Transient state analysis of biochemical reactor using coimmobilized system

The transient state analysis of the consecutive sequence of reactions S P₁ P₂ 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.List of Symbols 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/s₀) - d_p cm particle diameter - D_s, D_p cm²/s Diffusion coefficient of the substrate S and intermediate P₁ 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 P₂ 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/S₀) - 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 - S₀ 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, jGreek Letters ₁ Parameter, S₀/K_m1 - ₂ Parameter, S₀/K_m2 - _I1 Parameter, S₀/K_I1 - _I2 Parameter, S₀/K_I2 - _I3 Parameter, S₀/P_m - Dimensionless time defined as (D_st/R²) - ₁² V_max1R ²/K_m1D_s - ₂² V_max2R ²/K_m2D_s