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Chemische Reactorkunde - Coggle Diagram

- - - - Reaction types
        
        Reversible
        
        Irreversible
        
        Other
        
        Parralel/Series
        
        Homogeneous
        
        Heterogeneous
        
        Non-elementary reaction
        
        Elementary reaction
        
        Reaction order can be guessed because reaction is determined by collisions
      - Introduction
        
        Chemical reactor is defined as an enclosed vessel in wich an reaction takes place.
        
        It is easy to make a chemical reactor, it is hard to improve them
        
        Performance equation --> Output = f(input, kinetics, contacting)
      - Type of reactors
        
        Batch
        
        Plug flow
        
        CSTR
      - Critical concepts
        
        Reaction rate
        
        Conservation of species
        
        Balance equation
    - - Rate equation components
        
        Concentration dependent term
        
        Known for elementary reactions
        
        Dependent on the mechanism for non-elementary reactions
        
        Reactions order
        
        Total reaction order is the sum of all species reaction order
        
        General
        
        -r = dc/dt = k0e^(-E/RT)Ca^a
        
        Building blocks
        
        Rate equation
        
        Stoichiometry
        
        Reaction rates of reagents/products are coupled
        
        -ra/a = -rb/b = rc/c = rd/d
        
        Does not nessacarily determine the rate equation
        
        Mole balance
        
        Main steps
        
        Determine the type of differential equation for the rate equation based on the system
        
        Include the concentration and temperature dependence of the reaction rate
        
        Apply scaling to convert concentration to conversion
        
        Temperature dependent term
        
        Arhenious
      - Rate equation determination
        
        Batch
        
        Batch type reactions
        
        Varying volume
        
        Conversion/volume changes can be used to follow the reaction
        
        Good for gas analysis, volume change says something about reaction rate
        
        expansion factor
        
        e = V(x=1)-V(x=0)/V(x=0)
        
        Times the conversion it is the volume change
        
        Volume
        
        V = V0(1+eX)
        
        Constant volume
        
        accumulation = in - out + gen/cons --> ri = dc/dt
        
        Integrate to get the function of the concentration
        
        Concentration/conversion/pressure can be used to follow the reaction
        
        Methods
        
        Analyse rate behaviour
        
        Differential method
        
        Good for difficult reaction
        
        Bad for noisy data
        
        Use the slopes for fitting
        
        Integral method
        
        Always alter y/x axis to obtain a lineair relation y = mx+b of the raw data. Linearity can be easily determined using linear regression
        
        These relation can be found for different equations in the book
        
        Good for simple reactions
        
        Try again if the chosen reaction did no fit the data = line was not lineaer
        
        Try out known reaction rate equations for comparison
        
        Usually done with software
        
        Aquire raw data
        
        Test at different temperatures
        
        Sweep of relevant starting concentration
        
        Measure C using some method
        
        Obtain kinetic data
        
        rate constants
        
        Activation energy
        
        Batch reactor results can be exented to continuous reactors
        
        Concepts
        
        Conversion
        
        Defined by the limiting reagent
        
        c = c0(1-x)
        
        dc/dt = -c0(dx/dt)
        
        Xa = Nao-Na / Nao
        
        Can be used to reduce the number of variables
        
        Conversion at equilibrium
        
        Xae
        
        For concentration = Cae
        
        Needed for reversible reactions
        
        rate equation is usually an empirically determined equation
    - - Introduction
        
        For each new reactor type, derive the balance equation to obtain the performance equation
        
        Balance equations
        
        General
        
        Accumulation = in-out + gen/cons
        
        Energy
        
        Momentum
        
        Mass
        
        Always write down at first
        
        Solving Balance equation
        
        1 Seperation of variables
        
        2 Integrating factor
        
        I = e^(int(p(x))
        
        dy/dt + p(x)Y = Q(x)
        
        YI = int(IQ(x)
        
        Dont forget the constant of integration
      - Ideal reactors
        
        Single reaction
        
        Reactor types
        
        Continuous
        
        CSTR
        
        Has uniform mixing
        
        Operates in steady state
        
        3 more items...
        
        Performance equation
        
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        Plug flow
        
        Assumptions
        
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        Performance equation
        
        3 more items...
        
        Batch
        
        Has uniform mixing
        
        Performance equation
        
        Constant volume
        
        2 more items...
        
        Is in time
        
        Comparison MFR/PFR
        
        Reaction rate / volume
        
        For RO > 0
        
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        For RO=0
        
        1 more item...
        
        For RO < 0
        
        1 more item...
        
        Reactor design
        
        Multiple reactors in series
        
        Multiple PFR
        
        N PFR reactors with volume V = 1 PFR with volume V
        
        Multiple equal MFR
        
        Needed volume decreases with N MFR
        
        In the limit has plug flow behaviour
        
        Multiple different MFR
        
        Case 1: find conversion
        
        1 more item...
        
        Case 2: find best system for X
        
        1 more item...
        
        Different type
        
        Recycle reactors
        
        Recycle ratio
        
        R = Volume recycled (Rvf) / Volume leaving (vf)
        
        Volume to reactor = (1+R)vf
        
        Intial boundary condition will be changed to (R/(R+1))Xaf
        
        Will behave as MFR if R--> inf
        
        Main performance parameter
        
        Reactor volume
        
        Should be minimized
        
        Autocatalytic reactors
        
        A + R --> R + R reactions
        
        Highest r at Xa = 0.5
        
        With recycle
        
        minimisation if the reaction rate in the initial concentration is equal to the average heigt of the recycle area
        
        Has changing reaction order (first negative (MFR quicker), then positive (PFR quicker). Quickest to combine.
        
        Concepts
        
        Space time
        
        How long it takes the feed to refresh the reactor
        
        Same a the mean residence time = V/flow
        
        Comparable to time from the batch reactor
        
        Space velocity
        
        s = 1/space time
        
        Performance equation
        
        Equation that can be used to determine the (space) time or volume needed based on the type of reactor, reaction and conversion
        
        Can be found in the book for all reactor types and constant/varying volume or density
        
        Graphical representation
        
        y axis usually C/ra
        
        x axis conversion
        
        Area under the curve is then (space) time or volume
        
        Usefull to compare various reactors
        
        Reactivity system
        
        given by kt
        
        Stays constant if volume (flowrate) is constant
  - - - Parralel reactions
        
        Multiple products with one step reactions
        
        Form desired and undesired products
        
        Instantanious fractional yield
        
        Percentage desired product formed at a certain point
        
        phi = rr/(rr+rs) = dcr/-dca
        
        Depends only on reaction
        
        Overal fractional yield
        
        Percentage desired product formed at the end
        
        phi = crf/(Ca0-Caf)
        
        Depends on reaction and reactor
        
        How to steer
        
        Favourable concentrations for desired reaction
        
        Contacting pattern to obtain low/high concentrations
        
        Temperature
      - Ideal reactors
        
        Reactor type
        
        MFR
        
        iPhi=oPhi
        
        PFR
        
        oPhi = 1/(ca0-cf) int(phi*dca)
        
        Contacting pattern
        
        Allows reactors to have low and high concentrations feed
        
        Repeated addition of the low conc feed.
        
        Allows the low conc feed to be kept constant
    - - Multiple reaction steps and dissapearing products
      - Types
        
        Series ((irr)reversible)
        
        Series and parralel
        
        More complex
      - Desired products
        
        Intermediate products
        
        Final products
        
        Mixture of products
      - Quantitative distribution methods
        
        Simplifiy
        
        If rate constants differ (k1>>k2) you can make simplifying assumptions.
        
        Integrate
        
        Only possible by hand for first order irreversible, obtain al C/Ca0 values of the formed products.
        
        Read from plot
        
        Find the product distribution using the given reaction criteria
      - Ideal reactors
        
        Concentration R is always greater for PFR than for MFR
        
        You want to minimize mixing betweed aged streams to obtain high R concentrations
    - - Temperature effects cannots be described fully be the arhenius equation because the temperature affects also the equilibrium and the reaction influences the reactor temperature
      - 4 main concepts
        
        Impact on conversion /equilibrium
        
        Equilbrium constant K is a function of T
        
        Xae = K(T) / K(T) + 1 (for FO rev)
        
        Reaction is not operated at equilibrium
        
        Otherwise r = 0
        
        Isorate figure
        
        Shows reaction rate at certain T and conversion
        
        Top line is equilibrium, r = 0. Shifts upwards/downwards depending on endo/exothermic behaviour of the reactions
        
        Can be used to determine best T at a certain conversion for highest r
        
        Enthalpy of the reaction
        
        Endothermic --> T decrease
        
        Exothermic --> T increase
        
        Temperature profiles
        
        Natural temperature progression
        
        Temperature profile in an adiabatic reactor
        
        Use heat capacity and reaction enthalpy. Xa = dT*Cp / dHr
        
        Controlled temperature progression
        
        Add or remove heat from the system to follow optimal temperature
        
        Or have multiple reaction stages with cooling/heating in between.
        
        Optimal temperature progression
        
        Optimal means highest reaction rate at each conversion value
        
        Always maximum T for endothermic reactions
        
        Exothermic reactions
        
        Start at the maximum T
        
        Follow locus if rate is decreasing at maximum T
        
        Limits
        
        Maximum/minimum allowable temperature reactor
    - - Short summary is given in chapter 10
    - - Systems with multiple reactions occuring and thus a product distribution is formed.
      - Also the effect of temperature and pressure is added
      - Now a good product distribution and low volume may clash
      - Contacting pattern
        
        Different ways for reactant to come into contact wich each other
        
        Needed to maximize the desired products
- - - - MFR
        
        Short circuiting
        
        Stagnent zones
      - PFR
        
        Non-uniform velocity
        
        eddies/vortexes
    - - State of aggregation
        
        Microfluid
        
        Has no individial indentity
        
        Macrofluid
        
        Has individual indentity and can be considered small batch reactors
        
        Use the E-curve
      - Earliness/lateness of mixing
        
        Does not change RTD
        
        May change reactor performance
      - RTD
        
        General
        
        How to determine
        
        Pulse tracer
        
        Broadened C-curve
        
        E curve
        
        Normalised C-curve
        
        Area = 1
        
        Derivative of the F curve
        
        Step tracer
        
        Rising and leveling C-curve
        
        F-curve
        
        Normalised C-curve
        
        Divide C-curve by Cmax
        
        Integral of the E curve
        
        Effect on conversion
        
        Calculate the mean conversion by integrating the performance equation times the E-curve.
        
        Think of taking the mean of many batch reactors with slight time variations
        
        Quantification
        
        Mean residence time = t
        
        Variance = s^2
        
        Standard deviation = s
      - Luckily these factors can be taken into account as additon on the ideal reactors
  - - - General
        
        Volumes
        
        Plug flow region
        
        Mixed flow region
        
        Dead region
        
        Flow types
        
        Bypass flow
        
        Recycle flow
        
        Active flow
        
        Non-ideal systems can be described by combination of different reactor volumes and flow types
      - Behaviour E/F-curves
        
        MFR
        
        Ideal
        
        Exponential decay
        
        Non-ideal
        
        Sudden drop (bypass)
        
        Time lag (plug flow)
        
        Bumps (poor mixing)
        
        Quick decay (dead volume)
        
        Multiple reactors
        
        Time lag followed by exponential decay or switched
        
        PFR
        
        Ideal
        
        Step response at t
        
        Non-ideal
        
        Quicker response (dead volume)
        
        Multiple peaks (internal mixing)
        
        Double peaks (different fluid velocity)
    - - Tanks in series
        
        Now the number of reactors in series is the variable
        
        N = dt^2/ds^2
      - Dispersion
        
        Causes
        
        Diffusion
        
        Turbulence
        
        Different velocities
        
        How to account for
        
        D/ul
        
        Non dimensional number
        
        D = axial dispersion coefficient, sum of all contributing terms
        
        D/ul < 0.01 small dispersion, D/ul > 0.01 large dispersion
        
        Can be calculated with the variance and mean residence time = ds^2/dt^2 *0.5
        
        Solution strategy
        
        Small dispersion
        
        Fill in equation
        
        Gaussian curve around MRT
        
        Large dispersion
        
        Open vessel
        
        Fill in equation
        
        Closed vessel
        
        Fill in equation
        
        Has a larger tail, more diffusion governed
        
        Reactor in series
        
        Determine variance and MRT of one reactor
        
        ds^2 = s^2out - s^2in
        
        dt^2 = (tout-tin)^2
      - To account for the broadening of the RTD, Dispersion model and tanks in series are comparable
    - - Not treated in lectures
- - - - Increase reaction rates
      - Steer selectivity
    - - Packed bed reactor
      - Fluidized bed reactor
        
        Efficient heat transfer
        
        Large fluid-solid interaction area
    - - Heterogenous system
        
        Rate equation
        
        Now includes mass transfer terms between phases
        
        Contacting pattern
        
        Much more difficult
  - - - Types
        
        Absorption in catalyst
        
        Film diffusion to particles
        
        Convection
        
        Pore diffusion in particles
      - Mass transfer limitations
        
        General
        
        Impact on r
        
        robs = eta(i)eta(e)rins
        
        Types
        
        Internal mass transfer
        
        Eta(i)
        
        Pore diffusion in particle
        
        Is usually limiting
        
        Bigger particles have larger IMTR
        
        External mass transfer
        
        Film diffusion to particle
        
        Eta(e)
        
        External
        
        Film diffusion limiting
        
        Carberry number
        
        kg*S
        
        kg =mass transfer coefficient
        
        s = surface area
        
        Internal
        
        Thiele modulus
        
        First order
        
        Mt = L root(k/D)
        
        L = charesteric length (differ for shere,plate,cylin)
        
        D = effective diffusion transport
        
        K = reaction rate
        
        Effect on eta(i)
        
        If Mt<0.4 no mass transport lim eta(i)=1
        
        If Mt >4, strong MTL, eta(i) = 1/Mt
        
        So if particle size doubles, reaction rate halves
        
        Higher order reactions
        
        Use difficult Mt equation
        
        n order reaction turn into (n+1)/2 order reactions at limiting internal diffusion.
    - - K
        
        Now has units m3/kgcat*s (first order)
        
        Is no longer constant
      - observed reaction rate is usally slower than intrinsic reaction rate
    - - Same performance equation can be used but V has to replaced by Vcat or WCat(kg)
      - Space time
        
        Volume time t = Vcat/u
        
        Weight time, t = Wcat/u
    - - PFR
        
        Differential condition
        
        Small variations in r, C, T
        
        Valid at low X
        
        Integral condition
        
        Large variations in r
        
        Requires complex modelling
      - MFR
        
        Besty reactor (solid bed in MFR)
        
        Recycle reactor with large R
        
        Carberry reactor (catalyst in agitator)
      - Batch
        
        Have external catalyst tube with recycle