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This chapter deals with fermentation processes, converting low cost renewable feedstocks into valuable bio-products, with the help of microorganisms or mammalian cells in bioreactors or fermenters. In industrial vessels, the volumetric conversion rate, i.e. the fermentation intensity, is limited by a transport step: mass transfer, liquid mixing or cooling. In special processes where the growth of the cells is marginal, intensification is possible by active cell retention. A comparison with chemical process intensification reveals that the same four main principles are valid, i.e. (1) maximize the rate at optimal selectivity, (2) minimize the impact of substrate concentration gradients, shear rate gradients and other local differences, (3) relieve the transport limitations and (4) arrange smart integration of operation steps of which cell retention is the most important. In essence, optimized microorganisms in fermentations can be viewed as efficient, smartly integrated cell factories. The main principles are illustrated with four intensification examples, showing that debottlenecking of the oxygen transfer capacity is most important, followed by liquid mixing. The limits of fermentation intensity have been estimated for fed-batch fermentations supplied with air or pure oxygen and point at significant optimization space. In contrast, aerobic continuous fermentation is expected to remain difficult due to fundamental restrictions.

In recent years, process intensification (PI) has been coined as a game-changing concept within the chemical engineering field.1  Innovative processing equipment, techniques and methods hold the promise to transform chemical plants into more sustainable processing concepts that are compact, safe, environment-friendly and energy-efficient. This is thought to be essential to enable a transition, or rejuvenation, of the chemical engineering field and make it more fit for addressing global issues, with less incremental and with more radical, impactful solutions. Key topics are micro reactors, innovative gas/liquid/solid (G/L/S) contactors, integration of reaction and separation steps, and the use of alternative power input methods such as ultrasound or microwave radiation. Focus has mostly been on dramatic improvements, such as a reduction in equipment size of a factor 100 or more, or combination of at least five unit operations into one, and there are various examples that indeed illustrate such intensification potential.2  The problem of the PI field resides in a somewhat fuzzy definition – sometimes the goal is a reduction of the size and physical footprint of plants, in other cases only the engineering is in scope and not the chemistry that delivers the reaction concept and catalyst, while others claim all sorts of process improvements to be contributing to PI. Attempts have been made to define PI more sharply in terms of the underlying basic principles, of which four are dominant:3 

  • Time – Improve kinetics: maximize the speed and effectiveness of molecular events.

  • Space – Maximize homogeneity: create identical conditions for each molecule.

  • Thermodynamics – Relieve transport limitations: such as maximize thermodynamic driving forces and transfer area.

  • Synergy – Arrange smart integration: maximize the synergy between the separate parts.

Each principle covers the relevant domains of time, structure (space), energy (thermodynamics) and synergy (combining functions), and is applied across three length scales: the microscale (molecules, microorganisms), the mesoscale (bubbles, particles, films, flow patterns) and the macroscale (operations, plant, site), see Figure 1.1.

Figure 1.1

Four main principles for PI, linked to four main approaches, applied in a multi-scale framework. Adapted from ref. 3.

Figure 1.1

Four main principles for PI, linked to four main approaches, applied in a multi-scale framework. Adapted from ref. 3.

Close modal

It is often stated that application of PI principles to bioprocesses will be possible using the same, or at least similar, tools. The purpose of this chapter is to investigate this premise and clarify the opportunities and limitations of the PI approach to bioprocesses, especially the bioreaction engineering operation known as fermentation that is core to the transformation of renewable feedstocks into bio-based products.

As a first check, the hit frequency on internet search machines of the term “fermentation intensification” is only 1/500 of the term “process intensification”. The more general term “bioprocess intensification” is more common, but still only 1/100. In this chapter, the significance of this observation will be explored.

Fermentation processes are commonly defined as operations in which bacteria, yeasts and fungi are employed. There are similar processes in which other types of cells are used, such as mammalian cells for the production of biopharmaceuticals (immunoglobulins, monoclonal antibodies, etc.), and these will get attention in the current analysis as well. Phototrophic organisms (microalgae, cyanobacteria) represent another fermentation category. These organisms convert carbon dioxide with the help of light into valuable products. Although the same PI principles apply, this group is left out of the scope.

A final category that will be only briefly mentioned is waste-water treatment. There, the properties of cell populations to form granules4  have been exploited to maximize the concentration of active biomass in continuous processes for waste-water treatment.5  This has, in recent years, resulted in PI (in e.g. the Nereda process and the Circox process) of more than a factor 10 compared to traditional installations, allowing large reductions in the size of modern installations for domestic (Nereda) and industrial (Circox) waste-water treatment.

Traditionally, fermentation processes have utilized the general property of microorganisms to convert renewable feedstocks into naturally occurring products, such as ethanol, organic acids (citric, lactic, succinic, itaconic, etc.), amino acids (lysine, glutamic acid and threonine) and antibiotics (penicillins, cephalosporins, polyketides, etc.). Employing classical strain improvement techniques, the performance of fermentation processes has been steadily improved over the years, sometimes by several orders of magnitude. Later on, along with the advent of recombinant DNA techniques, both the range of products and the process performance have been tremendously increased, e.g. for amino acids, organic acids, heterologous enzymes, lipids and also including non-natural compounds such as tailored antibiotics (adipoyl-7-ADCA6 ), therapeutic drugs (e.g. pravastatin7 ) and monomers for plastics (e.g. caprolactam,8  adipic acid,8  1,3-propanediol (PDO),9  1,4-butanediol (BDO)10 ). Application of engineering tools has helped to scale-up to commercial scale, with intensive gas–liquid and sometimes solid contacting, optimal control of the environment of the microorganisms (temperature, pH, controlled supply of a growth-limiting substrate, sufficiently high nutrient concentrations, sufficiently low inhibitory compound concentrations) and with adequate design of the process system (operations and utilities). However, there is still significant room for improvement because, in most industrial fermentations, the product titers, rates (productivities) and yields (TRY) are still far from theoretically possible values.

Industrial fermenters have evolved over more than a century for many different applications in parallel, and there is little standardization – fermenters come in different sizes and geometries. The main workhorses for processes in which oxygen (or another gas) needs to be supplied are the stirred tank reactor (STR) and the (unstirred) bubble column (BC), while a third type is the air-lift loop reactor (ALR). Typical sizes for commercial application are between 50 and 1000 m3 and, in factories, a series of parallel units is usually installed (often 4–10). Stirred tanks are more versatile than unstirred tanks, but are also more expensive and require more maintenance because of the moving parts. In some fermentations, next to the suspended microorganisms that form a separate solid biotic phase, other solids can be present that must be kept fluidized or suspended and may follow the flow. These solids could be immobilized or agglomerated cells/biofilms, or non-soluble feedstocks or products. In anaerobic fermentations, microorganisms thrive in the absence of oxygen, and this can be adequately accomplished in very simple and large (larger than 1000 m3) fermenters, e.g. for the manufacturing of beer, lactic acid and ethanol. The CO2 gas produced then causes mixing. A separate category comprises trickle-bed fermentations, with microorganisms contained in a bed with a structured packing (e.g. wood shavings), as applied for production of citric and acetic acid, special antibiotics and in waste-water treatment, respectively. Related to this, in solid-state fermentation, the organisms grow on a solid substrate. This is mostly used in traditional food processing. Finally, in waste-water treatment, bioreactors are used that use biofilms, immobilized on inert carriers such as sand, in a fluid bed.

Positioning the fermenter types on a scale that describes the degree of backmixing is insightful. Stirred tanks typically have the highest degree of G/L/S mixing and packed bed reactors the lowest (see Figure 1.2).

Figure 1.2

Various fermentation vessels, with indication of the governing G/L/S flow. Most important are the stirred tank reactor, STR, the bubble column, BC, and the airlift loop reactor, ALR.

Figure 1.2

Various fermentation vessels, with indication of the governing G/L/S flow. Most important are the stirred tank reactor, STR, the bubble column, BC, and the airlift loop reactor, ALR.

Close modal

Four other types of auxiliary equipment are flanking the main fermenter in a plant or biorefinery, i.e. the seed train, the utilities, equipment for cell separation and buffer/feed tanks (Figure 1.3). The seed train is usually a sequence of vessels that go up in size in steps of a factor 10, to propagate the initial amount of cells from a working cell bank into an inoculum for the main fermenter. Utilities involve equipment for sterilization (e.g. in line heat shocks, or steam), a compressor for air (or other gas) supply, a motor for driving the agitator and a system for pumping cooling water through coils or a jacket in contact with the fermentation broth. The separation of the cells from the rest of the fermentation broth can be accomplished with membranes or centrifuges. Finally, supply of feed solutions, titrants, anti-foam agent and nitrogen sources, as well as storage of broth between fermentation and the purification line, requires a series of separate vessels, which all need to be cleanable, sterilizable and require controlled filling, mixing and discharge into the bioreactor or downstream processing unit.

Figure 1.3

Main fermenter with four groups of auxiliary equipment.

Figure 1.3

Main fermenter with four groups of auxiliary equipment.

Close modal

A fermentation process is governed by the microbial conversion kinetics and the stoichiometry of the process reaction on one side and fermenter transport phenomena on the other side.

The stoichiometry determines the molar ratios of the various compounds that take part in the reaction. The main goal is to produce the desired product in as high a yield as possible from the substrate, while at the same time, the substrate is needed as a carbon source for growth of the microorganisms. In addition, substrate must be catabolized to provide energy to drive biomass synthesis, product formation and cell maintenance. The first two metabolic sub-reactions, for product and biomass, seldom consume oxygen directly but need biological energy. This energy is most efficiently generated in aerobic, oxygen consuming catabolism that gives maximal oxidation of the carbon source to CO2. The product sub-reaction is the most important as it gives the theoretical limit for the yield (selectivity), molp/mols, and the fate of other essential molecules. For example, the conversion of glucose to ethanol inevitably produces CO2, and the same applies to PDO. However, the formation of succinic acid (SA) consumes CO2 and produces water, and the formation of BDO again produces both CO2 and water; see Table 1.1.

Table 1.1

Examples of theoretical product reactions (for 1 mol product) of glucose into bio-products and theoretical maximum product yields

Bio-productProduct reaction (1 mole produced with glucose as feedstock)Theoretical stoichiometry/molp mols−1
Ethanol 1/2C6H12O6 → 1C2H6O + 1CO2 
1,3-Propanediol 2/3C6H12O6 → 1C3H8O2 + 1CO2 1.5 
Succinic acid 7/12C6H12O6 + 0.5CO2 → 1C4H6O4 + 0.5H212/7 = 1.71 
1,4-Butanediol 11/12C6H12O6 → 1C4H10O2 + 1.5CO2 + 0.5H212/11 = 1.09 
Bio-productProduct reaction (1 mole produced with glucose as feedstock)Theoretical stoichiometry/molp mols−1
Ethanol 1/2C6H12O6 → 1C2H6O + 1CO2 
1,3-Propanediol 2/3C6H12O6 → 1C3H8O2 + 1CO2 1.5 
Succinic acid 7/12C6H12O6 + 0.5CO2 → 1C4H6O4 + 0.5H212/7 = 1.71 
1,4-Butanediol 11/12C6H12O6 → 1C4H10O2 + 1.5CO2 + 0.5H212/11 = 1.09 

When the product sub-reaction, the biomass sub-reaction and the cell maintenance reaction are properly accounted for, then the process reaction for 1 mole product would read, for example (for BDO, with formation of biomass (CH1.8O0.5N0.2), µ = 0.012 h−1, qp = 0.020 molp (molxh)−1, see ref. 11):

Equation 1.1

in which the actual product yield on glucose, Yps, is 0.69 molp mols−1, significantly lower than the theoretical maximum of 1.09 molp mols−1 (Table 1.1), because of growth (0.60 molx molp−1) and oxygen consumption for energy generation (2.54 molo molp−1). Note that the stoichiometry of a process reaction depends on the specific growth rate, µ, and the specific product formation rate, qp, which determine the weighting factors in the linear combination of the biomass reaction (µ/qp), the product reaction (1) and the maintenance reaction (ms/qp).

The kinetics are a specific property of the cells under study and can vary a lot depending on the organism and the conditions (pH, temperature, concentrations). The number of independent conversion rates is governed by a degree of freedom analysis.12  For aerobic, black box systems (i.e. not using any information from thermodynamics or ATP-metabolism) without major by-products, the number of degrees of freedom is usually three (µ, qp, ms). Assuming a process reaction with one nitrogen source, one product and no by-products, there are eight compounds: substrate, N-source, oxygen, biomass, product, protons (H+), CO2 and water, which usually consist of four different elements. The eight conversion rates are then constrained by five conservation relations, i.e. for C, H, O, N and electrical charge, which leaves three independent rates. The first Law of Thermodynamics provides the rate of heat formation, as a dependent outcome, but three independent rates still remain. Adding information from energy (Gibbs free energy or ATP) metabolism gives one extra relationship, e.g. the Herbert–Pirt relation linking the substrate consumption rate to the biomass and product formation rates, and the maintenance rate.13  A final constraint comes from the organism, which is the qp(µ) relation, a kinetic relation between qp and µ under single nutrient limited conditions. In conclusion, for aerobic systems, there is usually 3 − 2 = 1 degree of freedom left, i.e. one specific reaction rate, such as the specific growth rate, µ, must be specified and then all the other rates are dependent. In that case, the process reaction (with stoichiometric coefficients qi/qp) has a fixed stoichiometry at a constant µ. For anaerobic systems, the qp(µ) relation follows from the energy metabolism. Again, there is only one free rate left.14  At the given µ, all biomass specific reaction rates are therefore directly coupled to the process reaction, for 1 mole product. The coefficients in this reaction read as qi/qp ratios.

The stoichiometry given in eqn (1.1) is expected to improve by targeted improvements in the rate of product formation and the metabolic efficiency, resulting in lower glucose and oxygen requirements and lower CO2 and heat production. This is depicted in Figure 1.4, illustrating that kinetic/stoichiometric improvement and relief of transport limitations go hand in hand.

Figure 1.4

Plots of the relative rates of glucose consumption, heat formation and CO2 production as a function of oxygen consumption. The rates are all normalized with respect to BDO formation. The ratio of biomass and BDO formation is kept the same as in eqn (1.1).

Figure 1.4

Plots of the relative rates of glucose consumption, heat formation and CO2 production as a function of oxygen consumption. The rates are all normalized with respect to BDO formation. The ratio of biomass and BDO formation is kept the same as in eqn (1.1).

Close modal

Fermentations can be run in different modes. The batch mode, where all nutrients are present in excess from the start, is simple but, in many cases, maximizes the cell growth and not the formation of the desired product. Further, it does not utilize the invested utilities (oxygen transfer, heat removal, mixing, carbon dioxide removal) in an efficient way: the maximal mass and heat transfer rates and mixing are used only at the end of a batch. Therefore, fed-batch processes have been developed, which can maximize the formation of product by controlling the specific growth rate at an optimal level and operate with maximal use of the invested utilities for a large part of the time.

A plant normally operates around 8000 hours per year; the remaining 640 hours are for maintenance and other planned stops. Of these 8000 hours, only a part is used for the main goal of the fermentation: produce product at optimal rate and efficiency, using the maximal capacity of invested utilities (compressor, stirrer motor, cooling equipment, etc.).

In batch and fed-batch processes, there are three periods during which the fermenter does not use the utilities to the max:

  1. Preparation of a new batch, including sterilization and filling.

  2. Start-up of a new batch, with a period first to grow enough biomass before entering the stage of high productivity.

  3. End-of-fermentation, with emptying and cleaning the vessel, and sometimes scheduling constraints, resulting in extra waiting time.

The objective is to minimize the duration of these three phases, but they cannot be completely avoided in batch and fed-batch processes. Only in continuous operation is it possible to most efficiently use the utilities. However, continuous operation in aerobic processes is still far from reality, due to metabolic instabilities (degeneration), especially associated with product reactions that consume metabolic energy, as well as increasing risks of technical failures (e.g. sensors) and microbial contamination in prolonged cultures.15  For anaerobic processes, where the product pathway delivers the biological energy, degeneration does not occur and continuous processing is feasible (see example 1.6.1).

In large-scale industrial fermenters, operated in fed-batch mode, the maximum production rate is not determined by the organisms but is fully determined by a limiting fermenter transport process. This determines the production rate, or process intensity. For the majority of aerobic fermentation processes, the limiting step is either (1) mass transfer, i.e. oxygen supply or carbon dioxide removal, (2) heat transfer (cooling, or on rare occasions, heating) or (3) liquid mixing (to distribute added compounds from the inlet point to the full reactor space). For anaerobic processes, the electrons from the substrate finally end up in the main product, leaving little metabolic energy for microbial growth, and therefore, the amount of cells usually limits the production rate and mixing plays a minor role. Special groups are the syngas fermentations, where gaseous electron donors such as CO or H2 are supplied to produce ethanol and other compounds. Although in principle anaerobic, there is also mass transfer and, for large reactors, mixing will be mostly limiting because of very low solubility of the gaseous substrates. Further, these gas-to-liquid processes result in a significant heat production due to entropy decrease, which can limit this anaerobic process.

We are interested in high transport rates, and therefore, transport is usually convective or by transfer between two phases. Convective transport of e.g. gas is limited by the bubble rise velocity, which means that the broth mass-specific gas flow decreases with increasing vessel size. Convective liquid flow inside the vessel (mixing) depends on energy input, geometry and scale. Transfer rates can be described by three terms: transfer coefficient, transfer area and driving force, which are all a function of scale, geometry and power input. A basic understanding of each of these is governed by knowledge of the G/L flow patterns, or hydrodynamics. This shows that there are various flow regimes (e.g. homogeneous–heterogeneous flow in BCs, impeller flooding-loading in stirred tanks, gas recirculation regimes in loop reactors), and notice should be taken that flow regimes depend on scale and have an impact on transport rates.

In anaerobic processes, as well as in aerobic processes optimized for product yield, or in processes with slow growing organisms such as mammalian cells, the maximal growth rate and biomass yield are low. In combination with dilution (fed-batch) or wash-out (continuous), the biomass concentration is then also low. Further, because there is little or no demand for oxygen and heat evolution is minimal, a transport limitation may well be absent. A well-known limit is the (by)product toxicity (e.g. ammonia, lactate in mammalian cell cultures). To keep the inhibiting concentrations low, this requires the removal of liquid without the biomass.

A solution to both problems can be obtained by implementing cell retention or cell recycle systems. Keeping the cells in the reactor while feeding fresh substrate and removing cell-free liquid with the toxic (by)products will then steeply increase the biomass concentration, resulting in a much smaller fermenter.

From this short overview on fermentation process fundamentals, it follows that PI of fermentation requires increased fermenter transport rates, sometimes biomass retention and continuous processing, if feasible in practice. In the following sections, the most important hydrodynamic factors will be explained in detail, based on the fact that transport is governed by three main factors – energy input, geometry and scale – and there are hydrodynamic flow regimes where the rates of the transport steps can be different.

We will only consider systems that display a low dynamic viscosity, i.e. less than about 100 mPa.s. If the viscosity gets higher, usually in combination with non-Newtonian rheology, then the transport rates will be progressively reduced. This viscosity restriction is outside the scope of the current chapter and is extensively elaborated e.g. by ref. 16. In PI terms, the objective should be to produce the desired bioproduct with non-filamentous microorganisms at cell concentrations that will not exceed 150 kg m−3 of cell dry mass, which will keep the viscosity well below 100 mPa.s.

This category comprises gassed BCs, gas-producing anaerobic vessels and gas/air-lift fermenters.

The flow of gas implies the input of power, via broth displacement by the gas, which increases the potential energy. A common scaled quantity to express the gas flow rate, FV, is the superficial velocity vGs = FV/A. Because the (hydrostatic) pressure changes as a function of height, both the gas volume flow rate and superficial gas velocity change with height, and the actual injection vGs or FV at the bottom is considerably lower than the value at the top (depending on headspace pressure). This can be accommodated by a pressure correction of the superficial gas velocity. Then, the pneumatic power input, PG, is directly related to the (pressure corrected) superficial gas velocity, vGsc, which is linear in the mass specific power input. This quantity, being the only input variable in BCs, is always used in (cor)relations to describe phenomena in pneumatically-driven systems. Because of this equivalence, it will be impossible to discern if a phenomenon (such as gas hold-up) is mechanistically related to vGsc or power input per broth mass (eG).

As a result, the gassed power input equals

Equation 1.2

which is equivalent to a mass-specific power input

Equation 1.3

Assume a large cylindrical vessel with an ideal sparger, where bubbles are generated homogeneously at the bottom of the vessel at their equilibrium diameter in clean water, i.e. 4–6 mm. At low gas flow rates and sufficient distance between the sparger holes, these bubbles will develop and rise with a velocity similar to single bubbles in stagnant liquid, i.e. at about 0.25 m s−1, without mutual interaction. The result is a homogeneous distribution of bubbles. The rising bubbles will displace liquid and entrain some liquid in their wakes, but there is no large liquid circulation. This is called the homogeneous flow regime.

When the gas flow rate is increased, or if the sparger is not ideal, then the bubble concentration increases and there are more mutual interactions. First, clusters of bubbles will develop: swarms of bubbles relatively close together moving upward with a velocity larger than the single bubble rise velocity, creating local density differences. In and around such a cluster, the liquid velocity is upward, contrary to other areas with a relatively low bubble density. There, the liquid moves downward. This is all happening in a non-steady, chaotic pattern, with larger and smaller liquid circulation loops. Interaction between bubbles results in collisions, creating larger, unstable, faster moving bubbles – this is called coalescence. Larger, unstable bubbles can easily break-up again. Due to coalescence and break-up, the size distribution of the bubbles becomes wider, while power input determines the bubble size. The bubbles in the bulk of the tank then have a different size than those generated at the sparger. This is called the heterogeneous flow regime.

The switch between homogeneous and heterogeneous flow occurs with an ideal sparger at vGsc of 0.04–0.08 m s−1, and sometimes even higher under tightly controlled conditions. However, when the sparger is not well distributed all over the bottom, then a homogeneous flow regime may never develop. This is always the case in large-scale bioreactors, even under conditions where no gas is supplied but motion is determined by the biochemical generation of gas bubbles, e.g. carbon dioxide and methane in beer or biogas installations.

In ALRs, three flow regimes may be encountered, depending on the gas status in the downcomer section: (1) no bubbles, (2) stationary bubbles and (3) downward flowing bubbles.17  These regimes depend on vGsc, scale and geometry of the vessel and the draught tube. The regimes change in this sequence when the gas flow rate increases, and so does the gas hold-up difference between riser and downcomer, as well as the liquid velocity in the downcomer. The vGsc where a switch from regime (2) to (3) occurs depends on scale and can vary between 0.01 and 0.10 m s−1. In large scale ALR, it is even expected that regime (3) rules under all gas flow conditions.

In an ALR, the upflow and downflow areas are set by the design. This allows the axial upward liquid flow velocity, vL, to be modelled using the fermenter energy balance (assuming equal cross-sectional areas, A, of riser and downcomer):

graphic

Equation 1.4

There is equilibrium between gas energy and friction energy, expressed via a friction factor Kf (combining pipe wall friction and a relative large contribution of flow reversal at the top and bottom – see Figure 1.5).

Figure 1.5

Simplified flow diagrams for ALR (left) and BC (right) reactors.

Figure 1.5

Simplified flow diagrams for ALR (left) and BC (right) reactors.

Close modal

Kf at full scale mostly depends on flow reversal (top and bottom) and is typically about 4. At lab-scale, due to wall friction, Kf can easily be much larger, e.g. 50. Under typical operation conditions at lab-scale, with vGsc 0.03 m s−1 and Kf = 50, with a height of 0.5 m, the liquid velocity is about 0.22 m s−1. At full scale, with a height of 20 m, the velocity is 1.8 m s−1. This means that at lab-scale regime 1 occurs and at full scale regime 3.

In the heterogeneous flow regime in a BC, short-lived fluid circulation cells at BC diameter scale are induced by the same mechanism: a difference in bubble density, and hence average density, between the upflowing and downflowing side of the rotating cell. In principle, the same equation of motion rules, but it is very hard, or even impossible, to predict the – much lower – friction factor. On average, over longer time, there is a central upflowing area and an annular downflowing area. Numerous measurements have been performed on these average velocities, showing that the axial liquid velocity, vL, mainly depends on the tank diameter, D (Figure 1.5) and the superficial gas velocity, resulting in the correlation:

Equation 1.5

Experiments have shown that k = 0.72 for the average axial velocity16  and k = 0.9 for the axial velocity at the central axis.18 Eqn (1.5) is very similar to eqn (1.4). This also predicts liquid velocities of more than 1 m s−1 in large vessels, even at the lower boundary of the heterogeneous flow regime.

Using dimensional analysis, a dimensionless group, the Power group or Newton group Ps/ρN3Ds5 is found that is characteristic for the power draw of an impeller with diameter Ds.16  An expression for the power draw follows from the pumping capacity, Fp, and the extended Bernoulli equation or mechanical energy balance. The result is Ps = Fp1/2ρLvL2 indicating that all power is primarily converted into kinetic energy. Assuming that:

  • the outflow rate or pumping capacity Fp equals πcDs2vL, the velocity times the surface at the tip of the impeller, where cDs is the blade height (standard c = 0.2)

  • the liquid velocity, vL, equals the impeller tip velocity πDsN

and combining the expressions then gives Ps = 1/2cπ4ρLN3Ds5. The constant 1/2cπ4 or Power group Np = 10 is characteristic for a multi-blade Rushton impeller in the fully turbulent regime in an unaerated vessel with baffles.

This analysis applies to liquids that are agitated without gas bubbles present and in the turbulent flow regime, with Reynolds numbers (Re) higher than 5000. Under laminar or transitional flow conditions, Np becomes dependent on the Re and progressively higher at lower Re.

In practice, for ungassed, radially pumping impellers, it has been measured that Np = 6, which means that the efficiency to convert the power into liquid motion is about 60%. This is equivalent to a pumping capacity Fp = 1.2NDs3. This pump flow is distributed in a circulation flow. Assuming that, for a radial impeller, half of the flow is directed upward and the other half downward, then the average liquid velocity vL = 1/2Fp/(1/2π0.25D2). At Ds/D = 0.4 it follows vL = 0.24NDs, which is only 8% of the impeller tip speed.

When gas is present, then gas cavities develop behind the impeller blades and the power draw is reduced, depending on the geometry of the cavities. As an example, for radially pumping flat-blade disk impellers (Rushton), Np can drop from 6 to about 2–3. However, for curved-blade disk impellers, there are hardly any cavities and Np is nearly independent of the presence of gas, albeit that the ungassed Np is at a lower value of about three. For axially pumping impellers, the ungassed Np is usually around one or lower.

While in BCs the liquid flow is completely determined by the gas flow rate (or pneumatic power input), vessel geometry and scale, in gassed stirred vessels there are two sources of power input – pneumatic and mechanical (by the stirrer). The ratio of the two power sources influences the liquid circulation patterns. In practice, three flow regimes have been identified:19 

  1. If the energy of the gas is higher than that of the gassed impeller, i.e. PG > Ps under gassed conditions, then the bubbles will hardly be dispersed. This is the impeller flooding regime, which is to be avoided because it can bring a poor process performance (especially mass transfer) and mechanical instabilities.

  2. The other extreme is when the gas energy is much lower than that delivered by the impeller. Under these conditions, the bubbles are very well dispersed and present in all parts of the vessel, and the cavities behind the blades are small (complete gas recirculation). However, the impeller power draw will either be excessively high or the gas flow too low for proper mass transfer.

  3. Intermediate is when the impeller power is about 1–5 times the gas power. Under these conditions, the bubbles are well dispersed but not circulated below the bottom impeller. This may sound non-ideal, but in practice, this does not pose serious limitations to mass transfer. This flow regime (loading) is typical for large-scale operation, as it presents a good balance between performance and cost.

The flow regimes can be well illustrated via a ‘flow map’,20  in which the relative acceleration of the liquid flow by the impeller (expressed as the Froude number, Fr) is plotted against the gas flow rate relative to the impeller pumping capacity (i.e. the gas flow number, FlG), see Figure 1.6.

Figure 1.6

Flow map for a pilot plant, showing the major hydrodynamic flow regimes in three types of fermentation, as a function of two dimensionless quantities: Froude, Fr, and the gas flow number, FlG. Adapted from ref. 21.

Figure 1.6

Flow map for a pilot plant, showing the major hydrodynamic flow regimes in three types of fermentation, as a function of two dimensionless quantities: Froude, Fr, and the gas flow number, FlG. Adapted from ref. 21.

Close modal

The significance of the Fr and FlG numbers is their relationship to the power inputs by the stirrer and the gas. From the above, it can be derived that:

Equation 1.6

Then, for gassed conditions with Np = 3 and H/Ds = 3 it follows that FlG/Fr equals the power input ratio from gas to stirrer.

For PI, a key question is how to maximize mass transfer. Mass transfer is, in general, a combination of:

  • The supply of oxygen (or CO, H2 for syngas and CO2 for phototrophic fermentation) from the bubbles via the liquid to the cells.

  • The transfer of CO2 (or methane, O2) away from the cells via the liquid to the bubbles.

Mass transfer to and from a solid phase to the cells is also possible, such as in packed or biofilm fluid bed fermenters, as well as in the case of biofilms and agglomerates of cells that form a separate solid phase. These will not be discussed here.

The rate of oxygen transfer is most important. The rate is a product of three factors: the transfer coefficient, KL [m h−1], the volume specific gas bubble area, a [m2 m−3], and the driving force for transfer, Co*Co [molo m−3]:

Equation 1.7

The oxygen solubility, Co*, is determined by the Henry coefficient and the partial pressure of the oxygen in the gas phase. In large-scale bioreactors supplied with air, the mole fraction of oxygen in the off-gas can be substantially lower than 21%, which reduces oxygen partial pressure and herewith the solubility compared to fresh air.

Under steady state conditions, the oxygen transfer rate equals the oxygen consumption rate, Ro, which follows from the process reaction and the desired production rate, Rp. Likewise, the transfer of CO2 can be described, where the Henry coefficient of CO2 is about 30–40 times higher than for oxygen. Because the gas can accumulate a large CO2 mole fraction (e.g. 0.2 mol mol−1), the dissolved CO2 can become very high (5–10 mol m−3) and cause inhibition.

The transfer rate of oxygen is the end result of many interrelated factors – see Figure 1.7 (adapted from ref. 18).

Figure 1.7

Interrelations of various geometry, scale, design and operation factors on the mass transfer rate.

Figure 1.7

Interrelations of various geometry, scale, design and operation factors on the mass transfer rate.

Close modal

The most important operation factors for mass transfer are power input, headspace pressure and stirrer speed/gas flow rate. The vessel design factors are gas sparger configuration, the vessel geometry (especially height) and scale. These determine the gas hold-up (ε), the product of KL and a, and the solubility, Co*. In BCs, there are adequate expressions for estimating ε and KLa in the heterogeneous flow regime.18  For the gas-hold-up this reads:

Equation 1.8

which applies to both coalescing and non-coalescing broths and spargers that produce bubbles larger than 4–6 mm. If the sparger produces smaller bubbles, in a non-coalescing medium, the hold-up will be higher.

A suitable KLa correlation is:

Equation 1.9

This applies to coalescing broths, where bubbles merge relatively easily. In non-coalescing fluids, in which bubbles tend to stay separate, the mass transfer coefficient can be up to two times higher.

For homogeneous flow, a similar expression for KLa applies; however, the gas hold-up is higher, because of the longer residence time of the bubbles in the liquid:

Equation 1.10
Equation 1.11

In stirred tanks, the contribution of the impeller power needs to be added:22 

Equation 1.12
Equation 1.13
Equation 1.14

These correlations make it clear how to maximize oxygen transfer:

  • Increase the transfer area, a, by using smaller and/or more bubbles.

  • Increase the transfer coefficient, KL; however, in practice this is a fairly constant parameter, not much influenced by the bubble diameter or medium properties.

  • Increase the oxygen solubility via higher absolute and partial oxygen pressure.

  • Minimize the dissolved oxygen concentration via better mixing and/or a higher microbial hypoxia tolerance.

  • Ensure that, in stirred vessels, the operation is in the desired loading flow regime.

  • Prevent coalescent broth properties by proper medium design and, especially, limited antifoam dosing.

In aerobic and, to a much lesser extent, in anaerobic fermentation processes, a sizeable amount of heat is generally produced. This heat has to be removed, otherwise the temperature will quickly rise at, for example, 10 °C h−1. The cooling water that is used is usually available at a temperature range of 5–20 °C. The temperature driving force for heat transfer from the broth (at 20–40 °C) to the coolant can be as low as 15 or 20 °C, and therefore, a good heat transfer design is important to be able to control the broth temperature at the optimal value. When the cooling capacity is insufficient, the broth temperature will rise, which will negatively affect the process performance.

In the overall heat balance, the microbial heat produced in the process reaction is the largest contributor. For aerobic fermentations, there is a direct link with oxygen consumption: for each mole of oxygen consumed, 450 kJ heat are produced,13  which is equivalent to 400–1200 kJ per mole product. For anaerobic processes, this is usually a factor of ten lower but, because anaerobic fermentations are often carried out at a larger scale, with less area per volume available for cooling, cooling strategies are equally important. In STRs, the second most important source of heat production is the impeller. Energy dissipation via the impellers can add another 10–30% of heat on top of the reaction heat. The advantage of the BC and the ALR is then clear because there is no impeller (and pneumatic power input of gas at fermentation temperature has no heat effect). There can be other sources of heat as well, such as hot, sterilized feed streams or hot, compressed gases that are introduced in the broth. A possible sink of heat is evaporation; water has a high enthalpy of vaporization, and therefore, water evaporation can have a considerable cooling effect. However, these effects are generally not more than 10% of the total heat balance and therefore can be neglected in early phase design. Water evaporation as a heat sink is more prominent in BC than in STR, as a BC is typically operated at larger airflow as well as lower headspace pressure, both of which promote the water evaporation rate.

The cumulative heat generated then needs to be transferred away from the fermenter. This can be done in various ways, for example via coils (either mounted as a long spiral inside the reactor or welded at the outside wall as half-pipes), the vessel wall, baffles or via an external brothloop with a heat exchanger in which the heat is transferred to cooling water.

A series of steps is required to transport heat from the broth inside the fermenter via the coils to the cooling water. First, there is convective flow of heat from the bulk of the liquid to the coil. Second, there is transfer through liquid films outside and inside the coil and conduction through the coil material, and third there is convective heat flow away from the system via the cooling water. In addition, there can be fouling layers at the broth and coolant sides that add additional resistance and further reduce the overall heat transport rate.

There are two central terms that are used to quantify heat transfer. First is the cooling area specific overall heat transfer coefficient, U [kJ m−2K−1h−1]. More specifically, it indicates how much heat is transferred over time per transfer surface area and per degree Kelvin of driving force ΔT. The second is the volume-based heat capacity of the cooling fluid, ρLcp [kJ m−3K−1], the product of the cooling fluid density and its mass-based heat capacity [kJ kg−1K−1]. The heat capacity is thus related to the convection of the cooling fluid. These terms, together with the temperature driving forces, determine the heat transfer and heat removal rates per volume:

Equation 1.15
Equation 1.16

It is important that U gets moderately higher at higher energy input,16,23  and that, in wall cooling, A/VL (the cylinder wall of the fermenter) is equal to 4/T, i.e. cooling via the fermenter wall gets more difficult upon scale-up for a given process intensity.

The Stanton number, St, is a very important quantity in the design of a cooling system. It is a dimensionless number that indicates the ratio of the transfer and convective capacities of a system:

Equation 1.17

In an optimal situation, where the investment in transfer capacity (cooling area) and coolant flow both contribute to the overall cooling capacity, the Stanton number should be close to one. If the Stanton number is much lower than one, then there is an overcapacity of the cooling water flow and the temperature of the cooling water at inflow is close to the temperature at outflow. If the Stanton number is much higher than one, say about 10, then there is too much cooling area installed and/or the cooling water flow rate is too low, and the outlet temperature of the cooling water is equal to the temperature inside the fermenter. A St far away from one indicates a wasteful investment.

As an alternative to using coils for cooling, an external cooling loop can be applied. This presents some challenges, but also brings opportunities. The main advantage of external cooling is that there is greater freedom in design, meaning that the external loop can be designed in such a way that a lot more heat is transferred. Using a cooling coil may result in a slightly lower temperature in the thin liquid film on the broth side. In comparison, the external loop can easily generate five degrees of cooling for all broth elements every 10 or 20 minutes. This is very effective, but the relatively high shear rate can be challenging for the microorganisms, and they also have to be capable of handling such cyclic temperature changes (cold shocks). Another disadvantage of external cooling is that an extra pump is needed, which requires a capital investment as well as operational costs for electricity and maintenance and risks of contamination.

In terms of PI, heat management can be improved by a combination of:

  • Improving the product yield on feedstock, which lowers the heat production (stoichiometrically coupled to oxygen consumption and heat formation).

  • Maximizing the overall heat transfer coefficient via better flow around the cooling area, proper cleaning of both the broth and coolant side and a sufficiently thin wall design.

  • Maximizing the cooling area in the fermenter, or applying an external cooling loop with a cooling machine.

  • ∘ Applying meso- or thermophilic microorganisms

    ∘ Using special cooling fluids (brine or non-aqueous) that can be applied at sub-zero temperatures.

When liquid mixing limits the overall reaction rate, then there will be concentration gradients with not all cells in an optimal environment for production of the desired compound: part of the cells are confronted with concentrations higher than the ideal, which can cause a change of metabolic regime, e.g. overflow of a by-product, while other cells suffer from depletion, also causing metabolic regime changes detrimental for product formation. At this point, it is stated that, in large-scale bioreactors in which substrates (glucose, oxygen) are gradually supplied, there will always be concentration gradients, but the magnitude depends on the specific uptake kinetics and the mixing conditions. As a simple rule, the characteristic substrate consumption time, Cs/Rs [unit: s] will be shorter than the average loop circulation time of the broth, tc. For large-scale bioreactors, a convenient measure of mixing is the 95% mixing time, tm. This is the time needed for a dosed tracer to be homogenized within 95–105% of its final concentration at a selected point of measurement. The average loop circulation time is usually about 1/4 of the 95% mixing time,16 i.e. about four recycle loops are required to arrive at full homogeneity. This is consistent with the liquid circulation flow rates that are determined by the impeller action and gas supply.

An analysis of the mixing process in terms of dispersion and turbulence has resulted in a useful set of expressions to estimate the 95% mixing times, valid for a large range of vessels covering STR, BC and ALR designs.24  For BC in the heterogeneous flow regime, the following dimensionless relations apply:

Equation 1.18

graphic

In addition, for multi-impeller STR's with a relatively poor axial exchange between impeller zones (‘zoning’), operated in single phase or gassed in the incomplete gas circulation (‘loading’) regime:

Equation 1.19

In which eG+ esG is the total broth mass-specific energy input from gas plus impellers [W kg−1]. In the impeller flooding regime, tm is roughly twice as low, i.e. the axial mixing is better, and in the complete gas recirculation regime, tm is about twice as high.

Comparing these results, it is clear that general mixing in a BC is significantly faster than in a multi-impeller STR (see Figure 1.8).

Figure 1.8

Dimensionless mixing time (also known as mixing number) plotted against the aspect ratio, H/D, for three types of fermenters. For stirred tank reactors (STRs), the higher the aspect ratio, the more impellers are needed. For gas-driven reactors, etotal = eG. For gassed stirred tanks, etotal = eG + esG. A lower mixing number means better mixing.

Figure 1.8

Dimensionless mixing time (also known as mixing number) plotted against the aspect ratio, H/D, for three types of fermenters. For stirred tank reactors (STRs), the higher the aspect ratio, the more impellers are needed. For gas-driven reactors, etotal = eG. For gassed stirred tanks, etotal = eG + esG. A lower mixing number means better mixing.

Close modal

For the ALR, tm is fairly independent of the aspect ratio H/D, based on data reported in ref. 24:

Equation 1.20

This means that, at low H/D, mixing is worse than in an STR, while at very high H/D (>500.5 = about 7), mixing is even better than in BC.

At this point, still, it is reiterated that a long mixing time per se is not enough to confirm a mixing issue. The key indicator is the consumption time of the limiting substrate, which is strongly dependent on the residual broth concentration: only when this is shorter than the circulation time, will there then be significant concentration gradients and the cells may suffer. The most powerful method to investigate this further is from the perspective of the microorganisms: tracking the dynamic environment which individual cells experience while traveling through the fermenter (‘life-lines’) will clarify the magnitude and impact of inhomogeneous environment in large-scale fermenters.25–27  It is emphasized that this requires insight into the dynamic response of microorganisms at a timescale of seconds to a minute. Black box models must then be replaced by metabolically structured models.28,29 

It may be good to stress a difference with catalysts in chemical reactors. There, local depletion of substrate or accumulation of product will also slow down the reaction rate. However, microbial cells have a level of complexity that sets them apart from chemical catalysts: the genetic control system will react to gradients, as a result of which, even when the cells are back in a region with optimal conditions, the enzyme levels may have become suboptimal. In addition, the different histories of the individual cells will result in population heterogeneity, which can further deteriorate the overall performance. These aspects are essential in metabolically structured models.

Fermentation intensification (FI) means maximizing the key economic fermentation performance indicators TRY: titer [kg m−3], rate (or: productivity [kg m−3h−1]) and yield [kg kg−1]. The question is now if and how the PI tools could be applied to this field. If we take another look at the fundamentals of PI, as outlined in Figure 1.1 (Introduction) and elaborated in a fermentation context in Section 1.3, then we could reformulate the four main PI principles in the following manner, as principles of FI:

  1. Improve kinetics: maximize Rp, which is the product of qp and the cell concentration, Cx. qp should be maximized by decreasing all moli/molp ratios at fixed transport limits. The ultimate objective is to go anaerobic, where the qo hits the zero limit (Figure 1.4). Cx can be maximized by adding less water and/or using cell retention (see below).

  2. Maximize homogeneity: minimize the impact of gradients in substrate concentration, temperature and shear rate via reducing the average broth circulation time, minimizing zones with extremely long circulation time, elevating the residual substrate concentrations via adjusting the uptake kinetics, creating organisms with lower viscosity at equal biomass concentration and creating organisms that are more robust against the gradients and inhibitory levels of reaction products (including CO2), i.e. are better fit for full scale, gradient-prone conditions. Note that higher rates (see previous point) generally conflict with the aim of maximizing homogeneity.

  3. Relieve transport phenomena limitations: increase (1) driving forces for mass and heat transfer (a higher broth temperature or a lower coolant temperature for heat transfer; a higher solubility (via higher pressure and/or higher gas mole fraction) or lower residual level in the broth), (2) transfer coefficients and (3) transfer area.

  4. Arrange smart integration: combine multiple operations. The most impactful option, and fundamental to fermentation in general, is that organisms harbor efficient metabolic networks that are ideally programmed to maximize the flux to a desired end-product and minimize unwanted by-products. The overall conversion of a low cost, renewable feedstock into a valuable product can easily comprise 10 or 20 biocatalytic steps that are highly specific and of which part is irreversible, allowing near complete conversions. The latter also minimizes the need for a plug flow type of operation, as recommended for chemical processes. Fermentations can be an alternative for processes with multiple chemical reaction steps, usually separated in different operations. Thus, a single metabolic network (“cell factory”) enables major PI benefits. Other integration possibilities are moving from batch to continuous processing (see example 1.6.1), continuous removal of (inhibiting) product from the fermenter via the gas or a second liquid (oil) phase (stripping/extraction), rapid transfer of unstable product to another phase or outside the fermenter to prevent degradation, and cell retention as a means to maximize the cell concentration.

These four points make clear that, for FI, there are complementary biological and technological solutions. For example, a better transfer of CO2 away from the cells could very well relieve inhibition, but at the same time, a more CO2-tolerant host could present an alternative solution. Judgment is then based on a techno-economic comparison of installing a larger compressor for better CO2 ventilation versus a research and development (R&D) project to find or construct a more tolerant strain or cell line.

A further note is made regarding the preceding analysis of fluid flow patterns in different reactors. These are dependent on geometry (e.g. aspect ratio), scale and power input. Regime changes (switches between flow patterns) have consequences for the rates of mixing, cooling and mass transfer, which therefore also depend on geometry, scale and power input. When designing and scaling (up), one should be aware to be, and remain, at the intended, optimal flow regime, and at the same time, remain in the right kinetic regime. An optimal balance between transport and kinetic rates will allow proper scaling, both scale-up and scale-down, and a minimum cost level at large scale.

The four FI principles will be illustrated with four examples.

The production of fuel ethanol has greatly expanded in recent decades to an annual current level of more than 100 billion liters, and this represents by far the largest market for a fermentation product. The two main production countries are Brazil, which produces ethanol from sugar cane juice in continuous or fed-batch mode, and the USA, which uses corn syrup and fed-batch operation.

The main cost factor in ethanol production is the cost of sugar. With a maximum theoretical yield of 2 mol ethanol per mol glucose (0.51 kg kg−1) and a sugar cost of around $250 per tonne, the cost contribution of the feedstock alone is already $500 per tonne ethanol, which is more than 70% of the total cost. It is therefore no surprise that all commercial processes operate with an actual yield of more than 0.45 kg kg−1, i.e. more than 90% of the theoretical maximum. Further improvement of the yield is now pursued by diverging co-products, e.g. glycerol and CO2, back to ethanol via rewiring and optimizing the metabolic network.30,31 

Let us further use this example to investigate the benefits of a continuous operation over batch and fed-batch.

Until the 1980s, batch fermentation using about 350 kg m−3 sugar at the start was the most dominant mode of operation. The benefits are a short process and a high ethanol titer, i.e. higher than 150 kg m−3 was common. However, the productivity was usually limited to about 3 kg m−3h−1,30  related to inhibition effects from high initial substrate concentrations and toxic effects from high final ethanol. Similar productivities have been achieved in single stage continuous fermentation,31  albeit at lower ethanol titers of 60–80 kg m−3, due to the high dilution which presents additional costs in distillation.

Because of this, alternative configurations have been proposed and implemented, which are:

  1. the fed-batch mode, including extension variants such as repeated fed-batch, where a small part (e.g. 10–20%) of the broth is left in the fermenter to restart a new batch with high speed, or extended fed-batch, where withdrawals are regularly taken and transferred to the downstream section.33 

  2. the multi-stage continuous process, minimizing product inhibition, set by passing on the broth from a batch process to a series of subsequent vessels, thereby mimicking a continuous, plug-flow overall process. Advantages have been reported for bioethanol, such that the productivity was up to 13 kg m−3h−1 at ethanol concentrations above 100 kg m−3.32,34 

  3. cell retention or recycling systems, to keep the cells in the process but remove the product and inhibitory compounds. In industrial practice, in Brazil, cell recycling is achieved by centrifugation of used cells followed by a low pH treatment (pH < 3) to control the level of contaminants, especially lactic acid bacteria. There are many publications that advocate active immobilization or membrane techniques; however, these are still rarely seen in industrial practice. An exception is yeast flocculation, which can be applied to keep cells in the bioreactor and is widely applied in brewing.35,36 

Compared to microbial fermentation, the intensity of mammalian cell cultures is an order of magnitude lower. Typically, products are made in agitated bioreactors smaller than 10 m3, with relatively low power input such that mixing and mass transfer seriously limit the reaction rate and cell concentrations are not higher than about 106–107 cells per mL (i.e. 0.5–5 kg cell dry matter per m3). The low power input is due to the perceived shear sensitivity of the applied cell lines, although it has been convincingly demonstrated that transport issues are more likely causing problems, e.g. pH excursions from poor mixing of titrants or poor CO2 removal causing CO2 inhibition.37  In addition, any shear sensitivity has been resolved by adding protective agents such as Pluronic.38  In recent years, however, major improvements have been made in the production of therapeutic proteins,39  and it is expected that other types of products, e.g. viral vaccines, will follow soon.40  The inventions have been a result of two sequential steps: first the change from batch to fed-batch processes, followed by the implementation of continuous cultivation, multi-stage reactors and, especially, cultures with cell retention, e.g. via perfusion or hollow-fiber units. The perfusion allows the inhibitory lactate and ammonia to be kept to low levels, due to fast removal, while keeping the cells in the reactor. Thus, the cell density has increased 10–100-fold to values of 108 cells per mL, which is equivalent to about 50 kg cell dry matter per m3, i.e. like microbial fermentations.

Because of the FI steps made, cultivation can be done in 10–100 times smaller vessels. This brings several synergistic advantages:

  • Mixing problems will be less prominent because of shorter distances.

  • Cooling will be facilitated because of a higher vessel wall area per volume (albeit possibly counteracted by a higher rate of heat formation).

  • Cell retention systems are far easier to implement.

  • Disposable reactors can be introduced, minimizing cleaning efforts and risks for cross contamination.

  • Modular solutions become possible. For example, after intensification by a factor 20, a certain amount of product can be made in four disposable, well-characterized vessels of 250 liter instead of one large steel bioreactor of 20 m3.

  • Manufacturing flexibility is increased, which helps to support gradual market introduction and varying market demands for the product.

Related to these advances in upstream processing, it is no surprise that the main cost for manufacturing of biopharmaceuticals has shifted to the downstream section, and further efforts should be focused on this discipline.

The production of bakers’ yeast (Saccharomyces cerevisiae) is one of the oldest bioprocesses, but still important to serve the baking industry. The fermentation is usually performed in aerobic BC fermenters, where the feeding rate of molasses and production of the cells is limited by oxygen transfer, under conditions that the local dissolved oxygen concentration is close to zero. Using air, the driving force for oxygen transfer, Co*Co, is then determined by the partial pressure of oxygen in the gas phase and the superficial gas velocity. In the following example, based on ref. 41, it will be demonstrated how a large-scale fermentation could be debottlenecked by injecting pure oxygen, increasing the driving force for mass transfer.

Groen et al.41  first presented data on the mass transfer rate of an industrial-scale reference fermentation, operated in a BC using air, and report an oxygen transfer capacity of

Equation 1.21

for vGsc 0.20 m s−1 and oxygen depletion in the rising bubbles of about 0.5% per meter broth height.18  Assuming a liquid height of 16.5 m, then the depleted oxygen at the top will be 8.25%, equivalent to a remaining oxygen fraction of 12.75%. With a headspace pressure of 1 bar (absolute) and using a solubility for air at this pressure of 0.23 molo m−3, then the solubilities at the top and bottom are

Equation 1.22
Equation 1.23

and the linear average oxygen solubility in the vessel is 0.38 molo m−3.

With an average KLa of 373 h−1, using eqn (1.8), then the oxygen transfer rate is 140 molo m−3h−1. Because eqn (1.8) applies to coalescing broths, this would mean that the general coalescence-inhibiting properties of molasses are, in this case, counteracted by the added anti-foam.

In an FI project, separate to air, pure oxygen was applied via a specially constructed nozzle, where the volumetric oxygen/air ratio was 1 : 6. The injection nozzle of the pure oxygen created a supersonic shock wave and a bimodal bubble size distribution with peaks at a mean bubble diameter of 0.2–0.3 mm and 2–4 mm. The latter was similar to the 4–6 mm air bubbles that were injected using a standard sparger. The large oxygen bubbles probably coalesced with air bubbles, increasing the oxygen mole fraction resulting in an additional oxygen transfer rate of 90 molo m−3h−1. However, a major additional contribution of 270 molo m−3h−1 was obtained via the non-coalescing small bubbles that transferred virtually all their content to the liquid phase, i.e. at a transfer efficiency of close to 100%. This is much higher than the transfer efficiency of regular air bubbles, which is 15–20%. The total oxygen transfer rate was then about 500 molo m−3h−1, i.e. an intensification factor of about 3.6.

Finally, in large-scale fermentation this additional mass transfer capacity was utilized by feeding more molasses, and indeed, the bakers' yeast productivity was enhanced 3.6-fold from about 4.5 to 16 g dry cells per kg broth per hour; altogether a good demonstration of FI principle 3.

One might wonder how these results compare to the simpler application of oxygen enriched air to increase the oxygen partial pressure and solubility. It can be calculated how much an additional supply of pure oxygen, with an oxygen : air ratio of 1 : 6 through the same sparger, would increase the oxygen mass transfer rate. The oxygen fraction in the inlet gas is then 32.3%. As a result, the average oxygen solubility is increased from 0.38 to 0.53 molo m−3 and, because of a slightly higher superficial gas velocity, KLa increases from 373 to 404 h−1. The cumulative effect would then be an oxygen transfer rate of 212 molo m−3h−1, which is about 50% higher than for air only, but much less than the 500 molo m−3h−1 with the separate oxygen injection.

Kinetics covers one of the four main FI principles, and it is probably the most powerful for applications in biotechnology. Improvement of the biokinetics via strain development has long been recognized as a key success factor for fermentation. The area is very diverse, with examples in all product segments. For example, the performance of many antibiotics fermentations has been improved several orders of magnitude over periods of decades via introduction of classically improved strains – that is via random mutagenesis. Or, in more recent years, it has become possible to rationally design and introduce metabolic pathways capable of synthesizing non-natural chemicals, such as BDO, caprolactam and other monomers for plastics,8,10  or tailored antibiotics such as adipoyl-7-ADCA,6  that have replaced processes with multiple chemical reaction steps by one single, efficient fermentation step.

It is underlined (see Section 1.3.1) that an efficient metabolism with yields close to the theoretical maximum will simultaneously alleviate a couple of transport limitations in a synergistic manner, as the oxygen demand will be reduced (even become zero at the theoretical limit), and with this the heat formation rate, and also there will be less biomass, resulting in reduced risks for rheology issues that also limit the transport rates.

Of course, the research on one-pot synthesis concepts is also intensive in chemical processes and could provide synergistic advantages as well (e.g.ref. 42 and many other examples), but it is more difficult to keep the formation of unwanted by-products low and proceed the conversion to (near) completion.

The previous analysis and examples have made clear how limitations in fermenter transport rates and cell concentration can be relieved. In practice, there are restrictions to which level this is possible. In general, the maximum production rate in fermenters is restricted by six main factors:16 

  1. Mass transfer. The maximum power input by impellers is limited to about 5 kW m−3, due to mechanical and capital cost reasons, and because of possible shear rate damage to cells. Moreover, for larger fermenters, the impeller motor can never be bigger than about 1 MW. Superficial gas velocities, corrected for local pressure, can be increased to about 0.2 m s−1 before excessive compressor costs will become prohibitive. However, high power inputs from impeller and gas together will result in high gas hold-up, leading to ‘slugging’ and foaming problems, and therefore, in STR's the gas flow rate needs to be lower than in a BC. In order to avoid operation in the inefficient impeller flooding and complete gas recirculation regimes, the ratio between power input by impeller and gas needs to be between one and five, and preferably between one and two for energy efficiency reasons. The headspace pressure can be elevated to 2–3 bar, but not higher because of process safety risks and costs associated with construction of large pressure vessels, CO2 inhibition and inefficient compressor performance. To get an impression, applying eqn (1.8) and eqn (1.10)–(1.12) and assuming that the oxygen transfer efficiency is 4 kg O2/kWh,23  the maximal To and gas hold-up ε can be estimated, as given in Table 1.2.

  2. In conclusion, applying air, the maximum To in BCs is around 500 molo m−3h−1 and in stirred tanks up to 750 molo m−3h−1. Although there are several assumptions behind these calculations, it can be preliminarily concluded that the maximum mass transfer rates of BC and STR are rather similar, at 500–700 molo m−3h−1, for bioreactors of 500 m3 and non-coalescing broths. Smaller vessels will allow a relatively higher impeller power input and then they will outcompete the BC.

  3. Mixing. An estimation of the 95% mixing times, tm, in STR and BC vessels with different aspect ratio's follows from applying eqn (1.18) and (1.19). In Table 1.3, results are provided. It is clear that a BC has a much better mixing than a multi-impeller STR with zoning. In addition, a higher aspect ratio (from three to five) increases the mixing time (a factor of two to three). In absolute terms, in the BC examples, a mixing time of about 60 s would mean an average circulation loop time of only 15 s, which is much lower than usually considered in currently published scale-down studies. Further, STR's with a high aspect ratio perform relatively poorly in terms of mixing.

  4. Comparing the average broth loop circulation time (tm/4) with the substrate consumption time (Cs/Rs) then reveals, for a given Rs, the Cs in the fermentation broth close to the feed inlet point.

  5. Heat transfer. Because of the direct link between oxygen consumption and heat production, the examples in Table 1.2 also present good guidance to heat transfer design. Assuming an oxygen consumption rate of 600 molo m−3h−1, then the metabolic heat production is about 600 × 450/3600 = 75 kJ m−3s−1. Because the heat removal rate for wall cooling scales inversely with the reaction diameter (TH = UAΔT/V = 4UΔT/D), the larger the scale, the more difficult it is to cool the broth. In Table 1.4, three fermenter scales have been compared that illustrate that cooling on a larger scale is more demanding than on a smaller scale.

  6. At liquid volumes larger than 50 m3, removal of a metabolic heat of 75 kJ m−3s−1 will already be impossible through the fermenter wall only. In the 500 m3 vessel, an additional area could be installed of 1100 m2 to solve the issue, e.g. in the form of coils and/or cooling baffles or an external cooling loop, which is challenging but practically feasible. In general, cooling will not present a serious issue, although a good design is important.

  7. Gas hold-up. From Table 1.2, it is clear that intensified fermentations have a high gas hold-up, i.e. 30–40% is common. This means that only 60–70% of the volume can be occupied by broth. If the gas hold-up tends to become higher, or when the broth starts foaming, then addition of an antifoam agent will solve the issues. This also does not present a serious limitation to FI.

  8. Cell concentration. High dry cell weight concentrations, in the range of 100–150 kg m−3, will create another restriction. At these cell densities, the cell wet volume in liter m−3, which is about three to four times the cell dry mass in kg m−3, is approximately 50% of the total liquid broth volume. Under these conditions, even the free movement of the yeast will become largely restricted, with shear-thickening rheology and very high viscosity as a result. Further, if cells tend to be sticky, or filamentous, then agglomeration will already bring issues at even lower cell concentrations.

  9. Cell morphology/rheology. In addition to the cell density, the cell morphology also has a strong influence on the rheology. Filamentous organisms and clusters of agglomerated cells (clumps, pellets) tend to get entangled and restrict the free fluid flow. Usually, shear-thinning behavior is observed, sometimes in combination with a yield stress. Consequently, bubbles tend to coalesce, which reduces the bubble area available for mass transfer. Further, fluid flow and mixing in zones where the power input is relatively low are largely reduced or zones can even become stagnant, which is disastrous for the fermentation performance. For FI, it is strongly advised to avoid working with filamentous microorganisms and agglomerates at all, and select or develop round, freely suspended cells like yeasts or bacteria instead.

From the previous analysis and examples, we can now attempt to estimate quantitatively these limits to FI. We will do that for two specific aerobic cases: fermentative production of bakers' yeast and BDO.

Table 1.2

Estimated oxygen transfer capacity, To, and gas hold-up, ε, for different reactor configurations, operation and power input. Reactor volume is 500 m3, height 25 m and stirrer power input is 1 MW (2000 W m−3). The headspace pressure is 2.25 bar (higher pressure will result in excessively higher costs due to more demanding fermenter construction and high compressor outlet pressure), resulting in a bottom pressure of 4.75 bar and an average pressure of 3.5 bar. Air is applied as inlet gas. The oxygen transfer efficiency is assumed to be 4 kg O2 per kWh in coalescing cases.23 ,a

Impeller power/W m−3Gas power/W m−3vGsc/m s−1To/molo per m3hε (−)
BC coalescing — 2000 0.20 250 0.19 
BC non-coalescing — 2000 0.20 500b 0.39 
BC small bubbles non-coalescing — 400 0.04 167c 0.50 
STR coalescing 2000 1000 0.10 375 0.35 
STR non-coalescing 2000 1000 0.10 750b 0.35 
Impeller power/W m−3Gas power/W m−3vGsc/m s−1To/molo per m3hε (−)
BC coalescing — 2000 0.20 250 0.19 
BC non-coalescing — 2000 0.20 500b 0.39 
BC small bubbles non-coalescing — 400 0.04 167c 0.50 
STR coalescing 2000 1000 0.10 375 0.35 
STR non-coalescing 2000 1000 0.10 750b 0.35 
a

BC: bubble column; STR: stirred tank reactor.

b

Factor 2 higher than coalescing at same superficial gas velocity.

c

Applying the power 0.7 to vGsc.

Table 1.3

95% mixing time, tm, for different fermenter sizes (100 and 500 m3), types (STR and BC) and geometries (H/D 3 and 5), with a total power input of 2 W kg−1 in all cases. The last column presents the substrate concentration close to the feed inlet point, at the beginning of a circulation loop, for Rs = 100 kg per m3ha

TypeV (m3)H (m)D (m)H/D (−)D/Ds (−)eG (W kg−1)esG (W kg−1)tm (s)Cs,feedpoint (kg m−3)
STR 100 10 3.5 0.4 245 1.5 
100 15 2.9 0.4 608 4.2 
500 18 6.0 0.4 351 2.2 
500 25 5.0 0.4 870 6.0 
BC 100 10 3.5 n.a. n.a. 29 0.2 
100 15 2.9 n.a. n.a. 65 0.5 
500 18 6.0 n.a. n.a. 42 0.3 
500 25 5.0 n.a. n.a. 93 0.6 
TypeV (m3)H (m)D (m)H/D (−)D/Ds (−)eG (W kg−1)esG (W kg−1)tm (s)Cs,feedpoint (kg m−3)
STR 100 10 3.5 0.4 245 1.5 
100 15 2.9 0.4 608 4.2 
500 18 6.0 0.4 351 2.2 
500 25 5.0 0.4 870 6.0 
BC 100 10 3.5 n.a. n.a. 29 0.2 
100 15 2.9 n.a. n.a. 65 0.5 
500 18 6.0 n.a. n.a. 42 0.3 
500 25 5.0 n.a. n.a. 93 0.6 
a

STR: stirred tank reactor; BC: bubble column; n.a. not applicable.

Table 1.4

Heat removal rates for different fermenter volumes, all with aspect ratio H/D = 5, temperature driving force 25 K and U = 1000 J per m2 K s

Volume, V/m3Height, H/mDiameter, D/mWall area, A/m2Heat removal rate, TH kJ−1 per m3s
5.4 1.1 18.4 92 
50 11.7 2.3 86 43 
500 25 5.0 393 20 
Volume, V/m3Height, H/mDiameter, D/mWall area, A/m2Heat removal rate, TH kJ−1 per m3s
5.4 1.1 18.4 92 
50 11.7 2.3 86 43 
500 25 5.0 393 20 

Let’s assume a cylindrical BC reactor with a liquid volume of 500 m3 and an aspect ratio H/D = 5. Then, the height is 25 m and the diameter 5 m. The headspace pressure is 2.25 bar, resulting in a bottom pressure of 4.75 bar. What would be the FI limits? First, we will assess transport limitations, and then judge the possible impact on the process reaction and fermenter productivity.

Mass transfer. In the bakers' yeast example, operated in a BC with oxygen injection separate from air sparging, the cumulative superficial gas velocity is 0.22 m s−1 (pressure-corrected), resulting in a mass transfer coefficient for the large bubbles of approximately 400 h−1, while the average oxygen solubility in the enriched gas is about 0.53 molo m−3, as calculated above. In order to secure the required oxygen transfer capacity and prevent oxygen starvation in the liquid, the contribution from the small bubbles, which contain pure oxygen, needs to be added. Assuming that about half of the sparged pure oxygen gas is present as small bubbles (i.e. 1/12 of the total gas flow), and applying the same correlation for KLa as for the larger bubbles, then KLa for the small oxygen bubbles is approximately 70 h−1. The total oxygen transfer rate is the sum of the large and small bubble contributions, i.e.:

Equation 1.24

With an average liquid pressure of 3.5 bar, then To = 70 × 3.5 × 0.23 × 1/0.21 + 400 × 0.53 = 268 + 212 = 480 molo m−3h−1. From this analysis, it is clear that further optimization of the oxygen injection method is possible. If all air were to be replaced by pure oxygen, such that vGsc is 0.20 m s−1, and all the bubbles were to be small and transfer all oxygen to the liquid, then this could result in an oxygen transfer rate of 0.373 × 3.5 × 1.25 = 1500 molo m−3h−1. Of course, there will be pure CO2 bubbles formed, which need to be ventilated, and this will cause significant inefficiencies e.g. due to diffusion of oxygen into the bubbles, and in reality, a lower oxygen transport rate To.

Assuming that, under these conditions, the same product yield on sugar can be obtained as before, then the process reaction still holds:

Equation 1.25

For Ro = 1500 molo m−3h−1, the glucose consumption rate Rs = 0.3 × 1500/0.75 = 600 mols m−3h−1 or 108 kg glucose per m3h, and a biomass production rate Rx = 1 × 1500/0.75 = 2000 molx m−3h−1 or 48 kg biomass per m3h. Benchmarking this productivity value with other published data confirms that this is way higher than the highest reported productivities.43  Further, if we assume that the sugar concentration in the feed (dilute molasses) is 315 g kg−1, then the cell dry mass concentration (following from the total mass balance) is at a maximum of approximately 150 kg m−3 and the biomass specific rates are:

Equation 1.26
Equation 1.27

These are fortunately still below the maximum fluxes that the S. cerevisiae cells can handle, i.e. qsmax is 0.3 mols per molx h and µmax is 0.5 h−1,42  and therefore biomass retention is not needed. Still, the high µ could trigger ethanol formation (Crabtree effect) and this is to be avoided e.g. by selecting Crabtree-negative strains.

The productivity is compared with the critical mixing and cooling rates as follows.

Mixing. Using eqn (1.18) the required energy input in the BC eG = 2.2 W kg−1, the pressure corrected superficial gas velocity, vGsc = 0.22 m s−1, the average liquid velocity, vL = 1.6 m s−1 and the 95% mixing time, tm = 90 s. The average circulation time of a full axial loop, tc, follows from the liquid velocity as 2H/vL = 30 s, which is slightly longer than the rule of thumb tc = tm/4. If glucose is fed at the bottom or top section of the tank, then the minimum glucose concentration at the feed inlet needed to avoid depletion at the end of the circulation can be derived from Cs = tc × Rs = 25 × 108/3600 = 0.75 kg m−3 or 4.2 mols m−3. This result can be compared with real data from large scale fermentations with S. cerevisiae.27  Because the steady state glucose concentration is closely related to the affinity of the glucose uptake systems and the specific glucose uptake rate, it could be judged, based on the proper uptake kinetics, whether local glucose depletion is likely or not. If so, then measures should be taken on either the biology side (e.g. lowering the affinity of the uptake system)45  or the fermenter design (geometry, scale) and operation side (power input, headspace pressure, sugar feed inlet position, feed rate). A good indicator for the actual growth-limiting glucose concentration is the affinity constant for glucose uptake. For S. cerevisiae, the affinity for glucose uptake has been reported as Ks = 1 mM (0.18 kg m−344 ), which is below the calculated critical limit of 0.75 kg m−3. This means that the mixing will be a clear bottleneck and should be relieved. Other microorganisms usually have lower Ks values, which means that, for such fermentations, mixing problems may even be more significant.

Cooling. The metabolic heat production is 1500 × 450 = 675 000 kJ m−3h−1, which translates to 675 000 × 500/3600 = 93 000 kJ s−1 for the full fermenter. Assuming a good cooling design (St = 1), with an overall heat transfer coefficient U = 3 kJ s−1 m−2 K−1,23  a full coverage of the tank wall with a cooling jacket (A = 25 × π × 5 = 393 m2) and an average temperature driving force of 25 K, then the heat removal capacity of the fermenter is only 3 × 393 × 25 = 30 000 kJ s−1. This is not sufficient to control the fermentation temperature, and therefore, an alternative solution needs to be found, e.g.:

  • Optimize the metabolic network towards increased biomass formation so that the oxygen consumption rate is minimized.

  • Increase the cooling area, e.g. also involve the bottom of the tank and the baffles or add an internal coil or other surface.

  • Choose another cooling design, most likely an external loop with a heat exchanger.

  • Find another host cell, capable of performing well at higher fermentation temperatures, to increase the driving force for heat transfer.

  • Minimize the thickness of the fermenter wall to reduce the heat conduction resistance.

  • Increase the heat transfer coefficient via more effective liquid flow around the cooling surface, e.g. via a higher power input and altered geometry.

  • Use a non-aqueous coolant at subzero °C temperatures.

In practice, there are adequate engineering solutions available and this will not pose serious design and operation problems.

This case assumes operation in the same BC as the previous case, applying the process reaction as before, producing 1 mol BDO (C4H10O2):

Equation 1.28

For simplicity of this case example, we assume that this process reaction holds for a wide range of µ values.

Again taking a maximum oxygen transfer capacity To = 1500 molo m−3h−1, then the glucose consumption rate Rs = 1.44 × 1500/2.54 = 849 mols m−3h−1 or 153 kg glucose per m3h, the biomass production rate Rx = 0.6 × 1500/2.54 = 354 molx m−3h−1 or 8.7 kg biomass per m3h, and the BDO production rate is Rp = 1 × 1500/2.54 = 591 molp m−3h−1 or 53 kg BDO per m3h. This productivity value is much higher than currently reported for BDO.10 

Assuming a glucose inlet concentration of 540 g kg−1, from an overall mass balance the biomass dry mass concentration follows as 39 kg m−3, which is relatively low. As a consequence, the relative biomass specific reaction rates will be high, e.g.

Equation 1.29
Equation 1.30
Equation 1.31

The high qs value is higher than most microorganisms can handle, and therefore the high To cannot be utilized in a regular continuous or extended fed-batch mode of operation.

Still, there is an opportunity via application of cell retention. Assuming a cell dry mass concentration of 150 kg m−3, achieved via retaining part of the cells inside the fermenter, while the process reaction is unchanged, then the biomass specific rates are: qs = 0.14 mols per molx h, µ = 0.06 h−1 and qp = 0.10 molp per molx h. This specific glucose consumption rate can be satisfied.

As in the previous case, a further feasibility check of the kinetics and a comparison of the reaction rates with the transport rates can now be made. This analysis is analogous to the previous example and will therefore not be repeated here.

Van Gerven and Stankiewicz3  have formulated four useful main principles of PI: improving kinetics, enhancing mixing, maximizing mass and heat transfer, and smart integration of steps. We have applied these to bioprocesses in order to test the validity for FI. In general, we conclude that the four principles are fit for use in bioprocesses and apply well. However, the rare occurrence of the term FI in the literature suggests that there is apparently limited value in separately coining this term. We think this could be related to the younger and more dynamic field of bioprocess technology, relative to the more mature chemical process technology. While the former field is developing fast because of the revolutions in molecular biology, and provides radical business opportunities, the latter has been challenged to move to the next level of development to solve major (global) obstacles, replacing the mostly incremental improvements by more disruptive approaches.

An investigation of the field of FI has made clear that, in large-scale bioprocesses mixing, mass transfer and heat transfer are most likely limiting the rate of the aerobic fermentation process, and possibly also in anaerobic fermentations but to a lesser extent. Transport limitations result in concentration and temperature gradients and in (product) inhibition, which compromise cells and therewith process performance. The kinetic capacities of the cells are usually higher than those permitted in the fermenter by the rate-limiting fermenter transport steps. Still, kinetic improvements are important because the sensitivity of the cells to concentration gradients and inhibition can be reduced. In addition, in aerobic processes, an improvement of the substrate flux to product will immediately reduce the need for oxygen, and reduce the formation of biomass, by-products, heat and CO2 in a synergistic way.

The wish to switch from batch to continuous operation is understandable, to maximize on-stream times and to control the product quality better. This may already be feasible for anaerobic processes; however, as already reported before, for aerobic processes there are still fundamental bottlenecks that prevent such turnaround or render only marginal productivity improvements. It is not expected that either will be resolved in the coming years, and therefore, fed-batch solutions, either as such or repeated/extended variations of this type of operation, will remain the dominant mode of operation.

Another main topic is the development and implementation of cell recycle or cell retention systems, especially in anaerobic fermentations, less developed processes with mammalian cells, or highly optimized metabolic networks, operating close to the theoretical limits for product formation. This has already proven to increase the process intensity by one or two orders of magnitude in some cases and is expected to take a bigger role for other fermentation processes as well.

Furthermore, today it has become feasible to efficiently introduce novel pathways in microbial and mammalian cells to make complex or unnatural compounds in a process sequence that is more integrated than for the multitude of chemical process steps required to produce the same products. This is the most important way in which fermentation processes in fact constitute an application of PI, compared to chemical processes.

In the chemical PI field, new approaches have been advocated, such as rigorous miniaturization and the use of alternative energy sources. We believe that these tools will not likely find their way in fermentations because of the different requirements: by definition, fermentation conditions are mild, without toxic compounds – of which the inventory needs to be minimal, and there is little incentive to control the temperature because runaways will not happen. In addition, microwave or ultrasound radiation will not be possible because these are expected to damage the microorganisms. In contrast, microbial systems already possess efficient energy coupling mechanisms, which can run with multiple energy sources.

The remaining question is whether the bioprocess domain needs special emphasis on PI tools because, in general, there are already good continuous improvement practices in place to achieve solutions that are beyond incremental. We therefore expect that the term FI, although referring to a good set of instruments, will not take the same strong position in bioprocess technology as PI has in chemical process technology.

Important on the path to continuous improvement of fermentation processes, though, is that more accurate estimates are needed to find the optimal balances between transport/mixing/kinetics and thus give minimal fermentation costs. Concluding this chapter, from the application of approximate engineering correlations, it is almost certain that in aerobic processes the oxygen transfer and mixing are (simultaneously) limiting, while in anaerobic processes and mammalian cell processes the biomass concentration is limiting. Cooling, on the other hand, tends to be overdesigned. New computational methods towards integrated fluid dynamics–metabolic kinetics models to design geometry/operation of bioprocesses with high resolution25–29  hold a promise to fill part of this gap in the coming years.

SymbolUnitMeaning
A m2 Area 
a m2 m−3 Specific area for mass transfer 
Ci moli m−3 Concentration 
c Height of the impeller blade 
cp J kg−1 K−1 Heat capacity 
D Tank diameter 
Ds Impeller diameter 
e W kg−1 Energy 
F m3 s−1 or h Flow rate 
g m s−2 Gravity constant 
H Liquid height 
Kf — Friction factor 
KL m s−1 Mass transfer coefficient 
KLa 1 s−1 Volumetric mass transfer coefficient 
k — Proportionality constant 
N 1 s−1 Impeller rotation speed 
P J s−1 (W) Power 
p bar Pressure 
qi moli per molxBiomass specific rate 
Ri (mol or kJ)/m3Rate per volume 
Ti (mol or kJ)/m3Rate per volume 
T Temperature 
t Time 
U W m−2K−1 Heat transfer coefficient 
V m3 Volume 
v m s−1 Velocity 
Yps kg kg−1 or molp mols−1 Yield of product on sugar 
SymbolUnitMeaning
A m2 Area 
a m2 m−3 Specific area for mass transfer 
Ci moli m−3 Concentration 
c Height of the impeller blade 
cp J kg−1 K−1 Heat capacity 
D Tank diameter 
Ds Impeller diameter 
e W kg−1 Energy 
F m3 s−1 or h Flow rate 
g m s−2 Gravity constant 
H Liquid height 
Kf — Friction factor 
KL m s−1 Mass transfer coefficient 
KLa 1 s−1 Volumetric mass transfer coefficient 
k — Proportionality constant 
N 1 s−1 Impeller rotation speed 
P J s−1 (W) Power 
p bar Pressure 
qi moli per molxBiomass specific rate 
Ri (mol or kJ)/m3Rate per volume 
Ti (mol or kJ)/m3Rate per volume 
T Temperature 
t Time 
U W m−2K−1 Heat transfer coefficient 
V m3 Volume 
v m s−1 Velocity 
Yps kg kg−1 or molp mols−1 Yield of product on sugar 

Circulation 
Cooling water 
Carbon dioxide 
Downcomer 
Gas 
Gs Gas superficial 
Heat 
Liquid 
Mixing 
Oxygen 
Product 
Pumping 
Riser 
Substrate or glucose 
Stirrer 
sG Stirrer under gassed conditions 
Cells or microbial biomass 
Circulation 
Cooling water 
Carbon dioxide 
Downcomer 
Gas 
Gs Gas superficial 
Heat 
Liquid 
Mixing 
Oxygen 
Product 
Pumping 
Riser 
Substrate or glucose 
Stirrer 
sG Stirrer under gassed conditions 
Cells or microbial biomass 

Corrected for local pressure 
max Theoretical maximum 
Solubility 
Corrected for local pressure 
max Theoretical maximum 
Solubility 

ΔT Temperature driving force 
ε — Gas hold-up 
µ 1 h−1 Specific growth rate 
ρ kg m−3 Density 
ΔT Temperature driving force 
ε — Gas hold-up 
µ 1 h−1 Specific growth rate 
ρ kg m−3 Density 

FlG Gas flow number 
Fr Froude number 
NP Power number 
Re Reynolds number 
St Stanton number 
FlG Gas flow number 
Fr Froude number 
NP Power number 
Re Reynolds number 
St Stanton number 

ALR

Airlift loop reactor

BC

Bubble column

BDO

1,4-Butanediol

CFD

Computational fluid dynamics

FI

Fermentation intensification

G/L/S

Gas/liquid/solid

PDO

1,3-Propanediol

PI

Process intensification

SA

Succinic acid

STR

Stirred tank reactor

Thanks to colleagues of DSM for fruitful discussions.

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