Multiphase Chemical Reactor Engineering Quak Foo Lee Ph.D. Candidate Chemical and Biological Engineering The University of British Columbia

Different Types of Reactor Fluidized Bed Reactor Trickle Column Reactor Slurry Bubble Column Reactor Batch Reactor Fixed Bed Reactor

Fixed Bed Rector Fixed Bed Reactor that converts sulfur in diesel fuel to H 2 S

Fluidized Bed Reactor Fluidized Bed Reactor using H 2 SO 4 as a catalyst to bond butanes and iso-butanes to make high octane gas

Batch Reactor Stirring Apparatus

Straight Through Transport Reactor Riser Standpipe Settling Hopper The reactor is 3.5 m in diameter and 38 m tall. Sasol/Sastech PT Limited

Slurry Phase Distillate Reactor

Packed Bed Reactor

CSTR Agitator Connection for heating or cooling jacket Hand holes for charging reactor

C A,in C A,out Gas + solids Plug Flow Model Particle surrounding by fluid of essential constant concentration, C A,m Particle surrounding by fluid of essential constant concentration, C A,m

Batch Mix Flow: Charge Reactor Residence time distribution Particle stays in the reactor for certain length of time

Countercurrent Flow If solids are moving plug flow and we have constant flow composition  If solids are moving plug flow and we have constant flow composition  Residence time of solids: Residence time of solids: Heat Effects !! Heat Effects !!

Heat Effects on Reactions of Single Particles Normally (developed) dealing with exothermic and endothermic reaction. Normally (developed) dealing with exothermic and endothermic reaction. If reaction occurs at a rate such that the heat absorbed (endothermic) or generated (for exothermic) can’t be transferred rapidly enough, then non-isothermal effects become important: If reaction occurs at a rate such that the heat absorbed (endothermic) or generated (for exothermic) can’t be transferred rapidly enough, then non-isothermal effects become important: The particle T ≠ the fluid T The particle T ≠ the fluid T For exothermic reaction, T p will increase and the rate of reaction will increase above that expected for the isothermal case. For exothermic reaction, T p will increase and the rate of reaction will increase above that expected for the isothermal case. Two conditions: Two conditions: i) Film ∆T (external ∆T) T f (bulk fluid) ≠ T p (particle) i) Film ∆T (external ∆T) T f (bulk fluid) ≠ T p (particle) ii) Intraparticle ∆T (internal ∆T) T r=Rp ≠ T r=∞ ii) Intraparticle ∆T (internal ∆T) T r=Rp ≠ T r=∞

Non-Reacting 1. Small particles  highly conductive particles 2. Small particles  volumetric reaction

1)Small Particles: Highly Conductive Particles Particle initially at uniform T = T p Particle initially at uniform T = T p At t = 0, we drop it into our furnace At t = 0, we drop it into our furnace Fluid at T f TpTp

Energy Balance Heat in by convection and radiation = change in enthalpy of particle Where, Area of sphere = 4πR 2 H cv = convection coefficient σ = Stefan-Boltzman constant Є m = emissivity of the particle (wall has Є = 1)

Energy Balance Can solve this equation to get T p =f(t)

Find h cv Have film: ∆H T f ≠ T p Have film: ∆H T f ≠ T p Use mass transfer analogy to get h cv Use mass transfer analogy to get h cv

2. Small Particles: Volumetric Reaction Small such that no internal gradients Small such that no internal gradients Heat generated by reaction = Heat transferred to surrounding Steady State: Volume of particle Rate of reaction Exothermic Rxn: -∆H r = (+) -r Av = (+)

3. Large Particles: Possible Internal Particle Gradients We have to solve the conduction equation We have to solve the conduction equation Non reacting particle: the conduction equation for sphere: Non reacting particle: the conduction equation for sphere: Heat conducted into particle at r =R p Heat transferred into particle Note: accommodate radiation in the definition of h if that is the case K e = effective thermoconductivity within the particle ∂T/∂r = 0 at steady state

Boundary Conditions Symmetry condition Initial condition Internal gradient External gradient

Reacting Systems General equation for volumetric reactions General equation for volumetric reactions (Reaction in porous particles) Recall continuity equation: Recall continuity equation: continuity for A

Solve (1), (2), (3) Together Continuity for A Energy balance (1) (2) (3) Coupled through the reaction rate

In Steady State Showed that for steady conditions: Showed that for steady conditions: Integrate at r = 0, r = R For sphere

Some Notes If we know C A,s (surface concentration) and C A,r=0 (C A within pellet at r = 0), we can calculate temperature gradient, previous equation tell us either we need or don’t need to worry about T gradient within particle. If we know C A,s (surface concentration) and C A,r=0 (C A within pellet at r = 0), we can calculate temperature gradient, previous equation tell us either we need or don’t need to worry about T gradient within particle. Where isothermal (approach) approximation can be used and where internal T gradients must be considered. Where isothermal (approach) approximation can be used and where internal T gradients must be considered. Volumetric reaction for porous particles, heat is generated in a volume. Volumetric reaction for porous particles, heat is generated in a volume.

Shrinking Core: Non-Isothermal Heat generated at reaction front, not throughout the volume Heat generated at reaction front, not throughout the volume In Steady State, In Steady State, Solve Solve R r rcrc TsTs TfTf TcTc

T Conditions

Boundary Condition 1: r = r c Heat is generated = Heat conducted out through product layer Area

Boundary Condition 2: r = R Heat arriving by conduction = Heat removed for from within particle convection Bi -1 Can be obtained from B.C. 1

Solution Combine equations and eliminate T S to get T c -T f Combine equations and eliminate T S to get T c -T f

Recall from Isothermal SC Model Substitute C A,c into (T c –T f ) equation

T c - T f ConductionConvection Diffusion in Product Layer Reaction Mass Transfer

Can Heat Transfer Control the Rate in Endo- and Exothermal Rxn? Consider C A,c ≈ C A,f ; initially rapid reaction Consider C A,c ≈ C A,f ; initially rapid reaction a) Endothermic with poor heat transfer, heat will be consumed in reaction, and if can’t transfer heat in, T C will drop  reaction rate ↓ markedly and rate of reaction become the slow step occurring at a rate dictated by the flow of heat. b) Exothermic initial rapid reaction and with poor Q, T C will increased, then rate of reaction ↑ and eventually reach point where gaseous reactant can’t be transferred fast enough (external mass transfer or diffusion). Hence rate is limited.

Fixed Bed Reactor

Solids take part in reaction  unsteady state or semi-batch mode Solids take part in reaction  unsteady state or semi-batch mode Over some time, solids either replaced or regenerated Over some time, solids either replaced or regenerated 12 C A,in C A,out Regeneration t C A,out /C A,in Breakthrough curve

Isothermal Reaction: Plug Flow Reactor Plug flow of fluid – no radial gradients, and no axial dispersion Plug flow of fluid – no radial gradients, and no axial dispersion Constant density with position Constant density with position Superficial velocity remains constant Superficial velocity remains constant

Plug Flow Model z + dz C A,f + dC A,f z C A,f U 0 (m/s) superficial velocity

Mass Balance Input – Output – Reaction = Accumulation Divide by ∂z and take the limits as ∂z  0 ε is void fraction in bed

For first order reaction, fluid only: For steady state: Therefore, Volume of reactor Void fraction

Conversion as a function of Height Integrating with C A,f = C A,f,in at z = 0 Note 1: Same equation as for catalytic reactor with 1 st order reaction Note 2: Can be used in pseudo-homogeneous reaction

Balance on Solid aA (fluid) + S (solid)  Products aA (fluid) + S (solid)  Products Input – Output – Reaction = Accumulation Input – Output – Reaction = Accumulation Over increment of dz: input = 0, output =0 Over increment of dz: input = 0, output =0 Volume fraction of solid = m 3 of solid m 3 of reactor volume mol m 3 of solid · s

Balance on Solid

Solve These Equations = 0 (In quasi steady state, we ignore the accumulation of A in gas) Substitute r Av

a) Shrinking Core Model Shrinking Core Model Shrinking Core Model b) Uniform reaction in porous particle, zero order in fluid Uniform reaction in porous particle Uniform reaction in porous particle c) Uniform reaction, 1 st order in fluid and in solid Uniform reaction Uniform reaction d) Park et al., “An Unsteady State Analysis of Packed Bed Reactors for Gas-Solid Reactions”, J. Chem. Eng. Of Japan, 17(3): (1984) e) Evans et al., “Application of a Porous Pellet Model to Fixed, Moving and Fluid Bed Gas-Solid Reactors”, Ind. Eng. Chem. Proc. Des. 13(2): (1974)

a) In Shrinking Core Model Recall that Solid Phase Liquid Phase For SCM Solve C A,f = f(z) r c = f(z,t)

Conversion vs Time z t = 0t > 0

Overall Conversion of Solid

Height Vs time (Graphical) z/L t/ All C A has been reacted Particles at bed entrance are completed reacted Unreacted bed depth Reaction zone Completely reacted

b) Uniform Reaction in Porous Particle and Zero Order in Fluid where

c) Uniform Reaction and 1 st order in Fluid and in solid

Non-Isothermal Packed Bed Reactor For mass continuity  did balance on fluid and on solid For mass continuity  did balance on fluid and on solid For energy balance, we do balance on each phase For energy balance, we do balance on each phase

Non-Isothermal Packed Bed Reactor Assumptions: Assumptions: 1)Adiabatic reaction – no heat lost through shell to surroundings (no radial temperature gradients) q = 0 2)Bi λ is small – uniform T within particle (an exothermic reaction T p > T g ) 3)Plug flow of gas and use T ref =0 for enthalpy calculations 4)Assume an average density can be used (ρ g = constant)

Modeling T f + dT f TfTf z + dz z T f,0 U0U0 q =0

Moving Bed Reactor Solids in Solids out Gas in Gas out U0U0 VsVs ∆z

Moving Bed Reactor (MBR) Steady state reactor where solids moving at near their packed bed voidage Steady state reactor where solids moving at near their packed bed voidage Counter or co-current operation Counter or co-current operation Solid usually move downward (vertical shaft reactor or furnace) Solid usually move downward (vertical shaft reactor or furnace) Voidage is near that of a packed bed Voidage is near that of a packed bed Slightly above random loose-packed voidage Slightly above random loose-packed voidage Solids move mainly in a plug floe, but region near wall have a velocity distribution Solids move mainly in a plug floe, but region near wall have a velocity distribution

Advantages of MBR True counter-current flow True counter-current flow Uniform residence time (essentially plug flow) Uniform residence time (essentially plug flow) Reasonable ∆P Reasonable ∆P Throughput variable Throughput variable Generally larger particle d p > 2-3 mm Generally larger particle d p > 2-3 mm Difficulties coping with wide size distribution of particles (fines tend to block up the void spaces) Difficulties coping with wide size distribution of particles (fines tend to block up the void spaces)