-formation processes creates a need for efficientmeans of transferring new experimental findingsinto RTMs.

[5] Here, a unified modeling approach for imple-menting complex reaction networks in RTMs ispresented. Our simulation environment is based ona modular approach to facilitate incorporation of

new theoretical and experimental information onthe rates and pathways of biogeochemical reac-tions. The key novel feature of the modelingenvironment is a Web-distributed Knowledge Base(KB) of biogeochemical processes, which acts asthe evolving repository of up-to-date informationgained in the field of geochemistry. The implemen-tation of such a library within a simulation envi-ronment is a major step toward the model’sflexibility, because it is at the level of an easilyaccessible open resource, the KB, that process-based theoretical and experimental advances areincorporated in the modeling process. Model gen-eration is conducted via a graphical user interface(GUI) on a Web-based ‘‘runtime’’ server, whichallows for the development of biogeochemicalreaction network modules. That is, informationstored at the level of individual biogeochemicalprocesses can be combined into mathematicalexpressions defining completely the (bio)chemicaldynamics of the system. Since the reaction networkis assembled from information stored at theprocess level, almost any conceivable combina-tion of mixed kinetic and equilibrium reactionscan be implemented in our model architecture.The selected RN can easily be merged withexisting transport models, hence creating a flex-ible framework in which to assemble RTMs. Theproposed approach allows the RTM communityto test and compare, in close collaboration withexperimentalists, alternative mathematical descrip-tions of coupled biogeochemical reaction networks.For example, increasingly detailed representationsof biogeochemical processes can be incorporated inthe Knowledge Base. Reaction network modules ofincreasing complexity may then be assembled andcoupled to surface or subsurface flow models, inorder to determine which level of biogeochemicalcomplexity is adequate to simulate chemical systemdynamics at variable spatial and temporal resolu-tions. By taking a ‘‘reaction-centric’’ approachwhich utilizes the unifying conceptual and math-ematical principles underlying all RTMs, one-dimensional (1D) transport descriptions relevantto many compartments of the Earth system (rivers,estuaries, groundwater or sediments) can be in-corporated in our simulation environment. Theproposed approach should thus help overcometraditional disciplinary barriers between the differ-ent subfields of RTMs.

[6] The paper is structured as follows: First, themass conservation equation describing 1D coupledtransport and reaction is briefly presented. A gen-eralized continuum representation is proposed,

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which allows for the simulation of reactive-trans-port problems characterized by different flowregimes and dispersion intensities. A brief descrip-tion on how an existing Automatic Code Generator(ACG) based on symbolic programming [Regnieret al., 2002] can be used to create the modelspecific source code necessary to the numericalsolution of the governing equations is then given.We demonstrate how our Web-distributed Knowl-edge Base concept, which combines InformationTechnology with symbolic computing techniques,directs the mathematical formulation of the bio-geochemical reaction network and leads to a mod-eling environment offering full flexibility. Finally,the workings of our KB-RTM are illustrated withtwo contrasting examples of complex redox andacid-base geochemistry in an aquatic sediment andan aquifer, respectively.

2. Mathematical Representation ofReactive-Transport Equations

[7] A one-dimensional continuum representationof coupled mass transport and chemical reactionsin Earth systems can be described mathematicallyby a set of partial differential equations (PDEs) intime and space of the form

x@Cj

@t¼ @

@xD � x � @Cj

@x

� �� @

@xv � x � Cj

� �� �j|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

T

þXNr

k¼1

lk;j � sk|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}

R

; j ¼ 1; . . . ;m; ð1Þ

where t is time and x denotes the position alongthe 1D spatial domain. Particular solutions ofequation (1) require specification of initial andboundary conditions. Further discussion about thegeneralized continuum representation of theadvection-dispersion-reaction (ADR) equation isgiven by Regnier et al. [2002] and Meile [2003].The first two terms on the right hand side, insquare brackets, compose the transport operator(T); the last one (R) represents the sum oftransformation processes (e.g., reactions) affectinga species j of concentration Cj. Table 1 shows thatx, D and v are generic variables which takedifferent meanings depending on the environmentconsidered. sk represents, for kinetic reactions, therate of the k-th reaction and lk,j is the stoichio-metric coefficient of species j in that reaction.Currently, it is assumed that the reaction processes

(R) have no effect on the physical or transport (T)properties of the system (i.e., x, D and v areunaffected by reactions). The rate sk is of arbitraryform, even nonlinear, and can be a function ofseveral concentrations of the system. Through thiscoupling by the reaction terms, most multicompo-nent problems result in a set of coupled nonlinearpartial differential equations (PDEs) of size m,number of species of the reaction network. In theevent that some of the reactions considered areassumed to be at equilibrium, algebraic expressionsbased on mass action laws are introduced into thesystem of equations to be solved [Regnier et al.,2002]. By replacing one or more of the mdifferential equations associated with reactions withalgebraic relations based on a mass action expres-sion in the local equilibrium case, the set of ODEs istransformed into a set of differential-algebraicequations (DAEs) [Chilakapati, 1995; Hindmarshand Petzold, 1995a, 1995b; Brenan et al., 1989].This transformation leads to a system ofm equationsto solve, including mk equations associated withkinetic reactions, and me algebraic equations basedon mass action expressions.

[8] The numerical solution of the set of discretizedPDEs and DAEs (@t ! Dt, @x ! Dx) commonlyrequires the use of implicit methods in order to becomputationally efficient [Steefel and MacQuarrie,1996]. We currently make use of the time splittingtechnique, which consists of solving first the trans-port and then the reaction terms in sequence for asingle time step. This method is referred to as the

Table 1. Meaning of the Generalized Variables x, D,and v for Different Environmentsa

Surface FlowAquaticSediment

GroundwaterFlow Path

Solutes orSuspended Solids Solids Solutes Solids Solutes

x A 1 � f f 1 � f fv Vflow w w + vflow 0 Vflow

D Kturb Db Db + Dsed 0 Ddisp

aFrom Meile [2003]. In porous media flow, distinction between an

aqueous and a solid phase must be considered, and C is either aconcentration of solute or solid. A[L2], cross-section area of the surfaceflow channel; f [�], porosity; Vflow[LT

�1], externally imposed flowvelocity; w[LT�1], burial velocity defined with respect to the sediment-water interface (SWI); vflow[LT

�1], flow velocity acting only on solutesexternally imposed or from porosity change; usually defined withrespect to the SWI [e.g., Boudreau, 1997]; Kturb[L

2T�1], longitudinalturbulent dispersion coefficient; Db[L

2T�1], bioturbation coefficient;Dsed[L

2T�1] = Dmol/(1 � ln(f2)), tortuosity corrected moleculardiffusion coefficient for solutes at in situ temperature and salinity[Boudreau, 1997]; Ddisp[L

2T�1] = aL � jVflowj, longitudinal dispersion,where aL [L] is the longitudinal dispersivity [Freeze and Cherry,1979].

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sequential noniterative approach (SNIA). Whensolving the reaction part an iterative method isrequired to numerically find the roots of thefunction residuals, fj, which correspond to massbalance equations and, if equilibrium reactions areincluded, mass action equations. This is becausethe reaction terms can be nonlinear functions ofthe species concentrations. By far the most com-mon approach for finding the root of nonlinearsets of equations is the Newton-Raphson method[Press et al., 1992]. This method involves the useof a first degree Taylor series expansion tolinearize the problem for every single iterationstep. The function residuals, fj, representing thereaction network (RN), and the Jacobian matrix,which contains the partial derivatives of thefunction residuals with respect to the unknownconcentrations, are the most important pieces ofinformation required to implement the Newton-Raphson algorithm [e.g., Dennis and Schnabel,1996]. Once linearized, the resulting problem issolved using linear algebra methods, such as theLU decomposition [e.g., Strang, 1988]. A precisedefinition of the function residuals and the Jaco-bian matrix is given by Regnier et al. [2002].

3. Reactive Transport Modeling Withthe Knowledge Base

[9] Inspection of the transport and reaction oper-ators T and R in equation (1) shows that thefollowing information is required to define a spe-cific reaction transport application:

[10] 1. Domain definition: spatiotemporal size andresolution (xtot, Dx, ttot, Dt), where xtot and ttot standfor the total domain length and simulation time,respectively, and Dx and Dt are the space and timestep used for numerical integration, respectively.

[11] 2. Transport coefficients x, v and D (Table 1).

[12] 3. Reaction Network (RN): processes; rateparameters and equilibrium constants; species in-volved and stoichiometry.

[13] 4. Boundary (BC) and initial (IC) conditionsfor every species of the RN.

[14] In a modeling environment offering full flex-ibility, this information is specific to each RTMapplication and needs to be automatically translatedinto source code. This task is relatively easy forthe physical domain definition, transport parame-ters, BC and IC. However, if flexibility in choos-ing process formulations is also important, then

the stiff system of differential equations using alinearization method (such as the above-citedNewton-Raphson algorithm) necessitate automaticdifferentiation schemes for the calculation of theterms in the Jacobian matrix. Automatic symbolicdifferentiation offers the advantage of producingderivatives of potentially complicated functionswhich are accurate up to the precision of theprogramming language used (e.g., FORTRAN),plus the convenience of updating the derivativeseasily if the original functions are changed [Steefeland MacQuarrie, 1996]. Automated differentiationfor stiff sets of differential equations is one of thekey features of our Automatic Code Generation(ACG) procedure [Regnier et al., 2002].

[15] The simultaneous implementation of a libraryof biogeochemical processes into a KnowledgeBase (KB) is an additional crucial component ofthe proposed simulation environment. The KBmakes it possible to take full advantage of theACG. The integration of these two componentswithin a Web system shows how the combinationof Information Technology with advanced symbolicprogramming allows the use of the Internet as asoftware provider in the area of Reactive-Transportmodeling (Figure 1).

3.1. The Internet as a Software Provider

[16] An Internet system developed in PHP lan-guage (http://www.php.net) provides the adaptiveJavaScript and HTML code for the Graphical UserInterface (GUI), as well as the Web-based ‘‘run-time’’ server to our modeling environment. It isaccessible at http://www.geo.uu.nl/�kbrtm. TheGUI is of evolutionary nature, that is, it dynami-cally adapts to changes in structure and content ofthe KB system as well as to the selections made bythe user.

[17] Initially, the user accesses an interface for theKB system in the style of a Web form forselection of desired biogeochemical processes(Figure 1, step 1; further detailed in Figure 2).Species-independent physical parameters (defini-tion of spatiotemporal domain and most transportcoefficients in Table 1) are also defined at this stage.

[18] Figure 2 gives a detailed description of themodel design procedure. The KB system consistsof a set of biogeochemical processes, containingdefault formulations for reactions, which are avail-able to all users of the system (common KB) andwhich cannot be modified. However, these com-mon processes can be edited if desired, or new

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processes created using a standard template, andstored in a ‘‘private’’ KB library which is inacces-sible to other users. To facilitate model develop-ment, processes can be grouped in differentsubsets, for instance, in terms of reaction types(see below).

[19] The selected processes specify the user-definedreaction network. The latter is then analyzed todetermine the list of chemical species involved inthe RN. A second Web submission form is subse-quently created to specify all species-dependentparameters (such as molecular diffusion coeffi-

Figure 1. Structure of the Knowledge-Based (KB) Reactive Transport Model (RTM) environment which uses theWeb as a software provider: 1, form submission; 2, parsing of the ASCII files into MAPLE; 3, MAPLE/MACROFORT symbolic computing; 4, translation of MAPLE results into FORTRAN; 5, linking and compilation ofthe FORTRAN code; 6, transfer of the executable file to the user via e-mail.

Figure 2. KB-Internet model design process (detailed description of step 1 in Figure 1): (1) Process edition orcreation. Templates can be used to speed up the implementation of new processes. Modified or new process files arestored in a ‘‘private’’ KB which is accessible only to a single user. (2) Process selection from the common and privateKB process pools, and specification of the physical support. (3) Analysis of the selection and creation of adynamically adaptive Web form to input reaction network dependent parameters. (4) Submission of complete modelinformation (processes selected, physical parameters, and species-dependent parameters) to the ACG via our Webserver.

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cients, initial and boundary conditions. At thisstage, default parameter values for reaction dynam-ics expressions can also be modified. All modelsettings can be stored on the server and used againor modified in future modeling sessions.

3.2. Knowledge Base (KB)

[20] The common KB (Figure 2) contains subsetsof biogeochemical process libraries and parame-ter values, including default formulations forbiogeochemical reaction rates and equilibria.The design provides an expandable structurepermitting the easy addition of new elements(processes, variables, parameters) into a ‘‘pri-vate’’ KB library. Several formulations can beimplemented for the same biogeochemical pro-cess, simply by naming the respective processfiles differently. This permits a ready-made set ofspecialized process descriptions for a number ofdifferent scenarios, and therefore the formulationthat best fits the simulation requirements can beselected.

[21] The biogeochemical processes currentlyimplemented are distributed among the followingclasses, which form the architecture of our KB:primary redox reactions (PRR) involving organicmatter oxidation pathways, secondary redox pro-cesses (SRR, biotic and abiotic redox reactions),aqueous complex formation (ACF), homogeneousacid-base equilibrium reactions (ABE), nonredoxmineral precipitation and dissolution (MPD), ad-sorption and ion exchange (AIE) and gas-waterreactions (GWR). These classes represent only oneof the many possible categorizations. In fact, modelspecific categories can be added to the system.According to different criteria, one process couldbe assigned not solely to one, but potentially toseveral classes.

[22] The file structure for each process consists ofthe set of species (dissolved or solid) involved inthe specific process, the definition of the reactiontype (kinetic or equilibrium) and the stoichiometry.The corresponding rate or mass action law anddefault parameter values are also specified. Fieldsof informative nature (e.g., reaction class, key-words for searching, documentation, units forparameters and concentrations) complete the pro-cess file description. As an example, Figure 3shows the process file for aerobic degradation oforganic matter as an example. Finally, the set ofvariables and parameters for the entire selectionof process files, along with the respective functionscharacterizing kinetic or equilibrium processes and

their corresponding stoichiometries, fully determinethe RN.

3.3. Parsing Procedure and AutomaticCode Generation

[23] After the reactions of interest have beenselected and their list submitted in addition tothe remaining application-specific data (step 1 inFigure 1), an automated procedure is launchedthat parses all this information into ASCII files.This completes the model setup procedure carriedout by the user on the GUI of the Web-distributedKB. It is illustrated in detail by means of exam-ples in the next section.

[24] The parsing procedure involves reading infor-mation from files directly generated by the Internetsystem (e.g., definition of the physical domain) andfrom files originated by the KB system (reactionnetwork). The former can easily be processed bythe Automatic Code Generator (ACG), whereas theinformation contained in the KB files must first beconcatenated in the appropriate format. The mainfeatures of the parsing involves extracting andassembling, from the set of selected processes, anumber of lists containing all the species involvedin the RN, along with appropriate initial andboundary conditions, the complete set of kineticexpressions and equilibrium constraints necessaryto define the function residuals fj, and all theparameters appearing in fj, including their associ-ated numerical values. Stoichiometric coefficients,which relate the changes in species concentrationsto the progress in any individual reaction, isanother crucial component extracted from the KBprocess files. A check for unit consistency for bothspecies concentrations and parameters values iscarried out at this stage.

[25] Once parsing is completed, the followingoperations are performed in background on ourWeb-based ‘‘runtime’’ server (Figure 1, steps 2–5).First, the information from the ASCII-files is usedto assemble the stoichiometric matrix, that is, themathematical representation of the user-definedreaction network (Figure 1, step 2). Second, a setof symbolic programming operations is performed(Figure 1, step 3) using the MAPLE softwareenvironment [Chilakapati, 1995; Regnier et al.,1997; Amberg et al., 1999; Regnier et al., 2002].The most important one involves the constructionof the Jacobian matrix from the series of functionresiduals. Third, the function residuals, the Jaco-bian matrix, plus all user-dependent informationare translated into fully structured FORTRAN code

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(Figure 1, step 4) using the MACROFORT package[Gomez, 1990] combined with our own library ofMAPLE procedure (ACGLIB#). The resultingroutines are then linked with our numerical engine,which contains standard routines for solving trans-port equations and a linear algebra solver for thesets of linearized process equations generated bythe preprocessor (Figure 1, step 5). Finally, uponcompletion of the automated generation procedure,the ‘‘runtime’’ server compiles and sends the result-ing model executable to the user via e-mail(Figure 1, step 6).

[26] The accuracy of the numerical engine and theACG (referred to as Biogeochemical Reaction

Network Simulator (BRNS) by Regnier et al.[2003]) has recently been evaluated by Thullneret al. [2005], from a comparison between theirmodel results with those obtained with two wellestablished RTMs for porous media flow applica-tions (e.g., STEADYSED [Van Cappellen andWang, 1996; Hunter et al., 1998] and TBC [Schaferet al., 1998a, 1998b]). Comparison with field datafrom Skagerrak sediments [Canfield et al., 1993]and a sand column experiment [von Gunten andZobrist, 1993] was also performed by theseauthors. Here, the performance of the KB-RTMis evaluated further by means of two contrastingscenarios. However, the focus is mainly on theWeb-distributed KB system and how this concept

Figure 3. Example of the process file for oxic degradation of organic matter: ‘‘oxic.txt.’’ The reaction expressiondescribed by the process file, with the corresponding stoichiometric coefficients (underlined), is

1 ch2oþ SDo2 ! x�yþ2zð Þ�SDx

co2þ y�2zð Þ�SDx

hco3þ y�SDxnh4. The values for the entries [Solids], [Stoichiome-

try], and [Variable_units], on the one hand, and [Default_parameter_values] and [Parameter_units], on the other hand,follow the column-wise order of the entries for [Names_of_variables] and [Names_of_parameters], respectively.

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facilitates the incorporation and modification ofcomplex biogeochemical reaction networks intoRTM applications.

4. Applications

4.1. Introduction

[27] Two applications of redox dynamics in porousmedia are presented: an early diagenetic (ED)model(saved in our server system as ‘‘EDscenario’’) ofshelf sediments and two simulations of a ground-water aquifer (GWA) contaminated by a landfillplume (saved respectively as ‘‘GWscenario1’’ and‘‘GWscenario2’’). All model applications can befound on our Web-based ‘‘runtime’’ server as part ofthe KB, at http://www.geo.uu.nl/�kbrtm. In whatfollows, the discussion addresses only the majorfeatures, that is, similarities and differences betweenthe applications. The user is referred to the Website for exact parameterization.

[28] In short, the focus is on redox processes, acid-base chemistry and carbonate/sulfide mineralphases precipitation-dissolution. Since the inter-play of these processes determines the pH in bothsystems, which itself is sensitive to relative imbal-ances in reaction rates [Jourabchi et al., 2005, andreferences therein], computation of realistic pHprofiles with mechanistic process models repre-sents a challenging and important test application.

[29] The structure of the reaction network (RN) issimilar for the sediments and groundwater appli-cations, with organic matter serving as the primaryelectron donor. The RN combines 23 species and24 reactions for the ED scenario, and 25 speciesand 36 reactions for the GWA application. Thisincludes kinetic transformations (all primary andsecondary redox reactions and nonredox mineralprecipitation-dissolution processes) and equilibriumacid-base reactions (see below). Almost 50 param-eters are used in the definitions of rates and equi-librium constraints. Even though the set of reactionsis similar in both applications, reaction parametervalues may contrast. For example, the quality of theorganic matter may differ, leading to faster degra-dation rates near the contaminant site, or differencesin ionic strengths affect the apparent solubilityconstant in the marine setting. Note also that differ-ent units are used in both applications, with soluteand solid concentration respectively expressed inmol/Lpore water and mol/gsolid in the ED application,and concentrations in moles/Lpore water for thesolutes, and moles/Ltotal volume for the solids inthe GWA examples. We will adopt the units used

in the ED simulation in what follows. The readershould refer to the GWA scenario files in ourserver (http://www.geo.uu.nl/�kbrtm) for moredetails about the unit system selected. The respec-tive RNs are complex and involve many param-eters and rate formulations, yet they can be easilyassembled through the KB and the Web interface.The system of DAEs is stiff in both environments,which presents a rigorous test for the proposedmodeling approach.

[30] Time and space scales of the ED and GWAsimulations are fundamentally different (dm andmillennia versus km and decades, respectively;Table 2). In addition, the mechanisms and relativeintensities of transport processes are not the same,with dominant diffusional transport by bioturbationand molecular diffusion in the ED and dominantadvective transport in the GWA. Another majordifference between the two applications is thetreatment of solid species in the model: in theGWA, a moving fluid percolates through a fixedsolid matrix, while in the ED, solids are mixed bybioturbation.

4.1.1. Groundwater Aquifer

[31] In the GWA application, the focus is on thebiogeochemical evolution of the major constituentsin a landfill leachate plume infiltrating an initiallyoxic, pristine aquifer of low porosity (f = 0.25).Simulations are carried out over a 400 m flow path

Table 2. Web Submission Form I (Physical Para-meters): Definition of the Physical Domain, MajorTransport Coefficients and Forcing Functions as Well asGlobal Output Parameters for the Early Diagenetic andGroundwater Aquifer Applications, Respectivelya

ED GWA

Total time 1500 yr 22 yrTime step 1.0 10�4 yr 5.0 10�4 yrTotal length 40 cm 40000 cmNumber of nodes 401 101Porosity 0.85 0.25Cross section 1.0 cm2 1.0 cm2

Flow velocity 0.0 cm/yr 250.0 cm/yrBurial velocity 0.04 cm/yr 0.0 cm/yrBioturbation coefficient 3.0 cm2/yr 0.0 cm2/yrLongitudinal dispersivity 0.0 cm 400 cmTemperature 10�C 15�CSalinity 35.0 PSU 0.1 PSUFirst output time 1.0 yr 1.0 yrOutput interval period 2.0 yr 1.0 yr

aED, early diagenetic; GWA, groundwater aquifer. All entries are

species independent and hence are not influenced by the selected RN.For each selected kinetic process, the Web interface prompts the userwhether a spatial distribution of rates should be generated at outputtimes.

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which is infiltrated at the upstream boundary by theanoxic landfill-leachate recharge. In this case, themodel setup (see the scenario files in our Websystem) is based on Hunter et al. [1998] and VanCappellen and Wang [1996]. On the inflow side ofthe domain (x = 0 cm), a specified concentration(i.e., Dirichlet boundary condition) is applied forall solute species. The chemical composition of theleachate is characterized by a high dissolved or-ganic carbon (DOC) loading represented by twofractions of different reactivity. At the outflow(xtot = 4 � 104 cm), a concentration gradient (i.e.,Neumann boundary condition) is specified for alldissolved chemical species. Solids are consideredimmobile and therefore are only affected by localbiogeochemical transformations. Solutes are trans-ported by fluid flow motion (250 cm � yr�1) andmacroscopic dispersion (dispersion coefficient D =4 � 105 cm2 yr�1 or dispersivity aL = 400 cm). Theoverall redox dynamics and the resulting effect onpH evolution are investigated along a flow line aftera transient simulation period of 22 years. Table 2presents the values of the coefficients implementedto define the GWA physical framework via the Websubmission form I.

4.1.2. Shelf Sediment

[32] In the ED simulation, transient depth distribu-tions of redox sensitive species and rates arecomputed for the case of a typical shelf sediment(total depth: 40 cm, T: 10�C, S: 35%) of highporosity (f = 85%). The simulation period is1500 years, starting from constant concentrationprofiles. The model setup is a slightly modifiedversion of the shelf case presented by VanCappellen and Wang [1996]. The exact definitioncan be found in our Web system (http://www.geo.uu.nl/�kbrtm). The primary driving force forbiogeochemical transformation is the solid flux oforganic matter (32 mmol cm�2 yr�1) depositing atthe sediment-water interface, assumed to be con-stant in time. The length scale of the simulation(xtot = 40 cm) is chosen such that at x = xtot, allrates are very close to zero, a condition whichallows the specification of a Neumann boundarycondition. At the sediment-water interface (x =

0 cm), a flux boundary condition is assigned for allsolids, while typical bottom-water concentrations(Dirichlet condition) provide the upper boundarycondition for solutes. Externally impressed flow isneglected here, and hence the advective velocity(0.04 cm/yr) is solely due to the burial rate. Allchemical species are subject to bioturbation, andsolutes are further transported by molecular diffu-sion. Table 2 presents the values of the coefficientsimplemented to define the ED physical frameworkvia the Web submission form I.

4.2. Reaction Network

[33] The reaction network, which is common to thetwo simulations, consists of the six major metabolicpathways for organic matter degradation (aerobicdegradation, denitrification, Mn and Fe reduction,sulfate reduction and methanogenesis), and a set of10 secondary reoxidation reactions (Table 3a). Inaddition to the microbial and chemical reduction ofMn and Fe oxides, precipitation/dissolution ofMnCO3, FeCO3 and FeS mineral phases are alsoincluded, which have an effect on redox and acid-base chemistry. Over 45 parameters (such as kPRR,KEA, kSRR, kd, kp, SSA, Ksp, and Keq, see below)are extracted from the KB for these simulations.

[34] The shelf sediment application is also forcedby a constant flux of calcite (8 mmol cm�2 yr�1).Calcium carbonate buffering is ignored in thegroundwater application, as it is assumed that thelandfill plume percolates through a noncalcareousgroundwater aquifer. Larger pH changes are thusexpected in this case. Finally, the acid-base chem-istry of the ED application includes the dissociationof carbonic, sulfidic and boric acids. Since totalboron is negligible in freshwater environments, thedissociation of the latter weak acid is ignored in theGWA simulation.

[35] According to the mathematical functionalexpressions and the ‘‘taxonomy’’ proposed in ourKB, four types of chemical processes are includedin our RN (Table 3a). For primary redox reactions(PRR), the rates of the respective metabolic path-way (PRR i) are given by [e.g., Van Cappellen andGaillard, 1996]

if EAi�1½ � > KEA;i�1 then PRRi ¼ 0

if EAi�1½ � KEA;i�1 then

if EAi½ � > KEA;i then PRRi ¼ kPRR � CH2O½ � � fi

if EAi½ � KEA;i then PRRi ¼ kPRR � CH2O½ � � fi �EAi½ �KEA;i

8><>:

8>>>>><>>>>>:

ð2Þ

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where kPRR[yr�1] is the rate constant, CH2O rep-

resents the electron donor (complex macromolec-ular organic matter) and EAi is the electronacceptor of the ith metabolic pathway, and

fi ¼ 1�Xi�1

j¼1

EAj

� �KEA;j

� � !: ð3Þ

[36] The proposed rate law assumes first-orderdependency with respect to the electron donorand a pseudo Michaelis-Menten type relationshipwith respect to the EA. Equation (2) indicates that aspecific metabolic pathway is inhibited if a morefavorable EA is present in the system at sufficientlyhigh concentrations, that is, if a reaction yielding

more free energy takes place [e.g., Van Cappellenand Wang, 1996; Berg et al., 2003].

[37] Rates of secondary redox reaction (SRR) arecurrently implemented as bimolecular rate lawswith a first-order dependency with respect to eachof the reactants [e.g., Van Cappellen and Wang,1996]:

SRR ¼ kSRR � EDO½ � � EA½ �; ð4Þ

where EDO is an inorganic electron donor (e.g.,Fe+2, Mn+2, H2S, . . .) and kSRR is the rate constantwith units of Lporewater � mol�1yr�1 if all reactantsare solutes, or gsolidmol

�1yr�1 if a solid species isinvolved in the SRR (e.g., MnO2 or Fe(OH)3).

[38] Nonredox Mineral Precipitation/Dissolution(MPD) rate laws are given by [e.g., Appelo andPostma, 1999]

MPD ¼ kd � MIN½ � � 1� IAP=Ksp

� �nif IAP < Ksp

MPD ¼ kp 1� IAP=Ksp

� �nif IAP > Ksp

ð5Þ

where kd[yr�1] and kp[mol � gsolid�1 � yr�1] are the

rate constants for dissolution and precipitation,respectively, [MIN] denotes the concentration ofthe dissolving mineral [mol/gsolid], IAP is the IonActivity Product, Ksp the equilibrium constant (orsolubility product), and n the order of the reaction.In the groundwater scenario, equilibrium constantscorrected for the in-situ temperature (15�C) areused, while in the early diagenetic simulations,apparent equilibrium constants which incorporateboth temperature (10�C) and electrolyte effects ofmarine solutions have been applied [Boudreau,1997].

[39] Acid-base equilibriums (ABE) are con-strained according to [e.g., Van Cappellen andWang, 1996]

ABE � Keq � HmAn�½ � � Hþ½ � � Hm�1A

nþ1ð Þ�h i

¼ 0; ð6Þ

where A stands for the fully dissociated form ofthe protolytic species (e.g., CO3

2�, S2� or BO32�),

m is the number of protons (e.g., m = 2 inH2CO3), n is the negative charge of thedissociating species (e.g., n = 0 for H2CO3, n =1 for HS�), and Keq is the equilibrium constantfor a specific acid-base reaction. Corrections forin-situ conditions are performed identically thanfor solubility products.

[40] Adsorption-desorption reactions (ADS) arecurrently implemented as equilibrium-type pro-

Table 3a. Web Submission Form I (Reaction Net-work): List of Processes Incorporated Into the ReactionNetwork, Following the ‘‘Taxonomy’’ Proposed in OurKnowledge Base Systema

Group of Processes Reaction

Acid-base reactions(ABE)($)

1) Carbonate2) Bicarbonate3) Sulfide4) Borateb

Primary redox(PRR)(!)

5) degradation6) Denitrification7) Mn(IV) reduction8) Fe(III) reduction9) Sulfate reduction10) Methanogenesis

Secondary redox(SRR)(!)

11) Nitrification12) Mn2+ reoxidation by O2

13) Fe2+ reoxidation by O2

14) Fe2+ reoxidation by MnO2

15) Sulfide reoxidation by O2

16) Sulfide reoxidation by MnO2

17) Sulfide reoxidation by Fe(OH)318) Methane reoxidation by O2

19) Methane reoxidation by SO42�

20) FeS reoxidation by O2

Precipitation-dissolution (MPD)(!)

21) FeS dissolutionc/precipitation22) MnCO3 dissolution

c/precipitation23) FeCO3 dissolution

c/precipitation24) CaCO3 dissolution/precipitation

c

Adsorption-Ionexchange

25) Ammonium adsorptionc

aInformation similar to the one shown in Figure 3 is parsed into the

ACG for each of the selected processes. For each selected kineticprocess, the Web interface prompts the user whether or not a spacedistribution of kinetic rates should be generated at output times (seeTable 2). In the GWA case, two fractions of organic matter withdifferent reactivities have been taken into consideration, whichtherefore have separate respective primary redox reactions.

bSpecific to ED.

cSpecific to the GWA.

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cesses [e.g., Langmuir, 1997], using a classicaldistribution coefficient (Kd):

ADS � Kd � Xaq

� �� Xads½ � ¼ 0; ð7Þ

where Xaq and Xads denote the dissolved andadsorbed species, respectively.

[41] Table 3b gives the complete list of variableswhich is automatically concatenated from the se-lected RN. Since in the convention used in the EDapplication, solid and solute concentrations areexpressed in moles/gsolid and moles/Lpore water,respectively, a conversion factor has to be appliedto the stoichiometric coefficients of solutes, if arate is expressed in moles of solid transformed perunit time and vice-versa. This conversion factor,SD, is given by

SD ¼ r � 1� ff

� �� 1000; ð8Þ

where r[g/cmsolid3 ] is the density of the bulk solid

phase and f[�] the porosity. Note that suchcoefficient is not needed for the GWA application,since, in this case, the convention used forconcentrations is moles/Lpore water for the solutes,and moles/Ltotal volume for the solids.

[42] For instance, the rate of reoxidation of Fe2+ byMnO2 (reaction 14 in Table 3a) is given by R14 =�d[MnO2]/dt = kSRR,14[Fe

2+] � [MnO2]. Since therate law is given in moles of MnO2 reduced perunit time per unit gram of solid (i.e., kSRR has unitsof L/(molFe2+ � yr)), the appropriate stoichiometriccoefficients for each species are

HCO�3 þ Fe2þ þMnO2 ! Fe OHð Þ3 þ Mn2þ þ CO2

�2SD � 2SD � 1 þ 2 þ 1SD þ 2SD

ð9Þ

[43] As explained in the previous section, theconcatenated list of variables (Table 3b) is used

to generate a new Web submission form in whichall variable-specific parameters are constrained.The information to be provided is identical forevery variable of the RN. As an example, Table 4shows such parameterization for O2 in the case ofthe ED application.

[44] The information provided in Tables 2, 3a, 3b,and 4 completely specifies the problem at hand.This information is then parsed in the ACG forcreation of the model executable via our Web-based runtime server. Examples of model resultsare succinctly discussed below.

4.3. Results and Discussion

4.3.1. Groundwater Simulation

[45] A stepwise approach is used here to inves-tigate redox and acid-base chemistry. In the first

Table 3b. Complete List of Variables Automatically Associated With the Selected Reaction Networka

Common

Specific

GWA ED

H+ (d) Mn2+ (d) CO32� (d) Fe(OH)3 (s) (CH2O)lab (d) CH2O (s)

Ca2+ (d) MnO2 (s) H2CO3 (d) MnCO3 (s) (CH2O)ref (d) B(OH)3 (d)CaCO3 (s) O2 (d) CH4 (d) HS� (d) NH4(ads)

+ (s) B(OH)4� (d)

NH4+ (d) NO3

� (d) H2S (d) FeS (s)SO4

2� (d) HCO3� (d) Fe2+ (d) FeCO3 (s)

HPO42� (d)

aVariables are either solids (s) or dissolved (d) chemical species. Note that the GWA application includes organic matter as both labile (lab) and

refractory (ref) fraction. CH2O denotes complex macromolecular organic matter characterized by the formula (CH2O)x(NH3)y(H3PO4)z, where x:y:zis the stoichiometric C:N:P ratio.

Table 4. Web Submission Form II: Species-DependentParameters Associated With Oxygen for the EDApplicationa

Parameter Group Field Assignment

Molecular diffusioncoefficient

value at 0�C 380.45

temperaturedependency a

0.06

Upper boundarycondition

type fixed concentration

value 250.0e-6

Lower boundarycondition

type fixed gradient

value 0.0

Output file generate yesname o2.dat

aSimilar information must be provided for every chemical species

of the RN (Table 3b).

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simulation (scenario 1, Figures 4 and 5), onlythe primary redox reactions and acid-base equi-libria are considered (reactions 1–10, Table 3a).In a second scenario (Figures 6 and 7), reoxi-dation reactions of the reduced products oforganic matter degradation and precipitation/dis-

solution of carbonate and sulfide minerals areadded to the reaction network.

4.3.1.1. Scenario 1

[46] In this first simulation, only the six primarybiodegradation reactions as well as the carbonate

Figure 4. Pathways of CH2Oref degradation obtained in the GWA application for scenario 1 after a transientsimulation time of 22 years.

Figure 5. The pH distribution along the flow path in the GWA application for scenario 1 after a transient simulationtime of 22 years.

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and sulfide dissociation reactions are considered(reactions 1, 3 and 5–10, Table 3a). The locationand magnitude of the overall rate of organic matteroxidation are subject to the value of the rateconstant selected for each of the two CH2O frac-tions. The highly reactive pool (CH2Olab, kPRR =30 yr�1) is rapidly depleted within the first 12 mdownstream of the recharge point (not shown)

while the more refractory fraction (CH2Oref,kPRR = 0.3 yr�1) disappears after 300 m (Figure 4).There, it is clearly shown a general invertedsequence of degradation pathways, starting withsulfate reduction and methanogenesis at the leach-ate source, followed by an extensive zone withcoexisting Fe(III) and Mn(IV) reduction, denitri-fication and, finally, a plume front dominated by

Figure 6. Pathways of CH2Oref degradation obtained in the GWA application for scenario 2 after a transientsimulation time of 22 years.

Figure 7. The pH distribution along the flow path in the GWA application for scenario 2 after a transient simulationtime of 22 years.

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oxic respiration. Such a reversed pattern in theorder of primary redox reactions is frequentlyobserved in groundwater systems contaminatedwith high loads of organic carbon [Chapelle,2001].

[47] The individual effect of each of the PRR onthe proton balance can be estimated from themodeled process rates (Figure 4), taking into ac-count appropriate stoichiometric coefficients ofprotons produced or consumed per mole of metab-olized organic matter. The stoichiometric coeffi-cients have been calculated from the chargebalance constraint, using the proper speciation ofthe aqueous carbonate and sulfur species at the insitu (computed) pH (not shown). For a detailedmethodology, see Jourabchi et al. [2005]. A pos-itive value for proton production rates leads to adecrease in pH and vice-versa. The pH distributionresulting from the effect of redox kinetic processes,combined with the buffering capacity of the car-bonate-sulfur system, is shown in Figure 5. Theprofile is characterized by three distinct areas: Inregion A, a sharp increase in pH close to the pointof recharge is predicted, which is caused by sulfatereduction of the CH2Olab pool. The steady increasein the middle of the profile up to point B corre-sponds to a region where organic carbon degrada-tion of CH2Oref is dominated by Fe(III) andMn(IV) reduction processes, both of which causea net proton consumption. The subsequent decreasein pH from B to C results from aerobic degrada-tion, which is the major respiratory pathway be-tween 200 and 300 m downstream of the recharge(Figure 4).

4.3.1.2. Scenario 2

[48] In scenario 1, the reduced end-products oforganic carbon degradation (NH4

+, Mn2+, Fe2+,H2S and CH4) were accumulating along the flowpath without possibility of further reoxidation. Inscenario 2, secondary redox reactions are consid-ered. Figure 6 shows that these reactions signifi-cantly influence the relative contributions andspatial distribution of the various organic carbonmineralization pathways. Although sulfate reduc-tion and methanogenesis still predominate at theleachate source, the Mn reduction zone between10–200 m is no longer observed in Figure 6.MnO2 is instead reduced by the chemical reoxida-tion of Fe2+ (Table 3a, reaction 14) produced by theFe(III) reduction process. When compared to theprevious simulation, the latter process dominatesthe other organic matter degradation pathwaysbetween 20–225 m. This trend can be explained

from the fact that the rate by which Fe(OH)3 isbeing produced through Fe2+ reoxidation by O2/MnO2 (Table 3a, reactions 13 and 14) is faster thanthe Fe(OH)3 consumption rate by total sulfide (TS)oxidation (Table 3a, reaction 17).

[49] Another significant difference between thetwo scenarios is the increased relative importanceof denitrification at the downstream edge of themoving CH2Oref front when secondary redox reac-tions are incorporated in the RN. The additionalsource of NO3

� is the nitrification process (reaction11, Table 3a), which consumes O2 and henceincreases the relative contribution of denitrificationat the expense of aerobic respiration. The contri-bution of O2 as an oxidant for organic carbon (OC)degradation is further reduced by the other second-ary redox reactions (Mn2+, Fe2+ and TS oxidationby O2) which operate right at the edge of theCH2Oref front (approximately 300 m).

[50] The resulting pH distribution obtained forscenario 2 is shown in Figure 7. Precipitation ofFeS and FeCO3 at the leachate source leads to aconsiderable pH drop from the boundary value of6.5 down to 5.6 (region A). The sharp increase inpH in region B is predominantly due to thecombined effect of TS reoxidation reactions byFe(OH)3 and MnO2, both of which are localized ata distance of around 280 m. The slight pH drop(about 0.1 unit) in area C results from the reoxi-dation of Fe2+ by O2 (Table 3a, reaction 13) andMnO2 (Table 3a, reaction 14), respectively. Furtherdownstream of area C, the results are still depen-dent on the initial conditions since the CH2Oref

front has not yet propagated into this area.

4.3.2. Early Diagenetic Simulation

[51] Figure 8 shows a classical redox sequence oforganic matter degradation pathways which devel-ops over the first 15 cm of the sediment column.Since sulfate is present in excess, all metabolicpathways except methanogenesis are active in thesystem. Integration of the rates indicates the pre-dominance of sulfate reduction, followed by oxicdegradation, denitrification, iron reduction andfinally manganese reduction in the overall rate oforganic matter degradation. These calculations takeinto account the contributions of the various reox-idation reactions in the carbon balance. The latterhave a predominant influence on the depth distri-bution of pH (Figure 9). Indeed, except for ironreduction, which is an important proton consump-tion reaction in the system, the major processescontrolling the H+ balance are nitrification, oxy-

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genation of TS and Mn2+, reoxidation of Fe2+ byMnO2 as well as reoxidation of TS by Fe(OH)3(Table 3a). The former four reactions produceprotons while the latter is a proton-consumingprocess. Two zones in the sediment profile canthus be distinguished: a zone of pH decrease (�0–2 cm) dominated by the aerobic oxidation of Mn2+

and TS, and a zone of pH increase (�2–4 cm)dominated by Fe(III) reduction and reoxidation ofTS by iron oxides. Note that the proton productionby secondary redox reactions in the uppermostlayer leads to a significant dissolution of calcitewhich is buffering the pH drop. Further analysis ofthe complex interplay between redox, pH dynamicsand carbonate precipitation/dissolution is providedby Jourabchi et al. [2005].

5. Conclusions

[52] This paper presents a simulation environmentfor one-dimensional reactive transport applications

Figure 8. Redox sequence of organic matter degradation pathways which develops for the ED application over thefirst 15 cm of the sediment column.

Figure 9. The pH distribution for the ED applicationover the first 15 cm of the sediment column after1500 years.

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that addresses the major hurdles for the commonuse of complex reactive transport models. In par-ticular, the KB-RTM approach provides completeflexibility in the choice of model components(chemical species) and the description of the inter-action between them (reactions) by using a genericform of the advection-dispersion equation and bytaking a ‘‘reaction-centric’’ approach which utilizesthe unifying conceptual and mathematical princi-ples underlying all RTMs. Thus 1-D transportdescriptions relevant to many compartments ofthe Earth system (rivers, estuaries, groundwateror sediments) can be incorporated in our simulationenvironment. The proposed approach should thushelp overcome traditional disciplinary barriers be-tween the different subfields of RTM. In addition,the use of symbolic programming and automaticcode generation allows testing and comparison ofalternative process formulations. As a result, itfacilitates the evaluation of the effect of competingmodel structures on predictions and uncertainties.

[53] The shear volume of ever growing knowl-edge on process dynamics in the natural environ-ment can also impede its timely incorporation intoRTMs. We argue that the Knowledge Base (KB)is a particularly efficient approach for constructingreactive-transport applications of increasing com-plexity, as well as testing and comparing alterna-tive process formulations. The KB system allowsexpertise to be stored in a dynamically evolving,Web-distributed Knowledge Base and provides aplatform where both modelers and experimental-ists can share expertise. The KB-RTM is availablevia our Web server at http://www.geo.uu.nl/�kbrtm.

[54] Further development and maintenance of thesimulation environment will involve the progres-sive implementation of a larger number of pro-cesses, and a continuing effort to keep the contentof the KB up-to-date with new results from thescientific community. A Web-based KnowledgeBook, consisting of documentation material forevery process implemented in the KB, will alsobe implemented with complete reference to thesource material, following the strategy alreadyused for the CONTRASTE model [Regnier etal., 2002]. The Web-based system further offersthe prospect for use as a forum for discussion,open to user feedback and contribution.

[55] Here, we have illustrated the workings of oursimulation environment using two model applica-tions dealing with redox and coupled acid-basechemistry in sediments and groundwater environ-

ments. Our examples demonstrate the flexibilityand potential of the proposed simulator.

[56] Our objectives have been achieved by adher-ing to a modular structure, where informationassemblage precedes symbolic process formula-tion, followed by automatic code generation andcombination with numerical algorithms for solu-tion. Finally, accessibility through the Internet is akey feature for such dissemination and combina-tion of expert knowledge on modeling and processdescription. To our knowledge, this is the firstattempt to use a Web-distributed flexible systemto provide dynamically adaptive reactive transportmodels in the field of geosciences.

Acknowledgments

[57] This research has been financially supported by several

grants from the Netherlands Organization for Scientific Re-

search (NWO), the European Commission (METROL project

EVK3-CT-2002-00080), the Belgian Science Policy Program

(SISCO project, EV/11/17A, EV/02/17B), and DHI-Water and

Environment. We are also thankful to A. Dale and three

anonymous referees for constructive comments on this paper.

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