Reaction Block Energy Balance

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Navigation: Models ➔ Sub-Models ➔ Reaction Block (RB) ➔ Energy Balance

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

Final Temperature of a Reaction Block (1st 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] 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 (Tref) - H (Tfeed)

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: DHr + DHrxn @25 °C = DHp

DHr + DHrxn @25 °C = -4378.06 + (-84725.73*0.04085) = -7839.11 = DHp

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 Toutlet.

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:

DHr + DHrxn @25 °C = -7839.11 = DHp

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 RB.dH@0.Nett 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.
  1. users should get a balance of totHs equal to that of the dH@0.nett 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
  2. For users using function HeatOfReaction in a reaction block. Please check what temperature the HeatOfReaction supplied is based on.
  3. 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.
  4. If users are using Bayer Species model, an extra error will appear when comparing Hs calculated from Cp to that displayed in reaction block.
  5. 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;