Gas iquid and Gas- iquid Solid Reactions A. Gas iquid Systems
Proper Approach to Gas-iquid Reactions References Mass Transfer theories Gas-liquid reaction regimes Multiphase reactors and selection criterion Film model: Governing equations, problem complexities Examples and Illustrative Results Solution Algorithm (computational concepts)
Theories for Analysis of Transport Effects in Gas-iquid Reactions Two-film theory 1. W.G. Whitman, Chem. & Met. Eng., 29 147 (1923). 2. W. K. ewis & W. G. Whitman, Ind. Eng. Chem., 16, 215 (1924). Penetration theory P. V. Danckwerts, Trans. Faraday Soc., 46 300 (1950). P. V. Danckwerts, Trans. Faraday Soc., 47 300 (1951). P. V. Danckwerts, Gas-iquid Reactions, McGraw-Hill, NY (1970). R. Higbie, Trans. Am. Inst. Chem. Engrs., 31 365 (1935). Surface renewal theory P. V. Danckwerts, Ind. Eng. Chem., 43 1460 (1951). Rigorous multicomponent diffusion theory R. Taylor and R. Krishna, Multicomponent Mass Transfer, Wiley, New York, 1993.
Two-film Theory Assumptions 1. A stagnant layer exists in both the gas and the liquid phases. 2. The stagnant layers or films have negligible capacitance and hence a local steady-state exists. 3. Concentration gradients in the film are onedimensional. 4. ocal equilibrium exists between the the gas and liquid phases as the gas-liquid interface 5. ocal concentration gradients beyond the films are absent due to turbulence.
Two-Film Theory Concept W.G. Whitman, Chem. & Met. Eng., 29 147 (1923). p A Bulk Gas p Ai p Ai H A C Ai Gas Film iquid Film C Ai Bulk iquid x x + x C Ab δ x δ G x 0 x δ
Two-Film Theory - Single Reaction in the iquid Film - A (g) + b B (liq) P (liq) B & P are nonvolatile R A kg -moles A m 3 liquid - s - k mn C A m n C B Closed form solutions only possible for linear kinetics or when linear approximations are introduced
Film Theory Model for a Single Nonvolatile A( g) + bb( l) P( l) Gas-iquid Reaction Diffusion - reaction equations for a single reaction in the liquid film are: 2 d A * D r at x 0 A A at x δ A A A 2 dx 2 d B db DB br at x 0 0 at x δ B B 2 dx dx In dimensionless form, the equations become dependent on two dimensionless parameters, the Hatta number Ha and q * : m n For r kmn A B 1/2 2 ( * ) m 1 D n * BDB A mn * R 1 + A t Ha D k A B q t m ba D
Diffusion - reaction equations for a single reaction in the liquid film are: A A A A R x C D t C + 2 2 B B B B R x C D t C + 2 2 Penetration Theory Model
Comparison Between Theories Film theory: k D, δ - film thickness Penetration theory: k D 1/2 Higbie model t * - life of surface liquid element Danckwerts model s - average rate of surface renewal k k k R D ' A * C C δ R D ' A 2 * * C C πt R ' A * C C Ds
Gas-iquid Reaction Regimes Instantaneous Fast (m, n) Instantaneous & Surface Rapid pseudo 1st or mth order General (m,n) or Intermediate Slow Diffusional Very Slow
Characteristic Diffusion & Reaction Times Diffusion time t D D k 2 Reaction time t R C r C E Mass transfer time t M 1 k a B
Reaction-Diffusion Regimes Defined by Characteristic Times Slow reaction regime t D <<t R k k 0 Slow reaction-diffusion regime: t D <<t R <<t M Slow reaction kinetic regime: t D <<t M <<t R Fast reaction regime: t D >>t R k E A k 0 >k 0 Instantaneous reaction regime: k E A k 0
For reaction of a gas reactant in the liquid with liquid reactant with/without assistance of a dissolved catalyst A g + b β l P l ( ) ( ) ( ) The rate in the composition region of interest can usually be approximated as k mol A R m s A 3 k C m A C n B Where C A, C B are dissolved A concentration and concentration of liquid reactant B in the liquid. Reaction rate constant k is a function of dissolved catalyst concentration when catalyst is involved For reactions that are extremely fast compared to rate of mass transfer form gas to liquid one evaluates the enhancement of the absorption rate due to reaction. For not so fast reactions the rate is ( R A ) k a E ( p A H A ) ε Ag n ( RA) η k CB ε Where η effectiveness factor yields the slow down due to transport resistances. o p H A g m S30
Gas Absorption Accompanied by Reaction in the iquid Assume: - 2 nd order rate Hatta Number : Ei Number: Enhancement Factor: 1 K 1 k + 1 k H g S31
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2 In this notation ϕ N& A ( k mol A m s) is the gas to liquid flux R R ' A A N& ε A 3 a ( k mol m liquid s) ' 3 ( R )( k mol m reactor s) A S33
Eight (A H) regimes can be distinguished: A. Instantaneous reaction occurs in the liquid film B. Instantaneous reaction occurs at gas-liquid interface High gas-liquid interfacial area desired Non-isothermal effects likely S34
C. Rapid second order reaction in the film. No unreacted A penetrates into bulk liquid D. Pseudo first order reaction in film; same Ha number range as C. Absorption rate proportional to gas-liquid area. Non-isothermal effects still possible. S35
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Maximum temperature difference across film develops at complete mass transfer limitations Temperature difference for liquid film with reaction Trial and error required. Nonisothermality severe for fast reactions. e.g. Chlorination of toluene S38
- Summary - imiting Reaction-Diffusion Regimes Slow reaction kinetic regime Rate proportional to liquid holdup and reaction rate and influenced by the overall concentration driving force Rate independent of k l a B and overall concentration driving force Slow reaction-diffusion regime Rate proportional to k l a B and overall concentration driving force Rate independent of liquid holdup and often of reaction rate Fast reaction regime Rate proportional to a B,square root of reaction rate and driving force to the power (n+1)/2 (nth order reaction) Rate independent of k l and liquid holdup Instantaneous reaction regime Rate proportional to k and a B Rate independent of liquid holdup, reaction rate and is a week function of the solubility of the gas reactant
Key Issues Evaluate possible mechanisms and identify reaction pathways, key intermediates and rate parameters Evaluate the reaction regime and transport parameters on the rate and assess best reactor type Assess reactor flow pattern and flow regime on the rate Select best reactor, flow regime and catalyst concentration Approximately for 2 nd order reaction A( g) + b B( l) P( l) R R p H k E E A k ( atm) A Ag A A 1 a H mol A 3 m s local partial pressure of 3 atm m liquid Henry's constant for A k mol A a H, k a volumetric mass transfer coefficient for gas and liquid film, respectively. liquid reactor observed local reaction rate per unit volume of ( 1 s) H A 1 a E dimensionless enhancement factor m m 3 3 k Ag A A A + P k A A 1 + k C ε β A in the gas phase local liquid volume fractin in reactor reactor S29
Gas- liquid solid systems
et us consider: A + νb Gas-iquid-Solid Reactions Catalyst ν Reaction occurring in the pores of the catalyst particles and is gas reactant limited A Reactant in the gas phase B Non-volatile reaction in the liquid phase Number of steps: Transport of A from bulk gas phase to gas-liquid interface Transport of A from gas-liquid interface to bulk liquid Transport of A&B from bulk liquid to catalyst surface Intraparticle diffusion in the pores Adsorption of the reactants on the catalyst surface Surface reaction to yield product E E The overall local rate of reaction is given as R A A k * 1 1 1 a + k s a p + η c w k 2 B l 1 S45
Gas iquid Solid Catalyzed Reaction A(g)+B(l)P(l) KINETIC RATE Gas imiting Reactant (Completely Wetted Catalyst) ( per unit catalyst volume) ( per unit reactor volume) ( per unit reactor volume) R A η k o v : k RATE IN CATAYST: TRANSPORT RATE - Gas - liquid - iquid - solid ( 1 ε ) B v a A 3 ( mol m cat. s) 3 ( 1 ε ) A ( mol m react. s) 3 ( mol m react. s) a p A H B ( A A ) g A k v A H l η OVERA (APPARENT) RATE : : k K s 1 p g a l s 1 K a B A 1 B 3 ( mol m react. s) s Ω s p A g H 1 + + k a A A : 1 ( 1 ε B ) kvη p S21
Dependence of Apparent Rate Constant (k app ) on Transport (k ls, η p ) and Kinetic Parameters (k v ) Reaction : A ( g ) + B( l) P( l) iquid limiting reactant (nonvolatile) - Case of of completely wetted catalyst Kinetic rate (per unit catalyst volume) Rate in catalyst (per unit reactor volume) Transport rate (per unit reactor volume) : : : k k η B k v v ls B 3 ( mol m cat. s) p 3 ( 1 ε )( mol m react. s) 3 ( B B ) a ( mol m react. s) l s s B p GAS IQUID FIM CATAYST B l BUK IQUID S- FIM B s SOID PHASE η k p Overall(apparent)rate v ( 1 ε ) B B 1 k app B 3 ( mol m react. s) 1 k a ls p B p + η k v 1 ( 1 ε ) B r p 0
Our task in catalytic reactor selection, scale-up and design is to either maximize volumetric productivity, selectivity or product concentration or an objective function of all of the above. The key to our success is the catalyst. For each reactor type considered we can plot feasible operating points on a plot of volumetric productivity versus catalyst concentration. m& v m& vmax m& S a v max x x max specific activity catalyst concentration x max Clearly is determined by transport limitations and by reactor type and flow regime. S a x m kg P kg cat h kg 3 cat reactor S a Improving only improves m& v if we are not already transport limited. S38
Chemists or biochemists need to improve S a and together with engineers work on increasing x max. Engineers by manipulation of flow patterns affect m& v. max In Kinetically Controlled Regime m& v x, Sa x max limited by catalyst and support or matrix loading capacity for cells or enzymes In Transport imited Regime m& v p a S, 0 p 1/2 x p Mass transfer between gas-liquid, liquid-solid etc. entirely limit m& v and set m& v. max Changes in S a, do not help; alternating flow regime or contact pattern may help! Important to know the regime of operation S39
Key Multiphase Reactors
Bubble Column in different modes
Key Multiphase Reactor Parameters Trambouze P. et al., Chemical Reactors From Design to Operation, Technip publications, (2004)
Depending on the reaction regime one should select reactor type For slow reactions with or without transport limitations choose reactor with large liquid holdup e.g. bubble columns or stirred tanks Then create flow pattern of liquid well mixed or plug flow (by staging) depending on the reaction pathway demands This has not been done systematically Stirred tanks Stirred tanks in series Bubble columns & Staged bubble columns Have been used (e.g. cyclohexane oxidation). One attempts to keep gas and liquid in plug flow, use small gas bubbles to increase a and decrease gas liquid resistance. Not explained in terms of basic reaction pathways. Unknown transport resistances. S39
2-10 40-100 10-100 10-50 4000-10 4 150-800 S40
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Multiphase Reactor Types for Chemical, Specialty, and Petroleum Processes S42
Multiphase Reaction Engineering: 3. Basic Design Equations for Multiphase Reactors P.A. Ramachandran, P.. Mills and M. P. Dudukovic rama@wustl.edu; dudu@wustl.edu Chemical Reaction Engineering aboratory
Starting References 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, 679-739, (1996) 3. Trambouze, P., H. Van andeghem, J.-P. Wauquier, Chemical Reactors: Design, Engineering, Operation, Technip, (2004) 4. Dudukovic, Mills and Ramachandran, Course Notes (1990s and 2000s)
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
Hierarchy of Multiphase Reactor Models Model Type Empirical Ideal Flow Patterns Phenomenological Volume-Averaged Conservation aws Implementation Straightforward Insight Very little Point-wise Conservation aws Very Difficult or Impossible Significant
Basic Reactor Types for Systems With Solid Catalyst ( three or four phase systems) Systems with moving catalysts - stirred tank slurry systems - slurry bubble columns - loop slurry reactors - three phase fluidized beds (ebulated beds) Systems with stagnant catalysts -packed beds with two phase flow: down flow, up flow, counter-current flow - monoliths and structured packing - rotating packed beds
Phenomena Affecting Slurry Reactor Performance Flow dynamics of the multi-phase dispersion - Fluid holdups & holdup distribution - Fluid and particle specific interfacial areas - Bubble size & catalyst size distributions Fluid macro-mixing - PDF s of RTDs for the various phases Fluid micro-mixing - Bubble coalescence & breakage - Catalyst particle agglomeration & attrition Reactor Model Heat transfer phenomena - iquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc. Energy dissipation - Power input from various sources (e.g., stirrers, fluid-fluid interactions, )
Phenomena Affecting Fixed-Bed Reactor Performance Fluid dynamics of the multi-phase flows - Flow regimes & pressure drop - Fluid holdups & holdup distribution - Fluid-fluid & fluid-particle specific interfacial areas - Fluid distribution Fluid macro-mixing - PDF s of RTDs for the various phases Heat transfer phenomena - iquid evaporation & condensation - Fluid-to-wall, fluid-to-internal coils, etc. Reactor Model Energy dissipation - Pressure drop (e.g., stirrers, fluid-fluid interactions, )
Elements of the Reactor Model Micro or ocal Analysis Macro or Global Analysis Gas - liquid mass transfer iquid - solid mass transfer Interparticle and inter-phase mass transfer Intraparticle and intra-phase diffusion Intraparticle and intra-phase heat transfer Catalyst particle wetting Flow patterns for the gas, liquid, and solids Dynamics of gas, liquid, and solids flows Macro distributions of the gas, liquid and solids Heat exchange Other types of transport phenomena
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 Activity Inlet C & T Transport Micro Heat exchange
Idealized Mixing Models for Multiphase ( Three Phase) Reactors Model Gas-Phase iquid Phase Solid-Phase Reactor Type 1 Plug-flow Plug-flow Fixed Trickle-Bed Flooded-Bed 2 Back mixed Back mixed Back mixed Mechanically agitated 3 Plug-Flow Back mixed Back mixed Bubble column Ebullated - bed Gas-ift & oop
Ideal Flow Patterns in Multiphase Reactors Example: Mechanically Agitated Reactors δ (t-τ g ) δ (t) EG(t) X(t) QG Q 0 τ g t 0 t X G (t) δ (t) QG H E(t) - t / τ e τ 0 t or V R v G + V + V C 1 ε G + ε + ε C Q 0 t τ G Vr ε Q G G τ V ( 1 ε ε ) r G Q
First Absolute Moment of the Tracer Response for Multi-phase Systems For a single mobile phase in contact with p stagnant phases: µ 1 V 1 + p j 2 Q 1 K 1j V j For p mobile phases in contact with p - 1 mobile phases: µ 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
Relating the PDF of the Tracer Impulse Response 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 - ( W /Q ) t p - X e E (t) dt e W E ext (t) dt 0 k 1
Illustrations of Ideal-Mixing Models for Multiphase Reactors Stirred tank Bubble Column z z Trickle - Bed Flooded - Bed G Plug-flow of gas Backmixed liquid & catalyst Batch catalyst Catalyst is fully wetted G Plug-flow of gas Plug-flow of liquid Fixed-bed of catalyst Catalyst is fully wetted
imiting Forms of Intrinsic Reaction Rates Reaction Scheme: A (g) + vb (l) C (l)
Gas imiting Reactant and Plug-Flow of iquid Reaction Scheme: A (g) + vb (l) C (l) Key Assumptions G z 1. Gaseous reactant is limiting 2. First-order reaction wrt dissolved gas 3. Constant gas-phase concentration 4. Plug-flow of liquid 5. Isothermal operation 6. iquid is nonvolatile 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients C / >> 1 D C / νd C >> 1 B C Al 0 B B A A l
Gas Reactant imiting and Plug Flow of iquid Concentration or Axial Height Q l A Relative distance from catalyst particle (Net input by convection) l z Ql Al z+ dz + k l a B Constant gas phase concentration valid for pure gas at high flow rate + (Input by Gas- (oss by iquidsolid Transport) 0 iquid Transport) - (1) Dividing by Ar.dz and taking limit dz ( * A A ) A dz- k a ( A A ) A dz 0 l r s p l s r (2) (3) (4)
Gas Reactant imiting and Plug Flow of iquid
Gas Reactant imiting and Plug Flow of iquid Solving the Model Equations
η R Concept of Reactor Efficiency Rate of rxn in the Entire Reactor with Transport Effects Maximum Possible Rate
Conversion of Reactant B (in terms of Reactor Efficiency)
Gas Reactant imiting and Backmixed iquid Stirred Tank Key Assumptions Bubble Column z G 1. Gaseous reactant is limiting 2. First-order reaction wrt dissolved gas 3. Constant gas-phase concentration 4. iquid and catalyst are backmixed 5. Isothermal operation 6. iquid is nonvolatile 7. Catalyst concentration is constant 8. Finite gas-liquid, liquid-solid, and intraparticle gradients
Gas Reactant imiting and Backmixed iquid Concentration or Axial Height 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
Gas Reactant imiting and Backmixed iquid 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)
Gas Reactant imiting and Backmixed iquid Solving the Model Equations
A Flow Pattern Concepts for Various Multiphase Systems A - Single plug flow 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
Flow Pattern Concepts for Various Multiphase Systems C D C, D - Co current or countercurrent two-phase flow (plug flow or dispersed 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
Strategies for Multiphase Reactor Selection Strategy level I: Catalyst design strategy gas-solid systems: catalyst particle size, shape, porous structure, distribution of active material gas-liquid systems: choice of gas-dispersed or liquid-dispersed systems, ratio between liquid-phase bulk volume and liquid-phase diffusion layer volume Strategy level II: Injection and dispersion strategies (a) reactant and energy injection: batch, continuous, pulsed, staged, flow reversal (b) state of mixedness of concentrations and temperature: wellmixed or plug flow (c) separation of product or energy in situ (d) contacting flow pattern: co-, counter-, cross-current Strategy level III: Choice of hydrodynamic flow regime e.g., packed bed, bubbly flow, churn-turbulent regime, densephase or dilute-phase riser transport
Strategies for Multiphase Reactor Selection R. Krishna and S.T. Sie, CES, 49, p. 4029 (1994)
Two-Film Theory: Mass and Heat Transfer C g g i ( j ), T ( J ) Ci ( j ),T ( J ) Gas Bulk Gas Film f N i,( j ) X 0 D iquid Film i Cell J th 2 d C dx f i 2 NR j 1 υ R ji f j Heat Film f N i,( j ) X 1 iquid Bulk f q i,( j ) X 0 2 d T κ dx 2 f NR j 1 R f j ( H R ) f q i,( j ) X 1 δ m δ h g Ci ( j 1 ),T ( J 1 ) g Ci ( j 1),T ( J 1 )
Gas-iquid Film Model: Mass Transfer p gi, B.C.1 Gas Film g p g, i Z0 dc Z f i, z 0 g D i k g i i, z dz iquid Film N f i, Z 0 0 Z Z δ f N i, Z δ C f i, Z 0 f C b i, Z δ C i m m g ( C C 0 ) Bulk iquid m Bi m, i Bi D i 2 d C dz f i 2 NR j 1 υ R [ ( )] * f f c c h θ m, i g, i δ m k i g D H i ξ 0 ref, i i c ξ 0 * g, i ji H j p ref, i g, i C dc f i d ξ ref, i ξ 0 B.C.2: Dirichlet conditions g f f Ci, z 0 H i Ci, z 0 Solubility or Violability H f ( θ ) f ref Si H i H i exp ( ) H f ref h ξ 0 R T Z 0 Tref 1 1
NR j j j r f R H dz T d 1, 2 2 ) )( ( λ B.C.1 B.C.2 ( ) 0 1, 0 0 ) )( ( + Z f i i NS i i s f z g out g Z f dz dc D H T T h dz dt λ ( ) m h f Z Z f m h T T dz dt δ δ λ λ δ δ ) ( g T f T g A C g B C f B C f A C h δ b A C b B C Z Gas Film iquid Film iquid Bulk Heat Transfer Film Mass Transfer Film b T m δ Gas-iquid film Gas-iquid Film Model: Heat Transfer
Bubble Column Mixing Cell Model Cells in series: G and mixed flow Cells in series: G plug flow, mixed flow Cells in series-parallel combination Cell N Cell j Exchange between Upward and downward moving liquid Cell 1 iquid Gas iquid Gas Prototype cell - Cells arranged in different modes to simulate the averaged flow patterns - These averaged flow patterns can be obtained from the CFD simulations
Mixing Cell Model for gas-liquid systems Prototype Gas Cell Prototype iquid Cell Novel features Non-isothermal effects in the gas-liquid film and in the bulk liquid Effect of volatility of the liquid phase reactant on the interfacial properties Interfacial region modeled using film theory and solved using integral formulation of the Boundary Element Method (BEM) Model validity over a wide range of dimensionless numbers like Hatta, Arrhenius, solubility parameter, Biot, Damkohler Application to oxidation reactions like cyclohexane, p-xylene, etc. in stirred tank and stirred tank in series (Ruthiya et al. under progress) (Kongto, Comp.&Chem.Eng., 2005)
Gas-iquid Reactor Model Variables Non-Dimensionalized parameters c g i C C g i g i, ref and f i C C Reaction based B j H ρ C r,j p C T ref ref Heat of reaction parameter c M f i i, ref Z ξ δ m g θ T T θ g f ref 2 Vcell ( ε aδm ) E ref 2 R j δm aj j R γ j Ha j j Q C D RTref ref ref C ref Bulk reaction number Hatta number Arrhenius number g ref T T ref Q Q g g ref β j γ fi u u g ref ( H r, j λ T ref H i, ref Effective G/ ratio ) D ref ref C Heat of reaction parameter ref Mass transfer based avcellk αg u ref Ar Damkohler number Bi H hgδ m λ β S, i Bi M, i δ mh D Heat transfer based Biot number ref i, ref Biot number ( HS, i ) DC i λ T Heat of solution parameter i k g i, ref g C i, ref Ci, ref / H i, ref S a m gl V C cell p, λ δ m iquid heat transfer number S g ω i g C m i,ref a glvcellλ m δ C p, g Gas heat transfer number C ref e λ Di s i D ρ C ref Diffusivities ratio p D ewis number ref
Studies for Complex Gas-iquid Reactions - Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F., Mass transfer with complex chemical reaction in gas-liquid, Chem. Eng. Sci., 54, 121-136, (1999) - Vas Bhat R.D., van Swaaij W.P.M., Kuipers, J.A.M., Versteeg,G.F., Mass transfer with complex chemical reaction in gas-liquid, Chem. Eng. Sci., 54, 137-147, (1999) - Al-Ubaidi B.H. and Selim M.H. (1992), Role of iquid Reactant Volatility in Gas Absorption with an Exothermic Reaction, AIChE J., 38, 363-375, (1992) - Bhattacharya, A., Gholap, R.V., Chaudhari, R.V., Gas absorption with exothermic bimolecular (1,1 order) reaction, AIChE J., 33(9), 1507-1513, (1987) - Pangarkar V.G., Sharma, M.M., Consecutive reactions: Role of Mass Transfer factors, 29, 561-569, (1974) - Pangarkar V.G., Sharma, M.M., Simultaneous absorption and reaction of two gases, 29, 2297-2306, (1974) - Ramachandran, P.A., Sharma, M.M., Trans.Inst.Chem.Eng.,49, 253,(1971)
Types of Heat Generation 1. Heat of solution ( H s ), which is generated at the gas-liquid interface due to the physical process of gas dissolution 2 Heat of vaporization ( H v ), of volatile reactants due to evaporative cooling in oxidation reaction 3. Heat of reaction ( H r ), which is generated in the film near the gas-liquid interface (for fast reactions), or in the bulk liquid (for slow reactions). Uncontrolled heat generation can lead to: 1. Undesired production of by-products 2. Thermally-induced product decomposition 3. Increased rate of catalyst deactivation 4. ocal hot spots and excess vapor generation 5. Reactor runaway and unsafe operation Modeling of simultaneous mass and heat transport effects in the film is necessary for accurate predictions
How Heat Generation Can Affect Mass Transfer Rates in Gas-iquid Reactions 1. Physical, transport, and thermodynamic properties of the reaction medium exhibit various degrees of temperature dependence 2. Kinetic parameters exhibit exponential dependence on the local temperature 3. Instabilities at the gas-liquid reaction interface that are driven by surface tension effects (Marangoni effect) and density effects
Typical Systems with Notable Heat Effects Shah & Bhattacharjee, in Recent Advances, 1984.
Properties and Interfacial Temperature Rise for Some Practical Systems Shah & Bhattacharjee, in Recent Advances in the Engineering Analysis of Multiphase Reacting Systems, Wiley Eastern, 1984.
aboratory Reactors for Gas - iquid Reaction Kinetics
Case 1: Single non-isothermal reaction Reaction Scheme: A + vb C 2 2 d A d B D A k 2 A B D vk A B 2 B 2 2 dx dx G second order reaction Non-dimensionlizing 2 a 2 dy 2 2 d b Ha Ha a b ab where 2 dy q d 2 y x δ q DBB zd A A 0 * 2 k2b0 Ha 2 δ D A d 2 dy a 2 q d 2 dy b 2 E E Ha For no depletion of B (interface concentration bulk, tanh ( Ha) first order reaction Ha bi tanh ( Ha bi ) For depletion of B 1 Ha bi bi q + 1 q tan( Ha bi ) 2 2 δ k2b Ha D A i
Case 1: Single non-isothermal reaction Reaction Scheme: A + vb C Ha 10, q 0.05, γ 22, γs -7.5, γvap 2, βs0.001, β vap -0.005, B ihg 1 Gas (A) Reactant (B) Product (C) Enhancement Nonvolatile 0.70 0.58 0.42 13.0 Volatile 0.76 0.33 0.31 6.7 การกระจายของความเข มข น และอ ณหภ ม ในฟ ล มของเหลว ส าหร บการถ ายโอนมวลของ ปฏ ก ร ยาเด ยวแบบ ผ นกล บไม ได ส าหร บระบบท ม การระเหย (Bim1.5) และ ไม ม การระเหย (Bim0) Dimensionless Temperature Dimensionless Concentration 1.055 1.050 1.045 1.040 1.035 1.0 0.8 0.6 0.4 0.2 0.0 Temp. Conc. c A c B c P No vaporization Vaporization of B Non-volatility (Bi m 0) Volatility (Bi m 1.5) 0 0.2 0.4 0.6 0.8 1 Dimensionless Film Thickness
Case 1: Single non-isothermal reaction Dimensionless Temperature 1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 Bi Hg 0.75 Bi Hg 1.5 Bi Hg 10 Bi Hg Temp Ha Rxn Temp. 0 5 10 15 Ha 20 25 30 35 Bi Hg δ h m κ g Ha 2 2 k ref δ m D A C b B
Case 2: ocal Supersaturation in the film No C reaction here Shah, Y.T., Pangarkar, V.G. and Sharma, M.M., Criterion for supersaturation in gas-liquid reactions involving a volatile product, Chem. Eng. Sci., 29, 1601-1612, (1974)
Axial Dispersion Model (Single Phase) C t @ z 0 et τ C t 2 C C Dax u + 2 z dz η @ η 0 u 0 z C 0 1 Pe C ax 0 uc D Pe ax 2 C 2 η C u D R C z ax ax 1 Pe C dη ax τ + C η u τr Basis: Plug flow with superimposed diffusional or eddy transport in the direction of flow C z @ z 0 C η @ η 1 0
Axial Dispersion Model C τ t @ η 0 Pe 1 C ax 0 2 η C 2 C C + dη 1 Pe ax C η τr C η @ η 1 0
Axial Dispersion Model for the iquid with Constant Gas-Phase Concentration - 1 Mass Balance of A in the liquid phase (Net input by convection) + (Net input by (oss by iquidsolid Transport) axial dispersion) + (input by gasliquid transport) - 0 <A l > mean X-sectional area occupied by liquid at z
Axial Dispersion Model for the iquid with Constant Gas-Phase Concentration - 2
Axial Dispersion Model for the iquid with Constant Gas-Phase Concentration - 3
ADM Model: Boundary Conditions
Axial Dispersion Model - Summary D ax d 2 dz A l 2 u l da l dz + k l a B ( * A A ) k a ( A A ) l s p l s ( Al As ) ηck was ksap 1 @ z 0 u l A li u l A l D ax da dz l da l dz @ z 0
Comments regarding axial dispersion model (ADM) The model is very popular because it has only a single parameter, axial dispersion coefficient, D ax, the value of which allows one to represent RTDs between that of a stirred tank and of a plug flow. The reactor model is usually written in dimensionless form where the Peclet number for axial dispersion is defined as: Pe ax U / D ax 2 / D / U ax characteristic axialdispersiontime characteristicconvectiontime Pe ax plug flow Pe ax 0 complete back mixing
ADM comments continued-1 Use of ADM was popularized by the work of Danckwerts, evenspiel, Bischoff, j. Smith and many others in the 1960s through 1970s. Since D ax encompasses the effects of the convective flow pattern, eddy as well as molecular diffusion, prediction of the Axial Peclet Number with scale up is extremely difficult as a theoretical basis exists only for laminar and turbulent single phase flows in pipes. Moreover use of ADM as a model for the reactor is only advisable for systems of Peclet larger than 5 (preferably 10).
ADM comments continued -2 However, ADM leads to the boundary value problem for calculation of reactor performance with inlet boundary conditions which are needed to preserve the mass balance but unrealistic for actual systems. Since at large Peclet numbers for axial dispersion the RTD is narrow, reactor performance can be calculated more effectively by a tanks in series model or segregated flow model.
ADM comments continued -3 ADM is not suitable for packed beds, since there is really never any dispersion upstream of the point of injection (Hiby showed this conclusively in the 1960s); a parabolic equation does not describe the physics of flow in packed beds well. A hyperbolic equation approach (wave model) should be used as shown recently by Westerterp and coworkers (AICHE Journal in the 1990s). ADM is not suitable for bubble column flows as the physics of flow requires at least a two dimensional convection- eddy diffusion model for both the liquid and gas phase (Degaleesan and Dudukovic, AICHEJ in 1990s). ADM is clearly unsuitable for multiphase stirred tanks
Final Comments To improve predictability of multiphase reactor models and reduce the risk of scale-up, they should be increasingly developed based on proper physical description of hydrodynamics in these systems. Improved reactor scale descriptions coupled with advances on molecular and single eddy (single particle) scale will facilitate the implementation of novel environmentally benign technologies by reducing the risk of such implementations.
Return to Systems Approach in selecting best reactor for the task Expansion in capacity of a best selling herbicide provides an opportunity to assess the current reactor and suggest a better solution Detailed chemistry is kept proprietary
Reaction System S46
Disadvantages of Semi-Batch Slurry Reactor Batch nature variable product ow volumetric productivity (due to low catalyst loading and limited pressure) Pressure limitation (shaft seal) High power consumption Poor selectivity (due to high liquid to catalyst volume ratio and undesirable homogeneous reactions) Catalyst filtration time consuming Catalyst make-up required Oxygen mass transfer limitations S47
Potential Advantages of Fixed Bed System S48
Slurry vs Fixed Bed With proper design of catalyst particles a packed-bed reactor with co-current down-flow of gas and liquid both in partial wetting regime and in induced pulsing regime can far surpass the volumetric productivity and selectivity of the slurry system, yet require an order of magnitude less of the active catalyst component. Undesirable homogenous reactions are suppressed in the fixed bed reactor due to much higher catalyst to liquid volume ratio Father advantage is accomplished in fixed beds by operation at higher pressure (no moving shafts to seal). Fixed bed operation requires long term catalyst stability or ease of in situ regeneration. S49
References 1. Suresh, A.K., Sharma, M.M., Sridhar, T., Engineering Aspects of iquid-phase Air Oxidation of Hydrocarbons, Ind. Eng. Chem. Research, 39, 3958-3997 (2000). 2. Froment, G.F. and Bischoff, K.B., Chemical Reactor Analysis and Design, Wiley (1990). 3. evenspiel, O., Chemical Reaction Engineering, Wiley, 3 rd Edition (1999). S50
References 1. Dudukovic, M.P., arachi, F., Mills, P.., Multiphase Reactors Revisited, Chem. Eng. Science, 541, 1975-1995 (1999). 2. Dudukovic, M.P., arachi, F., Mills, P.., Multiphase Catalytic Reactors: A Perspective on Current Knowledge and Future Trends, Catalysis Reviews, 44(11), 123-246 (2002). 3. evenspiel, Octave, Chemical Reaction Engineering, 3 rd Edition, Wiley, 1999. 4. Trambouze, P., Euzen, J.P., Chemical Reactors From Design to Operation, IFP Publications, Editions TECHNIP, Paris, France (2002). S45
For any process chemistry involving more than one phase one should : Select the best reactor flow pattern based on the kinetic scheme and mass and heat transfer requirements of the system, Assess the magnitude of heat and mass transfer effects on the kinetic rate Assess whether design requirements can be met based on ideal flow assumptions Develop scale-up and scale-down relations Quantify flow field changes with scale if needed for proper assessment of reactor performance Couple physically based flow and phase contacting model with kinetics