reproducing the results of an inverse model

[grk1]

Hello David and Phreeqc community.

I try to simulate remineralization of water artificially recharged into a coastal sandy aquifer, specially interested in Mg. We are assuming only Calcite precipitation/dissolution and cation exchange reactions are present, based on previous studies (of mainly the unsaturated zone).
Currently Im trying to improve a PHT3D model that simulates the whole artificial recharge operation.
For this, a better understanding of initial conditions of the minerals in the aquifer are needed (pre-artificial recharge). 
To establish them I ran an inverse Phreeqc model, where the starting solution ("1") is the recharged water when it reaches the saturated zone, and the final solution ("2") is the recharged water reaching the production well (~1 km away from the recharge pond) before it mixes (50-50) with the native GW.

this is the resulting Phase mole transfers from my simple inverse model (with phreeqc.dat):
Calcite      1.140e-03     
CaX2     -5.046e-04   
KX      8.702e-06   
MgX2      3.877e-04 
NaX      2.251e-04   
 
I'm trying to understand what is the correct way to reproduce solution 2 with a forward phreeqc
model (i.e. solution 1+deltas +calcite dissolution/precipitation + cation exchange reactions= solution 2), especially considering the negative contribution of CaX2.




Here is the input and output of the inverse model:

Code: [Select]

SOLUTION 1
    temp      22.6
    pH        7.78
    units     mg/l
    density   1
    Ca        41.1
    Cl        13.3
    K         0.83
    C(4)      174
    Mg        3.13
    Na        20.7
    S(6)      12.5
    -water    1 # kg

SOLUTION 2
    temp      22.2
    pH        7.35
    units     mg/l
    density   1
    Ca        54.15
    Cl        6.67
    K         1.17
    C(4)      323
    Mg        12.55
    Na        25.87
    S(6)      7.82
    -water    1 # kg

INVERSE_MODELING 1
    -solutions      1        2
    -uncertainty    0.16     0.16
    -phases
        Calcite
        CaX2
        KX
        MgX2
        NaX
    -tolerance         1e-10
    -mineral_water     false

WARNING: Cl is included in solution 1, but is not included as a mass-balance constraint.
WARNING: S(6) is included in solution 1, but is not included as a mass-balance constraint.
WARNING: Cl is included in solution 2, but is not included as a mass-balance constraint.
WARNING: S(6) is included in solution 2, but is not included as a mass-balance constraint.

Solution 1: DSW beneath pond3

                         Input          Delta    Input+Delta
             pH      7.780e+00  +   0.000e+00  =   7.780e+00
     Alkalinity      2.773e-03  +   1.292e-04  =   2.903e-03
          C(-4)      0.000e+00  +   0.000e+00  =   0.000e+00
           C(4)      2.852e-03  +   4.564e-04  =   3.309e-03
             Ca      1.026e-03  +  -1.641e-04  =   8.616e-04
              K      2.123e-05  +   0.000e+00  =   2.123e-05
             Mg      1.288e-04  +   0.000e+00  =   1.288e-04
             Na      9.006e-04  +   0.000e+00  =   9.006e-04
           O(0)      0.000e+00  +   0.000e+00  =   0.000e+00
              X      0.000e+00  +   0.000e+00  =   0.000e+00

Solution 2: DSW reaching well M6 at May 2019

                         Input          Delta    Input+Delta
             pH      7.350e+00  +   0.000e+00  =   7.350e+00
     Alkalinity      4.855e-03  +   3.269e-04  =   5.182e-03
          C(-4)      0.000e+00  +   0.000e+00  =   0.000e+00
           C(4)      5.296e-03  +  -8.473e-04  =   4.448e-03
             Ca      1.352e-03  +   1.451e-04  =   1.497e-03
              K      2.993e-05  +   0.000e+00  =   2.993e-05
             Mg      5.164e-04  +   0.000e+00  =   5.164e-04
             Na      1.126e-03  +   0.000e+00  =   1.126e-03
           O(0)      0.000e+00  +   0.000e+00  =   0.000e+00
              X      0.000e+00  +   0.000e+00  =   0.000e+00

Solution fractions:                   Minimum        Maximum
   Solution   1      1.000e+00      0.000e+00      0.000e+00
   Solution   2      1.000e+00      0.000e+00      0.000e+00

Phase mole transfers:                 Minimum        Maximum
        Calcite      1.140e-03      0.000e+00      0.000e+00   CaCO3
           CaX2     -5.046e-04      0.000e+00      0.000e+00   CaX2
             KX      8.702e-06      0.000e+00      0.000e+00   KX
           MgX2      3.877e-04      0.000e+00      0.000e+00   MgX2
            NaX      2.251e-04      0.000e+00      0.000e+00   NaX

Redox mole transfers:   

Sum of residuals (epsilons in documentation):         4.383e+00
Sum of delta/uncertainty limit:                       4.383e+00
Maximum fractional error in element concentration:    1.600e-01