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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

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
Today’slecture
  • Energy Balance Fundamentals
    • Adibaticreactors
energy balances rationale and overview
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 overview1
Energy Balances, Rationale and Overview

The combinedmolebalance, rate law and stoichiometryyield:

energy balances rationale and overview2
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 f i
User Friendly Equations Relate T and X or Fi

1. Adiabatic CSTR, PFR, Batch or PBR

adiabatic
Adiabatic

T

T

Exothermic

Endothermic

XEB

XEB

T0

T0

0

0

slide8

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

slide9

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

slide10

User Friendly Equations Relate T and X or Fi

3B. PBR in terms of conversion

3C. PBR in terms of molar flow rates

slide11

User Friendly Equations Relate T and X or Fi

3D. PFR in terms of molar flow rates

4. Batch

slide12

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.

slide13

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

-

+

-

=

slide14

Energy Balance

Energy Balance on an open system: schematic.

slide15

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.

slide16

Intro to Heat Effects

Assumptions:

=0

=0

Other energies small compared to internal

Recall:

slide17

Intro to Heat Effects

Substituting for

slide18

Intro to Heat Effects

General Energy Balance:

For Steady State Operation:

slide19

Intro to Heat Effects

For the generalizedreaction:

Flow Rates, Fi

In general,

slide21

Intro to Heat Effects

For No Phase Changes

Constant Heat Capacities

Enthalpy of formation at temperature TR

Heat of reaction at temperature T

slide24

Intro to Heat Effects

Substituting back into the Energy Balance

slide25

T

Adiabatic Energy Balance:

T0

X

slide26

ExampleAdiabatic PFR

A ↔ B

1) Mole balance:

2) Rate Laws:

slide27

ExampleAdiabatic PFR

A ↔ B

3) Stoichiometry:

4) Energy Balance:

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

slide28

ExampleAdiabatic PFR

A ↔ B

XC

Adiabatic equilibrium conversion

T

slide29

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

FA0/-rA

X

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