### Instructors: Prof. K. Dane Wittrup, Prof. William Green, Jr

**MASSACHUSETTS INSTITUTE OF TECHNOLOGY**

#### Course Description

This course applies the concepts of reaction rate, stoichiometry and equilibrium to the analysis of chemical and biological reacting systems, derivation of rate expressions from reaction mechanisms and equilibrium or steady state assumptions, design of chemical and biochemical reactors via synthesis of chemical kinetics, transport phenomena, and mass and energy balances. Topics covered include: chemical/biochemical pathways; enzymatic, pathway, and cell growth kinetics; batch, plug flow and well-stirred reactors for chemical reactions and cultivations of microorganisms and mammalian cells; heterogeneous and enzymatic catalysis; heat and mass transport in reactors, including diffusion to and within catalyst particles and cells or immobilized enzymes.

# Lecture Notes

These lecture notes were prepared by Tiffany Iaconis, Frederick Jao, and Vicky Loewer for MIT OpenCourseWare. They are preliminary and may contain errors.

Instructors:

WHG = William H. Green

KDW = K. Dane Wittrup

LEC # | TOPICS |
---|---|

1 | Preliminaries and remembrance of things past. Reaction stoichiometry, lumped stoichiometries in complex systems such as bioconversions and cell growth (yields); extent of reaction, independence of reactions, measures of concentration. Single reactions and reaction networks, bioreaction pathways. (WHG) (PDF) |

2 | The reaction rate and reaction mechanisms: Definition in terms of reacting compounds and reaction extent; rate laws, Arrhenius equation, elementary, reversible, non-elementary, catalytic reactions. (WHG) (PDF) |

3 | Kinetics of cell growth and enzymes. Cell growth kinetics; substrate uptake and product formation in microbial growth; enzyme kinetics, Michaelis-Menten rate form. (KDW) (PDF) |

4 | Reaction mechanisms and rate laws: Reactive intermediates and steady state approximation in reaction mechanisms. Rate-limiting step. Chain reactions. Pyrolysis reactions. (WHG) (PDF) |

5 | Continuous stirred tank reactor (CSTR). Reactions in a perfectly stirred tank. Steady-state CSTR. (KDW) (PDF) |

6 | Concentration that optimizes desired rate. Selectivity vs. Conversion. Combining reactors with separations. (WHG) (PDF)
Lecture 6 correction (PDF) |

7 | Batch reactor: Equations, reactor sizing for constant volume and variable volume processes. (KDW) (PDF) |

8 | The plug flow reactor. (WHG) (PDF) |

9 | Reactor size comparisons for PFR and CSTR. Reactors in series and in parallel. How choice of reactor affects selectivity vs. conversion. (KDW) (PDF) |

10 | Non-ideal reactor mixing patterns. Residence time distribution. Tanks in series model. Combinations of ideal reactors. (KDW) (PDF) |

11 | Non isothermal reactors. Equilibrium limitations, stability. Derivation of energy balances for ideal reactors; equilibrium conversion, adiabatic and nonadiabatic reactor operation. (WHG) (PDF) |

12 | Data collection and analysis. Experimental methods for the determination of kinetic parameters of chemical and enzymatic reactions; determination of cell growth parameters; statistical analysis and model discrimination. (WHG) (PDF) |

13 | Biological reactors – chemostats. Theory of the chemostat. Fed batch or semi-continuous fermentor operation. (KDW) (PDF) |

14 | Kinetics of non-covalent bimolecular interactions. Significance; typical values and diffusion limit; approach to equilibrium; multivalency. (KDW) (PDF) |

15 | Gene expression and trafficking dynamics. Approach to steady state; receptor trafficking. (KDW) (PDF) |

16 | Catalysis. Inorganic and enzyme catalysts and their properties; kinetics of heterogeneous catalytic reactions; adsorption isotherms, derivation of rate laws; Langmuir-Hinshelwood kinetics. (WHG) (PDF) |

17 | Mass transfer resistances. External diffusion effects. Non-porous packed beds and monoliths, immobilized cells. (WHG) (PDF) |

18 | External mass-transfer resistance: Gas-liquid reactions in multiphase systems. (KDW) (PDF) |

19 | Oxygen transfer in fermentors. Applications of gas-liquid transport with reaction. (KDW) (PDF) |

20 | Reaction and diffusion in porous catalysts. Effective diffusivity, internal and overall effectiveness factor, Thiele modulus, apparent reaction rates. (KDW) (PDF) |

21 | Reaction and diffusion in porous catalysts (cont.). Packed bed reactors. (WHG) (PDF) |

22 | Combined internal and external transport resistances. (WHG) (PDF)
Biot numbers review. (PDF) (Courtesy of David Adrian. Used with permission.) |

23 | Pulling it all together; applications to energy/chemicals industry. Presentation of current research. (WHG) |

24 | Pulling it all together; applications to bioengineering and medicine. Presentation of current research. (KDW) |

25 | Course review. (WHG) (PDF) |

# Assignments

Special software is required to use some of the files in this section: .fig, .m, and .zip.

The following assignment solutions were prepared by David Adrian, Karen Daniel, and Bin Pan. Used with permission. In each solution there is a summary document along with supporting files. The archive contains each assignment’s problems, solutions, and supporting files.

ASSIGNMENTS | SOLUTIONS | ARCHIVES |
---|---|---|

Problem set 1 (PDF)
vinylethene1.txt (TXT) vinylethene2.txt (TXT) vinylethene3.txt (TXT) |
(PDF)
hwk1prob1.m (M) hwk1prob2.m (M) |
(ZIP) (The ZIP file contains: 3 .txt files, 2 .pdf files, and 2 .m files.) |

Problem set 2 (PDF) | (PDF) | (ZIP) (The ZIP file contains: pset02.pdf and pset02_soln.pdf.) |

Problem set 3 (PDF) | (PDF)
hw3prob3.m (M) |
(ZIP) (The ZIP file contains: pset03.pdf, hw3prob3.m, and pset03_soln.pdf.) |

Problem set 4 (PDF) | Solution to problem 1 (PDF) | (ZIP) (The ZIP file contains: pset04.pdf and pset04_01_soln.pdf.) |

Problem set 5Fogler problems:
2-5, parts a, b, f, g 6-6, parts a-e 13-19, parts a-h 14-3, parts a-b Additional information (PDF) |
||

Problem set 6 (PDF)
Amendment to the question: What magnitude of temperature perturbation would lead to a shift to a hotter steady state (ignition)? Batch reactor balances (PDF) (Courtesy of David Adrian. Used with permission.) |
(PDF)
hw6p1.m (M) stabilitydiagram.m (M) oneweek.fig (FIG – 1.7 MB) |
(ZIP – 1.9 MB) (The ZIP file contains: 3 .pdf files, 2 .m files, and 1 .fig file.) |

Problem set 7 (PDF) | (PDF) | (ZIP) (The ZIP file contains: pset07.pdf and pset07_soln.pdf.) |

Problem set 8
Fogler problems: 10-4, all parts 11-5, all parts There is a typo in the problem statement for 11-5. The length of the reactor pipe should be 20 cm, not 20 m. Also, please use the following viscosity and diffusivity data: At 500 |
||

Problem set 9
Fogler problems: 12-4 12-6 (For those with the 3rd edition of Fogler, the problems numbers are the same as in the 4th edition.) |
||

Problem set 10 (PDF) | (PDF) | (ZIP) (The ZIP file contains: pset10.pdf and pset10_soln.pdf.) |

## WebLab Experiment

This experiment was part of the Cambridge-MIT Institute funded Web Based Teaching Project. First, students completed a pre-lab assignment. Then students at MIT observed a reactor running at Cambridge University in real time. Finally, the students analyzed the data in a post-lab assignment. A short description follows below. More information about the nonideal reactor WebLab can be found here.

A reaction of phenolphthalein occurs in aqueous sodium hydroxide solution.

## Preliminary Analysis

From ideal batch reactor data, we can determine experimental rate constants for the reaction. The actual reaction is conducted in a non-ideal, continuous, stirred tank reactor. The ideal CSTR and bypass/dead volume models yield equations with unknown parameters. Tracer data can be used to find the unknown parameters for the bypass/dead volume model. The goal is to run the reactor at a given product flowrate and conversion. Equations can be derived that relate flowrate, conversion, and NaOH flowrate for both the ideal CSTR and bypass/dead volume models.

## Experiment

The reactor is operated first at the NaOH flowrate derived for the ideal CSTR model. Then the reactor is operated at the NaOH flowrate derived for the non-ideal bypass/dead volume model. The data collected from the WebLab experiment can be analyzed to test the assumption that the reactor behaves as an ideal CSTR and to test the non-ideal model parameters derived in the preliminary analysis.

These files are courtesy of Andreas Braumann and Michael Goodson. Used with permission.

Pre-lab Assignment: (PDF)

Data: Run 1 (TXT); Run 2 (TXT); Run 3 (TXT); Run 4 (TXT)

Post-lab Assignment: (PDF)

WebLab Files: (ZIP) (The ZIP file contains: 2 .pdf files and 4 .txt files.)

**Exams**

ACTIVITIES | PROBLEMS | SOLUTIONS |
---|---|---|

Review for midterm 1 | Not applicable | (PDF) |

Midterm 1 | (PDF) | (PDF) |

Review problems for midterm 2 | (PDF) | (PDF)^{#} |

Midterm 2 | (PDF) | (PDF) |

Final exam | (PDF) | Not available |

# Tools

Special software is required to use some of the files in this section: .m and .zip.

This review is courtesy of David Adrian. Used with permission.

MATLAB® Review (PDF)

Demonstrates the use of various ODE solvers to integrate a pair of interdependent ODEs: odesintegrate.m (M)

Finds the sides of a rectangle with a given perimeter and area: multiplefsolve.m (M)

Show how to use events in ODE integrators to keep track of user-defined significant time-points: learntouseevents.m (M)

Sample solutions to the exercises:

sampleproblem1.m (M)

sampleproblem2.m (M)

sampleproblem3.m (M)

sampleproblem4.m (M)

sampleproblem5.m (M)

The ZIP archive below contains the above files:

MATLAB® Review (ZIP) (The ZIP file contains: matlab_review.pdf, and 8 .m files.)