u T
= =
ensemble standard deviation residence time
OTHER ( ) = expectedvalue -
SUBSCRIPTS i = inside o
outside s shell wall 20 = tube wall 1 = fluid 1 or time period 1 2 = fluid 2 or time period 1 = =
=
sample average (for overlay bar)
literature Cited
Berryman, J. E., Himnielblau, D. M.,Ind. Eng. Chon. Process Drs. Dewlop., 10, 441 (1971). Buckle)., P. S.,Chem. Engr., 57 (9), 112 (1950). I ~ E C E I Vfor L Dreview X a y 1, 1972 A 4 ~ November ~ ~6, 1972 ~ ~
Relative and Absolute Rates of Decomposition of Light Paraffins Under Practical Operating Conditions H. G. Davis* and 1. J.
Farrell Cnion Carbide Corp., South Charleston, TI-. V a . 65305
A generalized correlation is presented for overall first-order rate constants of thermal decomposition of normal and isoparaffins in mixed gaseous and liquid cracking stocks. The correlation fits laboratory, pilot, and plant data obtained b y cracking light gases and naphtha at commercial cracking conditions. While the study was limited to c 2 - C ~ paraffins, the correlation has theoretical significance and i s amenable to extrapolation to higher carbon numbers.
D e f i n i n g the rates of pyrolysis of hydrocarbons in terms of t,he actual temperature and time profiles of plant pyrolysis furnaces has always been difficult. K e look on the problem as having three major parts. First, we must define the complex kinetics of cracking with simplified expressions. Second, we must interrelate the rates of decomposition of different hydrocarbons (for example ethane, propane, and the butanes) so that the behavior of niixed feeds is properly represented. Third, we must quantitatively define the cracking furnace operation in ternis of the usual kinetic variables of time, temperature, and perhaps pressure. These three parts are not entirely separable, and our discussion of them will inevitably overlap. There is, of course, a large body of literature on the kinetics and mechanism of hydrocarbon cracking. For example, see Purnell and Quinn (1967), Uenson (1960), Torok and Sandler (1969)) Laidler et al. (1962), Lin and Back (1966). 3Iuch of the accurate work has been carried out a t impract'ically low conversions because this region is most iiistructive as t o mechanism. I n plants, however, we are interested in conversions from 4 0 4 0 % up, in temperatures from 700-9OO0C, and in equivalent times (see below) in the range of about 0.05-0.2 see. We hare, therefore, used in-house data almost exclusively in developing a ivorkiiig model of plant cracking. r. I o interrelate the conversions of various paraffins, we extended a principle we had earlier used in a paper on ethane kinetics (Davis and Williamson. 1959). We reported t,hat
over a wide range of decompositions it was a good approximation t,o take ratios of overall specific rates of decomposition to be constants. This is consistent with t'he free-radical mechanism of paraffin decomposition as d l as empirically sound. It d l be discussed in more detail in the body of the report. There remained the problem of quantitatively defining and measuring the severity of cracking in plant furnaces., Our basic tool here was a proprietary computer program named T l P P (Temperature and Pressure Profiles). This is an improved version of a program de ibed elsewhere (Khite et al. 1970). T,\L-'P calculates temperature, pressure, velocity, and composition gradients in tubular cracking furnaces. It also calculates equivalent residence time a t the outlet temperature and combines time and teniperaturc as a severity function S (Linden and Peck, 1965). S is essentially an estimate of the uniform temperature required to give a specified degree of cracking when the residence time is 1 see. n'hilr the concept is inherently inexact, we have found it of use in kinetic modeling. Concepts of Severity
Qualitatively, we define severity of cracking in a tubular reactor as t,he summary effect of the increments of residence time through the reactor with t'heir corresponding temperatures and pressures. Setting aside pressure to be t,aken care of as a secondary variable, we weight each time increment, by a n exponential Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 2, 1973
171
~
:
hrrheriius factor, e-(E’RTj. Then we define “equivalent time,” r , for any increment of time as
where T i is the average absolute temperature during the increment of residence time, A t i . The high values of activation energy E , in the range of 5080 kcal/mol, found in low conversion kinetic studies, are inappropriate here. K h e n \ve compare overall specific rate constants determined a t high conversions and approximately constant residence times (isothermal) or equivalent times (nonisothermal), we obtain much lower temperature coefficients. An acceptable typical value of E is 46 kcal/mol, and we have ured this in our analysis of furnace operation. This value is shown below to be consistent with our results (see Equation 8’). Sandler and eo-workers (1961, 1963) also reported energies of activation for n-butane cracking in the range 42-4i kcal/ mol. Thus their values of Eactare similar to those shown here, even though their deconipositioiis are rather loiv-8-28%. They attribute these low apparent values to heat transfer effects, which indeed must account for t,he differences between tubular and annular reactors which they observed. Clearly their measurement of wall temperature could not be equated to truc reaction temperature. Their low activation energies, however, must arise from the same source as do oure. Their plots of k against temperature are all a t approximately corietant residence time, herice a t greatly varying decomposition. At the higher temperatures arid higher decompositioiis, product iriliibitiori becomes progressively greater, causing the overall value of k to be reduced from the zero decomposition value by larger and larger factors. If we choose to compare k’s along lines of approximately constant decomposition, we obtain much higher values of E. For example, n-ith ethane a t 587, decomposit’iori, we find Eact = 80 kcal. We have illustrated this effect in some detail in a microfilmed appendix. Since the ethane pyrolysis mechanism .i known in considerable quantitative detail (Benson, 1960; Davis and Williamson, 1959; Williamson bo be published) we pick it for our example. However, the higher paraffins behave similarly. If we plot log k vs. 1/T for successive t,emperature using IC’s measured a t constant reaction time, the slope a t very low conversions corresponds to a very highvalue of Eaet.At higher conversions the value falls, arid in the “practical” conversion range an Eaot of about 46,000 kcal/mol is appropriate. The total equivalent time a t the furnace outlet temperature is simply : e(-E!RT,
r =
( A t )i
1 ~~~
e(-L”IRTout)
(2)
The severity in the furnace operation is now represented b y r and Tout.These are combined in the severity function, S, AS’ = Tout(7)0.062, O C (sec)0.06*
(3)
I n general we report T in “C, but’ i t is understood t h a t in any exponential -1rrhenius factor it must be converted to O K . I t is xiow possible, for any given cracking furnace operating conditions, to compute equivalent time and severity function gradients. If, from independent studies, we can relate severity function to percentage decomposition of feed componeiits, expansion ratio 011 cracking (cracking ratio), and to yields of products, we can now also compute decomposition and composition gradients ad lib. T.QP thus becomes a n empirical 172 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 2, 1973
kinebic model of cracking in tubular furnaces and a useful tool for estimating the effects of design and operating variables. It should be noted that empirical cracking ratioseverity, and heat of reaction-decomposit,ion-severity relationships are required before even the basic residence time, temperature, and pressure gradients can be computed. S is the uniform temperature at’ which a given depth of cracking occurs in a 1-see residence time. “Depth of Cracking” can be defined in several ways which are unfortunately not completely consisteiit. We refer to these as “internal” measures of severity and often they can be determined more T which are “external” measures. accurately than S or r I n Table I we list a few of the possible internal measures, with comments on their usefulness and limitations.
+
Rates of Decomposition
Over a period of many years, we have developed in Union Carbide a large body of data on the rate of cracking of ethane, propane, and the butanes as functions of time and temperature. I n an isothermal laborat,ory reactor, the experimental residence time is identical to our defined “equivalent time a t the outlet temperature.” We can therefore calculate S accurately, withiii the limits of our ability to measure fairly high temperatures and calculate residence times. When we graph the decomposition portion of an overall first-order rate coiistant, -111 2, where 5 is the fraction uridecomposed, 2 i 3 ) in a semilog .Irrheniui plot, we find simple vs. l/(S relationships. If Ive limit the data to a narrow b a l d of part’ial pressures and a narrow band of residence times, we can fit straight lines to the points. Differences h e t w w i reactors shoiv u p and it is well to limit the plots to data from a single reactor with temperatures and times defined as closely as possible. Differences between reactors are att.ributed primarily to the difficulty of determining the absolute level of reaction temperature to better than about = t , j 0 Cby such means as a thermocouple in a central well. Our own experience, plus considerable evidence from the literature (see for example Sandler et al., 1961, 1963), rules out surface effects as a major factor in these differences. The quantity, -111 5, equals the overall first-order rate constant of decomposition if the time is 1 see. Since severity function is the temperature for a 1-see residence time, we define
-+
k , = -In
as a convenient rate parameter.
(4)
(2)
+
I n Figure 1 we have plotted log k , vs. 1/(S 273). Values of k , for ethane, propane, and butane are based on runs in a single reactor (see Appendix) which has given consistent decomposition results in the range of temperatures and residence times of interest. Values determined a t several residence times and two pressure levels are plotted, and effect’s of these variables are evident. LIost notable are substantially lower ks’s for et,hane a t long residence times. These reflect effects both of back reaction and of product inhibition. Modern plant furnaces have equivalent’ times of the order of 0.1 see. We have therefore drawn lines through the data obtained a t about this isothermal residence time. 1F7e have favored the atmospheric pressure points because they constitute a reasonably complete set. Values of k,9 a t the higher pressure level lie a little below these. Values of k , for isobutane are riot significantly different from those for n-butane. Figure 1 is the first attempt to define a fairly straight line representing the rates of decomposition of paraffins as a
~~
~
~
~
~~~
~
~~
Table 1. Commonly Used Internal Measures of Severity or Depth of Cracking Comments Measure
Use
yo 1)ecomposition
of ethane, propane or butane
Favorable
Gas cracking
Unfavorable
Readily determined
Rate constants are somewhat sensitive to pressure and to the range of residence times used % Decomposition of pen- Liquids cracking Good rational parameter for K o t usually determined and often diffitheoretical interpretation tanes or higher paraffins cult t o measure accurately Required for good operation Depends strongly on hydrogen-carboii Yield of Cd and lighter gas Liquids cracking or C4 and lighter ratio and structure of feedstock; requires calculation; goes through maximum as temperature is increased Methane analysis Liquids cracking; occaUsually available; increases Depends on structure of feedstock and sionally gas cracking monotonously with S somenliat on pressure and residence time Propylene analysis Liquids cracking; occa1-sually available, decreases Depends on structure, pressure, and sionally C3 and C4 monotonously with S;less residence time a t least slightly cracking sensitive to feed structure than CH,. Often the best choice Methane, ethylene, or pro- Same as analysis Same as analysis except less Depends strongly on hydrogen-carbon pylene yield easily available ratio of feed Liquids cracking; occaMethane/propylene ratio Easily available; rather inEmpirical; little theoretical basis. Kot sensitive t o feed structure, sionally C3-C4cracking completely insensitive to structure, pressure residence time. pressure, time Often best choice Propylene / ethylene ratio Mainly liquids cracking Easily available; related to Sensitive t o structure of fee& and other production requirements variables
Figure 1 . Laboratory cracking of gaseous paraffins (single feeds) 0 Ethane
C- -0.2 sec C k 0.25 sec - 1 sec 0 1.7 atm C= >1 sec
A Propane 0 Butane
b i-Butane
0 etc. 1
.01 1.k
1.14
1.12
1.10
1.08
1.W
1.04 lrn/(S
1.02 a
l.W
.p8
.%
.94
$92
atm, -0.1
sec
,'
273)
function of severity and of carbon number. We conclude that n-butane and isobutane points are indistinguishable and t h a t butane, propane, and ethane rates, at comparable residence times, are in the proportion 4.2:2.1:1.0 (*20%). These ratios appear to be rather insensitive to temperature, and 273) parallel lines with slopes equal to -44,00O/R(S represent the 0.1-sec data satisfactorily. Better estimates of the rate ratios can, however, be obtained b y methods discussed below.. The development mill indicate t h a t the slopes should not be identical but should depend on the number of primary, secondary, and tertiary hydrogens iri the particular paraffin. The differences will be too small, however, to be
+
seen in the experimental data on overall rate as a function of temperature. Relative Rates of Cracking
A direct approach to determining relative rates is the study of pairs of reactants. We have cracked under a variety of conditions the pairs ethane-propane, ethane-butane, and ethane-isobutane. Results taken from unpublished in-house data are shown in Figure 2, where we have plotted k , = -In (fraction unconverted) of the higher hydrocarbon vs. 12, = - 111 (fraction unconverted) of ethane. The apparent ethane conversion has been corrected for the small yield of ethane Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 2, 1973
173
1
7
I::
also be some effects, interrelated, of partial pressure, conversion. propane-ethane ratio and temperature because of their effect on tlic back reactioii of cthylene and hydrogen to ethane. Thesc deviation* can he estimated from a closer study of thc data and from equilibrium considerations. They will be large enough to be of significance under many plant cracking conditions. For example, a t SO%;;,ethane decomposition, in an
:: 6
F R A C T I O N ETHAYE UNDECCMDOSED
Figure 2. Cracking of mixed feeds 0
Propane-lab Propane-plant n-Butane-lab
oA
+
X i-Butane-lab (two series)
4 Butane-plant
frnni thc other membcr of the pair. a.; determilied in parallel i n tlic fecd (tlierc w e also minutc qiia~ititchts ~ i t l i o uethane t ties of propane aiicl n-l)utane formed on crackiiig cdianc, Ilavis and TYilliamsori, 1059). The straight line tlra\vii by eye through the etliane-propane points has a slope, k,(~)ro~~aiie)jk,(etliaiie)= 2.43. - i t vcry high propaiir convcrsiow (>977,), the analytical prccirion is such that th a t t r r from the linc lxconies large. ; \ t i average error of 0.1 mol % iii tlie propane anal account, for the averagr dcviatiou from the line, and Errors of 0.1 5 to 0.2 will account for the worst deviation. & i tthe lovi coriversion end of the curve! we have another problem. The data were all ohtailled at iiitermediate sampling points of plant furnaces. Percentage decompositioiis of ctliaue were small and t,he calculated yield of cthane from the ('a$. coristituents of the feed is a substantial fraction (typically about half) of the calculated n.et conversion. Shifts in the feed composition can and do occur and errors in analysis are important in this rang?. -1 line giving minimum average deviation of the points between 0 and 40% propane decompoqition has k,(l)rol)arie)/k,(ethane) = 2.8 -0.4. The point. correspond to an average temperature of --66OoC, and the slope i y expected to he higher here than a t higher conversions and higher temperatures. In the body of tlie cthane-propane graph we have plotted points from plaiit and laboratory, representing etliane/l)ropane ratios from 0.3-9, partial pressures of pyrolysis product from 0.9--2 atm., and net, ethane conversions from 46-84Y0. The straight line of slol)e 2.43 is an excellent first approximation to the data through these ranges. Small effects of temperature are exlxctetl and will be treated 1at)c.r. Thcre must
ethane-rich feed, 0.411 by weight stream dilution with high pressure droD in a plant furnace, the propane -ethane k , ratio was determined to be 3.02. K h e n we attempt t,he same t,ype of analysis for the ethanehutaiie hiriarip,90c0. Severthrless, the plots sho\r.n in Figure 2 arc rcasonably xitisfactory. The line drawn through the points has a slope k,(h~itatie)/h-,(etliarie) = 3.55. The commerit. and coiiditioiis applied t'o tlie etliaric--propane relationship apply her? also. Isohuta,rie and n-butane points were not dist inguisliahle. The lines of Figiire 2 have been d r a w in such a way tliat the lis ratios x11ply at ahoiit a inmil reactioii tcmperature of 840°C. T h r ratios \voultl be Ion-er if IW corrected for the rtli?.lenr-hydrogeti hack reaction. This cannot he done in any rigorow matiller. However, we observed that in the rims at hetwcm 60 and i5yGethane decomposition, the pressure ratio II?.C'J T 4 j ( ' J T B i q 10--30% of the erjiiilibriiini ratio, althoiigh the corrcsponding ratios for propane and liutane dehydrogenation arc vcry far from equilibriuni. \Ye estimate that on tlie average during a typical run which gives a k,v ratio along the propane line i n Figure 2, the hack rractioii is 15ycas fast as the forward rcwtion of ethane cracking. Thus the observed (rtliaii~)should 11r divided by about 0.85 to give a value corrcvtcd foi, hark reactioii. Similarly, iii tlic range of 3060yo etliaiie decomposition n'e find a 5 1 5 % approach to equilil~rium,assiinie average back reaction ccluals TCJ, of the forivarrl reaction diiiiiig the ruii and tlivitic. k,?(ethanr) by 0.93 to approximate a corrected value. TVc thus rstimate k,~"(ljrol,aiic)l~," (ethane) = Rp?', arid kh(lxitane)/ks"((>than(>)= Roy a t about 2.1 and 3.3, respectively, a t 840°C. \-e w e t,lie symbol R* since tile ratio applies to infiiiitc tlil~itioii,rather than any practical coiidition. Mechanism of Paraffin Cracking-Relative
- I t any practical tube-cracking conditions, very little feed by direct split into radicals. The over\r.lielmingly grrater ijart of the paraffin disappears by reactions of the type: (1)
R'+ R'H (2) R"
+
+
RH
+ R'
Products
For esample, in n-butane cracking \Ye have ( 3 ) ('t€Iio
*
174 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 2, 1973
Bond Reactivities
+ It'
+
CJIQ'
+ RH
where R' is primarily CEI,' or H', with some C2H{ a i d a little C 3 H i ' , and C4119' can be primary, CnH7CH2',or secondary C2H5--cH--CH3. The butyl radicals decompose mainly to CP&' C2Hi,and ('He' ,&I( respectively. The rate of Reaction 3 is determined by the combined conceiitration of free radicals [ E ] and , rate cwiistaiits \vhich are related to the number and reactivity of C-13 boiids in butane. Etliaiie, propaiie! or other hydrocarboils in mixtures with hutane nil1 be csposed to this same composite radical conceiitratioii, [R'], atid will react, according to the strerigt'h
+
+
and number of their C-H bonds. Essentially all the radicals formed decompose by Reaction 2. C2H; from ethane is a partial exception because of its involvement in the backreaction discussed above. If Jve assume all C-13 bonds of a specific type (primary, secondary, or tertiary) have the same activity, we can use Figure 2 to make a preliminary estimate of the relative activitier of the bonds. Let 1, a, aiid b equal the relative activities of primary, secondary, arid tertiary, respectively. Then R p m= 2.1 = (6 2a)/6, givinga = 3.3, and
+
4-
which also gives a = 3.3 -
while
2
15
I.
I3
IO00 I
r*,
Figure 3. Dependence of relative reactivity of hydrogens on temperature
which gives b = 10.2.
0 Jackson
An alternate method of calculatio~iis from the product distribution on pyrolysis of propane and the butanes. For this, we need estimates of tlie yields of major products extrapolated to zero decomposition, plus a 1movJedge of the primary 11011free radical products of decompositioii of the primary, secoiidary, aiid tertiary free radicals fornird ill Reactions 1. For example, tlie formation of primary propyl radicals from propane leads to the overall reaction
(4)
C3&+
CH4
+ C?H4
arid the secondary propyls lead to
( 5 ) C3Hg -+ €1,
+ C3Hs.
From unpublished data (see Appendix, deposited wit'h American Chemical Society Xicrofilm Depository Service) we estimate R4/R5 = 1.06 + 0.05 a t 800°C. Similarly the ratio of secondary butyl products to primary butyl products from n-butane is 2.0 k 0.1 a t SOO'C and of tertiary butyl products t o primary products in isobutane cracking is 1.1 i 0.1 a t 700°C. From the propane data, the average reactivity of the two secondary hydrogens relative to that of the six primaries is 6/(2 x 1.06) = 2.83 + 0.15 a t 8OOOC. From the butaiie data the secoiidaryiprimary reactivity ratio is (6 X 2.0)/4 = 3.0 + 0.15, also a t 800°C. *And from the isobutaiie yield data, the tertiary/primary reactivity ratio is (9 X l . l ) / l = 9.9 =t1 at '700°C. Jack3011 et al. (1962) have determined tlie relative reactivity of primary, secondary, and tertiary hydrogelis in CH3 estractions by internally consistent photochemical methods. From their reported rate expressions we calculate that a t 380'C (roughly the middle of tlie experimental temperature range) tertiary:secoiidary:priniary = 21.4: 5.0: 1.0. The difference in reactivities is attributed primarily t o a differeiicc in eiiergies of activation, the authors suggesting E,,t' = 3500 cal/niol, arid EactP- E,,,S = 1750 cal/moi. I11 Figure 3 we show a plot of relative reactivity vs. 1/T contaiiiiiig only tlie points from Jackson et al. aiid our estimated values a t pyrol? temperatures. Lines are drawn r q ~ r e m i t i i i gactivation energies of 3500 and 1750. These can be placed so as to represent the photochemical data and our own estimates from product, distribution within tlie uncertainty of tlie lattrr.
A
0
et ol., 1962 From relative rotes From product distribution
W i e n rve give some weight to our estimates from relative pyroly-iy rates at 840°C, we draw lines with smaller slopes (broken lines of Figure 3). Relative reactivitieb a t 840'C in the propoi tion
R 1 : R a : R= p 9.0:3.0:1.0 are reconcilable with all the inputs. If we take the activation energy differelices to be 3000 and 1600 cal/mol, we have
R', RTJ= 2.32 e
3000 RT
and
Rs,R p = 1.46 e
1600
RT
These equations are in satisfactory agreement with Jackson et al.'s recommended equations, R 1 / R p= 1.53 e 3500/RT and RS/R" = 1.30 e 175O/RT. Equatioiis 5 and 6 can therefore be used to extrapolate our conclusions about relative reactivities a t 840OC to other temperatures. Since errors in frequency factor5 are all too easily compensated for by adjustments in activation energy, tlie exact niagiiitride of tlie pree\;ponential~in Equatioiis 5 and 6 should not be taken too seriously. I t seemq probable, nevertheless, that the gieater reactivity of tlie tertiary and secondary hydrogens i, euplained partly by higher preeq)onentials i n the late eupressions of the extractioii reactions. Revised Estimates of Reactivity Ratios
We can no\v combine our conclusions about relat'ive reactivities of hydrogens with t,lie cmpirical rate ratios of Figure 2 to give a more rational estimate of these ratios. From the bond reactivities alone we calculate for 84OoC that values of lis should lie in the ratios butane = isobutane = 3.0, propane = 2.0, ethane = 1.0. l3ut Figure 2 shows that under practical cracking conditions these ratios are higher and, a t least partly, dependent on factors n-liich we interpret as a dependency on degree of approach to the cthane-ethylene-hydrogeii equilibrium. If we insist that lc,(propane) ,'k,(ethane) = lnd. Eng. Chem. Process Des. Develop., Vol. 12, No. 2, 1973
175
T o make the relative rates correct we must take B equal to 1 for ethane. so that we have
k,(C2Hs) =
e 2 1 41e-44,OOO
/R(S
+ 273)
(1 0)
The values of E and A in Equations 8 and 10 are very low compared to the parameters which come from mechanistic studies of the decompohition of paraffins a t low conversions. Frequency factors likc 101"1016 (t32-e37) and activation energies of 60,000-85,000 are found. We are here comparing rates a t constant equivalent time rather than at constant (or zero) decomposition. I t is not because we have used the pwidotemperature, S, as a variable, for we can convert to a temperature basis simply by using the fact that the time is uniformly 0.1 sec. The overall first-order rate constant for equivalent times of about 0.1 ser is simply kJ0.1 while the temperature 111 "C IS S(10)O Os? or 1.153 AS, "C. We can thus readily transform Equations 8 and 10 t o 8' and 10': k ( = ~ 0.1)
+ 1.23(5,
= e Z 2 65[l.22
-16,500 -
2)le
RT
(8')
-16,500
and
.'V I
I
L 1 I04
I02
I
IO0
el,
I
I
96
01
1000/IS*273l
Figure 4. Laboratory cracking of mixed feeds 0 Ethane in E, P
b Ethane in E,
0
Ethane in
A
n-B
E, imB
Propane in
0 n-Butane in E, 0- A 0 -0.2
6 +Butane
n-B set
in E, i.8 pressure, 0.1 5-0.2 sec
OA.* 1.7 atm
E, P
2.45 aiid u;.c the relative hydroqeii rcactivitiei t o calculate higher hydrocarboii~oiily, v, e havc., for Cs arid higher paraffins of carbon Ilumllc~r'VC,
\Vet makc the c x p r r 4 o n absolute as folloa s. M'r ahsum(' tlie 44,000 cal/mol s l o l ) ~deduced from Figure I aiid pick the gcncr a l i ~ c ~p~ l cwponeritial to give k,(proparie) = 1.20 a t 10O/(S 2 i 3 ) = 1.000. l'hiq gives us
+
13clow, thci paranieters of the equation will be checked against the data of Figure 1 aiid additional plant arid laboratory results. The more general form of Equation 8,
is used bclovv as an empirical basis for fitting overall rates of decomposition of paraffin components of iinphtlia mixtures. Ilere d is the gcrierdizetl frequency factor, B, D ,aiid E are paraniet(~rsnliosc pliy,&d sigiiificance is clear from the dcrivatioii of Equation 8, and we have incorporated a factor f which can be iraried to allow for secondary effects of equivalent time aiid p e r h a p pressure. Thus i f f = 1 at equivaleiit times of xhout 0.1 wc, it will be somewhat less than one a t 0.2 scc and somewhat greater than one a t 0.01 sec. 176 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 2, 1973
k ( 7 = 0.1, CZH6)= e2* 6ne R F
(10')
As with Equations 8 and 10 we can incorporate a minor change in the preexponential factor to allow for deviations of equivalerit time from 0.1 sec and for other second-order effects like those of pressure. Rates of Decomposition in Mixed Feeds
Equations 8 and 10 give values of Iz, valid for single feeds in laboratory reactors. In Figiire 4 \ve havc plotted valurs of k , derived from t h overall percentage docomposition of ethane, propa~ie,and the butanes in binary mixtures cracked in tlie laborat,ory. The straight lines drawn are calculated from Equations 8 and 10. From Figure 4 lve verify our earlier coriclusioii that the rates of disappearance of the two but,anes are iiidistiiiguisliable. The actual positioii of the butane liiic is apl)reciably lower than tho best line for these particular data. 'l'lie shift, liowcvrr, correspoiids to an iuicertaiiity iii severity or tem~ieratureof less than 5"C, which is u-ithin our ability to drfiiic tlic absolute tcnil)cratiirr levcls. ?'hr propane liiic is similarly c1isi)litcd by approximately 6 O C from thc best liiic we would draw throiigh tlic tlirw atmospheric pressure, 0 . l - s i ~csperinic~iital ~ points. The 1.iatni poirits lie below the propme l i t i ~however, ~ lly inore than can reasonably be attributed to tlic cffwt of ~ ~ r e s s ialone. u~ lye coiicludr: that Equatioii 8 pwdicts thP ahsilutc iiitegral rates of ticcortiposition i i i thebe niistures witliiii the i i ~ i c ~ ~ r taiiitics of' data aiid calculatioli aiid of iiica.;uriiig absolutt. tcinpcrature i i i ,+elmrat(' seriw of rslic~inic~iits. If ratrs of decompositioii arc iiidred rliaitgeti by the 1)rcwiiw of other paraffins, the effects are 10s thaii we (4iiiiIici.etictcwriiiic,. .lgain with cithanc't we might prefer a slightly higlier liiic, but oiie displac~edby oiily about 3°C. .I riior(1 important observation is that k,\(ctliaiic) i; [lot sigiiificwitly diff(awnt r ( ~ i i ci(t i~k , i t i the‘ riiisture.: from k, in 11ure ethane it is bmaIl---too xitiall t o h i t 1 iii 111r~er s l r r i merits. S e c o n d a r y Effect of Temperature
IVc can deduce from Equatioiis 5 aiiti 6 tlint the relative rates of decoml)ositioli of 1)araffiiis coiitniniiig differelit num-
2
1
1.02
I
l.w
.w
.p8
IWO/iS
+
.Q4
I
,
.P2
273)
Figure 5. Plant cracking of gaseous paraffins (single and mixed feeds) 0 Ethane
A 0
Propane n-Butane
O@@Furnace types A, 8, C
Q4QMixed feeds
Ind. Eng. Chem. Process Des. Develop., Vol. 12, NO.2, 1973
177
Therefore, when we extend the relative rate relationships to higher paraffins we relinquish the insistence that k,(ethane) = 1 (Equation lo), and start with the generalized Equation 9. K e put this in linearized form aiid determine parameters b y a
Table II. Mass Spectrographic Analysis of Feed Naphthaa
Teight
yo
03 C7-Cycloarieb 48 n-Heptanr 89 Ibolieptaiieq 08 (3 7) Styrene 44 (1 4) o-Xylene 05 m-X>leiir 10 p-Xj leiie 06 E t h ? Ibeiizcne 15 C'SEI16 7 8h n-Octaiie 1 23 I.octaiie5 0 03 ('j-13eiizciie. 1 72 1 37 8 21 13 80 Decniies 1 80 Othei Clo'i ('(7tI1L 0 06 ITndecanei a Valiie, i n paleiithe+ indicate butane alia1 iecorid half of e\peiimeiital peiiod
Propane czs-2-llutene trans-2-Butene n-Butane 15obutane Cypentadieiie Cj-clopentene Pentenes n-Pentane Isopeiitaiie\ Beiizerie C6-Cycloerieq Cyclohewne lIe-Cypentane n-Hexane Isohexanes Toluene
0 0 0 3 0 0 0 0 9
"I
0
5 6 4 0 0 1 0 0 2
53 23 33 01 59 11 27 73 40 4 10 3 70 1 60
5 12 0 96 2 48
-1
Figure 6. S from experimental measurements vs. SB from k, (butane) X Flat gradient 0 Steep gradient
0 Steep
Average temperature = section outlet temperature
gradient recalculated,
section
Extension to Cj+paraffiiir is discussed in the remainder of this report. Extension to Higher Paraffins
It will be clear from tlie above discussion that LT-e can obtain useful generalizations about, the relative rates of cracking of paraffins by consideration of the kinetic behavior of ethane, propane, arid butane. The greatest deviatioiis from our zirnplistic relations can he attributed to tlie particular chemical propertjes of ethane; iianiely, the uiiiquely large effect of back-reaction eqecially at high coilversions or elevated partial pressures, and the gradual increase of the apparelit activation energy as severity falls belolv about 750 from 46 kea1 t o 78 kcaljniol. Certainly eithcr lxopane or butane is a better model for comparison than etliniip. 178 Ind. Eng. Chem. Process Des. Develop., Val. 12, No. 2, 1973
111 -
D(S,
ks -.
2)
+B
I.' - a -. - ~ _ _
S + 273
(11)
statistical least-squares analysis The input for our study was the detailed data from 22 runs with a full-range naphtha in a small steam-cracking pilot plant. A mass spectrometer analysis of the naphtha is ~ h o w nin Table 11. The feed contained a small amount of butanes, whose decomposition as a function of severity could be calculated from the yield data nith reasonable reproducibility. This gave us a tie-in with the separate study on gaseous paraffins. Naphtha Cracking Pilot Plant
While we are concerned primarily with data analysis, a brief descriptioii of the experimental apparatus is in order. The runs It-ere made iii a small pilot plant, so designed t h a t teniperaturP and pressure profiles similar to those fouiid in plant scale can be imposed. The reactor consists of a number of 64-iii. long sectioiis of electrically heated 3/8-in. stainless tubing, with temperatures measured by thermocouples a t the out'let of each section. Pressure profiles were iinposed with precision orifice plates and temperat'ure profiles controlled by individually regulated electric heaters. Gaseous and liquid samples were taken for each run and analyzed by a variety of methods, including distillation, gas chromatography, aiid mass spectrometry. The individual analyses n-ere then put toget,lier into one overall total product The apparatus and analytical procedures have been described more complet,elyelsewhere (Khite et al., 1970). X h e n we attempted to relate observed decompositions of feed components to values of S calculated from measured temperatures of the pilot plant runs, our statist,ical studies indicated that random and syst,ematic uncertainties in S were more important than uncertainties in t,he measured percentage decompositions. Investigation showed that' there were insufficient temperature check points to determine accurately the temperature gradient, especially for runs n i t h steep gradients. S o r d i d it seem possible to calculate the gradients accurately in a small, electrically heated reactor. K e fouiid better-defined relationships betiyeen conversion data and p t i c u l a r internal measures of severity (see Table I). Fortunately it proved possible, in a consistent ~ a y to , assign values of S to each pilot plant run through correlations r\-ith these internal measures. The procedure is given in an a 11peiid i x . 111 Figure 6, we plot Sex, against this assigned severity ( S B ) .S,,, scatters from the 45' line d r a w l more t'han we'd like. By defining a steep temperat,ure gradient as one in which tlie temperature rises more t,liaii 40°C in one of the last three sections of tubing, we can divide the runs into groups with dients. Points representing runs rvith steep ematically low in Figure 6, probably because the use of rnedian section temperature to represent average temperature is inadequate (the open circles, which fit' the 45" h i e , are based on the assumption that the proper average for cadi section is the outlet temperature from the section). & h i d e from this, S, is a fair representation of Sex,.Hon-ever, our primary juqtification for re1)lacing S,,,,nith the assigned Se is that the latter correlated best with decompositioli data.
10.
9. 8.
7. b. 5. 4.
3 2
2
I
0
0 0
0 0
1.04
1.02
1.00
lOOO/CS
0.98 273)
0.w
0.94
Figure 7. Single least-squares fit of first-order paraffin rate constants
c4-C~
A n-Heptone A lsoheptane
0 n-Butane
0 lsobutone n-Pentane
Plant butane data
r_lsopentone
Pentane Decomposition
I0
I
I
I
I
I
I I2
' l l r Iwiitaiic. data (Figure
7) showed the least scatter.
with all tlic> tlata at high beverity tlie scatter iiicreases a> tlic roiiccmtratioii of uiidecomposed petitaiiei approaches Z(W. .It valuni of k,, abo\.r 3 (95% tlecompositioii), or 4 (9876 dt,c,oinl,oiitioii)~tlic aiialytical accuracy is liinitiiig.
Figure 8. Single least-squares fit of first-order C4-G paraffin rate constants 0 n-Hexane 0 lsahexane
nIsooctane Plant hexane data
mn-Octane
Heptane and Octane Decompositions
l u Figure 7 , the siiiiultaiieous fittiiig teclitiicliic~ii to repremit the lieptaiie tlec.cjml~o.itioii tlata quite well. The octaiie decwinposit,ioii data (Figure 8) teiid to fall lielonthe least-square fit, of all tlie data. Tliis i:, iiot particiularly higiiificaiit. Iiowevcr. At the severitiefi of our test.
