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Transient state analysis of biochemical reactor using coimmobilized system

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Abstract

The transient state analysis of the consecutive sequence of reactions S → P 1 → P 2 taking place inside a porous spherical coimmobilized biocatalyst is discussed for the case in which each step follows Michaelis Menten type kinetics. The theoretical analysis includes intraparticle diffusional limitations. The model equations are solved by the explicit finite difference method. The effect of various parameters of importance on the batch reactor performance is discussed. Comparison of the model with experimental results has been shown.

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Abbreviations

c p :

Dimensionless substrate concentration inside the particle, (s p/ss o)

c pi, j :

Dimensionless substrate concentration inside the particle at i, j

c s :

Dimensionless substrate concentration at the surface of the particle, (s s/s 0)

d p cm:

particle diameter

D s, D p cm2/s:

Diffusion coefficient of the substrate S and intermediate P 1 inside the particle respectively

h :

Space step size inside the particle

i :

Grid point inside the particle

j :

Grid point along the time coordinate

k :

Time step size

K m1, K m2 g/l:

Michaelis constants for the first and second reaction respectively

K I1,K I2 g/l:

Substrate inhibition parameters for first and second reaction respectively

P m g/l:

Product inhibition parameter for the second reaction

P 1p , P 1s g/l:

Concentration of the intermediate inside the particle and at the surface of the particle respectively

P 2p , P 2s g/l:

Concentration of the product P 2 inside the particle and at the surface of the particle respectively

p 1p :

Dimensionless intermediate concentration inside the particle, (p 1p/s0)

p 1s :

Dimensionless intermediate concentration at the surface of the particle, (p 1s /S 0)

P 2p :

Dimensionless product concentration inside the particle, (p 2p /S0)

p 2s :

Dimensionless product concentration at the surface of the particle, (p 2s/S0)

p 1pi, j :

Dimensionless intermediate concentration inside the particle at i, j

P 2pi, j :

Dimensionless product concentration inside the particle at i, j

q :

Ratio of diffusion coefficients, D p/D s

r cm:

Radial position inside the particle

R cm:

Radius of the pellet

S 0 g/l:

Initial substrate concentration in the bulk liquid

S p g/l:

Substrate concentration inside the particle

S s g/l:

Substrate concentration at the surface of the particle

t s:

Time,

V max1 g/(ls):

Maximum reaction velocity for the first reaction

V max2 g/(ls):

Maximum reaction velocity for the second reaction

y :

Dimensionless radial distance, (r/R)

y 1, j :

Dimensionless radial distance at i, j

г1 :

Parameter, S 0/K m1

г2 :

Parameter, S 0/K m2

г I1 :

Parameter, S 0/K I1

г I2 :

Parameter, S 0/K I2

г I3 :

Parameter, S 0/P m

τ :

Dimensionless time defined as (D s t/R 2)

φ 21 :

V max1R 2/Km1Ds

φ 22 :

V max2R 2/Km2Ds

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology, 600036, Madras, India

    N. Chithra & A. Baradarajan

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  1. N. Chithra
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  2. A. Baradarajan
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Chithra, N., Baradarajan, A. Transient state analysis of biochemical reactor using coimmobilized system. Bioprocess Engineering 10, 83–89 (1994). https://doi.org/10.1007/BF00393390

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