BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS

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1 BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS

2 Starting Reference 1. P. A. Ramachandran and R. V. Chaudhari, Three-Phase Catalytic Reactors, Gordon and Breach Publishers, New York, (1983). 2. Nigam, K.D.P. and Schumpe, A., Three-phase sparged reactors, Topics in chemical engineering, 8, , , (1996) 3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier, Chemical Reactors: Design, Engineering, Operation, Technip, (2004) 2

3 Objectives 1. Review microkinetic and macrokinetic processes that occur in soluble and solid-catalyzed systems. 2. Review ideal flow patterns for homogeneous systems as a precursor for application to multiphase systems. 3. Derive basic reactor performance equations using ideal flow patterns for the various phases. 4. Introduce non-ideal fluid mixing models. 5. Illustrate concepts through use of case studies. 3

4 Types of Multiphase Reactions Reaction Type Degree of Difficulty Gas-liquid without catalyst Gas-liquid with soluble catalyst Gas-liquid with solid catalyst Gas-liquid-liquid with soluble or solid catalyst Gas-liquid-liquid with soluble or solid catalyst (two liquid phases) Straightforward Complex 4

5 Hierarchy of Multiphase Reactor Models Model Type Empirical Ideal Flow Patterns Phenomenological Volume-Averaged Conservation Laws Implementation Straightforward Insight Very little Pointwise Conservation Laws Very Difficult or Impossible Significant 5

6 Macrokinetic Processes in Slurry Reactors Hydrodynamics of the multi-phase dispersion - Fluid holdups & holdup distribution - Fluid and particle specific interfacial areas - Bubble size & catalyst size distributions Fluid macromixing - PDF s of the various phases Fluid micromixing - Bubble coalescence & breakage - Catalyst particle agglomeration & attrition Reactor Model Heat transfer phenomena - Liquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc. Energy dissipation - Power input from variouis sources (e.g., stirrers, fluid-fluid interactions, ) 6

7 Macrokinetic Processes in Fixed-Bed Reactors Hydrodynamics of the multi-phase flows - Flow regimes & pressure drop - Fluid holdups & holdup distribution - Fluid-fluid & fluid-particle specific interfacial areas - Fluid distribution Fluid macromixing - PDF s of the various phases Heat transfer phenomena - Liquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc. Reactor Model Energy dissipation - Pressure drop (e.g., stirrers, fluid-fluid interactions, ) 7

8 Elements of the Reactor Model Micro or Local Analysis Macro or Global Analysis Gas - liquid mass transfer Liquid - solid mass transfer Interparticle and interphase mass transfer Intraparticle and intraphase diffusion Intraparticle and intraphase heat transfer Catalyst particle wetting Flow patterns for the gas, liquid, and solids Hydrodynamics of the gas, liquid, and solids Macro distributions of the gas, liquid and solid Heat exchange Other types of transport phenomena 8

9 Reactor Design Variables Feed Q in T in C in Reactor Q out T out C out Product Reactor Process Reaction Flow = f Performance Variables Rates Patterns Conversion Flow rates Kinetics Macro Selectivity Inlet C & T Transport Micro Activity Heat exchange 9

10 Ideal Flow Patterns for Single-Phase Systems Q (m 3 /s) Q (m 3 /s) a. Plug-Flow Q (m 3 /s) Q (m 3 /s) b. Backmixed Flow 10

11 Impulse Tracer Response x(t) M T t y(t) Q (m 3 /s) t Reactor System t Q (m 3 /s) E(t) dt y(t) dt M / Q T Fraction of the outflow with a residence time between t and t + dt E(t) is the P.D.F. of the residence time distribution Tracer mass balance requirement: M T Q y(t) dt o 11

12 Fluid-Phase Mixing: Single Phase, Plug Flow Q (m 3 /s) 12

13 Fluid-Phase Mixing: Single Phase, Backmixed Q (m 3 /s) Mi = Mass of tracer injected (kmol) 13

14 Idealized Mixing Models for Multiphase Reactors Model Gas-Phase Liquid Phase Solid-Phase Reactor Type 1 Plug-flow Plug-flow Fixed Trickle-Bed Flooded-Bed 2 Backmixed Backmixed Backmixed Mechanically agitated 3 Plug-Flow Backmixed Backmixed Bubble column Ebullated - bed Gas-Lift & Loop 14

15 Ideal Flow Patterns in Multiphase Reactors Example: Mechanically Agitated Reactors or V R = v G + V L + V C 1 = G + L + C G Vr Q G G L Vr ( 1 G L ) Q L 15

16 First Absolute Moment of the Tracer Response for Multiphase Systems For a single mobile phase in contact with p stagnant phases: V = p j = 2 Q 1 K 1j V j For p mobile phases in contact with p - 1 mobile phases: 1 = V 1 + Q 1 + p j = 2 p j = 2 K 1j V j K 1j Q j K 1j = C j C 1 equil. is the partition coefficient of the tracer between phase 1 and j 16

17 Relating the PDF to Reactor Performance For any system where the covariance of sojourn times is zero (i.e., when the tracer leaves and re-enters the flowing stream at the same spatial position), the PDF of sojourn times in the reaction environment can be obtained from the exit-age PDF for a non-adsorbing tracer that remains confined to the flowing phase external to other phases present in the system. For a first-order process: H p (k c ) = pdf for the stagnant phase - H (k 1 c ) t A ext 0 - ( kww / Q 1) t e E ext 0 p - X = e E (t) dt = (t) dt 17

18 Illustrations of Ideal-Mixing Models for Multiphase Reactors Stirred tank Bubble Column z z Trickle - Bed Flooded - Bed G L Plug-flow of gas Backmixed liquid & catalyst Batch catalyst Catalyst is fully wetted G L Plug-flow of gas Plug-flow of liquid Fixed-bed of catalyst Catalyst is fully wetted 18

19 Intrinsic Reaction Rates Reaction Scheme: A (g) + vb (l) C (l) 19

20 Gas Limiting and Plug-Flow of Liquid Key Assumptions 1. Gaseous reactant is limiting 2. First-order reaction wrt dissolved gas 3. Constant gas-phase concentration G L z 4. Plug-flow of liquid 5. Isothermal operation 6. Liquid is nonvolatile 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients 20

21 Concentration or Axial Height Gas Limiting and Plug flow of liquid Constant gas phase concentration valid for pure gas at high flow rate Q l A Relative distance from catalyst particle (Net input by convection) l z Q A l l zdz + (Input by Gas- (Loss by Liquidsolid Transport) = 0 Liquid Transport) - (1) k Dividing by Ar.dz and taking limit dz l a B * A A A dz- k a A A A dz= 0 l r s p l s r (2) (3) (4) 21

22 Gas Limiting and Plug flow of liquid 22

23 Gas Limiting and Plug flow of liquid Solving the Model Equations 23

24 R Concept of Reactor Efficiency Rate of rxn in the Entire Reactor with Transport Effects Maximum Possible Rate 24

25 Conversion of Reactant B (in terms of Reactor Efficiency) 25

26 Gas Limiting and Backmixed Liquid Stirred Tank Key Assumptions Bubble Column z G L 1. Gaseous reactant is limiting 2. First-order reaction wrt dissolved gas 3. Constant gas-phase concentration 4. Liquid and catalyst are backmixed 5. Isothermal operation 6. Liquid is nonvolatile 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients 26

27 Concentration or Axial Height Gas Limiting and Backmixed Liquid Relative distance from catalyst particle -Concentration of dissolved gas in the liquid bulk is constant [ f(z)] [=A l,0 ] -Concentration of liquid reactant in the liquid bulk is constant [ f(z)] [=B l,0 ] A in liquid bulk: Analysis is similar to the previous case 27

28 Gas Limiting and Backmixed Liquid A at the catalyst surface: For Reactant B: (Net input by flow) = (Rate of rxn of B at the catalyst surface) (Note: No transport to gas since B is non-volatile) 28

29 Gas Limiting and Backmixed Liquid Solving the Model Equations 29

30 A Flow Patterns Concepts for Multiphase Systems A - Single phase flow of gas or liquid with exchange between the mobile phase and stagnant phase. Fixed beds, Trickle-beds, packed bubble columns B - Single phase flow of gas or liquid with exchange between a partially backmixed stagnant phase. Semi-batch slurries, fluidized-beds, ebullated beds B 30

31 Flow Patterns Concepts for Multiphase Systems C D C, D - Cocurrent or countercurrent two-phase flow with exchange between the phases and stagnant phase. Trickle-beds, packed or empty bubble columns E E - Exchange between two flowing phases, one of which has strong internal recirculation. Empty bubble columns and fluidized beds 31

32 Axial Dispersion Model (Single Phase) C z = 0 Let τ C t D η = 0 2 C 2 z u C dz R C u0c0 uc D ax z z L 1 Pe C ax 0 Pe ax 2 C 2 η C ul D 1 Pe ax C dη ax τ C η L u τr Basis: Plug flow with superimposed diffusional transport in the direction of flow C z = L 0 C =

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