Example for Stream Density Calculations

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Density Correction for Solutions & Data Fitting

Given the following data for (NH₄)₂SO₄ @ 20°C (Source: CRC Handbook of Chemistry and Physics, 60th Edition), data fitting gives the following:

MF	Density (g/cm3)
0.005	1.003
0.01	1.0059
0.02	1.0119
0.03	1.0178
0.04	1.0238
0.05	1.0297
0.06	1.0356
0.07	1.0416
0.08	1.0475
0.09	1.0534
0.1	1.0593
0.12	1.071
0.14	1.0827
0.16	1.0943
0.18	1.1059
0.2	1.1174
0.22	1.1289
0.24	1.1403
0.26	1.1516
0.28	1.1629
0.3	1.1742
0.32	1.1854
0.34	1.1966
0.36	1.2077
0.38	1.2188
0.4	1.2298

Thus, density correction equation used in SysCAD is Poly(1, 0.5973, -0.0305, -0.1316, 0.1661). See Density Correction Function.

Density Correction for Solution with two solutes

Consider the following example at a temperature of 40°C.

Species	Mass Wt%
H2O(l)	91.5
NaCl(aq)	2.4
H2SO4(aq)	6.1

From Density Correction Function we have the following equations:

1. 
2. 
3. 
4. 

Basis: 1 kg of Fluid.

Density of Water:

The Density of Water varies with temperature, please see Steam / Water Properties. At 40°C Water Density = 992.216 kg/m³.

Density of H₂SO₄(aq)

Where x is the mass fraction of H₂SO₄(aq) in solution.

(Ref: Lide D.R. Handbook of Chemistry and Physics 74^th Edition CRC Press)

Density of NaCl(aq)

Where x is the mass fraction of NaCl(aq) in solution.

(Ref: Lide D.R. Handbook of Chemistry and Physics 74^th Edition CRC Press)

Note: The valid range of this equation is between 0 and 30% NaCl(aq) solutions.

Therefore, using equations 2&3:

è

è

From Equation 4

If the user did not have the formulae for the ionic solution densities and used the densities of the pure substances, then the liquid density would be calculated as follows:

Using Equation described in Example 1,

This gives an error of ~1%.

Density and Volume display for mixtures:

Consider the following example at 40 °C & atmospheric pressure; determine the volumetric flow of the stream.

Basis: 1000 kg/h

Component	Mass Fraction	Density (kg/m3)	Density Correction	Individual Volume Display (m3/h)
NaCl(aq)	0.0900	*	As per example 3	*
H2SO4(aq)	0.0900	*	As per example 3	*
H20	0.6300	992.216	As per example 3	0.6349
CuO(s)	0.0550	6450	-	0.0085
Cu(s)	0.0450	8920	-	0.0050
MgCO3(aq)	0.0450	1000	-	0.045
CuSO4(aq)	0.0450	1000	-	0.045

To determine the stream volumetric flow of the stream, we need to first compute the corrected solution density the mixture of Water-NaCl-H₂SO₄. See Example 3 above for equations.

Component	Mass flow (kg/h)	MFi (Equation 2)	Correction Factor (Equation 3)
NaCl(aq)	90	0.125	0.0800
H2SO4(aq)	90	0.125	0.0832
H20	630

So using Equation 4 (see Example 3)