Ind. Eng. Chem. Res. 1987, 26, 2528-2532
2528
az-z+l E, =
a
al+l/n
E, = 6n
Literature Cited
2. The first derivative of (16) is defined as
a7 aa aa a t
#=--
7'
= a'
a7+ -a+
a# at
nEln-2E2 - 2n 6#l/"[(n- l)E3Eqn-2 + E4n-1E&s]+ J.
Davis, E.J. Znd. Eng. Chem. Fundam. 1969,8, 153. Dashpande, S. D.; Bishop, A. A. Paper presented at the 1983 AIChE Annual Meeting, Washington, D.C., Nov 1983. Eisenberg, A. E. M.; Weinberger, C. B. AZChE J . 1979, 25, 240. Johannessen, T. Int. J. Heat Mass Transfer 1972, 15, 1443. Kapitza, P. L. J. Ezpt. Theor. Phys. USSR 1948, 18, 3. Mahalingam, R. Advances in Transport Processes; Wiley-Halsted: New York, 1980; Vol. 1. Mahalingam, R.; Valle, M. A. Znd. Eng. Chem. Fundam. 1972,11, 470. Narasimhan, T. V.; Davis, E.J. Znd. Eng. Chem. Fundam. 1972,11, 490. Oh, C. H. Ph.D. Dissertation, Washington State University, Pullman, 1985. Oliver, D. R.; Young Hoon, A. Trans. Znst. Chem. Eng. 1968, 46, T106. Raghavan, K.; Mahalingam,R.; Oh, C. H. Paper presented at AIChE Diamond Jubilee Annual Meeting, Washington, D.C., Nov 1983; Paper 77. Strobel, W. J.; Whitaker, S. AZChE J . 1969, 15, 527. Taitel, Y.; Dukler, A. E.AZChE J. 1976, 22, 47. Whalley, P. B.; Hutchinson, P. Chem. Eng. Sci. 1973, 28, 974. Whitaker, S. Znd. Eng. Chem. Fundam. 1964,3, 132.
where
E, =
2(az - z a2
+ 1)
E2 =
4.z - 2az - 4 a3
Received for review March 9, 1987 Accepted August 24, 1987
Investigation of Coke Deposition during the Pyrolysis of Hydrocarbon Zou Renjun,*+Lou Qiangkun, Liu Huicai, and Niu Fenghui Hebei Institute of Technology, Tianjin, The People's Republic of China
An experimental system, which is designed and assembled by us for studying coke deposition during the pyrolysis of hydrocarbons, is reported in this paper. It shows excellent reproducibility and reliability. The surface effects and kinetics of coke deposition in the pyrolysis of hydrocarbon are studied; propane is taken as a representative of feedstock in this paper. The mechanism of coke deposition is proposed, and the model for coke formation is developed with ethylene and propylene as coke precursors. Coke deposition is one of the key factors that limits the run length of a pyrolysis furnace, so study of surface effect on coke deposition and how to reduce coke formation in tubes of the furnace is an urgent matter. *Hebei Academy of sciences, Shijiazhuang, l-ianjin, The People's Republic of China. 'In accordance with the authors' wishes, their family names are listed first.
Dunkleman and Albright (1976) studied the surface effects of different materials during pyrolysis of ethane and propane. Brown and Albright (1976) reported the role of the reactor surface in pyrolysis of ethane, propane, ethylene, and propylene. Lahaye et al. (1977) studied the mechanism of coke formation in steam cracking of hydrocarbons. Shah et al. (1976) reported the steady-state coking rate for cracking n-octane. Albright and Tsai (1983) summarized the surface reactions in pyrolysis units. A
0888-5885/87/2626-252~~01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 12, 1987 2529
-e‘ coke aepo
brae
tor
furnace
/
Figure 2. Flow diagram of the experimental system: 1, dryer; 2, saturator; 3, microinjector; 4,5, micropump; 6, reactor; 7, thermal gravity balance; 8, separator; 9, chromatography; 10, 11, integrator; A, liquid feedstock; B,-water; C, coking inhibitor; D, gaseous feedstock; E, air.
anti-leak
U balance carrier
Figure 1. Structural drawing of parts for measuring coke deposition.
series of research works on the subject of inhibiting coke deposition have been studied; see Sundaram and Froment (1979), Holmen and Lindvaag (1982), and Zou (1982). In this paper, an experimental system for studying coke deposition in the pyrolysis of hydrocarbons was designated and assembled by the authors. The surface effect, mechanism, and kinetics of coke deposition as well as coke precursors were studied on the system.
Experimental System For measuring the coke deposition, the method of a small cylinder (coke depositor) is suspended from the electrobalance into the reactor by means of a fine wire is widely used at present; e.g., Sundaram and Froment (19791, Holmen and Lindvaag (1982), and Pramanlk and Kunzru (1985). A new way for measuring coke deposition is developed in this paper. A thin pole brace which is installed on one arm of the balance is used to connect the balance with the small cylindrical coke depositor instead of wire, and a thermocouple is located just inside the cylinder through the brace to monitor the temperature. The brace is made of quartz or corundum. The amount of coking on it is extremely small by coke measuring, so it can be considered as an inert pole toward to coke deposition. The coke depositor has a diameter range of 3-4 mm and a length range of 10-20 mm. This design not only has good stability for coke measuring but can also measure the surface temperature of coke deposition accurately. The structure of the equipment is shown in Figure 1. In the system, some parts are designed to prevent the liquid products from leaking into the room of the balance. The experimental system consists of three parts: feedstock, reactor/coke measuring, and product analysis.
The schematic diagram of the system is shown in Figure 2. The reactor, 0.350-m total length and 0.016- or 0.02-m diameter, is made of quartz. The system is suitable for both gaseous and liquid feeds. For gaseous feedstock, reactant and diluent are controlled, measured, mixed, and preheated before entering into the reactor, whereas for liquid feedstock reactant is fed into the system by a nonpulsed meter pump. Either nitrogen or water steam can be used as the diluent according to the needs. In this study, nitrogen is used as the diluent. The dilution ratio N2:hydrocarbon = 0.82. Argon is used as a protective gas to prevent pyrolysis products from flowing into the room of the balance. In the feeding part of the system, the inhibitor injecting hole and related apparatus are also included so as to pretreat the surface of the reactor or research the coke inhibitors. The on-line analysis system is composed of a modified SP-2305 gas chromatograph. The Hz,Nz, and C1-CI components in the pyrolysis gas are separated on one column and detected through a way in which the TCD and FID are used in series. The composition of the pyrolysis gas is determined by means of a corresponding computing procedure; see Shen et al. (1985). The performance of the whole system is tested for reproducibility and reliability.
Surface Effect The effects of the surface property on coke deposition and the gaseous product distribution were studied through two runs of experiments: run a in which the material of the reactor tube remained constant and the formation of coke was measured on coke depositors (they are made of stainless steel (SS) lCrl8Ni9Ti) pretreated by different methods and run b in which the material of the reactor tube was varied or pretreated by different methods and the coke formation was measured on a coke depositor of the same material. In run a, the changing tendency of the yields of gas products and coke deposition rate was observed. The gas product distribution remained almost unchanged, but the coke deposition on the coke depositor varied greatly. The results are shown in Figure 3. From Figure 3, it can be seen that all the methods that can get rid of the metal oxides on the surface and form a passive layer on it have the function of inhibiting coke deposition. This is because when the surface is pretreated by chemical methods, these chemical compounds will react with metals and metal oxides to form a protective cover on the surface; therefore, the catalytic action of the metal surface to coke deposition decreases or even disappears completely. The tendency of coke deposition on SS coke
2530 Ind. Eng. Chem. Res., Vol. 26, No. 12, 1987 Table I. Effect of the Surface Property of the Reactor on the Gas Product Selectivity, Propane Remaining, and Coking Amount during Pyrolysis of Propane" coking amt in seieccivi
HZ
surface property of reactor quartz SS treated by H2S SS treated by H2 SS treated by mechanical erasing oxidized SS nickel
0.65 0.87
0.75 0.72 0.68 0.66 0.62 0.60
0.89 0.99 1.51 3.28
0.033 0.032 0.031 0.030 0.030 0.031
0.54 0.51 0.41 0.35 0.29 0.21
0.070 0.064 0.060 0.050
0.048 0.035
0.016 0.036 0.051 0.053 0.054 0.039
3.2 5.3 11.6 26.1 31.5 39.3
=Temperature,800 "C; residence time, 0.75 s; depositor, stainless steel, ICrlBNiSTi, pretreated by 3% diluted sulfuric acid before every experiment.
3o
I
30
E
E
-.
P
-
, 2
P
20
D .3
10
Y U
0
i
1
I
10
20
30
Time, m i n
Figure 3. Recorder curves of the effect of pretreatment methods upon coke deposition on quartz reactor (temperature, 850 O C ; residence time, 1 s; pressure, atmospheric; reactor, quartz; depositor, stainless steel, 1Crl8NiSTi): 1, distilled water; 2, mechanical erasing; 3, diluted hydrochloric acid; 4, hydrogen sulfide; 5, diluted sulfuric acid.
depositor after different pretreatments decreases successively in the order SS treated with oxygen > SS treated with distilled water > SS treated with mechanical erasing > SS treated with diluted hydrochloric acid > SS treated with hydrogen sulfide > SS treated with diluted sulfuric acid. Different pretreating methods result in different duration time of passivating function in coking/decoking operations. The more durable the protective layer, the more lasting the passivating function and vice versa. Since the surface area of the coke depositor is very small, ca. 1.89 cm2,in comparison with that of the reactor, >350 cm2,the change of the surface property has little influence on the composition of the products. So the change of the coke deposition rate on the coke depositor is the result of the change of its surface property. In run b, the material or surface property of the reactor was changed, but the surface property of the coke depositor was keeped unchanged. The depositor is washed with diluted hydrochloric acid before every experiment. The trend of the coke deposition rate on coke depositor in different reactors is shown in Figure 4. The catalyzing intensity of the reactor surface pretreated by various methods to the coke formation on the coke depositor decreases successively in the order SS treated with oxygen > SS treated with mechanical erasing > SS treated with hydrogen > SS treated with hydrogen sulfide > SS treated with diluted sulfuric acid. The property of the reactor surface effects the coke deposition on the coke depositor. This is because the
0'
10
20
30
40
Time, m i n
Figure 4. Recorder curves of the effect of the reactor surface property upon the coke deposition on a SS reactor (temperatwe,850 OC; residence time, 1 e; pressure, atmospheric; reactor and depositor, stainless steel, lCrldNiQTi,pretreated with 3% diluted sulfuric acid before every experiment; propane conversion, ca. 0.95 mole fraction): 1, no treatment after decoking; 2, mechanical erasing; 3, reduction by hydrogen; 4, pretreatment by hydrogen sulfide; 5, pretreatment by diluted sulfuric acid.
physical and chemical properties of the reactor surface will influence the radical and surface reactions in pyrolysis of hydrocarbons. The above results show that the influence of the coke deposition rate on the coke depositor in run b is in agreement with that in run a. The catalyzing intensity of different materials to coke deposition decreases in the order nickel > stainless steel > quartz. Both the nickel and SS reactor surfaces become more active after pretreatment with oxygen and lead to an increase in coke deposition on the depositor. This result also agrees well with that obtained in run a. The experimental results indicate that the trend of the coke deposition on the coke depositor is identical either by pretreating the reactor or by pretreating the coke depositor. In light of the study, the catalyzing intensity to coke deposition can be concluded as of the order oxidized Ni > Ni > oxidized SS > SS > SS treated with hydrogen > SS treated with diluted hydrochloric acid > SS treated with hydrogen sulfide > SS treated with diluted sulfuric acid > quartz. Since different reactor surfaces have different surface activities, the property of the surface not only influences the surface reaction and coke deposition but also has remarkable effects on the gas-phase product distribution. Table I shows the effect of the property of reactor surface on the product yields. The data in the table indicate that the greater the activity of the reactor surface, the lower the yields of ethylene and propylene and the higher the hydrogen yield accordingly. It indicates that the active
Ind. Eng. Chem. Res., Vol. 26, No. 12, 1987 2531 Table 11. Possible Kinetic Models for Coke Deposition (1) Single Reaction Models coke CzH4- coke IV '/&He I '/zCzH4 coke V C3H8 coke I1 C3Hs-coke VI CzH4 + C3Hs coke I11
t
1.2
C E
%.
0.8
VI1
D
VI11
0.6
IX 0.4
X XI
0.2
XI1 0
---+ + + -+
-
1.0
0 2
0 4
0 6
1 0
0 8
XI11
1 2
Residence t i m e . sec
xx
Figure 5. Steady coking rate vs residence time (reactor, quartz; depositor, stainless steel, lCrlBNiSTi, treated by mechanical erasing; propane conversion, ca. 0.95 mol fraction).
reactor surface enhances ethylene and propylene to form more coke by dehydrogenation and condensation reactions.
Mechanism and Kinetics of Coke Deposition On the basis of the study of surface effect on coke deposition, the mechanism of coke deposition can be suggested. It answers what courses are the process of coke deposition on the surface and what components are the key coke precursors. In run a, pretreating the coke depositor by different methods leads a remarkable variation of the coke deposition rate in the same reactor. Since the product composition in the gas phase is almost the same in this run, the coke formation reaction takes place only on the surface. From run b, the reactor material is changed or the surface is pretreated by different methods, the concentration of ethylene and propylene will decrease, and the concentration of hydrogen will increase with an increase of surface activity. Besides, olefin is easier to be adsorbed on the surface than paraffin due to its ?r electrons. Therefore, the key coke precursors for propane pyrolysis are ethylene and propylene. They form coke deposited on the surface via a series of complex steps:
1
--
ethylene, propylene cycloolefins benzene, alkylbenzene
2
3
4
nuclear condensed aromatics coke where step 1is the Diels-Alder reaction, 2 is dehydrogenation, 3 is dehydrogenation-condensation, and 4 is multistepwise dehydrogenation-polycondensation. Zou (1982) has written in more detail in his book. The experimental result of coke deposition under different temperatures and residence times is shown in Figure 5.
On the basis of the above discussion, 21 possible coke formation models are proposed. These models are listed in Table 11. In a tubular flow reactor, the conversion varies along the axis of the reactor; the change can be expressed by (Zou, 1982)
dx _
1-x Pe r d 2 --dl, 1' + ni + 6 x RT, 4 F The conversion in different positions along the reactor can be calculated by integrating (l), and the corresponding
--------
-
(2) Two Parallel Reactions Models XIX '/zCzH4 coke CzH4 coke coke C3H8 coke '/&He CzH4 coke XV CzH4 coke C3H8 C3H6 coke C3Hs coke '/zCzH4 coke XVI '/3C3H6 coke '/&He coke C3H8 3/zCzH4 coke 3CzH4 coke XVII '/3C&6 coke C3H8 CzH4 coke 2C3H6 coke C3HB coke XVIII C3H8 coke C3Hs C2H4 coke C3H8 coke 2C3Ha --c coke IXX C3H8 coke 3C3H6 coke '/&He + CzH4 coke C2H, coke C3H8 coke
-. ---
(3) Three Parallel Reactions Models C3Hs coke XXI C3H8 coke 3CzH4 coke CzH4 coke 2C3H6 coke C3Hs coke
-
product yield can be obtained according to the relationship between conversion and product yield. Therefore, the concentration of each component in the product can be obtained accordingly. With the concentration of coke precursors and corresponding steady coke deposition rate, the kinetic parameters for these models can be determined. Taking model VI1 as an example, ki C2H4
+
coke
kl
'/3C3H6
coke
(2)
(3)
The equation for the coke deposition rate can be written as rc = rcl + rcz = kl[C2H4] + k2[C3H6]1/3
(4)
The kinetic parameters in (4) are estimated by means of the least-squares method. The preliminary screening procedure is where the models in which at least one of the rate constants or activation energies is negative are discarded because of irrationality. Further screening is made by checking if the relationship between rate constants and -1/ T abides by the Arrhenius equation. The results show that only model VI1 among the 2 1 models is in accordance with the Arrhenius equation. So the coke deposition model for propane pyrolysis proposed in this paper is C2H4 A , = 5.89
X 1O1O
k1
El = 230.29 kJ/mol kl
'/3C3H6
A2 = 2.21
X
lo8
coke
coke
E2 = 165.22 kJ/mol
The coke deposition model has the following advantages in comparison with that of Sundaram and Froment (1979).
First, the possible models for screening are of a wide range; not only are the coke precursors considered, but also the reaction orders of these precursors are taken into consideration. Second, and most importantly, Sundaram and Froment's model includes the coke formation reaction of propylene only, but the model proposed in this paper includes parallel coke formation reactions of ethylene and propylene. The experimental result shows clearly that
Ind. Eng. Chem. Res. 1987, 26, 2532-2542
2532
ethylene is a more important coke precursor than propylene. For instance, the relative rate of the two steps is 264:l at 850 OC. Brown and Albright (1976) and Ghaly and Crynes (1976) have the same point of view also.
R = gas constant rc = coke deposition rate, mg/(cm2 min) T = pyrolysis temperature, K T , = reference temperature, K x = conversion
Conclusion We designed and assembled an experimental system for studying coke deposition in hydrocarbon pyrolysis. The system is reliable and feasible for a wide purpose of research work. The surface effects on coke deposition and gas product yield have been studied. The mechanism of coke deposition is proposed as where the coke precursors, ethylene and propylene, adsorb on the surface first and then the adsorbed coke precursors react on the surface via dehydrogenation, condensation, and other reactions to form coke. Relying on the mechanism, we developed the model including two parallel reactions of two coke precursors for propane pyrolysis:
Greek Symbol 6 = expansion factor Registry No. C, 7440-44-0; propane, 74-98-6; ethylene, 74-85-1; propylene, 115-07-1.
-
CzH4
k l = 5.89
X
X
coke
1O1O exp(-230.29/RT)
l/&H6
k2 = 2.21
kl
k2
coke
lo8 exp(-165.22/RT)
Nomenclature A = frequency factor d = reactor diameter, m E = activation energy, kJ/mol F = molar flow rate of hydrocarbons, mol/s k = specific reaction rate coefficient 1, = equivalent reactor length, m n, = dilution factor, mol/mol P, = reference pressure, Pa
Literature Cited Albright, L. F.; Tsai, T. C. In Pyrolysis: Theory and Industrial Practice; Albright, L. F., Crynes, B. L., Corcoran, W. H., Eds.; Academic: New York, 1983; Chapter 10. Brown, S. M.; Albright, L. F. In Industrial and Laboratory Pyrolysis; Albright, L. F., Crynes, B. L., Eds.; ACS Symposium Series 32; American Chemical Society: Washington, DC, 1976; pp 296-310. Dunkleman, J. J.; Albright, L. F. In Industrial and Laboratory Pyrolysis; Albright, L. F., Crynes, B. L., Eds.; Acs Symposium Series 32; American Chemical Society: Washington, DC, 1976; pp 241-273. Ghaly, M. A.; Cryunes, B. L. In Industrial and Laboratory Pyrolysis; Albright, L. F., Crynes, B. L., Eds.; ACS Symposium Series 32; American Chemical Society: Washington, DC, 1976; pp 218-240. Holmen, A.; Lindvaag, 0. A. ACS Symp. Ser. 1982,202,45. Lahaye, J.; Badie, P.; Ducret, J. Carbon 1977, 15, 87. Pramanlk, M.; Kunzru, D. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 1275. Shah, Y. T.; Stuart, E. B.; Sketh, K. D. Ind. Eng. Chem. Process Des. Deu. 1976, 15, 518. Shen, G.; Lou, Q.;Niu, F. J. Hebei Inst. Technol. 1985, 4, 48. Sundaram, K. M.; Froment, G. F. Chem. Eng. Sci. 1979, 34, 635. Zou Renjun Principles and Techniques of Pyrolysis in Petrochemical Industry; Chemical Industry: Beijing, 1982.
Received for review April 1, 1987 Revised manuscript received August 19, 1987 Accepted September 4, 1987
A Statistical Mechanics Based Lattice Model Equation of State Sanat K. Kumar,*t Ulrich W.Suter,* and Robert C. Reid Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
A statistical mechanics based lattice model equation of state (EOS) in a closed analytical form is developed for the modeling of the phase behavior of multicomponent mixtures of molecules of disparate sizes. The EOS is compared to others in the same genre. The lattice EOS is used to model quantitatively experimental VLE data across a broad spectrum of binary mixtures of molecules, using a single binary interaction parameter, which is temperature-independent for many systems. Results obtained also demonstrate that this EOS is successful in reproducing quantitatively trends observed in polymer-supercritical fluid equilibria across variations in temperature, pressure, and polymer chain length, again with one interaction parameter that is independent of operating conditions. The phase behavior of mixtures of molecules of disparate sizes, specifically polymer-supercritical fluid mixtures, is of considerable theoretical and practical interest. To model such systems, one needs an appropriate equation of state (EOS) that is applicable over a large range of densities. During the last decade, EOS's have been used increasingly to correlate and model the complex phase behavior of molecular mixtures under a variety of conditions. Cubic EOS's have been employed extensively (Soave, 1972; +Currentaddress: IBM Almaden Research Center, San Jose, CA 95120-6099. 0888-5885/87/ 2626-2532$0~50/0
Carnahan and Starling, 1972; Peng and Robinson, 1976), although others have also been used [see for instance Dieters (198111. This genre of EOS, however, proves inadequate when the size differences between component molecules become large. Modeling of mixtures of molecules of dissimilar sizes has in the past been performed by the use of either of two general techniques. The first one is based on perturbation theory; an example of such an EOS is the modified perturbed hard chain EOS (PHCT) (Donohue and Prausnitz, 1975; Vimalchand and Donohue, 1985; Sandler, 1986) which has been used successfully to model mixtures of 1987 American Chemical Society
