Hydrocarbon Processing - May 2022 - 59
Process
Optimization
K. LATURKAR, Facility for Rare Isotope Beams,
East Lansing, Michigan; and K. LATURKAR, Validation
Associates LLC, Framingham, Massachusetts
Sensitivity analysis of a plug flow reactor
A sensitivity analysis study evaluates
uncertainties in a model's output based on
the changes in the input parameters of the
model. A good sensitivity analysis model1
should have the following properties:
* Adaptability to scale and shape.
It is important to consider both the
range of variation of the input and
the form of its probability density
function when determining the
influence on the output.
* It should include the effect of
variation of all parameters on the
output, which would provide a
more multi-dimensional approach
to the analysis.
* The ability to be model
independent. Models can be
additive or linear, and the method
should work regardless.
* Allowing grouped parameters to
be treated as individual entities.
The ability to interpret the results
with agility is an essential feature.
Variations of the independent variables
are made, and the impact on
the outcome is examined. An output
that changes significantly as the input
changes from minimum to maximum is
classified as sensitive. An insensitive or
robust output is one where the output
does not alter significantly. The credibility
of a model is increased if its output
remains consistent regardless of the
variation in input parameters. By conducting
a sensitivity analysis, ideal parameter
settings can be determined for
a model and the risks associated with
them can be quantified. The repeated
use of sensitivity analysis allows for a
deeper understanding of the model's
strengths and weaknesses. Having this
knowledge is key to recommending
concepts or operational approaches.2
This article presents a sensitive analysis
of a typical plug flow reactor. For a
continuous flow, the plug flow reactor
model represents a cylindrical geometry
in which chemical reactions take place
across the length of the reactor. These
reactions inside the reactor can be projected
with the model so that vital reactor
parameters can be assessed.3
In this
article, an open source simulation tool
DWSIM4
is used to investigate the impact
of varying the inlet parameters of the
plug flow reactor (i.e., flowrate, temperature,
pressure and volume) on the outlet
parameter of hydrogen (H2
to ammonia (NH3
) conversion
). User-defined ranges
are used for varying these parameters
incrementally. Changes in the independent
variables lead to a change in the
dependent variables. The collected data
can be visualized in a variety of plots,
which can then be examined.
Theory. A glossary of terms is seen in
TABLE 1. The mass balance reaction for
Component A in the plug flow reactor at
steady state5
is given by Eq. 1:
ⅆFA
/ⅆV = rA
(1)
The molar flowrate of the component
at any point in the reactor is defined5
in
terms of the conversion factor as Eq. 2:
FA
= FA0(1 - XA
by Eq. 3:
ⅆP/ⅆz = -v[fF
)
(2)
For turbulent flows in an open plug
flow reactor, the pressure drop5
is given
(32m /π2
ⅆtube
5
)] (3)
For an adiabatic plug flow reactor,
factor as Eq. 4:
T = T0
the temperature at any point in the reactor5
is
given in terms of the conversion
+ [CA0(-∆Hrxn
)/ρCpm
]XA
Example. The formation of NH3
) and H2
(4)
is examined
for a first-order reaction using nitrogen
(N2
equimolar mixture of H2
as the reactants. An
and N2
enters
an adiabatic plug flow reactor at the rate
of 3,000 kg/hr at a temperature of 400°C
(752°F) and 200 bar. Simulation considers
the volume of the plug flow reactor to
be 1 m3
with a length of 1 m.
Parameter
FA
V
rA
FA0
XA
P
z
v
fF
m
dtube
T
T0
CA0
Cpm
ρ
ΔHrxn
TABLE 1. Glossary of terms
Description
Molar flowrate of Component A
Volume of the reactor
Rate of reaction
Initial molar flowrate
for Component A
Conversion of the limiting
reactant A
Pressure inside the reactor
Length of the reactor
Volumetric flowrate
Fanning friction factor
Constant mass flowrate
Diameter of the plug flow reactor
Temperature inside the reactor
Temperature of the reactor
at the entry point
Initial concentration of the
Component A
Mass average heat capacity
Density
Heat of the reaction
Hydrocarbon Processing | MAY 2022 59
Hydrocarbon Processing - May 2022
Table of Contents for the Digital Edition of Hydrocarbon Processing - May 2022
Contents
Hydrocarbon Processing - May 2022 - Cover1
Hydrocarbon Processing - May 2022 - Cover2
Hydrocarbon Processing - May 2022 - Contents
Hydrocarbon Processing - May 2022 - 4
Hydrocarbon Processing - May 2022 - 5
Hydrocarbon Processing - May 2022 - 6
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Hydrocarbon Processing - May 2022 - Cover3
Hydrocarbon Processing - May 2022 - Cover4
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