Example 11-3: Adiabatic Liquid-Phase Isomerization of Normal Butane
Problem Description
Normal butane, C4H10, is to be isomerized to isobutane in a plug-flow reactor. This elementary
reversible reaction is to be carried out adiabatically in the liquid phase under high pressure using a liquid
catalyst which gives a specific reaction rate of 31.1 h-1 at 360 K. The feed enters at 330 K.
(a) Calculate the PFR volume necessary to process 100,000 gal/day (160 kmol/h) at 70% conversion
of a mixture 90 mol % n-butane and 10 mol % of i-pentane, which is considered an inert.
(b) Plot and analyze X, Xe, T and –rA down the length of the reactor
(c) Calculate the CSTR volume for the same conditions as the PFR.
Components
Three components are considered in the Aspen model: C4H10 (n-butane), IC4H10 (isobutane) and
IPENTANE (2-methyl-butane). The liquid catalyst is not included because its flowrate is not known and
the specific reaction rate has been given for the reaction condition. These three components are called
directly from built-in Aspen pure component databanks.
Properties
Different property models can yield different predictions for various thermophysical properties used in
mass and energy balance calculations. PENG-ROB, Aspen Peng-Robinson equation-of-state property
model, is chosen to describe the thermophysical properties of this hydrocarbon liquid mixture. One of
several equations-of-state well-known to be suitable for hydrocarbon systems, Peng-Robinson equationof-state should provide reasonable calculations for heats of reaction and heat capacities.
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Within the temperature range of 330 K to 360 K, PENG-ROB predicts liquid heat capacity of 157-185
J/mol.K for C4H10, 161-214 J/mol.K for IC4H10, and 176-195 J/mol.K for IPENTANE. The higher the
temperature, the higher the heat capacity will be. Pressure also affects liquid heat capacity. The
predictions here are done at 1 atm.
The isomerization heat of reaction is also a function of temperature. PENG-ROB predicts the heat of
isomerization to vary from -7430 J/mol C4H10 at 330 K to -7080 J/mol C4H10 at 360 K.
Reactions
To describe the n-butane isomerization reaction, an Aspen reaction model of POWERLAW type is
created: ISOMER. The ISOMER reaction is rate-controlled. The reaction stoichiometry is shown below:
𝐾𝐶
𝐶4𝐻10 ↔ 𝑖𝐶4𝐻10
Both forward and reverse reactions are 1st order with respect to reactants.
𝑅𝑎𝑡𝑒𝑓𝑜𝑟𝑤𝑎𝑟𝑑 = 𝑘′𝐶𝐶4𝐻10
𝑅𝑎𝑡𝑒𝑟𝑒𝑣𝑒𝑟𝑠𝑒 = 𝑘"𝐶𝑖𝐶4𝐻10
𝑘" =
𝑘′
𝐾𝑒𝑞
The forward reaction specific rate is 31.1 h-1 (0.008639 sec-1) at 360 K with activation energy of 65.7
kJ/mol (65.7x106 J/kmol). The reactant concentration is given in terms of molarity (kmol/m3).
𝑘 ′ = 0.008639𝑒
65700000 1 1
[
(
− )]
𝑅
360 𝑇
2
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It is also known that the heat of reaction is -6900 J/mol of n-butane and the chemical equilibrium
constant is 3.03 at 60°C.
𝐾𝑒𝑞 = 3.03𝑒
−6900000 1 1
[
(
− )]
𝑅
333 𝑇
The above equation gives 𝐾𝑒𝑞 = 2.51 at 360 K. Therefore, the above equation can be rewritten as
follows.
𝐾𝑒𝑞 = 2.51𝑒
−6900000 1 1
[
(
− )]
𝑅
360 𝑇
From k’ and 𝐾𝑒𝑞 , we can derive at the rate constant for the reverse reaction, k”.
𝑘" = 0.003442𝑒
72600000 1 1
[
(
− )]
𝑅
360 𝑇
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Flowsheet
Aspen model library provides RPLUG (PFR) reactor model and RCSTR (CSTR) reactor model. They are
used to construct processes with proper feed streams and reactor conditions.
Problem (a)
Aspen RPLUG reactor model is used with reactor type Adiabatic Reactor and reaction model ISOMER.
Aspen requires input of reactor dimensions in lieu of reactor volume. To start the simulation, initial
values of 0.1 meter in diameter and 1000 meter in length are assumed.
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It is found that the conversion of C4H10 reaches a maximum of about 72%. 70% of C4H10 conversion is
achieved with reactor length of 410 meter, or 603 second of residence time. That gives reactor volume
of 3.22 m3.
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Problem (b)
Profiles for the molar compositions of C4H10 and IC4H10 and the PFR reactor temperature are given
below.
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Problem (c)
Aspen RCSTR reactor model is used with heat duty set to 0 (i.e., adiabatic) and reaction model ISOMER.
To start the simulation, initial value of 3 m3 is assumed for the CSTR reactor volume. C4H10 content
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drops from 90 mol % to 33.7 mol % (62.5% conversion) with this initial volume of 3 m3.
A DESIGN-SPEC block is set up to find the reactor volume required for 70% C4H10 conversion. The study
shows a reactor liquid volume of 20.6 m3 is required to achieve 70% C4H10 conversion. That
corresponds to a residence time of to 3678 seconds, more than 6 times that of the RPLUG residence
time.
Given the models, various reactor analyses can be performed. For example, a PFR reactor liquid volume
of 1.41 m3 is required to achieved 40% C4H10 conversion while a CSTR reactor requires only liquid
volume of 1.30 m3.
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