Immobilized Cell Bioreactors in Fermented Beverage Production: Design and Modeling

IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION: DESIGN AND MODELING

11

Georgi Kostov§, Vasil Iliev⁎, Bogdan Goranov†, Rositsa Denkova‡, Vesela Shopska§ ⁎

Weissbiotech, Ascheberg, Germany, †LBLact, Plovdiv, Bulgaria, ‡Department of Biochemistry and Molecular Biology, University of Food Technologies, Plovdiv, Bulgaria, §Department of Wine and Beer Technology, University of Food Technologies, Plovdiv, Bulgaria

11.1 Introduction Systems with immobilized cells provide a new kind of fermentation conditions, usually associated with a higher rate of the fermentation process. This, in turn, leads to a reduction in the fermentation time, which must be coupled with suitable equipment ensuring a high fermentation rate. Bioreactors, including industrial ones, can be divided into the following groups based on the organization of the mass flows: • Batch bioreactors; • Fed-batch bioreactors; • Semicontinuous bioreactors; • Continuous bioreactors. Although each immobilized biocatalyst may be applied to different types of bioreactors, the selection of an immobilization method and a bioreactor in which the respective fermentation process will take place is very important for the optimal operation of such a system. The bioreactors can be divided into three types based on the organization of the flow inside the apparatus and the movement of the solid phase (the immobilized biocatalyst): • Bioreactors with mixing of the solid phase; • Bioreactors with a fixed solid phase; • Bioreactors with a moving surface. Biotechnological Progress and Beverage Consumption. https://doi.org/10.1016/B978-0-12-816678-9.00011-4 © 2020 Elsevier Inc. All rights reserved.

339

340  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

Three phases are distinguished when using an immobilized biocatalyst in the reactor: solid phase—the immobilized biocatalyst; liquid phase—the nutrient medium; gas phase—the oxygen for the aerobic processes and/or gaseous metabolite (the most commonly formed gaseous metabolite during alcohol fermentation is CO2). In this connection, the design and modeling of two-phase liquid/solid systems is relatively simpler, whereas the presence of the gas phase changes the modeling conditions. Three-phase systems, especially those with additional aeration to provide the necessary oxygen for the process, involve additional difficulties. They are mainly related to the presence of additional shear stresses acting on the biocatalyst. Most often, these problems are solved with an extra circulating loop of the liquid where the aeration occurs. Bioreactors with immobilized cells can be classified according to different features and constructive elements, and each bioreactor type can be characterized by different advantages and disadvantages (Fig. 11.1). A major advantage of immobilized cell systems is their high productivity and easier purification of the end product. Some of the drawbacks of these systems, mainly related to the presence of diffusion constraints, can be avoided by proper apparatus design.

11.1.1  Main Types of Immobilized Cell Bioreactors 11.1.1.1  Bioreactors With Stirring This type of reactor is still the most common type, both at the laboratory and industrial levels. Various types of stirring devices are available: anchor, frame, propeller, open and closed turbine agitators. Despite the use of various stirrers, the main problem with these systems is the abrasion and destruction of the carrier. This effect is due, on the one hand, to the stirrer and the tension it generates on the particles and, on the other hand, to the presence of a gas phase in aerobic and heterofermentative anaerobic processes. Anchor stirrers are used quite often in this type of system as they provide soft stirring and low stresses on the carrier (Angelov and Kostov, 2009).

11.1.1.2  Bioreactors With a Packed Bed The immobilized biocatalyst in the form of granules, grains, chips, etc. can easily be packed into a dense bed and placed in a column bioreactor. In this case, a plug flow of the nutrient medium in the apparatus is formed, which is advantageous in product-inhibited processes such as alcohol fermentation. This type of equipment is used in continuous fermentation systems, single or cascade (Nedovic and Willaert, 2004).

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   341

Fig. 11.1  Major types of immobilized cell bioreactors used in beverage production.

342  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

Various immobilization carriers (DEAE-cellulose, wood bran, glass beads, silicates, ceramics, synthetic porous matrices, alginate, and other polymers) are used in this type of apparatus (Naydenova, 2014). Some of these carriers are mechanically unstable, which limits the liquid flow rate, thereby leading to bed compression. This can be solved by sectioning the bed by height using mechanical partitions. This, in turn, results in a more even distribution of the flow (Angelov and Kostov, 2011).

11.1.1.3  Fluidized Bed Bioreactors A good alternative of the use of a biocatalyst with a low mechanical stability that has to be stirred constantly is presented by the fluidized bed bioreactors. In the simple two-phase system, the fluid flow rate exceeds the minimal fluidization rate of the carrier. The minimum fluidization rate is the rate at which pressure losses in the bed become equal to the specific gravity of the particles, and the latter begin to float in the bed. At this rate, the dense bed begins to expand, resulting in an increase in the specific mass exchange surface. The bed exists in a fluidized state until the terminal particle settling velocity is reached, after which the catalyst starts to undergo a hydrotransport mode (Iliev, 2016; Kostov, 2007). This type of system is suitable for carriers with low mechanical stability such as alginate, carrageenan, chitosan, etc. Fluidized bed reactors have the following advantages and disadvantages (Iliev, 2016; Kostov, 2007): • The expansion of the bed ensures constant pressure losses and a high specific mass exchange surface without changing the hydraulic resistance; • The existence of intense stirring leads to uniform distribution of the substrate in the bed. In such systems, high heat and mass exchange coefficients are achieved in the liquid-solid interface area; • Fluidized bed reactors are suitable for performing aseptic and sterile processes due to the lack of rotating parts in them; • The mechanical stability of the particles is disturbed by the impact between the particles and the walls of the apparatus. In the presence of gaseous metabolites with a significant flow rate, it is also possible to use fluidized-bed cone devices that secure a rate gradient by bed height and improve the heat and mass exchange characteristics of the apparatus (Iliev, 2016; Kostov, 2007). In the three-phase liquid-solid-gas system, some of the main features of the two-phase system in fluidized mode are violated. Back mixing is usually observed, and in some cases bioreactors behave like bubbling columns (Iliev, 2016; Kostov, 2007).

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11.1.1.4  Bubbling Columns, Airlift, and Gas Lift Bioreactors Bubbling Columns This type of apparatus consists of cylindrical vessels with a bottom sprayer or a tank with a distribution device located at the bottom. Typical of this group of devices is the absence of special diffusers and barriers to distribute the liquid flow (Angelov and Kostov, 2009; Iliev, 2016). Systems of this type are used in highly foaming liquids, performing anaerobic fermentation processes, and using flocculation as an immobilization method. They have excellent heat and mass exchange characteristics and low operational losses, and are relatively compact (Puettmann et al., 2012). Airlift and Gas Lift Bioreactors This type of system provides ideal fluid mixing at low energy consumption, while in immobilized systems they also provide low stresses on the solid phase (Merchuk, 1990). Stirring is provided at the expense of a difference in the densities in the aerated and the nonaerated part of the apparatus. The presence of a gas phase may be due to the fermentation process or may be added, most commonly by the addition of inert gases which provide the stirring process. Effective stirring and mass exchange are carried out by means of an external or internal circulation loop. The gas phase enters the bottom of the apparatus and completely or partially leaves it at the top. This creates a difference in the gas holdup in the individual zones of the apparatus, thereby changing the density. The upper section of the apparatus also provides for retention of the carrier within the reactor (Martínez and Silva, 2013). Airlift bioreactors are suitable for virtually all types of immobilized cell systems due to effective stirring and low stresses on the carrier. They can also work with very low-density particles (similar to those of the liquid) and are suitable for biofilm-forming systems (Martínez and Silva, 2013).

11.1.1.5  Membrane Bioreactors With Immobilized Cells Cell immobilization in membrane modules itself also requires specific equipment. There are different membrane modules (with flat membranes, hollow fibers, spirally wound modules), but for the immobilization of microbial cells, flat membranes and hollow fiber membranes are used. These modules provide high specific surface area and easy separation of the target product from other fermentation products.

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Membrane systems ensure a high surface for immobilization, small volumes, and high productivity, and combine two processes, fermentation and separation of the desired product. Unfortunately, there are difficulties in the mass exchange as well as the possibility of clogging the membrane pores (Angelov and Kostov, 2011).

11.1.2  Selection of a Bioreactor and Application of Immobilized Cell Bioreactors to Beverage Production The choice of a type of operating system for beverage production should be based on the knowledge of the process and its main characteristics. The high cell concentration in the operating volume of the apparatus places high demands on the feeding of the substrate to the cells. Especially problematic is the presence of diffusional resistances in the system. The correct choice depends on all the advantages and disadvantages listed below. Part of the selection criteria are presented in Fig. 11.2. Immobilized systems are used in the production of various types of fermentation beverages: wine, beer, some types of low alcohol fermented beverages, secondary fermentation of beer and wine, ethanol, etc. (Naydenova, 2014; Kostov, 2015).

Biocatalysis

Matrix type

Particles Strong

Stirring Packed bed Airlift Fluidized bed

Fig. 11.2  Basic criteria for selection of immobilized cell bioreactors for use in beverage production.

Biofilm

Membrane

Packed bed

Membrane

Weak

Airlift Fluidized bed

Stirring Packed bed Airlift Fluidized bed

Flexibility Stirring

Airlift

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   345

11.2  Main Constructive Parameters of Immobilized Cell Bioreactors 11.2.1  Bioreactors With Stirring Although they are simple in design, bioreactors with stirring must meet a number of requirements in terms of design parameters. Typically, the working height of the vessel H is at least twice its internal diameter (H ≥ 2D). Effective stirring and energy consumption are controlled by the number of stirring units, the type of stirred liquid, the presence of a gas phase in the apparatus, etc. (Angelov and Kostov, 2009, 2011). The first and main constructive parameter of systems of this type is the type of stirrer used. They are divided into high-speed (propeller and turbine) and slow-moving (anchored, disc, blade) stirrers. Depending on the method of deployment, they provide radial, axial, or radial axial flow of the liquid and the biocatalyst. Turbine stirrers create radial flow, and this is the most commonly used variant of immobilized cell bioreactors (Angelov and Kostov, 2009, 2011). An important structural feature of the bioreactors with stirring is the presence of vertical baffles. Their absence leads to swirling in the apparatus, and often to the rotation of the liquid without mixing its individual elements. The number of baffles varies from 2 to 6, their width ranging from 1/12 to 1/10 of the diameter of the apparatus. The layout of the blades depends primarily on the viscosity of the fermenting liquid (Angelov and Kostov, 2009, 2011). Mixing in this type of system is almost ideal, which is their main characteristic. The movement of the fluid has a turbulent character. In this case, the stresses on the immobilized preparation decrease with an increase in the distance from the active stirring zone. The immobilized biocatalyst is subjected to significant mechanical stresses from the stirring and the collision between the particles and the elements of the reactor, and between the particles themselves (Nedovic and Willaert, 2004). The main operating parameters of these systems are: the stirrer rate, the geometric dimensions of the apparatus and the stirrer, the energy consumption per volume unit. The residence time of the fluid in the apparatus is essential in continuous bioreactors, while in aerobic systems the volume coefficient of mass exchange of the oxygen is essential. Some of these parameters are also used in the scaling up process of bioreactors with stirring (Nedovic and Willaert, 2004, 2005). In most cases, liquids that are fermented in order to obtain beverages can be considered as Newtonian liquids. In general, in this case the power consumed for stirring is a function of a large number of parameters (Angelov and Kostov, 2009, 2011):

346  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

N 0 = f ( n ,g ,ρ ,µ ,D ,ds ,H )

(11.1)

where n is the stirring rate, s−1; g is the ground acceleration, m/s2; ρ is the density of the liquid, kg/m3; μ is the viscosity of the liquid, Pa s; D is the diameter of the apparatus, m; ds is the stirrer diameter, m; H is the height of the liquid in the apparatus, m; In this case, a dimensional analysis is applied and the following equations are obtained: Eu = f ( Re,Fr )

(11.2)

where Eu is the Euler’s criterion; Re is the Reynolds criterion; Fr is Froude’s criterion, which can be represented in real form as: Eus =

N0 ρ n 3 ds5

Re s =

ρ nds2 µ

Frs =

n 2 ds g

(11.3)

where Eus is Euler’s modified criterion, often referred to as the power criterion; Res is the centrifugal Reynolds criterion or Re for stirring; Frs is the centrifugal criterion of Froude or the Fr criterion for stirring. In this case, Eq. (11.3) are reduced to some simpler dependencies of the type: Eus = cRe x

(11.4)

where С and х are the coefficients, the values of which depend on the agitator design and the mixing mode (Reb). The solution to Eq. (11.4) is accomplished by graphical dependencies related to the type of the stirrer. The parameters in it are strongly dependent on the current regime, but in general we can summarize that fermentation with immobilized cells develops in the area of the transient and turbulent modes. This is due to the fact that these modes reduce the influence of external diffusional resistances. The turbulent mode occurs at Res > 1000, and in this case it is possible to make calculations for the apparatus with or without baffles. This operation area of the apparatus is called the automodel area, the power consumed in it is no longer dependent on Reb, and the increase in the rotation rate leads to a disproportionate increase in the power consumption: N s = C ρ n 3 ds5

(11.5)

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As a substantial amount of CO2 is formed in the production processes in the beverage industry, and the medium can be considered as a Newtonian fluid, it is necessary to adjust the power. This correction takes into account the decrease in the density of the medium and therefore the power. The power spent for stirring in the gas-liquid system can be calculated by the energy consumption for stirring the nonair liquid N0. The Na/N0 dependence for all types of stirrers is as follows:  q 10 2  Na =c G 3  N0  nds 

p

(11.6)

where c, p are the constants for each type of stirrer, as given in the specialized literature. The gas holdup is an important feature that determines the retention capability of the apparatus on the gas phase. The power consumed for stirring of the gaseous medium is directly proportional to its density. There are dozens of equations for calculating the gas holdup in bioreactors with stirring, most of which can be developed into the form of: b

N  ε = a   wSG  VR 

(11.7)

where N/VR is the specific power for stirring, W/m2; wSG is the linear gas rate, m/s; c = 0.6; a, b are the coefficients determined by the specialized literature. Gas holdup is used as an indirect feature for finding the interfacial surface. However, the main thing is that the volume of the culture medium in the bioreactor can be determined by the gas holdup, and thus it is possible to assess the mean time of its stay in the apparatus.

11.2.2  Bioreactors With a Packed and Fluidized Bed Immobilized Biocatalyst The modeling of these two types of systems is closely related since the fluidization process begins from a solid bed under certain conditions. The first major characteristic of both beds is the solid phase contained in them. The basic parameters of each phase are: physical parameters (shape, dimensions, density, and morphology) and hydrodynamic parameters (terminal settling velocity, drag coefficient, minimum fluidization velocity) (Yang, 2003; Chalermsinsuwan et al., 2012). The particle size is one or more than one linear magnitude appropriate to define the characteristics of the individual particle.

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For example, for a spherical particle, it is its diameter. The remaining particles are typically characterized by two or three linear dimensions. Very often, the particles to be tested have an irregular shape. Their size is usually defined on the basis of some assumptions. Most often, this is done on the basis of assumptions that are important for the particle application. In practice, many different ways of describing the dimensions have been outlined (Wang et al., 2014): volume diameter, surface diameter, and Sauter diameter. The particle shape is usually irregular, which is why factors that equate particles to spherical particles are commonly used (Wang et al., 2014). Particle density can be defined in several possible ways which are wholly dependent on particle application. For nonporous particles, density is defined by the ratio of particle mass to particle volume (Yang, 2003). The hydrodynamic characteristics of the packed and fluidized bed systems are basic for their modeling. They include parameters such as terminal settling velocity, minimum fluidization velocity, etc., which will be discussed in more detail. The terminal settling velocity is the linear rate of the fluid flow at which the particles are washed away from the bed, that is, the bed ceases to exist. It is calculated by Stokes’ law for settling in a viscous media (Iliev, 2016; Kostov, 2015): ut =

4 gdP ( ρS − ρ ) 3 ρC Dt

(11.8)

In this equation, the drag coefficient of the medium depends on the nature of the particle motion determined by the Re number (Table 11.2) (Kelessidis, 2003; Yang, 2003). The coefficients in Table 11.1 have to be corrected quite frequently with the so-called wall effects, and the resistance force is calculated by the dependence (Iliev, 2016): dp   Fs = 3π dp µut  1 + kc  Lw  

(11.9)

where kc is the coefficient that depends on the particle shape; Lw is the distance from the center of the particle to the wall. The terminal settling velocity is both a fluidized bed hydrodynamic parameter and a particle parameter. Therefore, its calculation and/or experimental determination is essential for the proper modeling of the fluidized beds. In Yang’s work (Yang, 2003), a significant amount of data for calculating this parameter as well as interpretations of the results obtained by a number of authors are presented. In his work, Iliev (2016) discusses the behavior of various types of alginate particles in model solutions: distilled water, sugar, and

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Table 11.1  Drag Coefficients (Kelessidis, 2003) No.

Re Criterion Area

Equation for the Drag Coefficient

1

0.01 < Re ≤ 20

 C Re  log10  D − 1 = −0.881+ 0.82w − 0.06w 2  24 

2

20 < Re ≤ 260

 C Re  log10  D − 1 = −0.7133 + 0.6305w  24 

3 4 5 6

260 < Re ≤ 1500 1500 < Re ≤ 1.2 × 104 1.2 × 104 < Re ≤ 4.4 × 104 4.4 × 104 < Re ≤ 3.38 × 105 w = log10Re

log10CD = 1.6435 − 1.1242w + 0.1558w2 log10CD =− 2.4571 + 2.5558w − 0.9295w2 + 01049w3 log10CD =− 1.9181 + 0.6370w − 0.0636w2 log10CD =− 4.339 + 1.5809w − 0.1546w2

Table 11.2  Basic Dimensions, Terminal Settling Velocity, and Drag Coefficient in Water of the Used Model Particles (Iliev, 2016) Particle

Particle Density (kg/m3)

d ± σ (mm)

ut (m/s)

Ret

Cdt

Flow Mode

Alginate 2% Alginate 3% Alginate 4%

1020 1030 1040

1.52 ± 0.48 1.51 ± 0.49 1.50 ± 0.5

0.019 0.033 0.038

28.6 49.9 57.4

4.83 4.269 3.823

Transitional Transitional Transitional

alcohol solutions. Tables 11.2 and 11.3 show the dependencies for this parameter. It has been found that the terminal settling velocity decreases smoothly with the increase in the sugar solution concentration for the beverage production systems by fermentation in a fluidized bed reactor. The changes follow a second-order polynomial law. The decrease in the terminal settling velocity of the gel particles in water-alcohol solutions was changed according to a linear law as a function of the solution density. The functions reflecting the density-drag coefficient dependence also have a linear character (Iliev, 2016). The next major feature of the packed/fluidized bed is its minimal fluidization rate umf. It is defined as the linear rate of the fluid flow at which the bed goes from the packed to fluidized bed; above that

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Table 11.3  Regression Dependencies for the Changes in the Terminal Settling Velocity as a Function of the Density of the Sugar Solution (Iliev, 2016) Particle

Density of the Particles (kg/m3)

Regression Model

R 2

ut2 = 7E−07ρ2 − 0.0016ρ + 0.9008 ut3 = 2E−06ρ2 − 0.0048ρ + 2.6542 ut4 = 1E−06ρ2 − 0.0031ρ + 1.7066

0.7706 0.8634 0.8718

ut2 = 0.2585 − 0.0002ρ ut3 = 0.2281 − 0.0002ρ ut4 = 0.1754 − 0.0001ρ

0.8643 0.9369 0.8992

MODEL WATER-SUGAR SOLUTIONS

Alginate 2% Alginate 3% Alginate 4%

1020 1030 1040

MODEL WATER-ALCOHOL SOLUTIONS

Alginate 2% Alginate 3% Alginate 4%

1020 1030 1040

value, the bed only exists in a fluidized state until reaching the terminal settling velocity. This rate depends on the particle density, the bed porosity, and the density of the fluid used (Kostov, 2007, 2015; Iliev, 2016). The transition of the bed to a fluidized state is related to the balance of forces in the bed (Escudero and Heindel, 2011; Iliev, 2016). The fluidization process is complicated as it depends both on the hydrodynamic situation in the apparatus and on the nature and characteristics of the particles. Data in the literature can be summarized as follows: the functional pressure gradient of the bed height should be presented as the difference between the specific gravity of the suspension and the hydrostatic pressure (Iliev, 2016): −

dp f dz

= ρ ε g − ρ g = (1 − ε ) ( ρ P − ρ ) g

(11.10)

For initiation of the transition from a stationary to fluidized bed, it is initially judged by the changes in the nature of the dependence of the bed resistance Δp and the flow rate (Fig. 11.3). If ε0 is the initial porosity of the packed bed and Archimedes’ law is taken into account, the pressure loss condition can be overwritten as follows (Iliev, 2016; Kostov, 2007): ∆P = ( ρ S − ρ ) g (1 − ε 0 ) (11.11) H0

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Eq. (11.11) is theoretical, and different dependencies are recommended for the different flow zones: laminar, transient, and turbulent. The most famous among them is Ergun’s dependence, which can be used for the whole range of fluidization rates:

2 - Reverse process

gH0 1

µ u (1 − ε ) (1 − ε ) ρ u ∆P = 150 + 175 (11.12) L dp2ε 3 ε 3 dp2 2

1 - Normal process

∆P, Pa

2

2

The fluidization of the bed is related to the balance of forces acting between the particles forming the bed and the liquid flow. Experimental separation is difficult since only the general forces of interaction can be directly defined, and the attempts to interpret them are contradictory. This is due to the influence of the particles on the fluid flow, which leads to an additional force acting on the particles which is a function of the pressure gradient (Di Felice, 1995). In order to avoid the difficulties involved in interpreting the forces of interaction, the so-called “voidage function” f (ε) is used in practice. It is described with the dependence: f (ε ) =

FD FDS

(11.13)

where FD is the resistive force in the liquid-particles system; FDS is the resistance force for a single particle. The influence of the solid particle concentration in the bed is taken into account by introducing this function. In some cases, interaction forces are replaced by other proportional dimensions. Depending on the problem under consideration, characteristics such as the settling velocity in a batch process, the minimal fluidization rate, or the bed pressure loss are examined. In these cases, f(ε) is connected with the pressure characteristics by the following dependence (Di Felice, 1995): f (ε ) =

4Gaε 2

u 2   3C D Ret  ut 

2

u C =   Dt ε  ut  C D

(11.14)

In order to determine the parameters in the voidage function, that is, the dependence between the forces in the bed, it is necessary to know the expansion of the fluid flow. It is generally assumed that the liquid bed expands homogeneously, although this is not entirely true. Four cases of fluidization are known in the literature and are

umf, m/s u, m/s Fig. 11.3  Pressure losses in a real fluidized bed (Iliev, 2016).

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characterized by different dependencies. In the first case, the expansion is homogeneous and the following dependence is valid: u =εn ut

(11.15)

The known dependencies of Richardson and Zaki, which are valid for different flow modes in the fluidized bed, are used for the expansion index n in this case. In addition, equations derived by Rowe, Khan and Richardson, and others are used (Iliev and Kostov, 2013; Iliev et al., 2014a, b). In the second and third cases, the expansion is not homogeneous, and a deviation from the first case is possible depending on the nature of the particles. Typically, a change in the quality of the expansion is observed, and after a certain rate the bed expands more or less. The experimental data in the dissertation thesis of Iliev (2016) suggest that the fluidized bed of light particles should be described with a dependence characteristic of the second and third fluidization cases.

11.2.3  Bubbling Columns and Airlift Bioreactors 11.2.3.1  Bubbling Columns A basic parameter for modeling, controlling, and scaling up of this kind of fermentation equipment is the flow rate of the liquid intake and, in the presence of a gas phase, the gas flow rate. The homogeneous distribution of the liquid must provide for the overcoming of the external mass exchange resistances in the system (Nedovic and Willaert, 2004). An important direction for intensifying mass exchange in bubbling bioreactors is the search for opportunities to increase the driving force of mass exchange by increasing the height of the fluid in the apparatus. Thus, bubbling columns in which the H/D > 2 ratio were developed. This increases the renewal of the contact surface of the gas during its elevation in the column and the increase of the level of micro- and macroturbulence, as a result of which the transfer of oxygen to the microorganisms is increased (Angelov and Kostov, 2009; Iliev, 2016).

11.2.3.2  Airlift Bioreactors The mixing of the liquid in this type of system is defined by the gas holdup and the mixing time, which in turn determine the circulation of the liquid and the mass exchange characteristics. Liquid circulation is due to the difference in hydrostatic pressure and density in the aerated and the nonaerated zone and the total amount of gas released in the phase separator (Martínez and Silva, 2013).

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The operation of this type of system is difficult to summarize because the gas phase can be used for the biological process (aerobic processes), but it can also be an inert gas that moves the solids. The basic parameters for modeling and scaling up of these systems are the dependence between the areas of the downcomer and riser flows (AD/AR), the reactor height, and the height of the upper section as well as the linear velocities of the gas and liquid phases. These parameters determine the degree of fluid circulation, the gas holdup, the energy dissipation, and, as a result, the mass exchange and hydrodynamic conditions of the reactor (Martínez and Silva, 2013). Another major difficulty in modeling systems of this kind is the fact that the hydrodynamic environment in them strongly depends on the rheological characteristics of the liquid. This, in turn, leads to various asymptotic calculations to determine the nature of the fluid movement inside the reactor (Martínez and Silva, 2013). It can be concluded that the modeling parameters of the airlift bioreactors are related by complex interdependencies, and it is difficult to determine uniform dependencies for modeling the hydrodynamic environment within them. In this respect, the parameters can be divided into two main groups: modeling parameters—reactor height, the dependence between the areas of the downcomer and riser flows (AD/AR), the geometric parameters of the gas separator; and operating parameters—flow rate of the gas phase and distance from the bottom of the apparatus to the gas sprayer. These two sets of parameters determine the liquid rate inside the apparatus and the mutual influence of the pressure losses and the phase content in the apparatus. The viscosity of the liquid is an independent variable, which in its turn is a function of the gas holdup of the apparatus (Martínez and Silva, 2013). Another basic rule is that the operation of external loop reactors is more stable than that of internal loop reactors. The gas holdup can be regulated using different technical methods in the outer contour regardless of the operating parameters in the main column (Loh and Liu, 2001). The flow mode is determined by the following basic parameters of the bioreactor (Martínez and Silva, 2013): • Riser. In the riser, the liquid and the gas move upwards, with the gas phase rate exceeding that of the liquid. The two rates are equal only in the case of a homogeneous flow. Homogeneous flow is observed when the gas bubbles are with very small diameters. From a practical point of view, in this type of apparatus, two flow modes are distributed: 1. Homogeneous bubbly flow regime in which the bubbles are relatively small and uniform in diameter and turbulence is low. 2. Churn-turbulent regime in which a wide range of bubble sizes coexist within a very turbulent liquid. This mode is obtained

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from the homogeneous mode by increasing the gas flow rate or by increasing the turbulent liquid regime when changing the reactor cross-section. • Downcomer. The fluid moves in a downward direction and can carry bubbles from the gas phase. It is important for the liquid to move at a much faster rate than the free fall of the bubbles in order to release the bubbles. This can be achieved with a low liquid flow at the inlet of the apparatus, where the bubbles act out of the liquid very quickly. • Gas separator. The gas separator is often overlooked in the descriptions of experimental airlift bioreactor devices, although it has a significant influence on the fluid dynamics of the reactors. The geometric design of the gas separator determines the extent of disengagement of the bubbles entering the riser. The basic parameters for modeling the system are: - Gas holdup: the volumetric fraction of the gas in the total volume of a gas-liquid-solid dispersion (Martínez and Silva, 2013):

ϕ1 =

VG VL + VS + VG

(11.16)

where the subindexes L, G, and S indicate liquid, gas, and solid, and i indicates the region in which the holdup is considered, that is, gas separator (s), the riser (r), the downcomer (d), or the total reactor (T). Gas holdup is an indicator of the mass exchange characteristics of the apparatus and of the intensity of the fluid circulation. The latter is determined by the difference in the gas holdup in the riser and in the downcomer of the reactor. The geometric characteristics of the reactor significantly influence the gas holdup. The changes in the ratio of the riser and the downcomer section lead to changes in the residence time in each of the parts and affect the total gas holdup of the system (Martínez and Silva, 2013). In reactors with internal circulation, the gas holdup is described by the following general dependence: A  ϕr = a ( J G )α  d   Ar 

β

(µ ) ap

χ

(11.17)

where φr is the gas holdup in the riser of the reactor; JG is the linear rate of the gas phase; μap is the effective viscosity of the liquid; α, α, β, γ are the experimental constants depending on the reactor geometry and the liquid characteristics. This dependence can be used to determine the total phase content in the system by varying the reactor parameters. Depending on the reactors used, the constants have certain values and data for similar dependencies can be found in detail in Martínez and Silva (2013).

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   355

The circulation of the liquid inside these systems is important for their operation. The gas holdup in the riser element of the apparatus depends strictly on its geometrical configuration as well as on the geometric characteristics of the separator and on the level of the liquid in the separator. Data in the literature show that these factors affect the separation of the gas in the separator, and thus the gas circulation in the downcomer flow can be controlled (Martínez and Silva, 2013). Unlike the riser section, the gas holdup in the downcomer section is lower and depends largely on the gas separator design. The dependence between the two gas holdups is linear (Martínez and Silva, 2013).

11.2.4  Membrane Bioreactors The operation of this type of immobilized cell system depends on the following basic parameters: operating conditions (temperature, pressure, flow rate), membrane current mode (above all, the flow around the membranes is turbulent in order to avoid negative phenomena such as concentration polarization and clogging of the membranes), and the mass exchange conditions. The main difficulties are related to mass exchange in the system, and therefore we will discuss some major dependencies in this area (Iliev, 2016; Nedovic and Willaert, 2004). Mass transfer in this type of system includes six main components: transport of the substrate from the liquid phase to the membrane, transport through the membrane and transport and reaction in the immobilized cells, secretion of the product through the cell wall, transport of the product through the membrane, and transport of the product in the liquid phase (culture medium). Modeling is extremely difficult, and in some cases, it is simplified by modeling some of the elements with known dependencies. This mostly applies to convective mass exchange in the liquid phase, especially if the flow is known to be turbulent (Eq. 11.18): J i = kls (C b − Cex )

(11.18)

where Ji is the molar flow of the component; kls is the coefficient of mass exchange of the component; Cb and Cex are the concentrations of the component in the volume and on the surface of the membrane. The transport within the membrane is described by various equations which depend on the type of membrane and operating conditions used. In general, the Fick diffusion law may be used, depending on the type of the membrane:  C − Cin  J i = Dim ki  ex  l  

(11.19)

where ki is the partial coefficient of mass exchange inside the membrane of the given component; Cin is the concentration of the

356  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

component inside the membrane; l is the membrane thickness; Dim is the permeability of the membrane. Eq. (11.19) may be complicated if a flow passes through the pores of the membrane and should also be taken into account in the mass exchange.

11.3  Dependence Between the Structure of the Flows in Immobilized Cell Bioreactors and the Fermentation Kinetics—A Case Study Since modeling of immobilized cell systems is a complex task and we have to take into account the nature of the process carried out in the system, we will discuss a specific case of modeling of such a system—ethanol production for nutritional purposes in a fluidized bed bioreactor of alginate preparations. The study was conducted with Saccharomyces cerevisiae Safbrew-S33 cells and S. cerevisiae 46EVD cells immobilized in 3% Caalginate under the conditions given in detail in (Iliev, 2016; Parcunev et al., 2012). The experiments were performed with a medium of optimized composition (g/dm3): glucose: 118.40; (NH4)2SO4: 2; KH2PO4: 2.72; MgSO4·7H2O: 0.5 (Kostov, 2007, 2015), sterilized for 20 min at 121°C. For the particular system, 300 g of immobilized preparation were used and the fermentation was carried out at 28°C and pH = 4.5. The laboratory column bioreactor (Fig.  11.4) contained a plexiglass column 1 with a height of 980–1000 mm and an inside diameter of 56 mm located between stainless steel flanges. The column had a distribution grid 2 and a glass bead drain 3. The drain served to better distribute the liquid in the reactor. The model solution was circulated through an external circuit via pump 4. The flow rate of the liquid was measured by a calibrated rotameter 5. At the upper end of the reactor, there was a cylindrical phase separator 7 with a height of 200 mm and a diameter of 120 mm. Nipples 15 were positioned on the column 1, and they were used for sampling or for placing manometers (Iliev, 2016). The system could work with model solutions or with a nutrient medium. The hydrodynamic situation in the apparatus was determined by single step and impulse action methods according to the method described in Kostov et al. (2013). Before the immobilized biocatalyst was introduced into the apparatus, the apparatus and the biocatalyst had been washed several times with sterile saline solution. A portion of the sterile nutrient medium had been added to the immobilized biocatalyst and the resulting suspension was poured into the apparatus. Then the rest of the broth medium was added to the bioreactor and the total volume reached 3.5 dm3. The carrier was brought into a pseudo state. The temperature

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   357

13 12 2,345

7

16

10

11

Model liquid outflow

Outflow

8 15 14 Mahometbp

6 1 2 3

5

4

8

9

9

9

Water

Water

17

NaCl

18

Fig. 11.4  Scheme of a fluidized bed column bioreactor (Iliev et al., 2014a, b). (1) plexiglass column; (2) distributor; (3) drainage; (4) peristaltic pump; (5) rotameter; (6) ruler; (7) phase separator; (8) three-way valves; (9) reservoirs; (10) valve; (11) conductometric cell; (12) conductometer; (13) personal computer; (14) differential manometer; (15) nozzles; (16) exit cell; (17) peristaltic pump for nutrients; (18) syringe;

and the pH of the culture medium were adjusted. Batch alcohol fermentation was carried out for 24 h. At the beginning of the process, the height of the biocatalyst bed was determined in a nonfluidized state. The recirculation pump was then switched on by setting a flow rate of 0.5 or 0.63 cm3/(cm3 min). After stabilization of the fluidized flow, the bed height was measured. During the process, samples were taken from the bioreactor every 3 h for the determination of the alcohol and sugar content. During this period, the height of the fluidized bed was also measured.

11.3.1  Types of Reactors Depending on the Nature of the Flow The flow of the fluids (gas, liquid, or solid particle stream) into the reactors is uneven, that is, the individual parts of the flow have a

358  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

different rate. This, in turn, determines the different residence time of the flow elements in the reactor and hence the different duration of the biochemical processes in the reactor. The most complete flow structure information can be obtained by knowing the flow rate at any point in the reactor. The mathematical description of the rate profile using the hydrodynamic equations is obtained as a system of differential equations whose solution is possible only in extremely simplified cases (Angelov et al., 2012). Depending on the established fluid flow profile in the reactor, there are three main cases: a plug flow reactor; a reactor with ideal mixing; and real reactors. By definition, there is a full displacement mode (piston mode) without any radial mixing of the components in a plug flow reactor. In a continuous reactor with ideal mixing, the phenomena are considerably more complex. In this case, the average residence time of the liquid components in the reactor depends on the volume of the system and the flow rate of the continuous flow, and the actual residence time of the flow elements is different from the average residence time (Angelov et al., 2012). The determination of the system parameters is done by two functions, namely: integral function of the distribution I and differential function of the distribution E. Functions I and E characterize the distribution of the residence time of the particles inside the reactor, so they are also called internal functions. These two functions can be determined experimentally by the so-called tracer technique—insertion of a nonreactive substance called a tracer or an indicator into the reactor. The reaction of the system is determined by monitoring the changes in the indicator’s concentration in the output reactor flow at specific time intervals. Input disturbance signals may have different shapes: random, cyclic, stepped, pulsed, etc. As a result of this study, data which can determine the nature of the fluid flow in the reactor are obtained (Angelov et al., 2012). Virtually every random regime, that is, the real bioreactor, can be described by a combined model composed of the two ideal variants and arranged in a particular combination. The composition of combined models is based on the recording of the two main functions and the search for the maximum approximation of the real system to the selected combination of mathematical models (Angelov et al., 2012). First, it is necessary to clarify the structure of the streams in the presented bioreactor in order to establish the dependence between the hydrodynamic characteristics of the system and the fermentation process. The present work analyzes the structure of the flows in the fluidized bed column presented in Fig.  11.4, summarizing a series of data obtained by Kostov (2007), Iliev (2016), and Kostov et  al.

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   359

(2013). The recording of the experimental characteristics was performed with positive and negative one step influence in order to determine the nature of the fluid movement in the active zone of the fluidized bed (Fig. 11.5). The experimental data obtained were processed using RTD 3.14 specialized software (workbook RTD 3.14, n.d.; Iliev, 2016).

F(t)

Positive step

Ideal reactor

1 0.9 0.8 0.7

F(t)

0.6 0.5 0.4 0.3 0.2 0.1 0

(A)

0

200

400

600

800

1000

Time, s

F(t)

Negative step

Ideal reactor

1 0.9 0.8 0.7

F(t)

0.6 0.5 0.4 0.3 0.2 0.1 0

(B)

0

200

400

600

800

Time, s

Fig. 11.5  F-curve in the study of the flow structure in a light bead fluidized bed bioreactor. (A) Positive single step influence and (B) negative single step influence.

1000

360  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

11.3.1.1  Model of the Plug Flow Bioreactor With Back Mixing (Fig. 11.6) We will start the modeling with the simplest case, namely the ideal plug flow bioreactor with back mixing (Fig.  11.6). In this case, apart from the average residence time as a parameter of the model, the Peclet criterion (Pe) has to be used, which includes the presence of an axial dispersion coefficient, that is, of the mixing of the flow elements. The increase in the stirring is reflected in an increase in the axial dispersion coefficient. The presence of axial dispersion also increases the average retention time in the apparatus (Table 11.4).

11.3.1.2  Combined Reactor Model (Fig. 11.7) The presence of mixing in the core of the fluidized bed may also be described as a combination of reactors from the two groups. In this case, it is acceptable to consider the bed as composed of one ideal plug flow reactor and an m-number of cells with ideal mixing. The model parameter data are shown in Table 11.4. Similar to the previous model, the average residence time of the fluid decreases as the flow rate of the fluid increases, while the number of cells with ideal mixing varies within the range of 4–7. The total residence time in the piston and the cells with ideal mixing corresponds to the residence time in the plug flow reactor with back mixing. The data in Table 11.4 give us reason to conclude that the ideal plug flow system prevails in the fluidized bed, which is important when searching for a dependence between the hydrodynamics

Fig. 11.6  Parameters of a plug flow bioreactor with back mixing.

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   361

Table 11.4  Parameters of Models Describing the Nature of Fluid Movement in a Fluidized Bed Bioreactor Parameters of a Model of a Plug Flow Bioreactor With Back Mixing u (m/s)

ta (s)

Ре

Ε

Dax × 106 (m2/s)

0.00364 0.00728 0.0109 0.0146

265.4 145.9 86.17 65.83

345.8 176.9 132.3 88.8

0.410 0.562 0.69 0.901

10.31 40.33 80.07 161.21

Parameters of a Combined Model of a Reactor With Ideal Plug Flow and an m-Number of Reactors With Ideal Mixing u (m/s)

tap (s)

tas (s)

M

ta (s)

ε

0.00364 0.00728 0.0109 0.0146

210.2 115.3 58.3 42.4

10.7 8.4 4.0 3.7

6 4 7 7

274.4 141.7 86.3 68.3

0.410 0.562 0.69 0.901

Fig. 11.7  Scheme of a combined reactor.

362  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

in the apparatus and the fermentation process. Although at first it seems that such a dependence does not exist, in the next section we will prove that the dependence is very strict and should be taken into account in the process modeling of the immobilized cell systems.

11.3.2  Theoretical Analysis of the Influence of the External Diffusional Resistances on the Continuous Alcohol Fermentation Kinetics

100

22

90 80 70 60

10 9

20

8

18

7

16 14

6

12 5

10 8

4

6 50

4 0,2

0,4

0,6

0,8

1,0

3

6 5 4 3

Biomass, g/dm3

26 24

Productivity, g/(dm3 . h)

110

Ethanol, g/dm3

Redusing sugars, g/dm3

The presence of diffusional resistances in the immobilized cell systems (Shopska et al., 2019) leads to changes in the fermentation process. In most cases, the avoidance of diffusional resistances depends on the changes in the hydrodynamic conditions in the apparatus. Therefore, the dependence of the hydrodynamic parameters of bioreactors and the fermentation process can be made through the diffusional resistances. The suggested analysis is based on a series of fermentation process data given in detail in Kostov (2007) and Iliev (2016). The analysis starts with monitoring of the fermentation process dynamics in continuous mode at different dilution rates (Fig. 11.8). The data show that the system’s productivity has its maximum values in a given zone of

2 1

D, h-1 Ethanol - experimental Redusing sugars - experimental Productivity - experimental Biomass - experimental Biomass - model Ethanol - model Productivity -model Redusing sugars - model

Fig. 11.8  Continuous alcohol fermentation with immobilized S. cerevisiae 46 EVD cells (Kostov, 2007).

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   363

dilution rates. The limiting of this parameter depends entirely on the presence of diffusional resistances in the system. While in the accumulation of biomass in continuous mode we can assume that Dopt = μ, in the fermentation systems with immobilized cells for ethanol production the optimal dilution rate is determined by the ethanol accumulation in the medium. The latter gives little freedom in the choice of search parameters for the dependence between the hydrodynamics and the fermentation process. In the specific case presented in Fig. 11.8, the optimal dilution rate zone was in the range of 0.7–0.8 h−1. The data analysis performed in this zone indicated that the system’s maximum productivity of approximately 10 g/(dm3 h) was at Dopt = 0.725 h−1. However, this productivity, under the specific conditions of the experiment, resulted in a relatively low ethanol yield of only about 25% of the theoretical yield. This was mainly due to diffusional resistances. The search for the dependence between the hydrodynamics, the fermentation process, and the diffusional resistances requires the model to be simplified by introducing two constraints (Kostov, 2007; Iliev, 2016): the parameters of the continuous stationary mode model can be found by conducting batch processes; the concentration of cells in the apparatus determines the synthesis of ethanol by providing the necessary enzymatic systems for the transformation of the substrate to ethanol, that is, biomass is a constant providing only enzymatic systems. Under these two conditions for the continuous mode of alcohol fermentation, Monod’s model for continuous systems can be used: dX S = ( µm − mSYXm/S ) X − DX dτ KS + S dP = qp X − D ⋅ P dτ qp X dS = D ( S0 − S ) − dτ YP/S

(11.20)

The system of Eq. (11.20) does not include diffusional resistances, that is, the model of the immobilized cell process is matched to a free cell model. The parameters of the model can be calculated according to analogous processes with free cells. The next important condition for a proper analysis of the impact of diffusional resistances is to determine whether there is a substrate and/or product inhibition. The results presented and the stable operation of the system, especially in the area of the optimal dilution rates, indicate no substrate inhibition. The lack of product inhibition is also due to the fact that in the active zone of the apparatus, as already shown, we have a piston mode of motion that eliminates product inhibition to a large extent.

364  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

It is necessary to know certain parameters of the batch mode in order for system (11.20) to be solved. First, it is necessary to know the maximum specific growth rate of the population and the coefficient of effectiveness of the immobilized cell system. The research published in Kostov (2007) and Iliev (2016) suggests that the internal diffusional resistances in the fermentation system used and the inclusion of cells in Ca-alginate do not have a significant impact. Cells in the immobilization matrix grow at a maximum specific growth rate in the range of 0.37–0.38 h−1, and the efficiency factor with respect to the internal diffusional resistances exceeds 90%, that is, the influence of diffusion in the immobilization matrix is minimal. The mS coefficient is equal to the specific substrate consumption which maintains the viability of the existing cells at a given time. It is an important parameter characterizing the physiological state of the culture. This part of the total amount of consumed substrate is ultimately spent on cellular structure resynthesis, ion-gradient maintenance, and transport of neutral molecules between the cell and the medium, and between cell structures (Kostov, 2015). The mS value can vary widely. In the specific study, it was found to be high (mS = 4.5 g/(dm3 h)). This is due to the increased number of viable cells in the operating volume of the reactor, on the one hand, and to the reduced living space in the pores of the carrier, on the other (Kostov, 2015). As a result of the parameter identification, equation system (11.20) can be presented in real form, but it is more important to determine the zone of the optimal dilution rate. In this case, it varied within the range of 0.7–0.8 h−1, and for the particular study, it was found to have a value of 0.75 h−1. The data from the continuous processes presented in Fig. 11.8 and the quoted results of the batch process studies show that external diffusional resistances have greater influence on the fermentation process. Their impact is related to the formation of a fixed layer around the biocatalyst through which the product and the substrate are to be transferred by molecular diffusion. Depending on the hydrodynamic situation in the apparatus, the size of this film varies, and the substrate passage (through it) occurs extremely slowly and at low diffusional coefficient rates (Kostov, 2015). The elimination of the impact of external diffusional resistances requires the development of an optimization procedure that should include the knowledge of hydrodynamics within the investigated apparatus, the kinetics of the fermentation process, and other conditions. For this purpose, the following assumptions are made (Kostov, 2007; Angelov and Kostov, 2011): 1. The reactor diameter is constant and the height of the system is calculated from the height of the fluidized bed. 2. The apparatus works as a reactor with ideal mixing, and in the core area (the fluidized bed) as an ideal plug flow apparatus.

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   365

3. The immobilized preparation is evenly distributed in the volume of the apparatus, and the substrate and the product diffuse through the fixed layer according to Fick’s law. 4. The reaction is of the monosubstrate type, and the CO2 formation does not disturb the hydrodynamic environment in the apparatus due to the small diameter of the bubbles. The last assumption is controversial from a fermentation point of view, but since there is an equation only for the product, that is, ethanol, in the system of differential equations, this assumption is fair from the point of view of the flow hydrodynamics. One can describe the dependence between the fermentation process parameters and the hydrodynamic environment in the apparatus on the basis of these assumptions and using the equations for the fluidized bed: dS = u f A ⋅ ( S0 − S ) − φS dτ dP εV f = u f A ⋅ ( P0 − P ) − φP dτ

εV f

(11.21)

where φS and φP are the rates of transport of the substrate and the product through the immobile film on the surface of the particle. Eq. (11.21) indicates that the fermentation process rate may be associated either with increasing the amount of the solid phase or with even stirring, thereby providing a maximum contact surface between the particles of the biocatalyst. Since the first condition would violate the fluidization process, the second condition immediately comes into force. In this case, the equations for the specific transport rates of the substrate and the product in the stationary film take the form of: 6 φS = kS ( S − S in ) ε SV f dp (11.22) 6 φP = kP ( P in − P ) ε SV f dp where kS and kP are the coefficients of diffusion of the substrate and the product through the immobile film around the particle; Pin and Sin are the concentration of the product and the substrate on the particle surface. Eq. (11.22) immediately shows the influence of the solid phase amount on the reaction rate in the stagnant film. The rate of this process under conditions of constant concentration difference can be increased by reducing the particle size or by increasing the solid phase amount in the apparatus. A problem arises because the concentration difference is by no means constant, and it gradually changes during fermentation. The influence of ethanol concentration is of particular importance. The solid phase holdup in the bed gradually begins to change; therefore, the mass exchange process begins to be limited by the hydrodynamics in the apparatus.

366  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

The determination of the surface substrate and product concentrations is almost impossible, so it is necessary to calculate them. When both types of resistances (internal and external) influence the system, the equations for the particle surface concentrations are of the type (Kostov, 2007, 2015; Iliev, 2016): S in = S −

dp 6 kS

P in = P +

φP = η

η

dS dτ

kS ( S − S in ) kP

dS (1 − ε )V f dτ

(11.23)

(11.24)

where kS and kP are the coefficients of diffusion of the substrate and the product through the immobile film around the particle; Pin and Sin are the concentration of the product and the substrate on the particle surface. Eqs. (11.23) and (11.24) show that there is a definite dependence between the dynamics of the fermentation process, the diffusional resistances, and the hydrodynamic situation in the apparatus. It is interesting to note that the equation for the product does not include the specific surface of the biocatalyst, whereas in the substrate equation this component of the dependencies is involved. This is due to the fact that the transformation process takes place inside the carrier while the consumption of the substrate is to be carried out on the entire surface of the biocatalyst. The co-resolution of Eqs. (11.20) through (11.24) results in obtaining an optimization dependence that can optimize the flow hydrodynamics to ensure maximum system performance:

η

uf A   1−ε  X    DS0 − DS − qP  = PD + ε  εVF  YP/S D  

(11.25)

Eq. (11.25) is a generalized dependence and implies the possibility to calculate the hydrodynamic mode in the bioreactor so as to ensure maximum system productivity. It determines the existence of a strong dependence between the hydrodynamic situation in the apparatus and the fermentation process dynamics. This dependence is the reason for the observed reduced yield and the strongly reduced productivity of the ethanol system. The solution of Eq. (11.25) implies a constant solid phase holdup in the reactor volume, which, however, can hardly be achieved due to the changes in the medium density during fermentation. Therefore, the fluidization is achieved at a linear flow rate of 0.0088 m/s at the beginning of the fermentation process, while at the end the rate has to be about twice as high (Iliev, 2016). To explain this, let us look at the changes in the parameters during the fermentation process.

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   367

Glucose Ethanol - model

Glucose - model Biomass

Ethanol Biomass - model

140

25

120

15

80 60

10

40

Biomass, g/dm3

Glucose, g/dm3 Ethanol, g/dm3

20 100

5 20 0

0

3

6

9

12

(A)

15

18

21

24

27

30

0

Time, h 90 H = 0.0004T4 - 0.0329T3 + 1.0596T2 - 14.3T + 83.098 R2 = 0.9854

80

Bed height, cm

70 60 50 40 30 20 10 0

(B)

0

3

6

9

12

15

18

21

24

27

Time, h

Fig. 11.9  (A) Dynamics of the fermentation process at a flow rate of the circulating medium of 0.63 cm3/(cm3 min). (B) Dynamics of the changes of the fluidized bed height in alcohol fermentation in a fluidized bed with a circulating flow rate of 0.63 cm3/(cm3 min).

The results from the hydrodynamic situation data show that, for the system used, it is difficult to achieve a flow rate >0.63 cm3/ (cm3 min), whereas a decrease in the flow rate below 0.5 cm3/ (cm3 min) leads to a decrease in the bed porosity, which in turn can affect the fermentation process dynamics. The data of the fermentation process parameters and the fluidized bed height are presented in Figs. 11.9 and 11.10. In the first fermentation regime (flow rate of 0.63 cm3/(cm3 min)), the fermentation started intensively, resulting in an ethanol yield of

30

368  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

e

es

eCO2

0.900 0.800 0.700

e,es,eCO2

0.600 0.500 0.400 0.300 0.200

Fig. 11.10  Dynamics of the changes in the bed porosity during alcohol fermentation and at a circulating fluid flow rate of 0.63 cm3/(cm3 min).

0.100 0.000

0

3

6

9

12

15 18 Time, h

21

24

27

30

53% for 12 h. This, in turn, led to a decrease in porosity by 3.25 times and consequently to bed contraction. The changes in the bed height were due to the following reasons: decrease in the bed height due to the reduction of the medium density during fermentation and CO2 release. The increasing ethanol concentration, according to the 3% alginate models, should force the bed to increase its porosity (due to the increased expansion coefficient), but the absorption rate of the substrate led to the opposite trend—the decrease in the bed height. The changes in the bed porosity and the conclusion that the CO2 release changes the hydrodynamics of the flow (Fig.  11.10) are also interesting. The reason for this is that the gas bubbles are not prone to coalescence and move in a relatively stormy flow. This results in a reduction of the solid phase retention in the fluidized flow. This is the basis for the observations of local “outbursts” of the solid phase, which lead to changes in the hydrodynamic environment in the apparatus. Similarly, a study of the alcohol fermentation process at a flow rate of the circulating liquid of 0.63 cm3/(cm3 min) was carried out. The data are presented in Figs. 11.11 and 11.12. The fermentation process took place twice as fast and 90% of ethanol was obtained within only 15 h at this medium flow rate. The process took place at a 2.7-fold higher specific ethanol production rate, and the maximum specific growth rate was three times as low. This shows that biomass basically accumulates ethanol, and smaller amounts of the substrate are utilized to accumulate biomass. The second mode is optimal for ethanol production for the ­following reasons. In the first place, the lower rate implies increased residence time of the fluid in the fluidized bed area, and longer time

Glucose

Ethanol

Biomass

Glucose - model

Ethanol - model

Biomass - model

140

25

120

20

100 80

15

60

10

40

Biomass, g/dm3

Glucose, Ethanol, g/dm3

Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION   369

5

20 0

0 0

3

6

9

12

15

Time, h

(A) 60

Bed height, cm

50

y = 0.0005t 4 - 0.049t 3 + 1.2238t 2 - 11.403t + 51.079 R 2 = 0.9984

40 30 20 10 0

(B)

0

3

6

9

12

15

Time, h

Fig. 11.11  (A) Dynamics of the fermentation process at a circulating flow rate of 0.5 cm3/(cm3 min). (B) Dynamics of the changes in the fluidized bed height in alcohol fermentation in a fluidized bed with a circulating flow rate of 0.5 cm3/(cm3 min).

for the specific biochemical reactions to occur. Secondly, the lower flow rate allows easier degassing of the liquid in the column separator. Another reason is that the low flow rate of the liquid does not allow the formed CO2 stream to disturb the fluidized bed. In the second variant, a decrease in the bed height was observed as well, the variation rate of this parameter being close to that of the first variant. The changes in the height were again due to a decrease in the density of the medium during sugar consumption and to the ethanol and CO2 release. Again, the tendency to bed porosity decrease is noticeable and this decrease cannot be compensated for by the increase in the expansion index due to ethanol separation (Fig. 11.12).

370  Chapter 11  IMMOBILIZED CELL BIOREACTORS IN FERMENTED BEVERAGE PRODUCTION

e

es

eCO2

0.900 0.800 0.700

e,es,eCO2

0.600 0.500 0.400 0.300 0.200

Fig. 11.12  Dynamics of changes in the fluidized bed porosity during alcohol fermentation and at a circulating fluid flow of 1500 cm3/min.

0.100 0.000

0

3

6 Time, h

9

12

15

Some general conclusions can be drawn for both fermentation variants examined. First of all, at the beginning of the fermentation process, the fluidized bed porosity can be described with the dependencies of the expansion index as a function of the sugar solution parameters. In the fermentation process, the expansion can be described with the sugar solution equations and can be corrected by the equations for the influence of the alcohol solution concentration. In both cases, when solving Eq. (11.25), it is necessary to take into account the variation of the bed porosity, which must be compensated for by a change in the fluidization rate in order to preserve the constant parameters of the fermentation process.

11.4  Methods for Scaling Up Bioreactors With Immobilized Cells Scaling up is a process of reproducing the results obtained in equipment of a certain size when conducting the process in an apparatus with other dimensions or other construction. The complex hydrodynamic, thermal, mass exchange, and biotechnological processes exclude the possibility of theoretical calculation of apparatus design and the operating modes. Most dependencies for the growth of microorganisms are obtained in laboratory conditions. For the practical use of these dependencies, it is necessary to transfer them to the appropriate scale for industrial processes, that is, to find scaling up criteria. Obtaining these criteria involves many difficulties because of the need to take into account factors of a different nature (Angelov et al., 2012).

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The methods for determining scaling up criteria can be classified as (Angelov et al., 2012): (a) Analytical-functional method. The criteria are obtained by solving different balance equations (thermal, mass exchange, energetic) based on the theoretical knowledge of a given process. In most cases, simplified descriptions (lower order equations) of bioreactor flows are used. This method is used less frequently due to insufficient knowledge of the ongoing fermentation processes. (b) Empirical method. The dependence of the preselected parameter on the other process variables and the design characteristics of the reactor are determined experimentally and applied for different volumes. The values of this parameter are kept constant during scaling up. (c) Dimensional analysis. The basis of this method is the determination of nondimensional numbers (criteria) that characterize the process by several basic indicators. These numbers are maintained constant in bioreactors having different volumes. (d) Functional regime analysis. The determination of the functional mode in which the fermentation process takes place is used in cases where it is impossible to maintain constant several nondimensional numbers in reactors of different volumes. When analyzing the mode, there are different time constants characterizing the process. In scaling up the apparatus, various researchers propose using the theory of similarity by offering a method of hydraulic modeling, positioning devices across the apparatus cross-section to ensure flow irregularity in the apparatus (Viestur et al., 1986; Angelov et al., 2012). Kinetic dependencies for microorganism growth must be taken into account together with the theory of geometric similarity when scaling up bioreactors. Good results are achieved through the theory of similarity, which allows generalizing the results of experiments in a nondimensional form and extrapolating them into similar systems for relatively simple systems and single-phase streams. Recently, with regard to the scaling up of complex systems such as bioreactors with the processes being carried out in them, experiments are the main sources of information. It should be noted that, at present, there are no equations developed for the movement of multiphase flows in general and there are no possibilities for setting limiting conditions on the nonstationary contact surface. The proposed mathematical models for describing the process kinetics only view one side of the biological processes and are not universal (Viestur et al., 1986; Angelov et al., 2012). According to the theory of similarity, systems are considered to be similar if they are characterized by equal criteria of similarity. With regard to the fact that bioreactors are mass exchange apparatuses designed to create the required intensive conditions of stirring, heat, and mass exchange, they can be scaled up as mass exchange apparatus (Viestur et al., 1986; Angelov et al., 2012).

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Here are some terminological concepts. In the literature, the scaling up characteristics are often called criteria, which is not always correct. Indeed, there are scaling up criteria (modeling) among them corresponding to the term “similarity criterion,” while other dimensions are parameters that characterize a particular size or side of the process but are expressed as dimensionless parameters. Therefore, when we talk about the scaling up of bioreactors, we will stick to the term “similarity criterion,” and the characteristics that do not meet the criterion idea will be called scaling up parameters. Table 11.5 lists the basic criteria and scaling up parameters used in the practical calculation of the apparatus (Viestur et al., 1986; Angelov et al., 2012). Such a number of criteria and parameters once again highlights the complexity of scaling up and the lack of a unified approach to solving this problem. It turns out that a reliable scaling up can be obtained using the Nud criterion combined with the criteria Re, Eu, Fr, Pr, We, and others. However, in most cases, the expected effect is not observed. According to various authors, this is due to the fact that the criterial equation attempts to replace the description of the multiphase system with a model developed for each phase without taking into account the interaction between the phases. For example, the Rec criterion does not characterize the hydrodynamic environment in the apparatus. Using Rec even in a single-phase flow in a smooth-wall apparatus results in an error in the results because the dM and n parameters characterize the stirrer rotation rate but not the flow rate (Viestur et al., 1986; Angelov et al., 2012). The gas consumption criterion Q for geometrically similar apparatuses is used to model the power required to mix the gas mixture, but gives satisfactory accuracy in rare cases. At the same time, it is noted that Q characterizes the correlation between the incoming gas flow, the coalescence, and the operating conditions insufficiently and is used to estimate power (Viestur et al., 1986; Angelov et al., 2012). The specific stirring power Nv is an integral parameter that characterizes the hydrodynamic environment in the apparatus in nonreal mode. Various multinumber cases of satisfactory scaling up of this parameter are known. It can be said that it remains the basic parameter for scaling up the stirring apparatus. The torque M is proportional to the specific stirring power Nv. In this case, it is advisable to use the specific power as its determination is considerably easier. In addition, Nv has a deeper physical meaning for the scaling up process (Viestur et al., 1986; Angelov et al., 2012). The scaling parameter J = NvdM, which is proportional to Nv, is artificial because it has no physical meaning different from the basic parameter Nv (Viestur et al., 1986; Angelov et al., 2012). The scaling up parameters τ, nτ, and t characterize the hydrodynamic environment in the apparatus in nonreal mode. They are used

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Table 11.5  Scaling Up Criteria and Parameters Name

Designation

Nusselt’s diffusion criterion Reynolds’ criterion Modified Reynolds’ criterion Froude’s criterion Modified Froude’s criterion Weber’s criterion Euler’s criterion Prandtl’s criterion Pecle’s criterion Galileo’s criterion Criterion of gas consumption Criterion of dynamic similarity Specific mixing power Specific stirring power multiplied by the stirrer diameter Homogenization time Stirring number Circulation time Oxygen dissolution rate Volumetric coefficient of oxygen mass exchange Coefficient of mass exchange from the liquid phase to the cell Internal turbulence scale Average gas-holdup Specific contact surface between the phases Linear flow rate Peripheral stirrer rate Rate gradient of the flow leaving the stirrer Torque per volumetric unit Calculated rate of the gas phase Specific oxygen consumption Permeability of the apparatus Mixing rate

Nu∂ = KLlDg−1 Re = Wlv −1 Rec = nd 2s v −1 Fr = W 2(gl)−1 Fr = n 2dMg−1; Frc = n2d 2s(gH)−1 We = ρW 2lσ−1 Eu = KN = ΔP (ρW 2)−1 Pr = vDg−1 Pe = WlDТ−1 Ga = gD 3v−2 Q = Vg(nd 3s )−1 P = EuFr = Ng(ndM3)−1(ρgH)−1 Nv Nvds τ u = nτ t = Vpq−1 M KLa KL − t λ0 = lReц−3/4 φ a WП = qS −1 Wτ = πdsn gradW~ndM1/3 M = ρn 2d 5s VP−1 Wg Vv П = v (ndM3)−1 ss = (n/k)(ds /D)g ≡ Ng(ρn3d 5s )

to scale up both bioreactors and stirring apparatus. They give satisfactory results in some simple cases of fermentation and stirring (Viestur et al., 1986; Angelov et al., 2012). The internal turbulence scale λ0 is one of the most important features of turbulent flow. It is reported that the oxygen transfer is preferably effected by turbulent diffusion under the conditions of intense stirring. That is why the scaling up of this parameter is promising. The

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difficulty lies in the fact that no theory of turbulence has been developed until now to allow a quantitative assessment of the λ0 parameter and the existence time of the whirls. Significant difficulties arise in the different practical methods for determining λ0. The calculated λ0 (Table 11.5) for scaling up reactors with stirrers can be considered as a weight approximation. This follows from the fact that the equation to determine λ0 is obtained by assuming that the whirls will exist when the inertial forces are equalized by the viscosity forces (Reλ0 = λ0 Wλ0v−1 ≈ ~1) (Viestur et al., 1986; Angelov et al., 2012). Parameters such as WП, Wτ, gradW do not appear to be defining current characteristics and therefore do not give satisfactory results in scaling up (Viestur et al., 1986; Angelov et al., 2012). The gas holdup φ is an important hydrodynamic parameter, especially for bioreactors with energy input by the gas phase, as it has a significant influence on the gas phase rate, the contact surface between the phases, and the circulation and mass exchange, respectively. The use of gas holdup in a combination with other criteria and parameters gives very good results (Viestur et al., 1986; Angelov et al., 2012). The specific contact surface between the phases a is an important hydrodynamic feature if its direct influence on the rate of mass exchange is taken into account. Using a for scaling up in a combination with other parameters also gives good results. The difficulty in using it is that there is no reliable methodology for determining a in apparatus with industrial volumes (Viestur et al., 1986; Angelov et al., 2012). The calculated rate of the gas phase WG is the most important hydrodynamic parameter for the group of bioreactors with energy input by the gas phase. The same contact surface in the model and in the industrial bioreactor is formed under identical hydrodynamic conditions, determined primarily by WG. The permeability parameter P characterizes the ratio between the amount of fluid entering the apparatus and the stirrer productivity. The given parameter approximates the hydrodynamic situation in the apparatus but cannot guarantee reliable scaling up. The mixing rate SS characterizes the rate of reaching mixture uniformity. It connects homogenization time, power consumption, stirrer size, and rotation rates. This parameter gives good results when scaling up the suspension mixing process.

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