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.
TodaysLecture
Let’s calculate the volume necessary to achieve a conversion, X, in a PFR for a firstorder, exothermic and adiabatic reaction.
The temperature profile might look something like this:
T
k
X
V
V
V
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
User Friendly Equations Relate T and X or Fi
2. CSTR with heat exchanger, UA(TaT) and a large coolant flow rate
T
Ta
User Friendly Equations Relate T and X or Fi
3. PFR/PBR with heat exchange
Coolant
Ta
FA0
T0
3A. PFR in terms of conversion
User Friendly Equations Relate T and X or Fi
3B. PBR in terms of conversion
3C. PBR in terms of molar flow rates
User Friendly Equations Relate T and X or Fi
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=HiPVi
2. Express Hi in terms of heat capacities
3. Express Fi in terms of eitherconversion or rates of reaction
4. DefineΔHRx
5. Define ΔCP
6. Manipulate so that the overall energybalance is either in terms of the UserFriendlyEquations.
Substituting for
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
A ↔ B
3) Stoichiometry:
4) Energy Balance:
First need to calculate the maximum conversionwhich is at the AdiabaticEquilibrium.
Wecannow form a table. Set X, thencalculate T, VA, and FA0/rA, increment X, thenplot FA0/rA vs. X:
FA0/rA
X