Question 1

(i) Consider a plug flow reactor for producing a biological product. The substrate consumption rate is described by equation (1),

d[S]/dt = V_m[S]/K_m + [S]                            (1)

where [S] is the substrate concentration, t is time, V_m and k_m are known rate constants.

Assuming that:

• the substrate concentration at the inlet [S]₀, the residence time of the plug (τ) and the yield coefficient of substrate consumption for product formation (Y_P/S) are all known,
• there is no product at the inlet of the reactor and
• all the substrate consumed is used to produce a product,
determine the product concentration at the outlet of the reactor [P] in terms of the parameters.

(ii) If the substrate consumption rate also depends on dissolved oxygen concentration, e.g.

d[S]/dt = (V_m[S]/K_m + [S] )C_O2,L^0.5                                      (2)

where C_O2,L is the dissolved oxygen concentration, aeration is used and the reaction takes place in a well-mixed stirred tank reactor, explain how the product concentration at the outlet of the reactor can be determined

(c) Consider a fed-batch reactor with a given volume (V) for producing biomass. Assuming exponential growth of cells μ = μ_max where μ_max is a constant, develop a general equation for biomass concentration x(t) in the reactor and find out at what time x() reaches the maximum.

The volumetric flow rate of the entering feed stream (F) can be assumed to be a constant and there is no biomass in the feed stream.

Question 2

(b) Consider a batch bioreactor to produce biomass with specific growth rate (μ) given by Monod kinetic equation (1):

μ = μ_max[S]/K_S + [S]                                                                   (1)

where μ_max and K_s are rate constants, and [S] is the substrate concentration. Suppose the yield coefficient of substrate consumption for biomass synthesis y_X/S, the initial substrate concentration [S]_o, and the initial biomass concentration x₀ are known, and all the substrate consumed is used to produce biomass, explain how the time taken for the substrate concentration to drop to zero (t_f) and the corresponding biomass concentration x can be determined.

(c) Consider diffusion of a substrate to a spherical and porous support material with a known radius R in which an enzymatic reaction takes place

Assume:
- The substrate concentration in bulk liquid [S]_b is known.
- The substrate diffuses through a thin liquid film surrounding the support material and the inner pores to reach the surface. Both the external mass transfer resistance and the internal mass transfer resistance are significant. The liquid-film mass transfer coefficient k_L and the pore diffusivity of the substrate D are known.

The substrate consumption rate inside the support material varies with substrate concentration [S], given by - d[S]/dt = V'_m[S]/K_m + [S] where t is time: and V'_m and K_m are known constants.

Describe how the overall substrate consumption rate at steady state can be determined.

Question 3

(b) A fermenter with a diameter of 1m and working volume of 0.8 m³ is equipped with a Rushton turbine. When the fermenter is used for an aerobic microbial fermentation, it is sparged with air at 0.1vvm. If the dissolved oxygen concentration needs to be maintained at 60% of the saturation value, determine the power input in order to meet the requiirement.

Data:
The volumetric mass transfer coefficient: k_La(s^-1): for the fermenter can be determined by k_La = 0.0018x(P_g/V_m)^0.7u^0.3

where P_g/V_m (W m^-3) is the power input per volume of medium under the gassed conditions and u₂ (m s^-1) is the superficial gas velocity.

The solubility of O₂ in the medium at the temperature of the fermentation is 0.26 mnnols L^-1.

The oxygen requirement of the respiring microbial fermentation is 80 mrnols of O₂L^-1h^-1.

(c) For a stirred tank bioreactor with a volume V, which is operated at steady state for production of biomass,

the cell growth kinetics are given by the Teisser equation,

μ = μ_m(1 - e^-[s]/k )

where μ is the specific growth rate, [S] is the substrate concentration, μm and k are rate constants.

(i). For sterile feed, show that the productivity for biomass production (Dxp) from the reactor is determined by

Dxp = DY_x/S {[SI_F + k ln(1 - D/μ_m)}

where D is the dilution rate, x_p is the biomass concentration in the outlet, Yx/S  is the yield coefficient of substrate consumption for biomass synthesis, and [S]_F is the substrate concentration in the inlet.

(ii). Explain how the productivity for biomass production of the reactor can be optimised (It is riot necessary to work through a numerical answer).

(d) Make a list of key issues which should be addressed by tissue engineering.