Stream Properties using Standard Method

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Introduction

Given the following stream make up at 25°C and atmospheric pressure, stream properties are calculated in SysCAD using the Standard specie model, primarily a mass weighted mean method. These calculations are illustrated using the example below:

Table 1 Stream Make Up

Stream Make Up	Mass Flow	Mass Frac	Mole Flow
	kg/h	wt Frac	kmol/h
CaCO3(s)	200.00	0.20	1.998
SiO2(s)	300.00	0.30	4.993
H2O(l)	400.00	0.40	22.203
H2SO4(aq)	80.00	0.08	0.816
CO2(g)	10.00	0.01	0.227
N2(g)	10.00	0.01	0.357
Total	1000.00	1.00	30.594

Table 2 Component Data entered into the SysCAD Specie Database.

Component	Density (kg/m3	Hf at 25 (J/mol)	Cp Equation (kJ/kmol.K)	Temp Range (K)
CaCO3(s)	2650	-1208352	HTE_Cp(-9122, 23.8351, 3.2146, 5.1569)	298 - 1200
SiO2(s)	2650	-911550	HTE_Cp(-8654, 19.1651, -0.5456, 8.8977)	298 - 2000
H2SO4(aq)	1841	-886513	HTE_Cp(-7762, 19.1799, 23.2471, -0.0679)	298 - 500
CO2(g)	1.8	-393505.213	Poly_Cp(19.7961, 0.07344, -5.600221e-05, 1.71541e-08)	298.15 - 1000
N2(g)	1.15	0	Poly_Cp(31.1513, -0.0135659, 2.67968e-05, -1.16817e-08)	298 - 1000

Note:
Properties for H2O are NOT entered by the user - these values are calculated within SysCAD. See Water and Steam Properties.

From Heat Capacity (Cp), we will find the C_p equation formats for the HTE_C_p and Poly_C_p as follows:

HTE_Cp(a,b,c,d) :

[math]\displaystyle{ \mathbf{\mathit{C_p = 4.186*\left (b+2*c.10^{-3}*T-\frac{d.10^5}{T^2} \right )}} }[/math]

Poly_Cp(a,b,c,d):

[math]\displaystyle{ \mathbf{\mathit{C_p = a+b*T+c*T^2+d*T^3}} }[/math]

The C_p values for each individual component are calculated at the specified temperature, in K, using the above equations, and Enthalpies ('Hs') are calculated by integrating the above equations from Reference temperature 273.15K to the specified temperature. The results of these calculations are presented in Table 3. (Note that since the reference temperature of 273.15K is less than Ts (Start Temperature) of 298.15K, to calculate Hs the Cp at 298.15K will be multiplied by (298.15-273.15).See Heat Capacity (Cp) for more information.)

Table 3 Component Properties Summary at 25°C and 1 Atmospheric Pressure

Component Properties	MW kg/kgmol	Density kg/m3	Hf at 25°C kJ/kg	Hs kJ/kg	Cp kJ/kg.C
CaCO3(s)	100.09	2650.00	-12072.99	20.85	0.83
SiO2(s)	60.08	2650.00	-15171.18	15.36	0.62
H2O(l)	18.02	997.04	-15865.97	104.87	4.18
H2SO4(aq)	98.08	1841.00	-9038.72	35.33	1.41
CO2(g)	44.01	1.80	-8941.31	21.11	0.84
N2(g)	28.01	1.15	0.00	26.04	1.04

Notes:

1. The user specifies properties of individual compounds in the SysCAD specie database.
2. Hs and Cp values are derived from the Cp equations.
3. The individual component properties at different Temperature and Pressures can be obtained via the menu command View -- Species Data.

Table 4 Stream Properties Summary

			0°C	25°C, 1 atm			50°C, 1 atm
Stream Properties	MW	Density	Hs	Hf	Hs	Cp	Hf	Hs	Cp
	kg/kgmol	kg/m3	kJ/kg	kJ/kg	kJ/kg	kJ/kg.C	kJ/kg	kJ/kg	kJ/kg.C
Total	32.69	67.00	0	-14124.85	54.02	2.16	-14070.42	108.46	2.20
Solid Phase	71.52	2650.00	0	-	17.56	0.70	-	36.15	0.78
Liquid Phase	20.85	1079.53	0	-	93.28	3.72	-	186.34	3.73
Vapour Phase	34.24	1.40	0	-	23.58	0.94	-	47.31	0.96
Slurry (Sol + Liq)	32.66	1547.40	0	-	54.65	2.18	-	109.71	2.22

The methods used to calculate these values are shown in the following headings:

Stream Molecular Weight

[math]\displaystyle{ Stream Molecular Weight = \frac{\sum{m_i}}{\sum{n_i}} }[/math]

where: m_i = mass of individual component

and n_i = mole of individual component

So for the above example:

[math]\displaystyle{ Stream Molecular Weight = \frac{1000kg}{30.594kgmoles} = 32.69kg/kgmol }[/math]

Note:
SysCAD uses the atomic weight of the elements and the compound definition in the Specie Database to calculate the Molecular weight of each compound.

Stream Density

The Stream Density is calculated as:

[math]\displaystyle{ \frac{Total\ mass}{Total\ volume} = \frac{\sum{m_i}}{\sum{\frac{m_i}{p_i}}} }[/math]

where: m_i = mass of individual component

ρ_i = density of individual component

[math]\displaystyle{ \mathbf{\mathit{Stream Density = 1000 / (200/2650 + 300/2650 + 400/997.04 + 80/1841 + 10/1.80 + 10/1.15) = 67.00 kg/m^3}} }[/math]

Like wise,

• [math]\displaystyle{ \mathbf{\mathit{Solid Density = Total Solid Mass / Total Solid Volume = 500 / (200/2650 + 300/2650) = 2650 kg/m^2}} }[/math]

• [math]\displaystyle{ \mathbf{\mathit{Liquid Density = Total Liquid Mass / Total Liquid Volume = 1079.53 kg/m^2}} }[/math]

• [math]\displaystyle{ \mathbf{\mathit{Vapour Density = Total Vapour Mass / Total Vapour Volume = 1.40 kg/m^2}} }[/math]

• [math]\displaystyle{ \mathbf{\mathit{Slurry Density = Total (Solid + Liquid) Mass / Total (Solid + Liquid) Volume = 1547.40 kg/m^2}} }[/math]

See also: Density and Volume display for mixtures

For solution density calculations requiring correction functions, please see Density Correction for Solutions & Data Fitting.

Stream Enthalpy values (Hs)

Stream Enthalpy values are calculated using the mass weighted mean method. Using values in Table 3 Component Properties Summary, we have:

Hs @T	=	Stream Enthalpy (Heat Content)
	=	[math]\displaystyle{ \mathbf{\mathit{ \sum mf_i * Hs_i }} }[/math]
	where mfi and Hsi are mass fraction and enthalpy of individual components respectively
	=	[math]\displaystyle{ \mathbf{\mathit{ 0.2*20.85 + 0.3*15.36 + 0.4*104.87 + 0.08*35.33 + 0.01*21.11 + 0.01*26.04}} }[/math]
	=	[math]\displaystyle{ \mathbf{\mathit{ 54.02 kJ/kg}} }[/math]

SmsHs @T	= Solids Enthalpy
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ solids} * Hs_i = 0.2/0.5*20.85 + 0.3/0.5*15.36 = 17.56 kJ/kg }} }[/math]
	where mfi solids is the mass fraction of solids in the solid phase

LmsHs @T	= Liquid Enthalpy
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ liquids} * Hs_i = 0.4/0.48*104.87 + 0.08/0.48*35.33 = 93.28 kJ/kg }} }[/math]
	where mfi liquids is the mass fraction of liquids in the liquid phase

VmsHs @T	= Vapour Enthalpy
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ vapour} * Hs_i = 0.01/0.02*21.11 + 0.01/0.02*26.04 = 23.58 kJ/kg }} }[/math]
	where mfi vapour is the mass fraction of vapour in the vapour phase

SLmsHs @T	= Slurry Enthalpy
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ slurry} * Hs_i }} }[/math]
	where mfi slurry is the mass fraction of liquid/solid in the slurry (liquid+solid) phase
	= [math]\displaystyle{ \mathbf{\mathit{0.2/0.98*20.85 + 0.3/0.98*15.36 + 0.4/0.98*104.87 + 0.08/0.98*35.33}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{54.65 kJ/kg}} }[/math]

Stream Specific Heat values (Cp)

Stream Specific Heat values are calculated using the mass weighted mean method. Using values in Table 3 Component Properties Summary, we have:

Cp @T	= Stream Cp
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_i * Cp_i}} }[/math]
	where mfi and Cpi are mass fraction and Cp of individual components respectively
	= [math]\displaystyle{ \mathbf{\mathit{0.2*0.83 + 0.3*0.62 + 0.4*4.18 + 0.08*1.41 + 0.01*0.84 + 0.01*1.04 }} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{2.16 kJ/kg.C}} }[/math]

SmsCp @T	= Solids Cp
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ solids} * Cp_i = 0.2/0.5*0.83 + 0.3/0.5*0.62 = 0.70 kJ/kg.C }} }[/math]
	where mfi solids is the mass fraction of solids in the solid phase

LmsCp @T	= Liquid Cp
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ liquids} * Cp_i = 0.4/0.48*4.18 + 0.08/0.48*1.41 = 3.72 kJ/kg.C }} }[/math]
	where mfi liquids is the mass fraction of liquids in the liquid phase

VmsCp @T	= Vapour Cp
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ vapour} * Cp_i = 0.01/0.02*0.84 + 0.01/0.02*1.04 = 0.94 kJ/kg.C}} }[/math]
	where mfi vapour is the mass fraction of vapour in the vapour phase

SLmsCp @T	= Slurry Cp
	= [math]\displaystyle{ \mathbf{\mathit{ \sum mf_{i \ slurry} * Cp_i }} }[/math]
	where mfi slurry is the mass fraction of liquid/solid in the slurry (liquid+solid) phase
	= [math]\displaystyle{ \mathbf{\mathit{0.2/0.98*0.83 + 0.3/0.98*0.62 + 0.4/0.98*4.18 + 0.08/0.98*1.41}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{2.18 kJ/kg.C}} }[/math]

Stream Heat of Formation values (Hf)

Consider the stream is at 50°C; the stream enthalpy calculations are as follows:

Stream Heat of Formation values are calculated using the mass weighted mean method. Generally, the Heat of Formation data available are at 25°C. Thus, using these values, stream Hf at 25°C is calculated.

From Table 3 Component Properties Summary, we have:

Stream Hf25°C	= [math]\displaystyle{ \sum mf_i * H_{f \ i}^{25} }[/math] where mfi is mass fraction of individual components and Hfi25 is the heat of formation of individual components at 25°C
	[math]\displaystyle{ \mathbf{\mathit{= 0.2*-12072.99 + 0.3*-15171.18 + 0.4*-15865.97 + 0.08*-9038.72 + 0.01*-8941.31 + 0.01*0}} }[/math]
	[math]\displaystyle{ \mathbf{\mathit{= -14124.85 kJ/kg}} }[/math]

Stream Hf 0°C	= [math]\displaystyle{ \mathbf{\mathit{ H_f^{25} - \sum \int\limits_{0}^{25}Cp_i.dT}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{H_f 25^{\circ}C - (Hs 25^{\circ}C- Hs 0^{\circ}C)}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{-14124.85 - (54.02 - 0)}} }[/math] (See Table 4 Stream Properties Summary)
	= [math]\displaystyle{ \mathbf{\mathit{-14178.88 kJ/kg}} }[/math]

Stream Hf 50°C	= [math]\displaystyle{ \mathbf{\mathit{ H_f^0 + \sum \int\limits_{0}^{50}Cp_i.dT}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{H_f 0^{\circ}C + (Hs 50^{\circ}C - Hs 0^{\circ}C)}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{-14178.88 + (108.46 - 0)}} }[/math] (See Table 4 Stream Properties Summary)
	= [math]\displaystyle{ \mathbf{\mathit{-14070.42 kJ/kg}} }[/math]

Enthalpy Change (Hs) and (Hz)

Hs is the enthalpy change (excluding phase change) from 0°C to current temperature.

Stream Hs 50°C	= [math]\displaystyle{ \mathbf{\mathit{ \sum \int\limits_{0}^{50}Cp_i.dT }} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{(Hs 50^{\circ}C - Hs 0^{\circ}C)}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{108.46 kJ/kg}} }[/math] (See Table 4 Stream Properties Summary)

Hz is the enthalpy change (including phase change) from 0°C to current temperature.

Stream Hz 50°C	= Net Enthalpy @ temperature
	= [math]\displaystyle{ \mathbf{\mathit{ H_{phase \ change} + \sum \int\limits_{0}^{50}Cp_i.dT}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{(H final phase - H original phase) 0^{\circ}C + (Hs 50^{\circ}C - Hs 0^{\circ}C)}} }[/math]
	= [math]\displaystyle{ \mathbf{\mathit{0 + (108.46 - 0)}} }[/math] (See Table 4 Stream Properties Summary)
	= [math]\displaystyle{ \mathbf{\mathit{108.46 kJ/kg}} }[/math] (Note this example contains no phase change)

Note: For compounds without phase change, you will find that Hs@T = Hz@T. However, for streams involving Steam/Water, where it has [math]\displaystyle{ \mathbf{\mathit{H_lg = 2501\ at\ 0^{\circ}C}} }[/math] & Sat. Pressure, these two terms will not be equal. See Examples on calculating Energy change around a unit for more details.

Calculating Energy change around a unit

Calculating Energy change around a unit without phase change

The above is a "summary" of information you can obtain from SysCAD.

Now to check the numbers using the steam tables[#_ftn1 [1]]:

At [math]\displaystyle{ \mathbf{\mathit{100 ^{\circ}C\ at\ sat. P, H_g = 2675.572 kJ/kg}} }[/math]

At [math]\displaystyle{ \mathbf{\mathit{120 ^{\circ}C\ at\ sat. P, H_g = 2705.9342 kJ/kg}} }[/math]

Thus energy required to heat up the steam for 20°C is:

[math]\displaystyle{ \mathbf{\mathit{1 kg/s * (2705.9342 - 2675.572) kJ/kg = 30.3622 kJ/s}} }[/math] (answer = to that obtained from SysCAD.)

As demonstrated by the above example, you can use Hs (sensible heat), Hz (enthalpy) or Hf (heat of formation) values to work out the energy required to raise the stream by 20°C. It is whatever you are comfortable with.