Simulating Real World Aqueous Problems
or Getting an edge on the competition!
Reliable simulation of complex processes can provide insights for process optimization and reduced operating costs. The solubility of salts is significantly effected by the presence of other salts.
Gypsum (Ca O) production frequently involves recovering sulfur waste products from the off gas of power plants. This gas is scrubbed with a lime (CaO) solution which can form gypsum. This impure solid is re-dissolved and purified to make commercial wallboard.
There are many advantages to this process, notably the ability to recover a pollutant and use it for commercial purposes (reducing the cost of scrubbing) and reducing the need to mine a mineral. In this application we will see that there is a region where we can optimize the solubility of gypsum in the re-dissolving process.
What is a precipitation point calculation? Before we start the calculation, we should discuss what is involved in a precipitation point calculation. To do this we first need to discuss the chemistry model. When we added the inflow species for water and calcium sulfate, we created a model with many species;
We entered two Inflow species. These species are the same as what we entered on the inflow grid. O IN Ca IN
The IN indicates to the program (internally) that these are inflow entered in the grid. We also find additional inflow species in our database that have common elements as our species. These are: Ca. O IN 3IN Ca(O) IN IN Ca( ) IN These species are normally masked from the user but can be displayed if required.
Many aqueous species are retrieved from our database. These species are:
O - o 3 - Ca o o O - Ca CaO O VAP 3VAP VAP Ca. O (s) Ca (s) Ca(O) (s)
There are 16 species on this list. These, in terms of mathematical equations, are unknowns. We need to generate 16 mathematical equations.
Equilibrium Equations We automatically create in the software the mass action relationships.
O= O - 3 o O= o Ca o =Ca - o = - CaO =Ca O - - = - O VAP = O 3VAP = 3 o VAP = o Ca. O=Ca - O Ca (s) =Ca - Ca(O) (s) =Ca O -
These are then converted into the traditional equilibrium relationships.
O O O a O K = O aq aq a K 3 3 3 = o aq K = = CaO O Ca K CaO O Ca CaO = K aq aq Ca Ca Ca Ca Ca K =
Total o aq vap P Y K 3 3 3 3 φ = ) )( ( = O Ca K O Ca s O Ca Total o aq vap P Y K φ = Total O O Ovap P Y a K φ = ) (. O Ca s O Ca a Ca K = ) ( = Ca K Ca s Ca
This gives us 1 equations but we have 16 unknowns. This requires more equations.
Electroneutrality Ca CaO = O - - - This gives us one more equation for a total of 13. Three more equations are needed
Mass Balances ydrogen O IN Ca. O IN Ca(O) IN IN Ca( ) IN = O o O - CaO - O VAP VAP Ca. O (s) Ca(O) (s) Calcium Ca IN Ca. O IN Ca(O) IN Ca( ) IN = Ca o Ca CaO Ca. O (s) Ca (s) Ca(O) (s)
Mass Balances Sulfur Ca IN Ca. O IN 3IN IN Ca( ) IN = 3o Ca o o - - 3VAP VAP Ca. O (s) Ca (s)
This gives a total of 16 equations which match the total number of unknowns. The solution to these equations can now be computed.
Back to the precipitation point The precipitation point calculation is a bit different. In this, we hold the amount of a particular solid, in our case Ca O, at a specified amount. We then Back Solve our equations for an inflow amount that satisfies our specified amount.
Scaling Tendency This is the ratio of ions in solution to the thermodynamic solubility product for a particular solid. ST Ca. O = Ca Ca K Ca. O( s) a O
ST < 1.0 the solid is under-saturated there are insufficient ions in solution to form the solid. ST > 1.0, the solid is super-saturated there more than enough ions to form the solid. In the precipitation point calculation The scaling tendency for the indicated solid (Ca O) is forced to be exactly equal to 1.0. To do this, we must adjust some variable.
The easiest variable to adjust is an inflow variable that contains some or all of our solid. There are two mass balance equations of interest here:
Ca IN Ca. O IN Ca(O) IN Ca( ) IN = Ca o Ca CaO Ca. O (s) Ca (s) Ca(O) (s) Ca IN Ca. O IN 3IN IN Ca( ) IN = 3o Ca o o - - 3VAP VAP Ca. O (s) Ca (s)
In the program, we selected the inflow species Ca which has been bold-faced above. The other inflow values remain constant. The program varies the inflow amount to match the scaling tendency of 1.0. As this occurs, the relative amounts of the other species are also calculated. In a precipitation point calculation it is important to make sure you select the proper precipitating solid (it must be able to form under the conditions you specify) and the proper adjusting species.
NaCl added
The solubility of calcium sulfate (with Ca O as the precipitating solid) increases. Compare the solubility maximum of approximately 0.66 weight percent Ca (at approximately 11 percent NaCl) to the value at 5 o C in the solubility v. Temperature plot in Figure 6 (approximately 0.1 weight percent). Adding sodium chloride increases the solubility about approximately three times. The question remains, why does adding sodium chloride increase the solubility?
The aqueous sulfate species are displayed. The faint blue line is the concentration of Na -1 ion. It seems to follow the solubility curve for Ca. We can see that a great deal of sulfate ion is complexed as Na -1. What does this imply?
We have two equilibrium equations that are affected: Ca O Ca - O Na -1 Na - As Na -1 forms, sulfate ions are effectively removed from solution. The second equilibrium is shifted to the left. Since equilibrium must be maintained, the Ca O solid must increase its dissolution to replace the sulfate ion. This has the effect of increasing the solubility of the Ca O solid.
Conclusions The solubility of one salt in a complex aqueous mixture can be significantly affected by the presence of other salts. Accurate modeling of these types of systems requires a robust activity coefficient model that includes the interactions of all species. When done properly, reliable simulation of complex processes provide a powerful tool for process optimization and reducing operating costs.