View source for Stream Properties using Standard Method

[[Category:Properties]] [[Category:Examples]]
{{Navigation|[[Models]]|[[Models#Species Models|Species Models]]|[[Standard Species Model]]|altname=Stream Properties Calculations}}
{{Stream Properties Header tabs| currentpage=2}}
'''Related Links:''' [[Material Flow Section]], [[Model Examples]]
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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 species model, primarily a mass weighted mean method. These calculations are illustrated using the example below:

'''<u>Table 1 Stream Make Up</u>'''

{| border="1" cellpadding="5" cellspacing="0" 
|- 
! Stream Make Up !! Mass Flow !! Mass Frac !! Mole Flow
|-
!   &nbsp;  !! kg/h      !! wt Frac   !! kmol/h
|- 
| CaCO<sub>3</sub>(s) || 200.00 || 0.20 || 1.998
|- 
| SiO<sub>2</sub>(s) || 300.00 || 0.30 || 4.993
|- 
| H<sub>2</sub>O(l) || 400.00 || 0.40 || 22.203
|- 
| H<sub>2</sub>SO<sub>4</sub>(aq) || 80.00 || 0.08 || 0.816
|- 
| CO<sub>2</sub>(g) || 10.00 || 0.01 || 0.227
|- 
| N<sub>2</sub>(g) || 10.00 || 0.01 || 0.357
|- 
! Total !! 1000.00 !! 1.00 !! 30.594
|}


'''<u>Table 2 Species Data entered into the SysCAD Species Database</u>'''.

{| border="1" cellpadding="5" cellspacing="0" 
|- 
! Species || Density (kg/m<sup>3</sup>|| Hf at 25°C (J/mol) || S at 25°C (J/mol.K) || Cp Equation (kJ/kmol.K) || Temp Range (K)
|- 
| CaCO<sub>3</sub>(s) ||2650 || -1208352 || 92.9 || HTE_Cp(-9122, 23.8351, 3.2146, 5.1569) || 298 - 1200
|- 
| SiO<sub>2</sub>(s) || 2650 || -911550 || 41.84 || HTE_Cp(-8654, 19.1651, -0.5456, 8.8977) || 298 - 2000
|- 
| H<sub>2</sub>SO<sub>4</sub>(aq) || 1841 || -886513 || 20.1 || HTE_Cp(-7762, 19.1799, 23.2471, -0.0679) || 298 - 500
|- 
| CO<sub>2</sub>(g) || 1.8 || -393505.213 || 213.74 || Poly_Cp(19.7961, 0.07344, -5.600221e-05, 1.71541e-08) || 298.15 - 1000
|- 
| N<sub>2</sub>(g) || 1.15 || 0 || 191.61 || Poly_Cp(31.1513, -0.0135659, 2.67968e-05, -1.16817e-08) || 298 - 1000
|}

'''Note:'''
<br> Properties for H2O are NOT entered by the user - these values are calculated within SysCAD. (See [[Water and Steam Properties]].)

From [[Species Table - Specific Heat (Cp)|Heat Capacity (Cp)]], we will find the C<sub>p</sub> equation formats for the HTE_C<sub>p</sub> and Poly_C<sub>p</sub> as follows:

HTE_Cp(a,b,c,d) :

:<math>C_p = 4.186\left (b+2c.10^{-3}T-\frac{d.10^5}{T^2} \right )</math>


Poly_Cp(a,b,c,d):

:<math>C_p = a+bT+cT^2+dT^3</math>


The C<sub>p</sub> values for each individual species 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 [[Species Table - Specific Heat (Cp)|Heat Capacity (Cp)]] for more information.)


'''<u>Table 3 Species Properties Summary at 25°C and 1 Atmospheric Pressure</u>'''

{| border="1" cellpadding="5" cellspacing="0" 
|-
! Species <br> Properties !! MW <br> kg/kgmol !! Density <br> kg/m<sup>3</sup> !! H@T <br> kJ/kg !! Hs <br> kJ/kg !! S@T <br> kJ/kg.C !! Cp <br> kJ/kg.C
|- 
| CaCO<sub>3</sub>(s) || 100.09 || 2650.00 || -12073.03 || 20.85 || 0.93 || 0.83
|- 
| SiO<sub>2</sub>(s) || 60.08 || 2650.00 || -15171.18 || 15.36 || 0.70 || 0.62
|- 
| H<sub>2</sub>O(l) || 18.02 || 997.05 || -15865.97 || 104.87 || 3.89 || 4.18
|- 
| H<sub>2</sub>SO<sub>4</sub>(aq) || 98.08 || 1841.00 || -9038.81 || 35.33 || 0.20 || 1.41
|- 
| CO<sub>2</sub>(g) || 44.01 || 1.80 || -8941.37 || 21.11 || 4.86 || 0.84
|- 
| N<sub>2</sub>(g) || 28.01 || 1.15 || 0 || 26.04 || 6.84 || 1.04
|}

'''Notes:'''
# The user specifies properties of individual species (compounds) in the SysCAD [[Species Database]].
# Hs and Cp values are derived from the Cp equations.
# The individual species properties at different Temperature and Pressures can be obtained via the menu command '''Species''' -- '''View Properties'''. (Refer to [[Species Properties ($SDB)]] for more information.)

'''<u>Table 4 Stream Properties Summary</u>'''

{| border="1" cellpadding="5" cellspacing="0" 
|- 
!&nbsp; ||&nbsp; ||&nbsp;
! colspan="3" | 0°C, 1 atm 
! colspan="4" | 25°C, 1 atm
! colspan="4" | 50°C, 1 atm
|- 
! Stream Properties || MW || Density || Hf || S || Hs || Hf || S || Hs || Cp || Hf || S || Hs || Cp
|- 
!&nbsp; || kg/kgmol || kg/m<sup>3</sup> || kJ/kg || kJ/kg.C ||  kJ/kg || kJ/kg || kJ/kg.C || kJ/kg || kJ/kg.C || kJ/kg || kJ/kg.C || kJ/kg || kJ/kg.C
|- 
! Total || 32.69 || 67.00 || -14178.89 || 1.90 || 0 || -14124.87 || 2.09 || 54.02 || 2.16 || -14070.43 || 2.21 || 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 || 1547.41 || - || - || 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>Stream Molecular Weight = \cfrac{\sum{m_i}}{\sum{n_i}}</math>

where:
:m<sub>i</sub> = mass of individual species
:n<sub>i</sub> = mole of individual species

So for the above example:

<math>Stream Molecular Weight = \cfrac{1000kg}{30.594kgmoles} = 32.69kg/kgmol</math>

'''Note:'''
<br> SysCAD uses the atomic weight of the elements and the species definition in the [[Species Database]] to calculate the Molecular weight of each species.

== Stream Density ==

The Stream Density is calculated as:

<math> \cfrac{Total\ mass}{Total\ volume} = \cfrac{\sum{m_i}}{\sum{\frac{m_i}{\rho_i}}} </math>

where:
:m<sub>i</sub> = mass of individual species
:ρ<sub>i</sub> = density of individual species (for vapours this is the partial pressure)

<math>\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> 

Likewise,

* <math>\mathbf{\mathit{Solid Density = Total Solid Mass / Total Solid Volume = 500 / (200/2650 + 300/2650) = 2650 kg/m^2}}</math>

* <math>\mathbf{\mathit{Liquid Density = Total Liquid Mass / Total Liquid Volume = 1079.53 kg/m^2}}</math>

* <math>\mathbf{\mathit{Vapour Density = Total Vapour Mass / Total Vapour Volume = 1.40 kg/m^2}}</math>

* <math>\mathbf{\mathit{Slurry Density = Total (Solid + Liquid) Mass / Total (Solid + Liquid) Volume = 1547.41 kg/m^2}}</math>

See also: [[Density_Correction_Calculations#Density_and_Volume_display_for_mixtures:|Density and Volume display for mixtures]]

For solution density calculations requiring correction functions, please see [[Density_Correction_Calculations#Density_Correction_for_Solutions_.26_Data_Fitting|Density Correction for Solutions & Data Fitting]].

* The gas phase species are handled separately. In a vapour mixture, all species occupy the same volume.  The densities are evaluated at the ''partial pressure'' of the species in question and the mixture density is just the sum of the species densities.

* For mixtures with more than one phase present, the multiphase density is 

<math>\rho = \sum M_p/\sum_p M_p/\rho_p</math>

'''Vapour Phase Density'''
* In earlier versions of SysCAD (Build 135 and earlier), the gas phase density for mixtures was evaluated at the '''total pressure''' for each species, the corresponding specific volumes being mass-weight averaged. For ideal gases, this is equivalent to adding the densities. For non-ideal gases, particularly when one species is at saturation, this can lead to errors. As such, the partial pressure is used. This gives improved results for density and volume flows of vapours where there are multiple gas species (including steam) in the mixture.

== Stream Enthalpy values (Hs) ==

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

{|
|-
|rowspan="5" valign="top"| Hs @25 || = || Stream Enthalpy (Heat Content) 
|-
|  = || <math>\mathbf{\mathit{ \sum mf_i * Hs_i }}</math>
|-
| colspan="2"| where mf<sub>i</sub> and Hs<sub>i</sub> are the mass fraction and enthalpy of individual species, respectively
|-
|  = ||<math>\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>\mathbf{\mathit{ 54.02 kJ/kg}}</math>
|}


{|
|-
|valign="top" rowspan="3" |SmsHs @25 || = Solids Enthalpy
|-
|= <math>\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 mf<sub>i solids</sub> is the mass fraction of solids in the solid phase
|}


{|
|-
|valign="top" rowspan="3" | LmsHs @25 || = Liquid Enthalpy
|-
|= <math>\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 mf<sub>i liquids</sub> is the mass fraction of liquids in the liquid phase
|}
 


{|
|-
|valign="top" rowspan="3" |VmsHs @25 || = Vapour Enthalpy
|-
|= <math>\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 mf<sub>i vapour</sub> is the mass fraction of vapour in the vapour phase
|}
 


{|
|-
|valign="top" rowspan="5" |SLmsHs @25 || = Slurry Enthalpy
|-
|= <math>\mathbf{\mathit{ \sum mf_{i \ slurry} * Hs_i }}</math>
|-
|where mf<sub>i slurry</sub> is the mass fraction of liquid/solid in the slurry (liquid+solid) phase
|-
|= <math>\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>\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 Species Properties Summary''''', we have:

{|
|-
|valign="top" rowspan="5"|Cp @25 || = Stream Cp
|-
|= <math>\mathbf{\mathit{ \sum mf_i * Cp_i}} </math>
|-
|where mf<sub>i</sub> and Cp<sub>i</sub> are the mass fraction and Cp of individual species, respectively
|-
|= <math>\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>\mathbf{\mathit{2.16 kJ/kg.C}}</math>
|}
 

{|
|-
|valign="top" rowspan="3" |SmsCp @25 || = Solids Cp
|-
|= <math>\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 mf<sub>i solids</sub> is the mass fraction of solids in the solid phase
|}
 


{|
|-
|valign="top" rowspan="3" |LmsCp @25 || = Liquid Cp
|-
|= <math>\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 mf<sub>i liquids</sub> is the mass fraction of liquids in the liquid phase
|}
 


{|
|-
|valign="top" rowspan="3" |VmsCp @25 || = Vapour Cp
|-
|= <math>\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 mf<sub>i vapour</sub> is the mass fraction of vapour in the vapour phase
|}
 


{|
|-
|valign="top" rowspan="5" |SLmsCp @25 || = Slurry Cp
|-
|= <math>\mathbf{\mathit{ \sum mf_{i \ slurry} * Cp_i }}</math>
|-
|where mf<sub>i slurry</sub> is the mass fraction of liquid/solid in the slurry (liquid+solid) phase
|-
|= <math>\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>\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 Species Properties Summary''''', we have:

{| 
|-
|valign="top" rowspan="4" | Stream H<sub>f</sub> 25°C || = <math> \sum mf_i * H_{f \ i}^{25} </math>
{|
|-
|valign="top" rowspan="2" |where || mf<sub>i</sub> is mass fraction of individual species and
|-
|Hf<sub>i</sub><sup>25</sup> is the heat of formation of individual species at 25°C 
|}
|-
|<math>\mathbf{\mathit{= 0.2*-12073.03 + 0.3*-15171.18 + 0.4*-15865.97 + 0.08*-9038.81 + 0.01*-8941.31 + 0.01*0}}</math>
|-
|<math>\mathbf{\mathit{= -14124.87 kJ/kg}}</math>
|}


{|
|-
|valign="top" rowspan="4" |Stream H<sub>f </sub> 0°C || = <math>\mathbf{\mathit{ H_f^{25} - \sum \int\limits_{0}^{25}Cp_i.dT}} </math>
|-
|= <math>\mathbf{\mathit{H_f 25^{\circ}C - (Hs 25^{\circ}C- Hs 0^{\circ}C)}}</math>
|-
|= <math>\mathbf{\mathit{-14124.87 - (54.02 - 0)}}</math> (See '''Table 4 Stream Properties Summary''')
|-
|= <math>\mathbf{\mathit{-14178.89 kJ/kg}}</math>
|}



{|
|-
|valign="top" rowspan="4" |Stream H<sub>f </sub> 50°C ||= <math>\mathbf{\mathit{ H_f^0 + \sum \int\limits_{0}^{50}Cp_i.dT}} </math>
|-
|= <math>\mathbf{\mathit{H_f 0^{\circ}C + (Hs 50^{\circ}C - Hs 0^{\circ}C)}}</math>
|-
|= <math>\mathbf{\mathit{-14178.88 + (108.46 - 0)}}</math> (See '''Table 4 Stream Properties Summary''')
|-
|= <math>\mathbf{\mathit{-14070.42 kJ/kg}}</math>
|}

== Enthalpy Change (Hs) and (Hz) ==

'''<u>Hs</u>''' '''is the enthalpy change (excluding phase change) from 0°C to current temperature.'''



{|
|-
|valign="top" rowspan="3" |Stream Hs 50°C || = <math>\mathbf{\mathit{ \sum \int\limits_{0}^{50}Cp_i.dT }}</math>
|-
|= <math>\mathbf{\mathit{(Hs 50^{\circ}C - Hs 0^{\circ}C)}}</math>
|-
|= <math>\mathbf{\mathit{108.46 kJ/kg}}</math> (See '''Table 4 Stream Properties Summary''')
|}

'''<u>Hz</u>''' '''is the enthalpy change (including phase change) from 0°C to current temperature.'''


{|
|-
|valign="top" rowspan="5" |Stream Hz 50°C || = Net Enthalpy @ temperature
|-
|= <math>\mathbf{\mathit{ H_{phase \ change} + \sum \int\limits_{0}^{50}Cp_i.dT}} </math>
|-
|= <math>\mathbf{\mathit{(H final phase - H original phase) 0^{\circ}C + (Hs 50^{\circ}C - Hs 0^{\circ}C)}}</math>
|-
|= <math>\mathbf{\mathit{0 + (108.46 - 0)}}</math> (See Table 4 Stream Properties Summary)
|-
|= <math>\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>\mathbf{\mathit{H_lg = 2501\ at\ 0^{\circ}C}}</math> &amp; Sat. Pressure, these two terms will not be equal. See Examples on calculating Energy change around a unit for more details.

== Stream Entropy values (S) ==

Stream Entropy values are calculated using the mass weighted mean method. Generally, the Entropy data available are at 25°C. Thus, using these values, stream Entropy (S) at 25°C is calculated. 

 
From '''''Table 3 Species Properties Summary''''', we have:

{| 
|-
|valign="top" rowspan="4" | Stream S 25°C || = <math> \sum mf_i * S_{i}^{25} </math>
{|
|-
|valign="top" rowspan="2" |where || mf<sub>i</sub> is mass fraction of individual species and
|-
|S<sub>i</sub><sup>25</sup> is the entropy of individual species at 25°C 
|}
|-
|<math>\mathbf{\mathit{= 0.2*0.93 + 0.3*0.70 + 0.4*3.89 + 0.08*0.20 + 0.01*4.86 + 0.01*6.84}}</math>
|-
|<math>\mathbf{\mathit{= 2.09 kJ/kg.C}}</math>
|}

== Calculating Energy change around a unit ==

===<u> Calculating Energy change around a unit without phase change</u> ===

[[Image:Models-Main-image055.jpg]]

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

To verify the values using the steam tables (refer to [[Water and Steam Properties]]):

:At <math>\mathbf{\mathit{100 ^{\circ}C\ at\ sat. P, H_g = 2675.572 kJ/kg}}</math>

:At <math>\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>\mathbf{\mathit{1 kg/s * (2705.9342 - 2675.572) kJ/kg = 30.3622 kJ/s}}</math> (i.e. equal to the reported value)

As demonstrated by the above example, you can use Hs (sensible heat), Hz (enthalpy), or Hf (heat of formation) values to calculate the energy required to raise the stream by 20°C.