# Species Table 9.3 - Density

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## Table of Data

If the user has a table with density correction factors versus mass fraction in solution, then they may select the option:

Density Correction as a function of MF : Spline under Tension

And enter the data in 2 columns. SysCAD will interpolate the data using the TSpline method. The easiest way to enter the data is to copy the data from a spreadsheet.

Note: A fitted equation will be processed more quickly within SysCAD and hence is preferred to entering a table of data.

## Laliberte´ Function

NOTE: This method is only valid for aqueous species.

If the user has appropriate constants for the Laliberte´ equation, then they can select the option:

Density Value as a function of MF & T: Laliberte values

and enter the function in the following format: Laliberte_Rho(c0, c1, c2, c3, c4)

The solution density is calculated using the water density, pw and the solutes apparent density using following equation:

$\mathbf{\mathit{p_m=\frac{1}{\frac{m_w}{p_w}+\sum{\frac{m_i}{p_{app,i}}}}}}$

The Apparent density of each solute in aqueous solution is calculated from:

$\mathbf{\mathit{p_{app,i}=\frac{(c_0(1-m_w)+c_1)*e^{(0.000001(T+c_4)^2)}}{(1-m_w)+c_2+c_3*T}}}$

Where:

 mw = mass fraction of water mi = mass fraction of solute species i pw = density of water (at stream temperature and pressure), kg/m3 papp,i = solute i apparent density, kg/m3 pm = solution density, kg/m3 T = Temperature in °C c0 to c4 = dimensionless empirical constants for each solute species.

Notes:

1. If the user wishes to use the Laliberte´ method, then it is recommended that this method is used for ALL aqueous species in a project, as a mixture of Laliberte´ and other aqueous density methods may result in inaccurate solution density values.
2. It is important to note that the constants for many of the aqueous species are valid for temperatures between 0 and approximately 100°C.
3. If the unit temperature is outside of the species temperature range, then SysCAD will use the values at the temperature limit.
4. If the species Mass Fraction in a unit exceeds the maximum mass fraction, then SysCAD will continue to use the Laliberte equation, but will log a warning that the values are questionable.
5. Water density is calculated in SysCAD as described here: Water and Steam Properties.

Reference

Laliberte´ M. and Cooper W.E. Model for Calculating the Density of Aqueous Electrolyte Solutions J. Chem. Eng. Data 2004, 49.

# Gas Density

For gases the user may use one of the following three input formats (the formulation for Ideal Gas is also shown here):

• Constant Value; or
• Ideal Gas Density - The density value will be calculated based on the Ideal gas law. Equations used are:
(1) $\mathbf {\mathrm{Density_{T,P} = \frac{m}{V}}}$ and (2) $\mathbf {\mathrm{PV = nRT}}$ and (3) $\mathbf {\mathrm{m = nM}}$
Rearranging the above equations will give:
$\mathbf {\mathrm{Density_{T,P} = \frac{PM}{RT}}}$
Where:
m = mass of compound
V = Volume of compound
P = Partial Pressure of species
R = Universal Gas Constant = 8.314 472 J/mol.K (Reference: National Institute of Standards and Technology)
T = Temperature in Kelvin
n = number of moles of compound
M = molecular weight of compound
• Linear Gas Density - the density value provided (in brackets) is expected to be at 0°C and Std. Pressure. Density @ T, P will be corrected based on:
$\mathbf {\mathrm{Density_{T,P} = Density_{0,StdP}*\frac{P}{StdP}*\frac{273(K)}{T(K)}}}$; or