INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1955
1239
-0.7 -0.1
-0.6
-0:
-0.5
-0.1
-0.4
- 0.‘
-0.3
-1.1
-0.2
-0..1
3
< e
i? s
x-
x
$ -0.6 Y
x -1.
Y
-0.5
(3
0 -I
-0.4
-0.3 -0.9 -0.1 -2.1
0.0 -1.6
-1.2
-0.8
-0.4
0.10
LOGio (C = E W L )
Figure 7.
Figure 6. Adsorption isotherms 1. Trichloroacetic acid 2. Dichloroacetic acid
3. 4.
Chloroacetic acid Acetic acid
ACKNOWLEDGMENT
The authors are indebted t o the Chemical Process Co., Redwood City, Calif., for providing samples of Duolite 5-30 and to Irving M. Abrams of the Chemical Process Co. for his assistance and advice. LITERATURE CITED
(1) Brunauer, Stephen, “Adsorption of Gases and Vapors,” Vol. 1, “Physical Adsorption,” p. 5, Princeton University Press, Princeton, N. J., 1945,
0.90
0.99
x / m , GRAM
0.0 0.9 0.4
1. 2. 3.
Langmuir isotherms
n-Butyric acid Propionic acid Acetic acid 7.
4. Dichloroacetic acid 5. Chloroacetic acid 6. Trichloroacetic acid Acetic acid
(2) Griffin, K. M., Richardon, H. L., and Robertson, P. W., J. Chem. Soc. (London), 1928, p. 2709. (3) “Handbook of Chemistry and Physics,” C. D, Hodgman, ed., 32nd ed., Chemical Rubber Publishing Co., Cleveland, Ohio,
1950. (4) Smith, 0.C., “Inorganic Chromatography,” pp. 4 ff., Van Nosti-and, Xew York, 1954. RECEIVED for review January 7, 1954. ACCBPTED December 3, 1854. Taken from a thesis submitted by Robert J. Cooley t o the faculty of the University of Santa Clara, Santa Clara, Calif., in partial fulfillment of the requirements for the B.S. degree.
Preflarne Oxidation and Detonation of Cyclopentane and 2,2,4=Trirnethylpentane B. J. REITZER’ AND G . G . LAMB Northwestern Technological Institute, Evanston, I l l .
T
HE phenomenon of knock in internal-combustion engines has long been a subject of intense investigation, for it is the onset of knock that limits engine performance. A slight
increase in compression ratio results in a substantial increase in engine efficiency, but this gain cannot be achieved if the compression ratio cannot be raised because of knocking. The oxidation reaction of hydrocarbons, which leads to detonation and knock in spark-ignition engines, has a complex 1
Present address, Btandard Oil Co. (Indiana), Whiting, Ind.
mechanism involving a great number of simultaneous and consecutive reactions. This fact has been established experimentally by many investigators who have found a wide variety of intermediate products, such as aldehydes, peroxides, and ketones, present during the course of the reaction. Thus, a detailed kinetic evaluation of the reaction which considers the concentrations of initial and intermediate reactants and products is quite difficult because of the analytical problems involved. Added to the extreme complexity of the reaction are the experimental difficulties due to the speed of the reactions. At the
INDUSTRIAL AND ENGINEERING CHEMISTRY
1240
temperatures and pressures prevailing in the end gas of sparkignition engines, combustion is completed in a matter of a few milliseconds. However, in spite of the many different possible reaction mechanisms b y which the reactions might occur, there is extraordinary similarity in the over-all oxidation behavior of the N-, iso-, and cycloparaffins. Under the conditions usually employed for their study, the reactions are characterized by a relatively long induction period during which negligible pressure rise occurs, followed by a sudden increase in pressure and finally, under certain conditions, by an explosion.
TN = AN(ept
I
- 1)
(1)
where rN is the rate of appearance of N ; A Nand p represent combinations of reaction velocity constants for individual steps in the reaction scheme; and t is time. The derivation of Equation 1 is given by Semenoff ( I d ) . When r N reaches a certain critical value, T,, the liberation of heat cannot be dissipated t o the surroundings a t a rapid enough rate, the thermal equilibrium is destroyed, and the degenerate explosion becomes a thermal one. Thus, transition from the degenerate-branching reaction to a thermal explosion will occur when TN
T
Vol. 47, No. 6
= rc = A N ( e V
-
1)
(2) The delay time, 7 , represents the time elapsed from the beginning of the induction period to that of explosion. If it is assumed that A N is but a slowly varying function of temperature and pressure, then (07 = constant. As an approximation 'p = Cpne-BIT (3 1 whence
CPne-BITT = constant
Figure 1. Typical pressure-time trace for cyclopentaneair
Rogener ( 1 1 ) used Equation 4 to obtain the relationships between induction-period pressure, temperature, and delay time for the two-stage reactions he observed with n-heptane, n-pentane, and n-butane. Delay times varied from 1 to 100 ms. in the ranges 400' to 500' C. and 5 to 40 atmospheres.
T o explain similar occurrences, Semenoff ( l a ) proposed a degenerate-branching chain mechanism that is capable of describing the process in terms of pressure, temperature, time, and initial composition. The purpose of this work was to obtain delay time and rate equations for the oxidation reactions of cyclopentane-air and 2,2,4trimethylpentane-air mixtures a t fuel-to-air ratios stoichiometrically required for complete combustion. The range of temperature and pressure covered includes conditions that prevail in the end gas of spark-ignition engines. The experiments were carried out with the aid of a rapidcompression machine developed by Taylor and others (6). Its salient feature is the rapidity at which compression is achievedof the order 3 to 6 milliseconds (ms.).
T
Figure 2. KINETICS OF HYDROCARBON OXIDATION
Although the detailed mechanism of hydrocarbon oxidation is difficult to determine a t present, certain generalizations can be made which lead to equations that describe the process in terms of the gross variables. Let R represent a molecule of the original hydrocarbon, R' an excited molecule, M an intermediate product molecule, and N a molecule of the final product. Xow consider the following reaction scheme
R'
+ R = M + R' M = N M=N+R'
(i) (ii) (iii)
The first reaction is the primary chain of transformation, proceeding by means of the active centers, R'. The second reaction is not connected with the creation of initial centers for the primary chain. Reaction (iii), which occurs relatively infrequently, creates an active center for the continuation of reaction (i) by passing on the energy of the reaction to a molecule of R instead of dissipating this energy to the entire system as occurred in reaction (ii). This is the mechanism of degenerate branching. It leads to the rate equation
(4)
Typical pressure-time trace for iso-octaneair
Prettre (0) investigated the oxidation of n-pentane-oxygen mixtures in the temperature range 250" t o 300' C. and a t atmospheric and subatmospheric pressures. Of interest is the form of the equation he used to represent his data
AP
=
A(ed
-
1)
in which AP is the increase in pressure a t time, t . A is constant and, a t constant temperature, 'pis a function of initial composition 'p
= kP,Pi2
where P , is initial partial pressure of n-pentane and Pi is initial total pressure. When the initial pressure was sufficiently high, ignition occurred a t a constant critical rate, and Equation 4 was satisfied between 260" and 300" C. EQUIPMENT AND PROCEDURE
Under preflame conditions, the hydrocarbon oxidation reaotions are exceedingly rapid, and hence special techniques are necessary to follow the course of the reaction. The experiments in this investigation were made with a rather ingenious machine, which rapidly compresses fuel-air mixtures to desired reaction
.m
*
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1955
conditions. Details of the rapid-compression machine are adequately described elsewhere (6). Pressure in the reaction chamber was obtained as a function of time by photographing the sweep produced in a n oscillograph whose vertical input was connected to a pressure transducer located a t the wall of the chamber. An accurate 1000-cycle-persecond oscillator was used to superimpose vertical spikes a t I-ms. intervals on the pressure trace. I
I
I
I
0
by means of the ideal gas law. These settings resulted in ranges of 300 to 475 pounds per square inch aboslute and 925' to 1380" F. for induction-period pressure and temperature, respectively. ANALYSIS OF THE DATA
Typical pressure-time traces for cyclopentane-air and isooctane-air are shown in Figures 1 and 2, respectively. The events depicted by the traces are, in chronological order, a rapid compression of the charge; a relatively long induction period; a rapid pressure rise culminating in an explosion; and finally, a cooling period. Let us consider the period after compression. Relating the energy released by the over-all combustion reaction to the change in internal energy of the gas and the heat transferred to the walls, we have
O/
m
+ Ua(T - To)dt
Q,dnf = nc,dT
t
1241
(5)
Rearranging gives 0
0
0. I
0
oo/600 0
Making use of the ideal gas law and dividing both sides of the equation by the combustion chamber volume, we obtain the rate of conversion of fuel to final products loo0
1500
2000
2300
T-T. R:
3000
.
3500
4500
4000
Figure 3. Combustion chamber over-all heat transfer Coefficient
The cyclopentane that was used in the study was obtained from'phillips Petroleum Co. and has a specification of a t least 99 mole % purity. Eastman Kodak was the supplier of the isooctane which was of spectroscopic grade (99.95 mole % pure). Both hydrocarbons were used without further purification. A mixing tank, which contains a vibrating vane for agitation and is water jacketed for thermostatic control, was used to prepare the fuel-air mixtures. A hypodermic syringe and needle were used to inject fuel, through a small neoprene diaphragm, into the tank. Air was obtained from the laboratory supply and was passed through a drying tower, containing activated alumina, with which an estimated dew point of -75" F. was obtained. The air was then passed through a wound-string filter. I
I
0 4-
0 0
Using Equation 7, instantaneous rates may be determined directly from the pressure-time traces once the constants have been evaluated. The rate in Equation 7 differs from that of Equation 1 by a constant ratio determined by the stoichiometry of the overall reaction. The equations obtained in this work relate to the rate of reaction as defined by Equation 7. The thermodynamic constants, cv and Q., and their temperature dependence were obtained from the literature ( 1 , 2, 4, 13). During the cooling period, after the reaction has been completed, the rate is zero, and hence, from Equation 7
u=-
cvV dP R a ( T - TO)^
The over-all heat transfer coefficient, U, was found to be a function of temperature, as shown in Figure 3. The scatter of the data is believed to be due to the erratic behavior of the pressure transducer during the cooling period. This is caused by the high frequency vibrations set up by the explosion. Since the term in the rate equation involving heat transfer to the walls is of an order only 5 to 10% of the total, the correlation is quite satisfactory. The graph includes points obtained using both fuels.
.4I -
" 0
RESULTS AND DISCUSSION
I n the derivation of Equation 4 2-
CPne-BlTT
= constant
0
I
it was assumed that in Equation 1 O/'B
I 4
I 8
6
r
io
Figure 4.
r
I
=
A(&
-
1)
2
pt
Rate equation for cyclopentane-air Stoichiometric mixture
Pressure in the reaction chamber before compression was set a t 15 pounds per square inch absolute. Temperature before compression was varied from about 140" to 240" F. The range of compression ratio covered was 8.7 to 11.9. Pressure was obtained directly from the traces and temperature was calculated
A is constant. Unfortunately, during the course of the investigation, it became apparent that A is profoundly influenced by both temperature and pressure. If the temperature and pressure dependence of A is assumed to be of the form
A
a p n l e-BlIT
(9)
then the rate equation involves six unknown constants in a rather complex manner. A straightforward method of obtaining the constants was not obvious. Hence, no attempt was made to
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
1242
Table I.
Comparison of Observed and Calculated Delay Times Pi,
Run No.
Lb./Sq. Inch Abs
16 32 34 33 37
472 472 405 440 440 440 405 364 405 364 472 472 405 364 334 472 405 364 334 334
Ti, OR.
0b;;d.
7,
Calcd.
C yclopentane
41 42 43 44 36 45 47 48 51 19 20 21 22 25
'
4.7 6.4 11.1 8.4 6.8 7.9 9.3 13.4 10.4 12.7 5.0 3.6 6.4 8.2 14.6 3.7 3.4 5.5 6.5 9.4
6.0 6.2 10.4 7.6 7.3 7.6 10.1 14.4 9.5 14.2 6.4 4.1 6.3 8.7 10.9 2.9 4.4 6.2 8.2 8.2
6.1 10.7 16.5 4.2 6.4 8.3 16.4 4.3 6.2 8.3 6.6 10.9 7.6 7.5 12.2 7.3 6.8 6.5 4.7 5.7 3.1 6.4 9.4 6.5 12.2
5.9 9.8 11.9
Iso-octane 6 8 9 56 76 77 78 57 58 59
60 61 62 63 64 66 67 68 74 75 69 70 71 72 73
454 364 334 472 472 364 304 472 403 364 334 304 364 334 304 334 403 364 472 403 472 403 334 364 304
5.2
5.4 9.8 14.7 4.2 6.3 8.0 9.5 12.0 8.0 9.6 11.9 9.8 6.3 8.7 4.3 6.5
3.7
5.4 8.0 6.8 10.0
Vol. 41, No. 6
Since the reaction is chain branching, this slight difference can change the whole course of the reaction. Jost (6)has shown that the Arrhenius equation does not fit rapid-compression machine data. The applicability of the rate equations obtained in this study was tested by integrating the equations to obtain predicted pressure-time traces. For a number of runs the calculated curves coincided with the observed traces. Delay equations were obtained for the I I 0 twd fuels investigated. For cyclopentane =
886
pi-l.6ae7940/Ti
a n d for 2,2,4-trimethylpentane . . = 6980 pi - 1 . 6 7 e 8 9 1 0 / T i I n d u c t i o n - p e r iod pressures and temperatures together with a comparison of the observed and calculated delay times are presented in Table I. I n 0 Figure 6 the logarithm Figure 5. Rate equation for isoOf ( r / p i " ) is plotted octane-air for both fuels as a function of the recipStoichiometric mixture rocal of the absolute induction-period temperature. The linearity of the relationship indicates that the oxidation reactions studied are controlled by a single mechanism for the range of variables covered.
I obtain the rate of reaction in terms of instantaneous values of pressure, temperature, and time. However, it was found that the constants could be evaluated by considering the pressure and temperature of the induction period together with the instantaneous value of time. [Details of the evaluation of A and p are presented by Reitzer ( l o ) . ] This has been t,he usual practice in studies of reactions having an induction period (5,8, 9, 1 1 ) . The results are as follows: for cyclopentane A = 2.52 X 1 0 - 3 8 P , 1 3 . 7 e - 6 8 8 0 / T z 4.25
x
I
I
c'51 2.0
_ I
I
104 ~~0.21~--1940i~i
for iso-octane
5.5
A
=
5.39 X
= 1.99 X
6.0 IO'/T,;R
10-63P,31.7e-20,Q00/Ti
Figure 6. 107Pi-l.16e-3910/Ti
When pt is large, the value of unity in Equation 1 may be neglected, and a plot of log (r/A) versus pt will result in a straight line. This is shown in Figures 4 and 5 for cyclopentane and isooctane, respectively. The solid lines represent the evaluated rate equations. The data points include three rates that were determined for each run by Equation 7-the critical rate, the first discernible rate, and a rate intermediate to these two. The rates and the original pressure-time traces for each run can be found in (10). Although the points are scattered, it is believed that the correlations are about as good as the reproducibility of the data will permit. This is due to the manner by which active centers are originally produced-that is, by rapid compression. Compression time will vary somewhat in repetitive runs causing slight differences in the quantity of initial active centers.
'
6.5
7.0
Delay times for cyclopentane-air and iso-octane-air
The well-known sensitivity of cylopentane in C F R tests, a8 compared with iso-octane, can be explained by the stronger temperature dependence for cyclopentane, as shown in Figure 6. Consider the ratio of delay times for cyclopentane and iso-octane a t different temperatures for the same initial pressure:
Pi
Ti
365 365
1450 1860
T
(cyclopentane)/r (iso-octane) 1.44 0.82
Thus, a t low temperatures cyclopentane would be expected to have better antiknock characteristics than iso-octane, whereas a t high temperatures the reverse would be true.
