OPTIMAL DESIGN OF REACTIVE ABSORPTION
PROCESSES WITH DESIRED DYNAMIC
BEHAVIOUR
Natassa Dalaouti and Panos Seferlis
CERTH – Chemical Process Engineering Research Institute (CPERI)
P. O. Box 361, 570 01, Thermi-Thessaloniki, Greece
Abstract
The dynamic characteristics of reactive absorption processes are of great importance for the
smooth operation of the unit and the overall performance of the implemented control system under the
influence of process disturbances and the presence of tight environmental and safety constraints. In the
present study, the effect of the major design parameters and column configurations on the dynamic
behaviour of the environmentally sensitive NOx removal processes, through the use of rigorous ratebased dynamic models, is investigated. Static and dynamic disturbance rejection properties are
evaluated for the screening and assessment of alternative design decisions.
Keywords
Rate-based models, Reactive Absorption, NOx removal, Design sensitivity, Dynamic simulation
Introduction
Reactive absorption processes are gaining strong interest
in many industrial applications due to significant
equipment and capital cost reduction. Air pollution control
and specifically the cleaning of process gas streams from
pollutants and toxic substances are some of the key
applications of the technology.
Design decisions inherently affect the characteristics
of the dynamic behaviour of an absorption unit. Process
design imposes limitations on the dynamic performance of
the control system towards the alleviation of the
detrimental effects of process disturbances from the
control objectives. An existing and operating absorption
column may still have a substantial degree of design
flexibility, since feed and recycle streams may be directed
to multiple side positions of the column and the flow rate
of such streams may be manipulated. The ability of the
reactive absorption system and the implemented control
system to successfully compensate for the effects of
process disturbances and model parameter variations has a
direct impact on the satisfaction of key environmental
specifications and product quality requirements. The
disturbance rejection characteristics of the alternative
column design configurations and control topologies are
assessed based on (i) the required steady state effort for
the manipulated variables to maintain the controlled
variables within the desired region and (ii) the
characteristics of the achieved dynamic response to
compensate for model parameter variations.
Reactive absorption processes, are highly complex
unit operations characterized by coupled phase
equilibrium, mass and heat transfer and chemical reaction
phenomena. Detailed rate-based models for reactive
absorption introduce a significant degree of detail that is
absolutely necessary for the accurate representation,
simulation and optimal design of complex reactive
absorption processes (Kenig et al., 1997).
Rate-based Model for Reactive Absorption Processes
The rate-based model for reactive absorption
processes (Kenig et al., 1997, Dalaouti and Seferlis, 2004)
involving the rigorous description of mass and heat
transfer phenomena, phase equilibrium relations and
chemical reactions in both phases is calculated in a
number of equivalent stages. Mass transfer is described by
the thin-film model (Taylor and Krishna, 1993), which
assumes that mass transfer resistance is limited in the two
film regions adjacent to the gas-liquid interface. Gas and
liquid bulk phases are in contact only with the
corresponding films, while thermodynamic phase
equilibrium is assumed to occur only at the interface.
Chemical reactions are considered to take place in both the
film and bulk liquid and gas phase.
Mass and energy balances for equivalent stage s,
considering potential accumulation of mass in the liquid
and gas phases, denoted by terms miL and miG respectively,
are described by the following equations:
43
2004, Workshop of CPERI
dm
L
i ,s
dt
dm iG,s
dt
=Li ,s −1 −Li ,s +(φ L RiLb + N iLbα int ) Acol ∆h
(1)
=Gi ,s +1 −G i , s +(φ G RiGb − N iGbα int ) Acol ∆h
(2)
Liquid and gas phase volumetric holdups,
φL , φ G respectively, are related to component molar
holdups in the gas and liquid phese. Reaction rates of the
components RiLb, RiGb are calculated at the conditions at
each stage.
The dynamic mass balances in the liquid film in the
presence of chemical reactions in the film is defined as:
∂ciGf ∂N iGf
+
−RiGf =0 0<η Gf ≤δ Gf
∂t ∂η Gf
(3)
ηGf =0
N iint = N iGf
η Gf =δ Gf
i=1,...n
(4)
A similar equation describes the gas film region.
The interfacial diffusion molar flux terms Ni in eqs (1)
and (2) are calculated by the generalised Maxwell-Stefan
equations for multicomponent mixtures (Taylor and
Krishna, 1993). Thermodynamic equilibrium holds only at
the interface. Neglecting the heat transfer effects along the
film regions the overall dynamic energy balance at each
stage point becomes:
dU s
= Ls −1 H sL−1 +Gs +1 H sG+1 − Ls H sL −Gs H sG −Q
dt
(5)
Pressure drop in the column, the liquid hold-up, the
specific interfacial area, and the gas and liquid film
thickness were calculated from correlations that account
for the column internals and hydraulics.
Disturbance Rejection Properties
The main objective of this work is to perform a
systematic, effective and rigorous evaluation and
screening of a set of possible and realisable column
configurations and control structure alternatives based on
static and dynamic controllability criteria. Static
controllability analysis investigates the effort in terms of
steady-state variation for the manipulated and controlled
variables in order to alleviate the effects of multiple
simultaneous disturbances of finite magnitude on the
control objectives. The required steady-state effort for the
manipulated variables is indicative of the anticipated error
in the controlled variables during dynamic transition.
Controlled variables are either forced to remain at a
specified target value or allowed to vary within an
44
Ω SC (ζ )=∑ wi (ζ )
i
with boundary conditions
N iGb = N iGf
acceptable range around a set point. The importance of
each controlled variable and the prioritisation in the
utilisation of the available manipulated variables is
reflected through the rank ordering of the problem’s
control objectives and the preference in the use of the
available resources (Seferlis and Grievink, 2001).
Nonlinear process models are employed in order to
provide an accurate prediction of the system’s behaviour.
The static controllability performance index, ΩSC, as
defined in Seferlis and Grievink (2001) is utilised for the
evaluation of the disturbance rejection properties of a
given design and control configuration. This index
calculates the impact of disturbances and model parameter
variations on the steady-state operation of the process, and
is defined by:
u i (ζ )−u i (0)
y (ζ )− y i (0 )
+∑ wi (ζ ) i
u i (0)
y i (0)
i
(6)
where ui denotes the manipulated and yi the controlled
variables of the process. Symbol ζ denotes the co-ordinate
that represents the magnitude of variation for the
disturbance, while the terms w(ζ) denote the weighting
factors that reflect the relative importance of each
variable’s variation. A large numerical value for ΩSC
results from large steady state deviations for the selected
manipulated and controlled variables from target values,
and subsequently, implies large error in the controlled
variables during the dynamic transition from one steady
state operating point to another.
However, the dynamic behaviour is also necessary for
a complete and reliable evaluation of the achieved control
performance. The complete characteristics of the dynamic
response are calculated using a detailed dynamic process
model. The speed of response to process disturbances as
translated into the required settling time for the controlled
variables, the behaviour of the manipulated variables (e.g.,
saturation effects) and the characteristics of the dynamic
response (e.g., level of overshoot, oscillations and so
forth) are key factors that are taken into consideration in
the evaluation of the dynamic disturbance rejection
properties. System poles and transmission zeros calculated
from the state space realisation of the linearised problem
are indicative of the basic dynamic characteristics (e.g.,
speed of response, type of response – stable, unstable,
oscillatory, inverse response).
Reactive absorption of NOx
Reactive absorption of nitrogen oxides from a gas
stream by a weak HNO3 aqueous solution (Joshi et al.,
1985, Emig and Wohlfahrt, 1979), is an efficient way to
remove NOx from gas streams released to the atmosphere,
while it is used for the industrial production of nitric acid.
Environmental regulations impose strict constraints on the
allowable level of NOx concentration for the outlet gas
streams. The implemented control system in the absorber
Advanced Software Tools
aims at effectively anticipating for the effects of process
disturbances on the environmental and product quality
specifications.
However,
the
selected
column
configuration
and the operating point
Flue gases
for the process affect
NOx
the performance of the
specifications
H2O
control system in a
direct and profound
way. Reactions play an
important role in this
TC
H2O, HNO3
system, because they
enhance the absorption
TC
of otherwise insoluble
components (e.g. NO)
TC
through
their
transformation to more
LC
soluble
components
Air, NOx
(e.g. ΝΟ2). Moreover,
nitric acid is produced
subsequent
Figure 1: Column configuration through
reactions in the gas and
liquid phase. The mechanism of NOx absorption in weak
nitric acid solutions is very complicated and the reaction
scheme involves five gas-phase and four liquid-phase
reactions (Joshi et al., 1985).
The counter-current reactive absorption column
comprises 70 trays (Figure 1). A rich NOx gas stream
enters the bottom of column, a liquid water stream enters
the top of the column, a weak nitric acid solution stream
enters the side of the column, while the bottoms liquid
stream is partially recycled back in the column. A level
controller was used to control the inventory of the liquid
holdup at the bottom of the column. Reactions are highly
exothermal while the oxidation reaction and absorption are
favored by low temperature. Therefore, a tight control of
the column temperature profile is absolutely necessary for
the efficient operation of the column and cooling is
provided in the column stages for the removal of the
reactive heat and the control of the column temperature.
The partial differential equations describing mass
transfer in the films were discretized using orthogonal
collocation on finite element techniques. The rate-based
dynamic model was solved with gPROMS®. Model
validation was achieved with steady-state bibliographical
data for an industrial NOx removal reactive absorption
column (Emig and Wohlfahrt, 1979).
Disturbance Rejection Properties
The disturbance rejection properties of the NOx
removal process were investigated for different column
configurations. More specifically, the effect of the number
of total absorption stages in the column, the location of the
side feed stream, the location of the side recycle stream
and the percentage of the bottoms flow that was recycled
to the column on the dynamic performance of the control
system under the influence of multiple simultaneous
disturbances were explored. The examined disturbance
scenarios involved changes in the inlet gas temperature
and variations in the NOx content of the inlet gas stream.
Three separate cooling zones with independent
cooling water supplies were used. An equal flow rate of
cooling water was supplied to the cooling coils within
each stage for each zone. A proportional-integral (PI)
controller maintained the temperature at specific critical
stages within each cooling zone at a pre-defined level.
Temperatures at the critical stages act as inferential
variables for the overall NOx composition in the gas outlet
stream from the top of the column. The selection of the
critical stages was based on sensitivity information
between the stage temperature and the NOx concentration
level at the outlet gas stream. An upper bound on the
cooling water flow rate in each zone was imposed due to
capacity constraints.
The disturbance rejection properties were evaluated
based on the achieved steady-state NOx content in the tail
gas, the HNO3 composition in the bottoms product of the
column, the required steady-state cooling water flow rate
as well as the steady state value for the controlled
variables (e.g., stage temperature) that were allowed to
vary within a region around the set point. The static
controllability index, ΩSC (eq. 6), groups the above
quantities in a single metric. The system poles and the
settling time for the controlled variables are indicative of
the dynamic behaviour of the system. It should be noted
here that only a subset of three poles was traced for each
scenario. The selected poles were those that were closer to
the origin (i.e. larger real negative part) and were mainly
responsible for the slow modes in the dynamic response of
the system.
The effects of the location of the side feed and recycle
streams on the disturbance rejection properties were
explored for several disturbance scenarios. Four
configurations related to the position of the side feed and
recycle streams were considered. Figure 2 and Table 1
show the response to a 30 K increase of the inlet gas
stream. All four configurations showed adequate
performance with configuration (d) corresponding to side
stream locations at stages 30 and 60 having a slight
advantage. Configuration (c) that corresponds to side feed
and recycle stream locations at stages 30 and 55,
respectively, seems to compensate for the concentration
variation more effectively than all other configurations.
However, the percentage change in cooling requirements
in this case was as high as 47% from the nominal
operating point, while configuration (d) managed to
control the NOx concentration with an offset of only 2
ppm from the initial steady state value and an increase in
the cooling water flow rate of only 6%. The advantage of
configuration (d) is mainly attributed to the reduced
cooling requirements because the recycle stream enters at
a location closer to the bottom of the column where the
disturbance was first sensed. Recycling at a point closer to
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2004, Workshop of CPERI
the source of disturbance proved very helpful in
attenuating the temperature upset in the column.
A study of the effect of different column design
configurations and control structures on the disturbance
rejection properties of a NOx reactive absorption column
was performed. The proposed method combines the
benefits of an accurate and detailed modeling of the
complex reactive absorption process of NOx removal and
the results of a systematic controllability analysis to
guarantee a smooth operation, efficient disturbance
rejection and eventually a cleaner production.
555
NOx Concentration (ppm)
(a)
(b)
(c)
(d)
550
545
(i)
Cooling Water Flowrate
540
3500
(a)
(b)
(c)
(d)
0
3000
2.5
2500
2000
1500
(ii)
1000
0
0.5
1
1.5
2
2.5
Time (hr)
Figure 2: Dynamic response to an increase of the inlet
gas stream temperature. (i) Outlet stream composition (ii)
Cooling water flowrate. Side feed stream position (a)20,
(b)20, (c)30, (d) 30.Recycle stream position (a) 55, (b) 60,
(c) 55, (d) 60.
The column dynamic behaviour for simultaneous
disturbances on the temperature and NOx content of the
inlet gas stream was also investigated. The NOx content in
the inlet gas stream was increased gradually by 5% to a
total of 25% combined with a simultaneous one-time inlet
gas temperature increase by 30 K. Three independent PI
controllers, one for each cooling zone were used for the
temperature control of the column. The values of the static
performance controllability index obtained for each of the
column configurations are shown in Table 2.
Configurations (a) and (b), in which the side feed stream
was placed at a higher point in the column, achieved
smaller values for the static controllability performance
index compared to configurations (c) and (d) due to the
increased solvent flow rates in a larger section of the
column. Configurations (c) and (d), in which the side feed
stream enters the column at a lower point, resulted in
comparatively larger values for ΩSC, mainly due to of the
larger steady state NOx content in the flue gases. The
values of ΩSC, however, further increased as the cooling
system reached the saturation level (e.g., maximum bound
for cooling water flow rate). In conclusion, NOx
concentration variations in the inlet gas stream were
handled more efficiently with a side feed stream at a
higher point in the column, while pure temperature
variations in the inlet gas stream were better rejected with
a side recycle stream closer to the bottom of the column.
46
Conclusions
Table1: Static controllability performance index and
poles for increase in the inlet gas stream temperature
Stream positions
feed Recycle
20
55
20
60
30
55
30
60
system poles (·10-4)
ΩSC
0.417
0.401
0.487
0.086
-6.35
-6.79
-4.93
-4.96
-7.48
-8.04
-8.72
-1.60
-8.99±5.34i
-7.28±22.1i
-9.82
-7.28±22.1i
Table2: Static controllability performance index
for simultaneous disturbance on the inlet gas
temperature and NOx content
NOx content
5
variation (%)
Stream positions
feed
recycle
20
55
0.529
20
60
0.525
30
55
0.580
30
60
0.588
10
15
20
25
ΩSC
0.780
0.773
0.884
0.870
1.030
1.016
1.152
1.132
1.227
1.270
1.423
1.405
1.445
1.494
1.614
1.670
Acknowledgments
The financial support by the European Commission
is gratefully appreciated (Project G1RD-CT-2001-00649).
References
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absorption units for improved dynamic performance
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