reactor energy balance
TRANSCRIPT
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: [email protected]
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