1 your biotech company is interested in manufacturing catalyst particl
1. Your Biotech Company is interested in manufacturing catalyst particles to be used
(suspended) in a stirred tank reactor. The manufacturing process will generate porous,
cylindrically shaped particles (i.e. with a characteristic height - h, and radius-R) - which will allow
for diffusion only through the end caps (i.e. axial, NOT radial diffusion). A local pharmaceutical
company requests that you immobilize an enzyme that they use in the production of an antibiotic
onto the internal surface (i.e. within the pores) of the cylindrical catalyst particles. When these
catalyst particles are created, it is determined that standard Michaelis. Mention kinetics are
V (mol/m² s) = Vm"[S] / Km + [S]
Vm" = 1 mol/m² min, defined per unit of catalyst surface area
Km = 10 mol/l.
The catalyst particle having a density of 1.4 g/ml and 2.0 m² of internal surface area per gram of
catalyst particle. The concentration of substrate in the antibiotic production process is 0.25 mol/l. The
effective diffusivity of the substrate in the interior of the catalysts is 1 x 10-⁹ m²/s. There is no enzyme
bound to the exterior of the particle. The radius of the particles is 8mm. The conditions in the stirred
tank are such that the bulk substrate concentration is equal to the substrate concentration at the
entrance to the pores (i.e. no external mass transfer resistance), and is constant over time (i.e. CSTR).
a.) Develop a differential equation that represents the conservation of substrate inside the
catalyst particle. List the boundary conditions.
b.) Make this differential equation dimensionless, and identify the Thiele modulus (and the
parameters, such as De, that make it up).
c.) Solve the dimensionless differential equation, obtaining the concentration profile of substrate
versus position inside the catalyst particle. Apply the boundary conditions to obtain the specific
d.) Determine the relationship between the effectiveness factor and the Thiele modulus for this
cylindrical catalyst particle, and plot this relationship.
e.) Recommend the maximum particle length to use for the antibiotic production process, that
ensures that the reaction is not significantly (i.e. less than 5% reduction from the max possible
reaction rate) reduced by diffusional limitations inside the particle.
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