Lecture 17. Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Today’s lecture. Energy Balance Fundamentals Adibatic reactors. Energy Balances , Rationale and Overview.
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Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.
Let’s calculate the volume necessary to achieve a conversion, X, in a PFR for a first-order, exothermic and adiabatic reaction.
The temperature profile might look something like this:
The combinedmolebalance, rate law and stoichiometryyield:
Wecannotsolve this Equationbecausewedon’thave X either as a function of V or T. WeneedanotherEquation. That Equation is:
The Energy Balance
1. Adiabatic CSTR, PFR, Batch or PBR
2. CSTR with heat exchanger, UA(Ta-T) and a large coolant flow rate
3. PFR/PBR with heat exchange
3A. PFR in terms of conversion
3B. PBR in terms of conversion
3C. PBR in terms of molar flow rates
3D. PFR in terms of molar flow rates
5. For Semibatch or unsteady CSTR
6. For multiple reactions in a PFR (q reactions and m species)
Let’s look wheretheseUserFriendlyEquationscame from.
Rate of energy in by flow
Rate of energy out by flow
Heat added to the system
Work done by the system
Rate of energy accumulation
Energy Balance on an open system: schematic.
OK folks, here is whatwe are going to do to put the aboveequationinto a usable form.
1. ReplaceUi by Ui=Hi-PVi
2. Express Hi in terms of heat capacities
3. Express Fi in terms of eitherconversion or rates of reaction
5. Define ΔCP
6. Manipulate so that the overall energybalance is either in terms of the UserFriendlyEquations.
Other energies small compared to internal
General Energy Balance:
For Steady State Operation:
For the generalizedreaction:
Flow Rates, Fi
For No Phase Changes
Constant Heat Capacities
Enthalpy of formation at temperature TR
Heat of reaction at temperature T
Substituting back into the Energy Balance
Adiabatic Energy Balance:
A ↔ B
1) Mole balance:
2) Rate Laws:
A ↔ B
4) Energy Balance:
First need to calculate the maximum conversionwhich is at the AdiabaticEquilibrium.
A ↔ B
Adiabatic equilibrium conversion
Wecannow form a table. Set X, thencalculate T, -VA, and FA0/-rA, increment X, thenplot FA0/-rA vs. X: