1. No category

Applying fundamental and neural networks theories in the modeling of
a commercial FCC unit
S. Papadokonstantakis1, G. M. Bollas2, J. Michalopoulos1, A. A. Lappas2, I. A. Vasalos2,
and A. Lygeros1
1
School of Chemical Engineering, National Technical University of Athens, Athens, GR157 80, Greece; tel. +3010 7723973, e-mail: [email protected]
2
Chemical Process Engineering Research Institute (CPERI), Centre for Research and
Technology Hellas (CERTH), PO Box 361, GR-570 01, Thermi-Thessaloniki, Greece;
tel. +30310 498309, e-mail: [email protected]
Abstract
Three different scenarios for the modeling of a commercial FCC (Fluid Catalytic
Cracking) unit were examined. A fundamental kinetics-hydrodynamics coupled model
based on experiments performed in an FCC pilot plant unit, a simple "black box" neural
networks model trained with data of an industrial FCC unit and a hybrid approach
combining the fundamental model as prior knowledge and a neural model as a refining
tool. These three concepts of modeling a complicated process, as the fluid catalytic
cracking process is, were compared to each other in order to understand the advantages of
every approach. To achieve that, the interpolation and extrapolation abilities of each
model were examined and their applicability bounds were defined. The results have
shown the superiority of the hybrid model approach, since it is able to combine the
advantages of the other two approaches, which are the stability in the predictions of the
fundamental "pilot plant model" and the improved accuracy of the neural model.
1.
Introduction
Modeling of industrial Fluid Catalytic Cracking (FCC) units has been of interest to
engineers in academia and industry because of their complexity and the economic
incentives associated. Its complexity arises from the strong interactions between the
operational variables of the reactor and the regenerator. Moreover, there is a large degree
of uncertainty in the kinetics of the cracking reactions and catalyst deactivation by coke
deposition in the riser reactor and the coke burning process in the regenerator [1]. Due to
its complexity the modeling of the FCC poses great challenge.
In this paper three attempts in modeling a commercial FCC riser are presented: a) a
fundamental kinetics-hydrodynamics coupled model based on experiments performed in
an FCC pilot plant unit, b) a simple "black box" neural model trained with data of an
industrial FCC unit and c) a hybrid approach combining the "pilot plant model" as prior
knowledge and a neural model as a refining tool, for scaling up the theoretical basis, to
the actual industrial reality.
The fundamental approach of modeling the commercial unit was based upon a
kinetic-hydrodynamic model, developed for the simulation of the riser reactor of the FCC
1
pilot plant unit, located in Chemical Process Engineering Research Institute (CPERI) in
Thessaloniki, Greece [2, 3]. This model calculates, via a comprehensive hydrodynamic
scheme, the catalyst hold-up and its residence time in the reactor and predicts the
catalytic reaction conversion through a Blanding type kinetic model [4]. The operation of
the pilot unit provides the ability to examine the process under steady feed and catalyst
properties, in order to better understand the influence of operating conditions on the
reaction conversion and distinguish it from other effects. For the shake of comparison a
parametric linear model was combined with the pilot plant model, when this is
implemented to the commercial unit, so that the influence of feed and catalyst properties
is incorporated. The differences in unit geometry, feedstock quality and catalyst
properties between the ideal operation of the pilot plant and the reality of the commercial
unit are included in the "pilot plant model", as far as the prediction of the conversion of
the unit is concerned.
On the other hand neural networks are a promising alternative modeling technique.
They are mathematical models, which try to simulate the brain's problem solving
approach. Neural networks have been known for decades but the tremendous evolution of
digital technology over the past two decades provided the necessary computational power
in order to use neural networks in various fields. Applications of neural networks in
chemical engineering include fault diagnosis in chemical plants [5], dynamic modeling of
chemical processes [6], system identification and control [7], sensor data analysis [8],
chemical composition analysis [9], and inferential control [10]. Quite recently there have
been publications of applying neural networks in FCC modeling [11, 12]. Neural
networks appear to be suitable for FCC modeling because: a) they can handle non-linear
multivariable systems, b) they are tolerant to the faults and noise of industrial data, c)
they do not require an extensive knowledge base and d) they can be designed and
developed easily [13].
Neural networks can also be used as hybrid models. The term hybrid modeling is
used to describe the incorporation of prior knowledge about the process under
consideration in a neural network modeling approach. The way that this incorporation
can be done depends on the form of the prior knowledge available as well as on the
desired properties of the model to be created. The two main categories are the design
approach, in which prior knowledge dictates the overall model structure and the training
approach, in which it dictates the form of the weights estimation problem [14]. This paper
handles a serial design approach.
A successful hybrid modeling approach can lead to models with better generalization
and extrapolation abilities compared to pure neural network models, especially when
there are only a few and noisy data for the training of the neural models, which is often
the case, when it comes to industrial databases. Another advantage of hybrid models,
which arises from their internal structure, is that they can be much more easily interpreted
and analyzed than simple "black box" neural networks [14, 15]. In literature there exist
some efforts of hybrid modeling for the purposes of generalized on-line state estimation
[15], and for fed batch bioreactors [14, 16], but the scientific area of scaling up a pilot
plant model to a commercial unit using a hybrid modeling approach has not been
adequately explored.
2
2.
The Fundamental Approach
FCC technology continues to evolve for more than half a century. Modeling of the
FCC unit is nowadays accomplished via complicated lumping kinetic schemes and
detailed 3D fluid dynamics simulations. Such models have been presented in literature by
various authors [17, 18, 19, 20, 21]. The FCC riser is commonly simulated as a steady
state plug flow reactor. Since residence times in the riser are much sorter compared to the
response time of the regenerator, one can at any instance describe the riser reactor by a
set of steady state relations and all the dynamic behavior is attached to the regenerator
[17]. Complicated hydrodynamic schemes and advanced reaction networks are combined
in order to simulate the operation of FCC risers. However, simplified models based on
transparent hydrodynamic assumptions and fundamental catalysis theories are still
comprised among the "winner" models regarding actual commercial units simulation and
their prediction abilities and accuracy [22, 23].
Such a model was developed to study the strong coupling between hydrodynamics
and chemical reactions that occurs in commercial and pilot plant FCC risers. This model
was based on experiments performed in CPERI FCC pilot plant unit. The pilot plant
operates in a fully circulating mode and is consisted of the riser, the stripper, the lift lines
and the regenerator. The FCC pilot plant of CPERI, details of the riser geometry and
typical values for the hydrodynamic variables are given in Figure 1 and Table 1. A more
analytical description of the CPERI FCC pilot plant can be found in literature [2, 3].
Figure 1: Schematic Diagram of CPERI FCC Pilot Plant.
The operation of the pilot plant provides all the data required for a complete
description of the process. The design of the pilot riser of CPERI has not a constant
diameter with respect to height. The reactor is divided into three regions and for every
region different hydrodynamic assumptions are made. At every section (bottom,
3
intermediate, top) different empirical correlations are applied, depending on the
geometrical similarities between the CPERI and the empirical correlation developer
installation. Due to the comparatively larger diameter of the bottom region of the pilot
unit it is reasonable to assume that a considerable amount of the reaction occurs in this
region and the simplifying assumption of a dense bed regime for the total height of the
reactor bottom seems correct. Thus a turbulent flow regime is assumed for the whole of
the bottom region with low gas velocities and high solids densities and residence times.
The correctness of the flow regime assumed in every region is validated against pressure
drop measurements.
Fully Developed Flow Region Hydrodynamic Characteristics
Gas Superficial velocity (m/s)
2.5
2
Solids mass flux (kg/m s)
55
Solids mass density (bulk) (kg/s)
900
Riser diameter (mm)
7
Riser height (m)
1.465
Table 1: Fully developed flow region hydrodynamic characteristics for pilot plant riser
On the contrary in the commercial unit the riser diameter remains constant with
height and the high gas velocities constitutes fuzzy the determination of the height of the
reactor dense region. Thus in this case, the pressure drop measurements are used for the
estimation of the dense zone height, where the flow regime is assumed to follow the
"Dense Suspension Upflow" reported by Grace et al. [24]. For this dense region the
feedstock is assumed unconverted (in terms of molar expansion) and the total volumetric
flow and the superficial velocity are significantly lower. The height of this dense region
is computed around 5% of the total riser height.
Generally in high-density circulating fluidized bed, as in an FCC riser, a "Dense
Suspension Upflow" regime is often observed [22], the flow becomes core-annulus with
considerable re-circulation of the particles. The core-annulus flow type can be simulated
by detailed CFD (Computational Fluid Dynamics) models, or by means of a slip factor
concept, which delivers accurate average results [25]. For pilot and commercial units
simulation purposes and products conversion predictions, the axial density variation
models [25, 26, 27] appear ideal. However, the highly empirical nature of the existing
models restricts their generality and constitutes their applicability uncertain. Expressing
the riser density in terms of voidage delivers Eq.(1), where ε riser is the average riser gas
phase fraction:
ε riser =
Qg ρ p
yCCR + Qg ρ p
(1)
In Eq.(1) CCR and ρp are the catalyst circulation rate and density respectively, Qg is the
average gas volumetric flow rate and y is the average gas-solids slip factor, used to
ascribe the back mixing in the riser reactor. The slip factor stands for ts/tg, or ug/us [28,
29] with g and s representing the gas and solids phase respectively. Eq.(1) corresponds to
the final correlation for the calculation of the average riser voidage in a circulating
4
fluidized bed riser. For FCC reactors none of the gas phase variables used in Eq.(1)
remains constant with height, due to the cracking reaction yielding approximately four
times the initial molar (or volumetric) flow.
The application of Eq.(1) presupposes the determination of an accurate estimation
for the slip factor y. The gas-solids slip is the key issue when dealing with small diameter
FCC risers. In the case of pilot risers every hydrodynamic attribute of the flow becomes
significant and cannot be neglected. On the contrary for commercial risers with large
diameters it is common practice that the gas-solids slip velocity is assumed to be close to
the single particle terminal velocity and slip factors are relatively small. However
according to the literature the slip velocity is always greater than the single particle
terminal velocity [30, 28, 29]. The general idea of using the terminal velocity instead of
the slip velocity is correct only in case of high gas velocities and low solids mass flow
rates [30] and delivers slip factor values close to unity. In practice the knowledge of the
exact value for the slip velocity in commercial units provides more accurate results for
the determination of the hydrodynamic characteristics of the process and finally for the
kinetic parameters estimation (each phase residence time and the space velocity).
Understanding the operation of small diameter units, where slip effects become much
more important and influence significantly the kinetic and hydrodynamic features of the
cracking process, provides the knowledge for an integrated commercial unit simulation.
A widely used expression for the calculation of slip factor was proposed by Pugsley and
Berruti [25]. This correlation is based on the assumption that the slip factor is
independent of the gas properties and solids characteristics at gas velocities much greater
than the terminal velocity, but it is a function of the riser diameter, gas volumetric flow
and solids terminal velocity. The slip factor correlation proposed by Pugsley and Berruti
was presented as an improvement of the correlation proposed by Patience et al. [28] and
suggests that the "slip phenomenon" is inversely proportional to the gas velocity and
proportional to the riser diameter and the particle terminal velocity:
5.6
+ 0.47 Frt 0.41
2
Fr
(2)
uo
u
and Frt = t
gD
gD
(3)
y = 1+
where:
Fr =
In Eq.(2) and (3) Fr and Frt are the Froude numbers for the superficial gas and terminal
velocity (uo, ut) respectively and D is the riser diameter.
With the average slip factor known, the average reactor voidage can be easily
calculated via Eq.(1). Commonly, for commercial risers, by knowing the average reactor
voidage, the total pressure drop can be directly estimated, since the static head of solids is
the dominant pressure gradient. However, it is important to note that the direct
calculation of the riser voidage from the total pressure drop ignores the wall shear stress
contribution to the total pressure drop. Depending on the riser geometry and
hydrodynamic attributes, the frictional pressure gradient can be 20-40% of the total
pressure drop [31, 29] or more analytically 15% for the gas phase and up to 50% of the
total pressure drop for the solids phase [32]. Including every pressure gradient in the
5
pressure balance analysis should provide more accurate description of the actual flow
regime for both the pilot and the commercial unit. For this analysis all pressure gradients
must be taken into account and the following expression is valid:
∆P = ∆Pfg + ∆Pfs + ∆Pacc + ερ g g ∆z + (1 − ε ) ρ p g ∆z
where:
∆Pfg
(4)
: gas-wall frictional pressure drop estimated via the Fanning equation:
∆Pfg =
2 f gερ g ug2
D
∆z
(5)
with the friction coefficient fg estimated by [33]:
 16
 Re
fg = 
 0.079
 Re0.313
Re ≤ 2300
(6)
Re > 2300
∆Pfs
: solids-wall frictional pressure drop. Among several empirical correlations
available in the literature [34] the equation of Konno and Saito [35] is utilized, giving:
∆Pfs =
2 f s ∆z Gs2
D ρ p (1 − ε )
(7)
with the friction coefficient for the solids phase estimated via:
fs =
0.0285 gD


Gs


 ρ p (1 − ε ) 
(8)
∆Pacc
: pressure drop due to solids acceleration. Assuming that the particles are
accelerated from zero velocity at the riser bottom the acceleration term can generally be
expressed as follows:
∆Pacc =
Gs2
ρ p (1 − ε )
(9)
The pressure balance formulation presented is identical for both the commercial and the
pilot unit. The difference in the two approaches is that for the pilot plant the pressure
balance is used for the validation of the hydrodynamic model applied, whereas in the
commercial unit entering the pressure drop measurements in hydrodynamic model
presented, provides an estimate of the height of the dense bottom region.
The flow regime in the reactor determines each phase residence time and thereafter
the kinetic conversion of the reaction. Thus the hydrodynamic model presented is
combined with a Blanding type [4] reaction kinetics model, in order to have accurate
simulation of the process. In this paper the prediction of only the catalytic conversion is
presented. The application of the model for the prediction of the coke yield as well can be
found in literature [3]. Regarding the kinetic aspects of the cracking process it is well
6
accepted that the cracking reaction proceeds according to second-order rate kinetics [17,
26, 27]. The apparent kinetics are higher than first order, because of the existence of
many different compounds with different reaction rates, that cause a faster depletion of
the reacting species. As a result, the reaction rate slows down faster with conversion
comparing to the case of a single compound [28]. Considering riser reactor conditions
with concurrent plug flow of gas and solids phases, the final expression for the
conversion of hydrocarbons during the FCC process would be of a form of Eq.(1) [26]:
dx
2
= kφ ( c )(100 − x )
dτ
(10)
where τ is the space time (Catalyst Hold-up / Feed Rate), x is the %wt conversion of the
hydrocarbons, φ ( c ) is the catalyst deactivation function and c is the coke content %wt on
catalyst. In the k constant of Eq.(10) feed and catalyst effects and unit factors are
incorporated. The deactivation of the catalyst for catalytic cracking reactions essentially
parallels its deactivation for coke production, so the catalyst deactivation function can be
expressed via Eq.(11) [19]:
φ ( c ) = kc c1−1/ b
(11)
The value of b in Eq.(2) indicates the catalyst decay constant and is found in literature to
vary from 1/3 [19, 17] to 1/4 [36] or even 1/6 [18].
Changes in feedstock and catalyst supply correspond to different pre-exponential
factors in the Arrhenius type formulation of the k constant in Eq.(10) and differences in
temperature correspond to different values of k. In order to examine the consistency of
the kinetic model applied to the commercial unit Eq.(10) and Eq.(11) are combined and
after mathematical reformation Eq.(12) is delivered:
 x

ln 
WHSV  − ln ( ko exp ( − E / RT ) ) = n ln ( tc )
 100 − x

(12)
where kο the pre-exponential factor of the k constant and E the activation energy of the
cracking reaction.
In Eq.(12) it is clear that the product of conversion times space velocity is an
exponential function of contact time for given feed and catalyst properties and constant
reactor temperature. A strategy often applied for validating the correct operation of an
FCC unit, or the correctness of the hydrodynamic regime assumed, is plotting Eq.(12) on
logarithmic scale. The left hand side of Eq.(12) is a linear function of ln(tc) for given
catalyst, feed and constant temperature. The slope of this linear dependence would be n,
or better b-1, the catalyst decay constant. In the case of the pilot plant the steady feed and
catalyst properties hypothesis is indeed correct. On the contrary in the case of the
commercial test every experiment has different feedstock and catalyst supply quality,
thus the value of ko is different in every experiment. For the shake of comparison with
neural and hybrid models presented in the next sections, a linear function was created for
the insertion to the model of feedstock quality and catalyst supply influence. This
function was developed with linear regression of a portion of the industrial data set, and
validated against all other data. The value ko of Eq.(12) was simulated by building a
linear correlation of feed properties (namely specific gravity, refractive index, mean
7
average boiling point, wt% basic nitrogen and %wt sulfur) and the MAT activity test as
the characterizing property of catalyst quality. The final correlation for the conversion
prediction is presented in Eq.(13):
x
MAT


 E 
−1 n
=  ∑ ai xi + b
+ c  exp  −
 WHSV tc
100 − x 
100 − MAT

 RT 
(13)
where xi and αi are the current feed property and its calculated coefficient respectively.
The development of the kinetic theory for the cracking process is identical for both
the commercial and the pilot unit, since the occurring cracking reactions are exactly the
same. Differences in the hydrodynamic attributes of each reactor correspond only in
different pseudo-kinetic parameters estimations.
3.
The Neural Networks Theory
a.
Neural Networks Description
Artificial Neural Networks (ANNs) consist of a large number of simple computing
elements, called nodes or neurons, which are arranged in layers. The nodes of one layer
are connected to the nodes of the other layers and a real valued number called "weight" is
associated with each connection. The role of the weights is to modify the signal carried
from one node to the other and either enhance or diminish the influence of the specific
connection. There are three types of layers: the input layer, the output layer and the
hidden layer. The number of hidden layers varies from network to network. However one
hidden layer has been found to be sufficient in most applications [13, 38].
There also exist many network architectures [39]. The most common is the multilayer perceptron (MLP). In this type of network the nodes of one layer are connected only
to the nodes of the next layer of the network and there is no feedback of the output
signals (feed-forward) [13]. The nodes in the input layer are not associated with any
calculations and they only act as distribution nodes. The outputs from the output layer
represent the network's predictions. The role of any node in the hidden and output layer is
to receive a number of inputs from the previous layer, sum the weighted inputs plus the
bias, non-linearly transform the sum via an activation function (i.e. Tanh or Logistic) and
finally broadcast the output either to nodes of the next layer or to the environment [40].
In this work (MLP) networks, with hyperbolic tangent (tanh) as activation function
of hidden nodes and linear transformation as activation function of output nodes are
considered. The steps involved in every effort to build a functioning ANN model of an
industrial process are: a) Data collection, b) Data pre-processing, c) Model selection, and
d) Training and validation. The ANNs used in this study were trained using the EBP
(Error-Back-Propagation) algorithm and the determination of the optimum number of
nodes in the hidden layer was carried out by a trial and error procedure based on cross
validation. In the cross validation method various network architectures are constructed,
which are produced by changing the number of nodes in the hidden layer. Using a
specific training data set each one of them is trained several times with different initial
values of weights in order to find the combination of weights, which produces minimum
8
output error for a separate validation data set. In the end, all network architectures are
compared and the one with the minimum error is selected as optimum [40].
b.
Hybrid Modeling
In this paper in addition to the standard neural network approach a hybrid-modeling
scheme is implemented. It belongs to the design semi parametric approaches [14], namely
it tries to correct the inaccuracy of an existing model, which is considered to contain our
prior knowledge regarding to the process under consideration, by using a neural network,
which is trained to compensate for this inaccuracy.
Lets assume, that the fundamental or empirical model in hand is described in general
by the following functional form:
G G
y = f ( x, c )
(14)
G
G
c = g (a )
(15)
G
G
where x is the vector of the variables that the model uses to predict the variable y , c is
G
the vector of the constants which are included in the functional form and a is the vector
expressing the assumptions made during the construction of the model.
Even if we assume that the particular functional form expresses the influence of the
variable vector in every detail, there are still some limitations in the general
implementation of the model, due to the assumptions made. These often influence the
estimation of the constant vector (Eq.(15)). This can lead to inaccurate predictions, when
the model is implemented in cases, where some of the assumptions do not any more
apply and therefore the values of the constant vector are not any more appropriate.
Sometimes this problem can be rather easily overcome by simply recalculating the
constant vector for the new conditions. This presupposes that the relation between the
constant vector and the assumptions made (Eq.(15)) is either known or its functional form
is predefined and all it remains is adapting the constants of this new relation, for instance
by using regression analysis. But in cases, where our knowledge for this relation is very
limited, a very promising alternative is to use a neural network instead of regression
analysis.
The aforementioned approach is a serial semi-parametric hybrid modeling design
approach and it is presented in Figure 2. The neural model part is used to calculate the
new values of the constant vector, namely to approximate the function ( g ) in Eq.(15). It
G
is assumed that in the Eq.(15) the vector of the assumptions ( a ) refers to variables, which
were kept constant or were ignored during the construction of the Prior Knowledge
model (P-K model) and therefore their influence has not been adequately evaluated. In
our case the P-K model is the pilot plant model already described in Section 2 and the
assumptions of the model are that the feed and catalyst properties of the unit are constant.
Furthermore we have to take into account the overall different conditions under which the
industrial unit is operating compared to the pilot plant and the reactor geometry effect,
often called as unit factor, all which will be referred from now on as scale up factors in
this paper. All the above are included in the estimation of the constant ko (Eq. (12)),
G
which is the ( c ) vector in our case.
9
Variables Set-1
P-K Model
Hybrid
Prediction
G
c
Variables Set
Neural
Variables Set-2
Figure 2: A hybrid model according to the serial approach. The neural model is trained to
G
approximate the new values of c , which will be used from the P-K Model to produce a
more accurate Prediction (Hybrid Prediction)
Because of the change in feed and catalyst properties for every run of the industrial
process which we attempt to model, ko varies from run to run and it has not anymore a
constant value as it was considered during the development of the pilot plant model.
According to this, the first step in our approach is to solve Eq.(12) and obtain the
appropriate values of lnko by replacing the actual experimental values from the
commercial unit for all the variables included in this equation. This must be done for all
the available i-measurements. The i-values of lnko obtained this way are the target values,
which the neural model will try to approximate. The second step is the selection of the
variables used as input variables for the neural network during the training procedure
(Variables Set-2 referring to Figure 2. In addition to the variables that refer to the
G
assumptions' vector ( a ), variables included in the P-K model may also be used, if it is
believed that the P-K model does not capture their total amount of information. Then the
neural network is trained using the algorithms described in Section 3a and the values of
ko that the network calculates are used in the P-K model.
4.
Modeling the Commercial Unit
All the three models presented in this section attempt to predict the conversion of the
commercial FCC unit in the Aspropyrgos Refinery of Hellenic Petroleum S.A. (Athens).
The data set for this unit was collected every one day for a period of 15 months. Blocks
of data corresponding to process faults were excluded from the study and outliers that
may have been caused by some measurement errors were removed. A simple outlier
detecting method was followed, where any observation that differ more than three
standard deviations from the mean is removed from the set [40]. As a result, a set of 308
observations, representative of various operating conditions and a broad range of the
input variables, were used for the development of the models.
The available 308 runs were separated in four data sets. The training and the
validation set (178 and 50 runs respectively) were used for the needs of the training
algorithm (Section 3) as far as the neural and hybrid models are concerned and for the
calculation of the constants in the regression analysis of the pilot plant model. The
10
generalization set (50 runs) is used for testing the models, in case that all the variables
interpolate. The extrapolation set (30 runs) is used for testing the models, in case that
some of the operational variables extrapolate. We have let only the operational variables
to extrapolate for two reasons. The first is that their effect is supposed to be mainly
captured by the pilot plant model and we wanted to see how far this is helping the
extrapolation abilities of the hybrid model, in which this prior knowledge is included.
The second is that if we had let more variables to extrapolate, this would lead to a greater
extrapolation set and the other sets would have to be of smaller size. That could seriously
affect the training procedure of the neural networks. The maximum and minimum values
of all the variables used in this study are shown in Table 2.
No Variable
1
2
3
4
5
6
7
8
9
10
11
12
13
Specific Gravity (SG)
Mean Av. Boiling Point (MeABP)
Average Particle Size (APS)
Apparent Bulk Density (ABD)
Catalyst Circulation Rate (CCR)
Reactor Temperature
Reactor Pressure
Feed Rate
Riser inject steam
Sulfur (S)
Basic N2
Refractive Index (RI)
Micro Activity Test (MAT)
Conversion
Units
o
C
µm
G/ml
m3/h
o
C
kp/cm2
tn/h
kg/h
%w
wppm
%wt
Training
Min
Max
0.900 0.921
437.8 469.4
72.0
84.0
0.87
0.94
18.3
21.5
529.5 535.9
2.2
2.5
239.9 280.5
2852
3300
0.29
1.85
104
381
1.483 1.492
66
75
69.06 77.81
Extrapolation
Min
Max
0.901 0.917
438.3 463.3
73.8
83.0
0.88
0.93
17.8
22.0
528.8 536.0
2.2
2.5
235.8 283.6
2898
3322
0.32
1.46
112
241
1.484 1.491
66
73
70.53 77.81
Table 2: The limits of the available variables in the training and the extrapolation set
After this partition of the sets, the values of the variables were normalized. Both for
the input and output variables a linear normalization based on the training set was used.
After the normalization all the variables have values belonging to the interval [-1,1].
a.
Fundamental Model (Model 1)
The fundamental model was developed as described in Section 2. The optimum
values of ko in Eq.(12) were calculated from the industrial data and a linear model was
developed for the description of feed and catalyst quality influence. For the
implementation of the model to the commercial unit the values of activation energy E and
the catalyst decay constant n were estimated 24.800 Btu/lbmol/R and 0.72 respectively
[37]. All the variability of the values of ko computed for the commercial unit was
attempted to be simulated through the variance of the catalyst and feed properties
variables of Table 2. For the feed influence the variables used were variables 1, 2, 10-12
and the catalyst effect was represented by variable 13. The linear model was constructed
via linear regression of the industrial data for the training and validation sets, as they
11
were described above. The coefficients αi, b, c of Eq.(13) computed from the linear
regression procedure are presented in Table 3.
No
α1
α2
α3
α4
α5
b
c
Variable
Specific Gravity (SG)
Mean Av. Boiling Point (MeABP)
Sulfur (S)
Basic N2
Refractive Index (RI)
Micro Activity Test (MAT)
Intercept
Units
o
C
%w
wppm
Coefficient
-1170.33
-1.985
-227.83
1.193
-12615.46
280.088
22525.8
Table 3: Linear regression coefficients for the influence of feed and catalyst properties
The assumption of linear feed and catalyst effect function is of course
oversimplified, yet the main objective of this work was not to establish a complicated
model, capturing feed and catalyst properties effects in the catalytic cracking of gas-oil,
but to compare different approaches of modeling with the hybrid modeling approach
presented.
b.
Neural Model (Model 2)
This is a typical "black box" neural model. It uses as input variables all the available
variables of Table 2 and predicts the conversion (%wt) of the commercial FCC unit. It is
trained using the algorithm and procedures mentioned in Section 3a and the data sets
mentioned in the beginning of this Section. The structure of the winner neural model was
13-3-1 (input nodes, nodes of the hidden layer and nodes of the output layer respectively)
resulting to 46 weights and to a "data to weights" ratio of 3.9. This ratio has determined
the upper limit of the number of nodes in the hidden layer during the trial and error
algorithm. No networks with a ratio less than 3 were included as candidate "winner"
networks. Furthermore no network was trained for more than 20000 epochs.
c.
Hybrid Model (Model 3)
This is the hybrid model that was developed according to the analysis made in
Section 3b. The neural part of the hybrid has the task to approximate the values of the
constant lnko, which were calculated using for all the variables included in Eq.(12) the
respective experimental values in the database. The selection of the input variables used
by the neural network to perform its task was made based on the following aspects.
Referring to the pilot plant model, we can separate the variables of Table 2 in three
categories: Variables that were kept constant during the construction of the pilot plant
model but they are included in the model (Variables 1 to 4), variables that were kept
constant during the construction of the pilot plant model but they are not included in it
(Variables 10 to 13) and variables that were included in the pilot plant model and their
influence is believed to be satisfactorily explained by it (Variables 5 to 9). All the
variables from the first two categories were used, since the effect of feed properties and
catalyst quality is included in the pilot plant model only from their hydrodynamic
12
perspective and their actual influence on the cracking reaction may be underestimated,
when the pilot plant model is applied to the commercial unit. Furthermore two of the
operational variables (third category) were included, namely the Feed Rate and the CCR,
according to the following reasoning: Inaccuracies in the application of the empirical
equation of Pugsley et al. [25] to the commercial unit and in the pressure balance
formulation, could influence the prediction of slip effects on the commercial unit. Thus
the flow rates of gas-oil and catalyst were included in the hybrid model, in order to
examine if better predictions are accomplished. Finally the ko value obtained from the
neural part is used by the "pilot plant model", which calculates the conversion of the
commercial unit.
5.
Results
In this section we present the results for the three models developed. In Table 4 some
of the most common statistical pointers have been calculated for the shake of comparison
between all the models. In this Table the R2 and A, B are the correlation factor and the
coefficients concerning the "best fit" line. They are obtained with regression analysis
based on the minimization of the squared errors. The closer to 1 its correlation factor (R2)
is and the closer the coefficients of the line to 1 (A) and 0 (B) respectively are, the better
the model is. MSE is the Mean Square Error, ARE is the Average Relative Error (%) and
MaxRE is the Maximum Relative Error (%).
MSE
R2
A
B
ARE (%)
MaxRE (%)
Generalization Set
Model1
Model2
Model3
1.1
0.5
0.4
0.85
0.89
0.90
0.78
0.89
0.86
16.1
7.8
10.1
0.9
0.7
0.7
3.8
2.7
2.2
Extrapolation Set
Model1
Model2
Model3
1.0
0.9
0.7
0.78
0.77
0.83
0.80
0.84
0.92
14.0
11.8
5.6
1.0
1.0
0.8
3.2
3.3
3.3
Table 4: Common Statistical pointers for the generalization and extrapolation abilities of
the three models
The behavior of the model, which uses the linear factors for capturing the feed and
catalyst properties effects (Model 1), is satisfactory. It achieves a relative error less than
1% for the generalization set and it also maintains its abilities in the extrapolation set.
This is what someone would expect, since this model is mainly a fundamental model.
On the other hand the "black box" neural model (Model 2) performs clearly better in
the generalization set. This is also expected, since the effect of the feed and catalyst
properties is not likely to be adequately described by a linear model, as the one used in
Model 1. The neural model's excellence is due to the fact that it is able to capture the nonlinear effect of these variables and simultaneously simulate the non-linear function that
describes the effect of the operational variables. Furthermore it simulates better the
specific FCC unit, since it is fully developed with data of this unit. However, it is also
13
clear that the performance of this model gets worse for the extrapolation set. This trend
would be even clearer, if the extrapolation to be done was much more intense.
Unfortunately the industrial database did not allow such an intense extrapolation.
Figures 3 (a) and (b) refer to the scatter plots for the hybrid model as far as its
generalization and extrapolation abilities respectively are concerned. In these Figures the
x-axis has the experimental values and the y-axis the predictions. We use two lines to
show the success of the prediction. The one is the line with equation y=ax+b with a=1
and b=0, on which all the data of an ideal model should lay. The other line is the line that
best fits on the data of the scatter plot as it is already explained. The two lines are very
close to each other in both cases, confirming the accuracy and stability of the hybrid
model.
80
80
y = 0,86x + 10,1
R2 = 0,9
R2 = 0,83
77
Predicted
Predicted
77
y = 0,92x + 5,6
74
71
68
74
71
68
65
65
65
68
(a)
71
74
Experimental
77
80
65
(b)
68
71
74
Experimental
77
80
Figure 3: Performance of the hybrid model: (a) generalization, (b) extrapolation
6.
Conclusions
In this effort we have presented 3 models concerning the prediction of the
conversion of a Fluid Catalytic Cracking Unit. The first one was created based on the
experiments carried on a pilot plant, the second one was created based only on the
industrial data using a typical "black box" neural network approach and the third one was
a hybrid model. The hybrid consists of two parts: the pilot plant model part, which gives
the basis for the prediction and the neural model part, which tries to refine this prediction,
so that the influence of variable feed and catalyst properties as well as scale up factors are
taken into account. The combination of the two parts was made in a serial semi
parametric design approach.
The results have shown that the hybrid method has been proven the most successful
one. The already satisfactory predictions of the pilot plant model are clearly refined
through the neural part used and furthermore the hybrid model retains its abilities in the
extrapolation set, where the "black box" neural model starts getting instable. The reason
for the stability of the hybrid model is its fundamental part. The superiority of the hybrid
for its extrapolation properties is assumed to become clearer, as the extrapolation
14
becomes more intense. Finally it is important to be noticed that the advantages of the
hybrid model compared to the "black box" neural networks do not only concern the
accuracy of the predictions but also the interpretability of the model, which is a crucial
point when the created model is used for the study of the behavior of the process and for
optimization purposes.
15
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