Standard Species Model

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Navigation: Main Page -> Models -> Species Models


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:

mi = mass of individual species
ρi = 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: mi = mass of individual species

and ni = 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 mfi and Hsi 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 mfi and Cpi 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 mfi and Si 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:

  1. For Ka ≥ 10, SysCAD assumes total dissociation of the acid.
  2. 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:

  1. Silberberg M.S, Chemistry - The molecular Nature of Matter and Change. 3rd Edition. McGraw Hill 2003.
  2. 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.

Steam / Water Properties

See Water and Steam Properties.