Improving the load flexibility of industrial air separation units using a pressure‐driven digital twin

Abstract

Air separation units are one of the prime examples for studies on demand side management and (non‐)linear model predictive control due to their high power consumption and energy storage potential. These plants separate ambient air into its main components, nitrogen, oxygen, and argon, by means of cryogenic distillation at different pressure levels. Approximately two thirds of the industrially operated air separation units consider the separation of argon either as a value product or for reasons of energy efficiency. However, most of the studies in literature neglect the separation of argon since this requires additional equipment, increases the heat and process integration and, thus, the complexity of process control. In this work, a digital twin of an air separation unit with argon system is used to analyze and to improve load change procedures. Moreover, the potential of applying the digital twin as a soft sensor is demonstrated.

Full text

RESEARCH ARTICLE
Editor's Choice: Process Systems Engineering
Improving the load flexibility of industrial air separation units
using a pressure-driven digital twin
Robert Kender
1
| Felix Rößler
1,2
| Bernd Wunderlich
2
| Martin Pottmann
2
|
Ingo Thomas
2
| Anna-Maria Ecker
2
| Sebastian Rehfeldt
1
| Harald Klein
1
1
Department of Energy and Process
Engineering, TUM School of Engineering and
Design, Institute of Plant and Process
Technology, Technical University of Munich,
Garching, Germany
2
Linde GmbH, Linde Engineering, Pullach,
Germany
Correspondence
Robert Kender, TUM School of Engineering
and Design, Department of Energy and
Process Engineering, Institute of Plant and
Process Technology, Technical University of
Munich, 85748 Garching, Germany.
Email: robert.kender@tum.de
Funding information
German Federal Ministry of Education and
Research (BMBF), Grant/Award Number:
Kopernikus SynErgie (FKZ 03SFK3E1-2).
Abstract
Air separation units are one of the prime examples for studies on demand side
management and (non-)linear model predictive control due to their high power con-
sumption and energy storage potential. These plants separate ambient air into its
main components, nitrogen, oxygen, and argon, by means of cryogenic distillation at
different pressure levels. Approximately two thirds of the industrially operated air
separation units consider the separation of argon either as a value product or for rea-
sons of energy efficiency. However, most of the studies in literature neglect the sep-
aration of argon since this requires additional equipment, increases the heat and
process integration and, thus, the complexity of process control. In this work, a digital
twin of an air separation unit with argon system is used to analyze and to improve
load change procedures. Moreover, the potential of applying the digital twin as a soft
sensor is demonstrated.
KEYWORDS
air separation, digital twin, flexible operation, pressure-driven simulation, soft sensor
1|INTRODUCTION
Currently, one of the main global challenges in industry and politics is
climate change. A main contribution toward a more sustainable future
is the adaption of energy-intensive production processes, for instance
chemical plants, to the volatile availability of renewable energy
sources. Thus, the load flexible operation of air separation units
(ASUs) is investigated in the Kopernikus project SynErgie FlexASU.
This project is a collaboration of industry and several universities in
Germany. FlexASU project partners are Linde Engineering, MAN
Energy Solutions, the Technical University of Munich, RWTH Aachen
University, the University of the Federal Armed Forces in Munich and
the Technical University of Berlin. ASUs separate air into its main
components nitrogen (N
2
), oxygen (O
2
), and argon (Ar) by means of
cryogenic distillation. These plants are often used for studies
concerning the flexibilization of plant operation as their high energy
demand for the compression of air and the possibility to store energy
with high energy density using cryogenic liquids entail an outstanding
flexibilization potential.
1–8
A key factor toward efficient, flexible operation is
energy-optimized operational planning. Depending on the considered
time period, either process control (short-term) or scheduling (long-
term) aspects are of interest. For long-term operational planning,
demand side management (DSM) is widely used. Here, surrogate plant
models are subjected to mixed-integer optimization to minimize oper-
ating expenditures with regard to time-sensitive electricity prices.
9,10
As one of the first, Daryanian et al.
11
apply DSM to an ASU. They use
a linear dependency of product flow on the electricity consumption
without considering dynamic plant behavior in detail. However, only
N
2
and O
2
are considered as products. Current surrogate models are
Received: 22 November 2021 Revised: 11 February 2022 Accepted: 5 March 2022
DOI: 10.1002/aic.17692
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium,
provided the original work is properly cited.
© 2022 The Authors. AIChE Journal published by Wiley Periodicals LLC on behalf of American Institute of Chemical Engineers.
1of23 AIChE J. 2022;68:e17692.
wileyonlinelibrary.com/journal/aic
https://doi.org/10.1002/aic.17692

more complex as their data basis is either derived from historical plant
data
10,12–15
or from steady-state simulation of various operating
points.
13–23
Here, dynamic plant behavior is represented by optimiza-
tion constraints, for example, the maximum load change veloc-
ity.
10,13,14,16–19
The main focus of literature is on less complex plant
topologies such as O
211,16–18,23
or N
2
plants.
10,15,19,22
Only a few of
these studies consider the additional separation of Ar.
12–14,20,21
Due to the increasing share of renewable energies in the energy
supply, short-term fluctuations in the energy market can be observed.
Thus, advanced process control (APC) concepts based on nonlinear
model predictive control (NMPC) are necessary to efficiently operate
an ASU in this dynamic environment. Therefore, it is necessary to
combine short-term ASU operation with operational planning. To
cope with this task, two different paradigms can be applied: bottom-
up and top-down. The top-down paradigm follows a hierarchical
approach in which DSM problems are solved offline to calculate opti-
mal setpoints for the process control layer. Here, scale-bridging
models (SBMs) are used. These rely on low-order representations of
closed-loop process dynamics relevant for scheduling and, thus, bridge
the time scales between the long-term scheduling calculation and
short-term process control. Examples for the usage of SBMs for ASUs
can be found in literature.
10,15,24–27
However, these studies are con-
ducted using a N
2
plant. An example of the bottom-up approach is
the economic NMPC (eNMPC). Here, dynamic optimization of a rigor-
ous plant model (control model) with an economic target function is
performed. The operational planning as well as the input variables for
the process control layer are adjusted according to the optimization
result with regard to energy-optimal operation. Examples for the
application of eNMPC to ASUs in literature use either O
2
plants
28,29
or N
2
plants.
30,31
Caspari et al.
32
compare both paradigms using the
example of a N
2
plant. Vinson
33
considers the additional separation of
Ar reviewing model predictive control (MPC) strategies for air separa-
tion. Moreover, Blum et al.
34
present a model-based deep reinforce-
ment learning controller which is applied to a single control loop of an
ASU with Ar production.
Besides the development of complex NMPC strategies, the simu-
lation of isolated load change procedures of an ASU can be found in
literature as well. Engl et al.
35
and Kröner et al.
36
publish studies
regarding the optimization of a single load change procedure (operat-
ing range: 60%–100%) of an ASU with Ar separation. However, con-
sidering flexible plant operation, the complete load range is of interest
to investigate start-up processes or sudden plant shutdowns. For
instance, Caspari et al.
29,37
optimize the start-up procedure of a single
N
2
purification column and a N
2
plant. Wunderlich
38
develops a highly
detailed pressure-driven model for columns with structured packings.
This model is able to simulate the whole operating range of the ther-
mally coupled double column, the centerpiece of every ASU. Kender
et al.
3,4
refine this model and use it for the investigation of start-up
and shutdown procedures. Klein et al.
5
extend this model with the
remaining unit operations, for instance the main heat exchanger
(MHEX) according to Rößler et al.
39
, to investigate start-up proce-
dures of O
2
plants. Based on this work, Kender et al.
1
present a digital
twin (DT) concept for flexible ASUs. Here, industrially relevant load
changes, in particular a shutdown and cold restart as well as a hazard
analysis of the considered O
2
plant, are presented. Kender et al.
40
include the additional separation of Ar and simulate a warm start-up
of this ASU topology. Furthermore, Miller et al.
41
investigate a cold
restart of an ASU with Ar system. After validating their models with
plant data, they conduct dynamic simulation studies with various
measures to reduce the cold restart time. They discover that addi-
tional storage vessels, which collect the liquid that drains from the
argon column during shutdown and allow to reintroduce this liquid
during the subsequent restart, reduce the start-up time by ≈80%.
Cao et al.
42
evaluate the economic benefit of preemptive control
action in advance of an upcoming load change for an ASU with Ar
separation. They conduct various dynamic optimization studies using
two demand change scenarios with ±10% gaseous O
2
product load
with different degrees of freedom. As one of their findings, it is
shown that facilitating the liquid holdup of the pressure column
(PC) and the Ar reboiler as degrees of freedom is economically bene-
ficial during a load change. However, they claim that preemptive
controls tend to result in operations pushing the system closer to
the operating bounds and, thus, requires a careful monitoring of criti-
cal parameters.
Apart from studies to improve the flexible and energy-optimal
operation of ASUs, Cao et al.
19,43,44
conduct simulations using a N
2
plant as an example to identify potential limitations regarding opera-
tional agility (debottlenecking). In addition, Cao et al.
19
identify that
the usage of external liquid is a key modification to increase plant flex-
ibility. Furthermore, due to their high number of required separation
stages, the distillation columns in ASUs are often used as a subject to
model reduction approaches such as compartmentalization,
45
nonlinear wave propagation
46
or collocation.
47
However, only Cao
et al.
47
consider the Ar system.
As can be seen by this holistic review of simulation studies on ASUs,
only a few consider the additional separation of Ar. Nevertheless, the
main part of industrial ASUs (≈2/3 of all ASUs operated by Linde) include
the separation of Ar. In addition, large O
2
plants can include an Ar
removal column to remove a fraction of the intermediate boiling compo-
nent Ar and, thus, increase the overall energy efficiency of the O
2
plant.
48,49
Hence, considering the additional separationof Ar is highly rel-
evant for the energy-efficient, flexible operation of industrial ASUs. For
studies on plant operation requiring dynamic simulation or even optimi-
zation thisis particularly challenging. Due tothe small boiling point differ-
ence between Ar and O
2
, a high number of separation stages is required
to separate pure Ar from air. In addition, the degree of heat and process
integration increases and, hence, a more complex control scheme needs
to be applied to these ASUs. Furthermore, since Ar covers only a small
fraction of the air feed, a high simulation accuracy is necessary to accu-
rately predict the operation of Ar plants.
In addition, it is shown in literature that the specific utilization of
cryogenic liquids is beneficial for plant flexibility. Therefore, based on
the concept of Kender et al.,
1
a DT of an industrial ASU with Ar sepa-
ration is presented in this work and used to investigate the impact of
the systematic preemptive shifting of liquid holdup on the load change
agility. The remainder of this work is structured as follows: At the
KENDER ET AL.2of23

beginning, the basics of the DT concept are briefly described and
additional applications, such as the DT's utilization as soft sensor, are
introduced. Then, the focus is on the industrial air separation process
including the Ar system. The main part focuses on the ASU topology
and the increased complexity in terms of required equipment, heat
and process integration, control and the resulting challenges for (in sil-
ico) operations is highlighted. Then, the innovative smart liquid man-
agement (SLM) concept is introduced. Eventually, two simulation
studies of load change procedures, a 50% turn-down and subsequent
50% turn-up, are discussed, highlighting the benefits of the DT for
flexible plant operation.
2|DIGITAL TWIN OF AN
INDUSTRIAL ASU
The DT used in this work is based on the concept of Kender et al.
1
The main idea is that the DT includes a plant model, the virtual ASU,
which is intended to represent the plant's entire life cycle. The model
is implemented in the simulation framework SMI@LE (Simulation
Model Infrastructure at Linde Engineering) which provides interfaces
to databases of historical plant data and real-time operational data. It
is imperative that the data stream is allowed in both directions. This
enables, on one hand, the usage of simulation data to improve plant
operations and, on the other hand, the continuous refinement of sim-
ulation models using plant data. Additional information on SMI@LE
can be found in Kender et al.
3,4
To cope with the different simulation tasks during a plant life
cycle, the ability to adjust the virtual ASU's model granularity is cru-
cial. This characteristic is enabled by the modular-hierarchical model
structure. For instance, this allows for the replacement of design cor-
relations for column fluid dynamics by linear pressure drop and dis-
charge correlations for faster but less accurate simulations.
A top-down approach is applied for the development of the
DT. Currently, a highly detailed dynamic pressure-driven model of an
ASU, that is, the finest model granularity, is applied. However, the
modular-hierarchical unit operation models allow for the drag and
drop replacement of submodels and thus, the adaptation of the
model granularity. Further information on the unit operation models,
in particular the generic column model, can be found in Kender
et al.
1,4
For additional information on the generic heat exchanger
model, the interested reader is referred to Rößler et al.
39,50
All unit
operation models rely on the pressure-driven approach according to
Thomas et al.
51
In general, the plant life cycle can be divided into two phases:
plant design and plant operation. During the plant design phase,
steady-state simulation is predominant. In the (pre-)sales and equip-
ment and process design stages, steady-state simulation and optimiza-
tion are used to design the plant for its optimal operating point. In the
plant operation phase, dynamic simulation is used to reduce the over-
all plant commissioning time. When the plant is in normal operation,
the DT can be used to monitor and optimize the plant behavior (opera-
tion optimization) on different time scales applying DSM or APC.
Figure 1illustrates the typical plant life cycle of an ASU.
FIGURE 1 Simulation aspects during the life cycle of an ASU according to Kender et al.
1
with the new aspects of load change analysis and
soft sensor in stage 4
3of23 KENDER ET AL.

Further possible applications of the DT in stage 4 are its usage as
asoft sensor or for the purpose of a load change analysis (see Figure 1).
In general, the term soft sensing refers to approaches and algorithms
implemented on computer software-based systems or embedded sys-
tems which are used to estimate certain physical quantities or product
qualities in industrial processes.
52
Soft sensors can be defined as
mathematical models used to predict the behavior of real systems.
53
They can be classified in two main categories, data-driven and model-
driven.
54
The focus of this work is on model-driven soft sensors. For
more information on data-driven soft sensors, the interested reader is
referred to the works of Lin et al.,
54
Kadlec et al.
55
or Jiang et al.
52
The model-driven family of soft sensors is usually based on first prin-
ciple models, an (extended) Kalman filter, or adaptive observers.
52,55
The DT's application as a soft sensor can be associated with the cate-
gory of first principle model. The idea of using the DT as soft sensor is
as follows. The physical plant's measurement data is used as input or
as complementary data for the virtual ASU. Based on the given input
(for instance, air feed flow and pressure, product flows, indicated with
regular font in Figure 2) the remaining plant state can be calculated.
The complementary data (for instance, temperature measurement and
O
2
-analyzers in the low-pressure column (LPC), indicated with an italic
font in Figure 2) can be used to identify faults in the plant by compar-
ing the measured data with the results of dynamic simulations (bottle-
neck identification). Figure 2compares the available degree of
information using the LPC of an ASU as an example.
Using the measurement data from the conventional instrumenta-
tion as input, the DT provides full thermodynamic and fluid dynamic
information on every column tray, as well as internal column flows
and further non-measurable quantities such as the condenser/reboiler
duties. This abundance of data can be used to help with the monitor-
ing, control and optimization of industrial processes.
52
However, a
common challenge of a soft sensor, which is based on highly detailed
dynamic unit operation or plant models is the required computational
effort to solve these models. Currently, real-time capability cannot be
guaranteed for dynamic simulations of the entire plant using the finest
model granularity. However, an application of stand-alone unit opera-
tion models such as the double column system as soft sensor is possi-
ble. Furthermore, with an increase in computational capabilities the
usage of highly detailed dynamic plant models as soft sensor will
become more attractive in the future.
In this work, the potential benefits of the DT applied as soft sen-
sor are pointed out in an offline application. Load change procedures
are systematically analyzed and improved using non-measurable quan-
tities such as internal column flows. That is, the DT is used for
debottlenecking purposes. In the presented case studies, operating
and plant design data are used both as input for the basic controller
shown in Figure 3to establish the initial and end states. The remaining
plant state is predicted using the virtual ASU (first-principle models).
3|INDUSTRIAL ASU WITH ARGON
SEPARATION
In this section, the air separation process is introduced. Furthermore,
the increased complexity in terms of equipment, control, as well as
heat and process integration related to the separation of Ar is
FIGURE 2 Available data (highlighted): DT used as a soft sensor (left) and conventional instrumentation (right)
KENDER ET AL.4of23

explained in detail. In addition, the challenges and limitations for load
change procedures resulting from this increase in complexity are
described.
3.1 |Cryogenic air separation process
ASUs separate air into its main components N
2
,O
2
and Ar by means
of cryogenic distillation. The molar composition of air is as follows:
yN2,Air ¼0:78118, yO2,Air ¼0:20950, and y
Ar,Air
=0.00932.
38
Figure 3illustrates a process flow diagram of the ASU topology
with Ar separation. Here, the purification of air in molecular sieve
adsorbers is not considered. The purified air is compressed to a pres-
sure level of 0.6 MPa by the main air compressor (①). The pressurized
air (GAP, gaseous air pressurized) is then split into two streams. Both
streams enter the MHEX (②). The main air stream is cooled down
over the full length of the MHEX until it is partially liquefied. The par-
tially liquefied main air stream is then fed into the PC (⑤). The second
and significantly smaller air stream uses only part of the length of the
MHEX, is then expanded in a turbine (③) and is fed directly to the
LPC (⑥). The expansion provides the refrigeration duty required for
the cryogenic air separation.
The centerpiece of an ASU is the thermally coupled distillation
system, the double column.
48
It includes the PC at the bottom, the
condenser/reboiler or main condenser (MC, ⑦), and the LPC on top.
Here, air is separated into two of its main components: N
2
and O
2
.
The third component, Ar, cannot be separated in this column system
but in the additional distillation columns in the Ar separation part. The
PC operates at a pressure level of p
PC
≈0.5 to 0.6 MPa, whereas the
LPC operates at p
LPC
≈0.12 to 0.16 MPa. In the topology shown in
Figure 3, both columns are sieve tray columns with tray numbers of
n
tray,PC
≈50 and n
tray,LPC
≈100, which are typical values for ASUs.
1
The columns are thermally coupled via the MC, where the condensa-
tion of pure N
2
at the top of the PC at elevated pressure provides the
heat duty required to evaporate the liquid O
2
in the sump of the LPC.
The condensed liquid N
2
(LIN) is used as reflux for both columns. The
O
2
-enriched liquid air at the bottom of the PC (crude liquid oxygen
pressurized, CLOP) is used as liquid feed for the LPC. Both streams,
CLOP and LIN, are further cooled in an additional heat exchanger, the
subcooler (SC, ④), before they are fed to the LPC.
The main products of this ASU topology are gaseous O
2
(GOX),
gaseous N
2
(GAN) and liquid Ar (LAR). Furthermore, an impure N
2
stream (crude gaseous nitrogen, CGN) is withdrawn from the LPC and
vented to the atmosphere (ATM). In addition, a small amount of liquid
O
2
(LOX) is withdrawn from the bottom of the LPC as a purge stream.
Pressurized gaseous N
2
(PGAN) from the top of the PC is used as a
seal gas or product stream.
In order to produce pure Ar, two additional distillation columns,
the crude Ar (CAC, ⑧) and pure Ar (PAC, ⑩) column are required to
remove O
2
and N
2
from the Ar column feed which is withdrawn from
the LPC (crude gaseous oxygen, CGO). Both, the CAC and the PAC
are typically columns using high efficiency structured packings.
56
The
Ar column feed CGO is an O
2
-rich mixture, containing a relatively high
amount of Ar and traces of N
2
. The purpose of the CAC is to separate
O
2
from the Ar column feed CGO. Due to the low boiling point differ-
ence between O
2
and Ar (see Figure 5) a high number of theoretical
FIGURE 3 ASU topology—process flow diagram of an industrial ASU with Ar separation including the basic control layer
5of23 KENDER ET AL.

trays (n
tray,CAC
≈200) is required in the CAC. Here, the CAC is split
into two columns due to height limitations. The purpose of the PAC is
to remove the remaining traces of N
2
from the crude Ar stream crude
gaseous argon (CGAR), the top product of the CAC. Here, additional
n
tray,PAC
≈50 theoretical trays are required. The tray numbers for the
columns required for this simulation task are summed up in Table 1.
Moreover, two additional condenser/reboilers and another
reboiler are required for the separation of Ar increasing the complex-
ity of the ASU's thermal integration. The subcooled CLOP stream is
split in two, before one part is eventually fed to the crude Ar con-
denser/reboiler (⑨), whereas the other part is fed to the pure Ar con-
denser/reboiler (⑪). In the crude Ar condenser/reboiler, while
partially evaporating the CLOP at elevated pressure, the crude Ar is
condensed, generating the reflux for the CAC. Prior to that, the liquid
influx for the crude Ar condenser/reboiler is further split. One part of
this CLOP is subcooled, evaporating the liquid Ar in the pure Ar sump
reboiler (⑫) to generate vapor flow in the PAC. As for the liquid reflux
of the PAC, the other part of the first CLOP split is partially evapo-
rated in the pure Ar top condenser/reboiler. The increasing complex-
ity due to the additional Ar separation (see Figure 3, dashed line) is
explained in detail in Section 3.2.
In addition, the base control layer of the ASU is illustrated in
Figure 3. The main products, GOX and GAN, as well as the purge
stream LOX and the seal gas PGAN are subject to flow control. The
valve strokes h
v
of the corresponding product valves are adjusted to
achieve the desired amount of flow. Furthermore, the main air flow,
the amount of the Ar column feed CGO flow as well as the O
2
-
enriched liquid flow from the crude Ar condenser/reboiler are subject
to flow control. To obtain the desired air flow, the discharge pressure
of the main air compressor is adjusted. The controllers required for
the separation of Ar are explained in the following section. Further-
more, the N
2
concentration of the LIN reflux for the PC and the LPC
is controlled by a cascade of an AC and a FC. A PDC controls the
pressure difference in the PAC as a measure of the column load by
adjusting the CLOP split to influence the pure Ar sump reboiler duty
and, thus, the reboil ratio for the PAC. The remaining controllers are
level controllers. Except for the MC and the crude Ar condenser/
reboiler level, the liquid outflow is adjusted to control the levels. For
the MC level, a cascade controller is used, adjusting the turbine flow
and, hence, the refrigeration duty to meet the MC level requirements.
For the crude Ar condenser/reboiler the liquid inflow is adjusted to
control the level. The first order plus time delay method is used as a
basis for controller tuning.
57
Further information on the process of air
separation can be found in Häring
58
or Hausen and Linde.
59
3.2 |Ar separation
As already mentioned, air contains only a small quantity of Ar
(y
Ar,air
=0.00932), which indicates that the additional separation of Ar
increases the complexity of the ASU in terms of the equipment
required. Furthermore, the additional heat and process integration of
the Ar system limits the load change agility. In addition, the dynamic
simulation of an ASU with Ar separation is numerically highly chal-
lenging, which is explained later in this section. Figure 4visualizes the
Ar separation.
The Ar column feed CGO is withdrawn at a suitable location of
the LPC where the intermediate boiler Ar is accumulated. Figure 4
also shows the typical vapor concentration profile of the LPC includ-
ing the location and composition of the CGO stream. The Ar column
feed CGO typically consists mainly of O
2
, an increased amount of Ar
and traces of N
2
.
Figure 5shows the pressure of vaporization curves of N
2
, Ar and
O
2
. As can be seen, the difference between the boiling point tempera-
tures T
boil
of Ar and O
2
is small (ΔTboil,Ar,O2≈2:85 K) resulting in the
high number of theoretical trays required to separate O
2
from
the CGO stream. Since the Ar column feed CGO is withdrawn from
the LPC which operates at p
LPC
≈0.12 to 0.16 MPa, high separation
efficiency and a small pressure drop in the used packings in the CAC
are crucial. Due to the large quantity of O
2
in the CGO stream, the
CAC is operated close to total reflux.
56
The liquid reflux is generated in the crude Ar condenser/reboiler
condensing most of the CGAR vapor while partially evaporating a part
of the O
2
-rich CLOP stream at elevated pressure. Thus, the amount of
liquid reflux for the CAC is strongly dependent on the temperature
difference ΔT
cond/reb,CAC
=T
dew,CGAR
T
bub,CLOP
of the two fluids at
each side of the crude Ar condenser/reboiler, which is the driving
force for the condensation process. Both temperatures are dependent
on the pressure pand the composition z
i
of the corresponding fluid.
On the reboiler side, the pressure pis the key parameter to influ-
ence the bubble point temperature T
bub,CLOP
since the composition of
CLOP is almost constant over a wide operating range. The amount of
the Ar column feed CGO is controlled implicitly by adjusting the out-
flow of the partially evaporated CLOP stream leaving the crude Ar
condenser/reboiler. The amount of vapor leaving the crude Ar con-
denser/reboiler is used to adjust the pressure in this vessel and, thus,
the bubble point temperature T
bub,CLOP
. This directly impacts the
amount of liquid reflux in the CAC, which is decisive for the flow
resistance of the vapor in the CAC and thus the amount of CGO flow.
The liquid outflow of the crude Ar condenser/reboiler is subject to
flow control. The liquid inflow into this condenser/reboiler is used to
control its level.
On the condenser side, the composition of CGAR is crucial. On
the one hand, it is essential that the amount of N
2
in the Ar column
feed CGO is kept at a considerably low level (see Figure 4;
yN2,CGO ¼2:4105). Since N
2
is the low boiling component in air, an
increase in N
2
in the Ar column feed CGO is equivalent to a subse-
quent reduction in the dew temperature T
dew,CGAR
of the CGAR. Thus,
the temperature difference ΔT
cond/reb,CAC
decreases with an
TABLE 1 Required (theoretical) tray numbers for PC, the LPC, the
CAC, and the PAC
Column Number of theoreticalðÞtrays ntray
PC 50
LPC 100
CAC 200
PAC 50
KENDER ET AL.6of23

increasing amount of N
2
. At a certain threshold the dew temperature
of the CGAR drops below the bubble temperature of the CLOP on
the reboiler side (T
dew,CAr
≤T
bub,CLOP
) leading to the disappearance of
the liquid reflux due to a reversal of the heat flux _
Qcond=reb,CAC. That is,
with too much N
2
in the Ar column feed CGO, the Ar system col-
lapses. This event is to be prevented as it entails a prolonged product
loss during the restart of the Ar system. On the other hand, a high
purity of the Ar product LAR is required. The maximum amount of O
2
in the LAR in the demonstrated case is specified with
xO2,LAR ¼5 ppm.
60
However, an excess of O
2
in the Ar column feed
CGO does not lead to a collapse of the CAC liquid reflux due to the
similar boiling point temperatures of Ar and O
2
. Further purity con-
straints for the products of the considered ASU are shown in Table 2.
Maintaining the high purity requirements during a load change
procedures is highly challenging for an ASU with Ar separation. It is
required to limit the maximum load change rate to prevent, for
instance, temporary changes in the fluid dynamic conditions inside the
columns, which affect the separation efficiency, to be able to adhere
to the purity constraints at all time.
In addition, there is a strong dependency of the GOX product on
the CGO stream and vice versa. This further emphasizes the high
degree of process integration of an ASU with Ar separation. To visual-
ize the impact of GOX production on the Ar system, a steady-state
parameter study of the GOX product flow on the GOX and LAR prod-
uct purities is displayed in Figure 6.
Here, the amount of GOX product flow is slightly varied around
the operating point (from δ=1.2% to δ=0.5%), to represent a
FIGURE 4 Visualization of the topology of the Ar system and of a typical vapor concentration profile of the LPC including the location and
composition of the Ar column feed CGO
TABLE 2 Purity constraints for the ASU products
Product stream Threshold of O2vapor molar fraction yO2
CGAR (LAR) ≤5 ppm
PGAN ≤5 ppm
GAN ≤5 ppm
GOX ≥0.995
FIGURE 5 Pressure of vaporization curves of the main air
components
7of23 KENDER ET AL.

disturbance in plant operation. This flow variation impacts the GOX
product purity. A flow increase leads to a decrease in purity and vice
versa. The flow increase is limited by the purity threshold of the GOX
product (see Figure 6, left diagram). Here, the limit of the flow devia-
tion is δ
max
≈0.1%. A further increase in GOX flow violates the purity
threshold at first and leads eventually to the collapse of the Ar system
due to an increased amount of N
2
in the Ar column feed CGO.
The possible reduction in GOX flow is limited by LAR product
purity as visualized in Figure 6on the right. Here, only a deviation of
δ
min
≈0.001% is possible without violating any constraint. This indi-
cates that at the considered operating point the maximal amount of
LAR is withdrawn. Figure 7shows the vapor concentration profile of
the CAC at δ=0.001% and δ=0.0025% on the left and the O
2
vapor molar fraction graph of the uppermost CAC packed bed of both
cases on a logarithmic scale on the right.
As can be seen in the left diagram, the minimal deviation in GOX
product flow has a tremendous effect on the separation of O
2
from
the Ar column feed CGO although the changes in the composition of
the Ar column feed CGO (jΔy
O2,CGO
j=6.05 10
5
) are minimal. The
concentration profile of the CAC is significantly shifted upwards.
Thus, in the case of δ
0.0025%
there are insufficient trays to purify the
CGAR to the required value. The logarithmic scale (see Figure 7, right
diagram) reveals that even in the uppermost packed bed there is no
pinch but an ongoing separation of Ar and O
2
.
Eventually, the traces of N
2
are separated from the CGAR in the
PAC. The N
2
-rich fraction at the top of the PAC is vented to the
atmosphere whereas the pure Ar product LAR is withdrawn in liquid
form at the bottom of the PAC. Although the separation of the N
2
traces is a comparatively simple task, it still requires another
n
tray,PAC
≈50 as well as one additional condenser/reboiler and
another reboiler to provide the required boil-up and reflux for this col-
umn. Thus, the complexity of process integration is further increased.
The amount of LAR product is the result of the level control applied
to the sump of the PAC. The reboil ratio of the PAC is controlled via
the pressure difference control of this column. This kind of control
can be applied due to the almost constant composition of the CGAR
top product of the CAC (feed for the PAC) when the plant is operated
in its operating envelope. Thus, the effects of changing composition
on the pressure drop can be disregarded and the pressure difference
is a reliable indication for vapor flow in this column. The top of the
PAC is subject to pressure control manipulating the N
2
-rich vent
stream to the atmosphere. The pure Ar top condenser/reboiler is also
subject to level and pressure control.
It is evident that the additional separation of Ar from air is a com-
plex task. Not only the operation of this kind of plant but also its
FIGURE 6 Variation of normalized GOX product flow—impact on GOX product (left) impact on LAR product (right)
FIGURE 7 Variation of normalized GOX product flow—impact on
the CAC concentration profile
KENDER ET AL.8of23

dynamic simulation is challenging. The large number of required theo-
retical trays n
tray,total
≈400 and the accuracy requirements of the heat
exchanger models result in a large system of differential and algebraic
equations that needs to be integrated over time. In total, the pres-
ented virtual ASU contains 2011 differential and 57,325 algebraic
equations. In addition, the desired product purities (ppm scale) are
challenging for numerical simulation due to the solver tolerances to be
used for accurate dynamic simulations. Furthermore, the small differ-
ence between the boiling temperatures of Ar and O
2
and the resulting
demands on the separation task increase the accuracy requirements
for the calculation of fluid properties. Moreover, due to the small
quantity of Ar in air, there is a wide range of different magnitudes of
process streams which complicates the proper conditioning of the
equation system to be solved.
61
Besides, the high degree of heat and process integration of
an ASU with Ar separation increases the complexity of a load
change procedure further. Since undesirable effects, such as con-
centration shifts, as a result of an elevated load change rate,
quickly affect the entire ASU state due to degree of integration,
the importance of limiting the load change rate as a precautionary
measure is emphasized yet again. However, since flexible opera-
tion requires fast load changes, appropriate measures are required
to cope with these challenges. Therefore, in the following
section the SLM concept presented, which allows to increase the
load change rate of an ASU with Ar production without violating
purity requirements.
4|SMART LIQUID MANAGEMENT
As already outlined in the work of Miller et al.
41
and Cao et al.,
19,42
the (preemptive) utilization of cryogenic liquids during a load change
procedure allows for an increase of the load change agility and leads
to economical benefits. In this work, the SLM concept is developed,
which allows for faster load change procedures by preemptively and
systematically shifting the liquid in the column sumps of the PC and
the CAC during the presented load change procedures in Section 5.
The main idea of the SLM is to prevent a disproportionate accu-
mulation of the excess liquid holdup in the MC by actively distributing
it among all column sumps. Thus, the level setpoints of the PC and the
CAC are adjusted to their values optimized for part-load operation.
These values are determined in additional dynamic simulations
replacing the level controller of the corresponding column sumps with
flow controller. The liquid outflows of each sump are ramped down
linearly to their part-load value, which leads to the optimal level
setpoint. In addition, the changes of these level setpoints are shifted
in start time and duration compared to the remaining setpoint
changes. The temporal modifications to the level setpoints are a result
of additional simulation studies using the S-factor S
i
as indicator,
which can be used to characterize the separation of the component
ion a column tray or in a column section. It is defined as
Si¼Ki
_
L=_
G,ð1Þ
FIGURE 8 Controller inputs for the turn-down: normalized GOX flow (upper left), normalized air flow (lower left), normalized CGAR flow
(upper right) and normalized CGO flow (lower right)
9of23 KENDER ET AL.

where K
i
represents the vapor–liquid equilibrium ratio of component i,
and _
L=_
Gis defined as the ratio of liquid to gas flows of the considered
tray or column section. This figure can be related to the consider-
ations of Edmister.
62
Its general applicability to the distillation col-
umns in ASUs is shown in Ecker et al.
63
The S-factor quantifies,
whether the component iis stripped downwards (S
i
< 1), rectified
upwards (S
i
> 1) or accumulated in the considered part of the column
(S=1). Therefore, it can be used to quantify the effects of adding
excess or withholding liquid on the LPC fluid dynamics and separation
efficiency. In the SLM concept, the S-factor S
i
is mainly used as an
early indication of high boiler (GOX) purity in the MC to meet the
required purity constraints. This can be achieved by keeping the S-
factor S
i
, and, thus, the separation efficiency in the LPC column
section above the MC constant during the considered load change.
In the next section, the load change procedures of the presented
ASU with Ar separation are analyzed and the impact of SLM on the
maximum possible load change rate is evaluated. Based on the abun-
dance of data, these studies are intended to give a detailed insight
into the behavior of an ASU with Ar separation during a load change
procedure. In addition, as the SLM concept is based on quantities
which can hardly be measured in an industrial plant, the additional
value of the DT used as soft sensor is emphasized. Thus, further effort
required to overcome the challenges of the DT's real-time application
is justified.
5|CASE STUDIES
In the following, two load changes are analyzed via dynamic simula-
tions using the DT: a 50% turn-down and a 50% turn-up scenario. The
turn-down starts from the ASU's nominal operating point of 100%
load. The term load refers to the amount of main product GOX. The
plant load is then reduced to 50% load with the respective adjust-
ments to the remaining plant to ensure optimal part-load operation.
To reach the initial state of the turn-down scenario, a warm start-up
simulation as explained in Kender et al.
40
was conducted. The initial
state of the turn-up corresponds to the final state of the turn-down
scenario using the innovative SLM concept (see Section 4). Both sce-
narios are simulated with a load change rate of 8% min
1
, which is sig-
nificantly faster than a state-of-the-art load change procedure for
ASUs with Ar separation. The load change procedures are analyzed to
identify challenges and limitations using the abundance of transient
simulation data which is available using the DT. For the dynamic simu-
lation of the case studies, a Linde proprietary backward differentiation
formulas (BDF) solver was used. Further details on this solver can be
found in Kronseder.
64
An integration tolerance of 10
4
was chosen
by analogy to Kender et al.
1
Furthermore, the Soave–Redlich–Kwong
(SRK) cubic equation of state is used by analogy to previous
works
1,3,4,38,40
to describe the vapor liquid equilibrium of the ternary
mixture N
2
,O
2
, and Ar. All the simulations were conducted on a stan-
dard workstation with an Intel
®
Core™i5-7500 CPU (at 3.40 GHz)
with 32 GB RAM.
5.1 |Turn-down
The load change rate of the turn-down is limited due to the adherence
to purity constraints. The main challenge during a turn-down proce-
dure is to prevent the loss of high boiler purity (GOX) due to the
reduction in main air feed and the resulting decrease in the reboil ratio
in the LPC since the MC duty _
QMC decreases. As a further conse-
quence of the reduced vapor flow through the plant, a temporary
excess of liquid holdup can be observed in each column, pouring from
each (theoretical) tray into the column sumps. The excess liquid has
an increased amount of low boiler of the corresponding column which
affects the purity of the high boiler in each column. In addition, the
enhanced liquid pouring in the LPC is an additional challenge since it
increases the amount of N
2
in the liquid flowing down the LPC. This
can increase the molar fraction of N
2
at the Ar transition, which has to
FIGURE 9 Controller inputs for the turn-down: PC sump level
(top), CAC
1
sump level (middle) and sump CAC
2
level (bottom)
KENDER ET AL.10 of 23

be prevented to avoid a collapse of the fluid dynamics of the Ar sys-
tem (see Section 3). However, the purities of the low boiling compo-
nents N
2
and Ar are not critical during a turn-down procedure. The
purity constraints can be seen in Table 2.
Two different cases are compared for the turn-down. In the first
case, all controller setpoints for composition, flow and pressure con-
trol (see Figure 3for the control loops) are ramped down linearly to
their part-load values. The level setpoints for all condenser/reboilers
remain constant at 100% to keep the condenser blocks covered in liq-
uid at all times. In addition, the remaining level setpoints for the col-
umn sumps of the PC and both the CACs also remain at their nominal
value of 100%. This case is referred to as no liquid management (NLM).
In the second case, SLM as described in Section 4is applied.
For the analysis of the turn-down scenario a time period of
85 min is considered. In the first 20 min the ASU is operated in
steady-state at 100% load. Then at t
start
=20 min the turn-down
starts. At t
end
=26.25 min the required setpoint changes of the entire
control layer for part-load operation are finished. The total duration is
Δt=6.25 min, which corresponds to a load change rate of 8% min
1
.
The required setpoints for the part-load operation are pre-calculated
for an optimal 50% load case in an additional steady-state simulation
based on plant design data and all setpoint changes are linear in
nature. The term optimal refers to a maximized Ar yield at a minimum
power consumption for 50% load. The described load change proce-
dure corresponds to a state-of-the-art feedforward control.
Although not all relevant parameters have reached their final
part-load values at t=85 min, this time span is sufficient to describe
all relevant aspects of the plant response during the turn-down. In
some cases, the final steady-state is obtained after several more
hours, for instance the purities of the Ar products CGAR and LAR.
However, for a successful load change procedure, it is essential to
establish constant flow rates throughout the ASU, especially with
regard to column fluid dynamics. The slow concentration shifts do not
need to be finished, as the changes remain minor and the purity con-
straints according to Table 2are met. The required CPU time for the
simulation of both cases is approximately 1 h and 45 min on the used
workstation. The relevant setpoint changes for the turn-down are
presented in Section 5.1.1. Afterwards, the plant response and the
impact of SLM are discussed in Section 5.1.2.
5.1.1 | Controller inputs
In the following, the relevant controller inputs of the turn-down are
presented. Figure 8shows the setpoint changes for the GOX product
_
VGOX (upper left), the main air _
VAir (lower left), the CGAR _
VCGAR (upper
right) and the CGO flow _
VCGO (lower right) Furthermore, the start and
end times of the turn-down are marked with gray dotted vertical lines
in all of the following figures. In addition, except for molar fractions,
all considered parameters are normalized with respect to their nomi-
nal value at 100% load. This is indicated only in the figure captions
and the axis labels. In the text, normalized and non-normalized param-
eters are not distinguished.
In the case of NLM, all presented setpoint changes visualized in
Figure 8start and end at the same time. In the case of SLM, the dura-
tion of the setpoint changes for CGO, the Ar column feed, as well as
CGAR are twice as long (Δt=12.5 min). Figure 9shows the levels
L
PC
,L
CAC,1
, and L
CAC,2
and their setpoint changes for the PC and both
CACs. The index 1 refers to the first CAC column downstream of
the LPC.
For SLM, the setpoint changes of the levels start earlier at
t=16.875 min. Furthermore, the duration of the setpoint changes
varies. For the PC as well as the CAC
1
, the end of the setpoint change
is at t=29.375 min (Δt=12.5 min) and for the CAC
2
at
t=38.625 min (Δt=18.75 min). In addition, Figure 9illustrates that
the level control of the PC shows a higher inertia compared to the
FIGURE 10 Plant response during the turn-down: O
2
vapor
molar fraction of the top products of the distillation columns. LPC-
GAN (top), PC-PGAN (middle) and CAC-CGAR (bottom)
11 of 23 KENDER ET AL.

level controls of the CAC. As shown in Figure 3, the outflow of the
CAC sumps and thus the level are controlled via pumps, which allows
for a faster control compared to the PC level. The setpoint changes of
the remaining control loops (see Figure 3) to establish optimal part-
load operation, for instance, GAN product decrease or LPC pressure
adjustment, are not of particular importance for this case study and
therefore not visualized.
5.1.2 | Plant response
In this section, the plant response of the turn-down is presented. It is
structured as follows: first, the low boiling components N
2
at the top
of the PC and the LPC as well as Ar at the top of the CAC are consid-
ered. Then, the focus is on the lower part of the LPC including the Ar
column feed CGO and the high boiler O
2
(GOX) in the MC. After-
wards, the response of the Ar system is presented before LPC fluid
dynamics are discussed in detail.
Low boiling components
Due to the temporarily increased reflux during the turn-down, the
purities of the low boiling components N
2
and Ar are not critical. This
is illustrated in Figure 10. Here, the O
2
vapor mole fractions yO2,GAN,
yO2,PGAN, and yO2,CGAR of the process streams GAN (low boiler LPC),
PGAN (low boiler PC) and CGAR (low boiler CAC) are plotted
over time.
For all three streams, a maximum O
2
content of 5 ppm is not
exceeded. The difference of the O
2
purities of GAN and PGAN
between NLM and SLM can be explained with the different flow con-
ditions inside the PC and the LPC, which are caused by the different
handling of the excess liquid holdup in both cases.
LPC—lower part
Figure 11 shows the response of the lower part of the LPC, which
contains the most critical parameters during the turn-down scenario.
The level of the MC L
MC
(top) and the O
2
vapor molar fraction of the
GOX product yO2,GOX (bottom) are shown on the left side, whereas
the Ar column feed CGO vapor molar fractions (yO2,CGO at the top and
yN2,CGO at the bottom) are shown on the right side.
The graphs on the left side of Figure 11 illustrate the main chal-
lenges of the turn-down procedure. Without transferring the excess
liquid holdup to the corresponding column sumps, it is all accumulated
in the MC, causing the level to rise significantly (see 11 upper left).
Looking at NLM, the MC level rises to a maximum of L
MC,max
=139%
at t=41.8 min before it slowly decreases again. Applying SLM, the
MC level L
MC
initially decreases due to the fact that the level
setpoints are changed on purpose prior to the remaining load change
procedure (see Figure 9). However, the variation of the MC level L
MC
remains in a range of ±4%, which is not safety critical as the con-
denser is still covered with liquid sufficiently.
The lower left side of Figure 11 visualizes the molar fraction
yO2,GOX of the GOX product. In the case of NLM, at t
start
=20 min, the
FIGURE 11 Plant response during the turn-down: MC level (upper left), O
2
molar fraction of the GOX product (lower left), O
2
molar fraction
of the Ar column feed CGO (upper right), N
2
molar fraction of the Ar column feed CGO (lower right)
KENDER ET AL.12 of 23

O
2
vapor molar fraction yO2,GOX starts to decrease. The constraint for
the product purity yO2,GOX ≥0.995 is violated at t=25.07 min. At
t=41.42 min, the minimum O
2
vapor molar fraction of yO2,GOX,min ¼
0:985 can be observed. Afterwards, yO2,GOX increases and the purity
requirement is eventually met again at t≈5 h which is not displayed.
With SLM, the purity constraint for the GOX product is met at all
times. This can be explained by using the composition of the liquid
holdup in the sump of the CAC
1
(see Figure 12) and the S-factor of Ar
S
Ar
at the first column tray above the MC at the bottom of the LPC
(see Figure 13) which is explained later in this section.
At the lower right of Figure 11, the graph of the N
2
vapor molar
fraction yN2,CGO of the Ar column feed CGO illustrates another diffi-
culty of a rapid turn-down procedure. As can be seen in the case of
NLM, yN2,CGO increases rapidly after the setpoint changes are com-
pleted at t
end
=26.25 min. At t=33.53 min a maximum of the N
2
molar fraction of yN2,CGO =0.00403 is reached. This can be explained
with the increased molar fraction of N
2
in the excess liquid holdup, which
is pouring down the LPC to accumulate in the MC. During the presented
turn-downtheincreasedamountofN
2
intheArcolumnfeedCGOisnot
sufficient to significantly impact the crude Ar condenser/reboiler and,
thus, the liquid reflux of the CAC. However, a larger N
2
intake could occur
under similar operating conditions leading to collapsing fluid dynamics of
the Ar system. To avoid this, SLM can be applied resulting in an almost
constant vapor molar fraction yN2,CGO throughout the turn-down.
The graph of the O
2
vapor molar fraction yO2,CGO of the Ar col-
umn feed CGO (upper right) is similar to the graph of the O
2
vapor
fraction of the GOX product yO2,GOX. In addition, a small excerpt is
shown in this diagram, which illustrates the course of yO2,CGO over
1350 min. It shows that for both cases, a constant graph is eventually
reached at t≈200 min =3.33 h for SLM and t≈1000 min =16.67 h
using NLM. Thus, a steady-state for the ASU is reached, as a constant
course of yO2,CGO requires stationary LPC fluid dynamics. A require-
ment for this is a constant MC duty _
QMC, which is representative for
the overall plant state. However, using NLM, the magnitude of the
decrease in yO2,CGO after the setpoint changes are completed at
t
end
=26.25 min is larger compared to yO2,GOX . By analogy to the
GOX product, the slight decrease in yO2,CGO during the setpoint
changes can be explained using the S-factor S
Ar
(see Figure 13). The
significant drop of yO2,CGO to a minimum of yO2,CGO,min ¼0:71 at
t=54.15 min can be explained due to the composition changes of the
liquid holdup in the sump of the CAC
1
(see Figure 12) over time.
Ar system
Now, the relevant response of the Ar system is presented. How-
ever, since the Ar system is highly dependent on the Ar column
feed CGO, the graphs on the right side in Figure 11 are of addi-
tional importance here. Figure 12 shows the development of the
bottom liquid molar fractions of O
2
xO2,CAC1(top) and of Ar xAr,CAC1
(bottom) over time.
In the case of NLM, an increase in the molar fraction of Ar
xAr,CAC1at the expense of O
2
xO2,CAC1can be observed. This is a result
of the excess liquid holdup which accumulates in the column sumps.
In the sump of the CAC
2
, an Ar-rich liquid accumulates. The liquid
holdup in the CAC
1
contains mainly O
2
. The Ar-rich liquid from the
CAC
2
is then fed to the CAC
1
causing an accumulation of Ar with a
temporal delay. At t≈54.17 min, a maximum of the molar fraction of
Ar xAr,CAC1,max ¼0:289 can be observed in the sump of the CAC
1
. This
liquid is then fed back to the LPC. Since the LPC feed stage of the
reflux from the CAC
1
is identical to the withdrawal stage of the Ar col-
umn feed CGO, it impacts the CGO composition resulting in the graph
of the O
2
vapor molar fraction yO2,CGO at the upper right in Figure 11
after the end of the setpoint changes. However, the effect of the
CACs sump liquid on yO2,CGO is delayed in time compared to the
impact of the internal flow condition changes in the LPC, which influ-
ence the composition of the Ar column feed CGO right after the start
of the setpoint changes.
In the case of SLM, the Ar-rich liquid holdup is held back in the
CAC
2
sump preventing the accumulation of Ar in the sump of the
CAC
1
and, thus, preventing the reduction of the O
2
vapor molar frac-
tion yO2,CGO. In addition, due to the specific manipulation of LPC fluid
dynamics (see Figure 13), the O
2
vapor molar fraction yO2,GOX of the
GOX stream (see Figure 11, lower left) increases during the period of
setpoint changes.
LPC fluid dynamics
Finally, the focus is on LPC fluid dynamics during the turn-down.
Figure 13 shows the S-factor S
Ar
of Ar at the first column tray of the
LPC right above the MC (bottom) over time. The S-factor S
Ar
is
FIGURE 12 Plant response during the turn-down: Composition
development of the liquid holdup in the sump of the CAC
1
over time.
Liquid molar fraction of O
2
(top), liquid molar fraction of Ar (bottom)
13 of 23 KENDER ET AL.

defined according to Equation (1). As this parameter strongly influ-
ences the GOX purity, there will be references to the lower left dia-
gram of Figure 11.
Since the primary purpose of the column trays between the MC
and the withdrawal of Ar column feed CGO is the separation of Ar
and O
2
, the S-factor of Ar is of particular interest. The initial value of
S
Ar
is slightly below one. That is, there is a separation between Ar and
O
2
right above the MC. In detail, Ar is stripped downwards. With the
beginning of the load change, in the case of NLM, the S-factor S
Ar
decreases until it reaches a minimum at t=29.1 min. The minimum
value of the S-factor is S
Ar,min
=0.5, which is approximately the half
of the initial value. Afterwards, the S-factor S
Ar
eventually rises until,
at t=39.75 min, it reaches a value of S
Ar
≥1.
The graph of the S-factor S
Ar
canbeusedtoexplainthedevelopment
of the O
2
vapor molar fraction yO2,GOX over time, which is shown in the
lower left diagram of Figure 11. Using NLM, the decrease in the O
2
molar fraction yO2,GOX is evoked by S
Ar
< 1 due to the fact that Ar is
stripped towards the MC. With a delay of approximately 1.5 min after
S
Ar
≥1 (at t=39.75 min), yO2,GOX reaches its minimum and rises again
due to the fact that with S
Ar
≥1, Ar is increasingly rectified upwards.
As can be seen, the S-factor S
Ar
is an early indication of the
behavior of the GOX product purity yO2,GOX . Moreover, the
S-factor S
Ar
is used to derive the setpoint changes of the PC and
CACs sump levels in previous simulation studies. To prevent the loss
of GOX product purity yO2,GOX, the S-factor S
Ar
can be manipulated
accordingly. By applying SLM, that is, varying the liquid reflux to the
LPC by adjusting the level setpoints of the PC and the CACs (see
Figure 9), it is possible to increase the S-factor S
Ar
before the setpoint
changes start at t
start
=20 min evoking an increase in O
2
vapor molar
fraction yO2,GOX (see Figure 11, lower left). The liquid reflux to the
LPC is manipulated in a way that the minimum of the S-factor is
increased from S
Ar,min
=0.499 to S
Ar,min
=0.725 resulting in the
adherence of the GOX product purity constraints. Afterwards the
S-factor S
Ar
oscillates around one with a small amplitude due to
enduring changes of the internal column flows until it eventually con-
verges to a value slightly below one.
To sum it up, the SLM is used to manipulate LPC fluid dynamics during
the turn-down, which allows for the adherence to the GOX product purity
yO2,GOX during the whole load change procedure. Another aim of the
SLM is to prevent the accumulation of Ar in the CAC
1
sump (see
Figure 10) by accumulating the Ar-rich excess liquid holdup in the
CAC
2
, to prevent this liquid from being fed back to the LPC. The
prolonging of the setpoint changes of the Ar system (see Figure 8,
right side) is an additional measure to increase the GOX product
purity yO2,GOX during the load change procedure by temporarily
removing the intermediate boiling component Ar from the LPC dispro-
portionately. However, the influence of this deceleration is compara-
tively small.
The magnitude, start time and duration of the setpoint changes
shown in Figure 9are derived from additional simulation studies using
the S-factor S
Ar
as indicator (see Figure 13), which is explained in
Section 4. However, a constraint for the level setpoint changes is, for
instance, the impact on the MC level (see Figure 11, upper right).
Here, the early start times of the setpoint changes of the PC and CAC
levels result in a decrease in the MC level L
MC
before the turn-down
starts at t=20 min. This decrease needs to be minimized. Further
constraints are the actual sump geometries, which limit the maximum
liquid level of the corresponding column.
Eventually, the power consumptions of both cases are compared
as an indication of the operational expenses (OPEX). The main con-
tributors to the ASU's energy balance are the main air compressor and
the turbine. Since the graphs of the main air flows (see Figure 8, upper
left) of SLM and NLM are identical, the MAC power consumptions are
identical as well. Compared to the energy intake of the main air com-
pressor, the contribution of the turbine is marginal. Thus, the OPEX of
both concepts is equal.
This study outlines the importance and benefits of applying a
DT of an ASU to improve plant operations. Due to the abundance of
data, the DT provides a highly detailed insight into transient plant
behavior during load change procedures. It is of particular impor-
tance to analyze non-feasible load changes, that is, violating purity
constraints, in offline studies. This allows for the identification of
bottlenecks and the development of operational concepts such as
SLM and, thus, faster load change procedures. The SLM concept is in
accordance with the experience of plant operators and automation
engineers to accelerate load change procedures of ASUs at Linde.
However, these results are in contrast with the findings of Cao
et al.
42
as they claim that a preemptive control action tend to result
in plant closer to its boundaries. In this study, the preemptive action
of SLM is required to successfully conduct this load change proce-
dure without violating any purity constraint, that is, to increase the
load change rate of the ASU. An additional benefit of the DT is that it
allows quantification and visualization of the effects of operating
strategies on plant operation during load change procedures. Further-
more, by means of dynamic simulation, the DT enables an in-depth
analysis and optimization of existing operating concepts, which are
based on many years of experience. In addition, non-measurable
quantities such as the S-factor S
Ar
are identified as key parameters to
improve the presented turn-down, emphasizing the importance of a
FIGURE 13 Plant response during the turn-down: S-factor of Ar
S
Ar
at the first column tray in the LPC above the MC
KENDER ET AL.14 of 23

DT of the ASU or only of the LPC as a soft sensor for (flexible) plant
operations.
5.2 |Turn-up
During a fast turn-up, the main challenges are to compensate for a
temporary lack of liquid holdup on each column tray and the adher-
ence to the purity constraints for the low boiling components (see
Table 2). Both challenges are a result of an increase in the reboil ratio
in all columns during the load change. This is a result of a rapid
increase in the main air flow _
VAir coupled to an increased MC heat
duty _
QMC. Due to the higher amount of vapor flow, more liquid
holdup is required on each column tray to overcome the increased
flow resistance. Thus, the liquid flow to the corresponding column
sumps is slowed down, which leads to a level decrease in the
corresponding column sumps and the MC level L
MC
. This is challeng-
ing for two reasons. First, a decrease in MC level L
MC
impacts the duty
_
QMC and second, the MC needs to be covered in liquid to a certain
extent at all times for safety reasons. The decelerated liquid flow can
be observed in all columns.
Conversely, this means that during a turn-up fluid dynamics in the
LPC promote the high boiling component O
2
in the GOX product. The
separation of Ar between the withdrawal of CGO and the MC is
enhanced since a decrease in the liquid flow increases the S-factor
(see Equation 1). Here, the idea of SLM is to temporarily enhance the
liquid flow to the LPC at the expense of GOX purity yO2,GOX without
violating any constraints. Thus, on the one hand, a major drop in the
MC level L
MC
can be prevented. On the other hand, the adherence to
the low boiler purities can be achieved. This can be accomplished by
using the excess liquid, which is buffered in the PC and CAC sumps
during the turn-down.
In the case of SLM, the level setpoints of the PC and the CAC
areadjustedinstarttimeanddurationwithregardtotheremaining
load change. Furthermore, the setpoint changes for the Ar system
as well as the LIN reflux to the LPC are prolonged using SLM. In the
case of NLM, all controller setpoints for composition, flow and pres-
sure control (see Figure 3for the control loops) are ramped up line-
arly to their full load values. The level setpoints for all condenser/
reboilers remain constant at 100% to keep the condenser blocks
coveredinliquidatalltime.Inaddition,theremaininglevel
setpoints for the column sumps of the PC and both the CACs also
remain at their initial value.
For the analysis of the turn-up scenario, a time period of 250 min
is considered. Starting at the final steady-state of the turn-down with
SLM at 50% load, the turn-up starts at t
start
=20 min and ends at
t
end
=26.25 min. The total duration is Δt=6.25 min. The required
setpoints for the load change can be taken from steady-state opera-
tion at 100% load, which is equal to the initial state of the turn-down
and the setpoint changes are linear in nature.
Although not all relevant parameters have reached their final part-
load values at t=250 min, this time span is sufficient to describe all
FIGURE 14 Controller inputs for the turn-up: normalized GOX flow (upper left), normalized air flow (lower left), normalized LIN flow (upper
right) and normalized CGO flow (lower right)
15 of 23 KENDER ET AL.

relevant aspects of the plant response during the turn-up. In some
cases, the final steady-state is obtained after several days, for instance
the purity of the GOX product in the case of NLM. By analogy to the
turn-up scenario, a successful load change does not require all concen-
trations to reach steady-state as long as the changes are minor and the
purity constrains are met. The required CPU time for the simulation
using SLM is approximately 1 h and 15 min on the used workstation.
The NLM case required a CPU time of approximately 11 h due to the
N
2
breakthrough, which is explained later in Section 5.2.2. The relevant
setpoint changes for the turn-up are presented in Section 5.2.1.The
plant response and the impact of SLM are discussed in Section 5.2.2.
5.2.1 | Controller inputs
This section presents the relevant controller inputs for the analysis of
the turn-up. In contrast to the turn-down, noticeable deviations
between the setpoint changes and the controlled variables occur dur-
ing the turn-up due to a N
2
breakthrough, which is explained in detail
in Section 5.2.2. The N
2
breakthrough affects the whole plant empha-
sizing the high degree of heat and process integration of an ASU with
Ar separation.
Figure 14 shows the setpoint changes of the turn-up for the GOX
product _
VGOX (upper left), the main air _
VAir (lower left), the LIN _
VLIN
(upper right), and the Ar column feed CGO flow _
VCGO (lower right).
The CGAR flow change is not shown here as the duration and shape
of the CGAR and CGO setpoint changes are identical. In addition, the
start and end times of the load change are marked with vertical gray
dotted lines in all of the following figures.
By analogy to the turn-down, in the case of NLM, all setpoint
changes for the turn-up start and end at the same time. However,
apart from the main air flow _
VAir (lower left), the graphs of the con-
trolled variables differ from the setpoints. As for the LIN reflux _
VLIN to
the LPC (see Figure 14, upper right), the course of the actual LIN flow
can be explained by the type of control used (see Figure 3). Here, a
trim control configuration is used. That is, the manual output of the
AC is changed during the turn-up (feedforward) but the controller is
allowed to correct its output in a specific range (ε
Trim,AC
=22.5%)
around the manual output (feedback) to fulfill its task. This results in
the deviation of actual LIN reflux and the setpoint. In the case of SLM,
the deviations of setpoint and controlled variable are marginal. In
addition, the setpoint change for the LIN reflux _
VLIN to the LPC is pro-
longed ending at t=32.5 min with a duration of Δt=12.5 min.
By using SLM, the setpoint change for the Ar system (see
Figure 14, lower right) is shifted in time. It starts at t=26.25 min and
ends at t=32.5 min. However, the duration of the setpoint changes
remains Δt=6.25 min. Further, no deviations between setpoint and
controlled variable can be observed.
In the case of NLM, an oscillating behavior of the actual CGO
flow _
VCGO around its setpoint starting at t≈145 min can be seen,
which is a result of the N
2
breakthrough. This term refers to the
vapor molar fraction yN2,CGO of the Ar column feed CGO. If yN2,CGO
FIGURE 15 Controller inputs for the turn-up: LPC top pressure (upper left) and normalized turbine air flow (upper right), plant response for
the normalized MC pressure (lower left) and normalized MC heat duty (lower left)
KENDER ET AL.16 of 23

rises above a critical threshold, and starts to influence the crude Ar
condenser/reboiler duty _
Qcond=reb,CAC and, thus, the CAC fluid dynam-
ics, the term N
2
breakthrough is used. In general, this circumstance
causes oscillations of most of the considered parameters in the case
of NLM.
Using NLM, the behavior of the GOX product flow _
VGOX between
t≈23.33 min and t≈41.67 min is a result of the size of the GOX prod-
uct valve and the increased turbine flow (see Figure 15, upper right)
which is required due to the MC level control. The increased turbine
flow _
VAir,turb has a major impact on the further course of the entire
turn-up, which is discussed below.
Figure 15 shows the setpoint changes of the LPC top pressure
p
LPC,top
(upper left) as well as the turbine flow _
VAir,turb resulting from
the MC level control (upper right) and the plant response for the MC
pressure p
MC
(lower left) and the MC duty _
QMC (lower right) for both
cases. The graphs of these values are required to explain the devia-
tions between setpoint and controlled variable in the case of NLM,
illustrated in Figure 14.
ByanalogytothecontrolschemeoftheLINrefluxtothe
LPC, a trim control configuration is used for the MC level control
(turbine flow). In the NLM case, a larger range for possible cor-
rections of the turbine flow is required due to the massive lack
of liquid holdup in the MC (see Figure 18,upperleft).This
explains the different upper boundaries for the turbine flow of
_
VAir,tur b,ub ¼124:4%(NLM) and _
VAir,turb,ub ¼101:5%(SLM). A decrease
in MC level L
MC
requires additional refrigeration duty (cryogenic liquid
make-up).
However, the total amount of air _
VAir is equal in both cases. This
results in different amounts of air fed to the PC, which leads to differ-
ent MC duties _
QMC (lower right) causing different fluid dynamic condi-
tions in the LPC. Thus, a higher turbine flow results in a higher gas
load in the upper part of the LPC but a lower gas load in the part
below the turbine feed tray. This leads to the effect that, although the
setpoint changes for the LPC top pressure are identical in both cases,
the course of the MC pressure p
MC
differs. In the case of NLM, the
MC pressure levels are below the SLM pressure levels until
t≈145 min. Afterwards, using NLM, p
MC
starts oscillating around the
constant course of p
MC
using SLM. In addition, the pressure increase
in the MC is slower in the NLM case compared to SLM. The more
inert behavior of _
VGOX using NLM (see Figure 14, upper left) is a result
of the slower increase in the MC pressure p
MC
although the GOX
product valve is opened completely.
Figure 16 shows the levels L
PC
,L
CAC,1
, and L
CAC,2
and their
setpoint changes for the PC and both CACs.
By analogy to the turn-down scenarios, all level setpoint
changes start prior to the actual load change at t=16.875 min.
Here, all three setpoint changes end at a different time. The setpoint
change for the PC ends at t=26.25 min, for the CAC
1
at
t=32.5 min, and the CAC
2
at t=38.75 min. In addition, it is very
noticeable that the end values of the level setpoint changes for the
PC L
PC,end
=118% and for the CAC
2
LCAC2,end ¼88%differ from the
initial state (100%). Thus, the level setpoint changes of the turn-down
and turn-up are non-symmetrical. Despite this being interesting and
requiring further investigation, it is not subject of this work, consider-
ing the length of the article.
5.2.2 | Plant response
In the following, the plant response during the turn-up is presented.
First, the behavior of the low boiling components N
2
at the top of the
PC and the LPC as well as Ar at the top of the CAC is discussed. Then,
the focus is on the lower part of the LPC including the Ar column feed
CGO and the high boiler GOX in the MC. Afterwards, the response of
the Ar system is presented with regard to the N
2
breakthrough.
Finally, LPC fluid dynamics are discussed in detail.
FIGURE 16 Controller inputs for the turn-up: PC sump level
(top), CAC
1
sump level (middle) and CAC
2
sump level (bottom)
17 of 23 KENDER ET AL.

Low boiling components
A major challenge of the turn-up is to preserve the purity require-
ments for the low boiling components in the GAN, PGAN and CGAR
streams due to an increased vapor flow through the columns and the
resulting deceleration of liquid flow. Figure 17 shows the O
2
vapor
molar fractions yO2,GAN,yO2,PGAN , and yO2,CGAR of the GAN, PGAN, and
CGAR streams over time.
In the case of NLM, the purity constraints of GAN and CGAR are
violated during the load change. However, the purity constraint of the
PGAN stream is met during the entire load change with only minimal
deviations from its initial value. In the case of SLM, only the purity
constraint of the GAN stream is minimally violated for a short period
of time. The graphs of the GAN and PGAN purities yO2,GAN and
yO2,PGAN are a result of the behavior of the LIN reflux _
VLIN (see
Figure 14, upper right) over time. In the case of NLM, the LIN reflux
_
VLIN increases more slowly compared to the SLM case resulting in a
higher PGAN purity due to increased reflux to the PC. However, the
high PGAN purity yO2,PGAN in case of NLM comes at the expense of
the GAN purity yO2,GAN, which can be seen at the top of Figure 17.In
the case of SLM, the deceleration of the LIN reflux setpoint change
leads to a more equal distribution of LIN to either the PC or the LPC.
Thus, both purity constraints yO2,PGAN and yO2,GAN can be met apart
from the minimal violation of the GAN purity starting at t=27.28 min
until t=30.52 min with a maximum of yO2,GAN,max ¼5:61 ppm. Here, a
bottleneck for the load change rate is identified, which cannot be
solved by the presented operational strategy (SLM). This requires a
potential structural measure at the plant, for instance, an additional
LIN buffer vessel between the PC and the LPC.
Regarding CGAR purity yO2,CGAR, in the case of NLM, the purity
constraint is violated at t=70.25 min and the graph oscillates as a
result of the N
2
breakthrough starting at t≈145 min. In the case of
SLM, the CGAR purity constraint can be met during the entire load
change procedure. The delay of the setpoint changes of the Ar system
(see Figure 14, lower left) is an additional measure to keep the O
2
molar fraction of the CGAR stream yO2,CGAR ≤5 ppm.
LPC—lower part
Figure 18 illustrates the plant response regarding the MC level L
MC
(top) and the O
2
vapor molar fraction yO2,GOX of the GOX product
(bottom) on the left side, whereas the Ar column feed CGO vapor
molar fractions (yO2,CGO at the top and yN2,CGO at the bottom) are
shown on the right side.
The graph on the upper left side of Figure 18 illustrates the
impact of the fast increase in the reboil ratio in the LPC and the
resulting decelerated liquid flow to the columns sumps. In case of
NLM, the MC level L
MC
decreases rapidly with the beginning of the
turn-up at t
start
=20 min until it reaches its minimum L
MC,min
=60.3%
at t=37.55 min. Afterwards, it starts to converge to its initial value
slowly. The significant decrease in the MC level L
MC
requires an
increased amount of turbine flow _
VAir,turb (see Figure 15, upper right),
which eventually causes the N
2
breakthrough. By analogy to all the
remaining values affected by the N
2
breakthrough, the MC level L
MC
starts oscillating at t≈145 min. Furthermore, the decrease in MC level
would be intolerable in real plant operations emphasizing the impor-
tance of an in silico investigation of this procedure using the DT. With
SLM, the MC level L
MC
increases at first, as the level setpoint changes
start prior to the remaining load change (see Figure 16). The variation
of the MC level L
MC
is reduced to a range of ±7%.
The graph of the O
2
vapor fraction yO2,GOX of the GOX product is
shown in the lower left diagram in Figure 18. As can be seen, using
NLM, the O
2
vapor molar fraction of the GOX product yO2,GOX starts
to increase with the beginning of the turn-up until it reaches its maxi-
mum yO2,GOX,max ¼0:9985 at t=54.25 min. Afterwards, it starts to
decrease due to the increased turbine flow _
VAir,turb (see Figure 15,
upper right). At t≈145 min, an oscillating behavior can be observed
resulting in a violation of the purity constraint of 0.995 at
t=159.93 min. With the MC level L
MC
reaching the desired value of
FIGURE 17 Plant response during the turn-up: O
2
vapor molar
fraction of the top products of the distillation columns. LPC-GAN
(top), PC-PGAN (middle) and CAC-CGAR (bottom)
KENDER ET AL.18 of 23

L
MC
=100%, the required turbine flow _
VAir,turb decreases. Eventually,
this leads to a convergence of yO2,GOX with its desired value. As this
takes ≈1.75 d it is not visualized.
With SLM, the purity constraint for the GOX product is met at all
times. Nevertheless, the graph of yO2,GOX decreases, starting at the
t=16.875 min. At the expense of GOX purity yO2,GOX , a rapid
decrease in the MC level L
MC
is prevented. By analogy to the turn-
down, the S-factor S
Ar
shown in Figure 20 can be used as an indica-
tion to find a feasible trade-off between yO2,GOX and L
MC
using the
liquid in the PC and CAC sumps for SLM. At a simulated time of
t≈150 min, the graph of yO2,GOX decreases again as a result of the tur-
bine flow _
VAir,turb (see Figure 15, upper right), which is also slightly
above its desired value of 100% until the MC level eventually reaches
its target value of L
MC
=100%. However, the purity constraint of
yO2,GOX ≥0.995 is met at all times. During the turn-up, one aim of the
SLM concept is to find the maximum possible amount of liquid, which
can be fed from the remaining columns to the MC, without violating
the purity constraint of yO2,GOX ≥0.995 and while preventing a signifi-
cant decrease in MC level L
MC
. This helps to avoid a N
2
breakthrough
caused by an increased turbine flow _
VAir,turb over a long period
of time.
The graph of the O
2
vapor molar fraction yO2,CGO of the Ar col-
umn feed CGO (upper right) is similar to the graph of the O
2
vapor
fraction of the GOX product yO2,GOX in both cases. By analogy to the
turn-down, a small excerpt is shown in this diagram, which illustrates
the course of yO2,CGO over 3300 min. It shows that by using SLM, a
constant graph is reached at t≈250 min. For the NLM case, it is
shown that at t≈1400 min =1 d the oscillations have stopped and
the O
2
vapor fraction of the CGO stream has already recovered. At
t≈2520 min =1.75 d, yO2,CGO converges to the value of the SLM
case. In the case of NLM, a maximum of yO2,CGO,max ¼0:962 can be
observed at t=32.2 min. After that, a short decrease occurs and flat-
tens at t≈41.27 min. At t=145 min an oscillating behavior can be
detected due to the N
2
breakthrough. The fast decrease in yO2,CGO is a
result of the fast increase in the LPC's reboil ratio. In case of SLM, a
slight overall decrease in yO2,CGO can be observed due to the different
O
2
vapor fractions of the CGAR stream yO2,CGAR,50%¼0:53 ppm in
part-load operation and at the initial operating point of 100% load
yO2,CGAR,100%¼0:717 ppm. The larger the amount of O
2
in the CGAR
stream, the lower the O
2
vapor molar fraction yO2,CGO.
At the lower right of Figure 18, the graph of the N
2
vapor molar
fraction yN2,CGO is shown. In case of SLM, there is only a slight
increase in N
2
in the Ar column feed CGO with a maximum of
yN2,CGO,max ¼6:1104at t=23.62 min. For the considered turn-up,
this vapor molar fraction of N
2
yN2,CGO is tolerable as it does not influ-
ence the crude Ar condenser/reboiler duty _
Qcond=reb,CAC (see
Figure 19, bottom). In case of NLM, the N
2
breakthrough can be
observed as the vapor molar fraction of N
2
yN2,CGO starts to affect the
crude Ar condenser/reboiler duty _
Qcond=reb,CAC (see Figure 19, bottom)
and, thus, the overall plant.
FIGURE 18 Plant response during the turn-up: MC level (upper left), O
2
molar fraction of the GOX product (lower left), O
2
molar fraction of
the Ar column feed CGO (upper right), N
2
molar fraction of the Ar column feed CGO (lower right)
19 of 23 KENDER ET AL.

Ar system
The oscillating behavior as a consequence of the N
2
breakthrough can
be explained using the N
2
vapor molar fraction of the crude Ar prod-
uct CGAR yN2,CGAR (top) and the crude Ar condenser/reboiler duty
_
Qcond=reb,CAC (bottom), which are shown in Figure 19. These graphs are
a result of the N
2
vapor molar fraction in the Ar column feed
CGO yN2,CGO.
Using NLM, the first maximum of yN2,CGO,max can be seen at
t≈145.83 min (see Figure 18, lower right). There is a time delay of
Δt≈12.2 min until the N
2
is propagated to the top of the CAC due to
the vapor holdup and equilibrium changes inside the column. This
leads to the first maximum of yN2,CGAR,max at t≈164.03 min. Above the
critical amount of yN2,CGAR,crit ≈0:16, a further increase in N
2
leads to
a subsequent decrease in the crude Ar condenser/reboiler duty
_
Qcond=reb,CAC since the amount of N
2
significantly influences the dew
temperature of the CGAR T
Dew,CGAR
. This leads to a decrease in liquid
reflux for the CAC and consequently reduces the amount of Ar col-
umn feed CGO, which is withdrawn from the LPC. However, since the
amount of CGO is subject to flow control, the pressure on the reboiler
side of the crude Ar condenser/reboiler is adjusted to re-establish the
required duty _
Qcond=reb,CAC. Thus, the amount of liquid reflux is varied
to achieve the correct pressure resistance for the CGO feed to match
its setpoint (see Figure 14, upper right). However, the temporary
decrease in liquid reflux for the CAC impacts the entire plant. Since
the CAC liquid reflux is finally fed back to the LPC, it eventually has
an effect on the LPC's fluid dynamics and the MC. Thus, with a tem-
porary lower liquid flow from the CAC to the LPC, the MC level L
MC
(see Figure 18, upper left) and subsequently the MC duty _
QMC (see
Figure 15, lower right) decrease. In addition, the GOX product purity
yO2,GOX (see Figure 18, lower left) is influenced due to the develop-
ment of the MC duty _
QMC over time. This eventually feeds back to
the composition at the Ar column feed CGO, which causes the
oscillations.
Since the MC level L
MC
(see Figure 18, upper left) increases
slowly, the turbine flow _
VAir,turb converges to its nominal value of
100%. The final value is reached at t≈1 d, steadily increasing the
LPCs reboil ratio and the GOX product purity yO2,GOX during the level
build-up. This leads to a decrease in the N
2
vapor molar fraction
yN2,CGO at the Ar column feed CGO below the critical amount. Thus,
the crude Ar condenser/reboiler duty _
Qcond=reb,CAC is not affected any-
more. In other words, without SLM, the plant would suffer a product
loss for a period of t≈1 d. However, with manual interventions into
plant control, it might be possible to reduce the downtime. But a N
2
breakthrough always results in the loss of value products, which needs
to be prevented at all times.
LPC fluid dynamics
Figure 20 shows the S-factor of Ar S
Ar
at the first column tray right
above the MC over time.
In the case of NLM, S
Ar
is more than doubled, leading to the
increase in GOX product purity yO2,GOX at the expense of MC level
L
MC
(see Figure 18, left side). In case of SLM, the level setpoint
changes of the PC and CAC (see Figure 16) lead to a reduction in the
amplitude of the S-factor S
Ar
during the entire turn-up. Also, since the
setpoint changes of the levels start prior to the remaining load change,
an initial decrease in the S-factor S
Ar
can be observed. As already elab-
orated, the primary target of SLM is to prevent the decrease in MC
level L
MC
at the expense of GOX product purity yO2,GOX without vio-
lating the corresponding purity constraints. This can be achieved by
keeping the course of S
Ar
relatively constant.
However, the SLM for the turn-up requires excess liquid in the
plant. Therefore, it must be ensured in a previous turn-down that
FIGURE 19 Plant response during the turn-up: N
2
vapor molar
fraction of the CGAR stream (top), normalized crude Ar condenser/
reboiler duty (bottom)
FIGURE 20 Plant response during the turn-up: S-factor of Ar S
Ar
(bottom) at the first column tray in the LPC above the MC
KENDER ET AL.20 of 23

enough liquid is collected in the respective sumps. In addition, after
the turn-up with SLM has been completed, an equalization process is
required to restore the column sump levels to their initial values. Oth-
erwise, rapid load change sequences can lead to problems in liquid
management. By analogy to the turn-down, the power consumptions
of the NLM and SLM are compared as an indication of the OPEX,
which is also equal for both cases.
This case study emphasizes the necessity for DTs to a priori analyze
load change procedures. It is now possible to obtain valuable insight into
scenarios, which are to be avoided when operating a real plant. Hence,
no plant datais available and virtual studies are the only options ofinves-
tigation. Being able to simulate the NLM case allows for the analysis and
debottlenecking of the turn-up procedure without the consequences of
t≈1 d product loss. In addition,it is possible to investigate upset scenar-
ios such as the N
2
breakthrough in order to derive measures to prevent it
or develop strategies to reduce downtime afterwards.
6|CONCLUSION
In this work, the concept of a DT for ASUs introduced in Kender
et al.
1
is applied to an industrially relevant ASU with Ar separation,
emphasizing the increased complexity of this ASU topology. Apart
from the additional equipment requirements, the separation of Ar also
increases the degree of heat and process integration as well as the
complexity of the control scheme. This is challenging for (in silico)
plant operations, the simulation models and the used numerical solu-
tion algorithms. The presented case studies are challenging load
change procedures in terms of agility and range. A turn-down and a
turn-up from 50% to 100% and vice versa with a load change rate of
8% min
1
are simulated. Two operational concepts are compared,
NLM and SLM. The main difference between the two concepts is the
management of either the temporary excess (turn-down) or lack (turn-
up) of liquid holdups in the different distillation columns. Using SLM, dur-
ing the turn-down, the additional liquid holdup is buffered in the sumps
of the PC and the CACs. The buffered liquid can then be used to supply
the MC with the additional liquid requiredduring the turn-up. Additional
offline studies can be used to further optimize the magnitude, duration
and start time of the respective level setpoint changes. The SLM concept
allows for the performance of these load changes without the adherence
to purity constraints. In addition, the in silico analysis of load changes
using NLM, which entails a product loss as a consequence, reveals infor-
mation regarding bottlenecks for rapid load change procedures, helps to
identify new key parameters for an advanced plant operation evaluation
(S-factor) or enables the investigation of upset scenarios (N
2
break-
through), which have to be avoided during real plant operation. How-
ever, the derived setpoint changes using SLM are plant specific. These
analyses can be carried out for the different ASU topologies and used as
a starting point for individual adaptation of setpoint changes on-site to
allow for fasterload changes at real plants.
Furthermore, being able to monitor column fluid dynamics
(S-factor) in real time is an enormous benefit for plant operations as it
can be used as an early indication of the change of product purities.
Thus, additional work should be put into further developing of the DT
toward real-time capability to be able to use it as a soft sensor for the
entire plant, or at least for stand-alone unit operations, such as the
LPC. Real-time capability of the DT is a first step toward dynamic
optimization, which potentially allows to further increase the load
flexibility of an ASU, exceeding the presented linear load change pro-
cedures. In addition, the abundance of data generated by the DT
allows for a better formulation of the dynamic optimization problem
including the consideration of variables such as the S-factor.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial support of the
Kopernikus-project “SynErgie”by the Federal Ministry of Education
and Research (BMBF, FKZ 03SFK3E1-2) and the project supervision
by the project management organization Projektträger Jülich (PtJ).
Open Access funding enabled and organized by Projekt DEAL.
CONFLICT OF INTEREST
The authors declare no potential conflict of interests.
AUTHOR CONTRIBUTIONS
Robert Kender: Conceptualization (lead); formal analysis (lead); investi-
gation (lead); methodology (lead); validation (lead); writing –original
draft (lead). Felix Rößler: Conceptualization (supporting); methodology
(supporting); validation (supporting); writing –review and editing (lead).
Bernd Wunderlich: Conceptualization (supporting); investigation
(supporting); methodology (supporting); project administration (equal);
software (equal); validation (supporting); writing –review and editing
(equal). Martin Pottmann: Conceptualization (supporting); investiga-
tion (supporting); validation (supporting); writing –review and editing
(equal). Ingo Thomas: Methodology (supporting); software (equal);
writing –review and editing (supporting). Anna-Maria Ecker: Project
administration (equal); validation (supporting); writing –review and
editing (supporting). Sebastian Rehfeldt: Funding acquisition (lead);
project administration (equal); validation (supporting); writing –review
and editing (equal). Harald Klein: Resources (lead); supervision (lead);
validation (supporting); writing –review and editing (supporting).
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from
Linde Engineering. Restrictions apply to the availability of these data,
which were used under license for this study. Data are available from
the corresponding author with the permission of Linde Engineering.
NOTATION
Symbols
h
P
packing height (m
3
)
h
v
valve stroke (%)
K
i
vapor–liquid equilibrium ratio of component i(mol=mol)
_
L=_
Gratio of liquid to gas flows (-)
Lliquid level (%)
ntray number ()
21 of 23 KENDER ET AL.

ppressure (MPa)
_
Qheat duty (MW)
ttime (min)
Ttemperature (K)
Vvolume (m
3
)
_
Vvolume flow (m3=s)
x
i
liquid molar fraction (-)
y
i
vapor molar fraction (-)
z
i
bulk molar fraction (-)
δdeviation (%)
Δppressure difference (MPa)
Δtperiod of time (min)
ε
Trim
trim control range (%)
Subscripts
100% regarding 100% plant load
50% regarding 50% plant load
boil boiling point
bub bubble point
cond/reb condenser/reboiler
crit critical
dew dew point
max maximal
min minimal
ub upper bound
Superscripts
N normalized
ORCID
Robert Kender https://orcid.org/0000-0001-5389-0383
REFERENCES
1. Kender R, Kaufmann F, Rößler F, et al. Development of a digital twin
for a flexible air separation unit using a pressure-driven simulation
approach. Comput Chem Eng. 2021;151:107349.
2. Haider P, Freko P, Acher T, Rehfeldt S, Klein H. A transient three-
dimensional model for thermo-fluid simulation of cryogenic plate-fin
heat exchangers. Appl Therm Eng. 2020;180:115791.
3. Kender R, Wunderlich B, Thomas I, Peschel A, Rehfeldt S, Klein H.
Pressure-driven dynamic simulation of distillation columns in air sepa-
ration units. Chem Eng Trans. 2018;69:271-276.
4. Kender R, Wunderlich B, Thomas I, Peschel A, Rehfeldt S, Klein H.
Pressure-driven dynamic simulation of start up and shutdown proce-
dures of distillation columns in air separation units. Chem Eng Res Des.
2019;147:98-112.
5. Klein H, Fritsch P, Haider P, et al. Flexibler Betrieb von
Luftzerlegungsanlagen. Chem Ing Tech. 2020;92(12):1921-1940.
6. Fritsch P, Hoffmann R, Flüggen R, Haider P, Rehfeldt S, Klein H. A
cryogenic test rig for dynamically operated plate–fin heat exchangers.
Chem Ing Tech. 2021;93(8):1230-1237.
7. Haider P, Freko P, Acher T, Rehfeldt S, Klein H. Influence of inlet con-
figuration and distributor geometry on the performance of cryogenic
plate-fin heat exchangers. Appl Therm Eng. 2021;195:117197.
8. Klein H, Fritsch P, Haider P, et al. Flexible operation of air separation
units. ChemBioEng Rev. 2021;8(4):357-374.
9. Zhang Q, Grossmann IE. Planning and scheduling for industrial
demand side management: advances and challenges. Alternative
Energy Sources and Technologies; Cham: Springer; 2016:383-414.
10. Pattison RC, Touretzky CR, Johansson T, Harjunkoski I, Baldea M.
Optimal process operations in fast-changing electricity markets:
framework for scheduling with low-order dynamic models and an air
separation application. Ind Eng Chem Res. 2016;55(16):4562-4584.
11. Daryanian B, Bohn RE, Tabors RD. Optimal demand-side response to
electricity spot prices for storage-type customers. IEEE Trans Power
Syst. 1989;4(3):897-903.
12. Zhao S, Ochoa MP, Tang L, Lotero I, Gopalakrishnan A, Grossmann IE.
Novel formulation for optimal schedule with demand side manage-
ment in multiproduct air separation processes. Ind Eng Chem Res.
2019;58(8):3104-3117.
13. Zhang Q, Sundaramoorthy A, Grossmann IE, Pinto JM. A discrete-time
scheduling model for continuous power-intensive process networks
with various power contracts. ComputChem Eng. 2016;84:382-393.
14. Mitra S, Grossmann IE, Pinto JM, Arora N. Optimal production plan-
ning under time-sensitive electricity prices for continuous power-
intensive processes. Comput Chem Eng. 2012;38:171-184.
15. Kelley MT, Baldick R, Baldea M. Demand response scheduling under
uncertainty: chance-constrained framework and application to an air
separation unit. AIChE J. 2020;66(9):e16273.
16. Obermeier A, Windmeier C, Esche E, Repke JU. A discrete-time
scheduling model for continuous power-intensive processes consider-
ing fatigue of equipment. 28th European Symposium on Computer
Aided Process Engineering, Vol. 43 of Computer Aided Chemical Engi-
neering. Elsevier; 2018:955-960.
17. Obermeier A, Windmeier C, Esche E, Repke JU. A discrete-time
scheduling model for power-intensive processes taking fatigue of
equipment into consideration. Chem Eng Sci. 2019;195:904-920.
18. Obermeier A, Vollmer N, Windmeier C, Esche E, Repke JU. Genera-
tion of linear-based surrogate models from non-linear functional rela-
tionships for use in scheduling formulation. Comput Chem Eng. 2021;
146:107203.
19. Cao Y, Swartz CLE, Baldea M, Blouin S. Optimization-based assess-
ment of design limitations to air separation plant agility in demand
response scenarios. J Process Control. 2015;33:37-48.
20. Mitra S, Pinto JM, Grossmann IE. Optimal multi-scale capacity plan-
ning for power-intensive continuous processes under time-sensitive
electricity prices and demand uncertainty. Part I: modeling. Comput
Chem Eng. 2014;65:89-101.
21. Karwan MH, Keblis MF. Operations planning with real time pricing of
a primary input. Comput Oper Res. 2007;34(3):848-867.
22. Basán NP, C
occola ME, Dondo RG, Guarnaschelli A,
Schweickardt GA, Méndez CA. A reactive-iterative optimization algo-
rithm for scheduling of air separation units under uncertainty in elec-
tricity prices. Comput Chem Eng. 2020;142:107050.
23. Schäfer P, Schweidtmann AM, Mitsos A. Nonlinear scheduling with
time–variable electricity prices using sensitivity-based truncations of
wavelet transforms. AIChE J. 2020;99(10):e16986.
24. Kelley MT, Baldick R, Baldea M. An empirical study of moving horizon
closed-loop demand response scheduling. J Process Control. 2020;92:
137-148. Accessed 24 March 2022. https://www.sciencedirect.com/
science/article/pii/S0959152420302183
25. Tsay C, Kumar A, Flores-Cerrillo J, Baldea M. Optimal demand response
scheduling of an industrial air separation unit using data-driven dynamic
models. Comput Chem Eng. 2019;126:22-34. Accessed 24 March 2022.
http://www.sciencedirect.com/science/article/pii/
S0098135418313371
26. Tsay C, Cao Y, Wang Y, Flores-Cerrillo J & Baldea M. Identification and
online updating of dynamic models for demand response of an indus-
trial air separation unit. Accessed 24 March 2022. http://arxiv.org/pdf/
2009.13999v1.
KENDER ET AL.22 of 23

27. Tsay C, Baldea M. Integrating production scheduling and process con-
trol using latent variable dynamic models. Control Eng Pract. 2020;94:
104201.
28. Caspari A, Offermanns C, Schäfer P, Mhamdi A, Mitsos A. A flexible
air separation process: 2. Optimal operation using economic model
predictive control. AIChE J. 2019;65(11):e16721.
29. Caspari A, Lüken L, Schäfer P, et al. Dynamic optimization with com-
plementarity constraints: smoothing for direct shooting. Comput
Chem Eng. 2020;139:106891.
30. Caspari A, Faust JMM, Schäfer P, Mhamdi A, Mitsos A. Economic
nonlinear model predictive control for flexible operation of air separa-
tion units. IFAC-PapersOnLine. 2018;51(20):295-300.
31. Schulze JC, Caspari A, Offermanns C, Mhamdi A, Mitsos A. Nonlinear
model predictive control of ultra-high-purity air separation units
using transient wave propagation model. Comput Chem Eng. 2021;
145:107163.
32. Caspari A, Tsay C, Mhamdi A, Baldea M, Mitsos A. The integration of
scheduling and control: top-down vs. bottom-up. J Process Control.
2020;91:50-62.
33. Vinson DR. Air separation control technology. Comput Chem Eng.
2006;30(10–12):1436-1446.
34. Blum N, Krespach V, Zapp G, Oehse C, Rehfeldt S, Klein H. Investiga-
tion of a model-based deep reinforcement learning controller applied
to an air separation unit in a production environment. Chem Ing Tech.
2021;93(12):1937-1948.
35. Engl G, Kröner A, Kronseder T, von Stryk O. Numerical simulation and
optimal control of air separation plants. In: Bungartz HJ, Durst F, Zenger C,
eds. High Performance Scientific and Engineering Computing Lecture Notes in
Computational Science and Engineering. Springer; 1999:221-231.
36. Kröner A, Kronseder T, Engl G, Stryk OV. Dynamic optimization for
air separation plants. In: Gani R, Jørgensen SB, eds. European Sympo-
sium on Computer Aided Process Engineering, Vol. 9 of Computer-Aided
Chemical Engineering. Elsevier; 2001:433-438.
37. Caspari A, Fahr SR, Offermanns C, Mhamdi A, Biegler LT, Mitsos A.
Optimal start-up of air separation processes using dynamic optimiza-
tion with complementarity constraints. 30th European Symposium on
Computer Aided Chemical Engineering, Vol. 48 of Computer Aided
Chemical Engineering. Elsevier; 2020:1147-1152.
38. Wunderlich B. Entwicklung eines druckgetriebenen dynamischen
Kolonnenmodells zur Erhöhung der Flexibilität von kryogenen
Luftzerlegungsanlagen Dissertation. KIT Scientific Publishing; 2018.
39. Rößler F, Thomas I, Freko P, Rehfeldt S, Klein H. Dynamic simulation
with digital twins of heat exchangers. 2020 Virtual AIChE Annual
Meeting; AIChE; 2020.
40. Kender R, Rößler F, Wunderlich B, et al. Application of a digital twin
of an air separation unit with argon production. 2020 Virtual AIChE
Annual Meeting; AIChE; 2020.
41. Miller J, Luyben WL, Belanger P, Blouin S, Megan L. Improving agility of
cryogenic air separation plants.Ind Eng Chem Res. 2008;47(2):394-404.
42. Cao Y, Swartz CLE, Flores-Cerrillo J. Preemptive dynamic operation
of cryogenic air separation units. AIChE J. 2017;63(9):3845-3859.
43. Cao Y, Swartz CLE, Baldea M. Design for dynamic performance: appli-
cation to an air separation unit. American Control Conference (ACC).
IEEE; 2011:2683-2688.
44. Cao Y, Swartz CLE, Flores-Cerrillo J. Optimal dynamic operation of a
high-purity air separation plant under varying market conditions. Ind
Eng Chem Res. 2016;55(37):9956-9970.
45. Schäfer P, Caspari A, Kleinhans K, Mhamdi A, Mitsos A. Reduced dynamic
modelingapproach for rectification columns based on compartmentaliza-
tion and artificial neural networks. AIChE J. 2019;65(5):e16568.
46. Caspari A, Offermanns C, Ecker AM, et al. A wave propagation
approach for reduced dynamic modeling of distillation columns: opti-
mization and control. J Process Control. 2020;91:12-24.
47. Cao Y, Swartz CLE, Flores-Cerrillo J, Ma J. Dynamic modeling and
collocation-based model reduction of cryogenic air separation units.
AIChE J. 2016;62(5):1602-1615.
48. Stichlmair J, Klein H, Rehfeldt S. Distillation: Principles and Practice.
2nd ed. American Institute of Chemical Engineers; 2021.
49. Singla R, Chowdhury K. Comparisons of thermodynamic and economic
performances of cryogenic air separation plants designed for external
and internal compression of oxygen. Appl Therm Eng. 2019;160:
114025.
50. Rößler F, Krumova V, Gewald S, et al. Hazard analysis of fixed-tube-
sheet shell-and-tube heat exchangers. Chem Ing Tech. 2022.
51. Thomas I, Wunderlich B, Grohmann S. Pressure-driven dynamic pro-
cess simulation using a new generic stream object. Chem Eng Sci.
2020;215:115171.
52. Jiang Y, Yin S, Dong J, Kaynak O. A review on soft sensors for moni-
toring, control, and optimization of industrial processes. IEEE Sens J.
2021;21(11):12868-12881.
53. Graziani S, Xibilia MG. Deep learning for soft sensor design. Develop-
ment and Analysis of Deep Learning Architectures. Springer; 2020:31-
59. doi:10.1007/978-3-030-31764-5_2
54. Lin B, Recke B, Knudsen JKH, Jørgensen SB. A systematic approach
for soft sensor development. Comput Chem Eng. 2007;31(5–6):
419-425.
55. Kadlec P, Gabrys B, Strandt S. Data-driven soft sensors in the process
industry. Comput Chem Eng. 2009;33(4):795-814.
56. Moll A. Air distillation. In: G
orak A, ed. Distillation: Operation and
Applications. Elsevier/Acad. Press; 2014:255-295.
57. Skogestad S. Probably the best simple PID tuning rules in the world.
Proceedings of AIChE Annual Meeting, Paper 276h, Reno, NV; AIChE;
2001.
58. Häring HW. The air gases nitrogen, oxygen and argon. In: Häring HW,
ed. Industrial Gases Processing. Wiley-VCH Verlag; 2008:9-109.
59. Hausen H, Linde H. Tieftemperaturtechnik: Erzeugung sehr tiefer
Temperaturen, Gasverflüssigung und Zerlegung von Gasgemischen.
Zweite, völlig neubearbeitete auflage. Springer Berlin Heidelberg;
1985.
60. Linde GmbH Merchant and Packaged Gases, Gases & Applications;
2020. Accessed 24 March 2022. https://www.linde-gas.com/en/
images/0000378_C_HiQ_Gas_and_applications_handbook_branding_
update_V2_tcm17-168809.pdf
61. Deuflhard P, Hohmann A. Numerische mathematik 1: Eine algorithmisch
orientierte einführung. 4, überarbeitete und erweiterte auflage ed. de
Gruyter Lehrbuch. Walter de Gruyter; 2008. Accessed xxxx.
62. Edmister WC. Design for hydrocarbon absorption and stripping. Ind
Eng Chem. 1943;35(8):837-839.
63. Ecker AM, Thomas I, Häfele M, et al. Development of a new column
shortcut model and its application in process optimisation. Chem Eng
Sci. 2019;196:538-551.
64. Kronseder T. Towards Nonlinear Model-Based Online Optimal Control
of Chemical Engineering Plants: Parameterised Controls and Sensitivity
Functions for Very Large-Scale Index-2 DAE Systems with State Depen-
dent Discontinuities: Zugl.: Darmstadt, Techn. Univ., Diss., 2002, Vol.
977 of Fortschritt-Berichte VDI Reihe 8, Meß-, Steuerungs-Und
Regelungstechnik. Als Ms. Gedr Ed. VDI-Verl; 2003.
How to cite this article: Kender R, Rößler F, Wunderlich B,
et al. Improving the load flexibility of industrial air separation
units using a pressure-driven digital twin. AIChE J. 2022;68(7):
e17692. doi:10.1002/aic.17692
23 of 23 KENDER ET AL.