HP1

(HYDRUS-1D + PHREEQC)

Additional HP1 Exercises

Diederik Jacques1 and Jirka Šimůnek2

1Waste and Disposal, SCK•CEN, Mol, Belgium 2Department of Environmental Sciences, University of California, Riverside,

USA

Exercise I: Transient Flow and Cation Exchange Exercise II: Kinetic PCE Degradation Network

Exercise III: U surface complexation Exercise IV: Horizontal Infiltration of Multiple Cations and Cation

Exchange

1

2

HP1 Exercise Transient Flow and Cation Exchange

This exercise simulates the leaching of Cd from an initially dry soil sample. The adsorption process of Cd is described as cation exchange with other cations (Jacques et al., 2008). This exercise illustrates:

- the use of variables Total_O and Total_H as components in the inflowing water - the use of the PHREEQC.tmp file to prepare input for PHREEQC - recalculations of PHREEQC output variables to desired values

Consider a dry loamy soil column 50-cm long with an initial pressure head of –300 cm. Infiltration occurs under a constant upper boundary pressure head of –50 cm. Consider a free drainage bottom boundary condition. Following elements are considered: Br, Ca, Cd, Cl, K, Mg, and Na. In case of transient water flow conditions, the total amount of O and H in the inflowing water has to be defined. Because most O and H will be in the species H2O (e.g., in 1 kg of water, there is about 55 mol of O and 110 mol of H), O and H in H2O will be subtracted from the total amount. This has to be done prior to HP1 calculations with PHREEQC. The bulk density is 1.31 g/cm3 and CEC is 4.1 meq/100 g soil. In HP1, the amount of CEC should be expressed in MOL/1000 cm³ soil. Calculate the amount of CEC in mol/1000 cm³ soil. [Answer: 0.05371 mol / 1000 cm³ soil] You can define the initial concentrations using the HYDRUS-1D interface in the usual way. Changes of the initial concentrations due to geochemical reactions can be added to the phreeqc.in file. As initial concentrations take: [Cl] = 69 µmol/kg water, [Ca] = 6 µmol/kg water, [K] = 4 µmol/kg water, [Na] = 64 µmol/kg water, [Mg] = 8 µmol/kg water, [Cd] = 0.8 µmol/kg water and [Br] = 62 µmol/kg water. The inflowing solution has following composition: [Ca] = 0.01 mol/kg water and [Cl] = 0.02 mol/kgw. Note that while the initial concentrations can be defined in any concentration units used by PHREEQC (default is mol/kg water), the boundary concentrations have to be defined in mol/kg water. 1. HYDRUS input (general definition and water flow) Set up the defined problem:

- check water flow, solute transport, HP1 - adapt the depth of the soil profile - time: 200 days - check the appropriate conditions for water flow

2. HYDRUS input (solute transport) Solute Transport – General Information Number of solutes: 9

3

Solute Transport – HP1 Components and Database Pathway Database Pathway: Select phreeqc.dat database Components: Specify 9 components (Total_H, Total_O, Cl, Ca, K, Na, Mg, Cd, Br) Check: Create default phreeqc.tmp file

Solute Transport – Transport Parameters Bulk Density: 1.31 (g/cm3) Dispersivity: 1 cm Solute Transport – Boundary Conditions Upper boundary condition: Concentration Flux Lower boundary condition: Zero gradient Concentrations: Fill in Cl and Ca concentration Calculation of Total_O and Total_H using PHREEQC

A small PHREEQC program is used to calculate Total_O and Total_H: database path\phreeqc.dat SOLUTION 0 inflowing water -temp 20 -ph 7 charge -units mol/kgw Ca 0.01 Cl 0.02 USER_PRINT -start 10 print "Total_O" tot("O") - 1000/18.016 20 print "Total_H" tot("H") - 2*1000/18.016 -end SELECTED_OUTPUT

4

-high_precision true

Fill in the correct path (path) or delete this line and browse for the correct database file - PHREEQC for Windows: Calculations -> Files -> Browse database file - PHREEQC Interactive: Options -> Set Default Database -> Browse database file

SOLUTION keyword is used to define the inflowing solution USER_PRINT keyword is used to calculate the Total_O and Total_H required in HYDRUS-1D Run the program in PHREEQC and look at the output file

Total_O and Total_H are shown highlighted above. These values must be copied to the concentration of the boundary condition.

5

Soil Profile – Graphical Editor Define initial conditions for pressure heads Define initial conditions for concentrations Alternatively: use the Soil Profile – Summary to define the concentrations Add observation nodes at 25 and 50 cm Soil Profile – Summary Change the pressure head of the first node to fixed boundary pressure head (-50 cm) Add solute concentrations (e.g., by copying it from an Excel spreadsheet)

pH: Provide known initial pH, or leave it zero (pH will be calculated to charge the solution) O(0): leave it (definition of it in phreeqc.in) Add other concentrations

Save 3. PHREEQC input (chemistry) Open phreeqc.tmp from the project folder (e.g., using notepad or PHREEQC GUI) Save it as phreeqc.in in the project folder Information in phreeqc.tmp The file looks like this (in PHREEQC GUI):

A # sign is a comment line in the PHREEQC input file. The first comment line provides information on the project folder, the second comment line on the location of the used database file.

6

TITLE is a PHREEQC keyword – the title is taken from the Heading of the HYDRUS-1D GUI. The next comment line gives information on the number of soil layers (horizons), and the number of nodes corresponding to different layers. SOLUTION_SPREAD is basically the information given in the Soil Profile – Summary dialog window in the HYDRUS-1D GUI. It defines the solution compositions corresponding to different FE nodes. Information on various options that can be used behind this keyword is given in the SOLUTION_SPREAD PHREEQC manual. The first line defines units used in SOLUTION_SPREAD (here in mol/kgw). The next line defines the column headings:

- description: description of the solution -> gives the number of a soil layer - number: solution number -> solution number 1 corresponds to the first node,

solution number 2 to the second node, and so on - water: the amount of water (volumetric water content) -> calculated based on the

initial pressure head and specified soil hydraulic properties. - Temperature - pH: the pH of the solution - O(0): oxygen with redox state 0 - The components Cl, Ca, …

The next line (subheadings) specifies element-specific units, redox couples, concentration-determining phases. In this example, there is:

- charge: corresponds to the element ‘pH’; indicates that pH will be adapted to have a neutral initial solution

- O2(g) –0.68: corresponds to O(0); indicates that the O(0) concentration will be calculated to be in equilibrium with the O2(g) partial pressure of 10-0.68 atm (i.e., the partial pressure in the atmosphere)

- mol/kgw: corresponds to all other elements; indicates that the concentration unit for the element is mol/kgw

The columns are tab-delimited. Note that when you change your hydraulic properties and/or initial conditions, you have to copy the SOLUTION_SPREAD from phreeqc.tmp to phreeqc.in. At the end of the file, there is end PRINT -reset false TRANSPORT -cells 101 end

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PRINT keyword indicates that extensive printing in the output file (phreeqc.out) is suppressed. TRANSPORT keyword indicates transport calculations. You must only indicate the number of cells in the transport problem. All other information was provided in the HYDRUS-1D GUI. Two types of information must be added:

1. The geochemical model 2. The type of output

Definition of the geochemical model Processes defined in the geochemical model for this example are aqueous complexation and cation exchange. The first process is automatically included by the reactions defined in the database file. The second process has to be explicitly stated in the phreeqc.in file by the keyword EXCHANGE: EXCHANGE 1-101 X 0.05371 -equilibrate with solution 1 end Numbers after the keyword indicate the solutions (all nodes), for which the exchanger is defined. X is the exchange species (defined in the database file on line 1098) followed by the amount in moles/1000 cm³. The next line indicates that the initial composition of the exchanger has to be calculated in equilibrium with the initial solution. Selectivity coefficients for particular cations are defined in the database (lines 1103-1175). Definition of the output Two keywords are used to define the output. SELECTED_OUTPUT is used for a standard output: pH, total concentrations of the elements (the same as in the HYDRUS output files). USER_PUNCH is used for a user specific output. The user specific output can be calculated using small BASIC programs. All keywords are explained in the PHREEQC manual and GUI, except bulkdensity which is an HP1 specific keyword. It gives the bulk density for the node cell_no as defined in the HYDRUS-1D GUI. In this example, the adsorbed concentrations that are given in PHREEQC in mol/kgw (e.g., mol(“NaX”) are converted to the units of meq/kg soil. SELECTED_OUTPUT -file ce_Transient.hse -reset false -solution true -distance true -time true -pH true -totals Cl Ca K Na Mg Cd Br USER_PUNCH

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-headings Na_s(meq/kg) K_s(meq/kg) Ca_s(meq/kg) Mg_s(meq/kg) Cd_s(meq/kg) -start 10 bd = bulkdensity(cell_no) 20 PUNCH 1000*mol("NaX") *tot("water")/bd #in meq/kg 30 PUNCH 1000*mol("KX") *tot("water")/bd #in meq/kg 40 PUNCH 1000*mol("CaX2")*tot("water")/bd/2 #in meq/kg 50 PUNCH 1000*mol("MgX2")*tot("water")/bd/2 #in meq/kg 60 PUNCH 1000*mol("CdX2")*tot("water")/bd/2 #in meq/kg -end The file looks like:

Save phreeqc.in Run HP1 Look at the Output

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Cadmium concentrations at two observation nodes and at 5 print times:

0.0000

0.0005

0.0010

0.0015

0.0020

0 50 100 150 200

Time [days]

N1N2

Observation Nodes: Concentration - 8

-50

-40

-30

-20

-10

0

0.0000 0.0005 0.0010 0.0015 0.0020

Conc [mmol/cm3]

T0

T1

T2

T3

T4

T5

Profile Information: Concentration - 8

-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0.0000

0 50 100 150 200

Time [days]

Bottom Solute Flux

Extra: Compare the Cd breakthrough when adding CaBr2 instead of CaCl2

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0 50 100 150 200

Time [days]

N1N2

Observation Nodes: Concentration - 8

-50

-40

-30

-20

-10

0

0.0000 0.0005 0.0010

Conc [mmol/cm3]

T0T1T2T3T4T5

Profile Information: Concentration - 8

-0.00025

-0.00020

-0.00015

-0.00010

-0.00005

0.00000

0 50 100 150 200

Time [days]

Bottom Solute Flux

10

HP1 exercise Kinetic PCE Degradation Network

Background Perchloroethylene (PCE, also called tetrachloroethylene) degrades slowly under reducing conditions, mainly by microbiological transformations. One of the most important pathways for anaerobic biodegradation of PCE is by reductive dechlorination in a sequential way. Figure 1 (after Schaerlaekens et al., 1999) shows this pathway including six components: PCE, trichloroethylene (TCE), cis-1,2-dichloroethylene (cis-DCE), trans-1,2-dichloroethylene (trans-DCE), 1,1-dichloroethylene (1,1-DCE), vinyl chloride (VC). VC then eventually degrades to ethylene (ETH), which is environmentally acceptable and does not cause direct health effects. Although the reaction kinetics of the biodegradation depend on a variety of environmental conditions (such as redox potential, biomass, and compounds affecting solubility), the kinetics here are described independent of environmental conditions.

When the DCE (dichloroethylene) species are lumped, the transport problem can be formulated as transport of a single sequential degradation chain, which can then be solved using HYDRUS-1D (e.g., Schaerlaekens et al., 1999; Casey and Šimůnek, 2001; see also one of the HYDRUS-1D tutorials). However, the HP1 code can handle the full reaction network as defined in Figure 2 (i.e., with three separate DCE species), considering different distribution factors α and yield coefficients γ.

Figure 1 Perchloroethylene (PCE) degradation pathway. (picture from Schaerlaekens et al., 1999).

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Modelling First-Order Decay Using PHREEQC A contaminant Cont is assumed to be subject to first-order degradation:

where R is the decay rate [MaL-3T-1] and μw is the first-order rate constant for solutes in the liquid phase [T-1]. First-order decay (Eq. (1)) in PHREEQC is modelled using the keywords RATES and KINETICS. The implementation in PHREEQC is shown in Box 1. The kinetic reaction itself is defined under the keyword RATES (lines 1-8). In this example, the reaction is called 'degradation' (line 2). Between -start and -end a Basic-program is written for the kinetic reaction of the 'phase' degradation using standard Basic-statements (e.g., here only “rem” for comments) and special Basic-statements for PHREEQC (e.g., MOL, SAVE, TOT, and TIME).

CR wμ= (1)

PCE TCEk1 , y1 k2 , y2

cis-DCE

trans-DCE

1,1-DCE

α1

α2

α3

k3

k4

k5

y3VC ETH

k6 , y4 k7

Figure 2 Degradation pathway of PCE using first-order rate constants.

Table 1 Definition of parameters and their values for the PCE biodegradation problem (from Case 1 and 2 in Sun et al., 2004). Rate parameters are for a reference temperature of 20°C. Parameter Symbol Values

Unit

Verification Velocity Dispersion coefficient First-order degradation rate 1 First-order degradation rate 2 First-order degradation rate 3 First-order degradation rate 4 First-order degradation rate 5 First-order degradation rate 6 First-order degradation rate 7 Distribution factor, TCE to cis-DCE Distribution factor, TCE to trans-DCEDistribution factor, TCE to 1,1-DCE Yield coefficient, PCE to TCE Yield coefficient, TCE to DCE Yield coefficient, DCE to VC Yield coefficient, VC to ETH

v D k1 k2 k3 k4 k5 k6 k7 α1 α2 α3 y1 y2 y3 y4

0.4 0.4

0.075 0.070 0.020 0.035 0.055 0.030

0.000001 0.72 0.15 0.13 0.79 0.74 0.64 0.45

m d-1 m² d-1

d-1 d-1 d-1 d-1 d-1 d-1 d-1 - - - - - - -

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The first statement of the Basic-program (line 4) is only a comment indicating the meaning of the first parameter. The second statement evaluates the rate equation (Eq. (1)) with parm(1) being the value of μw, TOT("water") the amount of water in the cell, and MOL("Cont") the molality of the solute. The third statement (line 6) integrates the rate over the time subinterval with the special variable TIME. Finally, the moles of reaction during the time interval are saved with the last special statement SAVE. Note the negative sign on line 6 that results in a negative amount of moles saved in the last statement. In general, a positive sign represents decreasing amounts of a phase (i.e., dissolution), whereas a negative sign results in precipitation of that phase. Consequently, elements will enter the solution in the former case (dissolution) and will be removed from the solution in the latter case (i.e., precipitation, degradation, or decay). In this example the imaginary phase 'degradation' is precipitating. This is done to prevent the cessation of the kinetic reaction (i.e., when the phase 'degradation' is completely removed from the system). Note that the output of the kinetic statement has the unit of mol. The second keyword in Box 1 (KINETICS) defines the names of the rate expressions related to a specific cell. In this example we have one rate expression called 'degradation'. Since 'degradation' is used here as an imaginary phase (and not a phase defined in the database), the option -formula is used to define the elements produced (i.e., when the product of the stoichiometric element coefficient (i.e., 1 in the formula option) multiplied by the moles of the reaction during a particular time step is positive) or consumed (i.e., when the product is negative) during the kinetic reaction. Since in this example the coefficient for the element Cont is 1 (line 11) and the reaction progress is negative, the concentration of Cont will decrease with the formation of the imaginary phase 'degradation'. Note that we could write the input also with a negative coefficient and a positive reaction progress (i.e., dissolution of the phase). However, in that case we could reach complete dissolution of the phase and, consequently, termination of the decay reaction. The last option under KINETICS in Box 1 is -parms for the purpose of defining parameters in the rate expression. In HP1, the units of rate parameters should be the same as is defined in selector.in.

Box 1 PHREEQC input for first-order decay reactions 1 RATES 2 degradation 3 -start 4 10 rem parm(1) first-order degradation coefficient (sec-1) 5 20 rate = parm(1)*TOT("water")*MOL("Cont") 6 30 moles = - rate * TIME 7 40 SAVE moles 8 -end 9 KINETICS 1 10 degradation 11 -formula Cont 1; -parms 2.3148E-7

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Exercise In this example we will simulate the transport and degradation of PCE and its daughter products in a soil column. Degradation not only occurs as sequential reactions, but also partly as parallel degradation reactions (see Fig. 2). Degradation coefficients, yield factors and distribution factors are given in Table 1. Saturated flow conditions in a 2.0 m long soil column are maintained for 150 days. The inflowing solution contains only 10 mmol of PCE. Will a steady-state profile be obtained within this timeframe? At which depths do different components obtain a maximum value? Physical properties of the soil are a porosity of 0.5, the saturated hydraulic conductivity of 1 cm/day and a dispersivity of 10 cm. Other soil hydraulic parameters are irrelevant for saturated conditions. 1. HYDRUS input (general definition and water flow) Set up the defined problem with appropriate initial and boundary conditions (Uncheck Water Flow in the Main Processes dialog window since we have steady-state water flow conditions and check HP1 Solute Transport). 2. HYDRUS input (solute transport)

In this problem it is not required to define Total_O and Total_H because the considered reactions are not pH-dependent or redox sensitive. To define the kinetic reaction network, new components had to be defined either in the PHREEQC database or in the PHREEQC.IN input file. The latter is more appropriate as it is usually preferable not to modify standard databases. The problem consists of 7 components which will be called Pce, Tce, Dcecis, Dcetrans, Dceee, Vc, and Eth (to represent PCE, TCE, cis-DCE, trans-DCE, 1,1-DCE, vinyl chloride, and ethylene). Note that the name of a component should start with a capital letter, followed by small letters (and symbols as an underscore). Define the solute transport problem with appropriate boundary concentrations (in mol/kgw). Insert some observation nodes. Use spatial discretization of 2 cm. 3. PHREEQC input (chemistry) Open the prepared input file 'TCE_degradation_phreeqc.in' from the HP1 course folder. The first part of this file contains some database related information: the definition of the seven new components (or master species) using the keyword SOLUTION_MASTER_SPECIES, the corresponding solution species of the components using the keyword SOLUTION_SPECIES, and the rate equations as described above (using the keyword RATES). The second part defines the chemical problem. First the solutions are defined (SOLUTION) and then the reaction network by including seven rate definitions in the KINETICS block. Because the degradation reactions, e.g., PCEdegrad and so on, are not related to mineral

14

phases in the database, the user should identify which solution species appear or disappear. The coefficients are given after the solution species. For Dcecis, Dcetrans and Dceee, this coefficient is the product of the yield factor with the distribution factor. The ‘'TCE_degradation_phreeqc.in’ file contains also the TRANSPORT keyword with the number of nodes. Because only the aqueous concentrations of PCE and its daughter products are of interest, all needed information is given in the output files created by HYDRUS. The option –punch_hydrus false is used to suppress the initialization of the phreeqc-related output files. Save the file in the project folder as PHREEQC.IN. RUN HP1 Look at the output

1e-007

1e-006

1e-005

0.0001

0.001

0.01

0 20 40 60 80 100 120 140 160

Time [days]

S1S2S3S4S5S6S7

-200

-150

-100

-50

0

0.0000 0.0005 0.0010

Conc [mol/L]

T0T1T2T3T4T5

Profile Information: Ethylene

Observation nodes at the bottom of the profile. Ethylene profiles at different times.

15

Additional Modification – PCE Dissolution In this example, the boundary condition problem is changed to an initial condition problem: we will assume that the top 50 cm of the soil profile is contaminated with PCE. We assume that the amount of non-aqueous (immobile) PCE is 0.01 mol). The concentration in the aqueous phase is equal to the solubility limit and the solubility is described by (Knauss et al., 2000):

where R is the gas constant (8.31441 J/mol) and T is the temperature in Kelvin. The following equation is used in PHREEQC to define the temperature dependence of solubility constants (Parkhurst and Appelo, 1999):

Copy the previous exercise Define the boundary solution with no PCE Open PHREEQC.IN and add PHASES PCE_lq Pce = Pce -analytical_expression -125.5965344 0 5531.053038 42.14129445 0 just before the keyword RATES in the file. The keyword PHASES defines mineral phases in the database. Here a new phase is created 'PCE_lq' consisting of PCE. The equilibrium constant is defined by the option –analytical_expression with the parameters of Eq. (3). Add also Equilibrium_phases 1-26 PCE_lq 0 0.01 after Eth 1E-20 of the SOLUTION keyword block. This keyword defines the composition of the reactive part of the solid phase for which equilibrium dissolution/precipitation is assumed. In this example, this is only immobile PCE in the first 50 cm of the soil (which corresponds to node 26). An equilibrium phase is thus defined for nodes 1 to 26. The phase is PCE_lq, its desired target saturation index is 0 (meaning equilibrium conditions) and its amount is 0.01 mol (per 1000 cm³). Save PHREEQC.IN RUN HP1 Look at the output

TlnCT/E..KlnR ++−= 50589152404 (2)

25

43

21 TA)Tlog(AT

ATAA)Klog( ++++= (3)

16

1e-007

1e-006

1e-005

0.0001

0.0010.0010.001

0 20 40 60 80 100 120 140 160

Time [days]

S1S2S3S4S5S6S7

-200

-150

-100

-50

0

0.0000 0.0002 0.0004 0.0006

Conc [mol/L]

T0

T1

T2

Profile Information: Ethylene

Observation nodes at the bottom of the profile. Ethylene profiles at different times. REFERENCES Casey, F.M., Šimůnek, J., 2001. Inverse analyses of transport of chlorinated hydrocarbons

subject to sequential transformation reactions. J. Environ. Qual. 30, 1354-1360. Knauss, K.G., M.J. Dibley, R.N. Leif, D.A. Mew, R.D. Aines, 2000. The aqueous solubility of

trichloroethene (TCE) an dtetrachloroethene (PCE) as a function of temperature. Appl. Geochem., 15:501-512.

Schaerlaekens, J., Mallants, D., Šimůnek, J., van Genuchten, M.Th., Feyen, J., 1999. Numerical simulation of transport and sequential biodegradation of chlorinated aliphatic hydrocarbons using CHAIN_2D. Hydrolog. Processes13, 2847-2859.

Sun, Y., Lu, X., Petersen, J.N., Buscheck, T.A., 2004. An analytical solution of tetrachloroethylene transport and biodegradation. Transport Porous Media 55, 301-308.

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18

HP1 Exercise U surface complexation

This exercise simulates the leaching of U under saturated, steady-state flow conditions. U adsorbs on Fe-oxides in the soil profile. Following elements are considered: Ca, Cl, K, Mg, Na, U(6) and C(4). In this geochemical transport problem that is pH-sensitive (see below), also Total_O and Total_H need to be transported by the model. U adsorption is described by a non-electrostatic surface complexation model. This has as a consequence that a charge on the solid surface is not balanced by counter-ions in a double surface layer. Therefore, the aqueous phase will have a charge imbalance that will be of the same size as, but opposite to, that on the surface. The entire system (i.e., solid surface + aqueous phase) will be then charged balanced. Therefore also the 'charge' of the aqueous solution has to be transported. Note that when an electrostatic model that takes into account the composition of the double layer is used, the aqueous phase will be charged balanced, and so will be the solid surface and the double layer. A solution composition of rain water is assumed for both initial and boundary conditions: [Cl] = 69 µmol/kg water, [Ca] = 6 µmol/kg water, [K] = 4 µmol/kg water, [Na] = 64 µmol/kg water, [Mg] = 8 µmol/kg water. The solution is assumed to be in equilibrium with CO2(aq) and the atmospheric partial pressure of CO2(g) (10-3.5 atm). The U concentration in the initial solution composition is considered to be very low ([U] = 10-24 M), and much larger (10-7 M) in the boundary solution. This problem is carried out using the PHREEQCU.DAT database. This is the PHREEQC.DAT database with the definition of additional U-species (from Langmuir, 1997 – dabase from www.geo.tu-freiberg.de/~merkel/Wat4f_U.dat). Sorption is described using solid complexation reactions on the surface site called Hfo_w (line 3448 in the database). Solution complexation species are defined further in the database. Note that only one U-species adsorbs (uranyl):

Hfo_wOH + UO2+2 = Hfo_wOUO2+ + H+ log_k 2.8

Sorption of U is strongly pH-dependent. Several figures presented below result from speciation calculations with PHREEQC. Calculations were done with a constant U concentration of 10-7 M in rain water defined with 0.43 kg water and the specified amount of sorption sites. More acid conditions were obtained by adding HCl, more basic conditions by adding NaOH. U is then added to maintain the concentration of 10-7 M. The PHREEQC input file for these calculations and the file with the output data are in the course directory (U sorption – speciation.phrqc and U sorption – speciation.xls, respectively). Figure 1a shows total U (moles) in the system. A maximum amount of U is present between pH 6 and 7, indicating maximum values for the linear distribution coefficient Kd (L kg-1) defined as:

Kd = [U]sorbed / [U]water where [U]sorbed is the total sorbed U concentration (mol/kg solid) and [U]water is the total aqueous U concentration (mol/kg water). Plotting Kd versus pH shows indeed a maximum Kd between pH 6 and 7 (Figure 1b). Figure 1c shows that most U is sorbed in a pH range between 4.5 and 8. These changes in the percentage of adsorbed U and Kd as a function of pH

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are due both the surface speciation and aqueous U-speciation as illustrated in Figure 1d and 1c, respectively. Figure 1d shows the surface speciation of the 6 different surface species in the geochemical problem. In the lower pH range, the surface is mainly protonated so U sorption (and also sorption of Ca and Mg) is minimal. Figure 1e shows that in the higher pH range (above pH 8), the concentration of the uranyl ion (UO2

2+) is very low, and that the U-carbonate species are the main U aqueous complexes. This results in low sorption of U at high pH. More information on changing U sorption during transient flow simulations is found in Jacques et al. (2008).

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

3 4 5 6 7 8 9 10pH

U in

sys

tem

(mol

)

Figure 1a: Speciation of U: Total amount of U in the system for a constant aqueous

concentration of 10-7 M as a function of pH.

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02

1.E+04

3 4 5 6 7 8 9 10pH

Kd

of U

sorp

tion

(L/k

g)

Figure 1b: Speciation of U: A linear distribution coefficient of U as a function of pH.

0

20

40

60

80

100

3 4 5 6 7 8 9 10pH

Perc

enta

ge o

f ads

orbe

d U

Figure 1c: Speciation of U: Percentage of U adsorbed as a function of pH

20

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

3 4 5 6 7 8 9 10pH

Surf

ace

spec

ies

(mol

/kgw

) m_Hfo_wOH2+ m_Hfo_wOH m_Hfo_wO- m_Hfo_wOMg+ m_Hfo_wOCa+m_Hfo_wOUO2+

Figure 1d: Speciation of U: Surface speciation as a function of pH

0.00E+00

2.00E-08

4.00E-08

6.00E-08

8.00E-08

1.00E-07

1.20E-07

3 4 5 6 7 8 9 10pH

Solu

tion

spec

ies

(mol

/kgw

)

m_UO2+2 m_UO2OH+ m_UO2(OH)2 m_UO2(OH)3- m_UO2CO3m_UO2(CO3)2-2m_UO2(CO3)3-4

Figure 1e: Speciation of U: Solution speciation of U as a function of pH (only main species

are shown). To illustrate this effect, transport simulations are done with rainwater as defined above, but also with more acid or basic rainwaters by adding HCl and NaOH, respectively. For each of these boundary solution composition, Total_O, Total_H, Charge, C(4), and Cl or Na-concentrations have to be calculated.

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1. Calculation of boundary solution composition with PHREEQC

Open the file 'U sorption - inflowsolution.phrq' from the course directory Select the database PHREEQCU.dat Run the file This file contains three different boundary solution compositions together with statements for calculating Total_O and Total_H. Solution 1 is for regular rain water:

solution 1 rain water -temp 20 -ph 7 charge -pe 15.2939 -units mol/kgw C 1 CO2(g) -3.5 Ca 6E-6 Cl 69E-6 K 4E-6 Mg 8E-6 Na 64E-6 O(0) 1 O2(g) -0.68 U(6) 1E-7

The keyword SOLUTION has several identifiers/options and then the definition of the solution composition. After the identifier –pH there is a number (7), followed by charge. This indicates that during initial speciation calculations pH will be adopted to have a charged balanced solution. The concentration of the elements Ca, Cl, K, Mg, Na, and U is fixed as defined above. The concentration of C is adapted to have equilibrium with the CO2(g) partial pressure of 10-3.5

atm. The concentration of O(0) is adapted to have equilibrium with the O2(g) partial pressure of 10-0.68 atm. In the output window, you can find pH, Total_O, Total_H, Charge, and C concentration. [Answer: pH = 6.7

Total_O = 5.89 10-4 mol/kgw Total_H = 2.75 10-5 mol/kgw Charge = 4 10-20 mol/kgw C = 3.96 10-5 mol/kgw ]

Solution 2 is for a more acid solution obtained by adding HCl to it:

solution 2 HCl added to rain water to pH 4 -temp 20 -ph 4 -pe 15.2939 -units mol/kgw C 1 CO2(g) -3.5 Ca 6E-6

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Cl 69E-6 charge K 4E-6 Mg 8E-6 Na 64E-6 O(0) 1 O2(g) -0.68 U(6) 1E-7

In this solution, there is no charge option for pH anymore, but pH has a fixed value of 4. The element Cl is followed by the charge option, meaning that Cl will be added (or removed) to obtain a charged balance solution with pH of 4. In the output window, you can find pH, Total_O, Total_H, Charge, and C and Cl concentrations. [Answer: Total_O = 5.08 10-4 mol/kgw

Total_H = 1.02 10-4 mol/kgw Charge = -3.98 10-17 mol/kgw C = 1.24 10-5 mol/kgw Cl = 1.98 10-4 mol/kgw ]

Solution 3 is for a more basic solution obtained by adding NaOH to it:

solution 3 NaOH added to rain water to have pH 9 -temp 20 -ph 9 -pe 15.2939 -units mol/kgw C 1 CO2(g) -3.5 Ca 6E-6 Cl 69E-6 K 4E-6 Mg 8E-6 Na 64E-6 charge O(0) 1 O2(g) -0.68 U(6) 1E-7

Now pH has a fixed value of 9, and a charge option is added to the element Na. In the output window, you can find pH, Total_O, Total_H, Charge, and C and Na concentrations. [Answer: Total_O = 1.83 10-2 mol/kgw

Total_H = 5.61 10-3 mol/kgw Charge = 2.31 10-19 mol/kgw C = 5.94 10-3 mol/kgw Na = 6.29 10-3 mol/kgw ]

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PART 1: RAIN WATER 1. HYDRUS input (general definition and water flow) The flow problem is exactly the same as in the exercise involving cation exchange during transient flow conditions. Copy this project as a new project. Heading: U complexation: Rain water The saturated hydraulic conductivity is changed to 1 cm/day. 2. HYDRUS input (solute transport) Solute Transport – General Information

Change the number of solutes to 10 (Cd and Br are not needed, but U(6), C(4) and Charge are needed now)

Solute Transport – HP1 Components and Database Pathway Database Pathway: Select phreeqcU.dat database

Components: Specify 9 components (Total_H, Total_O, Cl, Ca, K, Na, Mg, U(6), Charge, C(4))

Solute Transport – Boundary Conditions

Concentrations: Fill in the boundary condition as calculated above (Solution 1 rain water - Total_H = 2.75116E-005, Total_O = 0.000589886, Cl = 6.9E-005, Ca = 6E-006, K = 4E-006, Na = 6.4E-005, Mg = 8E-006, U(6) = 1E-007, Charge = 4.07767E-020, C(4) = 3.96E-005).

Soil Profile – Graphical Editor Define initial conditions for pressure heads: saturated flow conditions Add observation nodes at 0.5, 2, 5, 15, 25 and 50 cm Soil Profile – Summary Nothing to be changed here, because the PHREEQC.TMP file will not be used.

Save 3. PHREEQC input (chemistry) Open 'U sorption - phreeqc.in' from the course directory. This file contains the definition of the initial solution: solution 1-101 initial solution -temp 20 -ph 7 charge -pe 15.2939 -units mol/kgw -water 0.43 C 1 CO2(g) -3.5

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Ca 6E-6 Cl 69E-6 K 4E-6 Mg 8E-6 Na 64E-6 O(0) 1 O2(g) -0.68 U(6) 1E-24 with the amount of water equal to the water content at saturation (steady-state saturated flow problem). Next, the surface is defined as: Surface 1-101 Hfo_w 0.00287 -no_edl -equilibrate with solution 1 end As with the cation exchange, Hfo_w is the name of the surface site as defined in the PHREEQCU.dat database, followed by the number of sites in mol/1000 cm³. The –no_edl identifier indicates that the non-electrostatic surface complexation model is used. The –equilibrate identifier indicates that the composition of the surface complex is calculated in equilibrium with the aqueous phase composition (of solution 1). The rest of the file is more or less equal to the information in the exercise on cation exchange: PRINT -reset false selected_output -reset false -solution true -distance true -time true -pH true -totals U user_punch -headings Usorbed_(mol/kg) Usorbed(%) log(Kd) -start 10 Usorbed = mol("Hfo_wOUO2+")*tot("water")/bulkdensity(cell_no) 20 PUNCH Usorbed 30 PUNCH mol("Hfo_wOUO2+")*tot("water") / SYS("U(6)") * 100 40 Kd = Usorbed / tot("U(6)") 50 PUNCH log10(Kd) -end TRANSPORT -cells 101 -end

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Slightly different output variables are calculated by USER_PUNCH: the concentration of sorbed U in mol/kg solid, the percentage of U in the system that is sorbed, and the log-value of Kd. This information will be printed into the NOD_INF_CHEM.out and OBS_NOD_CHEM.OUT files in the project folder. Save the file in the project folder as PHREEQC.IN. RUN HP1 Look at the output

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PART 2: ACID WATER Copy the previous project as a new project Headings: U complexation: pH 4 Change the composition of the boundary solution (see above) Save the project No changes had to be made in PHREEQC.IN RUN HP1 Look at the output PART 3: WATER WITH PH 9 Copy the previous project as a new project Headings: U complexation: pH 9 Change the composition of the boundary solution (see above) Save the project No changes had to be made in PHREEQC.IN RUN HP1 Look at the output

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COMPARISON OF U-PROFILES Figure 2 shows U-profiles after 200 days of infiltration. With the near neutral pH of rain water, adsorption is very high (see above). Consequently, U migration in the soil profile is very limited and aqueous concentrations near the soil surface are very low. U migration is more pronounced in the case when the soil profile is flushed with more acid or base solutions. This is directly related to lower Kd values at pH 3 and 9 compared to the one at pH 7.

0.00E+00

2.00E-08

4.00E-08

6.00E-08

8.00E-08

1.00E-07

1.20E-07

1.40E-07

0 5 10 15 20 25 30 35 40 45 50Depth [cm]

U c

once

ntra

tions

[mol

/kgw

]

rainwaterpH3pH 9

Figure 2: U-profiles after 200 days.

The leaching pattern of Ca, Mg and U for the last boundary solution (pH 9) is quite particular (see Figure 3). Can you explain the leaching pattern? Why was this not observed for the acid infiltration simulation?

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

7.00E-06

8.00E-06

9.00E-06

0 50 100 150 200

Time [days]

Con

cent

ratio

ns [m

ol/k

gw]

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

pH U Ca Mg pH

Figure 3: pH and Ca, Mg, and U breakthrough curves at a 15-cm depth for the last boundary

solution. Reference Jacques, D., J. Simunek, D. Mallants, and M. Th. van Genuchten, Modeling Coupled

Hydrologic and Chemical Processes: Long-Term Uranium Transport following Phosphorus Fertilization, Vadoze Zone Journal, 7(2), 698-711, 2008.

Langmuir, D., Aqueous Environmental Geochemistry, Prentice-Hall, Inc., New Jersey, 1997.

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HP1 Exercise

Horizontal Infiltration of Multiple Cations and Cation Exchange This exercise simulates horizontal infiltration of multiple cations (Ca, Na, and K) into the initially dry soil column. It is vaguely based on experimental data presented by Smiles and Smith [2004]. The cation exchange between particular cations is described using the Gapon Exchange equation [White and Zelazny, 1986]:

1/

1/

( )( )

xy xji

ij x yyij

ccKcc

+ +

+ += (1)

where y and x are the valences of species i and j, respectively, and Kij is the Gapon selectivity coefficient [-]. The adsorbed concentration is expressed in (molckg-1 soil). It is assumed that the cation exchange capacity Tc (molckg-1 soil) is constant and independent of pH. This exercise illustrates:

- the use of variables Total_O and Total_H as components in the inflowing water - the use of the PHREEQC.tmp file to prepare input for PHREEQC - recalculations of PHREEQC output variables to desired values

Consider a dry sandy soil column 15-cm long with an initial water content of 0.075 (estimate from Fig. 1a). Infiltration occurs on the left side of the column under a constant water content of 0.35 (estimate from Fig. 1a). Consider a free drainage right boundary condition. Following elements are considered: Ca, Cl, K, Mg, Amm, and Na. In case of transient water flow conditions, the total amount of O and H in the inflowing water has to be defined. Because most O and H will be in the species H2O (e.g., in 1 kg of water, there is about 55 mol of O and 110 mol of H), O and H in H2O will be subtracted from the total amount. This has to be done prior to HP1 calculations with PHREEQC. The bulk density is 1.75 g/cm3 and CEC is 55 meq/kg soil. In HP1, the amount of CEC should be expressed in MOL/1000 cm³ soil. Calculate the amount of CEC in mol/1000 cm³ soil. [Answer: 0.09625 mol / 1000 cm³ soil] You can define the initial concentrations using the HYDRUS-1D interface in the usual way. Changes of the initial concentrations due to geochemical reactions can be added to the phreeqc.in file. As initial concentrations take (estimate from Fig. 3): [Cl] = 1 mmol/kg water, [Ca] = 20 mmol/kg water, [K] = 2 mmol/kg water, [Na] = 5 mmol/kg water, [Mg] = 7.5 mmol/kg water, [Amm] = 0. mmol/kg water and [C(4)] = 1 mmol/kg water. The inflowing solution has following composition: [Ca] = 0.002345 mol/kg water, [Na] = 0.01 mol/kg water, [K] = 0.0201 mol/kg water, [Mg]=[Amm]=0, and [Cl] = 0.035 mol/kgw. Note that while the initial concentrations can be defined in any concentration units used by PHREEQC (default is mol/kg water), the boundary concentrations have to be defined in mol/kg water. 1. HYDRUS input (general definition and water flow) Set up the defined problem:

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- check water flow, solute transport, HP1 - adapt the depth of the soil profile and set the horizontal flow - time: 270 minutes, initial time step 0.01 min - check the appropriate conditions for water flow (select sand from the soil catalog,

constant water content upper BC and free drainage at the bottom; initial conditions in water contents)

2. HYDRUS input (solute transport) Solute Transport – General Information Number of solutes: 9 Solute Transport – HP1 Components and Database Pathway Database Pathway: Select phreeqc.dat database

Components: Specify 9 components (Total_H, Total_O, Na, K, Ca, Mg, Amm, Cl, C(4)

Check: Create default phreeqc.tmp file

Solute Transport – Transport Parameters Bulk Density: 1.75 (g/cm3) Dispersivity: 10 cm Solute Transport – Boundary Conditions Upper boundary condition: Concentration Flux Lower boundary condition: Zero gradient

Concentrations: Fill in Total_H=0.000210068, Total_O=0.00060404, Na=0.01, K=0.0201, Ca=0.002345, Mg=0, Amm=0, Cl=0.035, C(4)=1.232E-005

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Calculation of Total_O and Total_H using PHREEQC

A small PHREEQC program is used to calculate Total_O and Total_H: SOLUTION 0 artificial effluent Set 1 -temp 20 -ph 7 charge -units mmol/kgw Na 10 K 20.1 Ca 2.345 Mg 0 Amm 0 Cl 35 C 1 CO2(g) –3.5 #assume equilibrium with atmospheric CO2(g) partial pressure O(0) 1 O2(g) -0.68 #assume equilibrium with atmospheric O2(g) partial pressure USER_PRINT -start 10 print "Total_O" tot("O") - 1000/18.016 20 print "Total_H" tot("H") - 2*1000/18.016 -end SELECTED_OUTPUT -high_precision true

Fill in the correct path (path) or delete this line and browse for the correct database file

- PHREEQC for Windows: Calculations -> Files -> Browse database file - PHREEQC Interactive: Options -> Set Default Database -> Browse database file

SOLUTION keyword is used to define the inflowing solution USER_PRINT keyword is used to calculate the Total_O and Total_H required in HYDRUS-1D Run the program in PHREEQC and look at the output file

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Total_O and Total_H are shown highlighted above. These values must be copied to the concentration of the boundary condition.

Soil Profile – Graphical Editor Discretization by 0.5 cm (i.e., 31 nodes)

Define initial conditions for water content (0.075) Define initial conditions for concentrations Alternatively: use the “Soil Profile – Summary” to define the concentrations Add observation nodes at 1, 5, 10, and 15 cm Soil Profile – Summary Change the water content of the first node to fixed boundary water content (0.350) Add solute concentrations (e.g., by copying it from an Excel spreadsheet)

pH: Provide known initial pH, or leave it zero (pH will be calculated to charge the solution) O(0): leave it (definition of it in phreeqc.in) Add other concentrations (Na=0.005, K=0.002, Ca=0.02, Mg=0.0075, Amm=1E-020, Cl=0.001, C(4)=0.001)

Save 3. PHREEQC input (chemistry) Open phreeqc.tmp from the project folder (e.g., using notepad or PHREEQC GUI) Save it as phreeqc.in in the project folder Information in phreeqc.tmp The file looks like this (in PHREEQC GUI):

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A # sign is a comment line in the PHREEQC input file. The first comment line provides information on the project folder, the second comment line on the location of the used database file. TITLE is a PHREEQC keyword – the title is taken from the Heading of the HYDRUS-1D GUI. The next comment line gives information on the number of soil layers (horizons), and the number of nodes corresponding to different layers. SOLUTION_SPREAD is basically the information given in the Soil Profile – Summary dialog window in the HYDRUS-1D GUI. It defines the solution compositions corresponding to different FE nodes. Information on various options that can be used behind this keyword is given in the SOLUTION_SPREAD PHREEQC manual. The first line defines units used in SOLUTION_SPREAD (here in mol/kgw). The next line defines the column headings:

- description: description of the solution -> gives the number of a soil layer - number: solution number -> solution number 1 corresponds to the first node,

solution number 2 to the second node, and so on - water: the amount of water (volumetric water content) -> calculated based on the

initial pressure head and specified soil hydraulic properties. - Temperature - pH: the pH of the solution - O(0): oxygen with redox state 0

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- The components Cl, Ca, … The next line (subheadings) specifies element-specific units, redox couples, concentration-determining phases. In this example, there is:

- charge: corresponds to the element ‘pH’; indicates that pH will be adapted to have a neutral initial solution

- O2(g) –0.68: corresponds to O(0); indicates that the O(0) concentration will be calculated to be in equilibrium with the O2(g) partial pressure of 10-0.68 atm (i.e., the partial pressure in the atmosphere)

- mol/kgw: corresponds to all other elements; indicates that the concentration unit for the element is mol/kgw

The columns are tab-delimited. Note that when you change your hydraulic properties and/or initial conditions, you have to copy the SOLUTION_SPREAD from phreeqc.tmp to phreeqc.in. At the end of the file, there is end PRINT -reset false TRANSPORT -cells 31 end PRINT keyword indicates that extensive printing in the output file (phreeqc.out) is suppressed. TRANSPORT keyword indicates transport calculations. You must only indicate the number of cells in the transport problem. All other information was provided in the HYDRUS-1D GUI. Two types of information must be added:

1. The geochemical model 2. The type of output

Definition of the geochemical model Processes defined in the geochemical model for this example are aqueous complexation and cation exchange. The first process is automatically included by the reactions defined in the database file. The second process has to be explicitly stated in the phreeqc.in file by the keyword EXCHANGE: EXCHANGE 1-31 G 0.09625 -equilibrate with solution 1 end

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It is assumed here that CEC is 0.055 mol /kg soil. In PHREEQC we need to express exchanger in units of mol/1000 cm³ soil. Assuming that the bulk density of the soil is 1.75 kg / 1000 cm³, the soil CEC is equal to 0.09625 mol/1000 cm³ soil. Numbers after the keyword indicate the solutions (all nodes), for which the exchanger is defined. G is the exchange species followed by the amount in moles/1000 cm³. The next line indicates that the initial composition of the exchanger has to be calculated in equilibrium with the initial solution. Since we do not want to use the default exchanger used in the database (X), we defined a new exchanger G, the definition of which we need to provide. We define the exchanger G using the PHREEQC keyword EXCHANGE_MASTER_SPECIES and its presence in our soil profile using the keyword EXCHANGE_SPECIES. We need to also define the Gapon exchange constants (see the example below).

How is this approach related to Gapon equation?

2+ 1/ 22+

13 2+ 2+ 1/ 2

2+ +

14 + 1/ 22+

2+ +

15 + 1/ 22+

( )Mg Ca (Mg )Ca

( )NaCa= ( )CaNa

( )KCa= ( )CaK

=K

K

K

(2)

Exchange reactions are written in terms of half reactions. The reaction:

Na+ + K-G = Na-G + K+ KNa/K (3)

can be written as the sum of half reactions:

G- + Na+ = Na-G KGNa (4) G- + K+ = K-G KGK (5)

Equation (3) is equal to (4) – (5), and consequently:

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Log(KK/Na) = Log(KGNa) – Log(KGK) (6)

By assuming that Log(KGNa) equals 0, Log(KGK) = -Log(KK/Na). Thus, we can express the exchange coefficient relative to Na+. Similarly, for the reaction:

Na+ + Ca0.5-G = Na-G + 0.5 Ca2+ KNa/Ca (7)

Log(KCa) for the half reaction is then Log(KCa) = -Log(KNa/Ca). Finally, the exchange between Ca and Mg is written as:

0.5 Ca2+ + Mg0.5-G = Ca0.5-G + 0.5 Mg2+ KCa/Mg (8)

with Log(KCa/Mg) = Log(KGCa) – Log(KGMg). Since Log(KGCa) is known, Log(KGMg) = Log(KGCa) - Log(KCa/Mg). Note that all half reactions are then expressed relative to Na+. Definition of the output Two keywords are used to define the output. SELECTED_OUTPUT is used for a standard output: pH, pe, total concentrations of the elements (the same as in the HYDRUS output files). USER_PUNCH is used for a user specific output. The user specific output can be calculated using small BASIC programs. All keywords are explained in the PHREEQC manual and GUI, except bulkdensity which is an HP1 specific keyword. It gives the bulk density for the node cell_no as defined in the HYDRUS-1D GUI. In this example, the adsorbed concentrations that are given in PHREEQC in mol/kgw (e.g., mol(“NaX”) are converted to the units of meq/kg soil. SELECTED_OUTPUT -file pigslug.hse -reset false -solution true -distance true -time true -pe true -water true -totals Cl Ca K Na Mg USER_PUNCH -headings water_g pH Na(mol/kg) K(mol/kg) Ca(mol/kg) Cl(mol/kg) Ca(mmolc/kg) Mg(mmolc/kg) Na(mmolc/kg) K(mmolc/kg) -start 10 bd = bulkdensity(cell_no) #kg/1000cm³ soil 20 PUNCH tot("water")/bd 30 PUNCH -la("H+") tot("Na") tot("K") tot("Ca") tot("Mg") tot("Cl") 40 PUNCH mol("Ca0.5G")*tot("water")/bd*1000 #in meq/kg 50 PUNCH mol("Mg0.5G")*tot("water")/bd*1000 #in meq/kg 60 PUNCH mol("NaG") *tot("water")/bd*1000 #in meq/kg 70 PUNCH mol("KG") *tot("water")/bd*1000 #in meq/kg -end

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The file looks like:

Save phreeqc.in Run HP1 Look at the Output References: Smiles, D. E., and C. J. Smith, Absorption of artificial piggery effluent by soil: A laboratory

study, Australian J. of Soil Res., 42, 961-975, 2004. Smiles, D. E., and C. J. Smith, Absorption of gypsum solution by a potassic soil: a data set,

Australian J. of Soil Res., 46, 67-75, 2008. White, N., and L. W. Zelazny, Charge properties in soil colloids, In: Soil Physical Chemistry,

edited by D. L. Sparks, CRC Press, BOCA Raten, Florida, 1986.

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