Computers & Geosciences 60 (2013) 168–175

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Computers & Geosciences

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CRONO—A code for the simulation of chemical weathering

Alexey A. Novoselov n, Carlos Roberto Souza FilhoInstitute of Geosciences, University of Campinas (UNICAMP), PO Box 6152, 13083-970 Campinas, SP, Brazil

a r t i c l e i n f o

Article history:Received 10 October 2012Received in revised form29 June 2013Accepted 12 July 2013Available online 20 July 2013

Keywords:Kinetics of minerals dissolutionThermodynamic modelingWater–rock systems

04/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.cageo.2013.07.007

esponding author. Tel.: +55 19 3521 4696; faail address: alexey@ige.unicamp.br (A.A. Novo

a b s t r a c t

CRONO is a new code for simulating chemical weathering. This program allows for the simulation ofcomplex scenarios of interaction in water–rock–gas systems while accounting for mineral dissolutionkinetics and solution transport. The thermodynamic calculations are realized using the GEOCHEQprogram. CRONO was developed for simulations of regolith formation on the surfaces of early Earth andMars and can be applied to other targets formed mainly as a result of chemical weathering. In this paper,an application of the code using a simulation of modern subaerial weathering of basaltic rocks ispresented.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Water–rock interactions at Earth's surface occur at low tem-peratures. Therefore, these interactions are characterized by anincompleteness of chemical reactions and general disequilibriumbetween reacting minerals and solution. Disequilibrium prevailswhen the properties of the system change at rates faster thanthose at which the thermodynamically favored reactions proceed.For example, research on the serpentinization of oceanic perido-tites demonstrated that equilibrium during fluid penetrationcannot be reached at temperatures up to approximately 150 1С(Silantyev et al., 2009). To simulate low-temperature systems, it isnecessary to account for the kinetics of mineral dissolution.

Several simulation softwares that combine kinetic and thermo-dynamic calculations are available, including KINDISP (Made et al.,1994), PHREEQC (Parkhurst and Appelo, 1999), CrunchFlow (Steefel,2001), GEMS (Kulik et al., 2004), Geochemist's Workbench (Bethkeand Yeakel, 2012) and GEOCHEQ_M (Mironenko and Zolotov, 2012).At each timestep, these codes first calculate the quantity ofdissolved minerals and then determine the chemical equilibriumcomposition of the system, yielding precipitated solid phases andsolution compositions. Powerful universal codes, such as Geoche-mist's Workbench, CrunchFlow and PHREEQC, combine this proce-dure with transport models. These codes can be applied for thesimulation of regolith formation due to weathering. However, theirapplication requires special modifications that can be customizedby users or sufficient model simplifications.

ll rights reserved.

x: +55 19 3289 1562.selov).

The simulation of weathering involves various specific require-ments. The ligand concentrations in the simulating solutions arevery low due to both the low temperatures and limited time forreactions to occur. Therefore, a model must consider negligiblechanges in the solution and rock composition. The majority ofuniversal codes do not output these changes. An elevation of theduration of the interaction of the solution with minerals isrequired, which leads to an overestimation of the pH and incorrectestimation of mineral dissolution rates. The CrunchFlow multi-component reactive transport model was applied to simulate thelong-term chemical weathering of the 226 Ka Marine TerraceChronosequence near Santa Cruz, CA (Maher et al., 2009). Besidesthe commonly describing parameters, this code emulates thekinetics of precipitation of secondary phases as well as the mineralcation exchange using measured flow rates and water contents todescribe the unsaturated zone flow and transport. However, theCrunchFlow model is fitted using local field data with specificgeochemical parameters (e.g., a high Cl-ion content in the weath-ering fluids). The modeling of regolith formed in the early geologichistory of Earth and Mars requires the development of a highlyflexible model that considers the effects of elevated CO2 levels,reduced O2 pressure, specific dissolved iron contents, extremetemperatures and atmospheric pressure on the control of mineraldissolution rates. In addition, the reconstruction of regolithsrequires the use of specific transport and climatic models.

In this context, we produced an alternative modeling tool,termed CRONO, for the simulation of complex scenarios of inter-action in water–rock–gas systems while accounting for mineraldissolution kinetics. The code was developed using the DELPHIprogramming language. The CRONO software interface consists ofthe main panel containing the simulation parameters, a databaseeditor and a scenario editor with templates for simulation

Fig. 1. Relationship between different modules of the CRONO software and theinterface with external programs.

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175 169

scenarios (Fig. 1). Databases can be imported from EXCEL files. Theresults are also reported in run-time files in EXCEL format.

The calculation procedure (Fig. 2) was implemented using theapproach described by Zolotov and Mironenko (2007) andMironenko and Zolotov (2012). Thermodynamic calculations areperformed using the GEOCHEQ code , which consists of a code forequilibrium computation and a database developed by Mironenkowith co-workers (Mironenko et al., 2008) on the basis of athermodynamic database SUPCRT92 (Johnson et al., 1992). Thewater physical properties (water ionization constant (Kw) anddensity) is calculated considering the IAPWS formulation (Palmeret al., 2004). An equation proposed by Palandri and Kharaka(2004), as well as the kinetic database provided by these authors,is used to compute the mineral dissolution rates.1

2. Calculation procedure

The calculation algorithm simulates temporal changes in water–rock systems by coupling pH- and temperature-dependent rateequations of mineral dissolution with calculations of chemical equili-bria in aqueous solution. This approach uses an assumption that theprecipitation of solids is controlled by their solubilities and occursfaster than mineral dissolution. According to Barton et al. (1963), atany moment, all solution species reach equilibriumwith each other aswell as precipitating minerals. Thus, the dissolution of both primaryand newly formed secondary phases is assumed to be the rate-limitingprocess. At each modeling step, the thermodynamic equilibrium canbe calculated subsequent to the dissolution of minerals. To yield betterresults, a modeling iteration is divided by the maximum quantity oftimesteps. In the course of the simulation, the duration of each stepcan be determined as a function of the quantity of dissolved matter ormay be limited by time.

For the τth equilibrium computation (Fig. 2a), the moles bjτ of achemical element j in the system are calculated based on thechemical composition of the aqueous solution at the previoustimestep bj(τ–1) and the sum of the molar concentrations ofelement Δxiτ from minerals dissolved during the current step:

bjτ ¼ bjðτ�1Þ þ∑iΔxiτ⋅νji ð1Þ

1 The kinetic database of Palandri and Kharaka (2004) was complementedusing constants for illite from Alekseev (2007) and zeolites from Barnes et al.(2000). The constants describing the pH-dependence of albite dissolution werereplaced by analogous parameters from Bandstra and Brantley (2008). The latterprovides a better approximation of experimental data. The database of mineralsdissolution kinetics is given in Supplementary materials, Appendix 1.

where νji is the stoichiometric coefficient of a chemical element jin the formula of the ith mineral. The molar amount of the ithmineral dissolved at the τth timestep is calculated as follows:

Δxiτ ¼ Siτ⋅riτ⋅Δtτ ð2Þwhere riτ represents the current rate of mineral dissolution (molem�2 s�1), Siτ is the surface area of the ith mineral exposed tosolution (m2) and Δtτ is the duration of the τth timestep (s).At each timestep, the surface area of the ith mineral can beestimated based on the specific surface area (SSSA) of primaryand secondary minerals measured using BET-analysis:

Siτ ¼ φi � SSSA∑lml ð3Þ

where φi is the volume fraction of the ith mineral in the bulkvolume of primary or secondary minerals, and ∑lml is the mass ofall primary or secondary minerals. The SSSA values can be found inthe literature or, as in the example presented below in Section 7,specific surface areas of the fresh and most altered rock samplescan be directly determined.

The dissolution rate ðriτÞ equation at timestep τ has the generalform

riτ ¼ f ðpHÞf ðTÞf ðΔrGÞ ð4Þand consists of a Laidler term for the pH-dependence of thedissolution rate ðf ðpHÞÞ, an Arrhenius term for the T-dependenceðf ðTÞÞ, and an affinity term describing the reduction of the mineraldissolution rate near thermodynamic equilibrium ðf ðΔrGÞÞ. TheCRONO code uses a combination of equations proposed byPalandri and Kharaka (2004), Zolotov and Mironenko (2007), andBrantley (2008). The full equation includes terms for acidic,neutral, basic and carbonate mechanisms, as follows:

riτ ¼ kHþ ðaHþ ÞnHþ ðaFeþ3 ÞnFeþ3 expEaHþ

R1

298:15� 1T

� �� �

� 1� Qr

Kr

� �pHþ� �qHþ

þkH2OðaO2 ;aqÞnO2 expEaH2O

R1

298:15� 1T

� �� �� 1� Qr

Kr

� �pH2O� �qH2O

þkOH� ðKw=aHþ ÞnOH� expEaOH�

R1

298:15� 1T

� �� �� 1� Qr

Kr

� �pOH�� �qOH�

þkpCO2 ðapCO2 ÞnPCO2 expEapCO2

R1

298:15� 1T

� �� �� 1� Qr

Kr

� �ppCO2� �qpCO2

ð5Þwhere k and n are kinetic constants; Ea is activation energies of themineral dissolution reaction for different mechanisms; aHþ , aFeþ3

and aO2 ;aq are activities of Н+ (activity of OH� is calculated asaOH� ¼ Kw=aHþ ), Fe+3 ion and dissolved oxygen, apCO2 is the CO2

pressure in atmosphere (bars); R is the universal gas constant; T isthe temperature in Kelvin; Qr is the activity quotient; and Kr is theequilibrium constant of the dissolution reaction. The affinityparameters p and q are empirical and dimensionless constants.Currently, most minerals have parameters for acidic and neutralmechanism only; nFeþ3 is not equal to zero for pyrite and pyr-rhotite; nO2 ;aq is not equal to zero for pyrite only; and kpCO2 isdifferent from zero for carbonate minerals. Parameters p and qhave been quantified for only a few minerals and often for only asingle mechanism. In all other cases, the default value for theseparameters is set to 1 as a first approximation (Supplementarymaterials, Appendix 1). The dissolution rates of several minerals asa function of the pH and temperature are shown in Fig. 3.

Minerals dissolution rates at near-equilibrium conditions canbe reduced by the affinity term (Fig. 4). This term may beconsidered as a measure of the extent of saturation. The changein Gibbs free energy for a chemical reaction ðΔrGÞ can be presented

Fig. 2. Scheme of the CRONO algorithm: (a) calculation of the system composition at timestep τ (Zolotov and Mironenko, 2007); (b) rock–solution–gas interactions in thenth block during the flow of a solution pulse k; (c) the movement of solution pulses through blocks over time.

Fig. 3. Dissolution rates of several minerals (We use the following abbreviations forthe mineral phases: Ab, albite; Aug, augite; Cal, calcite; Fo, forsterite; Mc, micro-cline; Ca-Mnt, Ca-montmorillonite; Qtz, quartz; SiO2

n, amorphous silica): (a) as afunction of pH (at T¼25 1C and (b) temperature (at pH¼pOH (Water ionizationconstant (Kw) calculated for pressure¼1 bar at To100 1C. and for pressure ofsaturated vapor at T ≥100 1C) and pCO2¼4e–4 bar) and pCO2¼4e–4 bar). Ratescalculated at far-from-equilibrium conditions (Qr/Kr«1).

Fig. 4. Dissolution rates of quartz and amorphous silica at near-equilibriumconditions (at T¼25 1C (According to the kinetic constants used here, the rates ofquartz and amorphous silica dissolution are pH-independent)). In this case, thequotient of reaction (Qr) is equal to the activity of dissolved silica in solutionðaSiO2 ;aqÞ.

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175170

as follows:

ΔrG¼�RT lnðKrÞ þ RT lnðQrÞ ð6Þwhere ΔrG1¼�RT lnðKrÞ is the Gibbs energy at a reference statecalculated at a specific temperature and pressure, and RT lnðQrÞ isan extensive term that captures the compositions of the reactingsolution. When ΔrG is close to zero, i.e., near equilibrium, thedissolution rate also approaches zero. Far from equilibrium, whenΔrG « 0, the affinity term has a negligible effect, and a mineraldissolution rate can be simplified to be pH- and T-dependentonly. In terms of a reaction equilibrium constant ðKrÞ and anactivity quotient ðQrÞ, the far-from-equilibrium conditions occur atQr=Kro 0.05 (Fig. 4).

The equilibrium constants of dissolution reactions are calcu-lated using the following equation:

Kr ¼ exp �ΔrG1RT

� �ð7Þ

where ΔrG1¼∑prvpr⋅ΔG1pr�∑rcvrc⋅ΔG1rc , pr and rc are productsand reactants, respectively, vpr and vrc are stoichiometric coeffi-cients, ΔG1pr and ΔG1rc are the Gibbs energies of minerals and

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175 171

solution species products and reactants calculated by GEOCHEQ ata given temperature and pressure. The activity quotient of reac-tions is given by

Qr ¼∏praprvpr

∏rcarcvrcð8Þ

where apr and arc represent the activity of products and reactants,respectively. For example, the quotient of albite dissolutionreaction, NaAlSi3O8 þ 2Hþ-Naþ þ Alþ3 þ 3SiO2; aqþ 2OH�, iscalculated as follows:

Qr ¼ aNaþ ⋅aAlþ3 ⋅a3SiO2 ;aq⋅a2OH�=a2Hþ ;

where the activity of the solid phases is equal to 1.

3. Calculation of the equilibrium composition of the modelingsystem

At each timestep, after the calculation of the bulk compositionof the modeling system with Eq. (1) (Fig. 2a), the GEOCHEQalgorithm2 (Mironenko et al., 2008) is run by the OLE Automation,and the equilibrium composition of the system is calculated basedon the Gibbs free energy minimization using the simplex method(Capitani and Brown, 1987). The calculation procedure yields at agiven temperature T, pressure P and bulk composition of themulticomponent system. The minimum of the function is search-ing with the expression:

minGðxÞ ¼∑i∑mi

nmi G0T ;P;mi

þ RT lnnmi

Niγmi

� �� �� �ð9Þ

where i is a potential number of phases (minerals, gas phase,aqueous and solid solutions) in the system, each of them containsmi components, nmi is the number of moles and G0

T ;P;miis the

standard Gibbs free energy of mth component of ith phase, nmi=Ni

is the volume fraction of the mth component of ith phase, whereNi ¼∑minmi and γmi

is the activity coefficients calculated withDebye–Hückel equation. The solution is constrained by the systemof balance equation:

∑i∑mi

ðνjminmi Þ ¼ bjτ ð10Þ

nmi≥0, where νjmiis the stoichiometric coefficient of chemical

element j in the formula of mth components of ith phase (in thecase, if the phase i is a mineral with stable composition, νjmi

isequal to νji in Eq. (1)). The electroneutrality equation is alsoincome in the system; in this case νjmi

is the charge of mthcomponent of ith phase (solution species) and bjτ ¼ 0. The G0

T ;P;mi

values are calculated with formulation shown by Johnson et al.(1992). The GEOCHEQ code reports the computed equilibrium as alist of nmi values, including minerals and the composition of thesolution or solutions (in cases where the modeling system con-tains gaseous and/or solid solutions).

4. Model of chemical weathering

The numerical modeling of weathering profile evolution isimplemented by the replication of the iterative leaching of a rockby an aqueous solution (pure water equilibrated with the atmo-spheric composition). This system is considered open regarding

2 The GEOCHEQ algorithm was developed by Dr. M.V. Mironenko (VernadskyInstitute, Russia). The authors of the present paper did not participate in thedevelopment of the software nor the collection of this database. This algorithm isused here as an external program. This section is taken from the PhD thesis ofNovoselov (2010). All questions regarding the GEOCHEQ code should be addressedto Dr. M.V. Mironenko.

the atmospheric gases, allowing for an estimation of the impact ofdifferent atmospheric compositions on the chemistry of theproduced regolith. Simultaneously, the temperature and thewater–rock ratio reflect the climatic conditions and their changesover time.

Currently, the code applies a one-dimensional model of solu-tion transport. The weathering profile consists of blocks of rockthrough which a given number of pulses of the aqueous solutionpass in a sequential manner (Fig. 2c). This model calculates theresidence time ðΔtnkÞ, actual porosity ðFnkÞ and water–rock ratio(W/R) in the nth block during the passing of the kth solution pulse.According to the continuous equation in the flowing tube, giventhat the solution density is constant, the duration of the solution–rock interaction is estimated as the ratio of the thickness of eachblock ðΔhnÞ multiplied by its actual porosity and the rainfall rate(RFk) at the upper boundary of the rock column during the kthsolution pulse:

Δtnk ¼ΔhnFnkRFk

ð11Þ

Fnk is calculated by the expression

Fnk ¼ Fnk�1 þðVnk�1�VnkÞð1�Fnk�1Þ

Vnk�1ð12Þ

where Vnk�1 and Vnk are volumes of the minerals in block n beforeand after the passing of the kth solution pulse. The water–rockratio for each block is calculated from the solution inflow to theupper boundary of the nth block (in the case of the uppermostblock, this is the rainfall rate) during the kth solution pulse to themass of minerals in the block. The W/R value is used as a reductionfactor to calculate bj(τ¼0) (Eq. (1)).

5. Limitations of the approach

The performance of the numerical experiments is limited bytwo premises: (i) the modeling parameters (temperature, rainfallrates, porosity of weathering rock) and the initial composition ofthe minerals interacting with water solutions must be fullydetermined, and (ii) the results are limited by the availability ofthermodynamic and especially kinetic constants of mineral dis-solution. This approach extrapolates constants employed underideal conditions (25 1С and atmospheric pressure) from a singlemineral phase to complex multi-phase systems, and therefore, theestimation of the bulk calculation accuracy is problematic. Thesolubility and kinetics of individual minerals in natural conditionscan potentially differ from the laboratory analogs due to dissim-ilarities in the chemical compositions (Maher et al., 2009). How-ever, in addition to the accuracy of the constants, the list ofavailable components and consideration of different distinctnatural phenomena (e.g., the roughness of different mineralspecies, solute transport and secondary mineral precipitation) thatare, in practice, difficult to separate, have a greater effect on theresults.

Secondary mineral precipitation controls the dissolution ratesof primary minerals and previously deposited phases. Maher et al.(2009) summarized these influences by (i) controlling the satura-tion state of dissolving minerals in weathering solutions, (ii)changing the permeability of the porous media, and (iii) reducingthe reactive surface areas of minerals by the precipitation ofsecondary phases. In the CRONO algorithm, the relationshipbetween mineral dissolution and the saturation state of solutionsis realized by means of the affinity terms in Eq. (5). The perme-ability reflects the fluid residence time determined by the volumechange of weathering rock (Eqs. (9) and (10)). However, a modelfor changes in the mineral surface area of individual mineral

Fig. 5. Changes in the solution composition with time as a result of basalt dissolution. The lines with crosses are lab experimental data (Felitsyn et al., 2011). Solid linesrepresent data simulated by CRONO under the same conditions. Black lines mark the changes in the elemental composition. Equivalent gray lines are the pH values. The blackarrows indicate the precipitation of minerals that occurred during the experiment. Mineral names indicated along the simulated lines mark the beginning of precipitation ofthe corresponding solid phases: Ap, hydroapatite; Ill, illite; Mnt, Ca-montmorillonite; Nnt, nontronites; Py, pyrite; Qtz, quartz.

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175172

species in the course of dissolution is currently not available. Thisparameter can either decrease or increase during dissolution, andthe role of this variable in the simulations should be furtherstudied.

The central assumption of this approach is that the precipita-tion of secondary phases occurs faster than both the mineraldissolution and solute transport through the weathering profile.The precipitation kinetics are not considered in the current versionof the algorithm. It is difficult to evaluate the potential effects ofthe precipitation kinetics because it affects weathering profiles inthe same manner as the solute transport and soil pCO2 (Maheret al., 2009). However, the existence of secondary phases in theweathering profiles supports this assumption. There is a positivefeedback between the precipitation of secondary phases anddissolution rate of primary minerals. According to Maher et al.(2009), the fluid flow rates would need to be an order ofmagnitude greater to provide the observed weathering rates inthe absence of precipitation, or the duration of the weatheringwould be more greater than the obtained dating values. The fasterprecipitation rates can be attributed to the elevated specific sur-face area of secondary minerals (Alekseev et al., 1997); i.e., the SSSAvalue of clays is at least 10-times greater than the reactive surfaceof the primary minerals.

One additional limitation of this approach is that the solutionthermodynamic properties in the SUPCRT92-derivated databasedescribed by the Helgeson–Kirkham–Flowers model is applicablefor dilute solutions with a bulk mineralization of less than 50 g/kg.This limitation can be critical for the simulation of weatheringunder very dry conditions.

To estimate the accuracy of the approach, the simulation of alaboratory dissolution experiment from Felitsyn et al. (2011)3 wasperformed. In the course of this experimental investigation, a basalticrock was leached by an acidic solution for 100 h, and changes in thesolution compositionwere observed. This experiment corresponded tothe interactions in one block in the course of a CRONO run (Fig. 2b).A O–H–K–Mg–Ca–Al–C–Si–P–S–Na–Fe system open to atmosphericCO2 was modeled. The dissolving metamorphosed basalt consistedof chlorite—Si3Al2.268Fe2.036Mg2.689Ca0.013Na0.028H8O18.153 (31.0 wt%),albite—Si3Al1.032Fe0.005Ca0.014Na1.004O8.07 (41.4 wt%), microcline—Si3Al1.037Fe0.002Na0.041K0.82O7.988 (4.3 wt%), augite—Si2Al0.103Fe0.213Mg0.974Ca0.817Na0.016P0.043O6.274 (21.3 wt%), quartz—SiO2 (1.0 wt%),and magnetite—Fe3O4 (1.0 wt%). The following secondary phaseswere available in the system: amorphous silica, brucite, calcite,

3 The description and results of this experiment were provided by Dr. NadezdaAlfimova (Institute of Precambrian Geology and Geochronology, Russia).

chrysotile, clinochlore, daphnite, dolomite, goethite, greenalite,hematite, hydroxyapatite, illite, magnesite, magnetite, Ca,K,Na-montmorillonites, a solid solution of Ca,K,Mg,Na-nontronites,pyrite, quartz and siderite. The reacting aqueous solution hosted0.025 mol/l of H2SO4. The interactions occurred at 25 1C andW/R¼10. The specific surface area (SSA) of the basalt and itsweathering products, obtained by BET-analysis (Sorbi-M) usingnitrogen as an adsorbent gas in the Institute of Structural Micro-kinetics and Material Science RAS (Chernоgolovka, Russia), were1.4 m2/g and 53 m2/g, respectively.

The obtained results are shown in Fig. 5. The simulated systemis closed with respect to cations; therefore, the composition of thesolution is determined by the combined processes of mineraldissolution and precipitation. The calculated pH trend fully corre-sponds to that observed in the laboratory experiment, indicatingthat the kinetic constants adequately control the minerals dissolu-tion. It was unfeasible to observe the secondary phases during thelab experiment because a negligible portion of primary mineralswas dissolved. According to the calculated data, only 0.04 vol% ofthe initial rock reacted. However, the precipitation of secondaryminerals in the experimental system was marked by a decrease inthe cation concentrations (noted by black arrows in Fig. 5).As discussed above, the precipitation kinetics of clay mineralswas not considered during the simulations, which may cause asystematic underestimate of the cation contents in the solution,especially K, Al, and Na. As a result of this positive feedback, therates of plagioclase dissolution and the delivery of Al and Na in thesolution are elevated, as shown in the right portion of Fig. 5.On the other hand, there is an obvious disagreement in the datashown in the left part of the plots up to 1 h after the beginning ofthe experiment. This phenomenon is most likely caused by theelevated dissolution rates of fresh minerals, which is frequentlyobserved in the experimental investigations (Hochella & Banfield,1995) and is an experimental feature, rather than a fault in thenumerical simulations. In general, considering that both thethermodynamic and kinetic constants are far from perfect andprovided for end members of mineral series, the simulated resultscorrelate well with the experimental observations. Therefore, theprecipitation model is considered acceptable.

6. Calculation of the timestep values

Special attention is required for the choice of timestep valuesfor unitary computing of simulations. To appropriately describethe evolution of the modeling system, the timestep value should

Fig. 6. Comparison of the changes in pH during the basalt dissolution experiment(1) and simulation of the same system using various algorithms for the calculationof a timestep value with constant timestep values of Δtτ¼ 1e–5 (τ¼2000) (2), Δtτ¼1e–4 (τ¼200) (3), Δtτ¼ 1e–3 (τ¼20) (4); using the dissolved minerals-dependentalgorithm with DMlim¼1e–4 (τ¼31) (5), DMlim¼1e–3 (τ¼5) (6), DMlim¼1e–2(τ¼5) (7); and using the exponential algorithm with EF¼0.1 (τ¼31) (8), EF¼1(τ¼4) (9).

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175 173

be set to a minimum. On the other hand, this is a crucial parameterfor the computational time.

Currently, CRONO can apply three different algorithms tocalculate the change of time in the modeling system: (i) a constanttimestep value that should be provided by the user; (ii) a timestepcalculated from the limiting value of the dissolved minerals4 inmoles (DMlim) through the equation

Δtτ ¼ DMlim

∑iðriτ⋅SiτÞð13Þ

and (iii) a timestep estimated by an exponential law by theequation

Δtτ ¼ ∑τ�1

Δtτ⋅10EF�∑τ�1

Δtτ ð14Þ

where EF is an extension factor provided by the user.The system described above was simulated using different

timestep values calculated by all three algorithms (Fig. 6). Withtimesteps obtained with Eqs. (9) and (10), the code provides thesame results within a shorter computational time. The model alsoapproximates well the drastic changes in the modeling systemduring the initial stage of the interaction in each reacting block. Incertain cases, the use of the exponential algorithm is preferredover values obtained based on the dissolved mineral contentsbecause in the later stages of weathering, the proportion ofsecondary minerals increases, causing an unreasonable reductionof calculation timesteps considering their highly reactive surfaces.The use of the following maximal values to calculate the timestepis recommended: when using a constant timestep, Δtτ should notbe set above 1e–4 years; the application of the dissolved minerals-dependent algorithm requires a DMlim value of≤1e–3 mol; and theexponential algorithm may be run using an EF value of≤1. How-ever, such maximal values can provide the correct results only forthe modeling of weathering systems in which all drastic changesoccur during the initial stage of interaction in each block. Time-steps employed in the simulations in this study were computedusing the exponential algorithm with an EF¼0.1.

4 An approach for calculation of a timestep similar to illustrated by equation 13was primary described in (Mironenko and Zolotov, 2012).

7. An example simulated system

To demonstrate the execution of the CRONO model, a modernsubaerial weathering of a suite of basalts found in the centralportion of the Parana Basin, located near Campinas city (Sao PauloState, Brazil), was simulated. Fifteen samples were collected from10 equispaced depth levels in a 1.25 m vertical weathering profile.The uppermost levels showed distinct features in their structureand were subdivided into three fractions: M—monolithic, CG—coarse-grained, and FG—fine-grained (Fig. 7).

The samples were analyzed for major and trace elementconcentrations using a Philips PW2404 X-Ray fluorescence spec-trometer. The composition of primary and secondary minerals wasobtained using a scanning electron microscope (coupled to anOxford EDS Link/Isis EDS system). The SSAs of all samples wereobtained using the BET method with nitrogen gas using a Micro-meritics Accelerated Surface Area and Porosimetry (ASAP) 2020System.

The O–H–K–Mg–Ca–Al–C–Si–Na–Fe system open to atmosphericCO2 was modeled. To simplify the modeling system, several elementscommonly found in basaltic rocks, such as Ti, Mn and P, were omittedfrom the analysis. The initial rock consisted of plagioclase—Ca0.415Na0.478K0.014Fe0.024Al1.315Si2.382O8 (36.8 wt%), augite—Ca0.659Al0.065Mg0.718Fe0.411Si1.896O6 (36.3 wt%), microcline—K0.612Na0.278Al0.871Si2.847O8 (9.4 wt%), magnetite—Fe2.928Al0.053Si0.008O4 (5.9 wt%), olivine—Mg0.683Fe1.228Ca0.003Si1.031O4 (1.4 wt%), quartz—SiO2

(0.5 wt%) and Fe–smectite Fe1.691Mg0.623K0.028Ca0.063Al1.173-Si2.971O11.335H0.67 (9.7 wt%). This composition corresponds to thebasalt sampled from the lower portion of field test profile (112.5 cm,Fig. 7). The secondary minerals available for the precipitationincluded amorphous silica, aragonite, boehmite, brucite, clino-chlore, daphnite, diaspore, dolomite, gibbsite, goethite, hematite,illite, kaolinite, Ca,K,Na-montmorillonites, Ca,K,Mg,Na-nontronitesand siderite. The climatic conditions of weathering were adjusted tothe average monthly rainfall (23–280 mm/month) and temperature(18–25 1C) values observed in the Campinas region. The SSAs of thefresh basalt and its weathering products were 0.3 m2/g and 28 m2/g, respectively. The initial porosity of the basaltic rocks was 2.4 vol%.The overall duration of the simulated weathering was given as20,000 years.

The simulated mineral composition of the weathering profilefully reproduces the list of secondary minerals observed in theuppermost levels of the tested regolith and as described in theliterature for this region (e.g., Oliveira et al., 1998). Accordingly, thelower levels of the profile are negligibly altered. The mainsecondary minerals of the simulated profile are clays, such askaolinite and nontronite; during the course of weathering, theportion of kaolinite gradually increases (Supplementary materials,Appendix 2). The weathering profile contains minor volumes ofgibbsite and goethite, for which their stability in the regolith isstrongly dependent on the solution composition. Gibbsite andgoethite can be fully dissolved and re-deposited as a result of thedissolution of primary silicates or secondary clays. A negligiblevolume of carbonate minerals also precipitates throughout theleaching column. These phases are also unstable and disappearsoon after deposition.

The chemical evolution of the modeled profile, as well as thegeochemical data, is shown in Fig. 7. The chemical composition ofthe regolith changes significantly with time. The model providedinformation on all major weathering features: the redistribution ofelements with depth in the profile; the effective removal of Na, Ca,Mg and Si; and an accumulation of Al, Fe and banded water in theuppermost levels. The modeling results demonstrate the loss of Kfrom the near-surface blocks, although the actual geochemicaldata indicate the accumulation of this element at depths ofapproximately 20 cm. This is a well-known phenomenon caused

Fig. 7. Schematic of the weathering profile of the basaltic rocks, including their actual geochemical composition (points) and the corresponding simulated data (lines) in wt%. Different rock fractions in the profile are marked by different colors and letters: M (gray), monolithic; CG (dark gray), coarse-grained; FG (black), fine-grained. Themodeled duration of weathering in thousands of years are labeled with numbers near the corresponding lines (1, 10, 20 Kyr).

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175174

by the activity of vegetation (e.g., Ronov et al., 1990; White et al.,2009) and is beyond the framework of these simulations. Themodel also predicts that the formation of the weathering profilecontinued for at least 20,000 years. The consideration of mineralprecipitation kinetics would extend the duration of weathering.However, although there are dissimilar protolith and rainfallcompositions and climatic conditions, the obtained mineralogyand solute features (Supplementary materials, Appendix 2) arevery similar to those reported by Maher et al. (2009), whoperformed a detailed study on the effects of precipitation kineticson weathering.

The decrease in the Ca and Mg contents, as well as other minordiscrepancies of the simulated results from the weathering profilecomposition in the lower portion, is due to the overestimation ofpyroxene and plagioclase dissolution. According to the obtained backscattering SEM imagery, the solute transport at those levels occurs

through the olivine grains, which preferentially dissolve. Therewith,at the later stages of weathering, the plagioclase grains provide thepermeability of the basaltic rocks. This selective dissolution is likelycaused by the different roughnesses of certain minerals.

8. Conclusions

The CRONO algorithm introduced in this work was developedfor the simulation of regolith forming over a wide spectrum ofmodeling parameters. The described approach comprises thecomputation of mineral dissolution kinetics and equilibrium ateach timestep, as well as the reproduction of the solution trans-port. This allows for the representation of low-temperaturesystems that do not reach the equilibrium due to reactions thatoccur at low velocities, as well as the modeling of chemical

A.A. Novoselov, C.R. Souza Filho / Computers & Geosciences 60 (2013) 168–175 175

weathering process over time. The application of the model wasillustrated by an example of modern subaerial weathering ofbasaltic rocks. The model describes the formation of the mineraland chemical composition of regolith over time, and the obtainedresults correlate with the composition of the sampled weatheringprofile. The CRONO code will continue to be enhanced in futureversions, including new additions to the computation process andthe addition of other variables.

Acknowledgments

This investigation was financially supported by FAPESP (SãoPaulo Research Foundation), Grant no. 2011/12682-3. We thankDr. M.V. Mironenko (Vernadsky Institute, Russia) for providing theGEOCHEQ code and consultations; Dr. N.A. Alfimova (Institute ofPrecambrian Geology and Geochronology, Russia) for sharing theresults of the dissolution experiment; Dr. Dailto Silva (Institute ofGeosciences, Unicamp, Brazil) for helping to define the composi-tion of the basalts sampled in the field; and MSc. Kelly Roberta dePalma (School of the Chemical Engineering, Unicamp, Brazil) forthe determination of specific surface areas.

Appendix A. Supplementary materials

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.cageo.2013.07.007.

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