reactor energy balance

Graduate Seminars on Chemical Reaction Engineering and Kinetics

October 15 - Nov 26, 2009 Lecture 2:

Energy Equation for Reactors Brian G. Higgins

Department of Chemical Engineering and Materials Science

University of California, Davis

Lecture notes posted at http://www.ekayasolutions.com

Email: bghiggins@ucdavis.edu

Analysis of Chemical Reactors and the Connecting Disciplines

Chemical Reactor

Thermodynamics Fluid Mechanics

Kinetics Mathematics

Heat Transfer Mass Transfer

Chemical reactors are the linchpin in a chemical plant for controlling, optimizing, manipulating

the transformation of matter through chemical reactions

Nonisothermal Reactors

Real reactors generate or absorb large amounts of heat

Rate coefficient is function of temperature

or

Advantage to operate exothermic reactors nonisothermally is:

Higher temperatures lead to higher reaction rates and smaller reactors

If temperature to high equilibrium can limit conversion and

High temperatures can lead to hot spots and reactor failure

but

Analysis of Nonisothermal Reactors Mass flow rate

Control volume V

Molar concentration

Total energy

Rate of heat added Rate of work done

Reactor

The energy balance is an accounting of rate of

•  heat flow into the reactor with reactants •  heat flow out of the reactor with products •  heat generated/absorbed by reaction •  heat added/removed from reactor •  work done by stirrers and friction

Energy Balance for Chemical Reactors

Mass flow rate

Control volume V

Molar concentration

Total energy

Rate of heat added Rate of work done

Total energy per unit mass

Reactor

Rate of Work Done on System

Fluid density

Inlet pressure

Exit pressure

Energy Terms

Convenient to work with enthalpy

but

Complete energy analysis is complicated- simplifying assumptions often made!

Knowledge of thermodynamics important

reactor volume/mass

composition

Energy Equation for Batch Reactor

Definition for enthalpy

Rate of work due to change in volume

Neglect kinetic energy, potential energy and shaft work

Rate of Enthalpy change

Reactor volume

Rate of heat added

Expression for Enthalpy Thermodynamic expression for enthalpy in terms of P, T, nj

Heat capacity

Partial molar enthalpy Reactor volume

Coefficient of expansion

Moles of species j

Constant Pressure Liquid Batch Reactor Step 1

Enthalpy Expression

or

Substitute

Energy balance in terms of T and partial molar enthalpies

Rate of Enthalpy change

Rate of heat added

=0

Constant Pressure Liquid Batch Reactor Step 2

Use species balance to eliminate

Use heat of reaction to eliminate

Constant Pressure Liquid Batch Reactor Example 1

At what rate must heat be removed to maintain reactor at 300 K to reach a conversion of 90%?

Solution: Species balance:

For 90% conversion:

Time for 90% conversion:

Constant Pressure Liquid Batch Reactor Example 1 continued

Total heat removed:

Energy balance for isothermal operation: =0

Adiabatic Liquid Batch Reactor Example 2

Species balance:

Stoichiometry:

Balance for species A:

Balance for species B:

Conservation of mass:

Adiabatic Liquid Batch Reactor Example 2 continued

Energy Balance: =0

Integrating:

Formula for calculating temperature rise in reactor

Adiabatic Liquid Batch Reactor Example 2 continued

Reactor Parameters:

For 95% conversion:

Non-Isothermal Batch Reactors Example 3

Case 1: Constant Pressure Reactor:

Reactor pressure is held constant; reactor volume therefore changes

Case 2: Constant Volume Reactor:

Reactor volume is held constant; reactor pressure therefore changes

Which reactor converts the reactant more quickly?

Ideal gas mixture

Analysis Constant Pressure Case Example 3 continued

Species balance:

Energy balance constant pressure case:

Analysis Constant Volume Case Example 3 continued

Species balance:

Energy balance constant volume case:

Summary of Results Example 3 continued Ideal gas mixture

Case 2: Constant Volume Reactor:

Case 1: Constant Pressure Reactor:

By inspection

Reaction proceeds more quickly in constant volume case!

Energy Balance for CSTR

General design equation for CSTR reactors

Assumption: Perfectly mixed

Material Balance for CSTR

Energy Balance for Chemical Reactors

Mass flow rate

Control volume V

Molar concentration

Total energy

Rate of heat added Rate of work done

Total energy per unit mass

Reactor

Energy Balance for CSTR

General design equation for CSTR reactors

Energy balance in terms of enthalpy:

Enthalpy relation:

Energy balance in terms of temperature:

Substituting the species balance

Energy Balance for CSTR Some special cases

Liquid phase reactor:

Steady State:

For liquid phase

Then

Steady State Energy Balance for CSTR Example 1

What temperature must the reactor be operated at to achieve 80% conversion?

Solution: Steady state species balances:

Adding and noting that cB0=0

Steady State Energy Balance for CSTR Example 1 continued

Solution continued Rate Expression

Steady State Energy Balance for CSTR Example 1 continued

Solution continued Rate Expression

Species balance

Working equation

Solve for T with cA1=0.2 cA0

Appendix Derivation of key formulas

Energy Balance in terms of T and P Step 1

Rate of Enthalpy change

Reactor volume

Rate of heat added

Enthalpy Expression

or

Substitute

Energy balance in terms of T and P and partial molar enthalpies

Energy Balance in terms of T and P Step 2

Use species balance to eliminate

Use heat of reaction to eliminate