Definition of surface with fixed partition coefficient Kd

[llanduyt]

Hello,

Within the context of my master thesis, I am trying to model sorption of Sb onto a solid phase with a fixed (and thus pH-independent) Kd value. The partition coefficent Kd is defined as the ratio (Sb-concentration in the solid phase):(dissolved Sb-concentration) and the experimental value I would like to implement is 124 L/kg.

I have defined my surface as follows:

SURFACE_MASTER_SPECIES
Sorb Sorb
 
SURFACE_SPECIES
Sorb = Sorb 
   log_k 0
Sb(OH)3 + Sorb = SorbSb
   -no_check
   -mole_balance SorbSb
   log_k -98.6563
Sb(OH)6- + Sorb = SorbSb
   -no_check
   -mole_balance SorbSb
   log_k -98.6563

SURFACE 1
Sorb 1e100 1.0 1e100

I have done the conversion of Kd=124L/kg to log_k=-98.6563 as followed:
Concerning the sorption reaction: k = (SorbSb)/[(Sb(OH)6-)(Sorb)] => log_k = log[(SorbSb)/(Sb(OH)6-)] - log (Sorb) = log_Kd - 100 (since the amount of Sorb is defined as 1e100).
However, this log_Kd value should be dimensionless so I calculated the wet density of the surface (sediment). Considering a solid layer of 0.1 m with a porosity of 0.62 and an overlaying water column of 0.6 m, the total volume of water equals 0.5+0.062=0.562 m^3. Assuming a dry sediment density of 1 kg/L, there is 100 kg sediment present so the wet density would be 100 kg / 562 L = 0.178 kg/L. Thus, I calculated 124 L/kg x 0.178 kg/L = 22.064 (-) as dimensionless Kd and log_Kd = 1.3437.
Returning to the first equation: log_k = 1.3437 - 100 = -98.6563.

My actual problem is that when I run the simulation and process the results, I am not capable of reproducing this Kd-value. I exported the dissolved Sb-concentration and the molality of the SbSorb-complex and used the obtained values to calculate the % sorbed (as SorbSb/Sb_tot) and the Kd value (as SorbSb/Sb_diss). But the Kd value I obtain differs from the Kd value I originally wanted to implement.
Furthermore, I calculated the sorbed fraction should be around 99% (sorbed_fraction = 1 - 1/(density_sed*Kd+por) = 1 - 1/(1*124+0.62) = 0.992) whereas I only obtain 2% sorbed with this implementation..

soln     pH     Sb_diss (mol/kgw)   Sb(3)     Sb(5)   SorbSb (mol/kgw)   Sb_tot (mol/kgw)   % sorbed   Kd   log_Kd   log_k
1   3.00E+00   4.06E-06   2.50E-36   4.06E-06   9.26E-08   4.15028E-06   2.23157621   0.022825122   -1.641586891   -101.6415869
2   4.00E+00   4.06E-06   2.46E-37   4.06E-06   9.29E-08   4.15027E-06   2.238007442   0.022892408   -1.640308518   -101.6403085
3   5.00E+00   4.06E-06   2.43E-38   4.06E-06   9.29E-08   4.15027E-06   2.238658486   0.02289922   -1.640179307   -101.6401793
4   6.04E+00   4.06E-06   2.25E-39   4.06E-06   9.29E-08   4.15027E-06   2.238723593   0.022899901   -1.640166387   -101.6401664
5   7.18E+00   4.06E-06   0.00E+00   4.06E-06   9.29E-08   4.15027E-06   2.238728739   0.022899955   -1.640165366   -101.6401654
6   8.03E+00   4.06E-06   0.00E+00   4.06E-06   9.29E-08   4.15027E-06   2.238722345   0.022899888   -1.640166635   -101.6401666
7   9.00E+00   4.06E-06   0.00E+00   4.06E-06   9.29E-08   4.15027E-06   2.238656647   0.022899201   -1.640179672   -101.6401797
8   1.00E+01   4.06E-06   0.00E+00   4.06E-06   9.29E-08   4.15027E-06   2.237999964   0.02289233   -1.640310003   -101.64031
9   1.10E+01   4.06E-06   0.00E+00   4.06E-06   9.26E-08   4.15027E-06   2.231513591   0.022824467   -1.641599355   -101.6415994
10   1.20E+01   4.06E-06   0.00E+00   4.06E-06   9.02E-08   4.15027E-06   2.173183295   0.022214597   -1.653361564   -101.6533616

I suppose there is an error in my reasoning, but I cannot find it. I would be very grateful for hints on where I possibly went wrong, or on other ways of defining a surface with a fixed Kd value.

Thanks in advance for the help,

Lisa Landuyt

[dlparkhurst]

See if item 81 helps at http://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc/faq.html

[llanduyt]

Thank you for the fast response!

I didn't take into account that each sorption reaction is for a specific species, now my results match my assumptions.