# Solution Table

Navigation: User Guide -> Data Libraries -> Solution Table

## Solution Table

SysCAD allows the user defined solution data.

• Solvent eg. H2O(l)
• Solute eg. NaCl(aq) The solute is normally an aqueous specie (NOTE: You cannot define a solute twice in the same project with two different solvents)
• OtherPhase eg. NaCl(s)
• DensCorrFn,Limit Density correction versus solution mass fraction eg. Poly(a, b, c, d, e), Limit(Mf_max, MaxDensity, Warning)
• SolubilityFn Solubility versus temperature in Kelvin eg. Poly(a, b, c, d, e)
• HDilutionFn Heat of dilution versus solution mass fraction eg. Poly(a, b, c, d, e)
• Reference Optional

## Density Correction Function

The user may input a function describing the solvent density as a function of increasing solute concentration. The user may enter the function in the Solutions table in the field DensCorrFn.

Note The Default SysCAD species database (..:\SysCAD91\BaseFiles\Default.mdb) has density correction functions for a number of aqueous species. These may be copied into the user's project specie database. (they are not automatically copied into the user's database if the aqueous species is imported from the default database, but have to be copied in separately).

The function describing the solvent density has the following form:

Poly(a, b, c, d, e, f), Limit(Mf_max, MaxDensity, Warning)

Example for FeSO4(aq): Poly(0.998,0.951,0.62), Limit(0.2, 2200, On)

For the polynomial (shown below), only the required number of parameters need to be entered. The values in Limit define the boundary of the data and are described below.

$DensCorrFn(MF)_i = a + b.MF + c.MF^2 + d.MF^3 + e.MF^4 + f.MF^5 \,$

This is a function of mass fraction (MFi), where

$MF_i = \frac{Solute_i}{Solvent + Solute_i} \,$

SysCAD will then calculate the change in solvent density for each individual solute. Note: This equation is independent of temperature and pressure.

The density correction factor for each solute is calculated as follows:

$DensityCorrection_i = DensCorrFn(MF)_i - DensCorrFn(0)_i \,$

Note: The result of this is that the first term a in the Poly(a, b, c, d...) function has no effect.

Finally, the individual solute factors are summed and multiplied by the Pure Solvent Density to determine the adjusted density of the solutes in solution:

$Density_{solution} = Density_{PureSolvent} * \big( 1 + \sum{DensityCorrection_i} \big) \,$

The pure solvent density is at stream temperature and pressure. Normally the solvent is water, so the density for water that is used will be at stream temperature and pressure. The density correction function itself is independent of temperature and pressure.

SysCAD uses the Limit(Mf_max, MaxDensity, Warning) to calculate the density of the solution above the limiting value. Data is typically only available to a certain fraction, so this allows you to specify the behaviour outside of the normal range. The variables required are as follows:

Mf_max is the maximum mass fraction of the solute for which the equation is true.

MaxDensity is the density of the pure solute in kg/m^3

Warning is either On or Off. If it is On (recommended), SysCAD will warn the user if the mass fraction of the solute is above the specified Mf_max.

If the mass fraction of the solute in the solvent is above the Mf_max, then SysCAD calculates the density of the solution by linearly interpolating between the density at Mf_max and the density of the pure solute.

If Limit(..) is not specified with DensCorrFn(..) then at project load time SysCAD will give a warning and will assume Mf_max = 0.8, MaxDensity = 1000 and Warning = On.

The density of the pure solvent may also be a function of temperature. In which case the density of the solvent at the relevant temperature is first calculated and then this value is multiplied by the solute correction factor.

If the user does not have a function relating the change in solvent density with solute concentration, then SysCAD will use the density in the species database in a pure mass weighted mean calculation.

Note: This will not usually produce the correct liquid density or volumetric flow rates.

See Example for Stream Density Calculations for Density Calculation Examples.

## Solubility Function

The user may input a function describing the solubility of the solute as a function of temperature in Kelvin. The user may enter the function in the Solutions table in the field SolubilityFn.

Note The Default SysCAD species database (..:\SysCAD91\BaseFiles\Default.mdb) has a solubility function for a sodium chloride. This may be copied into the user's project specie database (it is not automatically copied into the user's database if the aqueous specie is imported from the default database, but have to be copied in separately).

The function describing the solubility has the following form:

Poly(a, b, c, d, e, f)

Example for NaCl(aq): Poly(0,0.003707,-1.348e-5,1.717e-8)

For the polynomial (shown below), only the required number of parameters need to be entered.

$SolubilityFn(T)_i = a + b.T + c.T^2 + d.T^3 + e.T^4 + f.T^5 \,$

This is a function of temperature in degrees Kelvin.

The answer obtained is the maximum mass fraction (MFi) of the aqueous species, relative to the solvent, where

$MF_i = \frac{Solute_i}{Solvent} \,$

SysCAD will then calculate the maximum mass fraction of the aqueous species for each individual solute based on the stream temperature. Note: This equation is independent of pressure. Therefore, while the user may use this functionality to model the solubility of gas species in a solvent, this will not allow the user to include the pressure contribution.

If the user chooses to switch on the solubility function in the model (see Qualities), then SysCAD will make use of this calculated maximum mass fraction as follows.

If required, SysCAD will adjust the mass fractions of the solute in the aqueous and the other specified phase, either solid or gas, in order to ensure that the maximum mass fraction of the aqueous species is not exceeded.

For example, if the maximum solubility is a mass fraction of 0.35 (ie. 35 g per 100g of solvent):

1. If the specified mass fraction of the aqueous species is greater than 35% (relative to the solvent), SysCAD will adjust the mass fraction of the aqueous species down to 35% and transfer the excess to the other phase of the same species.
2. If the specified mass fraction of the species in the other phase is greater than 35% (relative to the solvent), SysCAD will adjust the mass fraction of the aqueous phase of the same species up to 35% and the excess will remain in the other phase.
3. If the specified mass fraction of the species in the other phasse is less than 35% (relative to the solvent) then all of this will be transferred to the aqueous phase.

The changes described above will happen automatically in a feeder in which solubility has been switched on without adjusting the temperature of the stream. Once switched on, the solubility function will perpetuate through the flowsheet until it is switched off. If two streams meet, one with solubility switched on and one with solubility switched off, then the outlet stream will have solubility switched on.

NOTE: The associated enthalpy change with the change in the composition between the aqueous and other phases may result in a change in temperature of the stream.

For an example of the use of the solubility function, see the example project Solubility.spf, which is part of the standard installation (..:\SysCAD91\Examples\SS General\Solubility.spf).

## HdilutionFn

Not enabled. Heat of Dilution functionality is enabled in SysCAD 9.2 and later. Refer to Species Table in 9.2.