Fluid Mixing Chapter 9 PDF

Fluid Mixing Chapter 9 Objectives Significance of Fluid mixing Introduction of equipment's used for mixing in stirred tanks (e.g., Agitator, impellers, etc) Describe the mechanisms of mixing and their effect on mixing time Able to know how liquid properties, impeller size...

Fluid Mixing Chapter 9 Objectives Significance of Fluid mixing Introduction of equipment's used for mixing in stirred tanks (e.g., Agitator, impellers, etc) Describe the mechanisms of mixing and their effect on mixing time Able to know how liquid properties, impeller size and stirrer speed affect power consumption in stirred vessels What does fluid mixing mean ? Fluid mixing - a physical process- is happening within every bioreactor/ reactor. It aims at reducing non-uniformities in fluids by eliminating  gradients of concentration,  temperature gradients and  other properties Significance of fluid mixing In the chemical and other processing industries, many unit operations are highly dependent on mixing of substrates, biocatalysts/catalysts, solvents/cosolvents and others components:  Blending of two miscible liquids such as ethanol and water  Dissolving solids in liquids such as sugar in water  Dispersing a gas in a liquid as fine bubbles, such as oxygen from air in a suspension of microorganisms for fermentation  Suspending of fine solid particles in a liquid  Agitation of the fluid to increase the hear transfer between the fluid and a coil or jacket in the vessel wall Stirred Tank: Components Motor: Provide power to the agitator Agitator: The mixer Baffle: Promote the effective mixing (may or may not be used) Cooling Jacket: Control the temperature Fig. Typical configuration of a stirred tank Agitators Anchor Propeller Disc -turbine Paddle Gate anchor Helical and ribbon Fig. Different types of impeller designs Flow Patterns Developed in Agitated Tanks Flow patterns in a agitated tank depend on: the fluid properties the geometry of the tank the types of baffles in the tank the types of agitator Fig. Circular flow in a unbaffled stirred tank Flow Patterns Developed in Agitated Tanks (Cont’d) Side view bottom view Fig. Flow pattern produced by a radial-flow impeller in a baffled tank Axial-flow impeller Fig. Pitched-blade turbine Selection of agitator based on fluid viscosity 107 Helical ribbons 106 Helical screws 105 Viscosity (cP) anchors Gate 104 Flat-blade turbines Paddles Anchors 103 Propellers 102 10 1 Impeller type For viscosities greater than about 5000 cP, baffles are not needed since little swirling is present above this viscosities Geometric proportions for a standard agitation system HL = Liquid height Hi = Impeller clearance D t = Tank diameteri Wi = impeller width Di = impeller diameter Li =Impeller blade length Wb=Baffle width  HL / Dt = 1.0 Wi / Di = ¼ to 1/6 Li / Di = ¼ Wb / Dt = 1/10 to 1/12 Di / Dt = 1/4 to 1/2 Hi / Dt = 1/6 to ½ The number of baffles is four in most cases Mechanism of Mixing As illustrated before, large liquid-circulation loops developed in stirred vessels make mixing performance poor. For mixing to be effective, fluid circulated by the impeller must sweep the entire vessel in a reasonable time. The velocity of fluid leaving the impeller must be sufficient to carry material into the most remote parts of the tank. Turbulence must also be developed in the fluid; mixing is certain to be poor unless flow in the tank is turbulent. All these factors are important in mixing, which can be described as a combination of three physical processes like distribution and dispersion Mechanism of Mixing: Distribution The process whereby materials are transported to all regions of the vessel by bulk circulation currents is called distribution. Distribution is an important process in mixing, but can be relatively slow. In large tank, the size of the circulation paths is also large and the time taken to traverse them is long Distribution is often the slowest step in the mixing process. However, if the rotational speed of the impeller is sufficiently high, superimposed on the distribution process is turbulence. Turbulence flow occurs when fluid no longer travels along streamlines but moves erratically in the form of cross-currents. Mechanism of Mixing: Dispersion The kinetic energy of turbulent fluid is directed into regions of rotational flow called eddies; masses of eddies of various size coexist during turbulent flow. Large eddies are continuously formed by action of the stirrer; these break down into small eddies which produce even smaller eddies. Eddies, like spinning tops, posses kinetic energy. When the eddies become so small that they can no longer sustain rotational motion, their kinetic energy is dissipated as heat. The process of breaking up bulk flow into smaller and smaller eddies is called dispersion; dispersion facilitates rapid transfer of material throughout the vessel. The degree of homogeneity as a result of dispersion is limited by the size of the smallest eddies which may be formed in a particular fluid. Mechanism of Mixing (Cont`d) Mechanism of Mixing (Cont`d) Mechanism of Mixing (Cont`d) Flow pattern developed by a radial-flow impeller Assessing mixing effectiveness: Mixing time Mixing time is a useful parameter for assessing mixing efficiency. The mixing time tm is the time required to achieve a given degree of homogeneity starting from the completely segregated state. Mixing time in stirred tanks will depend on variables such as  the size of the tank  size and type of impeller,  fluid properties such as viscosity, and  stirred speed. How we can measure the mixing time? Assessing mixing effectiveness: Mixing time It can be measured by injecting a tracer into the vessel and following its concentration at a fixed point in the tank. Tracers in common use include acids, bases and concentrated salt solutions; corresponding detectors are pH probes and conductivity cells. Mixing time can also be determined by measuring the temperature response after addition of a small quantity of heated liquid. Let us assume a small pulse of tracer is added to fluid in a stirred tank already containing tracer material at concentration Ci. Before mixing is complete, a relatively high concentration will be detected every time the bulk flow brings tracer to the measurement point.The peaks in concentration will be separated by a period approximately equal to the average time taken for fluid to traverse one bulk circulation loop. In stirred tank this period is called the circulation time tc. After several circulations the desired degree of homogeneity is reached. Definition of the mixing time tm depends on the degree of homogeneity required. Usually, mixing time is defined as the time after which the concentration of tracer differs from the finial concentration C f by less than 10% of the total concentration difference (Cf− Ci ). At tm the tracer concentration is relatively steady and the fluid composition approaches uniformity. For a single-phase liquid in a stirred tank with several baffles and small impeller, there is an approximate relationship between mixing time and circulation time tm = 4tc We can predict that mixing time in stirred tanks will depend on variables such as the size of the tank and impeller, fluid properties such as viscosity, and stirred speed. The relationship between mixing time and several of these variables has been determined experimentally for different impellers; results for a Rushton turbine in a baffled tank are shown in the next slide. The dimensionless number Ni tm is plotted as a function of the impeller Reynolds number (Re)i.tm is the mixing time based on a 10% deviation from final conditions, and Ni is rotational speed of the stirrer. Ni tm represents the number of stirrer rotations required to homogenize the liquid. Assessing mixing effectiveness: Mixing time Assessing mixing effectiveness: Mixing time Fig. Variation of mixing time with Reynolds number for a six-blade Rushton turbine in a baffled tank Assessing mixing effectiveness: Mixing time (continue) Power Requirements for Mixing  Electrical power is used to drive impellers in stirred tanks  The power required depends on the resistance offered by the fluid to rotation of the impeller  Average power consumption per unit volume for industrial bioreactors ranges from 10 kW m−3 for small vessels to 1~2 kW m−3 for large vessels  Friction in the stirrer motor gearbox and seals reduces the energy transmitted to the fluid; therefore, the electrical power consumed by stirrer motors is always greater than the mixing power by an amount depending on the efficiency of the drive  Energy costs for operation of stirrers in bioreactors are an important consideration in process economics. Power Requirements for Mixing (Cont`d) The presence or absence of turbulence can be correlated with the the impeller Reynolds number defined as: where, Di = the impeller (agitator) diameter Ni = rotation speed impeller in rev/s (rpm) = ω/2π ρ = fluid density μ = fluid viscosity  The flow is laminar in the tank for Re < 10  The flow is turbulent for Rei > 10000  The flow is transitional for Re between laminar and turbulent. In fact being turbulent at the impeller and laminar in remote parts of the vessels Power Requirements for Mixing (Cont`d) Mixing power for non-aerated fluids depends on the stirrer speed, the impeller diameter and geometry, and properties of the fluid such as density and viscosity. The relationship between these variables is usually expressed in terms of dimensionless numbers such as the impeller Reynolds number (Rei) and the power number Np. Np is defined as: Where, P is power and n and Ni are same (rpm) Power Requirements for Mixing (Cont`d) Where, P is power, in baffled tanks, the Reynold’s no. larger than 10000 then P is independent of Re No. and Viscosity. Power Requirements Continued Example 6.1 Estimation of mixing time A fermentation broth with viscosity 10 −2 Pa.s and density 1000 kg.m − 3 is agitated in a 2.7 m 3 baffled tank using a Rushton turbine with diameter 0.5 m and stirred speed 1 s −1. Estimate the mixing time. Power Requirements for Mixing (Cont`d) Fig. Correlation between power number and Reynolds number Fig. Correlation between power number and Reynolds number for anchor and helical-ribbon impeller without sparging Scale-up of Mixing Systems Design of industrial-scale bioprocess is usually based on the performance of small-scale prototypes. Determining optimum operating conditions at production scale is expensive and time consuming; accordingly, it is always better to know whether a particular process will work properly before it is constructed in full size. Ideally, scale-up should be carried out so that conditions in the large vessels are as close as possible to those producing good results in the small vessels. As mixing is an important function of bioreactors, it would seem desirable to keep the mixing time constant on scale-up. Unfortunately, as explained below, the relationship between mixing time and power consumption makes this rarely possible in practice. As the volume of mixing vessels is increased, so too are the lengths of the flow paths for bulk circulation. Scale-up of Mixing Systems (Cont`d) To keep the mixing time constant, the velocity of fluid in the tank must be increased in proportion to the size. As a rough guide, under turbulent conditions the power per unit volume is proportional to the fluid velocity squared: P/V ∝ v2 For example, a cylindrical 1 m3 pilot-scale stirred tank is scaled up to 100 m3. If the tanks are geometrically similar, the length of the flow path in the large tank is about 4.5 times that in the small one. Therefore, to keep the same mixing time, fluid velocity in the large tank must be approximately 4.5 times faster. From above Eq. this would entail a 4.52 or 20-fold increase in power per unit volume. So, if the power input to the 1 m3 pilot-scale vessel is P, the power required for the same mixing time in the 100 m3 tank is about 2000P. This represents an extremely large increase in power, much greater than is economically or technically feasible with most equipment used for stirring. Improving Mixing in Fermenters Sometimes, it is impossible to reduce mixing times by simply raising the power input into the stirrer. So, while increasing the stirrer speed is an obvious way of improving fluid circulation, other techniques may be required. Mixing can be improved by changing the configuration of the system. Baffles should be installed; this is routine for stirrer fermenters and produces greater turbulence. For efficient mixing the impeller should be mounted below the geometric center of the vessel. In standard designs the impeller is located about one impeller diameter, or one-third the tank diameter, above the bottom of the tank. Mixing is facilitated when circulation currents below the impeller are smaller than those above; fluid particles leaving the impeller at the same time instant then take different periods of time to return and exchange material. Rate of distribution throughout the vessel is increased when upper and lower circulation loops are asynchronous. Improving Mixing in Fermenters (Cont`d) Another device for improving mixing is multiple impellers, although this requires an increase in power input. Typical bioreactors used for aerobic culture are tall cylindrical vessels with liquid depths significantly greater than the tank diameter. This design produces a higher hydrostatic pressure at the bottom of the vessel, and gives rising air bubbles a longer contact time with liquid. Effective mixing in tall fermenters requires more than one impeller.  Improving Mixing in Fermenters (Cont`d) In ungassed systems with spacing between impellers of at least one impeller diameter, the power dissipated by multiple impellers is approximated by the following relationship: Pn = nPs Additional mixing problems can appear in fermenters when material is fed into system during operation. If bulk distribution is slow, fermenters operated continuously or in fed-batch mode may develop highly localized concentrations of substrate or other added material near the feed point. This has been observed particularly in large-scale processes for production of SCP (single-cell-protein) from methanol. Because high levels of methanol are toxic to cell growth, biomass yields decrease significantly when mixing of feed material into the broth is slow. Also observed was that during animal cell culture when alkali such as NaOH was used to control pH, high local pH value seriously affected the growth of the cells, although experiment was carried out within a small fermenter. Problems like this can be alleviated by using multiple injection points to aid distribution of added material. It is much less expensive to do this than to increase the fluid velocity and power input. Effect of Rheological Properties on Mixing For effective mixing there must be turbulent conditions in the mixing vessel. Intensity of turbulence is represented by the impeller’s Reynolds number. As discussed before for a baffled tank with turbine impeller, once (Re)i falls below criteria turbulence is damped and mixing time increases significantly. (Re)i decreases in direct proportion to increase in viscosity. Accordingly, non-turbulent conditions and poor mixing are likely to occur during agitation of highly viscous fluids. Increasing the impeller speed is an obvious solution, but this requires considerable increase in power consumption and therefore may not be feasible. Most non-Newtonian fluids in bioprocessing are pseudoplastic.Because the apparent viscosity of these fluids depends on the shear rate, the rheological behavior of many culture broths depends on shear conditions in the fermenters. Effect of Rheological Properties on Mixing (Cont’d) Pseoduplastic fluids are shear thinning, i.e. their apparent viscosity decreases with increasing shear. Accordingly, in stirred vessels, pseudoplastic fluids have relatively low apparent viscosity in the high-shear zone near the impeller, and relatively high apparent viscosity when the fluid is away from the impeller. As a result, flow patterns similar to that illustrated below can develop. Stagnation Zones Fig. Mixing pattern for pseudoplastic in a stirred tank Effect of Rheological Properties on Mixing (Cont’d) The effects of local fluid thinning in pseudoplastic fluids can be countered by modifying the geometry of the system or impeller design. Stirrers of large diameter are recommended. For turbine impellers, instead of the usual tank-to-impeller diameter ratio of 3:1 used with low viscosity fluids, this ratio is reduced to between 1.6 ~2.0. Different impeller designs which sweep the entire volume of the vessel are also recommended. The most common types used for viscous mixing are helical impellers and gate- and paddle-anchors mounted with small clearance between the impeller and tank wall. Mixing with these stirrers is accomplished at low speed without highvelocity streams. Helical agitators have been successfully used to reduce shear damage and improve mixing in viscous cell suspensions. Effect of Rheological Properties on Mixing (Cont’d) Alternative impeller designs such as the helical ribbon and anchor improve mixing in viscous fluids; however their application in fermentaters is only possible when oxygen demand in culture is relatively low. Although large-diameter impellers operating at relatively slow speed give superior bulk mixing, high-shear systems with small, high-speed impellers are preferable for breaking up gas bubbles and promoting oxygen transfer to the liquid. in design of fermenters for viscous cultures, a compromise is usually required between mixing effectiveness and adequate mass transfer.