Lecture 17
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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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Lecture 17

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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’slecture

  • Energy Balance Fundamentals

    • Adibaticreactors


Energy Balances, Rationale and Overview

TodaysLecture

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:

T

k

X

V

V

V


Energy Balances, Rationale and Overview

The combinedmolebalance, rate law and stoichiometryyield:


Energy Balances, Rationale and Overview

Wecannotsolve this Equationbecausewedon’thave X either as a function of V or T. WeneedanotherEquation. That Equation is:

The Energy Balance


User Friendly Equations Relate T and X or Fi

1. Adiabatic CSTR, PFR, Batch or PBR


Adiabatic

T

T

Exothermic

Endothermic

XEB

XEB

T0

T0

0

0


User Friendly Equations Relate T and X or Fi

2. CSTR with heat exchanger, UA(Ta-T) 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

3D. PFR in terms of molar flow rates

4. Batch


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.


Energy Balance

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

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

4. DefineΔHRx

5. Define ΔCP

6. Manipulate so that the overall energybalance is either in terms of the UserFriendlyEquations.


Intro to Heat Effects

Assumptions:

=0

=0

Other energies small compared to internal

Recall:


Intro to Heat Effects

Substituting for


Intro to Heat Effects

General Energy Balance:

For Steady State Operation:


Intro to Heat Effects

For the generalizedreaction:

Flow Rates, Fi

In general,


Intro to Heat Effects


Intro to Heat Effects

For No Phase Changes

Constant Heat Capacities

Enthalpy of formation at temperature TR

Heat of reaction at temperature T


Intro to Heat Effects


Intro to Heat Effects


Intro to Heat Effects

Substituting back into the Energy Balance


T

Adiabatic Energy Balance:

T0

X


  • ExampleAdiabatic PFR

A ↔ B

1) Mole balance:

2) Rate Laws:


  • ExampleAdiabatic PFR

A ↔ B

3) Stoichiometry:

4) Energy Balance:

First need to calculate the maximum conversionwhich is at the AdiabaticEquilibrium.


  • ExampleAdiabatic PFR

A ↔ B

XC

Adiabatic equilibrium conversion

T


  • Wecannow form a table. Set X, thencalculate T, -VA, and FA0/-rA, increment X, thenplot FA0/-rA vs. X:

FA0/-rA

X


End of Lecture 17


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