Report

BASIC DESIGN EQUATIONS FOR MULTIPHASE REACTORS 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, 11-112, 679739, (1996) 3. Trambouze, P., H. Van Landeghem, J.-P. Wauquier, “Chemical Reactors: Design, Engineering, Operation”, Technip, (2004) 2 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 Types of Multiphase Reactions Reaction Type Degree of Difficulty • Gas-liquid without catalyst Straightforward • 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) Complex 4 Hierarchy of Multiphase Reactor Models Model Type Empirical Implementation Insight Straightforward Very little Ideal Flow Patterns Phenomenological Volume-Averaged Conservation Laws Pointwise Conservation Very Difficult or Impossible Laws Significant 5 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 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 Elements of the Reactor Model Micro or Local Analysis • Gas - liquid mass transfer Macro or Global Analysis • Liquid - solid mass transfer • Flow patterns for the gas, liquid, and solids • Interparticle and interphase mass transfer • Hydrodynamics of the gas, liquid, and solids • Intraparticle and intraphase diffusion • Macro distributions of the gas, liquid and solid • Intraparticle and intraphase heat transfer • Heat exchange • Catalyst particle wetting • Other types of transport phenomena 8 Reactor Design Variables Feed Qin Tin Cin Qout Tout Product Cout Reactor Reactor Process Reaction Flow Performance Variables Rates • Conversion • Flow rates • Kinetics • Selectivity • Inlet C & T • Transport • Micro • Activity • Heat exchange =f Patterns • Macro 9 Ideal Flow Patterns for Single-Phase Systems Q (m3/s) Q (m3/s) a. Plug-Flow Q (m3/s) Q (m3/s) b. Backmixed Flow 10 Impulse Tracer Response x(t) MT t y(t) t Q (m3/s) t Q (m3/s) y(t) dt E(t ) dt MT / Q Reactor System 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: MT Q y(t)dt o 11 Fluid-Phase Mixing: Single Phase, Plug Flow Q (m3/s) 12 Fluid-Phase Mixing: Single Phase, Backmixed Q (m3/s) Mi = Mass of tracer injected (kmol) 13 Idealized Mixing Models for Multiphase Reactors Model Gas-Phase Liquid Phase Solid-Phase Reactor Type Plug-flow Fixed Trickle-Bed Flooded-Bed 1 Plug-flow 2 Backmixed Backmixed Backmixed Mechanically agitated 3 Plug-Flow Backmixed Bubble column Ebullated - bed Gas-Lift & Loop Backmixed 14 Ideal Flow Patterns in Multiphase Reactors Example: Mechanically Agitated Reactors or VR = vG + VL + VC 1 = G + L + C G Vr G QG L Vr (1 G L ) QL 15 First Absolute Moment of the Tracer Response for Multiphase Systems For a single mobile phase in contact with p stagnant phases: p V1 + K1j Vj j=2 1 = Q1 For p mobile phases in contact with p - 1 mobile phases: p V1 + K1j Vj j= 2 p 1 = Q1 + K 1j Qj j= 2 K1j C j = C1 equil. is the partition coefficient of the tracer between phase 1 and j 16 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 (k ) t p c 1 - XA = e Hp(kc) = pdf for the stagnant phase 0 = e 0 Eext ( t ) dt - (k W W / Q1 ) t Eext ( t ) dt 17 Illustrations of Ideal-Mixing Models for Multiphase Reactors Stirred tank Trickle - Bed Bubble Column z Flooded - Bed z 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 Intrinsic Reaction Rates Reaction Scheme: A (g) + vB (l) C (l) 19 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 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 G L 20 Concentration or Axial Height Gas Limiting and Plug flow of liquid Constant gas phase concentration valid for pure gas at high flow rate Relative distance from catalyst particle (Net input by (Input by Gas- + convection) Liquid Transport) Ql Al z Ql Al (Loss by Liquidsolid Transport) =0 * k a A Al Ar dz- ks a p Al As Ar dz= 0 l B z dz (1) (2) Dividing by Ar.dz and taking limit dz (3) (4) 21 Gas Limiting and Plug flow of liquid 22 Gas Limiting and Plug flow of liquid Solving the Model Equations 23 Concept of Reactor Efficiency R Rate of rxn in the Entire Reactor with Transport Effects Maximum Possible Rate 24 Conversion of Reactant B (in terms of Reactor Efficiency) 25 Gas Limiting and Backmixed Liquid Key Assumptions Stirred Tank Bubble Column 1. Gaseous reactant is limiting z 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 G L 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients 26 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)] [=Al,0] -Concentration of liquid reactant in the liquid bulk is constant [≠f(z)] [=Bl,0] A in liquid bulk: Analysis is similar to the previous case 27 Gas Limiting and Backmixed Liquid A at the catalyst surface: For Reactant B: (Net input by (Rate of rxn of B at = flow) the catalyst surface) (Note: No transport to gas since B is non-volatile) 28 Gas Limiting and Backmixed Liquid Solving the Model Equations 29 Flow Patterns Concepts for Multiphase Systems A 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 B - Single phase flow of gas or liquid with exchange between a partially backmixed stagnant phase. Semi-batch slurries, fluidized-beds, ebullated beds 30 Flow Patterns Concepts for Multiphase Systems C D C, D - Cocurrent or E countercurrent two-phase flow with exchange between the phases and stagnant phase. Trickle-beds, packed or empty bubble columns E - Exchange between two flowing phases, one of which has strong internal recirculation. Empty bubble columns and fluidized beds 31 Axial Dispersion Model (Single Phase) C 2C C Dax u R 2 t z dz @z=0 Let C u0C0 uC Dax z z η L Peax uL Dax Basis: Plug flow with superimposed “diffusional” transport in the direction of flow @z=L C 0 z L τ u C 1 2C C τ τR 2 t Peax η dη @ = 0 1 C C0 C Peax η @ = 1 C 0 η 32