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*To*: Jung yoojin <aroma0922@xxxxxxxxxxx>*Subject*: Re: PHREEQC modeling*From*: "David L Parkhurst" <dlpark@xxxxxxxx>*Date*: Tue, 9 Sep 2003 10:04:09 -0600*Bcc*: "David L Parkhurst" <dlpark@xxxxxxxx>*In-reply-to*: <20030904103749.77707.qmail@web7315.mail.kr.yahoo.com>

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

**References**:**PHREEQC modeling***From:*Jung yoojin

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