Scale-Up of Bioprocesses

Abstract

The previous chapters in this book have dealt with stoichiometric, thermodynamic and kinetic analysis of bioreactions, as well as the operation of small-scale, “ideal,” bioreactors. These subjects constitute the basis for exploitation of microorganisms in fermentation processes. The ultimate goal for process development is, however, the realization of large-scale commercial production. The basis for a successful scale-up is to follow the advice of H. Baekeland, the inventor of Bakelite: “Commit your blunders on a small scale and make your profits on a large scale.” This is, however, not always easy. Many different engineering tools need to be applied (Leib et al. 2001), and the final scaled-up process will necessarily be a delicate compromise between inherently conflicting desirable options. Furthermore, even if the best engineering judgment is used, there are sometimes surprises in the final process which were difficult to anticipate from the lab-scale experiments.

Problems

Problem 11.1 Scale-up without maintaining geometrical similarity

In Example 11.9 and 11.10, linear scale-up of a stirred tank bioreactor from 600 L to 60 m³ was considered. It was found that the mixing time increased by a factor of ≈3. Suppose now instead that the impeller diameter of the 60 m³ reactor is chosen to 1.4 m (i.e., the reactor geometry is changed), but the requirement of a constant P/V (113 W m⁻³) is maintained.

• (a) How much larger is the mixing time in the large-scale bioreactor now?

• (b) Determine the value of N that would give the same t _mix as in Example 11.9 with [P/V, d _s] = [113 Wm⁻³, 1.4 m].

• (c) Would the choice of [N, P/V, d _s] in (b) increase or decrease the risk of flooding?

• (d) At a certain t _mix, and for n RJH with nozzle diameter d you have calculated a power input P/V and a corresponding liquid flow v ⁰_l for V = V ⁰. Show that for the same P/V, but at a different medium volume V ¹ the liquid flow must be v ¹_l = v ⁰_l (V ¹/V ⁰)^1/3. Use the data from Example 11.9 to calculate v _l for V ¹ = 3.4 m³ based on v _l = 199.2 m³ h⁻¹ that was obtained for V ⁰ = 60 m³.

Problem 11.2 Exchanging impellers

One drawback of the traditional Rushton impeller is that the ratio between aerated and unaerated power consumption falls rapidly with an increased aeration rate. The hydrofoil impeller typically has a lower power number, but the aerated power consumption falls less rapidly with increasing aeration rate. For a Rushton turbine and a Prochem impeller, and for stirring speeds close to 300 rpm, the ratio between aerated and unaerated power consumption is given in the figure shown below.

You are replacing a Rushton turbine in a 100 m³ reactor (T = 3 m, d _s = 1 m) by a Prochem impeller. Assume that the stirring rate should be maintained the same.

• (a) What diameter of the Prochem impeller will give the same unaerated power consumption as the Rushton turbine? The values of N _p for the Rushton turbine and the Prochem impeller are 5.2 and 1.5, respectively.

• (b) How much higher (approximately) will the k _l a value be for the Prochem impeller at an aeration rate of 0.5 vvm under the conditions in (a), (i.e., the same unaerated power consumption is achieved)? The k _l a value for the same specific power input has been found to be identical for the two impeller types. Assume a non-coalescing medium.

Problem 11.3 Design of a pilot plant bioreactor

In connection with the purchase of a new pilot plant bioreactor (41 L) to be used for penicillin fermentation, it is desired to examine whether one of the manufacturer’s standard-design bioreactors (equipped with Rushton turbines) can be used. The dimensions of this bioreactor are specified in the table below.

Aspect ratio (T/d s)	3
Tank diameter (T)	0.267 m
Stirrer diameter (d s)	0.089 m
Number of impellersa	3
Maximum stirring speed (N max)	600 rpm

1. ^aThe impellers are six-bladed Rushton turbines.

• (a) Show that with a non-Newtonian medium, for which the rheology is described by a power law expression (11.26), Re_s is given by (1)

  $$ {{\rm Re}_{\rm{s}}} = \frac{{{\rho_{\rm{l}}}{N^{{2 - n}}}d_{\rm{s}}^{{2}}}}{{K{k^{{n - 1}}}}}, $$

  (1)

  where k = 10 is the constant used for calculation of the average shear rate in (11.32). For a medium containing, respectively, 0, 20, and 40 g L⁻¹ biomass (of the fungus P. chrysogenum) you are required to plot Re_s vs. the stirring speed.

  Discuss the results.

• (b) Determine the power number with N = 600 rpm for the three cases considered in (a), and calculate the power input per unit volume when the bioreactor contains 25 L of medium. Calculate the average viscosity in the bioreactor.

• (c) For non-Newtonian media and the 41 L bioreactor, the following correlation was found:

  $$ {k_{\rm{l}}}a = 0.226 \times {10^{{ - 3}}}u_{\rm{s}}^{{0.4}}{\left( {\frac{{{P_{\rm{g}}}}}{V}} \right)^{{0.6}}}{\eta^{{ - 0.7}}}. $$

  (2)

  Can the dissolved oxygen concentration in the reactor be maintained above 30% (which for some strains is a critical level for penicillin production) when the oxygen requirement for a rapidly growing culture of P. chrysogenum is r _o = 2.3 mmol of O₂ (g DW)⁻¹ h⁻¹ Discuss how the bioreactor can be modified to satisfy the oxygen requirement.

• (d) You decide to examine the effect of increasing the stirrer diameter. Start with d _s /T = 0.4. Can the critical level of dissolved oxygen concentration be maintained with this diameter ratio?

Problem 11.4 Scaled-down experiment

The pH value is often controlled using only a single pH electrode and a single point of addition of base or acid, also in large-scale bioreactors. The pH electrode is typically located in a well-mixed region, and addition of base or acid is typically made at the liquid surface. Since concentrated solutions are used, pH gradients in large-scale reactors are likely to be present.

Amanullah et al. (2001) used of a scaled-down system to study effects of pH gradients. The scaled-down system consisted of a 2 L standard stirred tank reactor, with a working volume of 1 L, equipped with two Rushton turbines (d _s /d _t = 0.33). To the reactor was connected a piece of tubing (L = 2.75 m, d _i = 4.8 mm), through which liquid from the reactor was pumped. The pH value in the reactor was measured, and pH control was achieved by adding base to a small mixing bulb (volume about 1.5 ml) located just before the tubing (see figure below).

This system was used to experimentally simulate a three compartment reactor model, with a direct feed zone (bulb), a poorly mixed zone (tubing part), and a well-mixed zone (the reactor).

• (a) Discuss what residence time in the tubing that should be chosen to simulate a large-scale reactor (100 m³). The same residence time in the tube can be achieved by different ratios of tube volume, V _tube and recirculation flow, v _rec. Discuss how the values of V _tube and v _rec should be chosen.

  In their study, Amanullah et al. (2001) used a strain of Bacillus subtilis. This organism produces acetoin and 2,3 butanediol under oxygen-limited conditions. The formation of acetoin and butanediol is described by:

  $$ {\hbox{2 pyruvate}} \to {\hbox{C}}{{\hbox{O}}_{{2}}} + {\hbox{ acetolactate}} \to \left( {\hbox{acetolactate synthase}} \right) $$
  $$ {\hbox{Acetolactate}} \to {\hbox{C}}{{\hbox{O}}_{{2}}} + {\hbox{ Acetoin}} \to \left( {\hbox{acetolactate decarboxylase}} \right) $$
  $$ {\hbox{Acetoin }} + {\hbox{ NADH }} + { }{{\hbox{H}}^{ + }} \leftrightarrow {2},{\hbox{ 3 butane-diol}} \to \left( {\hbox{butanediol dehydrogenase}} \right) $$

  At pH values higher than 6.5 also acetate is formed.

• (b) Compare the residence time in the tube to the characteristic times for oxygen consumption and substrate consumption. Assume that the dissolved oxygen concentration in the reactor is 10% of DOT, and that the system is to be operated as a chemostat with a glucose concentration = 10 mg L⁻¹ and a biomass concentration of 4 g L⁻¹.

  What are your conclusions?

• (c) The experiments by Amanullah et al. were in fact made as batch cultivations, with oxygen-limited conditions also in the stirred tank reactor. A control experiment, in which base addition was made in the reactor instead of in the loop was also made. The following yields were found

  Residence time in loop (s)	Yield of acetic acid (g g−1)	Sum of yields of acetoin and butanediol (g g−1)	Biomass yield (g g−1)
  (no loop)	0	0.30	0.49
  30	0.002	0.31	0.52
  60	0.023	0.29	0.51
  120	0.076	0.23	0.50
  240	0.083	0.22	0.50
  120a	0	0.30	0.50

  1. ^apH control made in the stirred tank reactor instead of in the loop

  Discuss the results.

Problem 11.5 Calculation of the true v _l and the true power input for Rotating Jet Heads

In Example 11.10 the mass transfer coefficient k _l a was calculated from (4), assuming that for a given Δp, v _l was given by (11.37) and (11.35).

When the medium is aerated with v _g /v _l = n _t then, for a given Δp one must use (11.36) to calculate v _l rather than (11.35) which is derived for unaerated medium. v _l will be smaller than when calculated from (11.35), and consequently P will be smaller when calculated from (11.35). Since the power input is smaller the value of k _l a will be smaller for the given Δp.

The present problem will calculate the true value of v _l and the ratio between the “true” P and P = P ₀ calculated from (11.35). This will give us an analogue to N _p,g/N _p of Fig. 11.5.

• (a) For a fixed p _t = 1.04 and a fixed Δp = 1.23 bar, v _l = 199.2 m³ h⁻¹ (the result for v _l in Example 10.9 for t _mix = 29 s, when the correction factor in (11.36) is not included). But n _t = 10/199.2 = 0.0502, and when [n _t, p _t, Δp] = [0.0502, 1.04, 1.23] the correction factor is slightly smaller than 1, and v _l < 199.2 m³ h⁻¹.

  For different values of n _t $\subset$(0,1) calculate the true v _l by iteration of (11.36) – at most two iterations is enough to obtain convergence. Start with n _t = 0.0502, but use also other values of v _g at Δp = 1.23 bar to cover at least part of the interval 0 < n _t < 1.

  Calculate P for the series of v _g values used, and thereafter P/P(v _l = 199.2 m³ h⁻¹).

  How do these results influence k _l a for increasing v _g?

• (b) The results in (a) can be plotted in the same fashion as on Fig. 11.5.

  What is a reasonable variable to plot on the abscissa?

  Make your own conclusions concerning an analogue for N _A in the RJH-mixer.