1. Review/Theory on Kinetics and Reactors
By: Heetae Jeon, Matthew Hartung, Kevin Moy, and Sauradeep Sinha
Feburary 3, 2017
Group 15
CHBE 446
Honor Pledge: We pledge on our honors that we have neither received nor given unauthorized assistance on this assignment.
Information and diagrams are adapted from Dr. Srinivasa Raghavan's Reactor Kinetics and Design course at the University of Maryland. 

2. Basics of Reaction Kinetics
Reaction Rate – measure of how fast the reaction occurs 
r=(dC/dt) = (change in concentration)/(time)
Conversion – measure of the extent to which a reaction has progression (positive fraction between 0 and 1)
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 1 slides

3. Review on Rate Laws
For a given reaction, using a stoichiometric table will allow you to express concentration of components in terms of conversion (X)
Rate Law is an empirical representation of the rate in terms of concentration 
There is an Arrhenius dependence for the rate constant 
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 2 slides

4. Refresher on Determining Rate Laws
Rate law can be found by using: 
Differential Method: rate r vs. Ca plot is constructed by differentiating Ca(t)
Integral Method: Experimental Ca(t) is compared with a predicted Ca(t)

5. Common Expressions for 1st and 2nd order rxns
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 4 slides​

6. Basic Theory on Reactions and Reaction Mechanisms
Elementary Reactions: perfect connection between the rate law and the stoichiometry
Ex. A + B --> C (r=kCaCb) 
Collision Theory of Reactions: correct orientation and sufficient energy
Transition-State Theory and Activation Barrier 
Rate Determining Step (=slowest step)
Deriving the Rate Law from a Reaction Mechanism: 
Pseudo Steady State Assumption (PSSA) 
Equilibrium Assumption 

7. Design Equations: CSTR, PFR, Batch
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 10 slides​​​

8. Variable Density Reactors
Design equations in terms of conversion are valid for variable density reactors
Equations in terms of species concentration are not
Gas reactions with a change in moles are the variable density case
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 12 slides​​​

9. Transient and Semi-Batch CSTR's
Transient reactors are reactors which are not operated at steady state and therefor have time effects on species concentration 
Reactors starting while empty, reactors with no input or output, and reactors having another species added at a certain time are all transient
A semi-batch reactor is a reactor with no output stream, and operates like a cross between a batch reactor and a CSTR 
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 13,14 slides​​​

10. Bioreactors
Bioreactors involve the use of specialized cells to grow more cells and a desired product
Alcohol, Biologics, and Fuels can all be produced using bioreactors
Cell growth and bioreactor problems are done based on mass units
Most bioreactors operate by batch, but continuous operation is possible
Washout must be avoided in continuous operation 
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 15,16 slides​​​
For a simple cell reactor with substrate A reacting to form product and Cells C in a CSTR:

11. Reactions in Series
Series reactions involve maximizing the rate selectivity or overall selectivity
This is necessary to maximize the production of desired product, while minimizing the production of byproducts
In a CSTR, the optimal residence time can be found by plotting the normalized species concentrations (Cj/Cio) versus residence time
Results vary based on the values of each individual rate constant
The same approach can be taken for a PFR
Numerical solving softwares (Polymath, Matlab) are used to solve these complex systems of differential equations
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 16,17 slides​​​

12. Reactions in Series
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 16,17 slides​​​

13. Reactions in Parallel 
Again, with reactions in parallel, the rate selectivity of the desired component to the byproduct needs to be considered 
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 19 slides​​​

14. Non-Isothermal Reactor Design

15. Purpose of Non-Isothermal Reactors
Harder to remove heat from larger reactors
Non-isothermal is often the best way to run them (efficient, faster reactions, lower cooling costs for exothermic reactions)
Idea: create an adiabatic system
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 20 slides​

16. Assumptions Exothermic reaction Only reactant enters the stream
Steady state operation if not a batch reactor
An average heat capacity is used

17. Solve for Cooling Temperature
The energy balance equation is solved for needed cooling temperature,
U= Overall heat transfer coefficient
A= Area of cooling
T= T of reacting fluid, Tc= T of cooling water, T0= T of entering stream
Fj0= Flowrate of input
Cpj= heat capacity of the process fluid
HR= Enthalpy of the reaction
V= Volume of the reactor
r= reaction rate
Add diagram of cooled CSTR
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 21 slides​

18. Adiabatic Temperature Rise
Temperature varies linearly with conversion in both CSTR and PFR
Possible to determine maximum temperature rise, assuming conversion = 1
Equation for Tad
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 21 slides​

19. Steady States in Non-isothermal CSTRs
Idea: Simultaneously solve mass and energy balances
Due to non-linear mass balance, there are 2 stable steady states
K= =dimensionless heat transfer coefficient
CA0=initial concentration of component A
T0=feed T
  =residence time
Add MB and EB equations; graph on next slide
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 22 slides​

20. Graph of Steady States
If the slope of the mass balance line < slope of the energy balance line, the steady state is stable.
Graph of multiple steady states
Information and equations adapted from Dr. Raghavans CHBE 440 Lecture 24 slides​

21. Design of Reactors (Ch.15 Design 1 Textbook)

22. Procedure for Reactor Design
Collect required data
Parameters such heats of reaction, phase equilibrium constant, heat and mass transfer coefficient, etc.
Select Reaction Conditions.
Optimizing the process. 
 Determine Materials of Construction
Determine the Rate-limiting Step and Critical Sizing Parameters of the Reactor.
Residence time, Space Velocity, and Weight Hourly Space Velocity.
Information adapted from Chemical Engineering Design Principles, Practice and Economics of Plant and Process Design 2nd edition.

23. 5. Preliminary Sizing, Layout, and Costing of Reactor
Additional space needed. 
6.   Estimate Reactor Performance
7.   Optimize the Design
Step 2 to 6.
Information adapted from Chemical Engineering Design Principles, Practice and Economics of Plant and Process Design 2nd edition.