Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Transport phenomena in biotechnological systems
Heat transfer

In bioreactors, the need to remove heat from or supply heat to the culture broth may arise for the following reasons.

1. It is desirable to sterilize the nutrient solution fed into the Reactor by heating it in a continuous or batch sterilizer. The sterilization Temperature must ensure the destruction of virtually all microorganisms within the total residence time (Section 9.9.4).

2. If The amount of heat generated during substrate Processing is insufficient to maintain the temperature at the target level, the reactor must be heated. This situation is typical, for example, of waste Treatment processes under anaerobic conditions, where the optimal temperature is 55–60 °C (Section 14.4.7).

8. During substrate conversion, an excess amount of heat (relative to the optimal conditions that ensure, for example, Cell viability) is released and must be removed. This situation is characteristic of most microbial processes.

4. The Need for additional heating also arises in cell suspension drying processes.

Here, we will consider the first three cases related to Organism viability. As for drying, this physical process is discussed in detail in most chemical engineering textbooks.

Heat transfer between the culture broth and another medium is structurally achieved in several ways, including external jackets, helical tube heat exchangers (coils) immersed in the culture broth, Circulation of the reaction mixture through heat exchangers, and evaporation or Condensation of Water and other volatile Components of the cell-containing liquid phase. Examples of heat transfer Methods are shown in Fig. 8.16. Heat transfer also clearly plays a role in maintaining temperature differences between thermally stratified natural water bodies and the soil; established zones with specific temperature ranges define corresponding biological niches for communities of living organisms. In this section, we will focus primarily on heat transfer in bioreactors.

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FIG. 8.16. Examples of heat transfer equipment and natural heat transfer processes: a — jacketed reactor; b — reactor with an internal coil; c — circulation of the reaction mixture through a heat exchanger; d — phase transitions; e — natural temperature fluctuations.

Assuming that the rates of transfer and change of Other forms of energy are negligible, the governing steady-state heat transfer equation will reflect the relationship between The rate of heat removal (via a heat exchanger) and the rate of heat generation. Therefore,

Here, ∆T is the characteristic temperature difference between the reactor contents and the cooling or heating fluid; A is the heat transfer surface area; h is the overall heat transfer coefficient.

As with mass transfer, the greatest resistance to heat transfer is offered by the relatively stagnant thin fluid boundary layer near the solid wall separating the hot and cold fluids, since the bulk liquid phase is usually effectively mixed and can therefore be considered approximately isothermal. In this section, we are primarily interested in deriving the overall Energy balance equations and reviewing the mathematical expressions that determine h for various heating, cooling, and sterilization systems of interest in microbial processes. Methods for estimating the heat load associated with Microbial growth have already been discussed in Chapter 5.

Table 8.6. Approximate values of heat transfer coefficients h^a

^a From: Gröber H., Erk S., Grigull U., Wärmeübertragung, 3rd ed., p. 158, Springer-Verlag, Berlin, 1955.

The high heat transfer coefficients (Table 8.6) of boiling water and condensing vapors (usually steam) make these heat transfer fluids particularly suitable for sterilization processes (Section 9.9.4). If lower temperatures are required (e.g., in heated anaerobic digesters), it is more convenient to use water below 100 °C. Viscous liquids typically exhibit higher resistance to heat transfer compared to water; as with mass transfer, this is due to the reduced rate of exchange between the bulk liquid phase and the boundary film near the wall, as well as the lower thermal conductivity of viscous liquids (analogous to the low diffusion coefficient of O₂).

Examination of the heat transfer principles illustrated in Fig. 8.16 highlights several heat transfer challenges in biochemical reactors. In systems with an external cooling or heating jacket, the heat transfer surface area A is proportional to the square of the reactor diameter (or impeller diameter) D_i². At the same time, if we want the rate of microbial processes and power consumption per unit volume to remain constant, the heating or cooling rate of the reactor must be proportional to D_i³. Therefore, jacketed vessels that provide isothermal conditions in laboratory experiments must often be replaced, upon scale-up, by reactors with internal or external heating coils (e.g., in anaerobic Digestion) or cooling coils (particularly in The conversion of Hydrocarbons to Single-Cell Protein).

Understandably, the presence of internal piping alters the mixing pattern, the fluid velocity profile, and potentially the rate of gas bubble coalescence. The complexity of this situation underscores the necessity of experimentally determining parameters only in reactors whose design closely matches that of the large-scale vessel; in microbial processes, a priori reactor design yields even more uncertain results than in simpler systems. (Mixing issues in reactors are covered in the text and exercises of Chapter 9.) In particular, the equations presented in Section 8.10.1 show that the heat transfer coefficient h [expressed in kcal/(m^2⋅h)] changes when moving from a single cooling coil perpendicular to the fluid flow to an arrangement of multiple staggered rows of coils, also perpendicular to the flow. Consequently, the first row of tubes alters the flow pattern over the subsequent rows.

For very large reactors with high heat loads (for example, during bacterial growth on methanol in a 1500 m³ reactor), internal coils can no longer provide the necessary heat removal. In such cases, one must resort to circulation through an external heat exchanger or an integrated heat exchanger within a loop reactor. This example demonstrates that high heat loads, combined with other factors (such as high power consumption for aeration and mixing), sometimes necessitate The Development of specialized bioreactor designs that differ significantly from conventional stirred tanks. Various reactor designs, mixing methods, and agitation principles will be briefly reviewed in Chapter 9.

It is well known that the rates of heat generation and removal allow for a sufficiently accurate estimation of the system's heat balance, provided we clearly understand the physical basis of the calculations and take into account the level of reliability they offer. In this section, we will discuss methods for estimating the heat transfer requirements of biotechnological systems (analogous to oxygen requirements); the next section will address the Determination of the heat transfer coefficient h.

Determining the heating or cooling requirements of a system begins with an overall energy balance. At constant pressure in a system with negligible changes in potential and kinetic energy, the energy balance can be calculated through enthalpy changes, including the heats of Chemical Reactions, phase transitions (evaporation, condensation), heat flows accompanying mass transfer, and heat transfer from a secondary fluid used for cooling or heating. Let us introduce the following notation:

Q_met — the rate of heat generation during cell growth and maintenance;

Q_ag — the rate of heat generation due to mechanical agitation of the reaction mixture;

Q_gas — the rate of heat generation resulting from aeration;

Q_acc — rate of heat accumulation;

Q_exch — rate of heat transfer to the reactor surroundings or to the heat transfer fluid of the heat exchanger;

Q_evap — rate of heat loss due to evaporation;

Q_sen — rate of enthalpy gain due to the difference in heat content between the reactor inlet and outlet streams.

Then

Q_met + Q_ag + Q_gas = Q_acc + Q_exch + Q_evap + Q_sen      (8.119)

Cooney, Wang, and Mateles [52] used this equation to calculate Q_met based on the experimental determination of Q_acc by monitoring temperature changes in a virtually isolated reactor. Under such conditions, The values of Q_evap and Q_sen are very small, and Q_exch makes a significant contribution compared to the difference Q_acc — Q_ag, although the latter parameters themselves are higher than Q_exch. As we have just noted, Q_acc was monitored calorimetrically, and Q_ag was calculated for each gas flow rate and impeller speed using the Michel and Miller equation [Equation (8.81)].

When calculating the steady-state operation of the reactor, Q_acc is assumed to be zero, although additional complications may arise here with programmed temperature changes required to achieve optimal yield in a batch process (Section 10.7). The parameter Q_ag for aerated or non-aerated systems is determined using the previously discussed equations for calculating the power consumed by the reactor.

If we neglect Q_evap (although this parameter can be significant in jet-flow reactors), and also do not yet consider Q_sen, then the only important parameter remaining is Q_met. Methods for estimating and determining the value of Q_met were discussed in Chapter 5. In the design of large-volume reactors, the specified operating temperature and flow parameters determine Q_evap and Q_sen, while the impeller speed and diameter determine Q_ag (adjusted for the selected aeration rate). The sparger design and gas flow rate determine Q_gas. As for the remaining parameters Q_acc and Q_exch, regardless of whether the reactor is under isothermal conditions or not, at any given moment

The latter equation determines the rate of heat transfer required to maintain a given temperature or a specific rate of heat accumulation (if any is required at all).

We can use Equation (7.35a), which describes the instantaneous rate of cell mass formation per unit volume of a batch reactor:

The corresponding instantaneous rate of heat generation in the microbial process, Q_met (heat/time), will obviously be defined by the equation

Here, Y_∆ is the yield coefficient (g Cells/kcal) discussed in Section 5.10.4. Methods for determining Y_∆ were also presented there, along with illustrative material showing an increase in metabolic heat evolution when utilizing more reduced substrates (Table 5.12).

The corresponding equation for an isothermal steady-state process in a continuous flow reactor is as follows:

As mentioned above, Y_x/s may depend on the culture age in a batch process and the dilution rate D in a continuous system. The dependence of Y_x/s (and consequently Y_∆) on the maintenance Energy Requirements is reflected in Equation (7.26).

Table 8.7. Dependence of single-cell protein production costs on The Nature of the substrate^a

^a Abbott B., Clamen A., The Relationship of Substrate, Growth Rate, and Maintenance Coefficient to SINGLE CELL PROTEIN Production, Biotech. Bioeng., 15, 117 (1973).

Economic calculations performed in 1973 by Abbott and Clamen show that in The production of bacterial biomass, the costs of both heat transfer and mass transfer (oxygen transfer) constitute a significant portion of the total product cost (Table 8.7) [43].