Standard Species Model
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Contents
General Description
This is the standard method of computing the properties of any fluid or mixture. The individual properties of each species in the mixture are multiplied by the mass weighted fraction of that species and then summed to give the overall property of the mixture.
See Model Examples - Stream Properties using Standard Method for stream property calculations.
Density Calculations
The Stream Density is calculated as:
- [math] \frac{Total\ mass}{Total\ volume} = \frac{\sum{m_i}}{\sum{\frac{m_i}{p_i}}} [/math]
where:
- m_{i} = mass of individual species
- ρ_{i} = density of individual species
Related Links: Density, Density Correction Calculations, Density and Volume display for mixtures, Stream Properties using Standard Method - Stream Density.
Ionic Species Density
Since the density of ionic solutions does not stay constant with varying solution concentration, SysCAD has allowed the use of a solution density correlation. Please see Density Correction Calculations for a description of the methodology.
To use this special method, the user must input a function in the Density Correction field of the Species Table describing the solvent density as a function of increasing solute concentration.
Each solute should have a function describing the solvent density. SysCAD will then calculate the change in solvent density for each individual solute. The individual solute factors are summed and the Pure Solvent Density multiplies this result.
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.
Stream Molecular Weight
Stream Molecular Weights are calculated using the mass and moles of individual species. Example: Stream Properties using Standard Method - Stream Molecular Weight
[math]Stream Molecular Weight = \frac{\sum{m_i}}{\sum{n_i}}[/math]
where: m_{i} = mass of individual species
- and n_{i} = moles of individual species
Stream Enthalpy values (Hs)
Stream Enthalpy values are calculated using the mass weighted mean method. Example: Stream Properties using Standard Method - Stream Enthalpy (Hs)
Hs @T | = | Stream Enthalpy (Heat Content) |
= | [math]\mathbf{\mathit{ \sum mf_i \times Hs_i }}[/math] | |
where mf_{i} and Hs_{i} are the mass fraction and enthalpy of individual species, respectively |
Stream Specific Heat values (Cp)
Stream Specific Heat values are calculated using the mass weighted mean method. Example: Stream Properties using Standard Method - Stream Specific Heat (Cp)
Cp @T | = Stream Cp |
= [math]\mathbf{\mathit{ \sum mf_i \times Cp_i}} [/math] | |
where mf_{i} and Cp_{i} are the mass fraction and Cp of individual species, respectively |
Stream Entropy values (S)
Stream Entropy values are calculated using the mass weighted mean method. Example: Stream Properties using Standard Method - Stream Entropy (S)
S @T | = | Stream Entropy |
= | [math]\mathbf{\mathit{ \sum mf_i \times S_i }}[/math] | |
where mf_{i} and S_{i} are the mass fraction and entropy of individual species, respectively |
Acidity (pH) Calculations
SysCAD does calculate the negative log of the Hydrogen ion molar concentration in a solution at 25°C. This is often the basis for calculating the pH of a solution. However, since SysCAD does NOT include calculations for buffering, this is an estimate of the pH only.
SysCAD uses the standard equation for autoionisation of water at 25°C:
- [math]\mathbf{\mathit{pKw = 14 = pH + pOH}}[/math]
- where:
- pH = -log[H+]
- pOH = -log[OH-]
The steps executed in the acidity calculations are:
1. Check for the presence of acids or bases. See the tables below for 'standard' acids and bases included in SysCAD. Users may include other acids and bases in the project species database.
2. If both acids and bases are present, i.e. the user has not added a reaction, then calculate [H+] and [OH-].
- If [math]\mathbf{\mathit{[H+] \gt= [OH-]}}[/math], then [math]\mathbf{\mathit{negLogH = -\log([H+] - [OH-])}}[/math], or
- If [math]\mathbf{\mathit{[OH-] \gt= [H+]}}[/math], then [math]\mathbf{\mathit{negLogH = 14 - (-\log([OH-] - [H+])}}[/math]
- SysCAD will also display a message that both acids and bases are present.
3. If only acids exist, then [math]\mathbf{\mathit{negLogH = -\log([H+]}}[/math]
4. If only bases exist, then [math]\mathbf{\mathit{negLogH = 14 - (-\log([OH-])}}[/math]
Hydrogen Cation (H+) Species
In Build 137 or later, if H+(aq) is present as a species in a project then SysCAD calculates the pH directly based on the molar concentration of this species and the liquid volume of the stream at standard temperature and pressure (25°C and 101.325 kPa) as shown below:
pH.H_Cation = -log((moles of H+(aq)) / (Liquid volume at standard conditions))
This is useful if the H+(aq) concentration is being controlled such as by the FEM model or OLI Reactor model.
See Acidity to check how the values are displayed.
Standard Acids and Bases included in SysCAD
SysCAD does have default values of the acid-dissociation constants, Ka, of some acids and the base-dissociation constants, Kb, of some bases. The user may override these default dissociation values by editing the species database, see Dissociation Values in the Species Database
NOTES:
- For Ka ≥ 10, SysCAD assumes total dissociation of the acid.
- For Kb ≥ 1, SysCAD assumes total dissociation of the base.
Examples of some of the acids with Ka values in SysCAD:
Description | Acid | Ka1 | Ka2 | Ka3 |
Hydrochloric Acid | HCl | 1.0e+8 | 0 | 0 |
Sulfuric Acid | H2SO4 | 1000 | 1.02e-2 | 0 |
Phosphoric Acid | H3PO4 | 7.2e-3 | 6.3e-7 | 4.2e-13 |
Hydrofluoric Acid | HF | 6.8e-4 | 0 | 0 |
Carbonic Acid | H2CO3 | 4.5e-7 | 4.7e-11 | 0 |
Examples of some of the bases with Kb values in SysCAD:
Description | Base | Kb |
Sodium Hydroxide (Caustic) | NaOH | 1 |
Calcium hydroxide | Ca[OH]2 | 3.74e-3 |
Ammonia | NH3 | 1.76e-5 |
References
The Ka and Kb values used in SysCAD were obtained from the following references:
- Silberberg M.S, Chemistry - The molecular Nature of Matter and Change. 3rd Edition. McGraw Hill 2003.
- CRC Handbook of Chemistry and Physics. 60th Edition
Saturation Properties
The Standard model calculates the saturation properties of pure substances. The effect of any ionic species, or other liquids, is ignored by the calculations.
When the Vapour Liquid Equilibrium (VLE) sub model is selected, the model calculates the saturated temperature, or boiling point, of the liquid at the pressure in the unit. The Vapour Pressure equation is used - see Vapour Pressure. This calculates the Saturated Pressure for a given Temperature. Therefore, when calculating Temperature, SysCAD uses an iterative routine.