Chin.
J
Chem.
Eng.,
15(
1) 7580 (2007)
Multiobjective Optimization of the Industrial Naphtha Catalytic
Re
forming Process*
HOU Weifeng(@E@),
SU
Hongye(
5
&)**,
MU
Shengjing(+
&
$$)
and
CHU
Jian( @)
National Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou 310027, China
Abstract
In
this
article, a multiobjective optimization strategy for an industrial naphtha continuous catalytic reform ing process that aims to obtain aromatic products is proposed. The process model is based on a 20lumped kinetics re action network and has been proved to be quite effective in terms of industrial application. The primary objectives in clude maximization of yield of the aromatics and minimization of the yield of heavy aromatics. Four reactor inlet tem peratures, reaction pressure, and hydrogentooil molar ratio are selected as the decision variables. A genetic algorithm, which is proposed by the authors and named as the neighborhood and archived genetic algorithm (NAGA), is applied to solve this multiobjective optimization problem. The relations between each decision variable and the two objectives are also proposed and used for choosing a suitable solution from the obtained Pareto set.
Keywords
multiobjective optimization, catalytic reforming, lumped kinetics model, neighborhood and archived genetic algorithm (NAGA)
1 INTRODUCTION
Petroleum refining and petrochemical industries aim at maximizing one prime product while simulta neously minimizing another accessory product to im prove the quality of the prime product. Unfortunately, the two requirements are often conflicting or incon sistent. It is necessary to determine the tradeoff com promises to balance the two objectives[ 1,2]. As the core of aromatics complex unit, catalytic reforming is a very important process for transforming naphtha into aromatics feedstock[3]. In this process, the yield of aromatics, including benzene, toluene, paraxylene, metaxylene, orthoxylene, ethylbenzene, and heavy aromatics
(i.e.
9 and more carbon aromat ics), are regarded as the main index that determines the quality. However, heavier aromatics are not re quired and will increase the load on the downstream units of the aromatics complex process, especially on the disproportionation and xylene fractionation units. Thus, the design and operation of the catalytic re forming process require multiobjective optimization to balance the various objective functions. Multiobjective optimization, involving more than one objective function, was typically modeled and solved by transforming it into a single objective prob lem using different methods, such as the restriction method, the ideal point method, and the linear weighted sum method. These methods largely depend on the values assigned to the weighted factors or the penalties used, which are done quite arbitrarily. An other disadvantage of the above methods is that these algorithms obtain only one optimal solution at a time and may miss some useful information[4]. Recently, multiobjective evolutionary algorithms are used more popularly in industrial process model ing, optimal design, and operation[4]. These may pro duce a solution set, which is named as a Pareto set, in a single run of the algorithms. The Pareto solutions are extremely useful in industrial operations as these nar row down the choices and help to guide a deci sionmaker in selecting a desired operating point (called the preferred solution) among the (restricted) set of Pareto optimal points, rather than from consid erably large number of possibilities[5]. Coello[6] pre sented comprehensive reviews on the development
of
the evolutionary (especially genetic) multiobjective optimization. When compared with the previous methods, such as the nondominated sorting genetic algorithm (NSGA) [7], the niched Pareto genetic algo rithm (NPGA)[8], the Pareto archive evolutionary strategy (PAES)[9], and the strength Pareto evolution
ary
algorithm (SPEA)
[
o], the method employed in this study, the neighborhood and archived genetic al gorithm (NAGA)[l1,12], offers several advantages: (1) low computation complexity; (2) insensitivity of the efficiency to the method parameters; and (3) uniform distribution on the Pareto front. In this article, the multiobjective optimization strategy for an industrial naphtha continuous catalytic reforming process is built to improve the operation level. A 20lumped kinetic model is employed for the industrial catalytic reforming reaction and the corre sponding process model is validated by successful industrial applications[ 131. In the catalytic reforming unit, the objectives are to maximize the aromatics yield and minimize the yield of heavy aromatics. The multiple Pareto optimal solutions of the problem are obtained by applying the multiobjective genetic algo rithm, NAGA. It presents an operating parameter set for operators for various operational targets.
2
DESCRIPTION OF THE PROCESS AND MODELING
The simplified continuous catalytic reforming process flow diagram is shown in Fig.1. The naphtha, used as the catalytic reformer feedstock usually
Received 20051119, accepted 20060703.
*
Supported by the National Natural Science Foundation of China (No.60421002).
**
To whom correspondence should be addressed. Email: hysu@iipc.zju.edu.cn
76 Chin.
J.
Ch.
E.
Vol.
15,
No.1)
RIkR4: reformer to hydrogenconsuming unit cooler recycle gas naphtha feed R4 spent catalyst iromatics product
Figure
1
Flowsheet
of
a continuous catalytic reforming process
containing more than 300 chemical compounds of paraffins, naphthenes, and aromatics in the carbon number range of
C4
to
Clz,
s combined with a recycle gas stream containing
60
to 90% (by mol) hydrogen. The total reactor charge is heated and passed through the catalytic reformers, which are designed with four adiabatically operated reactors and four heaters be tween the reactors to maintain the reaction tempera tures at design levels. The effluent from the last reac tor is cooled, which then enters the product separator. The flashed vapor circulates to join the naphtha feed stock as recycle gas. Excess hydrogen from the sepa rator is sent to other hydrogenconsuming units. The separated liquid that chiefly comprised the desired aromatics together with light gases and heavy paraf fins is sent to the separation system to obtain aromat ics products. The aromatics products are obtained by the con version of nparaffins and naphthenes in naphtha to iosparaffins and aromatics over bifunctional catalysts such as PtSdA1203 in the four reactors. The domi nant reaction types of catalytic reforming are dehy drogenation of naphthenes, isomerization of paraffins and naphthenes, dehydrocyclization of paraffins, hy drocracking
of
paraffins, and hydrodealkylation
of
aromatics. Dehydrogenation is the fastest reaction followed by isomerization, which is moderately fast, whereas dehydrocyclization and hydrocrackmg are the slowest. As mentioned above, the naphtha feedstock is very complex and each of these undergoes various reactions.
To
reduce the complexity of the model to a manageable level, the large number of naphtha com ponents are assigned to a smaller set of kinetics lumps, each of which is composed of chemical species that are grouped together according to some criteria[ 141. Accordingly, various lumped lunetics models with varying levels
of
sophistication that represent catalytic reforming reactions have been reported in the litera ture[
1520].
In the previous study[l3], a simple lumped
h
netics model for catalytic reforming with
20
lumps involving 31 reactions was presented. The corre sponding reaction network is shown in Fig.2. In this model, the total reactor charge is characterized as par affins (P), naphthenes
(N),
and aromatics (A) lumps with the carbon number ranging from
6
to 9+(9+indicates a carbon number of 9 and above) and light paraffins (PIP5), in which the 8carbon aro matics are subdivided into their four isomeric com pounds,
i.e.
PX (paraxylene), MX (metaxylene), OX (orthoxylene), and EB (ethylbenzene). The rationale of selecting these lumps was based on both thermo dynamic and lunetics considerations for the aromati zation selectivity of paraffins and naphthenes. It is not necessary to split the paraffin or naphthene lumps into their individual isomers
e.g..
isohexane and nhexane) for achieving similar aromatization selectivity for the two lumps (except for methyl cyclopentane and hex ane) and for faster isomerization reaction rates relative to dehydrocyclization and hydrocracking[ 15,161. In this reaction network, except for isomerization, all the dominant catalytic reforming reactions are included.
Figure 2 Reaction scheme for naphtha reforming
All the 31 rate equations are nonlinear pseudomonomolecular in nature, with the rate coeffi cients obeying the Arrhenius law, as shown in Eq.(l),
kj
=kOj.exp(Ej/RT).Pf’
4
O
4
<l, j=131 (1)
February, 2007
Multiobjective Optimization of the Industrial Naphtha Catalytic Reforming Process
77
Under the normal reformer operating conditions, radial and axial dispersion effects were found to be negligible[ 131. For the radial flow reactor, the global material and the heat balance equations are given in Eqs.(2) and (3), respectively, where
Y
is the vector of the molar flow rates including 20 lumps and
HZ.
Eq.(2) is solved using a mixed nu merical algorithm of fourthorder RungeKutta and Gear method, and Eq.(3) is solved using the modified Euler method. The thermochemical properties of each lump are computed by talung an arithmetic average of the properties of the corresponding pure chemical components constituting the lump. The product separator was modeled to perform in isothermal flash operation. A PengRobinson equation was used to compute the vaporAiquid equilibrium constants. The socalled sequential modular approach is implemented for the computation of this flowsheet. Except for the separation system, the reactors, the heaters, the product separator, and the heat exchangers are included in this computation. If the activation energies
E),
he pressure expo nents
(@,
and the frequency factors
ko)
for all 31 re actions are estimated, there will be 93 kinetics pa rameters in total, and it is very difficult to determine these parameters synchronously. Generally,
E
and
0
values reported by different literatures for the specific catalyst are similar.
To
reduce the difficulty experi enced in estimating parameters, the parameters
E
and
0
in this model are taken from Ref.[18] and only thirtyone
ko,
which considers the difference between the estimation of parameters
E
and
0
and the unmod eled lunetics, are estimated. The procedure of parameter estimation is carried out by minimization of the sum of the squares of the deviations between the plant and the calculated values of the key variables such as the compositions of ef fluent from the last reactor and the outlet temperatures of the four reactors. The operating and assaying data samples of several months for the industrial process, which are first reconciled by material balance, are used to estimate
/Q
by the BFGS optimization algorithm.
3
FORMULATION OF THE OPTIMIZATION PROBLEM
The variables that affect the catalytic reforming process are the volume flow of naphtha charge to the volume of the catalyst (liquid hourly space velocity, LHSV), the latent aromatics content of naphtha charge (LA), the four reactor inlet temperatures (TI, T2, T3,
T4),
the reaction pressure
Pr),
the mole flow of hy drogen in the recycle gas to the mole flow of naphtha charge (hydrogentooil molar ratio,
nH nHc
,
the product separator temperature (T,),
etc..
Among the
9
process variables selected using mechanism analysis, the sensitivity analysis of each variable is performed using the process model presented in Section 2 to ob tain its quantitative corrections with the aromatics yield and the yield of heavy aromatics. It is shown that the appropriate set point value of one variable for maximizing the aromatics yield may not be suitable for minimizing the yield of heavy aromatics. There fore, the suitable tradeoff solutions for the two opti mal objectives should be considered. For the continuous catalytic reforming process in this study, the unit is in full load operation and the value of LHSV cannot be further increased. Similarly, the quality of naphtha feedstock
e.g.
LA) cannot be changed artificially for most domestic petro leumrefining enterprises. The product separator tem perature T, is not independent of other variables. Moreover, for further lowering of the temperature, coolers need to be included in the system, which in turn increase the operation costs. Hence, the remain ing process variables are selected as the decision variables for optimization in this study. These are the four reactor inlet temperatures (TI, T2, T3,
T4),
he re action pressure
(PJ,
and the hydrogentooil molar ratio Thus, the two independent objectives, namely, the maximization of the aromatics yield (AY) and the minimization of the yield of heavy aromatics (HAY) are formulated mathematically as follows:
(
ZH
lnHC
1.
maximize AY(T1, T2, T3,
T4,
Pr,
nH nHc
1
minimize HAY(T1, Tz, T3, T4,
pr
H nHc
subject to 520
G
Ti, T2, T3, T4
G
530 0.8<pr<0.9
3.0<
nH2 nHc
G4.0
65 GAY <68 18GHAY <23
(4)
The bounds of the decision variables and the ob jectives have been chosen based on industrial practice. Because NAGA deals with only the minimization objective[
1
I], the maximization of AY can be replaced by the minimization of a function
f
where fl=lIAY, without the replacement changing the location of the optima. To normalize the objective functions, the func tion
fi
is transformed to fi=KflAY, and the function
f2
may be simplified as f2=HAYlKc, where Kf=67 and
Kc=20
are the reference operating values of the aromat ics yield and the yield of heavy aromatics, respectively.
4
RESULTS AND DISCUSSION
The solution for the multiobjective optimization problem described in Section 3 is obtained using NAGA. Table 1 provides the parameters of NAGA applied in ths study. Figure 3 shows the typical optimal solutions ob tained by a single
run
of NAGA for the above formu lated problem. The top of Fig.3 denotes the relationship
Chin. J. Ch.
E.
15 1)
75 (2007)
78
Chin.
J.
Ch.
E.
Vol.
15,
No.1)
22
Table
1
Algorithm parameters used
in
this study
Parameters Values volume of the archive
100

maximum generation probability
of
crossover probability
of
mutation
500
0.8 0.01
population size
50
neighborhood size
0.05
between the two minimum objectives,
fi
vs
fi
whereas the bottom depicts the solutions of the two srcinal objectives. The conflict between the effects of the decision variables on the two objective functions, results in the optimum being a Paretooptimal set rather than a unique solution. The Pareto set has the property that when one point on the set is moved to another, one objective function is improved
eg.
the aromatics yield increases), but the other function be comes worse
e.g.
the yield of heavy aromatics in creases accordingly). Hence, within the Pareto set, neither the solution dominates an over the other, and both indicate the optimal solation for the two objec tive functions and the minimization of the yield of heavy aromatics with the given operating bound. The operators have to use the additional information, such as the market quotation, the operating cost, and the corresponding decision variable values to select an operating point (preferred solution) from the entire Pareto set for operation. Each point in Fig.3 represents a Pareto solution, which is associated with a set of the six decision vari ables. Fig.4 is a plot of the decision variables corre sponding to each
of
the points on the Pareto set. Ob
IS
ic.
1
00
0.95 0.90 0.985
0.990
viously, the relations between each decision variable and the two objectives can also be observed. Among the six variables,
T4
is unique in that all its points are close to its upper bound, which indicates that increas ing
T4
results in both an increase in the aromatics yield and a decrease in the yield of heavy aromatics. However, increasing the decision variables
TI, T2,
pr
and
nH2
nHc
results in a decrease in the yield of heavy aromatics, but a decrease in the aromatics yield. In other words, the four variables have opposing ef fects
on
the two minimum objectivesfi andfi. Besides the effects of the above variables, it is observed that the effects of
T3
on
the two objective functions are mild. All the above phenomena are confirmed by the process operators. These can also be rationally ex plained by the reaction mechanism. In the first and second reactors, the inlet temperature of
520°C
is adequate for the complete conversion of naphthenes to aromatics. A higher temperature is suitable for hydro craclung of paraffins, which results in the decrease of aromatics. In the fourth reactors, dehydrocyclization and hydrocracking of paraffins are the major reactions and are both aided by hlgher temperatures. In this study, the competition is more favorable for dehydro genation and results in an obvious increase in aromat ics. In any reactor, exothermic hydrodealkylation of aromatics increases with an increase of temperature, which indicates a decrease of heavy aromatics. On the other hand, lower pressure favors dehydrocyclization and dehydrogenation, but not hydrocracking and hydrodealkylation, which result in increase of both gross aromatics and heavy aromatics. Less
nH,
/
nHC
indicates low partial pressure of hydrogen. Hence,
nH2 nHc
and
pr
have
slmilar
effects
on
the
two objectives.
:..
c..
z
*
*
.
XI
::.
,
.
.,
~
:
5
.
.
0.995
1.000
1.005
1.010
1.015
1.020 1.025
A
.*
.*
..
8
18
I I
1
65.0 65.5 66.0 66.5 67.0 67.5
6
AY,
o
Figure
3
Paretooptimal set of solutions obtained from the simultaneous optimization nfi
vs
fi
nd in the srcinal objectives of the aromatics yield and the yield of heavy aromatics February,
2007
Multiobjective Optimization of the Industrial Naphtha Catalytic Reforming Process 79
520
65 66 61 68 530 25
r T
520'
I
65 66 67 68
0'90
TFJ
0.85
0.80
....
65 66 67
68
3.5 3.0 65 66 61 68
AY,
Yo
I
520
18
19
20
21
22 23
ow
520
18 19 20 21 22 23 525 520
18
19 20 21 22 23 52018 19 20 21 22 23
...
0.85 19 20 21 22 23
. .om..
3.5 3.0 18 19 20 21 22 23
HAY,
Yo
Figure
4
The decision variables corresponding to each of the Paretooptimal solutions shown in Fig3
The above relations between each decision vari able and the two objectives are useful for selecting a suitable solution from the entire Pareto set. For exam ple, the decision variable values and the corresponding objectives of several typical solutions, points
A,
B,
C,
D,
and
E
in Fig.3, are listed in detail in Table 2. The point
N
denotes the industrial normal operating point, which is above the Pareto solution front that is ob tained. If the aim is to increase the aromatics yield,
it
may be feasible to increase
T4
and (or) decrease
pr
and
nH,
/nHc
as listed in point
A
or
C.
While aiming to decrease the yield of heavy aromatics, it may be feasi ble to increase
TI, Tz,
T4
and (or) increase
pr
and
nH2
nHc
s listed in point
B
or
E.
In actual industrial operahons,
pr
and
nH,
/nHc
are always maintained at higher values to protect the catalyst from rapid coking.
As
a solution to the abovementioned problem, when other decision variables are approximately constant, only increasing
T4
by about
5°C
can lead
to
beneficial effects, an increase of 0.18 (by mass) in the aromat ics yield and a decrease of 1.77 (by mass) in the yield of heavy aromatics, as listed in point
D.
The law that the increase of aromatics yield can only be ob tained by slightly increasing
T4
has been validated in the same industrial continuous catalytic reforming unit, as reported in the previous literature[21].
CONCLUSIONS
The reallife challenge of promoting added value in the industrial naphtha continuous catalytic reform ing process is described in this article.
A
20lumped kinetics model for catalytic reforming is used to solve the multiobjective optimization problem: maximiza tion of the aromatics yield and simultaneous minimi zation of the yield of heavy aromatics. By performing the optimization based on the neighborhood and
Table 2 Comparison of the decision variables and objectives for normal operation and five possible cases
of
optimal operations
Parameters
Points
TI,
c
T2,
c
T3,
"C
T4
"C
pr,
MPa
n~~
~HC
mol.mol'
AY,
%
(by
mass)
HAY,
(by
mass)
N
522.1 521.3 522.6 524.0 0.88 3.5 66.85 22.60
A
520.0 520.0 523.8 528.6
0.80
3
O
67.63 22.57
B
523.1 527.5 ,523.8 529.3 0.85 3.6 66.79 20.76
C
520.2 520.6 524.5 528.6 0.83 3.4 67.20 21.71
D
521.5 521.0 523.8 529.3 0.88 3.6 67.03 20.83
E
523.1 522.0 530.0 530.0 0.90 4.0 66.17 19.51
Chin.
J.
Ch.
E.
15 1)
75 2007)