ENGG 199 Reacting Flows Spring Lecture 4 Gas-Liquid Mixing Reactor Selection Agitator Design

Transcription

1 ENGG 199 Reacting Flows Spring 2006 Lecture 4 Gas-Liquid Mixing Reactor Selection gitator Design Copyright 2000,.W. Etchells, R.K.Grenville & R.D. LaRoche ll rights reserved.

2 Background Roughly 25 % of processes involve gas-liquid contacting. variety of equipment types are used. Size of vessel and type of equipment will depend on: Concentrations Kinetics Diffusivities Solubilities May involve reaction or simple transfer between phases. Similar issues to single-phase mixing and reaction. ENGG 199 Lecture 4 Slide 2

3 Examples Sulphonation and Chlorination: Fast reactions - Gas is soluble in liquid - High mass and heat transfer required. Short contact times small reactor volume with high mixing rates. Oxidation and Hydrogenation: Solubility is low - Many reactions are very exothermic. Long contact times large reactor volume with high mixing rates. Fermenters (inc. WWT): Often dilute - Slow reactions. Long contact times very large reactor volume with low mixing rates. Heat transfer may be important. ENGG 199 Lecture 4 Slide 3

4 Examples May need to remove dissolved material from liquid: May be contaminant. May be by-product. Must be removed affects product quality. dd inert gas to liquid to strip out contaminant. Fermentation: erobic organisms produce carbon dioxide. Soluble in reaction mass changes ph. ir supplies oxygen and strips out carbon dioxide. 80 % of air supplied is inert. ENGG 199 Lecture 4 Slide 4

5 Equipment for Gas-Liquid Mixing From Mixing in the Process Industries ENGG 199 Lecture 4 Slide 5

6 Mass Balance Molecules transfer from gas into liquid (or vice versa): Where: K G Pa vnv a is the surface area to volume of a single bubble. v is the volume of a single bubble. n is the number of bubbles per unit volume of liquid. y C H P rv d dt ( VC ) Mass transfer resistance: 1 K G 1 k G H k L Usually, k G >> k L / H so 1 / k G can be neglected. ENGG 199 Lecture 4 Slide 6

7 Mass Balance Interfacial area per unit volume, a: a a nv Gas hold-up, G : G nv k L av P H y C rv d dt ( VC ) k L av x * mol C rv d dt ( VC ) k L av C * C rv d dt ( VC ) ENGG 199 Lecture 4 Slide 7

8 Comparison of G-L Contacting Devices Device k L a (s -1 ) V (m 3 ) k L av (m 3 s -1 ) a (m -1 ) L (-) Liquid Flow Gas Flow (W /kg) gitated Vessel B mixed Int to B mixed Bubble Column Plug Plug Packed Tower Plug Plug Plate Tower Int Plug Static Mixer Up to Plug Plug From Mixing in the Process Industries. ENGG 199 Lecture 4 Slide 8

9 Choice of Mixing Equipment diffuses through film into bulk. Without reaction, rate of mass transfer per unit area of interface will be: j D mol ( C * C ) k L ( C * C ) kmol m -2 s -1 Maximum mass transfer when C = 0: j max D mol ( C * 0) k L C * Note: higher mass transfer rate may be achieved if all reaction occurs in film - Enhancement Factor. ENGG 199 Lecture 4 Slide 9

10 Choice of Mixing Equipment Some will be consumed by reaction within the film. Maximum possible rate of reaction within unit area of interface will be: * r k C C Define Film Conversion Parameter, M: max R B M r j max max k C R D * mol C B C * k C R D * mol C C B * 2 D D mol mol M k R C D k B 2 L mol ENGG 199 Lecture 4 Slide 10

11 M < Infinitely Slow Reaction Mass transfer keeps concentration of in the bulk close to the saturation level. j k L a( C * C ) k R C C B L C Reactor needs: High liquid hold-up. * C k C R B k a Sufficient interfacial area - but not high. 1 Once k L a is high enough, rate is independent of mixing. L L Consider using Bubble Column. ENGG 199 Lecture 4 Slide 11

12 < M < 4.0 Intermediate Reaction Reaction consumes in bulk but not fast enough to drive concentration to 0. Most of reaction does occur in bulk (V L >> a ). Must not be mass transfer limited: Need sufficient interfacial area. Since C < C *, mixing can increase C : Consider using gitated Vessel. k L * dc a( C C ) k C C R B L dt ENGG 199 Lecture 4 Slide 12

13 M > 4.0 Instantaneous Reaction Reaction is so fast, compared to diffusion rate, that all is consumed in film. Hence, large a is needed but L is not. Consider using Motionless Mixer. Consumption of steepens concentration gradient enhancing mass transfer. Reaction occurs at plane within film: and B cannot exist together. Location of film depends on relative diffusivities of and B. ENGG 199 Lecture 4 Slide 13

14 Enhancement Factor For reaction with negligible gas phase resistance: + bb Products r * k C 1 L D bd mol,b mol, C B C * Max. mass transfer rate per unit area without reaction is: r k L C * Term inside bracket is Enhancment Factor, E: E rate of mass transfer with reaction rate for mass transfer alone ENGG 199 Lecture 4 Slide 14

15 Sample Calculation For a given system, how fast must reaction rate be in each regime? Diffusivity, D mol : Oxygen / Water m 2 / s Hydrogen / Water m 2 / s Chlorine / Water m 2 / s Carbon dioxide / Water m 2 / s Carbon dioxide / Ethanol m 2 / s Sulphur dioxide / Water m 2 / s ENGG 199 Lecture 4 Slide 15

16 Sample Calculation Concentration of liquid phase reactant, C B : For a pure liquid: C B Mw For water: C B = kmol / m 3 Mass transfer coefficient, k L : Estimate (from Coulson & Richardson) for bubbly flow: k L = m / s ENGG 199 Lecture 4 Slide 16

17 From definition of M: Estimates of k R Mk M (3 10 ) L k 0. 81M R 9 C D B mol M = 4.0: k R = 3.24 m 3 kmol -1 s -1 M = : k R = m 3 kmol -1 s -1 Look for some examples. ENGG 199 Lecture 4 Slide 17

18 gitator Design Equipment selection should be made by comparing rates of reaction and mass transfer: But these are often not known and can be very difficult to measure. gitated vessel is very commonly used: Offers compromise of high liquid hold-up and high interfacial area. Similarities with solid-liquid mixing: Buoyancy causes bubbles to rise and leave liquid phase. Bubble size is determined by intensity of agitation. Expect minimum speed for impeller (analogous to N JS for solids suspension)? ENGG 199 Lecture 4 Slide 18

19 gitator provides energy to: Break-up bubbles and create interfacial area. Re-circulate bubbles (prevent plug flow). Mix the liquid phase. Suspend solids - if present (catalyst). Promote heat transfer. Re-incorporate gas from head space - pure gas only. ENGG 199 Lecture 4 Slide 19

20 Need to be able to calculate: Calculations gitator speed: Minimum speed for dispersion. Maximum speed required to re-circulate bubbles. Power: Presence of gas affects power drawn by impeller. How to account for gas in power calculation? Mass transfer co-efficient: Power input and gas flow affect mass transfer. How to estimation of mass transfer co-efficient? ENGG 199 Lecture 4 Slide 20

21 Vessel Geometry Typical vertical, cylindrical vessel: May have 1/2 baffles with upper impeller to create vortex on surface. Re-incorporates gas from head space. Dished heads to withstand pressure. Often need mechanical seal. Sometimes H / T > 1.0: Increases pressure increase solubility increase driving force. Increases surface area per unit volume for heat transfer. Gas introduced low in vessel: Through pipe or sparge ring. Locate beneath impeller. ENGG 199 Lecture 4 Slide 21

22 Lowest impeller: Impeller Geometry Main gas dispersing impeller. Traditionally a Rushton turbine. New development - concave blade (Smith) turbine. High local energy dissipation rate high interfacial area. Upper impeller(s): nother radial flow impeller (Rushton or Smith). More usually an axial flow impeller (PBT or Hydrofoil). Recent development: Upward pumping hydrofoils. Seem to offer several advantages. ENGG 199 Lecture 4 Slide 22

23 Impellers used for Gas Dispersion Rushton Turbine Smith Turbine High-solidity Hydrofoil Chemineer BT-6 ENGG 199 Lecture 4 Slide 23

24 Nienow et al. (5th Europ Conf on Mixing) ENGG 199 Lecture 4 Slide 24

25 t (a): Impeller Speed Inertia of gas bubbles dominates flow. Vessel behaves as bubble column. Impeller starts rotating: Inertia of liquid flow starts to increase. Bubbles are driven radially towards wall of vessel. t (b) - the Flooding Speed: Bubbles reach wall at height of impeller. t (c) - the Complete Dispersion Speed : Bubbles re-circulate beneath the impeller. ENGG 199 Lecture 4 Slide 25

26 Dimensionless Numbers These speeds have been measured experimentally: Empirical correlations relating impeller speed and diameter to gas flow rate have been developed. Dimensionless numbers have been used to correlations. Fl e QG ND 3 Fr 2 N D g D T ENGG 199 Lecture 4 Slide 26

27 Flooding Speed For Rushton and Smith turbines (0.22 < D / T < 0.55): e F K F Fr F D T 3.5 QG N D F 3 K F 2 N D F g D T 3.5 N F Q K F g D G 4 T D 3.5 1/ 3 For a Rushton turbine: K F = 30. For a Smith turbine: K F = 70. ENGG 199 Lecture 4 Slide 27

28 Complete Dispersion For Rushton and Smith turbines (0.22 < D / T < 0.55): e CD K CD Fr 0.5 CD D T 1/ 2 QG N D CD 3 K CD 2 N D CD g D T 1/ 2 N CD Q ( Tg) G K D CD 1/ 2 4 1/ 2 For a Rushton turbine: K CD = 0.2. For a Smith turbine: K CD = 0.4. ENGG 199 Lecture 4 Slide 28

29 Power No Power No. vs. Flow No. Smith Turbine - Standard Baffles - No Coil 5 SCFM 10 SCFM 20 SCFM 30 SCFM 40 SCFM 53 SCFM 0 SCFM Flow No. ENGG 199 Lecture 4 Slide 29

30 Gas Cavity Structures ENGG 199 Lecture 4 Slide 30

31 s impeller rotates: Power Input High pressure region is formed on front of blades. Low pressure region is formed on back of blades. Gas cavities form in low pressure regions: Reduces drag on impeller. Reduces power required to move impeller reduces Po. Five cavity structures have been identified: 6 vortex cavities. 6 clinging cavities. 3 clinging and 3 large cavities on alternate blades. 6 large cavities of different size (3-3 structure). 6 ragged cavities (flooded impeller). ENGG 199 Lecture 4 Slide 31

32 Ratio of Gassed to Ungassed Power Vortex and clinging cavities little effect on power draw. Power drops as 3-3 cavity structure forms. Once ragged cavities form slight increase in power draw. Ratio of gassed to ungassed power is dependent on impeller type. great deal of work has been done to find impellers that minimize the fall in power. Smith and Upward Pumping turbines and others. ENGG 199 Lecture 4 Slide 32

33 For Rushton turbines: Prediction of Gassed Power Calderbank (1958) fitted two straight lines to curve: P P G U e for : e P P G U e for : e Volesky (1979): P P G U 0.10 QG NV 1/ 4 2 N D gwv 4 2 / 3 1/ 5 ENGG 199 Lecture 4 Slide 33

34 Prediction of Gassed Power Bakker, Smith & Myers (Chemical Engineering, 199x): P P G U d 1 ( b a ) Fr tanh( ce) a b c d Rushton Smith ENGG 199 Lecture 4 Slide 34

35 Gas Hold-Up Gas hold-up, G, is ratio of gas volume to total volume of dispersion. It is affected by: Bubble size generated by impeller. Distribution and circulation of bubbles throughout liquid. Growth (due to coalescence) of bubbles during circulation. Interfacial tension between gas and liquid determines: How much energy is required to break-up bubbles. How likely are bubbles to coalesce as they collide. Hold-up is important because: 6 d ENGG 199 Lecture 4 Slide 35 a G 32

36 Estimation of Gas Hold-Up Experimental measurements. Best correlation in terms of (gassed) power input per unit mass and superficial gas velocity. Chapman (1983): G G U SG Chapman correlated hold-up data from two sizes of Rushton turbine and two pitched blade turbines pumping up and down. Similar exponents found in other work. ENGG 199 Lecture 4 Slide 36

37 CFD:- eration: Gas Holdup in Eulerian Contours of vorticity magnitude (0-100) display on an iso-surface of contant gas volume fraction (0.25) N = << N amax = 0.45 P g /P u = 0.7 (0.83 for single impeller system; experiments) ENGG 199 Lecture 4 Slide 37 Contours of Gas Volume Fraction

38 Mass Transfer Co-efficient Researchers measure and correlate k L a. Best correlation in terms of (gassed) power input per unit mass and superficial gas velocity. Muskett (1987) k L a 0.41 G ( vvm T ) L G Non-coalescing, salt solutions, typical of fermentations Van t Riet (1979) k a ( vvm T ) Epsilon turbulent energy dissipation rate Calculated directly from CFD analysis Estimate using Power/Mass in the impeller swept volume bsolute k L a not required, but relative values compared to verifiable small-scale reactor ENGG 199 Lecture 4 Slide 38

39 k L a and G are related: G and k L a From turbulence theory and experiments: k L a k L 6 d G 32 d G k L a k L G G Relationship between hold-up and superficial gas velocity? ENGG 199 Lecture 4 Slide 39

40 CFD:- Volumetric Mass Transfer Coefficient (K L a) ENGG 199 Lecture 4 Slide 40

41 Scale-Up Gas flow is usually specified in terms of liquid volume: Defines productivity of vessel. Kmols of gas processed per unit time. Expressed as vessel volumes per minute (vvm s) of gas: e.g gallon vessel with 500 GPM gas flow 0.5 vvm. Especially true if mixed gas (e.g. air) is fed to the reactor: Gas bubble will be depleted of reacting gas decreasing driving force. What happens to mass transfer rate on scale-up? ENGG 199 Lecture 4 Slide 41

42 Scale-Up Scaling-up with constant vvm s: Q T 3 On scale-up: Q U 2 T U U SG, L SG, S T T L S T Superficial gas velocity increases on scale-up k L a will increase if vvm & are constant on scale-up ENGG 199 Lecture 4 Slide 42

43 Driving Force In order to calculate driving force need to know C *. For pure gas this is (relatively) easy. For mixed gas need to know representative gas composition. In stirred tank, gas phase is back-mixed: ssume that gas composition is that of exit gas. Not always true, especially in tall tanks (fermenters). Gas composition has been measured and modeled (see Mann, Vlaev et al., UMIST). ENGG 199 Lecture 4 Slide 43

44 Boiling Reactors Boiling reactors are often used: Remove a solvent. Remove heat of reaction. Etc. etc. Vapour is generated by boil-up. What happens to power draw? In gassed system, power draw decreases due to cavities forming in low pressure region on back of blades. ENGG 199 Lecture 4 Slide 44

45 Boiling Reactors How will cavity form in boiling reactor? Pressure in zone at back of blades must be less than the saturated vapour pressure of the liquid. Static head of liquid will suppress cavity formation. Power draw will not decrease (in most circumstances): Especially on scale-up. What will happen when gas is sparged into a boiling reactor? ENGG 199 Lecture 4 Slide 45