01 - Monte Carlo Analysis
This example shows how to parameterize a Phreeqc Study for running a Monte Carlo analysis.
Random variables chosen has been Temperature (normal distribution) and a Uraninite logK (triangular distribution).
Note that in geochemistry quite often certain combination of variables are not realistic since they are coupled and its combination could not occur in natural/equilibrium conditions (for example pH and CO2 pressure). This should be considered for the user when choosing random variables.
Studies
This project contains 2 Studies.
PhreeqcStudy: “study_phreeqc_hfstatistics_ex_1”
This model is extracted from the Example 1 of the Phreeqc manual
Db used: “Phreeqc_dat” database
TITLE Example 1.--Add uranium and speciate seawater.
SOLUTION 1 SEAWATER FROM NORDSTROM AND OTHERS (1979)
units ppm
pH 8.22
pe 8.451
density 1.023
temp @{$temp_param$}@
redox O(0)/O(-2)
Ca 412.3
Mg 1291.8
Na 10768.0
K 399.1
Fe 0.002
Mn 0.0002 pe
Si 4.28
Cl 19353.0
Alkalinity 141.682 as HCO3
S(6) 2712.0
N(5) 0.29 gfw 62.0
N(-3) 0.03 as NH4
U 3.3 ppb N(5)/N(-3)
O(0) 1.0 O2(g) -0.7
SOLUTION_MASTER_SPECIES
U U+4 0.0 238.0290 238.0290
U(4) U+4 0.0 238.0290
U(5) UO2+ 0.0 238.0290
U(6) UO2+2 0.0 238.0290
SOLUTION_SPECIES
#primary master species for U
#is also secondary master species for U(4)
U+4 = U+4
log_k 0.0
U+4 + 4 H2O = U(OH)4 + 4 H+
log_k -8.538
delta_h 24.760 kcal
U+4 + 5 H2O = U(OH)5- + 5 H+
log_k -13.147
delta_h 27.580 kcal
#secondary master species for U(5)
U+4 + 2 H2O = UO2+ + 4 H+ + e-
log_k -6.432
delta_h 31.130 kcal
#secondary master species for U(6)
U+4 + 2 H2O = UO2+2 + 4 H+ + 2 e-
log_k -9.217
delta_h 34.430 kcal
UO2+2 + H2O = UO2OH+ + H+
log_k -5.782
delta_h 11.015 kcal
2UO2+2 + 2H2O = (UO2)2(OH)2+2 + 2H+
log_k -5.626
delta_h -36.04 kcal
3UO2+2 + 5H2O = (UO2)3(OH)5+ + 5H+
log_k -15.641
delta_h -44.27 kcal
UO2+2 + CO3-2 = UO2CO3
log_k 10.064
delta_h 0.84 kcal
UO2+2 + 2CO3-2 = UO2(CO3)2-2
log_k 16.977
delta_h 3.48 kcal
UO2+2 + 3CO3-2 = UO2(CO3)3-4
log_k 21.397
delta_h -8.78 kcal
PHASES
Uraninite
UO2 + 4 H+ = U+4 + 2 H2O
log_k @{$-logK_param$}@
delta_h -18.630 kcal
END
/n
MonteCarloStudy: “Monte Carlo Study”
Analsyis
This project contains 1 Analysis.
UnivariantStatisticsAnalysis: “Stats Analysis”
Plots
This project contains 5 Plots.
Plot 1: “Temperature Histogram (input)”
Temperature values, as expected, corresponds to a normal distribution
Plot 2: “Uraninite log_K Histogram (input)”
LogK values generated correspond to a triangular distribution. Normal pdf does not fit.
Plot 3: “2D contour histogram (input)”
LogK and temperature values contour histogram
Plot 4: “Uraninite SI Histogram (Output)”
Uraninite distribution looks like a triangular distribution than a normal distribution, probably for the major influence of logK (which is triangular)
Plot 5: “SI Uraninite”
Uraninite SI depends mainly from logK. Marker color is Temperature value
Tables
This project contains 1 Tables.
Table 1: named “Statistics Table”
data type |
temp_param |
logK_param |
SI Uraninite |
|---|---|---|---|
sum_v |
24977.687803273973 |
3545.7893364768693 |
-12593.218579251617 |
count_v |
1000 |
1000 |
1000 |
mean_v |
24.977687803273973 |
3.545789336476869 |
-12.593218579251618 |
median_v |
25.008437692621747 |
3.5428928180496433 |
-12.59204288804688 |
variance_v |
1.0884303173203729 |
0.39269566050664984 |
0.4020693485797702 |
min_v |
21.972352476075606 |
2.0942708907755083 |
-14.06706549955 |
max_v |
28.973844917008904 |
4.945568646270721 |
-11.11230749564 |
perc_0.05 |
23.236795959265656 |
2.477410266997359 |
-13.664068992181877 |
perc_0.95 |
26.520074089372955 |
4.593482028306202 |
-11.514817056419707 |