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Multiple steady states in a CSTR with total condenser: Comparison of equilibrium and nonequilibrium models

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Abstract

Comparison of equilibrium and nonequilibrium models of a CSTR with total condenser focused on the multiple steady states and dynamic behaviour was carried out. The steady-state behaviour of the model system, MTBE synthesis from methanol and isobutene in a reactive distillation column, was studied in terms of the input parameters, i. e. feed flow rate of methanol or butenes, reflux ratio, and mass of catalyst. The dynamic behaviour of the system during the start-up was investigated and perturbations of manipulated variables were found to cause transitions between the parallel steady states.

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Abbreviations

a:

total interfacial area m2

c:

molar concentration mol m−3

C p :

heat capacity J mol−1 K−1

D:

diffusion coefficient m2 s−1

ε:

energy transfer rate J s−1

F:

feed stream mol s−1

h:

heat transfer coefficient J s−1 m−2 K−1

H:

molar enthalpy J mol−1

Δr H :

heat of reaction J mol−1

J:

molar diffusion flux relative to the molar average velocity mol m−2 s−1

[k]:

matrix of the multicomponent mass transfer coefficients m s−1

K i :

vapour-liquid equilibrium constant for component i

L:

liquid flow rate mol s−1

Le:

Lewis number (= λρ −1 C −1p D −1)

L TC :

liquid flow rate from the total condenser to the reactor mol s−1

m c :

mass of catalyst kg

N F :

number of feed streams

N I :

number of components

N R :

number of reactions

N:

mass transfer rate mol s−1

P:

pressure of the system Pa

P 0in :

vapour pressure of pure component i Pa

Q:

heating rate J s−1

r:

reaction rate mol kg−1 s−1

R:

gas constant J mol−1 K−1

R x :

reflux ratio

t:

time s

T:

temperature K

U:

molar hold-up mol

V:

vapour flow rate mol s−1

V Lr :

volumetric liquid hold-up in the CSTR m3

V Vr :

volumetric vapour hold-up in the CSTR m3

X MeOH :

conversion of methanol

x:

mole fraction in the liquid phase

y:

mole fraction in the vapour phase

ε:

heat transfer rate factor

γ:

activity coefficient

κ:

binary mass transfer coefficient m s−1

λ:

thermal conductivity W m−1 K−1

ν:

stoichiometric coefficient

ρ:

molar density mol m−3

o:

initial conditions

I:

referring to the interface

L:

referring to the liquid phase

V:

referring to the vapour phase

av:

averaged value

f:

feed stream index

i:

component index

j:

reaction index

m:

mixture property

t:

referring to the total mixture

TC:

referring to the total condenser

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Authors and Affiliations

  1. Institute of Chemical and Environmental Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37, Bratislava, Slovak Republic

    Z. Švandová, J. Markoš & L’. Jelemenský

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  1. Z. Švandová
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  2. J. Markoš
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  3. L’. Jelemenský
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Correspondence to J. Markoš.

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Švandová, Z., Markoš, J. & Jelemenský, L. Multiple steady states in a CSTR with total condenser: Comparison of equilibrium and nonequilibrium models. Chem. Pap. 60, 432–440 (2006). https://doi.org/10.2478/s11696-006-0079-8

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  • DOI: https://doi.org/10.2478/s11696-006-0079-8

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