STATIC MIXING IN FERMENTATION PROCESSES *

Transcription

1 STATIC MIXING IN FERMENTATION PROCESSES * INTRODUCTION MARIA GAVRILESCU Gheorghe Asachi Technical University of Iasi, Romania, Faculty of Chemical Engineering and Environmental Protection, Department of Environmental Engineering and Management, Iasi, Romania Process intensification is a relatively new concept that has been gaining importance because of its capacity to ensure process development with significantly reduced capital and operating costs, while enhancing process yield/selectivity and improving the inherent safety of many operations in industrial chemistry and biotechnology. The science and technology following the use of static mixers as mixing and micromixing devices has been reported by various sources (1 5). The processes from chemical industry and biotechnology involve the development of operations based on chemical and biochemical transformations and on physical transfer processes, momentum, mass, and heat transfer (6 9). Process intensification involves hydrodynamic conditions for turbulence development, the increase of interphase contact areas, or the intensification of driving forces for momentum ( p, pressure drop), mass ( C, concentration difference), and heat ( T, temperature difference) transfers, successively or simultaneously. The intensification of transfer processes in bioreactors using techniques that do not require additional energy costs is of great interest in biotechnology and, in particular, in fermentation processes. It is linked to multiple benefits in the area of process, environment, and business performance (4,10). Process intensification can make it possible to cut down on the number of industrial reactors, heat exchangers, and separation equipment, with favorable results on costs, reduced pipework, support structure, logistics, scaling-up, and the ability to introduce rapidly new products to the market (10,11). Adopting process intensification alternatives can contribute to a substantial improvement of process safety, mainly due to a reduced volume of potential hazardous chemicals in a smaller intensified unit (10,1). In addition, these alternatives greatly improve heat and mass transfer, which is often difficult or impossible to achieve In memory of Professor Radu Z. Tudose, Member of the Romanian Academy. with conventional technologies (5,11,13). The environmental implications of process intensification relate to the application of clean technologies based on the reduction of pollutants at source and waste minimization, improved energy efficiency, and resources conservation. A higher selectivity of operations in intensified systems could contribute to higher yields and fewer by-products, improved quality of valuable products, and lower loading of wastewater effluents (10 1,14). Some advantages of process intensification associated with process, environmental, and business are summed up in Fig. 1. In this context, the advantages of installing motionless mixers in bioreactors include the efficient use of energy for aeration, simple design, construction, and operation (5,15). Static mixers are helpful in processes involving an exchange of momentum, heat, and mass transfer (,4,5). They are able to operate over a wide range of temperatures, under high pressures and harsh chemical conditions, while the total capital and operating costs are significantly lower than those for dynamic mixers (5). Of the available strategies for bioprocess intensification, the enhancement of oxygen transfer has broader applicability than others (7,16). Static mixers essentially allow to obtain a plug flow ensuring uniform and short residence times (ranging in the order of seconds to minutes). In addition, static mixers are used especially in continuous processes, when component feed rates are uniform, the continuous phase is a gas, the space available is limited, and the pressure is high (17). Flow in such mixers may be laminar or turbulent, when they generate high turbulence levels, with favorable consequences on the degree of mixing, dispersion, and mass transfer. In addition, they act on hydrodynamic conditions for turbulence development, contributing to the increase of contact areas, or the intensification of driving forces, separately or simultaneously. In all cases, the energy for process intensification is extracted from the fluid flowing through the mixers (5). In fermentation processes, the static mixers could replace the impellers in agitated vessel or column bioreactors owing to their very efficient mixing in the radial direction with no backmixing in the axial direction and no dead spaces, with comparatively less energy input and lower shear rates compared to those in stirred tank bioreactors (4,5). Since static mixers have no moving parts, they are low maintenance and sealing problems are nonexistent (1). The concept of static mixing is not new, as the first patent on a static mixer belonging to Sutherland (15), dates back to However, the first applications of static mixers in industry was in the 1970s, when these devices were used as chemical reactors or for physical operations (fluid mixing, intensification of heat and mass transfer in heterogeneous (liquid liquid (extraction), gas liquid (absorption), solid liquid (sludge), solid liquid systems) (18 1). After a slow start, the development of static Encyclopedia of Industrial Biotechnology: Bioprocess, Bioseparation, and Cell Technology, edited by Michael C. Flickinger 013 John Wiley & Sons, Inc. Published 013 by John Wiley & Sons, Inc. 1

2 STATIC MIXING IN FERMENTATION PROCESSES Higher specific reaction rates Higher mass and heat transfer Higher selectivity Improved products purity Improved product properties Improved process safety Process intensification: impacted areas Industrial processes Environment Business Reduced polluting emissions and waste Energy conservation Raw materials conservation Reduced solvent use Smaller plants reduced land use Reduced capital costs Miniaturized plant Reduced operating costs Faster introduction of new products to market Distributed manufacturing Faster, safer, greener processing Cleaner and environmentally friendly processing Responsive and economically sustainable processing Sustainable industrial production Figure 1. Benefits of process intensification in relevant impacted areas: industrial processes, environment and business, resulting in sustainable industrial production. [Source: Reprinted with permission from Ref. 10, Fig. 10 p ]. mixers has been proceeding since At present, there are more than 8000 literature articles and 000 US patents describing static mixers and their applications (). The size of static mixers can range from a few millimeters in diameter to units with diameters beyond 3 m and volumes more than 100 m 3. They exist in both round and nonround cross sections (1). Owing to the special flow pattern developed by static mixers, a uniform distribution of concentrations and temperatures over the whole flow cross section can result, so as to attenuate input fluctuations in temperature or composition. Static mixers have attractive features such as closed-loop operation and no moving parts, unlike continuously stirred tank reactors. Static mixers are well established in multiphase turbulent flow and meet industrial requirements for absorption, reaction, extraction, and heat transfer/phase change (1). These specific features lead to an extension of the use of static mixers in practice, not only in biotechnological processes, but also in various homogenization processes in industrial operations such as polymer blending, chemical reactions, emulsification, food processing, heat transfer, cosmetics and pharmaceutics, nanoparticles synthesis, and also in wastewater treatment, biodiesel production from microalgae, and heat transfer (15,3 7). Studies on flow around these internals together with heat- and mass-transfer approaches of both theoretical and experimental nature are available. Experimental investigations have measured pressure drops, residence time distributions (RTDs), and power consumption (8 34). Despite their extensive usage over several decades, static mixers studies and characterization need to be further developed and the fundamental processes occurring in the presence of static mixers need to be better understood, considering the complexity of the flow structure and mixing behavior. CONFIGURATION OF STATIC MIXERS Static mixers are motionless devices of an appropriate structure and shape, for use as internals in pipes or columns, able to provide appropriate mixing and dispersion for fluids flowing around suitably arranged mixing structures. Pipes equipped with static mixing internals proved to be, in many cases, a better place for mixing and more economical than a vessel (1). Static mixers typically consist of a number of identical nonmoving mixing elements positioned in a pipe or channel. The mixing elements are usually rotated through 90 relative to the adjoining elements as this periodic change in the geometry of static mixers produces reorientation and distribution of the fluids (5,35). The application and the performance of static mixers are dependent on the geometry used for a particular system. Static mixers are built in many types, which can be grouped in several distinct categories (5,36): Open designs (with twisted plates, or blades and baffles of high or low aspect ratio; channels formed

3 STATIC MIXING IN FERMENTATION PROCESSES 3 by corrugated or folded plates; multilayer designs with crossing bars or tubes); Closed design (with channels or holes having variable cross sections for flow). Dickson (9) classified static mixers into groups as follows: helical-type, bar-type, hole-type (Ross-ISG), wafer-type (SMV), and baffle-type (HEV). Any difference in the design of static mixers leads to differences in the flow model, mixing efficiency, and intensity of transfer phenomena (momentum, mass, and heat). Static mixers are available in sizes from a few millimeters to several meters in diameter, in a wide range of designs from many manufacturers. Some of the most familiar and studied categories and configurations of static mixers are shown in Table 1. The two most important commercial open-blade designs available and used for many applications in the chemical process industry are Sulzer SMX and Kenics (37). Two different criteria are considered useful for assessing the efficiency of static mixers, especially for highly viscous liquids, namely, energy consumption (generally measured in terms of the dimensionless pressure drop) and compactness (measured in terms of dimensionless length) (5,15,1,38). STATIC MIXERS IN CHEMICAL AND BIOTECHNOLOGICAL PROCESSES AND OPERATIONS Static mixers differ considerably in their structure and performance characteristics. Technical criteria should be used to determine the best design for each specific application, as the process requirements should state the static mixer design. Fermentation Processes Microbial fermentation continues to be the only technique for commercial production of certain products that are made in considerable quantities (1). New fermentation production methods for customary drugs and drug precursors are being developed continually (16,39 41). Traditionally, a large part of bioprocesses, especially aerobic fermentations, are carried out in stirred tank bioreactors, which require substantial power input to achieve adequate oxygen-transfer rates. In addition to the conventional mechanically agitated fermenters, other types of gas liquid contactors are used, such as pneumatic or jet bioreactors with or without a loop (5,1,4). Today, static mixers mounted in column bioreactors are increasingly considered for application in fermentation industries, as they can replace the traditional mechanically agitated bioreactor design, particularly in shear-sensitive cell cultures because of their lower shear rates compared to those in mechanically agitated bioreactors (43). Because most aerobic fermentations are oxygen limited, and because the oxygen gas liquid mass transfer plays a critical role, the strategies applied for mass-transfer intensification are of great interest. In addition, some studies demonstrated that in highly viscous liquids, some problem could arise during fermentations of cultures with high oxygen demands and increasing viscosity (7,40,44). Consequently, factors taken into consideration upon the choice and the design of bioreactors for specific processes should include, besides the general factors, the population damage, the energy distribution, the oxygen demand of the aerobic culture, the oxygen-transfer rates, etc. The key for a successful chemical/biological process is obtaining mixing times of reagents equal to or better than the inherent reaction times, thus allowing reactions to advance at their natural reaction rates (9). The static mixers are devices able to help the process by intensification of momentum, mass, and heat transfer (4,5,1). Moreover, regular packings are used as catalyst support in chemical reactors or as support of microorganisms in biofilm reactors (45,46). Algae Production in Photobioreactors Photobioreactors became an attractive subject of research because of their potential use in algal biomass used for biodiesel production, amino acids, colorants, carbon dioxide mitigation, and bioremediation (8,47). The industrial photobioreactors for algal cultures can be faced with insufficient light availability in the center of tubes. In this situation, radial mixing could compensate the light gradients over the cross section if light dark cycles are generated (48 50). Static mixers proved to be promising tools in improving radial mixing, more than the turbulent flow mixers with Reynolds numbers greater than 9000 (48,51). Also, they increase mass-transfer capacity and ensure better light utilization (47). Water and/or Wastewater Treatment Mixing and contacting are key operations in water and wastewater treatment. The use of static mixers has positive effects on the performance of individual process stages and the quality of treated effluents. In addition, they can contribute toward cost saving by reducing the consumption of additives. Static mixers can be used in different stages of the treatment for mixing of flocculants with water or sludge, enrichment of drinking water with oxygen or biological treatment of wastewater, and ph control (5). The use of static mixers increases the treatment efficiency, with low consumption of chemicals and short contact times (53,54). Generation of Microemulsion in Production of Biopolymers Liquid liquid dispersions are often found in industry in processes such as liquid liquid extraction or in reactions involving an emulsification step. Nowadays, emulsions have a very large variety of applications. For most of the applications that involve emulsification, the control of the influence of process parameters on droplet size distribution is imperative. In the literature, it has been reported that the emulsification step has a strong impact on the final microparticle properties (3,5). Static mixers are largely used in industrial applications for mixing of miscible liquids, but they are also applied for emulsification. One of the most investigated static

4 4 STATIC MIXING IN FERMENTATION PROCESSES Table 1. Categories and Structural Type of Static Mixers Category Type Schematic Structure Static mixers from tubes or short pipes Ross-ISG PRM With guiding holes Static mixers of plates or sheets PSM Sulzer SMV Sulzer SMX Komax Koch C1 Koch C1

5 STATIC MIXING IN FERMENTATION PROCESSES 5 Table 1. (Continued) Category Type Schematic Structure Helical static mixers Kenics (perpendicular leading edges) Kenics (continuous helical surface) Erestat Yxzet N-shaped Lightin HI Wire matrix static mixers Source: Adapted upon Ref. 5 mixers for liquid liquid dispersion in turbulent flow in the literature is the classical Kenics-type mixer. The preparation of controlled-release biodegradable microparticles for pharmaceutical application is based on polymers as carrier matrix. The production of polymeric microparticles by the emulsion extraction method (5,55) needs an intensive agitation step. Miniemulsion polymerization involves droplets with diameters of nm, which needs a dispersing system able to generate them. Some authors studied the use of static mixers for the miniemulsification of single monomer systems (styrene, methacrylate, methylmethacrylate) and found that it is possible to obtain stable miniemulsion droplets (56,57). Static mixers proved to be efficient in droplet breakage, since they need only a small amount of the energy required for their operation (1 4%) (56,58). The work (W breakage ) necessary to generate a certain droplet surface area (DA) is correlated with the oil water interfacial tension (γ )as follows (Eq. 1) (58) DA = W breakage (γ ) 1 (1) Some studies showed that the droplet surface area depends on the liquid flow rate, presence of surfactants, and also on the configurations of the static mixers. For example, El-Jaby et al. (59) found differences between the droplet diameters generated using Kenics PAC and Sulzer SMX mixers, respectively. Therefore higher flow rates and well-defined mixer geometries are needed. Precipitation Processes Static mixers are used in the production of micro- and nanosized particles, enhancement of crystal nucleation, and growth at high suprasaturation of solutions as they are able to avoid the limitations of mixing. Usually their performances in these applications are assessed on the basis of computational fluid dynamics (CFD).

6 6 STATIC MIXING IN FERMENTATION PROCESSES Ultrafiltration An increase in permeate flux during the ultrafiltration of milk or whey was observed by some researchers (60,61) when Kenics-type static mixers were installed in the system. Gaspar et al. (6) have found that the mass-transfer coefficient of the membrane filtration is enhanced due to the presence of static mixers in the lumen side of the membrane. However, an optimum operating regime should be established to avoid the supplementary energy requirement. Applications of static mixers for homogenization of liquid streams, blending miscible and immiscible fluids, dispersing in liquids, heat exchange, some chemical reactions, biological processes, fermentation, food engineering, production of biopharmaceuticals and biopolymers are numerous and well documented (63). Some of these applications are illustrated in Fig. (1). Characterization of Flow and Mixing Developed in Static Mixers The pressure drop and energy consumption are quite important in many cases and may influence the final choice of different customers on the selection of the mixing device. The pressure drop and mixing behavior of these tools have been widely studied in experimental and theoretical frames. The pressure necessary for fluid flow is generated by pumping, while the energy for mixing is taken from the flow of fluids. Flow Structure in Static Mixers In static mixers, the fluid is split into individual streams at the open intersecting channels of the mixing element. In addition, modifications in velocity profiles result because static mixers produce variations in the flowing cross-sectional area. The number of elementary layers or partial streams n produced in laminar flow over a static mixer resulted through assembly of N mixing elements is usually calculated using Equation (5) n = ca N () where c and a are parameters specific for the type of static mixer, usually given in literature (5,64). The majority of static mixer designs are very diverse from a geometrical viewpoint, but sometimes they are operationally very similar. Sulzer static mixers are among the most applied in industry, mainly because they can provide the most compact mixing device as compared to the other static mixers (65). Sulzer configurations could be considered a model for basic studies on static mixing effects and performance. Flow behavior and mixing in an SMX static mixer is much more complex owing to their complicated 3D geometry, which is based on the number of crossing bars and the structure (Fig. 3). The flow pattern in a Sulzer SMV mixer was presented by Pahl and Muschelknautz (1,66) using a model consisting of two open triangular ducts forming two intersecting channels crossing at 90. The path of a tracer is distorted, as the fluid that exists along the left side of the triangle, representing the cross section of the duct I, shifts to the right side of duct II at the exit, performing a rotation. In addition, the stream that starts from the opposite position at the entrance of duct I is greatly distorted at the crossing point and flows into both ducts I and II (5). Mickaily-Huber et al. (67) found that increasing flow velocity in Sulzer SMRX static mixers determines linear increases in pressure drop. In addition, for a given flow velocity, the pressure drop increases with the internal mixer tube crossing angles: an angle of 90 was found to be optimal. Kenics static mixers are among the most commonly used in biotechnology and appear to have received the most attention, possibly because of their simpler geometry. The Kenics static mixers involve repeated cutting, reorienting, and stacking of material to generate a large number of striations. Straight plates usually of length 1.5D cross each other under an angle of 90. They are typically mounted in linear arrangements inside a rotating tube of diameter D (Fig. 4). The turbulence they use to generate is quite moderate (Re 10 ), but they are able to operate over a large domain of Re values (1 5,000), from linear to turbulent regimes. Numerical techniques have preponderantly been applied to find velocity profiles, RTD, and mixing performance. On the basis of CFD, direct simulations of three-dimensional flow and flowing maps were developed in different mixers configurations and blade twist angles (5,58). The axial and radial velocity profiles in a Kenics mixer change periodically owing to the use of alternating elements of right- and left-hand pitch that results in more intensive mixing of fluids. The screw, having the form of a continuous helical surface, divides the inside of the tube into two parallel channels, causing a secondary motion of the fluid in the tube (5,69). In these motionless mixers, circulating flow occurs in the r h plane (r and h being radial and tangential coordinates, respectively), which is caused by a slow twist in the partitioning chord so that it forms a helix. The actual velocity profiles can be calculated using a complex procedure, but an approximation can be made (70). Pressure Drop The pressure drop ( P) can be expressed as a function of the following six process variables (Eq. 3) f ( P, D, L p, L e, μ, ρ, v) = 0 (3) where D is the inner diameter of the pipe or column, L p is the length of the pipe (column height), μ is the fluid viscosity, ρ is the fluid density, ν is the fluid flow rate. The flow regime, laminar or turbulent, entails the mechanisms and the equations used in the choice and in depth design of the static mixing equipment (1). The understanding of fluid dynamics is essential in determining pressure drop, degree of mixing, energy expenses, heat transfer, and drop size in the case of multiphase processes. Various correlations have been developed in literature, which are required as flow changes from laminar to turbulent and vice versa. The flow through static mixers is due

7 STATIC MIXING IN FERMENTATION PROCESSES 7 Basic unit operation Fluids Application Mixer Narrow residence time distribution (laminar regime) Highly viscous fluids Plug flow laminar SMX/SMXL Laminar flow heat transfer Highly viscous heat sensitive Heart transfer with viscous liquids SMXL/SMR Laminar flow mixing/blending Highly viscous miscible High and low viscosity, miscible Blending laminar liquids Mixing high/low viscosity liquids SMX/SMXL SMX Laminar flow dispersing High and low viscosity, immiscible Dispersing hight/low viscosity liquids SMX Liquid as continuous phase with gas Mass transfer for dissolution of gases Mass transfer with chemical reaction SMV KMS SMV KMS Mass transfer for absorption SMV Turbulent flow dispersing Gas as continuous phase with liquid Mass transfer with chemical reaction SMV Vaporization SMV Dispersing, emulsifying SMV KMS Low viscosity, immiscible liquids Mass transfer for extraction, washing SMV KMS Mass transfer with chemical reaction SMV KMS Turbulent flow mixing/blending Low viscosity, miscible Blending low viscosity fluids KVM SMV HEV KMS Narrow residence time distribution Low to medium viscosity fluid Plug flow low viscosity fluids SMV/SMVP KMS Figure. Static mixers design and applications. [Source: Reprinted with permission from Ref. 1]. to the kinetic energy of liquid flow proportional to pressure drop in mixer, which can be characterized by the friction factor, f, pressure drop factor, Z, and power constant K p. The friction factor, f, was derived to express the ratio of total momentum transferred to momentum transferred by turbulent mechanisms, as a function of Reynolds number, f = φ(re). The general dependence of the friction factor f on flow conditions for empty pipes and static mixers is given by the relation (4) f = A + B Re C (4) A, B, andc are adjustable parameters, determined on the experimental bases and found in literature. Some relationships for the friction factor are given in Table (Eqs T.1 T.10).

8 8 STATIC MIXING IN FERMENTATION PROCESSES (a) (b) (c) (d) Figure 3. Design parameters of the SMX motionless mixer. (a) Design with four cross-bars and three parallel cross-bars. The angle between opposite cross-bars is 90. (b) Increased number of cross-bars over the channel width. (c) Increased number of parallel cross-bars. (d) Design with increased angle (10 ) between cross-bars. [Source: Reprinted with permission from Ref. 65, Fig. p 364 (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)]. (a) (b) (c) Figure 4. Kenics motionless mixers designs. (a) Standard right left layout with 180 twist of the blades. (b) Right right layout with blades in the same direction as the twist. (c) Right left layout with 10 blade twist. [Source: Reprinted with permission from Ref. 68 Carl Hanser Verlag, Muenchen]. One of the most used definitions of the friction factor is the Darcy friction factor (Eq. 4). A plot of the Darcy friction factor versus Reynolds number for flow in open circular pipes of various roughnesses from shows three distinct flow regimes (5,73): Re < 100 (Laminar flow) 100 < Re < 10,000 (Transition) Re > 10,000 (Fully turbulent) These regimes change when static mixers are mounted, owing to their shape, which changes the hydraulic diameter of the mixing channel. Static mixers are typically required in laminar flow, when the energy for mixing must be made available as pressure that will be dissipated in the process. In turbulent flow, if there are no time or length restrictions, static mixers accelerate the process by bringing the components into closer contact, but significant energy input may be required when dispersion is necessary, as the creation of surface area is more energy demanding (1). The plot f Re could be also used for comparing static mixers in the turbulent flow regime, as f is then approximately independent of the Reynolds number (Fig. 5). Compared with an empty tube, the pressure drop in static mixers is 7 00 times greater for laminar flow and times greater for turbulent flow (5) (Fig. 5). The analysis of energy dissipation in various mixers and reactors illustrates the potential ability of intensified system (such as static mixers) to provide a high level of mixing intensity, compared to the conventional stirred tank (bio)reactors. The benefits from the mixing process under intensified conditions have to be demonstrated by significant process improvements. Table 3 shows some data on energy dissipation rates in various mixing systems (10).

9 STATIC MIXING IN FERMENTATION PROCESSES 9 Table. Friction Factor Values at Various Reynolds Friction Factor Reynolds Number References f = PD i v L Hρ (T.1) Re = v id i υ f = Pd h v L Hρ (T.) Re = v Ld h υ f = PD i Kv L Hρ (T.3) Re = v LD i υ f = PD i v L Hρ (T.4) Re = v LD L υ f = PD i v i Hρ (T.5) Re = v id i υ (T.6) (71) (T.7) (7) (T.8) (73) (T.9) (66,74) (T.10) (75,76) v L, liquid velocity (m/s); v i, interstitial velocity; D i, diameter of empty pipe (m). align= left 10 4 Studies carried out on the pressure drop in static mixing flow using Z as the dimensionless factor revealed the existence of two zones (5,1,65,77): f a zone where Z is independent of Re, forre 10. zone where a nonlinear increasing of Z appears above Re>10, as a consequence of inertial effects The factor K p is considered almost constant for static mixing in the laminar regime (Eq. 6) Figure 5. Dependence of the friction factor as a function of Reynolds number for different static mixers (1, empty pipe;, Kenics; 3, Hi; 4, Sulzer SMX; 5, Sulzer SMV). [Source: TheFigure is taken from Ref. 5, Fig. 7 p 491]. Re Table 3. Comparative Data Regarding Energy Dissipation Rates in Various Mixing Systems Mixing System 5 Energy Dissipation Rate (W/kg) Stirred tank reactor Static mixers Impinging jet reactor Rotor stator spinning disc reactor <6000 Thin-film spinning disk reactor <000 Source: Taken from Ref. 10. A pressure drop factor Z is defined as being the ratio of pressure drop in a static mixer to that in an empty tube (Eq. 5) Z = f SM = P SM (5) f ET P ET where P SM is the actual pressure drop across the static mixer, P ET designates the pressure drop in the open tube, given by the Hagen Poiseuille equation. Ne is the Newton number (Eq. 7) K p = NeRe (6) Ne = PD ρv L L (7) Some relationships for the Z-factor for various static mixers are shown in Table 4 (Eqs T4.1 T4.1). Z and K p values are calculated by vendors for some commercial static mixers, or are based on CFD methods, or can be found in literature, calculated using various other methods (Table 5) (36). Pressure drop is low for mixers containing helical elements and increases with the complexity of structure (for mixers with elements that force more rapid changes in flow direction). System pressure drop limitation can be virtually accommodated by varying pipe diameter in combination with the number of mixing elements required for the specific application. The energy dissipation is a measure of the energy consumed for vortex generation per unit mass of fluid per unit of time (Eq. 8) (83) ε = ( w)3 D = λ w3 D where w is the change in the instantaneous velocity of fluid along the flow direction (m/s), D is the characteristic length (m) (equivalent diameter), w is the average velocity of fluid (m/s), and λ is the dimensionless coefficient of energy dissipation. (8)

10 10 STATIC MIXING IN FERMENTATION PROCESSES Table 4. Relationships for Z-Factor, Depending on Re and Static Mixer Category Equation Significance and Conditions References Z = ( P) SM ( P) ET (T4.1) ( P) SM the pressure along the pipe with static mixers (5) ( P) ET -pressure drop in empty pipe P ET = 3 ρv L Re D (T4.) L length of tube Re = ρv LD (T4.3) [ Z = 1 ( ) ] Re ε ε μ ρ density of fluid μ viscosity of fluid v L average liquid viscosity (T4.4) ε the void fraction of the static mixer (75) Z = 3.4[ Re 0.5 ]. (T4.5) Re Reynolds (78) Z = Re 3 (T4.6) Kenics (73) Re < 50 Z = 0.41Re 0.5 (T4.7) Kenics (79) Re < 10 Z = Re (T4.8) Re < 0 Kenics Z = Re (T4.9) Re < 300 (74) Kenics Z =.03Re 3/8 (T4.10) 10 < Re < 1000 (80) Z = 9.Re 0.07 (T4.11) 10 < Re < 17 (81) IEAP-PK Z = Re (T4.1) Lightnin (8) Table 5. Values of Z, f Factors and Power Constants K p for Some Commercial and Developmental Static Mixers Static Mixers Z f Vendor CFD Literature Kenics 8.1 ± Ross-LPD 7.4 ± N-form 16 ± Lightnin, Komax SMV 81 ± SMX 55 ± Ross/ISG 75 ± Source: Adapted upon Ref. 36. K p The hydraulic resistance of static mixers is given by the energy consumed per unit of fluid passing through the static mixer (Eqs 9 and 10). p = ετρ = ρw λl (9) D τ = L (10) w τ is the average time (s) required for the fluid to pass through a static mixer of length L and ρ is the average density of fluid (kg/m 3 ). Mixing Efficiency Static mixers are widely used because continuous mixing can be achieved with no moving parts. At present, the mixers are being applied at a wide range of scales, ranging from micro- to macroscale. The large applications of static mixers in chemical industry and biotechnological processes require the knowledge of their mixing performance both at large scales (macromixing) as well as that induced by molecular diffusion at small scales (micromixing). This information could be further useful in adjusting the properties of mixing devices. In addition, the mechanisms controlling the mixing at all scales can then be established with some reliability, as it is of vital importance to ensure that the mixing system used at laboratory scale is an accurate model of the large-scale system. Two categories of applications are feasible according to flow and mixing features of static mixers as follows (15):

11 STATIC MIXING IN FERMENTATION PROCESSES generating stratified systems with uniform layer distributions (originally dedicated to improving the melt temperature homogeneity in spin lines).. micromixing, at small Re and large Pe, when chaotic advection produces fluid mixing. In practice, laminar mixing is performed as a result of numerous and repeated divisions, transpositions, and recombinations of fluids flowing around static mixers. The layer refinement that conditions degree of homogenization of the mixture is dependent on the number of mixing elements. Effective mixing processes promote global uniformity by redistributing initially segregated components in space. In the laminar regime, the only efficient route to mix is through chaotic flows (8). In turbulent flow, the static mixers shorten the distance required to achieve good mixing (sometimes by a factor of at least 10). The analysis of turbulent micromixing at a typical length scale below the characteristic Batchelor scale can be successfully done by mass-transfer equations (63,84). It is important to quantify the micromixing as it is an important mechanism and is also a limiting factor in biological initiation processes (63). Therefore, a simple measure of mixing efficiency in laminar flow is given by the number of layers into which the fluid is divided, n, which is a function of the number of channels in the mixing element, number of elements or pinches, number of spirals, and number of plates in a multilayer design. Convective mechanisms in chaotic flows (stretching and folding) change fractions of materials into extended striations and reorient these threads with respect to the deformation direction. Continuous reorientation generates a continual exponential rate of increase in intermaterial contact area in chaotic flows (8). Flow structure is continuously changing and consequently, kinetic energy. In practice, it is recommended to assume that over the length h of a single stage of arrangement of static mixers, the flow stream is split into n = n 0 Re 3/4 layers (n 0 is the number of planes of mixing elements in the stage). The number of layers generated at the outlet is expressed by Equation 11 (83) N = n L/h (11) Mixture quality downstream of static mixers is usually quantified by coefficient of variation CoV as a measure of homogeneity, expressed as the normalized standard deviation of concentration measurements/mean concentration, which could be calculated in many ways, depending on how the data set is time averaged (85). It is often also called the intensity of mixing or degree of segregation and the final CoV is usually independent of the amount to be mixed (1). It is of interest to look at the original state of mixing, considering the initial mixture quality expressed by C 0 V 0 given by Equation 1 ( ) Cv C 0 V 0 = (1) C v The mixer performs as a reducer of variance, which means that the motionless mixer can be seen as a performing a transfer function that reduces the CoV from an initial value to a lower final value. Therefore, CoV reduction as a function of length is a measure of the quality of mixing achieved by a motionless mixer (1). Figure 6 shows the dependence of the variation coefficient on the mixer length for two Sulzer mixer designs (SMX and SMXL) operating in laminar flow at 0.1, 1, 10, and 50% additive rates. Mixing development in a SMX type static mixer is determined by three design parameters: N x, the number of cross-bars over the width of the channel (Fig. 3a and 3b). N p, the number of parallel cross-bars (Fig. 3a and 3c). θ, the angle between opposite cross-bars (Fig. 3a and 3d). Tracer techniques were able to illustrate the complexity of flow in SMX mixtures with multiple elements (Fig. 7). CFD techniques are able to develop a more rigorous characterization of flow and mixing in this complicated arrangement, based on tracer techniques (87). For example, results of Zalc et al. (86) showed that stretching values experienced by material elements span many orders of magnitude, even over a short distance in the mixer assembly (Fig. 8a). Since curves corresponding to greater axial distances show both lower peaks and distributions, it was suggested that scaling based on the mean and standard deviation (Eq. 13) of the probability distribution function (H) followed by a subsequent computation of the probability distribution of the transformed variable w (Eq. 14) was possible log λ log λ w = std(log λ) H(w) = 1 dn(w) N p dw (13) (14) where N p is the number of tracers used and dn(w) isthe number of particles having stretching logarithms between w and w + dn(w) (86). After that, a single curve for all subsequent cross sections would result (Fig. 8b). This information can be used to select a certain static mixing configuration suitable for a specific mixing task. However, it was found that mixing structures evolve along a self-similar model, established after the first mixer elements (86). Sir and Lecjaks (74) experimentally studied the homogenization of two liquids of differing viscosities (glycerol and tap water) via iodometric decolorization and determined the number of Kenics mixer elements for complete mixing. Jaffer and Wood (88) studied Kenics KM mixer elements with various L/D ratios. Laser-induced fluorescence (LIF) and image analysis were used to quantify laminar mixing by measuring the average striation thickness, variance of striation widths, and interfacial area (89).

12 1 STATIC MIXING IN FERMENTATION PROCESSES SMX SMXL σ x x = Practically Homogeneous x = 0.5 x = 0.1 x = 0.01 x = 0.05 x = L D Figure 6. Homogeneity expressed as variation coefficient versus mixer length for SMX and SMXL static mixers operating in laminar flow. [Source: Reprinted with permission from Ref. 1, Fig. 7 5, p 414)]. Macromixing or distributive mixing involves mixing on the macroscopic scale, achieved by convective transport of fluid elements resulting in an uniform spatial distribution within the reactor. Backmixing in static mixers is negligible and they behave as plug-flow systems, regardless of the mixer design. Consequently, many commercial scale static mixers are compact relative to the scale of fluid flow being processed. Owing to their short residence times and slight backmixing, appropriate dosing of the feed components can be done with no fluctuation in time, which is a condition for good performance. When backmixing is required, static mixers are incorporated into pump-around loops (1). Residence Time Distributions in Static Mixers Knowledge about the RTD in static mixers is of major importance when they are used or placed in a chemical reactor, when Newtonian or non-newtonian liquids are involved (5,9,37,90,91). The RTD models presented by Danckwerts (1953) are a good method for expressing the variation in residence time experienced by various elements of a fluid in a reactor system, as they can evaluate the degree of ideal or nonideal flows related to the fluid flow patterns or macromixing in a contacting device, as a quantitative measure of a temporal mixing (90,91). In the context of static mixers (disposed in-line, with continuous flow), spatial mixing is equivalent to radial mixing and temporal mixing is equivalent to axial mixing. Usually, transient experiments with inert tracers are used to determine RTDs. A large amount of literature and data has become available on the RTD analysis since this concept and its importance in flow processes were first developed by Danckwerts in 1953 (90 9). The models can be displayed in exit concentration form, E(t), or in cumulative form F(t) (9,90 9). RTD can be quantified using the Bodenstein (Bo) number (or referred to using the Peclet mass-transfer number), as a measure of the width of the in accordance with the Danckwerts dispersion model, and can be summarized as the ratio of bulk transport through the reactor to the axial dispersion coefficient (Eq. 15). The timescale can be converted in terms of t/t, wheret is the first moment about the mean or the mean residence time (Eq. 37) (9 94) t = 0 tf (t)dt = 0 E(t)dt Mass inventory in the system = Mass flow rate through the system = Hold-up Throughput (15) Since the flow path in static tends toward the ideal model of plug flow, this model is considered to have a delta distribution of residence times (Fig. 9), with variance, σ = 0.

13 STATIC MIXING IN FERMENTATION PROCESSES 13 (a) (b) (c) (d) (e) (f) Figure 7. Mixing patterns for a 10% centerline tracer injection at Re = 30 are shown for 0.5 (a), 1.0 (b), 1.5 (c),.0 (d), 3.0 (e) and 4.0 (f) mixer elements. [Source: Reprinted with permission from Ref. 86, Fig., p 879, Wiley]. Figure 9 shows an analytical distribution of residence times associated with different flow models. However, in the case of static mixers, this is difficult to do because of the complexity of flow of various volume elements and the many assumptions necessary for modeling. Usually, experimental measurements are fit to a simple model, and then analyzed to understand system performance and to diagnose abnormalities in flow. Little backmixing was found in static mixers, and therefore residence times can be very short (1). Residence time measurements are easiest in single-phase systems having one inlet and one outlet, while extensions to more complex, bi- and multiphasic systems make the analysis more difficult. METHODS AND TECHNIQUES IN FLOW MODELING AND MIXING STUDIES IN STATIC MIXERS Modeling of flow and mixing process in industrially relevant static mixers (Kenics, Ross Low Pressure, Sulzer, etc.) is of primary concern, as it generates support for mixing control so as to predict the resulting mixture properties (86). Some correlations are available but for a limited range of working conditions. Mixture quality was found to be a function of (85): flow regime mixer type feed arrangement mixer length (number of elements). Flow phenomenon and mixing processes are supported by a number of mechanisms, from agitation to sparging to static flow manipulation. Since the flow pattern in static mixers is very complex and difficult to describe quantitatively, a large number of experimental methods and techniques have been applied to quantify mixing processes, with various degrees of reliability. Experimental techniques for mixing characterization can be applied at laboratory and actual process plant equipment, but the instrumentation and techniques are often different, although they are based on similar principles. In some studies, the mixing efficiency in static mixers has been quantified based on the data acquired as computer tracer mixing patterns and stretching fields as well as image analysis techniques.

14 14 STATIC MIXING IN FERMENTATION PROCESSES (a) 1 Inc. n 1.0 Piston flow 3 log(h(log λ)) Washout function 0.5 CSTR Laminar flow in an empty pipe Static mixer (b) log(λ) χ = mixing criterion Dimensionless residence time Figure 9. Residence time distribution functions for various flow systems. [Source: Reprinted with permission from Ref. 9, Fig. 1 1, p 6]. log(h(log w)) log(w) Figure 8. (a,b) Self-similarity of the stretching field in the SMX for Re = 10, where inertial effects are negligible. [Source: Reprinted with permission from Ref. 86, Fig. 7,7p 883, Wiley]. Flow visualization provides information on flow and highlights the regimes of poor fluid motion. The simplest technique for examining flow patterns within static mixing system is light sheet visualization. Usually, video images of the reflections from particles can illustrate the bulk flow pattern in single-phase flow. Colorimetric methods involve the injection of dyes in the fluid. This method can be applied for mixing time measurements with off-line or on-line techniques. The LIF technique is nonintrusive and allows the entire cross section to be measured simultaneously, with a high temporal and spatial resolution. It is limited to optically clean systems with a constant refractive index. Pulsed ultrasonic velocimetry (PUV) technique is based on its ability of measuring instantaneous velocity profile over the measuring line. It is applicable to opaque pipes as well as emulsions with large concentration, mud, and liquid metals (34). The technique is based on the use of the echo of an ultrasound impulse emitted along a transducer measurement line, which records the signal reflected by surfaces of particles carried along by the fluid. The dispersed phase plays the role of a solid, liquid, or gas tracer within a continuous phase that is usually liquid. Positron emission particle tracking (PEPT) is a Lagrangian visualization technique for flow phenomena analysis in three dimensions that is based on the analysis of the movement of a radioactive particle (95). This technique was developed in the early 1990s and it enables a radioactively labeled tracer particle to be tracked during its movement between the detectors of a positron camera. It allows a noninvasive analysis of particle path and velocity profiles for static mixers, even in nontransparent fluids (95). CFD is a new and feasible alternative in understanding the flow and mixing structure in various mixing equipment and devices; it is based on numerical simulation of fluid motion. Over the last two decades, with the development of faster computers, it has become possible to numerically solve the three-dimensional flow through static mixers. In this way, the complex static mixer geometry can be modeled using appropriate grid generation software and the conservation equations solved using control volumes or finite element methods. CFD reduces scale-up problems, because the models are based on fundamental physics and are scale independent (96). The CFD models were applied to describe the bulk behavior of static mixers despite the chaotic nature of the mixing process developed by these structures, in particular, in laminar flow (15,86,87). CFD has proved to be an efficient tool for both supporting design and scale-up of various equipments and the understanding of mixing processes. CFD simulation, particle tracing, and the data processing algorithm offer an important means for understanding the flow patterns inside the mixer beyond what would be possible experimentally.

15 STATIC MIXING IN FERMENTATION PROCESSES 15 To find numerical solutions of velocity and pressure in such three-dimensional devices/systems, some steps must be considered (77): generating a computational model for the geometry of the system discretization of the 3D flow into small volumes solving the algebraic equation system for pressure and velocity fields. Data interpretation could be done on the basis of Eulerian and Lagrangian analysis (76). CFD can often be used in evaluating plant problems, to help understand the root cause of a problem and not just the effect (96). The mapping method is one of the most advanced and efficient modern tools applied to investigate the complex mixing processes based on chaotic advection (65). This involves the development of a mapping matrix based on backward particle tracking that involves dividing the cross-sectional area of the package of into particles into a grid of M M cells, considering the number of particles per cell sufficient for obtaining a converged quantitative mixing measure the flux-weighted intensity of segregation. The matrices are used to obtain the evolution of concentration of a number of elements N elem via a matrix vector multiplication that is computationally very fast (Eq. 16) (65) C 1 = 1 C 0 C = C 1. (16) C n = ( 1 ( (...( 1 ( C 0 ))))) }{{} N elem times where C 0 is initial concentration distribution, C 1 is mixing profile after the first element of mixing, C n is the mixing profile after the nth element of mixing, and N elem is the number of elements. For example, when mapping is applied for a Kenics static mixer, it is subdivided into independent functional mixing modules, which are subsequently assembled in an appropriate path so as to result in the real mixer design (68). In addition, the flow inside a module is assumed to be independent of upstream and downstream flows. At the rigid walls, a no-slip boundary condition is prescribed, and at both inlet and outlet, a fully developed Poiseuille profile is considered. If the fluid is assumed to be Newtonian, with a constant viscosity, the axial velocity in the Stokes flow through a vertical semicircular pipe can be expressed in polar coordinates (r, θ) as follows (68,97) (Eq. 17) u z = π π 8 u z ( r a sin θ + a a ) sin θ r 1 ( r ) 4 a a r sin(θ) ln r +ar cos θ + a r ar cos θ + a + 1 [ ( r ) ] a a ar sin θ r cos(θ) arctan a r (17) π r where u z denotes the average axial velocity. Within the mapping method, a flow domain is subdivided into N subdomains i with boundaries ϑ i represented by polygons and tracked from z = z 0 to z = z 0 + z using an adaptive front-tracking model and, consequently, deformed polygons result (68). The area of the intersections of the deformed subdomains with the original subdomains determine the elements of the mapping matrix, where ij equals the fraction of the deformed subdomain ϑ j at time z = z 0 + z that is found in the original subdomain i (z = z 0 ) (Eq. 18) j z = z 0 + j z z 0 d ij = (18) j z = z 0 d Krujit et al. (98) have performed detailed studies on the validation and accuracy of the mapping methods, which provide a powerful design tool for performing static mixers. In turbulent flow, the state-of-the-art CFD methods are applied to model three-dimensional, fully turbulent flows (Re 100,000) based on solving the dedicated equations (the Reynolds-averaged Navier Stokes (RANS)) equations in generalized curvilinear coordinates. The results of the CFD model the predicted flow field are usually presented in terms of mean velocity contours, cross-flow velocity vectors, and longitudinal vorticity contours to illustrate the complicated flow patterns that drive the mixing process in helical static mixers. The calculated flow field in the static mixer is presented in terms of mean flow quantities (99). STATIC MIXERS IN HETEROGENEOUS SYSTEMS Static mixers are regularly applied in multiphase turbulent flow and they can meet industrial requirements for absorption, reaction, extraction, and heat transfer/phase change. Static mixers in multiphase applications where the gas is continuous are typically highly structured designs, providing large surface area per unit volume. However, they are recommended for multiphase flow applications with a continuous liquid phase and a dispersed gas or immiscible liquid phase (1). Static mixers are applied in many heterogeneous gas liquid operations that require large contact areas, thermal homogenization, and mass transfer, such as processing of natural gas to remove hydrogen sulfide or carbon dioxide, wastewater treatment, dissolution of gases, hydrogenation, chlorination, and fermentation/biosynthesis (4,5). The processes of liquid mixing, generation of interface area, gas liquid mass transfer, especially in turbulent systems, are controlled mainly by the power dissipated in the fluids and the gas volume fraction ε G. In turbulent flow, static mixers develop plug flow in both phases. Designs are engineered to achieve specific results at minimum cost and energy expenses. Information such as RTD, liquid holdup, and heat and mass-transfer coefficients in static mixers are very important not only for the design of the system but also for process scale-up. In addition to creating interfacial surface area, the static mixer performs bulk homogenization so as to guarantee that all flow components are distributed uniformly in the cross section.