Re: PHREEQC modeling

["David L Parkhurst" <dlpark@xxxxxxxx>]

Looks like you have done some nice work with experimentation and modeling.

> However, I found some problems about my results and
had questions about them.
> 1.       To define SURFACE, are SURFACE and their
total mass also divided by 10 if I divided column to
10 cells?

It is easiest to define the surface to be the number of sites per kilogram
(liter) of water. Your solutions (and most PHREEQC SOLUTIONS) have 1 kg
water, so you should normalize the number of sites to 1 kg water, even if
the column is much smaller than this. You can change the mass of water in a
solution, but it is more confusing and can cause problems.

> 2.       In the case of my experiments, the removal
rate of cadmium was very low in a range of 5~200mg/L.
    So I changed reaction constants (log_K) of
SURFACE_SPECIES to negative values. Is it caused any
problem?

The amount of Cd sorbed should be a function of the log Ks. If they are
very small, cadmium sorption will be negligible; very large and cadmium
should be essentially immobile. Small values can include negative log K, so
it should not be a problem.


> 3.       I performed breakthrough experiment for a
single ion of cadmium. But the BTC showed the shooting
result that appears in multi-ion (I mean the
concentration near the breakthrough is over the
initial concentration).

> I think that result was caused by the other ions
that were defined for PHASES. How can I remove such a
phenomenon?

Overshoot can be a real phenomenon. We have seen it in phosphorus column
experiments. But if you did not see the effect then you want to adjust your
model. I think the effect is caused by the decrease in pH over the course
of the transport simulation. At high pH, Cd (a cation) will be strongly
sorbed in the surface complexation model. At low pH it will be desorbed. So
the real cause of the effect is in the Hfo_s/wOH protonation and
deprotonation reactions. If you know the pH through the experiment, you can
try to adjust the log Ks for these reactions (probably only want to use the
"_w" sites to avoid too many fitting parameters. Adjusting number of sites
and log Ks can be tricky; often the log K is inverse to the number of sites
and you can get a good fit with a wide range of Ks and number of sites.

You may want to skip the surface complexation model entirely and simply
define a new surface that reacts only with cadmium. I have included an
excerpt from the FAQ at the PHREEQC home page that hopefully you can figure
out.

> 4.       I included surface complexation to account
for the retardation of cadmium in a column.
>    So I expected that cadmium flowed out more slowly
in the low concentration.
>    Though I changed the initial concentrations from
50mg/L to 5mg/L, the breakthrough times are much the
same.
>    Why did the results appear?

I suspect it is the pH effect, but I have not studied your results in
detail. The pH is defined by the mineral reactions and is probably
insensitive to the amount of cadmium.  When the pH drops, the cadmium is
released, regardless of the amount of cadmium (at least for the range in
concentration that you are using.)

David

David Parkhurst (dlpark@xxxxxxxx)
U.S. Geological Survey
Box 25046, MS 413
Denver Federal Center
Denver, CO 80225

Project web page: https://wwwbrr.cr.usgs.gov/projects/GWC_coupled

   1. SORPTION WITH FREUNDLICH AND LANGMUIR ISOTHERMS: Can I model sorption
      according to Freundlich or Langmuir isotherms with PHREEQC?


      Yes. The derivation and examples are given here. The Freundlich
      equation is:


           q = Kf * C^n                                           (1)



      For PHREEQC, The mass-action equation is derived from the chemical
      reaction equation that defines a species. The following surface
      complexation reaction generates the correct mass-action equation for
      the Freundlich equation:


           Sites + n * C = SitesC                                     (2)



      The mass-action equation for reaction (2) is:


           K = [SitesC] / ([Sites] * [C]^n)                           (3)



      The brackets indicate activity, which for a sorbed species is the
      fraction of sites the sorbed species occupies. Now q = m(SitesC),
      where m(SitesC) is the number of moles of C that is sorbed. [SitesC]
      = m(SitesC)/TOT(Sites), [Sites] = m(Sites)/TOT(Sites), m(Sites) is
      the number of moles of unoccupied sites, and TOT(Sites) is the total
      number of sorption sites. Substituting into equation (3) gives the
      following equation:


           K = {q/TOT(Sites)} / ({m(Sites)/TOT(Sites)} * [C]^n)         (4)



      Canceling TOT(Sites) and rearranging 4 gives:


           q = (K * m(Sites)) * C^n.                                (5)



      Equation (1) and (5) are identical when K = Kf / m(Sites). The trick
      is to keep m(Sites) (the number of unoccupied sites) constant
      throughout the calculations. This can be arranged by making
      TOT(Sites) large relative to the amount of C that sorbs. In that
      case, the unoccupied sites, m(Sites), will stay nearly equal to the
      total number of sites, TOT(Sites). The value for the association
      constant of the SURFACE_SPECIES is then K = Kf / TOT(Sites).


      Note in equation 2 that the mass-action coefficient for C is n, but
      for SitesC it is 1. This equation is not balanced in C. PHREEQC-2
      allows unbalanced equations by defining SURFACE_SPECIES with the
      option -no_check, which disables the element- and charge-balance
      checking of an equation. However, when an unbalanced equation is used
      for mass-action, it is necessary to define the explicit stoichiometry
      of the product with the option -mole_balance. In this case, the
      option should be used as follows:


                   -mole_balance SitesC



      The Langmuir equation is:


           q = Smax * C / (Kl + C).                               (7)



      The equation can written as:


           q = (Smax - q) * C / Kl.                               (8)



      This is the mass action equation for:


           S + C = q;     K,



      since S = (Smax - q), and when K = 1/Kl. (Notice that mole fractions
      are used for the activities of the surface species in PHREEQC-2).


      The following input set for PHREEQC version 2 has two pollutants:
      Polf sorbs according to a Freundlich isotherm and Poll sorbs
      according to a Langmuir isotherm. The parameters for the Freundlich
      isotherm are Kf = 10, n = 0.8, and the parameters for the Langmuir
      isotherm are Smax = 30 and Kl = 2. The input file prints a selected
      output file with 6 columns. Column 1 is the dissolved concentration
      of Polf; 2 the sorbed concentration of Polf; 3 the amount of Polf
      sorbed as calculated from the dissolved concentration and the
      Freundlich isotherm; 4 is the dissolved concentration of Poll; 2 the
      sorbed concentration of Poll; 3 the amount of Poll sorbed as
      calculated from the dissolved concentration and the Langmuir
      isotherm. Columns 2 and 3 are equal and columns 5 and 6 are equal,
      which indicates the Freundlich and Langmuir isotherms are being
      calculated correctly.


      SOLUTION_MASTER_SPECIES
              Polf  Polf    0.0     Polf    1.0
              Poll  Poll    0.0     Poll    1.0
      SOLUTION_SPECIES
              Polf = Polf;  log_k 0.0
              Poll = Poll;  log_k 0.0
      SURFACE_MASTER_SPECIES
              Sites  Sites
              Smax Smax
      SURFACE_SPECIES
              Sites = Sites
                      log_k 0.0
              Smax = Smax
                      log_k 0.0
      # Freundlich: SitesPolf = Kf * Polf^0.8
              Sites + 0.8Polf = SitesPolf
                      -no_check
                      -mole_balance SitesPolf
                      log_k -99.0             # log ((Kf = 10) /
      TOT(Sites))
      # Langmuir: SmaxPoll = (tot_Smax - SmaxPoll) * Poll / Kl
              Smax + Poll = SmaxPoll
                      log_k -0.30103          # log (1 / (Kl = 2))
      END
      SOLUTION 1
                   -units mmol/kgw
              Polf 1e3                  # All concentrations 1 mol/l
              Poll 1e3
      SURFACE 1
              Sites 1e100 1.0 1e100
              Smax 30   1.0 30
                      -equil 1
                      -no_edl true
      REACTION 1 Removes 11 moles of Polf and Poll in 5 steps
              Polf -1.0  Poll -1.0
              11 in 5 steps
      SELECTED_OUTPUT
              -file freundl.sel
              -reset false
      USER_PUNCH
              -heading diss_Polf_  sorb_Polf_ _q_Freund_ diss_Poll_
      sorb_Poll_ _q_Lang___
      10 Kf = 10
      20 n = 0.8
      30 punch mol("Polf"), mol("SitesPolf"), Kf*mol("Polf")^n
      40 Kl = 2
      50 Smax = 30
      60 punch mol("Poll"), mol("SmaxPoll"), Smax*mol("Poll")/(Kl +
      mol("Poll"))
      END