-1- Hydrogeochemical Modeling with PhreeqC thermodynamic equilibrium reactions, kinetics, and reactive transport modeling Universidad de Concepción March 2009 Prof. Dr. Britta Planer-Friedrich Environmental Geochemistry, University of Bayreuth, Germany Reactions between groundwater and lithosphere Exercise 1 For the current drinking water well of the city (B3 in the cross section sketch on the following page) a hydrogeochemical analysis is given. How is it to be evaluated? Consider in particular the redoxsensitive elements (which ones show different behaviour compared to all others and why?), show the species distribution of the elements Ca, Mg, Pb, Zn (what is noticeable?) and point out all super saturated mineral phases with a bar chart. Temperature = 22.3°C pH = 6.7 pE = 6.9 Ca = 75.0 Mg = 40.0 K = 3.0 Na = 19.0 HCO 3 - = 240.0 SO 4 2- = 200.0 Cl - = 6.0 NO 3 - = 1.5 NO 2 - = 0.05 PO 4 3- = 0.60 SiO 2 = 21.59 F - = 1.30 Li = 0.030 B = 0.030 Al = 0.056 Mn = 0.014 Fe = 0.067 Ni = 0.026 Cu = 0.078 Zn = 0.168 Cd = 0.0004 As = 0.005 Se = 0.006 Sr = 2.979 Ba = 0.065 Pb = 0.009 U = 0.003 Exercise 2 2 a A new well has to be drilled. For logistic reasons (length of the water pipelines) this new well should be located closer to the city. The planed new location is shown in your sketch as B2. From a hydrogeochemical point of view would you advise this new location? Consider also drinking water standards (e.g. Germany: Ca = 400 mg/L; SO 4 2- = 240 mg/L). Assume a general groundwater flow direction from the east to the west and consider the analysis of the current drinking water well (B3) as characteristic for the aquifer in the east [EQUILIBRIUM_PHASES]. 2 b How does the water quality of B3 changes, if one assumes the retention times in the underground are so short that only a 50% saturation with the prevailing mineral phase will occur? [under the key word EQUILIBRIUM_PHASES you can not only indicate equilibrium reaction, but also defined certain disequiblibria over the saturation index, e.g. a 20% saturation means SI = log 0.2 = -0.7] -2- -3- Exercise 3 3 a More recent drillings in the vicinity suggest a certain geothermal influence in this environment. How would different temperatures in the under ground affect the water quality in the planed well (B2) (simulation range 10, 20, 30, 40, 50, 60, 70°C with 50% saturation)? [key word REACTION_TEMPERATURE] 3 b Only for comparison, which quantities of gypsum dissolve under the same temperature conditions in distilled water and how can the difference compared to the well water (B2) be explained? Exercise 4 4 a In the current drinking water well (B3) seasonally varying Calcium contents were measured. This phenomenon is correlated with karst weathering, which is dependent apart from the temperature also from the CO 2 -partial pressure in the soil (the CO 2 in the soil results from microbial degradation). Simulate the theoretical solubility of calcite over the year at temperatures on winter days of 0°C and a CO 2 partial pressure, which corresponds only to that of the atmosphere, without additional bio productivity (p(CO 2 ) = 0,03 Vol%) up to hot summer days with temperatures of 40°C and high bio productivity and corresponding high CO 2 partial pressures (p(CO 2 ) = 10 Vol%) according to the following table: Temp. °C 0 5 8 15 25 30 40 CO 2 (Vol%) 0.03 0.5 0.9 2 4.5 7 10 Where is the maximum of karst weathering (calcite dissolution) (show the results in a table and a diagram (temperature = x-axis, dissolved calcite = y-axis)? Why is there no linear correlation between temperature and calcite dissolution? [Like minerals gases can be put into equilibrium with aquatic phases, instead of SI the gas partial pressure p is set: CO 2 Vol% ÷ transform to [bar] and form log = p(CO 2 ); e.g. 3 Vol% = 0.03 bar = -1.523 p(CO 2 )] 4 b What happens, if not only pure calcium carbonate (calcite) but also magnesium calcium carbonate (dolomite) is present in the aquatic system? Represent your results in a graph. How does one call this type of reaction? [use the mineral phase dolomite(d) = “disperse“ for the simulation] -4- Exercise 5 During the simulations of exercises 4a and 4b you assumed that the exchange of CO 2 is unrestricted. One calls such systems "open systems ". Under real conditions, especially in an aquifer, the exchange of CO 2 with the atmosphere is often limited (“closed system”). Simulate for the hydrogeochemical analysis of B3 the calcite solution in the comparison in an open and a closed system at a temperature of 15°C and a partial pressure of 2 respectively 20 Vol%. How do both systems differ, what changes with increasing partial pressure and why? [closed system: key word GAS_PHASE; within this keyword one must define the total pressure which is 1 bar; the volume which is 1 L gas per 1 L water and the temperature of the gas, which is 35°C here; additionally, it has to be defined, which gas is used (here: CO 2 ) and which partial pressure it has (not as for EQUILIBRIUM_PHASES as log p(CO 2 , but in bar!] Drinking water treatment Exercise 6 6 a Common drinking water treatment technologies require that water should not be „aggressive“. Mostly this „aggression” refers to carbonic acid in the water. The reason for this restriction is not of toxicological nature, but reflects the aggression towards pipe line materials (concrete, metals, plastics). In Germany drinking water should fit within the pH-values 6.5 and 9.5. Additionally the measured pH value shall only deviate ± 0.2 pH units from the pHc (the pH value at calcite saturation). The target is to have a pH value which is slightly over the pHc value (0.05 pH units), because then a thin protecting calcite layer forms on the pipes. Clear super saturation leads to noticeable calcite precipitation clogging the pipeline and is at least as unwanted as under saturation, which leads to corrosion. Consider these requirements when checking whether the drinking water from the current drinking water well (B3) can be used without further treatment. 6 b Check whether an open aeration (equilibrium with atmospheric p(CO 2 ), open system) can help to fulfil the technological requirements. [For simulating both the aeration and the calculation of the new pHc in one job, use the keyword SAVE SOLUTION 1 after the calculation step for the aeration, then END for closing this first part and USE SOLUTION 1 for continuing with the calculation of the new pHc] -5- Exercise 7 7a Not far from the current drinking water well (B3) an older, abandoned well (B4) is located, which was already shut down years ago, since the quality requirements for drinking water couldn´t be fulfilled anymore. More recent investigations showed the following results: Temp. [°C] 26.9 Na [mg/L] 5 pH-value 6.99 K [mg/L] 2 Ks 4.3 [mmol/l] 4 Cl [mg/L] 130 Ca [mg/L] 260 SO 4 [mg/L] 260 Mg [mg/L] 18 NO 3 [mg/L] 70 Check this well water for drinking water and technological requirements. [input of the Ks-value can be done in the following way: Alkalinity 4 mmol/kgw Attention: units must be defined as mg/kgw (not ppm) (kgw = kg H 2 O) = mg/L = ppm] 7b A common and cheap method for drinking water treatment is mixing of different water types. Thereby often the building of an expensive treatment plant can be avoided. It is planed to re- establish the use well B4 for peak times, mixing it with the water from well B3. Check whether it is possible, and if so in which ratios, to mix those two waters, keeping up with the drinking water and technological requirements. [input: chemical analysis SOLUTION 1(B4) and SOLUTION 2 (B3), keyword: MIX Mix in 10%-steps according to the following syntax: 1 10 2 90 next step: 1 20 2 80, then: 1 30 2 70 etc.] Rehabilitation of groundwater Exercise 8 Nitrate reduction by methanol The following groundwater in an agricultural area shows extremely high nitrate concentrations due to heavy fertilizing over years. pH 6.7, temperature 10.5°C, Ca 2+ 185 mg/L, Mg 2+ 21 mg/L, Na + 8 mg/L, K + 5 mg/L, C(4) 4.5 mmol/L, SO 4 2- 200 mg/L, Cl - 90 mg/L, NO 3 - 100 mg/L. Infiltration wells shall be used to pump methanol (CH 3 OH) into the aquifer. Methanol as a reducing agent reduces the penta valent nitrate to zero valent elemental nitrogen. Nitrogen can degas and therefore contributes to the reduction of nitrate concentrations within the aquifer. -6- How many litres of 100% methanol solution (density = 0.7 g/cm 3 ) per m 3 aquifer are needed to reduce nitrate concentrations effectively? What could an overdose of methanol do? [To determine the most effective amount of methanol, you have to solve the problem iteratively. Via the keyword REACTION you can add different concentrations of defined compounds, here methanol, stepwise (e.g. 0.1 1 5 10 50 100 mmol/L). After the first run, you will have to refine the step width within the range of interest. Attention: the amount you define under REACTION refers to single elements within the compound e.g. CH 3 OH 1.0 mmol/L means 1.0 mmol/L C, 4· 1.0 mmol/L = 4.0 mmol/L H and 1.0 mmol/L O, in total 6.0 mmol/L CH 3 OH. The keyword SELECTED_OUTPUT can be used to obtain e.g. pe-value and molalities of N- species only, without the labour of reviewing the whole output file. SELECTED_OUTPUT -file Methanol.csv -pe -molalities NH4+ NH4SO4- NH3 N2 NO2- NO3-] Exercise 9 Reactive Fe(0)-Barriers Reactive barriers of elemental iron are used to reduce groundwater in situ, thereby e.g. transforming mobile Uranium (VI) to Uranium (IV), that precipitate as mineral phase Uraninite (UO 2 ). At the same time the elemental iron in the reactive barrier is oxidized, iron hydroxides and secondarily iron oxides form, that reduce together with the precipitating Uraninite the barrier´s reactivity over time, finally clogging it (aging effect). Simulate the rehabilitation of the following acid mine drainage, containing high concentrations of uranium: pe 10.56 Ca 400 Fe 600 Na 500 pH 2.3 temperature 10 Cd 1 K 4 Ni 5 Si 50 Al 200 Cl 450 Li 0.1 Nitrate 100 Sulphate 5000 As 2 Cu 3 Mg 50 Pb 0.2 U 40 C(4) --- F 1 Mn 20 How much iron per m 2 has to be taken in order to guarantee a reduction of the uranium concentrations from 40 mg/L to at least one third, assuming a percolation of 500 L/d·m 2 ? Additionally there is the requirement that the barrier should be in operation for approximately 15 years without clogging. How much uraninite precipitates during this time? [Solve the problem iteratively like Exercise 8. Watch for uraninite super saturation and actually precipitate uraninite where super saturated.] -7- Further examples for thermodynamic equilibrium reactions Exercise 10 Evaporation In arid areas evaporation plays a major role in the hydrogeochemistry of groundwaters by leading to an enrichment of species within the hydrogeological cycle. Neglecting the influence of evaporation in hydrogeochemical modeling may lead to enormous errors. Since evaporation calculation in PhreeqC is a little bit tricky, it is shown in the following example with a 90% evaporation. It is important to know that 1kg water contains 55 mol H 2 O. First step is a titration with a negative amount of water; finally the resulting solution has to be transformed back to 55 mol. Title 90% evaporation Solution 1 precipiation water ...... ...... REACTION 1 # evaporation H2O -1.0 # remove water: -H2O ! 49.5 moles # remove 90 %, since 100% = 1 kg H2O = 55 mol # ¬ 90% = 49.5 mol # the resulting 10% of the original amount of water contain # the same chemical composition as the 100% before ¬ same # freight in less solution = higher concentration = enrichment save solution 2 END use solution 2 MIX 2 10 # mix SOLUTION 2 10 times with itself to get back to 100% # of enriched solution (if you leave it with solution 2, PhreeqC # automatically transfers the 5.5 mol back to 55 mol by adding # water, therefore diluting the solution again save solution 3 END ....further reactions, e.g. equilibrium, etc. Your tasks is to simulate and compare the hydrogeochemical composition of infiltrating water with and without consideration of evaporation, assuming that annual average precipitation equals 250 mm, actual evaporation 225 mm and surface runoff 20 mm. The chemical analysis of the precipitation water is as follows: Na = 8, K = 7, Ca = 90, Mg = 29, Sulphate = 82, Nitrate = 80, C(+4) = 13 and Cl = 23 [all units in µmol/L]. pH-value: 5.1, temperature: 21°C. -8- [Attention: define C(+4) in PhreeqC actually as C(+4) not as Alkalinity, since the low concentrations in precipitation water do not enable „conventional“ determination as Alkalinity, only determination as TIC (total inorganic carbon, C(+4))] In the unsaturated zone consisting mostly of limestones and sandstones p(CO 2 ) is 0.01 bar. For estimating the influence of evaporation especially compare concentrations and saturation indices of elements or minerals that typically predominate or precipitate in arid areas, such as Na, Cl, Sulphate respectively halite, gypsum, etc. in both models with and without consideration of evaporation. Exercise 11 pe-pH-diagrams Species distributions under different pH and redox conditions can be calculated analytically and represented in a pe-pH-diagram. In the following examples it is shown how such a pe- pH-diagram can be modelled numerically with PhreeqC. The modelling itself is relatively simple, in the input file certain pe and pH values are defined apart from the species in solution. From the species distribution in the output file the predominant species (i.e. the species, which is represented in the highest concentration) is read. If one varies thereby both the pH value in a scope e.g. from 0 (acid) to 14 (alkaline) and pe-value in a scope e.g. from - 10 (reducing) to +20 (oxidizing) and notes the predominant species for all pe-pH- combinations, one can represent the results in a pe-pH-diagram as a raster picture. The smaller one chooses the step width for the variations of pH and pe, the finer the pe-pH- diagram-raster becomes. In order not to be obliged to input all pe-pH-combinations individually (alone with a step width of 1 for pH and pe that would be 15 pH values times 31 pe-values = 465 combinations!), a BASIC program was prepared that copies one PhreeqC master input file, in which the job is defined for any pH-pe-combination once, and changes pH and pe gradually. The program is started with “ph_pe_diagramm.exe”. Following a query for pH and pe minimum value, maximum value and step width (“delta”) appears. Additionally the prepared PhreeqC master input file and a new output file must be selected. The program considers automatically that the occurrence of aquatic species in each pe-pH-diagram is limited by the stability field of water. Therefore all pe-pH-combinations, which are above the line of transformation from O 2 to H 2 O or below the line of transformation from H 2 O to H 2 , are removed automatically from the program. A short program assistance can be find within the program (menu HELP). The output file with the mentioned step width of 1 would create 15 pH values times 31 pe- values equals 465 jobs numbered from SOLUTION 1 to SOLUTION 465 each with different pH and pe-values. In fact there are however only 377 jobs, since the SOLUTIONs with pe- pH-values above or below the stability field of water, are already missing (removed by the program). All other species defined in the input file under SOLUTION (Fe, Ca, Cl, C, S, etc.) -9- are alike in all 377 jobs. Opening this output file in PHREEQC might take 30 seconds up to one minute, files over 32k can not be opened any more with the Windows-editor for PHREEQC. They either have to be divided into smaller files or must be started directly with phreeqc.exe on DOS level (input: > phreeqc input-file-name output-file-name database- name). In order not to have to examine 377 output jobs for predominant species manually after the modelling, there are two assistances: First of all the PhreeqC master input file contains the keyword SELECTED_OUTPUT, creating a .csv file with the desired species, e.g. all Fe species, pH and pe-values. All desired species must be defined individually under the subkeyword “-molalities”, e.g. Fe2+, Fe3+, FeOH+, etc.. The BASIC reproduction program adds the 377 SOLUTION jobs before the keyword SELECTED_OUTPUT. Since the 377 SOLUTIONs are not separated by the keyword END from each other, one SELECTED_OUTPUT is produced from all SOLUTIONs. It contains one row for each of the 377 jobs with the columns pH, pe, m_Fe2+ (concentration of Fe2+ in mol/L), m_Fe3+, m_FeOH+, etc.. This .csv file can be opened and processed in PhreeqC under the folder GRID. Now for each row (i.e. for each pe-pH-combination), the predominant species (the species with the highest concentration) has to be determined. In order not to have to do this manually again, the data are copied to EXCEL and processed with a macro. One activates the macro by opening “makro.xls” and clicking on “activate macros” in the appearing query. Now one can either copy the own data into the table 1 instead of the given test data or open directly the .csv file, since the activated macro is disposable for all open Excel files. The macro itself can be opened within the menu extra / macro / macros under the name “maxwert”. Under the menu “processing” one can see and edit the script behind the. As well under processing the table area must be defined, in which the data transmitted from the .csv file are to be found, as well as the number of rows and columns, which cover the data range. For the test data the definition looks as follows: Sub maxwert() ’ adjust N% and M%, as well as the data range N% = 6: M% = 4 ’ N%= number of rows, M%= number of columns Dim name As Range Dim wert As Range Set name = Worksheets("Tabelle1").Range("A1:D1") Set wert = Worksheets("Tabelle1").Range("A1:D6") The digits printed bold have to be modified according to the current data range. If the data were copied in table 1 instead of the test data, the name of the worksheet does not have to be modified, if the .csv file was opened directly, the name of this worksheets has be put in. The macro is started with the Play button or the menu Executing / execute SubUserForm. Afterwards the macro automatically scans each row for the cell with the largest value (= the highest concentration). The columns pH and pe are skipped automatically. For each cell with a maximum value found the appropriate header cell is written into the first free column right -10- from the defined data range. The finished EXCEL table finally contains one more column than before in the .csv file. This column shows the names of the predominant species for the respective pe-pH-combination (caution: if the data range is inadvertently defined too small, the program overwrites a column of the original data set!). Note: The macro closes neither automatically, nor does it display the end of the calculation. After approximately 5 seconds at the latest, the calculation is terminated and one can close the Microsoft Visual basic window manually and come back to the modified EXCEL table. With the 3 columns pH, pe and predominant species a pe-pH-diagram as a raster picture can now be created in Excel. The easiest thing hereby is to first sort the three columns according to the column “predominant species” (menu data / sorting). The most suitable diagram type is point (XY) with Y = pe and X = pH. Marking the columns pH and pe and creating a point diagram automatically shows all points in the same colour (choose as point symbol by double clicking on the XY points a filled square, since this illustrates the following raster in the best way, vary the size of the squares in such a way that a completely filled surface develops, approx. 20 pt). Would one like to have the different predominant species as differently coloured points, one can select the window data source again (by click with the right mouse button into the diagram) and define there under “row” an own data set for each species (default there is only one data set with the name “pe” containing all species). Over “add” one can define further data sets, e.g. the series Fe2+, therefore add name (Fe2+), x-values (as written in the table, e.g. in column A from row 146 to 268) and appropriate y-values (B 146 - B 268). Most simply one can define the x and y-values by clicking with the mouse on the red arrow beside the fields for name, x-values, y-values and outlining then the appropriate fields in the table (A146-A268 for X, B146-b268 for Y). If one has defined own data sets for each species, different colours are automatically assigned for each data set. One receives a raster pe-pH- diagram, whose differently coloured surfaces stand for the predominancy of different species. 11 a pe-pH-diagramm Fe Create according to the procedure explained above a pe-pH-diagram for the predominant iron species in a solution of 10 mmol/L Fe and 10 mmol/L Cl. Vary pH and pe-values from 0 to 14 respectively -10 to +20 in steps of 1 unit. 11 b pe-pH-diagramm Fe-C pe-pH-diagramm Fe-S How does the pe-pH-diagram change considering an additional 10 mmol/L S(6) respectively 10 mmol/L C(4) in solution? Edit and complete a database / Uncertainty of thermodynamic data Exercise 12a: Edit thermodynamic data Assuming you obtained new data about the solubility product of a special dolomite in your area of interest - how can you enter this data? Of course you could open the database file (e.g. WATEQ4f.dat with any text editor (e.g. WordPad) and change the log(k) value directly. However it is recommended to test it first in a regular PhreeqC -11- input file. Therefore start your input file with the key word PHASES, copy the dolomite statement from the WATEQ4f database into your job-file, and change the log k to -18.5 (your new data). PHASES Dolomite(d) 11 CaMg(CO3)2 = Ca+2 + Mg+2 + 2CO3-2 log_k -16.54 delta_h -11.09 kcal Then model the dissolution of dolomite in distilled water with a pH of 5.3 for both log(k). Do you see a significant difference? Exercise 12b: Complete database for new species Download the file add_thermdyn_data.phrq from the web-side indicated for the course and plot the species distribution. Check that LLNL has none of the three uranium-arsenate species. Note that you have to define under SOLUTION_SPECIES each new species, e.g. UO2H2AsO4+ = UO2H2AsO4+, and then the reaction equation and the log(k) data. Exercise 12c: Add a new element Download the file add_thermdyn_Radium.phrq from the web-side indicated for the course. Run the job and look for the radium species and radium phases. As exercise 2 this is only to give you an idea how it works. As mentioned above, after testing in a job file, you may copy the new definitions into the appropriate sections of your own database. Please do not do this during this course! Exercise 12d: Uncertainty of thermodynamic constants Any thermodynamic constants and any numbers we measure have a certain uncertainty and this may have a severe impact on the modelling result. PHREEQC does not provide an option to deal with this problem. However, the probabilistic speciation code LJUNGSKILE (Odegard-Jensen et al 2004) couples PHREEQC with either a Monte Carlo or a Latin Hypercube Sampling approach to allow calculation of species diagrams with uncertainties. Species diagrams can be plotted by means of a chart template using LDP20.exe or via export to any scientific chart software. LJUNGSKILE and the viewing tool LDP20 can be downloaded from http://www.geo.tu-freiberg.de/software/Ljungskile/index.htm. Both programs install automatically (after unzipping) and can be started showing the following template: -12- A new project is created in LJUNGSKILE via File/new. Then a database has to be selected. This can be any valid PHREEQC database, however, two theoretical species must be included which are used by LJUNSKILE to maintain electrical charge balance. Thus chose example.dat. Then, the species of interest have to be edited via Edit project parameters. UO2+2 l ogk - 9. 1 UO2OH+ l og_k - 5. 2 UO2( OH) 2 l og_k - 12 UO2) 2( OH) 2+2 l og_k - 5. 62 UO2) 3( OH) 5+ l og_k - 15. 55 UO2CO3 l ogk 9 UO2( CO3) 2- 2 l ogk 17. UO2( CO3) 3- 4 l ogk 21. 6 UO2HPO4 l ogk 11. 64 UO2( HPO4) 2- 2 l ogk 33. 759998 UO2H2PO4+ l ogk 13. 44 UO2( H2PO4) 2 l ogk 35. 43 UO2( H2PO4) 3- l ogk 56. 68 Use SD 0.2 for all species and normal distribution. In the column “mean value” the log_k values from the database used have to be entered for the species of interest. The distribution for LHS or Monte Carlo simulation can be defined as “normal” distributed, then the assumed standard deviation of the log_k is entered in the column “SD or max value”. Alternatively, one can enter “uniform” in distribution and enter a maximum value of log_k in the column “SD or max value”. Add more species with right mouse click. Additional, a solid phase and the partial pressure of carbon dioxide can be entered. LJUNGSKILE will then maintain equilibrium with the mineral entered and the carbon dioxide partial pressure by means of EQUILIBRIUM_PHASES. Additionally, the master species of the solution has to be entered in the template edit water. The same template is used to define the pH, pe, and temperature. -13- Use the following data (mol/l): pH 6 pe 12 Ca 0.00167 Na 0.001 C 0.01 U 1e-6 P 1e-4 Cl 0.001 Edit sampling method is used to choose between LHS (Latin Hypercube Sampling) and Monte Carlo Sampling. Finally, LJUNGSKILE offers to calculate species concentrations at the given pH or by changing one parameter (e.g. pH or pe) within a certain range. This is done by checking in the multiple run box and edit the range and the interval length. LJUNGSKILE can be started from the GUI by means of Simulation from the main menu. Output is written in files named species.out respectively PHROUT.number with number running from 1 to the total number of e.g. pH steps. For visualization, the visualization tool LDP20.exe can be used either by Display from the LJUNGSKILE main menu or directly from the folder where LDP20.exe is installed. Kinetics As reaction rates can be fitted mathematically in very different manners, there is an option (and need) in PHREEQC to declare any mathematical term in the form of a little BASIC program within the keyword RATES as will be shown in the following example of a time- dependent calcite dissolution: Download the following file (Kinetics_solution of_calcite.phrq from the web side of the course. -14- SOLUTION 1 distilled water pH 7 temp 10 EQUILIBRIUM_PHASES CO2(g) -3.5 KINETICS 1 Calcite -tol 1e-8 -m0 3e-3 -m 3e-3 -parms 50 0.6 -steps 36000 in 20 steps // 36.000 seconds* -step_divide 10000 // first interval calculated with 3.6 sec.* RATES Calcite -start 1 rem Calcite solution kinetics according to Plummer et. al 1978 2 rem parm(1) = A/V, 1/dm parm(2) = exponent for m/m0 10 si_cc = si("Calcite") 20 if (m <= 0 and si_cc < 0) then go to 200 30 k1 = 10^(0.198 - 444.0 / (273.16 + tc) ) 40 k2 = 10^(2.84 - 2177.0 / (273.16 + tc) ) 50 if tc <= 25 then k3 = 10^(-5.86 - 317.0 / (273.16 + tc) ) 60 if tc > 25 then k3 = 10^(-1.1 - 1737.0 / (273.16 + tc) ) 70 t = 1 80 if m0 > 0 then t = m/m0 90 if t = 0 then t = 1 100 moles = parm(1) * 0.1 * (t)^parm(2) 110 moles = moles * (k1 * act("H+") + k2 * act("CO2") + k3 * act("H2O")) 120 moles = moles * (1 - 10^(2/3*si_cc)) 130 moles = moles * time //this line is a ”must“ for each BASIC-program* 140 if (moles > m) then moles = m 150 if (moles >= 0) then goto 200 160 temp = tot("Ca") 170 mc = tot("C(4)") 180 if mc < temp then temp = mc 190 if -moles > temp then moles = -temp 200 save moles //this line is a “must” for each BASIC-program* -end SELECTED_OUTPUT -file 4_Calcite.csv -saturation_indices calcite end Exercise 13a Run the job for CO2 partial pressure of 0.03 and 1 vol% and display it either by an excel graph or by means of the USER_GRAPH statement. Exercise 13b Add kinetic solution of K-feldspar You need for kinetics both the keyword KINETICS (and the keyword RATES). As long as an appropriate RATES section for the mineral of interest is in the database used this is sufficient, however, it might still be a good idea to copy the RATES segment from the database into the job-file into the RATES block (in case database is changed). So copy at least the “KINETICS”-part from the database into the kinetics -15- section and remove the “#” Display graphically the solution of both minerals: calcite with 1 vol% of CO 2 , and K-feldspar. Check for oversaturated minerals and model the precipitation of clay minerals thermodynamically since this is a very fast process. Transport Example 14 Column experiment (transport & sorption / exchange) Sorption, as a common retardation mechanism in mass transport, has an elementary meaning for the chemical quality of infiltrating water and groundwater. Within Phreeqc there are two possibilities of simulating linear transport with constant velocities: the keyword ADVECTION enables simple simulations using calculations based on the mixed cell model, the keyword TRANSPORT can consider additionally dispersion, diffusion and double porosity (mobile and immobile pores). The used units generally are meter [m] and seconds [s]. Linear modelling is suitable in order to simulate laboratory column experiments or processes in the aquifer along a theoretical flowline. The following example shows the results of a column experiment with a 8 m long column, which contains a cation exchanger. The column was equilibrated first with a conditioning solution, containing 1 meq/l NaNO 3 as well as 0.2 meq/L KNO 3 . The solution was applied until the concentrations at the outlet equalled those at the inlet. Then the solution was changed to a 0.5 meq/L CaCl 2 -solution and the concentrations of the dissolved ions measured at the outlet. The results are shown in the following figure; the time scale on the x axis begins with 0 at the point of time at which the input solution was changed to CaCl 2 . The x axis is scaled in water volumes and shows a three times exchange of the water in the column (shift=120). 0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04 6.E-04 7.E-04 8.E-04 9.E-04 1.E-03 0 20 40 60 80 100 120 140 time steps [shifts] c o n c e n t r a t i o n s i n m o l / L Na Cl K Ca -16- Chloride behaves like an ideal tracer, only impaired by dispersion. Calcium does not occur at the column´s outlet even after one entire exchange of the column volume (SHIFT = 40), since it is exchanged for Na and K. After all sodium is removed from the exchanger, Ca can only be exchanged for K, which leads to a peak of the K-concentrations. Only after the column volume was exchanged approx. 2,5 times, the Ca-concentrations at the outlet increase. In the following the Phreeqc-Job is specified, which reconstructs the experiment. For the adjustment of the model to the measured data the parameters exchange capacity (X under EXCHANGE, here 0.0015 mol per kg water), the selectivity coefficients in the data base Wateq4F.dat and the selected dispersivity (TRANSPORT, -dispersivity; here 0.1 m) are decisive apart from the spatial discretisation (number of cells, here 40). If one puts the dispersivity to a very small value (e.g. 1e-6), and does the modelling again, no more numeric dispersion occurs, since the numeric conditions of stability are kept. TITLE Column experiment with exchanger PRINT -reset false # no standard output SOLUTION 0 CaCl2 # secondary solution: CaCl2 units mmol/kgw temp 25.0 pH 7.0 charge pe 12.5 O2(g) -0.68 Ca 0.5 Cl 1.0 SOLUTION 1-40 Initial solution for column # original solution: NaNO3 + KNO3 units mmol/kgw temp 25.0 pH 7.0 charge pe 12.5 O2(g) -0.68 Na 1.0 K 0.2 N(5) 1.2 EXCHANGE 1-40 # whole column (exchanger) equilibrate 1 # equilibrate with solution 1 X 0.0015 # exchanger capacity in mol TRANSPORT -cells 40 # 40 cells -length 0.2 # á 0.2 m; 40*0.2= 8 m length -17- -shifts 120 # refill each cell 120 times -time_step 720.0 # 720 s per cell; --> v = 24 m/day -flow_direction forward # forward simulation -boundary_cond flux flux # boundary condition on top & bottom -diffc 0.0e-9 # diffusion coefficient m2/s -dispersivity 0.1 # dispersivity in m -correct_disp true # correction dispersivity: yes -punch_cells 40 # only cell 40 in selected_output -punch_frequency 1 # print each times step -print 40 # print only cell 40 (outlet) SELECTED_OUTPUT -file exchange.csv # output file -reset false # print no standard output -step # default -totals Na Cl K Ca # output of total concentrations END 14 a Run this job in Phreeqc, get familiar with the different subkeywords within the keyword TRANSPORT and the interpretation of the changing chemical conditions at the outlet. 14 b Modify now the above presented job for the following situation: A lysimeter with sedimentary filling (cation exchanger with the capacity 1.1 mmol/L), is equilibrated with the following water (units mmol/l): pH=8.0 pe=12 temp = 10,0 Ca=1 C=2.2 Mg=0.5 K=0.2 S=0.5 At one time point the original solution is replaced by acid mine drainage with the following chemical composition: pH=3.2 pe=16 temp=10.0 Ca=1 C=2.0 Mg=0.5 K=0.2 S=4.0 Fe=1 Cd=0.7 Cl=0.2 Model the concentration distribution in the column and plot the results in an Excel diagram (discretisation and time steps unchanged). Describe your results concerning the sorption and transport properties of the individual elements. Especially try to explain the behaviour of iron. Which iron species are most likely to be exchanged (consider species concentrations and exchanger properties)? Are selectivity constants defined for these species? To answer this, have a look inside the database, within the keyword EXCHANGE_SPECIES, almost at the end of the database, all species which will be considered during the modelling are defined with their respective selectivity constants. Modify in a second simulation the dispersivity from 0.1 m to 0.001 m and describe, what happens. -18- 14 c The following figure shows the results of an experiment conducted to determine the selectivity constant of one of the cationic iron complexes of example 1b (Fe(OH) 2 + ), which is not defined in standard databases. First the column (same exchanger material as in exercise 1b) was equilibrated with the same original solution as in example 1b, then a 0.5 mol FeCl 2 -solution (pe 16, pH 5.5, temperature 10°C, Fe = 0.5 mmol/L, Cl = 1.0 mmol/L) was added. Model the experiment and try to find the selectivity constant for the iron species by fitting your data to the following graphs. (mmol/L in PhreeqC always have to be defined as mmol(eq)/L, consider this for Fe. “Determination-Fe- Selectivity.xls” is the digital version of the following figure, for comparison the best thing to do is add your data to the existing Excel spread sheet so you can see easily how they fit) 0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04 6.E-04 7.E-04 8.E-04 9.E-04 1.E-03 0 20 40 60 80 100 120 time steps [shifts] c o n c e n t r a t i o n s [ m o l / L ] Ca Mg K Cl Fe Note: First try to find the right dispersivity for the experiment by fitting the Cl curve (Cl as ideal tracer is only subject to dispersion, not to sorption). With the so found dispersivity run the job again, this time defining a selectivity constant for Fe(OH) 2 + . One way of defining own species can be done by changing existing databases. Databases are not editable within PhreeqC, you have to open them in any text editor, change or add the desired section, save it and open again in PhreeqC. However it is much easier, especially if you are only going to use it for one job, to edit changes within the input file itself. Anything that is defined in the input file, is added to respectively overwrites information in the database. So instead of adding your species within the database under the keyword EXCHANGE_SPECIES, you can just define EXCHANGE SPECIES, a reaction equation and the selectivity constant (log_k) before the keyword TRANSPORT within the input file (take e.g. the definition of Fe+2 in the database as example for how to define EXCHANGE_SPECIES). By varying the selectivity constant log_k try to fit your points to the Fe-points predefined by the results of the experiment. That is the regular way how selectivity constants are defined. -19- Transport & Kinetics – more exercises Example 15 Tritium degradation in the unsaturated zone (transport & kinetics) Radioactive decay is a typical application where equilibrium modelling leads nowhere. Kinetics, exactly the half life time of the radioactive element, has to be considered. The following task is to model the tritium degradation within the unsaturated zone assuming tritium input as a (theoretical) single-peak function (tritium bomb peak 1963) and in a second step (more realistic) as a gradually decreasing function. If the unsaturated zone is formed by comparatively fine sediment (silt and fine sands) a quasi uniform movement of the infiltrating water can be assumed in humid climates considering long periods of time. Thus the transport of the infiltrating water can be simulated within PhreeqC2 as monotonous movement according to the “piston flow” model. For the modelling shown in the following constant movements of the infiltrating water of 0.5 m per year were assumed. Besides the simplification was made that the infiltrating precipitation showed a tritium activity of 2000 TU for a period of 10 years, and decreased to zero immediately after this period. How to model this in PhreeqC2 is shown in the following example. First of all a master and a solution species tritium T respectively T+ has to be defined. Since within SOLUTION_SPECIES a specification for log_k and gamma is needed, however not known, you can enter any value you like (“dummy”, e.g. 0.0). For kinetic calculations this value is not used any further, thus it causes no problems. All results for this “species” based on equilibrium reactions however (e.g. calculation of the saturation indices) are naturally nonsense. The tritium values are entered in tritium units. However in order not be obliged to specially define or convert them, you can leave PhreeqC with the fictitious unit µmol/kgw, since tritium reacts with no other species, the unit finally does not matter. The indicated µmol/kg in the output correspond likewise to tritium units. The unsaturated zone is determined to 20 meters and divided into 40 cells each 0.5 m. With a flow velocity of 0.5 m/a one “time step” equals exactly 1 year = 86400 * 365 seconds = 3.1536e+7 seconds. Also the half-life time of tritium (12.3 years) must be indicated in seconds within PhreeqC. The one dimensional soil column, created in that way, is watered first with a solution containing no tritium (solution 1-40) and then during the period 10 “shifts” (= 10 years) with tritium (solution 0 2000 TU). After this single peak the column is again operated with water without tritium for 30 more years. It has to be noted, that these are two jobs, which have to be separated by END. The tritium degradation is described as a first order kinetic reaction: (A) C dt (A) d k · ÷ = (A) = (A 0 )•e -C K • t ln2 C 1 t k 1/2 · = -20- PhreeqC job: Tritium in the unsaturated zone with single-peak input function TITLE tritium within the unsaturated zone PRINT -reset false # create no standard output SOLUTION_MASTER_SPECIES # define tritium as master species T T+ -1.0 T 1.008 SOLUTION_SPECIES # define tritium as solution species T+ = T+ log_k 0.0 # dummy -gamma 0.0 0.0 # dummy SOLUTION 0 tritium 1. phase # tritium concentration 2000 TU units umol/kgw temp 25.0 pH 7.0 T 2000 # 2000 (unit umol/kgw purely fictitious) SOLUTION 1-40 # equilibration with no Tritium first units umol/kgw temp 25.0 pH 7.0 end # end of job 1 RATES # define degradation T # for tritium -start 10 rate = MOL("T+") * -(0.63/parm(1)) # first order kinetics 20 moles = rate * time 30 save moles -end # end of job 2 KINETICS 1-40 T -parms 3.8745e+8 # 12,3 years in seconds (half life time tritium) TRANSPORT -cells 40 # 40 cells -length 0.5 # each 0.5 m; 40*0.5 = 20 m length -shifts 10 # 10 years -time_step 3.1536e+7 # 1 year in seconds -flow_direction forward # forward simulation -boundary_cond flux flux # boundary conditions on top & bottom -diffc 0.0e-9 # diffusion coefficient -dispersivity 0.05 # dispersivity -correct_disp true # correction dispersivity: yes -21- -punch_cells 1-40 # cell 1 to 40 in selected output -punch_frequency 10 # print every 10.time step SELECTED_OUTPUT -file tritium.csv # output in this file -reset false # print no standard output -totals T # print total concentration of tritium -distance true END # end of job 3 SOLUTION 0 no more tritium after 10 years units umol/kgw temp 25.0 pH 7.0 TRANSPORT shifts 30 # another 30 years END 15 a Run this job in PhreeqC, get familiar with the different subkeywords and create a diagram of the produced data showing the tritium concentration depending on soil depth after 10, 20, 30, and 40 years (y-axis tritium concentration [T.U.], x-axis soil depth [m]). 15 b A further task now is to modify this PhreeqC-Job in such a way that the input function of tritium is not a single-peak input function, but more realistic a gradually decreasing input function. The following figure shows the increase of tritium in precipitation from 1962 to 1963 and the following decrease from 1962 to 1997, based on a climatic station in Hof-Hohensass / Germany. tritium concentrations in precipitation 1962-1997 1 10 100 1000 10000 6 2 6 4 6 6 6 8 7 0 7 2 7 4 7 6 7 8 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 year t r i t i u m u n i t s [ T U ] -22- The definition of the gradually decreasing tritium input function based on these data is done in time intervals of 5 years each as follows: interval each 5 years tritium in the atmosphere (TU) 1 (06/1962 - 06/1967) 1022 2 (07/1967 - 07/1972) 181 3 (08/1972 - 08/1977) 137 4 (09/1977 - 09/1982) 64 5 (10/1982 - 10/1987) 24 6 (11/1987 - 11/1992) 17 7 (12/1992 - 12/1997) 13 Repeat the modelling of tritium degradation in the unsaturated zone with this new input function. Present your results in a diagram tritium concentration depending on soil depth again and compare it with the results from the modelling with a single-peak input function. Exercise 16 pH neutralization of acid mine drainage in a carbonate channel In the field of mining and especially abandoned mines acid mine drainages (AMD) often present problems for water quality due to increased concentrations of iron, sulphate and protons due to pyrite oxidation. Associated with this also other elements (e.g. heavy metals and arsenic) may be increased. A simple method of water treatment is conducting the AMD through a carbonate channel. Hereby the pH value is increased by carbonate solution, other minerals might become supersaturated and precipitate spontaneously. High sulphate concentrations combined with increasing calcium concentrations from calcite solution often lead to super saturation with respect to the mineral phase gypsum. Also iron minerals might become supersaturated, iron hydroxide e.g. can precipitated spontaneously. Though calcite solution occurs quite fast, this exercise shows again, that kinetics have to be considered in order to calculate the right dimensions of this water treatment plant. Given are an acid mine drainage („AMD“) and a surface water without anthropogenic influences, which first flows through the 500 m long carbonate channel („surface water“). At one point of time acid mine drainage is added. It is to be calculated how the water quality changes, how much calcite dissolves and how much gypsum and iron hydroxide precipitate. Problems of coating of carbonate grains by gypsum and iron hydroxide as well as the kinetics of gypsum and iron hydroxide formation are not considered in this example. Hydrogeochemical analysis of an acid mine drainage („AMD“) and a surface water without anthropogenic influences („surface water“): parameter AMD surface water parameter AMD surface water pe value 6.08 6.0 K 3.93e-05 mol/L 1.5 mgl/L temp. [°C] 10 10 Li 2.95e-06 mol/L value 1.61 8.00 Mg 1.47e-04 mol/L 3.5 mgl/L Al 1.13e-04 mol/L Mn 1.30e-06 mol/L -23- As 5.47e-07 mol/L Nitrat 2.47e-04 mol/L 0.5 mgl/L TIC*) 3.18e-03 mol/L Na 2.58e-04 mol/L 5.8 mgl/L HCO 3 - 130 mgl/L **) Ni 8.72e-07 mol/L Ca 9.19e-04 mol/L 36.6 mgl/L***) Pb 2.47e-07 mol/L Cd 2.27e-07 mol/L Sulfat 5.41e-02 mol/L 14.3 mgl/L Cl 6.07e-05 mol/L 2.1 mgl/L Si 6.20e-05 mol/L 3.64 mgl/L Cu 8.06e-07 mol/L U 2.15e-07 mol/L F 2.69e-05 mol/L Zn 1.09e-05 mol/L Fe 2.73e-02 mol/L 0.06 mgl/L *) total inorganic carbon **) set the inorganic carbon C to the atmosphere´s p(CO 2 ) by adding CO2(g) -3.5 behind the concentration ***) set Ca to „charge“ for forcing the equilibration of the ionic balance Assume the flow velocity as 1 m/s, so the whole reaction time within the channel is 500 s. Modelling is to be done as 1d-transport model with 10 cells (dispersivity 0.1 m) for 750 s. Consider also the contact with the atmosphere in the carbonate channel; p(CO 2 ) shall be varied within two different models from 0.03 Vol% (open channel) to 1 Vol% (closed channel), both times assuming p(O 2 ) = 0.21 Vol%. Set m0 and m within KINETICS to 1 mol/L. Display your results by showing the changing water chemistry along the carbonate channel (pH-value, SI calcite, Ca, Fe, C, SO 4 2- , CaSO 4 0 ). Further more the amounts of dissolved calcite and precipitated gypsum and iron hydroxide are to be displayed. Exercise 17 double porosity aquifer - in-situ leaching Double porosity aquifers (e.g. sandstones with fracture and pore volume) impose special requirements on transport modelling, even when there is no reactive mass transport sensu strictu to be considered. Mathematically double porosity aquifers can be considered as consisting of two zones: the fracture zone with very high mobility (“mobile zone”) and the porous zone with lower mobility or stagnant conditions (“immobile zone”). Both zones are connected to each other, only diffusive exchange takes place between them, which can be described by a first order kinetic reaction. ) c - (c α t c R θ t M im m im im im im = c c · = c c index „m“ = mobile, index „im“ = immobile M im = number of moles of one species in the immobile zone R im = retardation factor of the immobile zone determined by the chemical reactions c m and c im = concentrations in mol/kg water in the mobile and immobile zone a = exchange factor (1/s) -24- Integrating the above shown formula, one gets: ) R βθ αt exp( 1 f θ R θ R θ R β with f)c β - (1 c f β c im im im im m m m m im0 m0 im ÷ = + = · + · · = c m0 and c im0 = original concentrations of mobile and immobile zone u m and u im = water saturated porosities of mobile and immobile zone Therewith a mix factor mix f im can be defined, being a constant for a time t f β mixf in · = Inserting this in the integrated formula above: im0 im m0 im im )c mixf - (1 c mixf c + · = for the immobile concentration im0 m m0 m m C mixf )c mixf - (1 c · + = for the mobile concentration The exchange factor o depends on the geometry of the stagnant zone: 2 1 im e ) (af θ D α ÷ = s D e = diffusion coefficient in the sphere (m 2 /s) a = radius of the sphere (m) f s ÷1 = form factor (see table for examples) shape of immobile zone dimensions (x,y,z) or 2r,z f s ÷1 commentary sphere 2a 0.212a = diameter planar 2a, ·, · 0.5332a = thickness rectangle 2a, ·, · 0.312rectangle 2a,2a,16a 0.298 2a,2a,8a 0.285 2a,2a,6a 0.277 2a,2a,4a 0.261 2a,2a,3a 0.246 2a,2a,2a 0.22cube 2a,2a,4a/3 0.187 2a,2a,a 0.162 2a,2a,2a/3 0.126 2a,2a,2a/4 0.103 2a,2a,2a/6 0.0748 2a,2a,2a/8 0.0586 cylinder 2a, · 0.3022a = diameter 2a,16a 0.298 2a,8a 0.277 2a,6a 0.27 2a,4a 0.255 2a,3a 0.241 2a,2a 0.216 2a,4a/3 0.185 -25- The following example deals with the rehabilitation of a double porosity aquifer within an area influenced by uranium mining with in situ leaching (ISL) with sulphuric acid. Hydrogeochemical analysis of groundwater with anthropogenic influence (GW) and groundwater influenced by in-situ-leaching (ISL) (concentrations in mg/L): parameter GW ISL parameter GW ISL parameter GW ISL pe 6.08 10.56 Cu 0.005 3 Ni 0.005 5 temperature 10 10 F 0.5 1 Nitrate 0.5 100 Al 3.0 200 Fe 0.6 600 Pb 0.05 0.2 As 0.004 2 K 1.5 4 pH 6.6 2.3 C(4) 130 Li 0.02 0.1 Si 3.64 50 Ca 36.6 400 Mg 3.5 50 Sulphate 14.3 5000 Cd 0.0003 1 Mn 0.07 20 U 0.005 40 Cl 2.1 450 Na 5.8 500 Natural groundwater (GW) is pumped into the aquifer via an infiltration well, contaminated groundwater (ISL) extracted via an extraction well. The distance between both is 200 m, the kf-value is approximately 5·10 -5 m/s in fractures and 10 -8 m/s in pores (kf-values are for orientation only, they are not needed directly for solving the modeling). Scheme for the model of a double porosity aquifer (immobile cells connected to mobile cells by one box each, exchange between mobile and immobile cells is described by a first order kinetic reaction): extraction well infiltration well mobile cells immobile cells Flow velocity is 10 m/d, dispersivity 2 m. Assume that exchange between pores and fractures can only take place via diffusion (2·10 -10 m 2 /s). Fracture volume is 0.05, pore volume 0.15. Fracture shapes are planar with a fracture interval of approximately 20 cm, thus each fracture has a pore matrix of 10 cm thickness in average to each side. Homogeneous and heterogeneous reactions are not considered. Time for simulation is 200 days, wherein water within the 200 m long aquifer section is exchanged 10 times. Length of the elements is 10 m. -26- [within the keyword TRANSPORT use the sub keyword “stagnant” for referring to the immobile zone and define the four numbers for layer number (1), exchange factor o, as well as the porosities u m and u im each separated by a blank. The exchange factor o has to be calculated according to the formula shown above] Display the concentrations of the elements U, Fe, Al, and S over 200 days in the extraction well. How much uranium was stored in the fractured sections, how much in the porous sections and how much is extracted from the porous sections after 200 days? How long might it take for uranium to be completely extracted from the porous section provided the transfer from the pore matrix takes place by diffusion only? Change the parameter „immobile pore volume“ from 0.15 to 0.05 and the interval of the fractures to 2 cm (= thickness of the pore matrix attached to each side of the fractures 0.01 m instead of 0.1 m). Compare the results.