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
Email:
[email protected] Lecture notes posted at
http://www.ekayasolutions.com
Analysis of Chemical Reactors and the Connecting Disciplines Fluid Mechanics
Thermodynamics
Kinetics
Heat Transfer
Chemical Reactor
Mathematics
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
or Rate coefficient is function of temperature
Advantage to operate exothermic reactors nonisothermally is: Higher temperatures lead to higher reaction rates and smaller reactors
but If temperature to high equilibrium can limit conversion and High temperatures can lead to hot spots and reactor failure
Analysis of Nonisothermal Reactors Mass flow rate Molar concentration
Reactor Total energy Control volume V Rate of heat added Rate of work done
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 Molar concentration
Reactor Total energy Control volume V Rate of heat added Rate of work done
Total energy per unit mass
Rate of Work Done on System
Inlet pressure
Exit pressure
Fluid density
Energy Terms
Convenient to work with enthalpy reactor volume/mass
but
composition
Complete energy analysis is complicated- simplifying assumptions often made!
Knowledge of thermodynamics important
Energy Equation for Batch Reactor
Neglect kinetic energy, potential energy and shaft work Rate of heat added
Rate of Enthalpy change
Definition for enthalpy
Rate of work due to change in volume
Reactor volume
Expression for Enthalpy Thermodynamic expression for enthalpy in terms of P, T, nj Moles of species j
Heat capacity
Reactor volume
Partial molar enthalpy
Coefficient of expansion
Constant Pressure Liquid Batch Reactor Step 1 Rate of heat added
Rate of Enthalpy change
Enthalpy Expression
Substitute
=0
or
Energy balance in terms of T and partial molar enthalpies
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 Energy balance for isothermal operation: =0
Total heat removed:
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 =0 Energy Balance:
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
Ideal gas mixture
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?
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:
Ideal gas mixture
Summary of Results Example 3 continued
Case 1: Constant Pressure Reactor:
Case 2: Constant Volume Reactor:
By inspection
Reaction proceeds more quickly in constant volume case!
Energy Balance for CSTR
Material Balance for CSTR
Assumption: Perfectly mixed
General design equation for CSTR reactors
Energy Balance for Chemical Reactors Mass flow rate Molar concentration
Reactor Total energy Control volume V Rate of heat added Rate of work done
Total energy per unit mass
Energy Balance for CSTR
Energy balance in terms of enthalpy: Enthalpy relation: Energy balance in terms of temperature:
Substituting the species balance
General design equation for CSTR reactors
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 heat added
Rate of Enthalpy change
Reactor volume
Enthalpy Expression
Substitute
or
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
