Reaction Block Energy Balance

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Overview		Reaction Block Data Section		RB Sub Model (Model Theory)
Reaction Editor	Reaction Block Summary	Reaction Block Tabs (Main)	Individual Reactions	Reaction Extents	Source / Sink / Heat Exchange	Solving Order - Sequential or Simultaneous	Energy Balance	Heat of Reaction / Heat of Dilution / Partial Pressures

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Final Temperature of a Reaction Block (1^st Principles)

Consider the following reaction:

NiS(s) + CuSO4(aq) -> NiSO4(aq) + CuS(s)

Extent of Reaction: NiS(s) = 100%

Given 100 t/h (27.78 kg/s) of feed enters the reaction block at 80 °C, find the output temperature.

These calculations will use a Reference Temperature of 25 °C.

Note SysCAD uses a Reference Temperature of 0 °C for all enthalpy calculations, including Heat of Reaction.

	Water	NiS (s)	CuSO4(aq)	NiSO4(aq)	CuS(s)
Feed (kgmol/s)	0.974184	0.04085	0.04085	-	-
Product (kgmol/s)	0.974184	-	-	0.04085	0.04085

The CRC_Cp equations are in the format of (T is in Kelvin):

[math]\displaystyle{ C_p = a + b.10^{-3}*T + \cfrac{c.10^5}{T^2} + d.10^{-6}*T^2 }[/math]

	Hf (kJ/kgmol) @ 25°C	Cp a	Cp b	Cp c	Cp d	MW (kg/kgmol)	Range (K)
NiS(s)	-94140	38.911	26.778	0	0	90.76	298-500
CuSO4(aq)	-840787.27	73.408	152.85	-12.309	-71.588	159.61	298-500
NiSO4(aq)	-963969	77.38	0	0	0	154.76	298-600
CuS(s)	-55684	44.35	11.046	0	0	95.61	298-780

DHrxn @ 25 °C	= Hf @25 products - Hf @ 25 reactants
	= (-963969 + -55684) - (-94140 + -840787.27)
	= -84725.73 kJ/kgmol NiS(s) OR -933.52 kJ/kg NiS(s)

To work out the outlet temperature, we would do the following:

Determine the Change of Enthalpies of the inlet Stream:

Using our reference temperature of 25°C, it is assumed that the enthalpy at 25°C is 0 and the enthalpy at the feed temperature of 80°C is found by integrating the Cp equations from 25°C (298.15K) to 80°C (323.15K).(In this case, the enthalpy of the water relative to 25°C is found by taking the difference between the Hs calculated by SysCAD at 25°C and Hs calculated by SysCAD at 80°C)

DH = H (T_ref) - H (T_feed)

Component	Moles	H (Tfeed)	DH	DH
	(kgmol)	(kJ/kgmol)	(kJ/kgmol)	(kJ)
NiS(s)	0.04085	2619.73	-2619.73	-107.02
CuSO4(aq)	0.04085	5713.69	-5713.69	-233.40
Water	0.974184	4144.64	-4144.64	-4037.64	DHr = -4378.06

Now we know that: DH_r + DH_{rxn @25 °C} = DH_p

DH_r + DH_{rxn @25 °C} = -4378.06 + (-84725.73*0.04085) = -7839.11 = DH_p

The solution is solved by iterative process, ie, the outlet temperature is varied until the above equation is balanced:

Again, using our reference temperature of 25°C, it is assumed that the enthalpy at 25°C is 0 and the enthalpy at the outlet temperature is found by integrating the Cp equations from 25°C (298.15K) to T_outlet.

Guess Outlet Temp = 397.68K

Component	Moles	H Toutlet	DH	DH
	(kgmol)	(kJ/kgmol)	(kJ/kgmol)	(kJ)
NiSO4(aq)	0.04085	7701.17	-7701.17	-314.59
CuS(s)	0.04085	4796.37	-4796.37	-195.93
Water	0.974184	7522.79	-7522.79	-7328.58	DHp = -7839.11

Check the Answer:

DH_r + DH_{rxn @25 °C} = -7839.11 = DH_p

Energy balance around a Reaction Block (quick check):

To complete a quick energy balance check on the unit operation involving a Reaction block, the following hints and warnings apply:

1. Get values for inlet and outlet streams. NOTE SysCAD uses a reference temperature of 0 dC for all Enthalpy calculations.
2. Get Values from the Reaction block.
   The reaction block has two main sections:

   a. summary information given as a total for all reactions present;

   b. Heat of Reaction information for individual reactions present;

   c. Optional - any heat manually added or removed via the heat exchange function of the RB.

   For the purpose of quick check, use the summary information.
   NOTE 1 - in keeping the reference point correct, use the [email protected] value.
   NOTE 2 - User can change the reference temperature to view HOR at other temperatures. For example, if user wants to check the heat balance using first principles, then changing the reference temperature to can obtain values for Hrxn @ 0, Hrxn @ 25, Hrxn @ Feed T etc. See the above example for values needed.

3. users should get a balance of totHs equal to that of the [email protected] when the following conditions are met:
   

   a. User is using the standard species model.

   b. User has good species/compound data in the SysCAD.93.db3

   c. User is allowing SysCAD calculate the HOR based on the data provided in the SysCAD.93.db3
   

4. For users using function HeatOfReaction in a reaction block. Please check what temperature the HeatOfReaction supplied is based on.
5. For users using function HeatOfReaction in a reaction block, SysCAD will estimate the reaction block final temperature based on the Heat of Reaction supplied by the user. When checking for an energy balance around the unit operation, user should expect an error due to the Heat of Reaction specified is different to what SysCAD calculates using species properties defined in the SysCAD.93.db3.
6. If users are using Bayer Species model, an extra error will appear when comparing Hs calculated from Cp to that displayed in reaction block.
Error = Enthalpy calculated using Cp as specified in the SysCAD.93.db3 - Enthalpy calculated using Bayer Species model Cp.

For an example of the Mass & Energy Balance, please see to distribution projects: Energy Balance Example;