LOW DENSITY POLYETHYLENE GRADE TRANSITION CONTROL USING NEURAL WIENER MODEL PREDICTIVE CONTROL WITH SOFT SENSOR

linear as the layer’s transfer function, respectively. The FFNN model is widely used in
chemical processes and engineering applications, which demonstrates its capability in
modeling nonlinear systems (Hussain, 1999; Pirdashti et al., 2013). The soft sensor
development follows a dual MISO model approach rather than a standard MIMO model
scheme. The MISO model configuration is reported to provide a better prediction result
than the MIMO model (Abdullah, 2008).

Figure 3.12 Feedforward NN model with input delays
Here, the dual MISO model is utilized to predict the delayed desired process
output, which is the LDPE conversion and the MFI, as shown in Figure 3.13. From the
figure, the process inputs are allocated between the models, with specific inputs are
associated with the MFI model only. The determination of the number of sampling
delay is done using the ‘finddelay’ command in Matlab, which exploits the cross-
correlation effect linking the input and the output. Only the delay from the significant
input from the model inputs is taken into consideration.

3.7.1(a) Input Selection
The list of the input parameters for the soft sensor model is presented in Table

3.5. The input parameters are listed based on the availability of data measurement from
the Aspen Dynamic model. An input selection methodology is devised to select the

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appropriate inputs for the soft sensor model, which is presented in a flow chart as shown
in

Figure 3.14. This input selection methodology presents a systematic approach
in selecting the process input for the soft sensor model.

Figure 3.13 Dual MISO model scheme for soft sensor model

Input Input Pearson Process Final input
parameters preprocessing Correlation Knowlegde parameters
selection using box plot Coefficient selection
&
Parametric
Analysis

Figure 3.14 Flowchart for input parameter selections for soft sensor development
The selection process begins with a list of available inputs, as shown in Table

3.5. Firstly, the inputs undergo a preprocessing method using box plot. Box plot is used
in descriptive data analysis to visualize the data’s distribution and skewness through
data quartiles and averages. The input with a low distribution can be discarded using

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the box plot analysis since it would become too sensitive to be used as the input for the
soft sensor model. The Pearson correlation coefficient (PCC) is then utilized to identify
the linear correlation between the input and target parameters (May et al., 2011).
Finally, the selected input is further scrutinized based on process knowledge and
parametric analysis to finalize the selection process (Nogueira et al., 2017)

Table 3.5 Parameters for soft sensor model input-output selection

Input parameters Output parameters
Feed Temperature LDPE conversion
Peak Temperature Zone 1
Peak Temperature Zone 2 MFI
Peak Temperature Zone 3
Peak Temperature Zone 4
Peak Temperature Zone 5
Valley Temperature
Exit Temperature
Initiator 1 flow rate
Initiator 2 flow rate

CTA flow rate
Polymer exit density

3.7.1(b) Training method

The TDNN model is trained using the trainlm function in Matlab, which is
known as the Levenberg-Marquardt (LM) backpropagation. LM training is the fastest
available backpropagation technique available in Matlab, although it requires more

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memory than other algorithms. The early stopping method is applied during the training
to avoid overfitting the network. During the training, if the validation error begins to
rise compared to the training error for a specified number of iterations, the training is
stopped, and weights and biases at the minimum of the validation error are used. The
number of delays (or historical values) in the TDNN model is determined using the
finddelay command in Matlab. The best number of hidden neurons is selected using an
iterative validation method.

In order to speed up the training process, the parallel computing (PC) method
inside Matlab is applied. In parallel computing, the NN model training is done by
splitting the data into the ‘workers’. These ‘workers’ are Matlab computational engines
for parallel computing, which are associated with the cores in a multicore computer.
Thus, a considerable amount of time can be saved by distributing the tasks and
executing these simultaneously. In this study, two workers are available to train the
TDNN model using a computer with an Intel i3 4150 processor.

3.7.2 Soft sensor scheme

The soft sensor scheme for the LDPE polymerization process is shown in Figure
3.15. From the figure, the dotted line is the delayed process input, which is MFI and
polymer conversion. In practice, this problem can be caused by the laboratory testing
time, instrument, or measurement delay (Skålén et al., 2016). In order to produce an
estimated output, the process inputs (i.e., MVs), the fast process output (i.e., reactor
temperature), and the delayed output (i.e., MFI and polymer conversion) are fed into
the soft sensor. By using a trained NN model, the soft sensor could present an online
prediction of the delayed polymer properties.

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Inputs Outputs

Aspen Dynamic
model

Soft sensor

Estimated Output

Figure 3.15 Soft sensor model scheme
In order to cope with the delayed and estimated measurement in a continuous-
time process, an adaptive scheme based on Sharmin et al. (2006) work is used. The
adaptive scheme is a bias update that acts as a corrective action to the current soft sensor
measurement, for which it has been observed that, in open-loop calibration, good results
can be obtained. The implementation of the bias update scheme is based on equations
3.34 to 3.36. From the equations, ( ) presents the MFI with delayed or irregular
measurement, while ̂ ( ) is the estimated measurement from the soft sensor at time .

= 0, Ŷ( ) = ( ( )) (3.34)
(3.35)
= , ( ) = ( ) − ( ( )) (3.36)

< < 2 , ̂Y( ) = ( ( )) + ( )

where ( ( )) is the soft sensor model.

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However, this bias update algorithm is only applicable to the process with the
same sampling time. If there is a delay in the signal, the update would no longer be
correct since the ( ) value becomes ( + ), which would produce an incorrect
( ) at the respective time. In order to resolve this setback, a correction factor ( )
is introduced to form a modified bias, as shown in equation 3.37 (Quelhas and Pinto,
2009):

( )′ = ( ) × (− ) (3.37)

This correction factor serves as a bias adjustment, which has a value between 0 to 1.
The value of = 0 equals to ̂ ( ) following the normal (or estimated) response, and
= 1 shows that ̂ ( ) is following the delayed response. Thus, the choice of the
correction factor must consider such a trade-off between the normal and the delayed
response.

3.8 Controller performance test
In most polymerization processes, operational and economic requirements

involve three predominant problems, which are quality control, grade change, and load
change (Dünnebier et al., 2005). Thus, tests that include grade transition, conversion
change, disturbance rejection, and robustness test are performed to assess the controller
performances. These tests are performed to evaluate the controller in terms of ability in
tracking set points, rejecting disturbances, and handling process uncertainties.

3.8.1 Grade transition
In this test, the controller is evaluated based on its ability to manage several

grade transition operations. Grade transition involves changing the reactor's operating

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parameters towards a specific value based on a predetermined product recipe. This
process often results in a relatively large settling time or overshoot that would impair
the product specification, especially for the continuous polymerization process
(Ohshima and Tanigaki, 2000). Even though the transition operation needs to be quick,
a drastic change in the polymerization process is not permissible. Such a sudden change
in the reactor operating condition can influence the instantaneous polymer properties,
such as average molecular weight, and can deteriorate the quality of the final polymer,
as shown in Figure 3.16. Based on the figure, Pattern 1 offers a rapid grade transition
compared to Pattern 2. However, in terms of molecular weight distribution, the
instantaneous polymer (during the changeover operation) has developed into a different
MW, which is far from Grade A and Grade B. A difference in the polymer MW can
lead to a changed in its end-use properties. Hence, from the quality control standpoint,
it is more proper to keep the instantaneous polymer between the grades, as illustrated in
the figure.

Figure 3.16 Comparison of two different routes of grade transition effect towards
molecular weight distribution (Ohshima and Tanigaki, 2000)

Furthermore, a drastic change in the reactor condition, e.g., temperature can
produce a polymer with a more amorphous structure than a crystalline structure. A

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crystalline polymer is preferred in practice due to its more durable structure than an
amorphous polymer (Duchateau et al., 2019). In this study, several polymer MFI grades
that range from low (MFI 1.5), medium (MFI 5), and high (MFI 55) are used in the
grade transition test to evaluate the controller performance. These polymer grades are
selected based on typical commercial MFI grades available commercially (Azmi et al.,
2019). The operation is carried out simultaneously for low and medium grade
transitions, while for high grade transitions, MFI 22 is used as an intermediate grade
(Duchateau et al., 2019; Skålén et al., 2016).

In order to simulate the grade transition process as in industrial practice, the MV
rate constraint is implemented in the CTA flow rate. Such constraints would supply the
necessary limit to the CTA flow rate to control the grade transition process. The
calculation to find the MV rate is performed by observing several grade transition
operations in the industry and recalculating the rate based on the amount of CTA used
and the time to complete the transition. In the plant, other situations can influence the
grade transition time, such as the readiness of the additive system (e.g., anti-block and
antioxidant) in the extruder machine (Schuster, 2005) and the transition process, either
done manually or automated (Naidoo et al., 2007).

3.8.2 Conversion change

Apart from grade transition, the controller capability in dealing with the polymer
conversion change is also tested. Polymer conversion is defined by the ratio of the
amount of polymer being produced over the raw material supplied, as presented in
equation 3.38. In practice, the amount of LDPE produced is measured after the low-
pressure separator process before going into the extruder.

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LDPE conversion = LDPE flow rate (3.38)
Ethylene gas flow rate

The polymer conversion profile is imperative for the LDPE plant’s economic aspect,
which relates to the reactor’s throughput. Thus, the purpose of this test is to observe the
controller's capability in maintaining and increasing the conversion after reaching the
desired MFI grade. In this study, the LDPE conversion increased from nominal 0.3 to
0.33 and decreased from 0.33 to 0.3 to assess the controller’s ability in handling
conversion change. The purpose of increasing and decreasing the conversion is to study
the controller’s ability to handle the changes. The value of 0.33 is chosen based on the
highest conversion that the LDPE reactor can achieve safely. A conversion higher than
that can trigger the thermal runaway in the reactor. The value of 0.3 is the base case or
steady state operating condition. A value lower than 0.3 is not considered due to the
lack of economic incentive for doing so. These values are obtained from the observation
of the parametric study in sections 4.2.1(a), 4.2.1(b), and 4.2.1(c).

3.8.3 Disturbance Rejection

The controller's capability to reject disturbance is evaluated based on various
disturbance scenarios that can occur during the LDPE tubular reactor operation. The
disturbances that are studied are feed stream pressure loss, reduced flow rate, and
increased impurity. These disturbances are simulated to occur during steady state
operation, with LDPE conversion and MFI are at nominal conditions.

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3.8.3(a) Feed stream pressure loss

In the LDPE production, a hyper-compressor handles pressurizing the reactor
inlet stream into a high-pressure condition (around 2500 bar). It is one of the plant's
fragile units as the system continuously runs at a high operating pressure (Mok et al.,
2011). The first disturbance scenario simulates a pressure loss condition within the feed
stream due to the failure of a compressor valve (Białek and Bielawski, 2018). In this
test, an estimated pressure loss of 3% from the feed stream’s nominal condition is used
to disturb the LDPE polymerization process (Brun and Nored, 2012).

3.8.3(b) Reduced feed stream flow rate

Another common disturbance in the industrial plant is the fluctuating flow rate
in the feed stream, which is typical for any continuous system. Moreover, including a
recycling stream into the feed stream can introduce new dynamics to the reactor’s flow
rate profile. In this test, a reduction of 5% of the feed flow rate from the nominal value
is estimated to enter the LDPE process, which is commonly observed in an industrial
process (Bettoni et al., 2000).

3.8.3(c) Reduced ethylene gas feed purity

The general industrial specification for ethylene gas composition in the feed
stream is at 99.9 volume % (Whiteley, 2011). The purity of ethylene gas must be high
to reduce the feed stream’s impurities, such as C3 and C4 components. These
components can take part in the polymerization process through the chain transfer
process, which can influence the desired MFI grade. In this work, the nominal ethylene
gas feed composition is at 0.9803 kg/kg of mass fraction (or 0.9904 kmol/kmol in mole
fraction). In this disturbance scenario, the feed impurity content is increased to 10% to

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simulate the sudden change in the ethylene composition in the feed stream (Bettoni et
al., 2000).

3.8.4 Robustness Test

A robustness test evaluates the controller's capability in handling uncertainties
or internal disturbances inside the LDPE polymerization process. The polymerization
process can be affected by fouling, changes in the heat of polymerization, and variability
in the initiator’s efficiency. These situations are further discussed in the following
sections.

3.8.4(a) Fouling

Fouling is a common problem in the polymerization process. The polymer build-
up within the reactor inside the wall can cause a reduction in heat transfer due to the
low thermal conductivity of the deposited material. This situation can lead to an increase
in temperature near the affected area, which can stimulate the ethylene gas molecule to
decompose and release a considerable amount of energy. Based on Buchelli et al.
(2005), the rise in the fouling layer appears to be linear over time with 0.00004 kg/s of
calculated deposition rate. In this test, fouling resistance ( ) at 0.002 BTU is used
to simulate the reactor’s fouling effect using ramp signal change (Branan, 2005). Based
on equation 3.39, the heat transfer coefficient for a fouled reactor can be calculated
based on the fouling resistance information, with the assumption that the current reactor
is a clean reactor.

= ( 1 ) − ( 1 ) (3.39)

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3.8.4(b) Heat of polymerization

LDPE heat of polymerization (HOP) is the difference between the enthalpy of
the supercritical ethylene and the enthalpy of the polymer formed by the polymerization
reaction (Bokis et al., 2002). HOP values can change due to the differences in reactor
temperature and pressure (Jacob and Dhib, 2012). In this work, the current heat of
polymerization is changed to the one acquired from Brandrup et al. (1999), which is -
1.105 x 108 J/kmol compared to the present nominal value at -2.669 x 107 J/kmol.

3.8.4(c) Initiator efficiency

Initiator efficiency refers to the ability of the initiator molecules to break and
produce primary free radicals. In the LDPE polymerization model, the assumption of
initiator efficiency is typically set from 40% to 90% (Hutchinson and Penlidis, 2007).
Kiparissides et al. (1996) reported that initiator efficiency variations could influence the
reactor temperature profile, conversion rate, and molecular properties. The presence of
impurities in the mixture due to the recycling of the unreacted monomers and reactor
feed composition can cause adverse effects on the initiators’ overall efficiency
(Kiparissides et al., 2010). In this test, the current initiator efficiency is reduced to 60%
compared to 95% during the nominal condition to examine the controller capability in
handling uncertainty in the process (Hutchinson and Penlidis, 2007).

3.9 Performance criteria
A set of performance criteria needs to be set up as a benchmark in evaluating

the model and control results. In this work, the coefficient of determination (R2) and
normalized root mean square error (NRMSE) are used to evaluate the Neural Wiener
and neural network model performance. R2 is used to evaluate how close the values

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obtained from the model regression match the original data. The measurement ranges
from 0 to 1, with near 1 equals to perfect fit or shows that the regression data can explain
the original data's variability. The R2 value is calculated as:

2 = 1 − (3.40)


(3.41)

= ∑( − ̅ )2

=0

(3.42)

= ∑( − )2

=0

The model regression plot is obtained by using the regression command in Matlab.

Meanwhile, the NRMSE measures the average deviation of the regression values from

the original data. The NRMSE measurement also uses a similar range as R2 and can be

calculated by:

= √ 1 − ̅ )2 (3.43)

∑(

=1

= (3.44)
−

In order to assess the controller performances, the integral squared error (ISE) is

commonly used. The ISE works by integrating the square of the process error

throughout the simulation time, which is defined as:

(3.45)

= ∫ ( ( ) − ( ))2

0

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CHAPTER 4
RESULTS AND DISCUSSION

4.1 Aspen Plus simulation results and validation
The complete Aspen Plus flowsheet is presented in Figure 4.1. Based on the

figure, the five RPLUG models are the zones (namely Zone 1, Zone 2, Zone 3, Zone
4, and Zone 5) of the tubular reactor. By using such an arrangement, the zones can be
chosen as the cooling or reaction zone individually. From the figure, Zone 1 (Z1) and
Zone 2 (Z2) are the preheating zones, Zone 3 (Z3) and Zone 5 (Z5) are the reaction
zones, while Zone 4 (Z4) is the cooling zone. Typically, the reaction zone is recognized
by the initiator injection location at its inlet, which in this case are initiator 1 (INIT1)
and initiator 2 (INIT2). In the flowsheet, the mixer block is used to combine the
streams.

Figure 4.2 shows the validation results of the reactor temperature profile based
on the zones. Based on the figure, the Aspen Plus model has successfully simulated
the reactor temperature profile with R2 value of 0.981, which is favorably compared
to the industrial data reported by Asteasuain et al. (2001b). Moreover, the simulated
temperature profiles show a similarity with industrial reactor temperature, which
exhibits a rounded peak and gradual decrease (Bokis et al., 2002). It is important to
note that the Aspen Plus model performed better in estimating the reactor temperature
profile than the mechanistic model from Agrawal et al. (2006), which also used a
similar case study. This is due to the kinetic parameter’s fine-tuning procedure that
was employed by the Aspen model. Selected ethylene and LDPE properties regression
results using Aspen Properties with the PC-SAFT equation of state (EOS) are
presented in Appendix C.

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COUT-1
Z1

FEED FEED-ALL Z1-OUT
CTA FEED-MIX

86 CIN-1
COUT-5

OUTPUT Z5

CIN-5

Figure 4.1 LDPE tubular

COUT-2 M1 COUT-3
Z2 M1-OUT Z3

Z2-OUT

CIN-2 INIT1 CIN-3

M2 Z3-OUT
M2-OUT
COUT-4

Z4

Z4-OUT

INIT2

CIN-4

reactor model in Aspen Plus

Figure 4.2 LDPE reactor temperature validation profile
The LDPE final conversion and properties validation are tabulated in Table
4.1. The table highlights the comparison of LDPE conversion, number average of
molecular weight, and mixture density between the industrial data from Asteasuain et
al. (2001b) with the Aspen Plus model and Agrawal (2006) model. Based on the table,
the developed Aspen Plus model compares well with the industrial data (Asteasuain et
al., 2001b) within an acceptable percentage error. Therefore, based on the reactor
temperature and property validation results, the Aspen Plus model is deemed reliable
to represent the LDPE polymerization reactor.

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Table 4.1 LDPE conversion and properties validation

Properties Industrial Agrawal Error Aspen Error
data (2006) (%) Model (%)

(Asteasuain, 29.7 1 29.5 1.7
2001b)
0.8
LDPE Conversion 30.0
(%) 6.6

Number Average 21900 21901 0< 22070
MW (g/mol)

Mixture density 0.530 n/a 0.565
(gm/cc)

4.1.1 LDPE MFI grades

The generated LDPE MFI grades from equation 3.20 are presented in Table
4.2. The MFI grades were obtained by manipulating the CTA flow rate to match the
available commercial MFI grades from the literature (Teresa Rodríguez-Hernández et
al., 2007). In the table, the MFI grades are presented along with their respective CTA
flow rate, weight average molecular weight (MWW), temperature peak in Zone 3, and
temperature peak in Zone 5. MFI grade 2.22 is selected as the nominal condition since
its CTA flow rate is the steady state value of the LDPE process (Asteasuain and
Brandolin, 2008). In practice, such information from Table 4.2 is similar to the product
recipe to produce LDPE polymer based on the desired MFI grades (Naidoo et al.,
2007). These LDPE MFI grades would be used during the grade transition test to study
the controller’s performance.

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Table 4.2 Generated LDPE MFI grades

CTA Flow rate MWW MFI Peak Temp Peak Temp
(kg/h) (kg/kmol) (g/10min) Zone 3 (°C) Zone 5 (°C)
0.5 2.5 x 105
27.4 2.2 x 105 1.5 324.5 298.6
57.3 2.0 x 105 2.2 324.4 298.6
94.0 1.8 x 105 3.5 324.3 298.5
156.7 1.5 x 105 5.0 324.2 298.5
280.5 1.2 x 105 10 324.0 298.4
463.5 8.7 x 104 22 323.1 298.3
50 321.9 298.2

4.2 Model analysis results
The validated Aspen Plus model was further analyzed using parametric study,

degree of nonlinearity, and nonlinearity index (NLI). The results can be used to
describe the LDPE polymerization process dynamics in terms of input-output
relationships and nonlinearity behavior.

4.2.1 Parametric study results

4.2.1(a) Effect of Initiator 1 (TBPPI)
Figure 4.3 shows the effect of MV initiator 1 (TBPPI) flow rate variations on

selected reactor outputs. In this analysis, the initiator flow rate has been varied between
2.6 kg/h and 4.6 kg/h with 3.6 kg/h as its steady state condition. Based on the figure,
the higher initiator flow rate has increased the reactor peak temperature in Zone 3 and
vice versa. This relationship matches the typical initiator behavior to a reactor
temperature reported by Dhib and Al-Nidawy (2002). By increasing the amount of the

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initiator, the number of free radicals present in the mixture also increases (from
initiator decomposition reaction), thereby accelerating the polymerization reaction,
especially chain initiation and propagation reaction. The ethylene molecule double
bond is converted into a single bond during the chain propagation, releasing 22
kcal/mol of energy (Duchateau et al., 2019). Thus, the polymerization process has
become an exothermic process and increases the polymer mixture temperature.

Figure 4.3 Effect of Initiator 1 flow rate deviations
90

Considering the initiator 1 injection point, the change in its flow rate has also
driven a slight temperature deviation in Zone 5. However, the temperature rise in the
Zone 5 and LDPE conversion profiles shows inverse proportional relations to the MV
changes. This matter can be further examined by referring to Figure 4.4 and Figure
4.5. Figure 4.4 shows the polymer conversion profile based on different initiator 1 flow
rates. Based on the figure, the injection of initiator 1 with 4.6 kg/h flow rate has
contributed to a lower conversion at 850 m of reactor length and at the end of the
reactor than the 2.6 kg/h initiator flow rate. It should be noted that by increasing the
initiator amount, the reactor temperature would be increased. At the same time, its
peak location would be shifted to the front (i.e., near reactor inlet) (Duchateau et al.,
2019).

Figure 4.4 Polymer conversion profile based on different initiator 1 flow rate
Figure 4.5 shows the reactor temperature profile by varying the initiator 1 flow

rate. From the figure, the temperature peak in Zone 3 (160 m to 340 m of reactor
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length) has different locations from the nominal condition depending on the initiator 1
flow rate. When the temperature peak is at the front, the cooling region becomes larger
and colder than the steady state. Thus, the mixture temperature would become lower,
and the polymerization process is reduced as well. In contrast, when the initiator flow
rate is lower than the nominal, the reactor temperature peak becomes low and shifts to
the back. This makes the cooling zone length shorter and hotter than at the steady state
condition.

Figure 4.5 Reactor temperature profile based on different initiator 1 flow rate
Since the temperature in Zone 3 is high (due to a decrease of initiator 1 flow

rate), small traces of oxygen decompose into free radicals and continue the
polymerization process (Brandolin et al., 1996). This process is observable from the
steady state simulation analysis in Figure 4.6 when initiator 1 flow rate decreases.
Figure 4.6(a) shows Initiator 1 (TBPPI) and oxygen mass composition profile in Zone
3. Notice that although initiator 1 (TBPPI) is fully depleted, a small number of

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unreacted oxygen is still left and flows into Zone 4. Figure 4.6(b) shows the mass
composition of oxygen in Zone 4, which is further reduced (due to the decomposition
reaction) since the cooling zone is much shorter and the temperature is higher than
nominal. Therefore, this condition has caused a slightly higher LDPE composition
output in the final product stream.

(a) Block Z3: Composition

1.10e-4 OXYGEN
1.00e-4 TBPPI

Reactor mass composition (mass frac.) 9.00e-5

8.00e-5

7.00e-5

6.00e-5

5.00e-5

4.00e-5

3.00e-5

2.00e-5

1.00e-5

0
0 20 40 60 80 100 120 140 160 180

Length meter

(b) Block Z4: Composition

3.0e-8 OXYGEN
2.8e-8

Reactor mass composition (mass frac.) 2.6e-8

2.4e-8

2.2e-8

2.0e-8

1.8e-8

1.6e-8

1.4e-8

1.2e-8

1.0e-8

8.0e-9

6.0e-9

4.0e-9

0 50 100 150 200 250 300 350 400 450 500 550

Length meter

Figure 4.6 (a) Initiator 1 (TBPPI) and Oxygen composition inside Zone 3; (b)
Zone 4 using initiator 1 flow rate at 2.6 kg/h.

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There is a moderate effect on the polymer MFI grade by changing the initiator
1 flow rate. The increase in the initiator 1 flow rate causes the increase of free radicals
release, making the polymerization reaction more active. Thus, the reactor’s nominal
average temperature increases. Commonly, at a higher average reactor temperature,
more branching reactions occur (Duchateau et al., 2019). According to Duchateau et
al. (2019), the probability of long-chain branching (LCB) occurring is proportional to
that polymer's length, which becomes dominant at higher molecular weights. Based
on the simulation results, the polymer shows an increase in molecular weight during
the temperature increase. Thus, this condition favors the LCB over the short-chain
branching (SCB) reaction. These long-chain molecules produce a more viscous melt
that can lower the final polymer MFI (Seavey et al., 2003).

4.2.1(b) Effect of Initiator 2 (TBPIN)

Figure 4.7 shows the effect of initiator 2 flow rate deviations on selected reactor
outputs. The initiator flow rate is varied from a steady state value of 0.567 kg/h to 1.0
kg/h, 1.5 kg/h, 2.0 kg/h and 2.5 kg/h. Based on the figure, the effect of the initiator 2
flow rate variation is most pronounced in Zone 5 peak temperature profile. Dhib and
Al-Nidawy (2002) reported that the type of initiator and its amount directly influence
the reactor temperature. Since the initiator 2 injection point location is located further
down the reactor, the initiator flow rate changes do not affect Zone 3 temperature. In
terms of final product composition, the initiator 2 flow rate amount correlates directly
with the amount of LDPE produced. The increase in initiator amount can escalate the
LDPE polymerization reaction, speeding up the ethylene monomer conversion rate.
Thus, the initiator 2 flow rate can be used to increase the LDPE conversion for higher
product throughput. However, it should be noted that the maximum reactor

94

temperature should not exceed 340°C to avoid a thermal runaway condition (Albert
and Luft, 1999).

In terms of quality, a higher amount of initiator 2 can lower the final polymer
MFI. This can be verified from the molecular weight (MW) profile, which shows a
higher MW for a larger initiator amount. The high MW condition is attributed to the
increasing amount of long-chain branching in the polymer due to the propagation
reaction and temperature rise. This condition has made the polymer flow viscous and
has lowered the MFI values (Luft et al., 1982).

Figure 4.7 Effect of Initiator 2 flow rate deviations
95

4.2.1(c) Effect of Chain Transfer Agent (CTA)
Figure 4.8 shows the effect of CTA (i.e., Propane) flow rate variation on

selected reactor outputs. The CTA flow rate is changed to 0.5 kg/h, 1.0 kg/h, 50 kg/h
and 100 kg/h from its steady state condition of 27 kg/h. The effect of varying CTA
flow rates is small on the maximum reactor temperature. CTA molecules are only
involved in chain transfer reactions during the polymerization process, which only
influence chain sizes rather than chain initiation reactions (which release heat when
the ethylene double bond is converted to a single bond). Thus, only a minimal amount
of heat is released while varying CTA flow rates. Since the reactor temperature
remains constant, the final LDPE composition also does not change much.

Figure 4.8 Effect of CTA flow rate deviations
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Despite that, the CTA amount has a significant direct relationship with the MFI
grades. The addition of the CTA can control the excessive production of long polymer
molecules, escalating the polymer mixture viscosity and affecting the reactor heat
transfer and control system (Asteasuain et al., 2001b). This can be observed in the
decline in the polymer's molecular weight during the addition of the CTA. Therefore,
the manipulation of the CTA flow rate is commonly done in the industry to control
polymer grade due to its direct effect and fewer side effects on the polymerization
process (Pinto et al., 2017).

4.2.1(d) Effect of feed temperature

The effect of feed temperature variations is presented in Figure 4.9. The feed
temperature is varied with ±3°C and ±5°C from the nominal value. Based on the figure,
feed temperature changes have a moderate impact on all the reactor outputs, especially
for the peak temperature in Zone 5. This is due to the usage of Zone 1 and Zone 2 as
preheating zones. These two zones function as temperature buffers to minimize the
effect of the feed temperature changes. When the feed reaches Zone 3, the initial
temperature rise has already been reduced, and the start temperature of the
polymerization (in Zone 3) is only moderately affected (refer to peak temperature Zone
3 profile). Such temperature changes in the polymer mixture have also affected the
polymerization reaction, which causes the changes in molecular weight and melt flow
index (Cao et al., 2007). This shows that the polymerization reaction is influenced by
the changes in the polymer’s mixture temperature. A similar effect of reactor inlet
temperature was also reported by Yoon and Rhee (1985) and Dietrich et al. (2019).

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Figure 4.9 Effect of feed temperature changes towards selected rector outputs

4.2.1(e) Effect of feed pressure loss

The effect of pressure loss on the feed stream is shown in Figure 4.10. In this
case, the feed pressure loss is varied from minus 25 bar to minus 100 bar from the
nominal feed pressure at 2250 bar. Based on the figure, the feed pressure loss effect
can be observed significantly at zone 3 peak temperature profile than zone 5 peak
temperature profile due to the reactor’s horizontal distribution. As the feed pressure
loss is increased, the reactor's pressure will also drop from the nominal condition and
decrease the chain initiation rate. This would cause the polymerization velocity to

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become slower and bring down the reactor’s average temperature. Since the peak
temperature in zone 5 is slightly changed, the LDPE conversion profile remains the
same.

Figure 4.10 Effect of feed pressure loss variations towards selected rector outputs
If the feed pressure loss is further increased, the polymer conversion reduction

would be more significant (Kiparissides et al., 1993a). The reactor’s low pressure
condition has made the polymer branching more active than the propagation rate
(Kiparissides et al., 1993b). This situation has promoted more short polymer chain
formation than long polymer chains, which eventually decreases the polymer

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molecular weight and density. A polymer with a lower molecular weight has more
fluidity that would increase the polymer MFI.
4.2.1(f) Effect of feed flow rate

Figure 4.11 shows the outcome from the feed flow rate variations towards
selected reactor outputs. In this simulation, the feed flow rate is subjected to ±3% and
±5% changes from the steady state flow rate at 40392 kg/h.

Figure 4.11 Effect of Feed flow rate deviations towards selected rector outputs
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Based on the figure, the changing feed flow rate has contributed to moderate
changes in peak temperature in Zone 3 and small changes in Zone 5. By decreasing
the feed flow rate while maintaining the initiator flow rate, the free radical to monomer
ratio has increased. This situation would promote a more active polymerization
reaction and thus, would increase the reactor temperature. This situation also
influences the final polymer composition due to a slight deviation in the zone 5 peak
temperature. In the molecular weight profile, the decrease of the feed flow rate
contributes more influence on the polymer properties due to the increased amount of
initiator to monomer ratio in the mixture (Kiparissides et al., 1996). A polymer with a
higher molecular weight commonly produces a more viscous melt flow and reduces
the polymer MFI value.

4.2.1(g) Effect of impurity in feed composition

Figure 4.12 shows the effect of impurity in reducing the ethylene composition
in the feed stream. The nominal ethylene composition in the feed stream is 98% kg/kg
(equivalent to 99% kmol/kmol). In this case, the impurity selected is butane (Agrawal
et al., 2006). Based on the figure, the effect of impurity increase in the feed stream has
produced a slight temperature change in peak temperature in zone 3 and zone 5. A
similar behavior is also observed in the LDPE output conversion profile. However, the
effect of feed impurity associated with polymer molecular weight is more explicit. In
this situation, the impurity component (i.e., butane) acts as a chain transfer agent and
inhibits the growth of the polymer chain. As a result, more short-chain branching
polymer is generated than the longer ones (Kiparissides et al., 1993b). This situation
has significantly decreased the polymer’s overall molecular weight and increased the
MFI value. Furthermore, certain impurities can cause problems regarding safety (e.g.,

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high oxygen concentration can cause thermal decomposition) and product quality (e.g.,
sulfur can affect smell). Therefore, it is common to have a high purity of ethylene feed
in the LDPE industrial production to avoid such problems (Whiteley, 2011)

Figure 4.12 Effect of impurity in ethylene feed composition towards selected
rector outputs

4.2.1(h) Parametric study summary
Based on the parametric study conducted, the summary of the relationship of

the effect of the input variables on selected significant LDPE reactor output is
presented in Table 4.3. Based on the table, some parameters show a strong effect, and

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some can be neglected. The amount of initiator has a substantial effect on all the
outputs. Thus, the initiator’s flow rate control performance can directly influence the
polymer conversion and quality. Moreover, CTA is the primary influencer for the
polymer end-use quality (i.e., MFI) control. Thus, tight control of the CTA flow rate
would bring the polymer quality within the desired specification.

Table 4.3 Overview of the input effects towards reactor outputs

Properties effect Reactor Ethylene Melt Flow
Temperature Conversion Index (MFI)

Effect of Initiator (↑) ↑↑↓

Effect of CTA (↑) ~~↑

Effect of Feed temperature (↓) ~ ↑ ↓

Effect of Feed Pressure Loss ↓ ~ ↑
(↑)

Effect of Feed flow rate (↑) ↓ ↓ ↓

Effect of Feed composition ↓ ~ ↑
impurity (↑)

Note: ↑ = increased effect; ↓ = decreased effect; ~ = negligible effect;

Apart from that, polymer conversion can be affected by changing the feed flow

rate, which relates to the amount of monomer present inside the reactor. The effect of

feed pressure loss, flow rate, and impurity also influence the polymer MFI. Thus, these

parameters should be monitored, and the controller should be able to reject their effect

(i.e., disturbances) in the process. In addition, the effect of feed temperature deviations

provides small changes in the reaction start temperature in Zone 3. Thus, these changes

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are considered moderate. Similar findings are also reported by Azmi (2019), Schuster
(2005), and Bicerano (2002), which are in line with industrial LDPE reactor
observation.

4.2.2 Degree of nonlinearity

The degree of nonlinearity test consists of three separate parts, which are
asymmetric, harmonic, and multiplicity responses. The results for these tests are
presented in the following Sections 4.2.2(a), 4.2.2(b), and 4.2.2(c), respectively.

4.2.2(a) Asymmetric response

The asymmetric response in the LDPE reactor output parameters is shown in
Figure 4.13 to Figure 4.15. In Figure 4.13, the effect of initiator 1 manipulation is
observed in Zone 3’s peak temperature in a deviation form. Based on the figure, the
upper region of response values (higher than the steady state) do not match the lower
region response values (lower than the steady state). Thus, this creates an asymmetrical
response between the higher and lower values, which is an indicator of nonlinear
behavior.

A similar phenomenon can also be observed in Figure 4.14. The figure shows
the behavior of LDPE conversion (in deviation form) in the product stream from the
increase of initiator 2 flow rate from steady state condition. In this test, only the step-
up test was considered due to the economic benefit from the increase of polymer
conversion. Based on the figure, LDPE conversion corresponds nonlinearly towards
the even increment of the initiator 2 flow rate. Thus, such behavior is a characteristic
of a nonlinear process.

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Figure 4.13 Asymmetric response for peak temperature in Zone 3 (in deviation)

Figure 4.14 Asymmetric response for LDPE mass fraction in product stream (in
deviation)

Figure 4.15 shows the effect of CTA flow rate variation on the LDPE polymer
quality (i.e., MFI) in deviation form. Based on the figure, the low CTA flow rates (in
this case, 0.1 kg/h and 0.5 kg/h) produced nearly similar MFI values. However, as the
CTA flow rate increases higher than steady state value, the MFI values also increase
drastically. The variation of the CTA flow rates have produce a nonlinear response in
the polymer MFI grades, which signify the LDPE process nonlinearity.

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Figure 4.15 Asymmetric response for LDPE polymer MFI (in deviation)
The asymmetric and nonlinear behaviors observed from the figures in this

section have demonstrated the intrinsic nonlinearity of the LDPE polymerization
process. Pearson (2003) has classified the asymmetric response phenomena as mildly
nonlinear behavior.

4.2.2(b) Harmonic response

The LDPE process output responses due to periodic inputs are shown in Figure
4.16, Figure 4.17, and Figure 4.18. A similar inputs and outputs pairing is used as in
the previous section. Based on the figures, the overall response of process outputs can
be classified as a sinusoidal harmonic response with a fixed period. This is a common
situation for a linear process. However, Figure 4.16 shows that the respective output
response is observed to produce irregular shapes (i.e., nearly flat at the top peak)
compared to the common sinusoidal signal. Such behavior can be attributed to mild
nonlinearity process behavior (Pearson, 2003). The delay for LDPE conversion and
MFI output responses, as seen in Figure 4.17 and Figure 4.18, is due to their dynamic
behaviors.

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Figure 4.16 Harmonic response of Initiator 1 flow rate towards Peak temperature
in Zone 3

Figure 4.17 Harmonic response of Initiator 2 flow rate towards LDPE conversion

Figure 4.18 Harmonic response of CTA flow rate towards polymer MFI
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4.2.2(c) Multiplicity
Figure 4.19 shows the effect of selected temperature points in Zone 3 by

increasing the initiator 1 flow rate. These temperature points are selected due to their
location near the temperature peak in Zone 3 during nominal operation. Based on the
figure, there are particular locations for the different initiator flow rates to produce a
similar temperature in Zone 3. For example, the T18 profile, which represents the
reactor temperature at point 18, can be achieved by two different initiator flow rates,
i.e., 3.2 kg/h and 4.4 kg/h in the similar zone. Thus, if point T18 is used as the control
variable, the controller would have difficulties controlling that temperature location
since it can be attained using two different initiator flow rates. This situation is called
input multiplicity.

Figure 4.19 Distinct temperature profiles in Zone 3 by increasing initiator 1 flow
rate

However, the situation in Zone 5 is different, as shown in Figure 4.20. Based
on Figure 4.20, the selected reactor temperature points in Zone 5 show linear behaviors

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with an increased initiator 2 flow rate. These temperature situations are similar, as
presented in section 4.2.1(b). Thus, the input multiplicity does not occur in Zone 5.

Figure 4.20 Distinct temperature profiles in Zone 5 by increasing initiator 2 flow
rate

Figure 4.21, Figure 4.22, and Figure 4.23 show the steady state operation
results for varying initiators and CTA flow rates towards reactor peak temperature in
Zone 3, LDPE composition, and MFI, respectively. In this test, the process inputs are
changed based on increasing and decreasing trends to obtain steady state conditions
from a different operating route. The observation from these figures reveals that all the
process outputs produce the exact steady state location even though different operating
routes are used. The existence of a single steady state condition for every process
output demonstrates the absence of output multiplicity situation.

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-+.
Figure 4.21 Steady state operation points by changing the initiator 1 flow rate in

ascending and descending routine

Figure 4.22 Steady state operation points by changing the initiator 2 flow rate in
ascending and descending routine

Figure 4.23 Steady state operation points by changing the CTA flow rate in
ascending and descending routine
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4.2.3 Nonlinearity Index (NLI)

Based on the calculation procedures in section 3.5.3, the nonlinearity index
(NLI) for LDPE tubular reactor model is 2.2, which corresponds to the degree of
nonlinearity. The higher the NLI value, the higher its degree of nonlinearity.
According to Uddin et al. (2018), any process that has a NLI larger than one represents
sufficient nonlinearity to use nonlinear model identification. Thus, the development of
the LDPE tubular reactor model is performed using nonlinear model identification.

4.2.4 Summary for sensitivity analysis

The summarized results for the nonlinearity test are tabulated in Table 4.4.
Based on the table, certain parametric study results such as initiators and CTA flow
rates produce a nonlinear behavior towards the output parameters. The observation
from the asymmetric, harmonic, and input multiplicity responses suggests the LDPE
process has a mild degree of nonlinearity. The quantitative results from the NLI also
present the same notion that confirm the LDPE process nonlinearity. Thus, it can be
concluded that the LDPE tubular reactor process exhibits a mild degree of nonlinearity
and needs to be represented by a nonlinear model.

4.3 Neural Wiener modeling results

4.3.1 Input-Output selection

Based on the model analysis results in section 4.2.1, the relevant input and
output variables are identified to represent the LDPE tubular reactor model. The

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selected variables are tabulated in Table 4.5. From the table, there inputs variables are
used to estimate two output variables in a MIMO model scheme.

Table 4.4 Summary of nonlinearity test results

Tests Observations Outcomes
Parametric study Nonlinear behavior
Specific parameters such as
initiators and CTA shows a
nonlinear profile

Asymmetric Existence of uneven or A mild degree of
response nonlinear output response nonlinearity

Harmonic response Sinusoidal harmonic response A mild degree of
with the same period nonlinearity

Input multiplicity Multiplicity occurred in a A mild degree of
particular region for selected nonlinearity
temperature points in Zone 3

Output multiplicity No multiple steady state is -
observed

Nonlinearity Index NLI calculation = 2.2 Sufficient to use a
nonlinear model
identification

Based on the observations in section 4.2.1(a) and section 4.2.1(b), the initiator
flow rate directly influences the reactor temperature, conversion, and melt flow index.
In the meantime, the CTA flow rate is used to manipulate the MFI grade in the LDPE
production, as presented in section 4.2.1(c). In any chemical process, production
throughput and quality are the essential CV to be controlled (Seborg et al., 2004).
Thus, in this case, LDPE conversion and MFI are selected as the model outputs. Both
parameters are measured at the exit of the tubular reactor and before entering the
extruder section.

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Table 4.5 Selected input and output variables for Neural Wiener model

Inputs Outputs
Initiator 1 flow rate LDPE conversion
Initiator 2 flow rate
MFI
CTA flow rate

4.3.2 Data Generation results

A total of 4080 minutes of simulation time with a sampling time of 0.1 minutes
is generated for each model training and validation purpose. In order to produce a
reliable empirical model, a large amount of data covering all the process dynamics is
needed (Baughman and Liu, 1995). In addition, the short sampling time is chosen as it
is able to capture the process dynamics better (Seborg et al., 2004). A section from the
full data generation results is presented in Figure 4.24, Figure 4.25, and Figure 4.26.

Figure 4.24 shows the input excitation results from initiator 1, initiator 2, and
CTA. Based on the observation, the inputs perturbation signal covers a uniform
scattering throughout the minimum and maximum range In Figure 4.25, the reactor
peak temperature in Zone 3, Zone 5, and LDPE conversion are presented. Based on
the figure, the output parameters have responded adequately towards the excitation
from the inputs. Finally, Figure 4.26 shows the polymer molecular weight (MW) and
its correlated MFI results. Since MW has a larger time constant than other output
variables, its data distribution is less congregated.

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(a)

(b)

(c)
Figure 4.24 Process input excitation data; (a) Initiator 1 flow rate (b) Initiator 2

flow rate (c) CTA flow rate
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(a)

(b)

(c)
Figure 4.25 Process output variable results: (a) reactor peak temperature in Zone 3

(b) reactor peak temperature in Zone 5 (c) LDPE conversion
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(a)

(b)
Figure 4.26 Process output variable results (a) polymer molecular weight (b) MFI
4.3.3 Model Identification results

The model identification results for the state space (SS) and Neural Wiener
(NW) models are presented here. The complete SS and NW model parameters are
shown in Appendix D. The SS model order is obtained based on Hankel singular
values, as shown in Figure 4.27. From the figure, model order six is selected for its
moderation in terms of model accuracy and complexity trade-off.

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Figure 4.27 Linear model order selection based on Hankel Singular Values
The number of hidden neurons for the nonlinear static block (i.e., neural

network model) in the NW model is acquired from the iterative validation method. The
results for the NN model’s hidden neurons selection are shown in Figure 4.28.

(a)

(b)

Figure 4.28 Number of hidden neurons selection for NW static nonlinear block for
(a) LDPE conversion (b) MFI
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Based on the figure, the hidden neurons number nine presents the best fitting in terms
of the number of hidden neurons and lowest error (i.e. the highest RMSE) in estimating
LDPE conversion and MFI. Thus, nine hidden neurons are used in the NN model
hidden layer. The hidden neuron for the validation test is stopped at 15 due to the
increasing error.

The results for State space (SS) and Neural Wiener (NW) model identification
are shown as regression plots in Figure 4.29 and Figure 4.30, which show the results
for the LDPE conversion and the MFI in scaled form, respectively. The value “0”
represents the steady state condition. The linear correlation of both data is represented
by the fit line, which is calculated by Matlab. Based on the observation in Figure
4.29(a), the NW model’s output data is scattered closer along the diagonal line (Y=T)
compared to the SS model. This indicates that the estimation from the NW model fits
the original data better than the SS model. The SS model has difficulties estimating
the maximum and minimum region of the data, which can be observed based on its
inaccurate data distribution at both ends in Figure 4.29(b). Based on R2 calculation, the
NW model produces R2 = 0.9889, which is better than the SS model with R2 = 0.9509.

Figure 4.30 shows the regression plot of the NW model and SS model for
estimating the MFI values. From the figure, the NW model output data scatters closely
along the fit line compared to the SS model. The SS model output data has higher
residuals, scattering far from the fit line and concentrating at the minimum values.
Thus, the NW model has managed to estimate the MFI values better than the SS model,
with R2 = 0.9860 compared to R2 = 0.6693 for the linear model.

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(a)

(b)
Figure 4.29 Regression plot for LDPE conversion (Y1) for (a) Neural Wiener

model (b) State space model
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(a)

(b)
Figure 4.30 Regression plot for MFI (Y2) for (a) Neural Wiener model (b) State

space model
A snippet of the model validation results from time 1900 to 2000 minutes is
shown in Figure 4.31. Based on the figure, the NW model has succeeded in fitting the
validation data profile with small error on both parameters compared to the SS model.

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