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Energy & Fuels 2008, 22, 2892–2901
Optimal Hydrogen Production through Revamping a Naphtha-Reforming Unit: Catalyst Deactivation Roberto Galiasso Tailleur* and Ytalo Davila Department of Thermodynamics, Simo´n BoliVar UniVersity, Sartenejas, Baruta, Miranda 1012, Venezuela ReceiVed March 6, 2008. ReVised Manuscript ReceiVed May 3, 2008
Generating the necessary volume of hydrogen to produce high-quality gasoline has become a critical issue in some refineries, where an important hydrogen source is an old semi-regenerative catalytic naphtha-reforming unit. We studied the possibility of redesigning this unit to obtain an additional ∼0.1 millon of standard cubic metric per day of hydrogen while fulfilling the 15 ppm sulfur specification with the refurbished naphtha hydrotreater. The reforming unit (which has three equal-size reactors in series) was simulated using a previously developed kinetic lump model and a new catalyst deactivation model. The constants for the apparent kinetics model were adjusted using commercial data from one cycle of operation. The deactivation model was developed on the basis of pilot-plant and commercial data from an operating unit. The constants for both models were obtained using a genetic algorithm. The integrated model was used to both estimate the impact of including a new reactor and optimize existing reactor configuration. In addition, the model included redesigning the heater, debutanizer, and recycle compressor. The simulation indicated that optimal hydrogen production depends upon catalyst deactivation, cost of revamping, reactor configuration, and integration to the refinery. The optimal economical cycle length was obtained for a particular set of reactor volumes and additional naphtha throughput.
Introduction Catalytic reforming transforms naphtha into high-octane gasoline and aromatics for aromatic production plants. Because of the dehydrogenation reactions involved, catalytic reforming constitutes one of the main hydrogen sources in the refinery. In our case, the need for hydrogen optimization was established in one refinery that used a semi-regenerative process. Optimization was needed to expand a new naphtha hydro-desulfuration process that reduces sulfur content in the gasoline pool. This conventional naphtha reforming plant has three equal-sized reactors (90 m3) loaded with PtReCl/Al2O3 catalyst (Figure 1). The existing capacity is 2000 m3/day, while the operation cycle length is around 20 months. After each cycle, the catalyst is regenerated.1 The heater is divided into three sections: one is for feed preheating, and two reheat the intermediary streams coming from the first and second reactors. Each section has an independent temperature control system. The heat exchanger increases the feed temperature from 360 to 737 K using the high-temperature reformed naphtha from the third reactor as heating fluid. The operating conditions are specified in Table 1. Current centrifugal compressors recycle about 65% of the gas produced in the high-pressure separator, while the rest is sent to a hydrotreating process. The high-pressure separator receives the cooled reformed naphtha plus the hydrogen coming from the third reactor; the top and bottom products are gasrich hydrogen and a reformed naphtha stream, respectively. The debutanizer [part of the fluid catalytic cracking (FCC) plant] is used to adjust the volatility of the C5+ reformed naphtha for the gasoline pool. * To whom correspondence should be addressed: Texas A&M University, College Station, TX 77843. E-mail:
[email protected]. (1) Parera, J.; Fı´goli, N. Reactions in the commercial reformer. In Catalytic Naphtha Reforming: Science and Technology; Antos, G., et al., Ed.; Marcel Dekker, Inc.: New York, 1996; p 45.
The chemistry of the naphtha-reforming process is wellknown (see for example, Parera and Fı´goli2). Different strategies are used to simulate this process, starting with using a simple lump of reaction (Smith3), a simple molecular lumps system (Ramage et al.4), a 32 molecular lamp (Taskar and Riggs5), and a large number of molecular lamps (Mobil6). Ancheyta and Villafuerte,7 Xie et al.,8 and Froment9 have used more fundamental approaches, such as single-event methodology. In this paper, a simplified lump of 12 reactions was selected to model the reactor (discussed below) while incorporating two deactivation functions, one for metal sites and the other for acid sites. This optimization strategy takes into account that desirable reversible reactions involved in hydrogen production are favored by low hydrogen partial pressures and high temperature, and all reactions are favored by increasing residence time (catalyst volume) and feed molecular weight.2 However, increasing severity leads to faster coke deposition and catalyst deactivation, contributing to shorter cycle length. Therefore, determining optimal operating conditions involves studying catalyst deactivation. Coke production is slow under real, mild operating conditions, with a normal cycle length between 18 and 20 months on stream. In our previous results in a pilot plant,10,11 we demonstrated that, with a PtReCl/Al2O3 catalyst, coke (2) Dachos, N. UOP platforming process. In Hand Book of Petroleum Refining Process; Meyers, R., Ed.; McGraw-Hill: New York, 1994; p 4.7. (3) Smith, R. B. Chem. Eng. Prog. 1959, 55 (6), 76. (4) Ramage, M. P.; Graziani, K. R.; Krambeck, F. J. Chem. Eng. Sci. 1980, 3541. (5) Taskar, U.; Riggs, J. B. AIChE J. 1997, 43, 740. (6) Krambeck, F. J. CHEMTECH 1992, 22 (5), 292. (7) Ancheyta-Juarez, J.; Villafuerte, M. E. Energy Fuels 2000, 14, 1032. (8) Xie, X. A.; Peng, S. H.; Liu, T. J. Pet. Ref. Eng. 1995, 25 (6), 49. (9) Froment, G. F. Catal. Today 1999, 52, 154. (10) Galiasso Tailleur, R. ReV. Latinoam. Ing. Quı´m. Quı´m. Apl. 1982, 12, 185. (11) Galiasso Tailleur, R. PtReCl/A2O3 catalyst deactivation in semiregenerative nafta reforming unit. 2008, manuscript sent for publication.
10.1021/ef8001718 CCC: $40.75 2008 American Chemical Society Published on Web 07/25/2008
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Figure 1. Process scheme for the commercial plant. Table 1. Commercial Operating Conditions commercial operating conditions feed flow (kmol/h) molecular weight molar rate of H2/HC space velocity (h-1) produced gas (MMSCMD) percent volumetric composition of recycle gas
H2 C1 C2 C3 C4
166.78 108.00 3.73 2.03 0.48 84.00 3.57 2.62 2.32 0.66
deactivation depends upon temperature and the partial pressures of cyclopentane and hydrogen, results confirmed by others.12,13 We use an approach similar to Beltramini et al.,14 which employed the deactivation of both the acid and metal functions of the catalyst to model the process. The optimal catalyst volume distribution between the reactors depends upon deactivation because the volume changes during the course of the run.10 The refinery may run in a 12-14-month cycle without compromising the schedule of its products; therefore, there is some room to optimize cycle length and operating conditions in current facilities. Optimization strategies must also consider that dehydrogenation reactions are endothermic, while hydrocracking and isomerization reactions are exothermic. The heat balance is different in each reactor because of the intensity of these reactions as a function of the current reactor volume and cycle lifetime; thus, the heat supply per preheating zone depends upon catalyst deactivation. The operation (cycle) progresses by increasing the inlet temperature at quasi-constant delta of temperature in each reactor along the cycle length (for similar feed quality and RON, octane number, in the product). The optimal revamp of the heater zones depends upon the heat balance in each reactor along the cycle. The compressor revamp is the other important cost in reforming optimization. The current compressor can be debottlenecked to obtain 20% higher throughput, but we must consider the quality of hydrogen (amount of C1-C4) along the cycle (12) Novaro, O.; Li, Ch. L.; Wang, J. A. Deactivation by coking. Catalytic Naphtha Reforming, 2nd ed; Chemical Industries (Dekker): New York, 2004; p 391. (13) Franck, J. P.; Martino, G. P. Deactivation of reforming catalysts. DeactiVation and Poisoning of Catalysts; Chemical Industries (Dekker): New York, 1985; p 205. (14) Beltramini, J. N. Deactivation by poisoning and sintering. Catalytic Naphtha Reforming; Chemical Industries (Dekker): New York, 1995; p 313.
because of hydrocracking reactions. The debutanizer in this particular plant also needs to be revamped to accommodate higher than normal C4 production generated by operation at high temperature). The hydro-desulfurization capability of reforming itself can be extended by a densely loading catalyst to process an additional 20% throughput and produce the same sulfur content (1 ppm) in the reformer unit feed. Finally, the refinery supplies two sulfur-content grades to the gasoline pool in different proportions as part of its commercial strategy. This complex problem is meriting an integrated optimization approach, which will provide the best holistic solution. This study shows the feasibility of increasing hydrogen production in a catalytic reforming plant by increasing throughput, incorporating an additional reactor, and revamping (as limited by the total investment set by the refinery) the heater, the recycle compressor, and the fractionation equipment. Revamping the semi-continuous process into a continuous regeneration system was not considered for this study. The maximum size for the new reactor is limited to 100 m3 by physical layout restrictions. Particular emphasis was placed on developing a model able to account for catalyst deactivation and how it affects current feedstock quality and gasoline pool composition. A Gulf Coast plant location was arbitrarily chosen for preliminary cost estimation of plant expansion. Finally, the best volume, throughput, and reactor sequence for the expanded scheme was determined, and an operation variables sensitivity analysis was performed to verify the robustness of the solution. Data for the Model Pilot Plant Kinetics Data and Deactivation Model. Kinetic and deactivation rate constants were obtained from a previously developed 12-lump kinetic model and two-site deactivation model10,11 and adjusted with data obtained from four long-term micro-pilot-plant tests (3000 h) (Figure 2). The micro-pilot-plant data were obtained with the same naphtha and catalyst used at the refinery but using an isothermal reactor. Three of the pilot plant tests were run at different temperatures: 740, 760, and 780 K, with all of them using a 0.1 L isothermal reactor filled with a PtReCl/Al2O3 catalyst and operating at the same H2/HC ratio (4) and total pressure (3.8 MPa) as commercial units. The fourth test was run at a different H2/HC ratio (6) with all of the other operating conditions kept constant. The catalyst activity as a function of time on stream was followed using a weekly analysis of the product (with a
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Figure 2. Simplified reaction path for a reforming kinetic model. Figure 4. Mathematical model flow scheme and genetic algorithm for obtaining kinetic and deactivation constants.
Figure 3. (a) Pilot plant results for catalyst deactivation at three temperatures and two H2/HC ratios. (b) Model calculations of the metal and acid site activity evolution as a function of time on stream.
GC-PONA column) and octane number, and the results are reported in Figure 3a. Activity values were calculated for the metal (am ) (khyd)t/(khyd)t ) 0) and acid (aa ) (kcycl.)t/(kcycl.)t ) 0 sites, with (ki)t being the kinetics rate constant at any time, using the model to adjust the hydrogenation and cyclization reaction rate constants until the model predicted the reformed quality (see Figure 4). The program calculated the amount of paraffins, naphthenes, and aromatics for C6-10 carbon numbers, and then it calculated the equilibrium concentration of iso- and n-parafins. With this information, the program predicted the octane number by molar contribution (from lumped compounds), a value that was compared against the octane number experimentally measured. During the optimization, the deviation of the predicted quantity of paraffins, naphthens, and aromatics (PNA) from the experimental quantity was used to calculate new values for the kinetic constants for the particular operating conditions. At this
point, the octane number comparison was only used as a check point for model accuracy, but we did not use it as convergence criteria. Kinetic constants for a particular time on stream were divided by the original value to give an activity constant. Calculated catalyst activity values for metal and acid sites as a function of time on stream are plotted in Figure 3b. Commercial Data for the Kinetic and Deactivation Model. Constants obtained in the pilot plant run were updated using commercial data from one operation cycle of the unit that needed to be revamped (data run 1); another set of data from a similar unit (three equal reactors in series) operating with slightly different naphtha was also used (data run 2). The commercial unit to be revamped was run at nearly constant RON production by increasing the inlet temperature in all of the three reactors at different proportions. In addition to daily data, monthly test runs were performed, in which a full analysis of the feed and the debutanized products was obtained. Gasoline quality was checked by PONA analysis and engine testing.15 The naphtha reformer process generated 20 data points once a week. These were from the feed, product, and recycle gas analyzers, feed product and recycle gas mass flow measurements, and various temperature measurements. Commercial data standard deviation values were based on typical measurement uncertainties. Flow measurement uncertainty was assumed to be 2% of the measurement range. A fixed 2 °C uncertainty was assumed for all temperature values. A 1% standard deviation was used for all analyzers and was based on instrument specifications, except for the recycle H2 gas analyzer, which has a standard deviation of 3% because of sampling errors. A standard data reconciliation procedure was performed using the method of Romagnoli and Stephanopoulos.16 This gave us 28 reliable data points about reformated compositions spread across the 20 month cycle length. Nine points were used to check model validity at the start of run (SOR), middle of run (MOR), and end of run (EOR). Table 1 shows the general operating conditions in the commercial unit, and Table 2 shows the temperature and pressure at SOR, MOR, and EOR. Table 3 shows the typical paraffin, naphthenic, and aromatic composition (PNA) of the feed. Tables 4–6 present the product composition after the (15) Rosario, T.; Graboski, J. Personal communication about refinery data, 2000. (16) Romagnoli, J. A.; Stephanopoulos, G. Chem. Eng. Sci. 1981, 360 (11), 1849.
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Table 2. Reactor Operating Conditions at SOR, MOR, and EOR reactor
T in (°C)
T out (°C)
P in (MPa)
P out (MPa)
1 2 3
526 529 531
SOR 470 500 528
1 2 3
532 536 545
MOR 480 506 530
3.23 3.00 2.90
3.07 2.94 2.78
1 2 3
738 740 550
EOR 484 510 528
3.34 3.12 3.00
3.11 3.00 2.80
3.15 2.94 2.81
3.00 2.82 2.76
Table 3. Commercial Feed Properties by Carbon Number feed
P
ACP
ACH
A
C1-C4 C5 C6 C7 C8 C9 C10 total
0.00 1.17 15.52 15.96 15.28 7.03 0.67 55.65
0.00 0.69 4.15 6.97 8.32 0.97 0.05 21.14
0.000 0.000 2.22 6.96 5.30 3.23 0.06 17.77
0.00 0.00 0.94 2.07 2.31 0.34 0.02 5.69
Table 4. Reformed Naphtha Properties by Carbon Number at SOR SOR
P
ACP
ACH
A
C4 C5 C6 C7 C8 C9 C10 total
1.16 4.80 16.88 14.76 6.06 0.86 0.05 44.57
0.00 0.48 0.89 1.12 0.88 0.03 0.00 3.40
0.00 0.00 0.07 0.17 0.10 0.09 0.08 0.46
0.00 0.00 5.68 18.24 18.24 7.86 0.71 50.72
Table 5. Reformed Naphtha Properties by Carbon Number at MOR MOR
P
ACP
ACH
A
C4 C5 C6 C7 C8 C9 C10 total
0.88 5.4 12.4 14.86 5.06 2.26 0.55 42.15
0 0.5 0.77 1.05 0.92 0.32 0.1 3.9
0 0 0.07 0.13 0.08 0.12 0.15 0.52
0 0 4.65 17.22 17.84 9 1.1 49.4
debutanizer at SOR, MOR, and EOR. During operation, the capacity of the compressor, debutanizer, and furnace were verified once a month while on stream using a Provision II commercial package. Model Apparent Kinetic Lump Model, Mechanism of Reaction, and Components Lumping. The process feed consists of a mixture of a several hundred types of paraffinic, naphthenic, and aromatic compounds. To simplify kinetic calculation, different compounds were lumped into families. This method has the advantage of considering a group of compounds with similar chemical and physical properties as a single pseudocompound (refs 3, 4, 6, and 10 among others). Thus, the feed and product PNA was arranged into four hydrocarbon families: all-paraffins, cyclopentanes, cyclohexanes, and aromatics. Paraffins were assumed to be at equilibrium (n-paraffins T monobranched paraffins T di-branched paraffins).
Table 6. Reformed Naphtha Properties by Carbon Number at EOR EOR
P
ACP
ACH
A
C4 C5 C6 C7 C8 C9 C10 total
0.78 5.6 12.7 16.3 7.06 0.96 0.25 44.1
0 0.44 0.67 0.78 1.1 1.05 0 4.15
0 0 0.05 0.14 0.15 0.1 0.08 0.41
0 0 4.22 16.24 20.2 8.33 1.5 51.5
The kinetic model distinguishes compounds according to the number of carbons in the molecule and incorporating reactivity coefficients. The metal sites catalyze dehydrogenation reactions. Dehydrogenation is the fastest of all of the reforming reactions, is endothermic, and increases the product octane number. This reaction is favored by high temperature and low total pressure. The dehydrocyclization of paraffins to naphthenes that occurs on acid sites is a relatively slow reaction that increases with an increasing carbon number. This reaction is endothermic and favored by high temperature and low pressure. Isomerization on acid sites produces branched paraffins with a higher octane value than linear paraffins, and its ratio increases with an increasing temperature, molecular weight, and total pressure. This reaction is faster than cracking, cyclization, and aromatization, and the isomer is always present in a proportion close to its equilibrium. The program considers paraffin migration from a higher to lower number of carbon atoms as a consequence of cracking; similarly, the program includes the migration of naphthenes and aromatics into lighter products because of hydro-dealkylation reactions. Paraffin cracking is an endothermic reaction that produces lighter paraffins, occurs on acid sites, and increases with temperature, pressure, and paraffin carbon number. Aromatic, naphthene, and paraffin cracking are irreversible reactions. All other reactions are reversible. A proposed model reaction scheme is presented in Figure 2. Reactions 1-3 represent the main reactions, which are subdivided according to the number of carbon atoms in the reactant (5-10 carbon atoms for reaction 1 and 6-10 carbon atoms for reactions 2 and 3). Reactions 4-7 represent dealkylation reactions, classified according to the produced light paraffin. For instance, reaction 4 produces methane and the corresponding aromatic pseudo-compound with one fewer carbon. Cracking reactions are treated in a similar way. Reactions 8-12 represent paraffin cracking reactions, classified according to the light paraffin produced. Reaction 8 includes migration of paraffin from j to j - 1 carbon atoms, which generates a common subproduct of all reactions, methane. Similarly, reaction 9 contains all of the reactions that generate ethane as a subproduct. On the basis of this assumption, kinetic equations were grouped using a two-dimensional vector. The first dimension (i) indicates the reaction number according to the description shown in Figure 2, while the second dimension (j) indicates the number of reactant carbon atoms that participate in this reaction. Thus, the generic apparent kinetic expression is shown in eq 1 ri,j ) Ri,j(kodiexp(-Eadi/RT)Cm,jCH2n1i - koiiexp
(-Eaii/RT)Cm,jCH2
n2i
)
(1)
where Cm,j is the concentration of component m, j; m is the subindex that indicates the type of compound according to the following nomenclature: m ) 1 for paraffin, m ) 2 for alkylcyclo-pentanes, m ) 3 for alkyl-cyclo-hexanes, and m ) 4 for alkyl-aromatics; j is the subindex that indicates the number of carbons of the reactant that is consumed in the reaction; i is the
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subindex that indicates the number of the reaction according to the scheme shown in Figure 2; n1i is the order of hydrogen in the kinetic expression of reaction i, in the case of cracking and dealkylation, otherwise n1i ) 0, which eliminates the dependence on hydrogen concentration; n2i is the order of hydrogen in the kinetic expression for the inverse reactions, valid for reactions 1 and 3, otherwise n2i ) 0; and Ri,j is the reactivity coefficient of reactant m, j in the reaction i, j and is dimensionless. The pre-exponential factor (kij), activation energy (Ea), and reaction orders regarding hydrogen were found from commercial data and are presented in Table 5. Reactivity coefficients are defined as a gauge of the relative ease of which each compound of a family participates in a given reaction with respect to compounds of six carbons; thus, reactivity depends upon molecular weight and temperature. They were calculated from the following smooth correlation obtained in pilot-plant runs:
(∑
-5000+1000
j)10
Ri,j )
(
MWje
Rg T
j)6
∑ (1 + 0.1
j-6
j)6
j
)
-5000+1200
j)10
84 +
j+1
)MWj-6e
Rg T
j+1 j
)
)
[kod]iCj [kod]iC6
)
[kor]iCj [kor]iC6
(2)
where MW is the molecular weight. Heats of reaction were selected inside the range proposed by Kugelman17 and Galiasso10 to reproduce the temperature delta between each reactor. The n-isoparaffin equilibrium as a function of the molecular weight is calculated by the equation: ln Ki,j ) ∆Hc,j + T∆Sj. Here, ∆Hc,j is the heat of combustion of the j carbon and ∆Sj is the entropy change, a decreasing linear function of the carbon number, which was calculated using Table 12 of ref 18. The concentration of the isomeric species was independent of the hydrogen and total pressure. Model for Catalyst Deactivation. Reforming catalyst deactivation has been extensively studied, and while different approaches have been used to model it by coke formation, there is no generally accepted model. Turpin’s model proposes an exponential correlation between catalyst deactivation and coke deposition.19 Other authors demonstrate that deactivation depends upon the catalyst metal content20 and quality of the naphtha.21 Bishara et al.22 and Rahimpour23 employed a catalyst deactivation function of the activity and exponentially proportional to the temperature. Our previous deactivation model for a PtReCl/Al2O324 was based on the Levenspiel approach to model deactivations.25 Here, we considered catalyst activity to depend upon temperature, activity level, hydrogen partial pressure, and cyclopentane concentration according to the following equations: (17) Kugelman, A. Hydrocarbon Process. 1976, 34, 67. (18) Scott, D. W. J. Chem. Phys. 1974, 60 (8), 3144. (19) Turpin, E. Modelling commercial reformers. Catalytic Naphtha Reforming (Science and Technology); Marcel Dekker: New York, 1995. (20) Grau, J. M.; Parera, J. M. Appl. Catal. 1991, 70 (1), 9. (21) Frank, J. P.; Martino, G. DeactiVation and Poisoning of Catalysts; Oudar, J., Wise, H., Eds; Marcel Dekker: New York, 1985; p 205. (22) Borgna, T. F. G.; Apesteguı´a, C. R. Stud. Surf. Sci. Catal. 1997, 111, 495. (23) Bishara, A.; Stanislaus, A.; Hussain, S. S. Appl. Catal. 1984, 13 (1), 113–125. (24) Rahimpour, M. R.; Esmaili, S.; Bagheri, G. N. A.; Iranian, J. Sci. Tech., Trans. B: Tech. 2003, 27, 279. (25) Galiasso Tailleur, R.; Bruzzanesse, A. Criterio de Operacio´n de Unidades de Reformacio´n de Naftas Semi-regenerativas con Desactivacio´n. Preprint 56 Iberoamerican Congress on Catalysis, 2002; pp 345-352.
da1 0.5 ) koae-Eaa⁄RTa1CACP dt
(3)
0.5 da2 CACP ) kome-Eam⁄RTa2 dt 1 + bPH2
(4)
ra ) rm )
where a1, a2, Eam, Eaa, kom, and koa are the activity coefficients, the deactivation energies and deactivation rate constants for the metal and acid sites of the catalyst, respectively; CACP is the concentration of alkycyclopentane; and PH2 is the hydrogen partial pressure. In the present model, t is the time on stream and tf is the life of the catalyst, which is defined as the time when the maximum inlet temperature is reached. The numeric values of these parameters were determined using the pilot plant data. In catalytic reforming of naphtha with less than 1 ppm of sulfur, the catalyst is deactivated mainly by coke deposition with constant sulfur content, thereby reducing the aromatic yield and delta (inlet - outlet) of temperature in the reactors. In a commercial plant, deactivation is mitigated using a higher reactor inlet temperature, so that the RON (octane) of the debutanized product is kept constant during the cycle. Inlet temperatures for the three commercial reactors were adjusted by controlling the specific zone of the heater while respecting the temperature limits of the tube skin. This way, the desired temperature profile was established throughout the reformers, and the outlet aromatic mole fraction was maintained in a suitable range. At the catalyst acid site, the deactivation rate depends upon the alkyl-cyclopentanes concentration (eq 3). Deactivation kinetics of the metallic sites depends upon not only the alkylcycle pentanes concentration (ACP) but also on the inverse of the hydrogen partial pressure (eq 4). Because the concentration of these compounds changes along the catalyst bed, deactivation also varies as a function of the catalyst volume. Using this equation, a criterion was developed for an optimal volume of catalyst and feed flow rate in a semi-regenerative reforming unit,25 and the value of the model constants depend upon the catalyst and feedstock used. In the pilot plant, the catalyst bed was deactivated at a constant temperature along the cycle length in an isothermal reactor. Despite this, the data were useful to confirm model validity and generate the constants for eqs 3 and 4 to predict the deactivation sites for the commercial reactor. Notice that in Figure 4 that the activity is calculated point by point instead of using a weight average temperature to calculate the activity, as is common in the literature.24,27 Mass Balance. The reactors were modeled as an axial plug flow under steady-state conditions with no external mass- or heat-transfer limitations. The balance is made in a differential element of volume, as shown in eq 5 O dXi,j ) Fm,j
∑ (-r
i,j)dV
(5)
where Fm,jO is the inlet molar flow of component m,j, Xi,j is the conversion in reaction i of the reactant with j carbon, and V is the volume. A differential equation matrix was used to include all reactions according to eq 1 (see Figure 4 for details of the algorithm that calculated the outlet composition for a given volume of the reactors). Energy Balance. The operation is carried out under adiabatic conditions. The energy balance of all reactions is shown in eq 6 (26) Levenspiel, O. J. Catal. 1972, 25, 262. (27) Hou, W. F.; Su, H. Y.; Hu, Y. Y.; Chu, J.; Chin, J. Chem. Eng. 2006, 14 (5), 584.
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dT ) dV
Energy & Fuels, Vol. 22, No. 5, 2008 2897
∑∑r
i,j∆Hi,j
i
j
(6)
∑∑F m
j
m,jCpm,j
NumericalMethodforIntegration. A Runge-Kutta-Felberg fourth-order numerical method with a corrective-predictor algorithm for the integration step was used to solve the system of differential equations associated with the mass and energy balances. Thermodynamic properties estimated in provision II were included in the simulations. The Peng-Robinson equation of state was used to calculate molar volumes and specific heats. Mixture properties were calculated assuming ideality. Genetic Algorithm (GA) To Adjust Kinetic and Deactivation Parameters. Multiple objective functions were modeled and solved in the past by transforming them into a single objective problem using different methods, such as the restriction, ideal point, and linear weighted sum methods. These methods largely depend upon the arbitrarily chosen values assigned to the weighting factors or penalties used. Multi-objective evolutionary algorithms are used more widely in industrial process modeling, optimal design, and operation because there algorithms may produce a solution set with a single run. The solutions are extremely useful in industrial operations, providing narrow choices to help guide decision makers in selecting a desired operating point (called the preferred solution) among a restricted set of optimal points rather than from a considerably larger number of possibilities. Coello28 presented a comprehensive review on evolutionary multi-objective optimization techniques, focusing especially on genetic algorithms. Genetic algorithms were used by several authors to optimize naphtha reforming with different objectives25,27 because genetic algorithms have the advantage that, in a wide searching range and in highly nonlinear systems, they are able to obtain the best global solution and not just a local optimum. The program was used to first fit the kinetic parameters for the 12 reactions shown in Figure 2, so that the product composition was reproduced. It was then used to fit the five kinetic parameters for deactivation. Because of the nonlinearity of the equations and adjustment of these parameters, the genetic algorithm of Carrol29 was used to adapt the population (K) with the pass of generations (ıˇ) to fulfill the objective. The objective function chosen for this algorithm was the summation of the relative errors between the output of the simulation and the real concentration (Z) for aromatics, naphthenes, and paraffins, as shown in eq 7. The logic diagram of this algorithm is shown in Figure 4. The data input required to start the program are (a) the equipment operating conditions, (b) the feed and product (PNA) composition, and (c) the genetic parameters (population size, seed, number of generations, and mutation probability). Using these data, the program iterated and reported the reactivity, kinetic, and deactivation constants. objective function )
(
∑ ABS
real simulation Zout - Zout i i real Zout i
)
(7)
(28) Coello, C. C. A. A short tutorial on evolutionary multiobjective optimization. In Proceedings of the First International Conference on EVolutionary Multi-criterion Optimization; Zitzler, E., Deb, K., Thiele, L., Coello, C. C. A., Come, D., Eds.; S Drinaer: Zurich, Switzerland, 2001; p 67. (29) Park, T.; Froment, G. F. Comput. Chem. Eng. 1998, 22, S103– S107.
Sequential calculations were performed to adjust the predictions for increasingly lower PNA content, starting with less than 4% difference in PNA content, then less than 2%, and finally to less than 1%. The GA was stopped and reported the last converged value if the target was not met at the specified mutation number. Genetic Algorithm for Cycle Optimization. The variables studied in the catalytic reforming process are the flow rate of naphtha (FNap), the volume of the new reactor (Vr), the octane in the debutanized product, and in some cases, the cycle length for a given reactor sequence. The set point for maximum annual hydrogen production may not be suitable for maximizing the cycle length. Suitable tradeoff solutions should be considered using the benefits function (eq 9) defined in incremental dollars per year because of unit operation and a 15-year capital payment required for the revamping. The total pressure, quality of naphtha feedstock, product separator temperature, and fractionation efficiency were kept constant along the cycle length. However, this is not true for the operation costs, which depend upon heating and cooling, gas compression, and fractionation costs. Other process variables could be selected for optimization, such as the initial inlet temperature profile (Ti) and the H2/HC ratio (gas throughput). The objective of the present optimization is to maximize hydrogen (G1) production, a function mathematically expressed as follows: G1 ) funtion(Vr, FNap, RON, tF)
(8)
Subject to 40 < Vr < 270 m3 515 < Ti < 540 ° C current < FNap < 1.2current 87 < RON < 92 14 < tF < 20 months The bounds of these variables and objectives were chosen based on refinery constrains. To proceed with the system optimization, the central algorithm that integrates the differential equations for mass and energy balances for all of the systems of the reactor (RungeKutta-Felberg fourth-order method programmed in VB6, Figure 8) was used inside the genetic algorithm. This took the product and quality production during the year and proceeded to adjust the Vr, FNap, and RON values using the economic function (eq 8). This scheme is summarized in Figure 9. An internal subroutine calculated the product quality and amount of hydrogen produced for a given reactor arrangement (cases) as a function of the operation time. The genetic algorithm repeated the calculation while adjusting the throughputs, RON, and added reactor volume until the annual benefit was maximized. objective function (F1) ) (incremental gross benefits incremental capital) (8a) The program reported the equipment size, product composition (PNA), properties of the streams, incremental capital and operational costs, and the parameters used to converge. Other Equipment Calculations. Both the high-pressure separator and the debutanizer were assumed to act as ideal separation equipment, with efficiency independent of composition and operating conditions (specifically, pressure, and temperature). Both pieces of equipment were simulated in provision II using current plant operating conditions to obtain separation coefficients corresponding to each pseudo-compound used in
2898 Energy & Fuels, Vol. 22, No. 5, 2008
Galiasso Tailleur and DaVila
Figure 5. Model prediction of the product concentration versus experimental measurements of different product compounds: (a) aromatics, (b) alkyl-cyclohexanes, and (c) paraffins. (d) Temperature delta of the commercial plant versus model predictions. SOR: ([) 740, (9) 760, and (b) 780 K. MOR: ([) 740, (9) 760, and (b) 780 K. EOR: ([) 740, (9) 760, and (b) 780 K.
Figure 6. Model prediction of the metal and acid site activities along the reactors at MOR and EOR time points. (Black curve) metal site, (gray curve) acid site. Figure 8. Flow scheme for reactor deactivation modeling using different flow rates and reactor volume to optimize hydrogen production.
ity of the heater was verified outside of the optimizer.30 After different cullings, only 12 cases were retained. Economic Evaluation
Figure 7. Comparison of octane number (RONC) in the commercial plant (two sets of data) and that predicted by the model (full line). (9) Run 1, (b) run 2.
the main program. The compressor capacity was verified at each operating condition selected by the optimizer. Optimal heat distribution (enthalpy balance) of the most restrictive situation in the cycle was calculated, and mechanical revamping feasibil-
Product prices were fixed at $0.02/MMSCM (million standard cubic meter) for H2 ($450/ton), a marginal price of $2.8/octane m3 for gasoline and $0.1/MMSCM for fuel and an incremental price of $0.4/m3 of low sulfur premium gasoline. Incremental investment costs (new reactor, expansion of the heater, a new driver for the compressor, and new trays and heat-exchanger capacity in the FCC debutanizer) were calculated using the Icarus commercial software package. The location of revamping (30) Davila, Y. Evaluacio´n del Impacto Te´cnico-econo´mico de la Adicio´n de un Reactor a la Planta de Reformacio´n Catalitica de la Refinerı´a de El Palito. Thesis, Simo´n Bolivar University, Venezuela, 2002. (31) Srinivas, N.; Deb, K. Multiobjective optimization using nondominated sorting in genetic algorithms. EVol. Comput. 1994, 2 (3), 221–248.
ReVamping a Naphtha Reforming Unit
Figure 9. Comparison between one- and two-site activities calculated from the commercial data during the operation cycle. (9) Metal site, (b) acid site.
was chosen to be in the Gulf Coast in 2004. In doing so, the balance between higher hydrogen production and the impact at the refinery level could be evaluated. The results were integrated into a more general refinery linear program simulator (PIMS) to determine the impact of hydrogen production on the size of the new hydro-desulfurization units that produce 15 ppm sulfur gasoline for the SOR, MOR, and EOR calculations. Incremental (revamping) capital cost for the hydrotreater was estimated at $5000/m3. The most realistic cases considered in this study are reported in Table 7. Results and Discussion Catalyst Deactivation in the Pilot Plant. Figure 3a shows the change in octane number versus time on stream obtained in the pilot plant at three different temperatures and two H2/HC ratios. The RON exponentially decreased as a function of time on stream with greater deactivation at higher temperatures. The test focused on the effect of temperature because the deactivation energy is large. The program calculated the kinetic parameters using the PONA analysis at different times on stream. Acid and metal activity values are plotted in Figure 3b as a function of cycle length. These activities follow a trend similar to the octane number. Apparent reaction rate and deactivation constants for eqs 1, 3, and 4 were determined and used to seed the commercial plant simulation. Current Plant Simulation. The genetic algorithm was seeded with the constants obtained in the pilot plant. A similar program as shown in Figure 4 allowed adjustment of the kinetic and deactivation parameters. Typical results obtained from the commercial plant at SOR, MOR, and EOR are shown in Tables 4–6. Results indicated the composition as a function of the carbon number change along the cycle length. The GA obtained a new set of apparent rates and deactivation constants that had changed with respect to those determined in the pilot plant (with a difference typically less than 10%). The results of the simulation indicated errors of less than 1.5% when predicting the molar composition of characteristic C6-C10 compounds (PNA). On average, a population size between 8 and 12 and between 30 and 40 generations were enough to fit the data within this error. Most of the computational time was consumed by the integration of the differential equations step-by-step. As a reference, the program took 10 min to converge using a conventional parallel processor Pentium V laptop computer. Apparent kinetic rate constants obtained for C6 compounds are shown in Table 7. Notice the important difference in cyclization and aromatization activation energies with respect to isomerization, which is in agreement with previous research. A comparison between simulation results and real data [an independent set of experimental values (9)] at SOR, MOR, and
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EOR is presented in parts a-d of Figure 5. The model predicted the production of C7-C8 (
