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. 

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

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

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)

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

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 

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

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​​​

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​​​

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:

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​​​

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

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​​​

Non-Isothermal Reactor Design

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​

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

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​

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​

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​

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​

Design of Reactors (Ch.15 Design 1 Textbook)

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.

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.