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Computer-aided chemical reaction engineering CACRE Teachers: Tapio Salmi, Johan Wärnå, Heikki Haario, Paolo Canu, Matias Kangas, Sébastien Leveneur,

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Presentation on theme: "Computer-aided chemical reaction engineering CACRE Teachers: Tapio Salmi, Johan Wärnå, Heikki Haario, Paolo Canu, Matias Kangas, Sébastien Leveneur,"— Presentation transcript:


2 Computer-aided chemical reaction engineering

3 CACRE Teachers: Tapio Salmi, Johan Wärnå, Heikki Haario, Paolo Canu, Matias Kangas, Sébastien Leveneur, Fredrik Sandelin, Dmitry Murzin Forms of work: Lectures Demonstrations /case studies Computational exercises Final exam

4 Contents 1Introduction 2Stoichiometry and kinetics 3Homogeneous reactors 4Catalytic two-phase reactors 5Catalytic three-phase reactors 6Fluid-fluid reactors 7Reactors with a reactive solid phase 8Laboratory reactors and parameter estimation 9CFD Bilagor 1-8

5 Approach- procedure 1Generalized models for chemical reactors (mass and energy balances) 2Identification of the mathematical structure of the model (NLE, ODE, PDE…) 3Modularization of the model 4Selection of numerical strategy and methods 5Selection of software 6Model implementation 7Test simulations 8Final simulations Bilagor 1-8

6 Chemical process in general

7 A chemical reactor Transforms Raw material  Products Can be batchwise, semicontinuous or continuous Can be stationary or non-stationary Classification often basen on the number of phases  gas, liquid, solid, catalyst The process chemistry determines very much the reactor selection Reactor outIn

8 Why is modelling and computation needed It cannot be done in this way !

9 Mathematical model Reactor design in nutshell Reactor ready Idea Experiment Parameter estimation Optimization

10 Principles of reactor modelling Kinetic model Mass and heat transfer model Flow model REACTOR MODEL

11 Ingredients in the model Stoichiometry Kinetics and termodynamics Reaction & diffusion Reactor model

12 Stoichiometry and och kinetics Desired reactions Non-desired reactions (side reactions) Often multiple reactions Example: Methanol synthesis CO + 2H 2 W CH 3 OH (desired reaction) CO 2 + H 2 W CO + H 2 O (side reaction) Parallel reaction with respect to hydrogen Consecutive reaction with respect to CO

13 Stoichiometric matrix Reactants - Products +

14 Stoichiometric matrix - example CO + 2H 2 = CH 3 OH CO 2 + H 2 = CO + H 2 O -1 CO - 2 H 2 + 1CH 3 OH = 0 - 1CO 2 -1 H 2 + 1CO + 1H 2 O = 0 (1) (2)

15 Reaction kinetics Reaction rate R (mol/s m 3 ) gives how many moles of substance is generated /time/volume Important to know the difference between elementary and non-elementary reactions Elementary reaction reflects directly the events, collisions on the molecular level

16 Rate expressions 2A + B = 2C If the reaction is elementary: The construction of rate expressions for elementary reactions is straightforward and can be done automatically by a computer; just the stoichiometric matrix is needed as an input

17 Component generation rate r i For methanol synthesis reaction r H2 = - 2 R och r CH3OH = +1 R Systems with many reactions and components r H2 = -2R 1 - 1R 2 r CH3OH = +1 R 1 + 0 R 2

18 Generation rate 2A + B = 2C r A =-2R r B =-R r C =2R

19 Homogeneous reactors Only one phase present (incl. a homogeneous catalyst) Tubular reactor (plug flow reactor(PFR)) Tank reactor (CSTR, semibatch reactor, batch reactor)

20 Homogeneous reactors One phase  Gas or liquid Tank reactors can be continuous (CSTR), semibatch (SBR) och batch reactors (BR) Tubular reactor with plug flow (PFR) or axial dispersion (ADR, ADM)


22 Batch reactors

23 Mixing in tank reactors

24 Tubular reactor (PFR)

25 Tubular reactor

26 Advanced reactor technology -parallel tube reactors

27 Cooling systems for reactors

28 Definitions Total molar flow Total molar amount

29 Definitions: mole fraction

30 Definitions: concentration Concentration and mole fraction For continuous systems and batch reactors

31 Definitions: volumetric flow rate, mass flow, density Volumetric flow rate Mass flow Combination gives

32 Conversion

33 STIRRED TANK REACTORS WITH COMPLETE BACKMIXING General mass balance Rearranged to For batch reactor, all flows zero:

34 The initial condition is CSTR at steady state: dn i /dt = 0 With arrays we can write Batch reactor (BR)

35 a ) Isothermal liquid phase CSTR τ = V/V 0, τ = space time Special cases

36 b) Batch reactor, gas and liquid phases V= V 0

37 Liquid-phase semibatch reactor (SBR)

38 Gas-phase CSTR at steady state

39 Denote which imply An infinitesimal volume element ΔV is considered: Tubular reactors: Plug flow (PFR) and axial dispersion model (ADM) DADM

40 The volume element ΔV: Plug flow (PFR) and axial dispersion model (ADM) The accumulation term General mass balance

41 Let Δl  0: where For the plug flow model, the eqn. is reduced to (Adl = dV): At steady state conditions the time derivative of the concentration vanishes: We obtain ADM PFR ADM PFR

42 where w 0 = the superficial velocity at the reaction inlet, ADM Liquid phase reactions: PFR

43 A differential equation is obtained for δ: For isothermal cases dc/dz is 0, and δ is easily obtained by integration (c = c 0 ) Gas-phase reactions For both isothermal and steady state conditions, dc/dt = 0 and we get: PFR

44 At steady state conditions the natural choice of variable is n i and we get for the plug flow model: The concentrations which are needed in the rate lows are obtained from The initial condition is The volumetric flow rate is updated by the formula

45 Energy balances  general considerations A general energy balance for a volume element can be written as The use of molar enthalpies: The difference is split to two terms, What is Σ Δh mi n i ? This becomes clear, when the molar heat capacity is introduced: is valid, provided that the pressure effect is neglected. What is Σ H mi Δn i ? - The mass balance give

46 The generation rate where the sum Σ i υ ij Hm i is de facto the reaction enthalpy, Δ H rj. and the molar amount being present in the volume element is The term Σ H mi Δn i becomes

47 We get

48 v mi is the molar volume. The energy balance becomes ΔV  0

49 Tank reactors Because of the homogeneous contents, the integration over the entire tank volume can be carried out:

50 For liquid phase reactions the term Steady state Heat transfer from/to the reactor

51 Tubular plug flow reactor Steady state S is the total heat transfer area. For cylindrical tubes where R T, D T and L T denote the radius, the diameter and the length of the tubes. The temperature outside the reactor is

52 Batch reactor Reactor volume is constant, differentiation leads to where and

53 Batch reactors are very frequently used for liquid-phase processes, for which ΔU rj  ΔH ij. where the product ρ 0 c p is the heat capacity of the reacting liquid.

54 The mathematical structures of homogeneous reactor models MODELPROBLEM STRUCTURE Steady state CSTRf (y) = 0(N)LE Dynamic CSTRdy/dt = f (y)ODE (IVP) Steady state PFR dy/dz = f (y)ODE (IVP) Dynamic PFRdy/dt = -A dy/dz + f (y) PDE (IVP) Batch reactor (BR) Semi batch reactor (BR) dy/dt= f (y)ODE Steady state axial dispersion model (ADM) A d 2 y/dz 2 + Bdy/dz + f (y) = 0 ODE (PVP) Dynamic axial dispersion model (ADM) dy/dt = A d 2 y/dz 2 + B dz/dz + f (y) = 0 PDE (N)LE =(non)linear equations ODE =ordinary differential equations initial value problem PD =partial differential equations, hyperbolic type IVP =initial value problem BVP =boundary value problem

55 input of chemical engineering data (initial concentrations, temperatures, reactor dimensions, kinetic, thermodynamic as well as mass and heat transfer parameters) input of data for steering of the numerical solution (numerical methods, system step-length selection, convergence criteria e.t.c. definition of the kinetic and thermodynamic models (reaction rates, calculation of rate and equilibrium constants) definition of the mass and heat transfer models (e.g. correlations for diffusion and dispersion coefficients, heat and mass transfer coefficients and areas) definition of mass and energy balances along with equations for pressure drop definition of partial derivatives needed for the model solution numerical solver for the differential and/or algebraic equations involved in the model output routines, which tell not only the results (e.g. concentration, temperature and pressure profiles) but also give information about the success or failure of the numerical solution process Software build-up; tasks

56 MAIN PROGRAM INPU T c 0, T 0 OUTPUT c, T SOLVER -mathematical library routine for NLE or ODES RATE -routine for calculation of reaction rates MODEL (FCN) -routine for the model eqs, e.g. dy/dt = f(y) CORRE -routine for calculation of correlations for mass/heat transfer THERMO -routine for calculation of thermodynamics properties MODEL DERIVATIVES (FCNJ) -Jacobian routine J, contains  fi/  y Simulation programme modules Program flowsheet

57 where k is the iteration index, f (k), is the function vector and J -1 is the inverted Jacobian matrix Solution of algebraic equations Newton-Raphson algorithm End criterion One unknown case

58 Solution of ordinary differential equations

59 If the coefficient a il = 0 for l = i the method is explicit; if a il  0 for l = i the method is implicit. where I denotes the identify matrix: : where y n and y n-1 give the solution of the differential equation at x and x-Δx. Runge-Kutta methods where h=Δx. and J is the Jacobian matrix

60 Semi-implicit Runge-Kutta method An extension of semi-implicit Runge-Kutta methods is the Rosenbrock-Wanner method (ROW)

61 Adams-Moulton (AM) and backward difference-methods; Linear multistep methods

62 Backward difference-method: Adams-Moulton method:

63 Temperature and concentration

64 Temperature dependence of the rate constant Jacobus Henricus van’t Hoff and Svante Arrhenius: Transition state theory

65 Activation energy

66 Liquid-phase systems Equilibrium constant often determined experimentally Gas-phase system  Equilibrium constant can be calculated theoretically, one knows Reaction thermodynamics 0 0.2 0.4 0.6 0.8 1 1.2 0246810

67 Reaction thermodynamics Temperature dependence Often approximately Change in internal energy Change in entropy

68 Reaction thermodynamics Equilibrium constant K p integration gives

69 Reaction enthalpies Reaction enthalpy At reference temperature T 0 (often 298 K) From enthalpies of formations See for example in Reid,Prausnitz, Poling, The Properties of Gases and Liquids Reaction enthalpy from Molar heat capacities exist as temperature (C pmi ) functions

70 CSTR- steady state multiplicity

71 Catalytic two-phase reactors From reaction mechanism to reactor design

72 20  m Catalyst materials 20  m 200  m Cu/SiO 2 SAPO-5 Elektron microscopy (SEM) reveals catalyst morhpology

73 Isobutene i 10 MR H – FER pores

74 Fibre catalysts 4 nm TEM image of the 5 wt.% Pt/Al 2 O 3 (Strem Chemicals) catalyst SEM image of the 5 wt.% Pt/SiO 2 fiber catalyst 1 mm 125-90  m particles D = 27% d Pt = 4 nm D = 40% d Pt = 2.5 nm

75 Catalysts in micro- and nanoscale 5  m TEM-bildSEM-bild 4 nm 5  m 5wt.% Pt/SF (Silikafiber) 5wt.% Pt/Al 2 O 3 (Strem) 4 nm

76 New products and processes from renewable sources  Chemicals from biomaterial, particularly wood  Catalytic production of biodiesel

77 From wood to food Isomerization of linoleic acid was first time carried out on a heterogeneous catalyst

78 Catalytic two-phase reactors Heterogeneous catalytic reactor  Solid catalyst accelerates reactions  Gas or liquid present in the reactor

79 Molecular path to the catalyst diffusion to the outer surface of the catalyst particle diffusion through the catalyst pores Molecules come to the active sites on the surface

80 Molecular path to the catalyst  molecules adsorb on the active sites and react with each other  Product molecules desorb and diffuse out

81 Concentration and temperature profiles in catalyst particles

82 Catalytic Reactors Packed bed Fluidized bed

83 Packed bed: traditional design

84 Gauze-reactor Oxidation av ammonia High temperature, 890  C Network of Pt catalyst

85 Monolith reactor

86 Multibed reactor Catalyst beds in series (often adiabatic) Heat exchangers between the beds

87 Multibed reactor, SO2 to SO3


89 Multitubular reactor

90 Models for packed beds Pseudo-homogeneous model  concentration and temperature in the catalyst particle on the same level as in the fluid bulk  neither concentration- nor temperature gradients in the catalyst particle  Diffusion resistance negligible in the catalyst particlen  Pore diffusion can be included with the aid of an effectiveness factor

91 Models for packed beds Heterogeneous model  Separate balance equations for bulk phase and catalyst particles

92 Catalyst bulk density

93 One-dimensional pseudo- homogeneous model - stationary [in] + [generated i] = [out] + [accumulated]

94 One-dimensional pseudo- homogeneous model The diffusion of the molecules through the fluid film around the catalyst particle and their diffusion through the pores Influences the reaction rate The real reaction rate becomes c B = concentration in the bulk phase ρ B = mass of catalyst / reactor volume

95 Effectiveness factor Real diffusion flow/Intrinsic kinetics =1 if diffusion resistance negligible

96 Diffusion i porous particle Catalyst surface

97 Diffusion in pores

98 Fick’s law N i diffusion flow mol/(time surface) D ei effective diffusion coefficient

99 Mass balance for a catalyst particle – steady state If diffusion coefficient is constant:

100 Form factor – shape factor (a=s+1) Rcharacteristic dimension of the particle A p outer surface of the particle V p particle volume

101 Form factor S=0 slab S=1 cylinder S=2 sphere

102 Biot number Relation between the diffusion resistance in the fluid film and the catalyst particle Biot number is usually >>1 for porous particles

103 Thiele modulus: first order reaction Reaction rate / diffusion rate

104 Effectiveness factor

105 Asymptotic effectiveness factor Semianalytical expressions for arbitrary kinetics Good approximation for positive reaction orders Erroneous if the reaktion order is negative, reaction is accelererated with decreasing concentration

106 Heat effects in catalyst particles Fourier’s law (heat conduction) Temperature gradient inside the particle typically small Temperature gradient can exist in the fluid film around the particle  The film is thin

107 Heat effects in catalyst particle Energy and mass balances for catalyst particle are coupled via reaction rate and should be solved numerically Effectivity factor can be >1 for strongly exothermic reactions, rate constant increases with temperature ! Steady state multiplicity possible

108 Steady state multiplicity

109 Lactose hydrogenation - diffusion Concentration profiles Inside the particle -various particle sizes Yta Center lactose + H2 = lactitol

110 Concentration profiles of lactose in the particle No deactivationDeactivation surface center time x x

111 Two-dimensional model Large heat effect induce a fradial temperature gradient, which leads to concentration gradients  Reaction rates vary in radial direction  Concentrations gradients created

112 Catalytic hydrogenation Hot spot Hydrogenation of av toluene

113 Oxidation of o-xylene Dependence of Hot spot on the the coolant and inlet temperature

114 Two-dimensional model: temperature profile

115 Two-dimensional model Mass balance [ in plug flow] + [in radial disp.] + [generated] = [out plug flow] + [out radial disp.]

116 Two-dimensional model Energy balance

117 Numerical solution Parabolic PDEs converted to ODEs Finite difference + (RK, Adams Moulton, Backward difference) Orthogonal collocation + (RK, Adams Moulton, Backward difference)

118 Fluidised bed Fluidisation  Solid particles in vertical bed  Gas blown from the bottom  Particles remain stagnant at low gas velocities  At higher gas velocities the particles fluidise  The bed is expanded and the particles become dispersed in the gas phase  Minimum fluidisation velocity

119 Fluidised bed With increasing gas velocity a bubble phase is formed – rich in gas Most part of catalyst in the emulsion phase Fluidised bed resembles boiling liquid

120 Fluidised bed If the gas velocity is increased even more, the bubbles become equal to the bed diameter (slug flow)  Limit velocity for slug flow = w s

121 Fluidised bed and pressure drop Fluidisation is recognised by measuring the pressure drop Pressure drop increases monotonically with the gas velocity (Ergun equation) At minimum fluidisation, the increase of pressure drop stops

122 Fluidiserad bed: hydrodynamics Bubble phase Emulsion phase Wake Cloud Reactions proceed in all phases !

123 Phase structure in detail

124 Fluidised bed Matematical model - principles Separate balance considerations for each phase Catalyst particles are very small (in micrometer scale) so internal diffusion can be ignored Vigorous turbulence implies that the bed is isothermal

125 Fluidised bed Matematical model Plug flow model  Unrealistic but gives the maximum limit Backmixing model  Sometimes tanks-in-series model is tried

126 Fluidised bed Matematical model Kunii-Levenspiel model  Realistic description  Bubble phase in plug flow  Gas flow in the emulsion phase is negligible  Cloud and wakephases have the same concentrations

127 Kunii-Levenspiel model Transport of a reacting gas from bubble phase to cloud-wake phase and further to emulsion phase Three parts in the volume element

128 Kunii-Levenspiel model

129 Bubble phase Cloud-wake phase Emulsion phase Kunii-Levenspiel model, mass balances

130 Kunii-Levenspiel model structure 3 * N mass balances (N= number of components) 1 * N ODEs 2*N algebraic equations Numerical solution with DASSL

131 Kunii-Levenspiel model parameters Volume fractions V c /V b och V e /V b K bc och K be from correlations Mean residence time of bubbles

132 Diffusion coefficients Depend on molecular structure – in general dependent on concentrations, too Fick’s law gives a simple relation between the diffusion flux and the concentration gradient

133 Effective diffusion coefficients Effektive diffusion coefficient in a porous particle D i molekular diffusion coefficient  p  porosity  1  p tortuosity or labyrinth factor, 

134 Effective diffusion coefficient

135 Molecular diffusion Intermolecular diffusion  collisions between molecules Knudsen diffusion  Collisions between molecules and pore walls

136 Fuller-Schettler-Giddings equation Ttemperature Mmolar mass vvolyme contribution Diffusion coefficient Gas phase

137 Volyme contributions Diffusion volumes of simple molecules He2.67CO18.0 Ne5.98CO 2 26.9 Ar16.2N 2 O35.9 Kr24.5NH 3 20.7 Xe32.7H 2 O13.1 H 2 6.12SF 6 71.3 D 2 6.84Cl 2 38.4 N 2 18.5Br 2 69.0 O 2 16.3SO 2 41.8 Air19.7 Atomic and Structural Diffusion Volume Increments C15.9F14.7 H2.31Cl21.0 O6.11Br21.9 N4.54I29.8 S22.9 Aromatic ring-18.3 Heterocyclic ring-18.3

138 Diffusion coefficient Gases Knudsen’s diffusion coefficient  S g specific surface area, which can be determined by nitrogen adsorption, BET (Brunauer-Emmett-Teller)- theory

139 Diffusion coefficient Liquids Not as well developed theory as for gases General theory for calculation of binary diffusion coefficients in liquids is missing Correlations typically describe a solute in a solvent Correlations exist for neutral molecules and ions

140 Diffusion coefficient Liquids Stokes-Einstein equation  Molecule radius R A is the bottleneck !

141 Diffusion coefficient Liquid Wilke-Chang equation V A solute molar volume at normal boiling point  B solvent viscosity

142 Molar volumes Methane37.7 Propane74.5 Heptane162 Cyclohexane117 Ethylene49.4 Benzene96.5 Fluorobenzene102 Bromobenzene120 Chlorobenzene115 Iodobenzene130 Methanol42.5 n-Propylalcohol81.8 Dimethyl ether63.8 Ethyl propyl ether129 Acetone77.5 Acetic acid64.1 Isobutyric acid109 Methyl formate62.8 Ethyl acetate106 Diethyl amine109 Acetonitrile57.4 Methyl chloride50.6 Carbon tetrachloride102 Dichlorodifluoromethane 80.7 Ethyl mercaptan75.5 Diethyl sulfide118 Phosgene69.5 Ammonia25 Chlorine45.5 Water18.7 Hydrochloric Acid30.6 Sulfur dioxide43.8

143 Atomic increments for estimation of V A

144 Diffusion coefficient Liquids Wilke-Chang equation has been extended to solvent mixtures Association factor   water 2.6  methanol 1.9  ethanol 1.5  non-polar solvents 1.0

145 Viscosity Use experimental data if available Correlation equations A, B, C och D from databanks

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