Accuracy of Analytical Numerical Solutions of the Michaelis Assignment

Assignment Task

Problem

1. A new process is developed with an enzyme to catalyze a reaction and exhibits Michaelis-Menten kinetics. The kinetic data obtained with the system is given in the following table:

a. Use an appropriate linearization technique to estimate and with linear regression in Excel.

b. Use the Excel iterative solver to estimate and with nonlinear regression. You can assume an ‘unweighted regression’ with a constant measurement error

A non-isothermal CSTR is operated at steady state for the following 1st order reaction: A+D→B+D

2. Where the non-reactive species D is added as a diluent. The reaction has the following parameters:

• Q = 5 m3 h−1
• V = 20 m3
• cp =100 kJ−1 (for each species) 
• A = 100,000 kJ kmol−1 A = 1 1012 h−1 =−10,000 kJ kmol−1
• A,in=5 kmol m−3 
• B,in=0 kmol m−3 D,in=15 kmol m−3

a. Calculate the outlet temperature and conversion when the temperature of the inlet feed-in is varied at the following values:

b. What happens when you remove the diluent D entirely from this reaction? Does the reactor display hysteresis like the interactive simulation ‘Regulate the Reactor’? If so, quantify this hysteresis

3. Consider a steady-state catalytic plug flow reactor for the following reaction: A+B→C+D

4. The reactor is fed with a gas mixture containing 20 mol s−1 of A and 40 mol s−1 of B at a constant temperature of 400 °C and a pressure of 3 bar. The reaction follows Langmuir-Hinshelwood kinetics:

With the following parameters:

• k2=0.05 mol kg−1 s−1 bar−2
• kA=0.1 bar−1
• kB=0.05 bar−1
• kc=0.05 bar−1 kD=0.1 bar−1
• Reactor cross-sectional area: ????=0.1 m2
• Bed depth: L=4m
• Catalyst bed density: qp =600 kg m−3
• Bed porosity: b=0.6
• Catalyst pellet diameter: p=8 mm
• Catalyst pellet porosity: c=0.3
• Catalyst pellet tortuosity: ø=4

5. Approximating the diffusivities to be DA=9×10−5 m2/s and DB=1×10−5 m2/s, the pressure at the outlet to be 2 bar, and assuming our target conversion is 75%.

a. Calculate whether the axial dispersion needs to be considered when modeling this reactor.

b. Calculate which reactant is most diffusion limited at the outlet. Use the ‘Nonsteady State Concentration Profiles Catalyst’ code to conduct a parametric study of the porosity and tortuosity of the catalyst particle.

a) Fill in the following table for concentration of hydrogen (H), hexene (E) and hexane (A) at the center of the catalyst (r=0):

b) Use mathematical and/or physical arguments to explain your results

6. Run the code for the ‘Laminar Tubular Reactor’ for sucrose inversion, assuming a higher concentration and more viscous solution of sucrose reactant. Use the following parameters: Dj=1×10−10 m2 s−1 and an inlet concentration ????inlet=5 mol L−1.

a) Assuming the same average velocity in all cases, run the code at different values for the reactor tube radius (from 5 cm downwards). Record the conversion values in a table. Do these values change much if you use 5 or 19 internal grid points? Record those values as well. At what radius does the conversion exceed 80%?

b) This simulation assumes laminar flow, as verified in the notes. Is it reasonable to make this assumption at this higher concentration? Justify your answer with mathematical arguments.

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