Precision of Expansion Tests on Coal RELATION OF EXPANSION TO OTHER VARIABLES B. W. NAUGLE, J. D. DAVIS,
AKD
J. E. WILSON
Central Experiment Station, U . S . Bureau of Mines, Pittsburgh, Pa. T h e material in this report' was assembled to assist chemists interested in the selection and carbonization of coking coals for coke used in iron and steel production. The Bureau of Mines has data on a large variety of coals, which should provide reliable information on the reproducibility and numerical values of the relation between expansion and other coal variables. Statistics on the reproducibility of both the sole-heated oven and the large vertical expansion oven are given in terms of the normal probability law. They include the correlations between expansion and coal particle size as well as wall pressure and internal gas pressure. Formulas are presented for the estimation of the expansion of coals and certain blends of coals. Especially in wartime, any information which will lead to a more efficient use of raw coal supplies, and which may help to avoid costly repairs to coke ovens by prevention of damaging expansion pressures, carries considerable significance and furthers the war effort through increased iron production.
I
pairs) of results of expansion tests made in the sole-heated and vertical expansion ovens were analyzed to determine the precision of methods for determining expansion and t o correlate expitnsion with other variables. The results of these studies are presented in the hope that they may stimulate further research on other variables, which when included will improve the relation. These precision studies and estimating equations have been developed solely from experimental data obtained by the Bureau of Mines Coal Carbonization Laboratory. STATISTICAL CONSIDERATIONS
Some of the studies were made on less than 30 pairs of determinations. Although this sample is not usually considered large enough to follow closely the normal law, the material is presented a t this time. Small sample methods were not followed in correlations. When the sample is small, the usual statistical equations are modified because small samples seldom contain the extreme values found in a large mass of data from the same source. No attempt is made to define the statistical terms which are used or to describe the computational methods of statistics because they may be found in standard textbooks (7, 10, 13, 17, 19).
NTEREST in the expansion of coal during coking is steadily increasing owing to the necessity of using coals of unknown expanding properties. The well-known low-volatile blending STANDARD EXPRESSIONS FOR EXPANSION coals are being rapidly depleted. The user of coals of unknown In this report most correlations of expansion with other variexpanding properties faces the probability of oven damage if he ables are based on the dry, solid-coal expansion rather than the employs blends that are too highly expanding. The Bureau of expansion a t 55.5 pounds per cubic foot. This method ( 1 ) of Mines uses the sole-heated oven ( 1) and the large vertical expancalculation s h o w the theoretical expansion of a charge of moission oven (11) to determine the expanding properties of coal. In ture-free solid coal without voids and eliminates differences in the sole-heated oven, a charge weighing about 40 pounds is carcoals cau5e.d by varying moisture content and specific gravity. bonized under a constant applied pressure of 2.2 pounds per The equations for calculating observed test expansion or consquare inch, and the per cent linear expansion or contraction is traction in the sole-heated oven t o dry, solid-coal expansion, Es, measured. In the vertical expansion oven, a charge of about 325 and expansion or contraction at the standard bulk density of 55.5 pounds of coal is heated from two sides to simulate oven coking, pounds per cubic foot, Ejj.j, are respectively, and the pressure required to maintain a constant thickness of charge is measured in pounds per square inch. 62.32 (specific gravity) The cause of expansion (3,6, 6, 9, 12, 16, 18) is (1.00 test expansion) - k tulk density (1.00 - moisture content) generally recognized to be the pressure of the = gas enclosed in the plastic layer. Blending, w h i c h i s usually practiced for improveO F STATISTIClL STUDIES FROM SOLE-HEATED b l \ D 1-ERTICAL EXPANSION. T.4BLE I. RESULTS ment of coke quality, also OVENDATA modifies the expanding properValues of Indicated Statistics, ties of a coal. Moisture con(Sole-Heated Oven) or Lb./Sq. In. (Vertical Expansion Oven) tent and size distribution are Distribution of Differencea. Distribution of Single Between Pairs Tests About Their Average other factors that modify the N ~ of. KO. of Different Probable Standard 95% Probable Standard 95% expansion of a coal. Item Tests Samples error deviation range error deviation range A d e q u a t e expansion data Sole-Heated Oven have been studied to provide Precision of tests, density 55.5 lb./ou. f t . 440 202 0.6 0.8 1.5 0.7 1.1 2.1 reliable and informative anaPrecision of tests on dry, solidc o d basis 442 201 0.8 1.2 2.4 1.2 1.7 3.4 lytical correlations with other Vertical Expansion Oven coal p r o p e r t i e s . S e v e r a l 36 16 0.4 0.5 1.1 0.5 0.8 1.5 Precision of test hundred- groups (mostly
m
2916
+
INDUSTRIAL AND ENGINEERING
December 1951
E65
=
+
55.5 (1.00 text expansion) test bulk density
The equation for calculahing =i
-
CHEMISTRY
2911
l.oo
from Es is
(1 +Ea.) (I - moisture) (55.5) - l,oo (62.32) (specific gravity)
STATISTICS OF PREClSION STUDIES AND CORRELATIONS
The statistics of the precision studies and correlations are given in Table I. The variance of the Y values on the various graphs is large but Table 11, column 3, indicates the percentage of that variance which is due to its relationship with the variable X. This percentage is found by squaring the correlation coefficient which may be interpreted quantitatively by stating that the square of the correlation coefficient equals the fraction of variance of one variable that has been accounted for by its relation to another variable. The values in this column would be 100% in a perfect correlation. The standard error of estimate is the maximum distance vertically above or below the regression curve between which 68% of the residuals lie.
DIFFERENCE ON A 4-MESH SIEVE BETWEEN PAIRS OF TESTS, PERCENT
Figure 1. Relation of Expansion to Particle Size OF STATISTICAL STUDIES FROM SOLE. TABLE11. CORRELATIONS HEATEDAXD VERTICALEXPAKSION OVENDATA
No. of Item Tests Bole-Heated Oven Relation of expansion to coal uarticle size 31 Es’timation of expansion of Pocahontas No. 3 coal from dry, mineral matter-free fixed-car18 bon content Estimation of ex ansion of 20y0 low-volatile brends from ex30 pansion of their constituents Estimation of the expansion of 30% low-volatile blends from 23 expansion of their constituents Estimation of expansion of coals from their dry, mineral matter-free fixed-carbon content 83 and plasticity Vertical Expansion Oven Relation of wall pressure t o in26 ternal gas pressure
Standard Variance Error of Corre- Accounted Estimate lation for by inUnitsof Coeffi- Relation- Dependent cient ship, % Variable 0.93
86
1.09
0.95
90
2.48
0.89
79
3.18
0.85
72
3.19
0.92
85
9.2
0.95
90
0.72
error of the average of two tests will be 0.5 X
1 2/2 = 0.4.
The
expected probable error of the average of three tests will be 0.5 X 13 = 0.3. As the number of tests increases, the probable error G decreases and the average value of two or more testa approaches more closely the true average. If the difference between two tests is greater than that which prevailed 95% of the time in the 202 samples, the samples are said to differ significantly a t the 0.05 level. ThisTtatement indicates that if two tests differ by more than 2.10/, andone says they differ significantly, he will be correct 19 times out of 20 on an average. In this case, “differ significantly” means that: the two samples did not come from the same source; the samples were
Each correlation coefficient was tested for significance by means of Fisher’s 2 function, which is related to r and used as a transformation for r in testing the reliability of a correlation wefficient. The lower the probability, the greater the significance that can be attached to the correlation coefficient. The probability of getting the correlation coefficients reported in Table I1 is less than one in a million if the indicated correlation did not exist. PREClSION OF SOLE-HEATED OVEN TESTS
.
The sole-heated oven of the Bureau of Mines is used to determine the expanding properties of all coals evaluated for the production of coke, gas, and coal chemicals by the BM-AGA test method (14). The degree of precision of the sole-heated oven enables one fo state the allowable observed differences in expansion or contraction before the samples are said to differ significantly and to know the odds applicable to that statement. The statistical values for expansion a t a charge den4ty of 55.5 pounds per cubic foot are given in Table I. The probable error of any one test is the limit on each side of the average between which one half of the test results lie. The other half of the test results lie outside these limits. The probable error of the arithmetic mean of a series of observations varies inversely as the square root of the number of tests. If an individual test result has a probable error of 0.5, the expected probable
4 79
81 a2 a3 a4 DRY. MINERAL MATTER-FREE FIXED-CARBON. PERCENT
85
Figure 2. Relation of Expansion of Pocahontas No. 3 Coal to Dry, Mineral Matter-Free FixedCarbon Content
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INDUSTRIAL AND ENGINEERING CHEMISTRY
sieve between any pair of tests are plotted against the differences in dry, solid-coal expansion between the corresponding pair of tests. The correlation coefficient between dry, solid-coal expansion and percentage of coal on a 4-mesh sieve is 0.93 from 31 pairs of tests, Tvhich were dup1icat)esexcept for sieve size. Correction of expansion for change in percentage of coal on a 4-mesh sieve should be made such that the greater expansion is obtained, because then the correction represents the more dangerous condition to oven walls. The equation for obtaining an estimated expansion of a more finely crushed coal is Expansion of the more finely crushed sample equals expansion a t the coarser size 0.2 times the change in percentage of coal on a 4-mesh sieve between the pair of samples
+
The formula for converting dry, solid-coal expansion to expansion at 55.5 pounds per cubic foot can then be used to convert to the standard bulk density or any ot,her bulk density. There are insufficient large differences in the 4-mesh sieve for very accurate determination Of the regression Figure 3. Relation of Observed and Calculated Expansions of 20% line and the regression equation. The very small coiiLow-Volatile Blends stant (-0.04) appearing in the Iegression equation can be considered insignificant, The standaid error of estimate is shown graphically in Figure 1 accidentally interchanged; or one sample received treatment, such as the broken line above and be lo^ the regression curve (solid as oxidation, which altered its expanding properties by more than line). Sixty-eight per cent of the results should not differ from 2.1%. the solid line by more than the vertical distance from the solid Analysis of the data shows that for most of the differences of 1% line to either of the broken lines. Theory predicts that there or more between duplicate tests, the charge weights have differed should be 21 out of the 31 results within this band. There by 1 kg. or more or the test bulk densities differed by at least 1 actually are 24, which is a good check. pound. These differences in bulk densities and charge weights For very small differences in the percentage of 4-mesh coal, the affect the average heating rate and consequently modify the standard error of estimate coupled Kith the standard deviation of expansion. The formula used for correcting the expansion at the test method does not give estimated changes in expansion test bulk density to expansion at 55.5 pounds per cubic foot corthat have much significance. However, if the diferences in the rects for effect of bulk density but not for the effect caused by a proportion of 4-mesh coal are large enough-for example, above difference in heating rate. These factors have been ignored in G.O%-then the estimated change in expansion is greater than the present work, which makes these results have a larger standthe standard deviation of the test method, and the estimating ard difference between pairs than is expected in the future. equation affords a suitable means whereby the expansion deterThe dry, solid-coal expansion results obtained in the solemined for coal of a given sieve analysis may be calculated for a heated oven were treated similarly to those a t 55.5 pounds per different size. cubic foot and their statistics are given in the second line of Table Bureau of Mines experience indirates that changing the sieve I. The latter values are somewhat larger than the former because dry, solid-coal expansions range from 9.6 t o 124%, whereas the range on the 55.5 basis is -27.1 t o $42.2, or a ratio in ranges of 1.65 to 1.0. RELATION OF EXPANSION T O PARTICLE SIZE
Expansion values in the sole-heated oven were observed to increase with increase in the degree of pulverization. Sapozhnikov (15) studied the influence of the degree of pulverization of the coal charge on its fluidity index and tested the hypothesis that as coal is crushed to finer sizes, the total surface area is increased and under like conditions of coking a given coal should produce the same amount of total liquid, but when the grains are small they mill be coated with a thinner layer and the plasticity will be reduced, which in turn should affect the expansion. Preliminary studies shoxed that the correlation of expansion and the size of coal would be nearly, as good by using the percentage of coal on a 4-mesh sieve (Tyler standard series) as by using the calculated surface area. Within the limits studied, the test with the least percentage of coal on a 4-mesh sieve generally has the greater expansion. I n Figure 1 the differences in percentage of coal on a 4-mesh
Figure 4. Relation of Observed and Calculated Expansions of 30% Low-Volatile Blends
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1951
2919
TABLE 111. RELATIONOF EXPANSION OF POCAHONTAS No. 3
120
COALSTO DRY,MINERAL MATTER-FREEFIXED-CARBON CONTENT Mine
Dry, Mineral Matter-Free Fixed-Carbon, % '
Expansion Calculated to 55.5 Lb. of Dry Coal/Cu. Ft., %
Unknown Crozer Buckeye No.^3 Carswell Carswell Carswell Mead Coal Co Nos. 2 and 3 Mead Coal Co:: No. 2 Mead Coal Co., No. 2
80.3 80.9 81.7 81.8 82.2 82.6 83.3 83.4 83.4
9.6 12.7 14.9 24.7 23.1 27.4 30.8 30.7 32.8
110
100
90
0
E 70
Pf
free) and ash content. He plotted expansion against volatile matter for samples containing 3, 5, and 7% ash.
60
i4
9 50 51
ESTIMATION OF EXPANSION O F 20 AND 30% BLENDS
4 0
30
X High wlatile A e Medium volatile
20
10
analysis of a coal does not noticeably change the maximum pressure developed in the vertical expansion oven. ESTIMATION OF EXPANSION OF POCAHONTAS NO. 3 COAL /
Pocahontas No. 3 coal is widely used in blending with highvolatile coals for improving the physical properties of the coke. Experience has been that the addition of Pocahontas No. 3 cod, because of its strong expansion, may cause damage t o oven walls. Table I11 and Figure 2 show the variation in the expanding properties (sole-heated oven) of Pocahontas No. 3 coal from various mines with its dry, mineral matter-free fixed-carbon content. Expansions range from 9.6 to 32.8%for these coals. The geometric slope of the straight line in Figure 2 is close to unity but the actual physical slope is 7.3. This very steep slope shows a change of 7.3% in expansion for a change of 1.0% in dry, mineral matter-free fixed-carbon content. The standard error of estimate is f2.5 expansion units or 3.1 times the standard error of a single test. Standard error of estimate - -2.5 = Standard deviation of test 0.8
3.1
This result shows that other variables, in addition t o dry, mineral matter-free fixed-carbon content, which have not been considered in this correlation are exerting an influence on expansion. In the other correlations in this paper involving sole-heated oven results, the denominator would be 1.2, because they are all made on the dry, solid-coal basis. The effect of ash in these nine samples was not determined because the higher ash contents occul'red simultaneously with the lower volatile matter contents. However, Brown (6) tested 47 samples of Pocahontas coal and correlated expansion with volatile matter (ash- and moisture-
Fieldner and Rice (8)commented in 1942 on the dependence of the dry, solid-coal expansion of a blend upon the dry, solid-coal expansion of the constituents. If the constituent coals of a blend expanded the same as when they are carbonized singly, then the expansion of blends could be calculated precisely because the relation would be additive. Assuming an additive relation, the expansion of a 20% blend would be 0.20 times the expansion of the low-volatile coal plus 0.80 times the expansion of the high-volatile coal. Expansion values derived in this manner are called calculated expansions. The broken lines on Figures 3 and 4 are these calculated expansions plotted arbitrarily as Y = X and are for reference only. The solid lines obtained by correlation methods best fit the experimental data. These curves indicate that a correction should be added to or subtracted from the calculated values to approximate the observed values. Values of calculated expansion of about 54% need no correction. If HVEs equals dry, solid-coal expansion of the high-volatile constituent of the blend and LVEs equals dry, solid-coal expansion of the low-volatile constituent of the blend, then the mathematical expression for values on the broken line for 20230 blends of lowand high-volatile coal is 0.20 LVEs 0.80 HVEa. This expression has been used in the past for estimating. The expression for values on the solid line is 0.12 LVEs 0.48 HVEs 21.4. The corresponding expressions for 30:70 blends of low- and high-volatile coals, respectively, are 0.30 LVES 0.70 HVES and 0.143 LVES 0.333 HVEs 28.5. The correlation coefficients and number of blends in each figure for the 20 and 30% blends of low-volatile coals are 0.888, 30 and 0.850, 23, respectively. These new expressions for estimation of the expansion of a blend are by no means perfect, but estimates of
+
+ +
+
+
+
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INDUSTRIAL AND ENGINEERING CHEMISTRY
fixed-carbon content (log of maximum fluidity held fixed) +0.65; between expansion and log of maximum fluidity (dry, mineral matter-free fixed-carbon content held fixed) - 0.65; between log of maximum fluidity and dry, niineral matter-free fixed-carbon content (expansion held fixed) 0.00. The separate influences of dry, mineral matter-free fixed-carbon content and log of maximum fluidity on expansion are approximately the same, except that they are in opposite directions. Increase in rank increases the expansion, whereas increase in log of maximum fluidity decreases the expansion. Since there is no relation remaining between log of maximum fluidity and dry, mineral matter-free fixed-carbon content when expansion is held constant, the same factors of dry, mineral matter-free fixed-carbon content which are measured by plasticity must also be measured by expansion.
10 000
E B
Vol. 43, No. 12
1000
x VI
p VI
5 -
i
P
I 50
I
I
'
i
I
I
I
II
60
70 DRY, MINERAL MATTER.FREE FIXED,CARBON
80 PERCENT
Figure 7. Relation of Fluidity in Gieseler Plastometer to Rank of Coal
expansions made from the solid line are superior to previous estimates or calculated values made from the broken line. The variation of the solid line from the broken line probably is due to plastic characteristics because the points on the left represent high-volatile coals of high fluidity, whereas the points on the right represent high-volatile coals of low fluidity.
The variability in expansion in Gieseler data and in the chemical analyses themselves causes variations that lower this correlation. Evidence exists that storage or oxidation of a coal changes the expanding properties a t a greater rate than these factors change the dry, mineral matter-free fixed-carbon content. The same ia generally assumed to be true of Gieseler plastometer data. The correlation of expanding properties, dry, mineral matter-free fixed-carbon content and Gieseler data has been lowered by slight oxidation because the testing of some samples was unavoidably delayed. This delay probably caused variations in results that would not be shown in freshly tested coal samples. This correlation study has included coals of a wide range of physical, chemical, and petrographic composition and should thereby have included extreme$ in each of these properties, which in turn decrease the correlation coefficients. The spread of estimated values i s about 7 . 5 times the spread expected from errors in expansion tests alone. Plastic characteristics of coal have been shown by Brewer ( g ) to be a function of petrographic composition in addition to other properties. When plasticity data were plotted as a function of dry, mineral matter-free fixed-carbon content, coals containing 100 area % bright coal and coals containing an average of 80.25 area yo bright coal group themselves into two distinct portions of the plot, and a best straight line can be d r a m for each group.
ESTIMATION OF EXPANSION OF COALS FROM THEIR DRY, MINERAL MATTER-FREE FIXED-CARBON CONTENT AND PLASTICITY
Expansion of coal during coking is believed to depend on both dry, mineral matter-free fixed-carbon content and maximum fluidity; therefore, a study was made of 83 coals (50 high-volatile A, 16 medium-volatile, and 17 low-volatile) on which data for dry, solid-coal expansion, dry mineral matter-free fixed-carbon eontent, and maximum fluidity in the Gieseler plastometer ( 4 ) were available. The simple correlations among the three named properties of coals are shown in Figures 5, 6, and 7, and the best straight lines are drawn. The following simple correlation coefficients were obtained: expansion and dry, mineral matter-free fixed-carbon content, $0.83; expansion and log of maximum fluidity -0.83; dry, mineral matter-free fixed-carbon content, and log of maximum fluidity -0.69. The multiple correlation coefficient between expansion and the combined effect of dry, mineral matter-free fixed-carbon content and log of maximum fluidity is 0.92. The equation connecting these three variables is
+
Estimated expansion, % = -19.3 1.49 (dry, mineral matterfree fixed-carbon content) - 11.04 (log of maximum fluidity) When more than two variables are interrelated, the simple correlation coefficients between pairs of such variables may give misleading information. It is necessary t o fix all other closely related variables. The correlation coefficients between two variables when the remaining variables are held fixed are known as the partial correlation coefficients. These partial correlation coefficients are: between expansion and dry, mineral matter-free-
WALL PRESSURE, POUNGS PER SQUARE INCH
Figure 8. Relation of Maximum Wall and Gas Pressures in Vertical Expansion Oven
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1951
2921
than 0.5 pound per square inch from the observed average of WALLPRESSURES DEVELOPED three tests. The best average is that obtained from 30 or more TABLE IV. AVERAGEMAXIMUM IN
VERTICALEXPANSION OVEN
Description 50% Beckley bed 50% Pittsburgh bed 50% McAlester bed 50% McCurtain bed 75% Pittsburgh bed 25% Pocahontas No. 3 bed 75% Pittsburgh bed 25% Pocahontas No. 3 bed 85Y Pittsburgh bed 1 6 2 Upper Kittanmng bed 809 Thick Freeport bed 2 0 2 Pocahontas No. 3 bed 80% Thick Freeport bed 20% Lower Ktttanning bed Coal from Rosita, Mexico 49 5% Eagle bed 50 5% Pocahontas No.3 bed 4 0 9 Lower Freeport bed 606 Pittsburgh bed Lower and Upper Freeport beds Lower and Upper Freeport beds Upper Freeport bed Upper Freeport bed 821/9% Thiok Freeport bed 171/2% Lower IGttanning bed Upper Freeport bed
Mine
Avera e Test Maximum Bulk Bensity, Pressure, Dry Coal Lb./Sq. Lb./Cu. Pi. In.
Testa Warden Buckeye No. 3 Warden Buckeye No. 3 Crucible Jerome Harkar Buckeye No. 3 Hal mar
Kramer Bannin and Hutcginson Kent Nos. 1 and 2 Kent Kos. 1 and 2 Watson Ernest Harmar Eureka No. 40 Sigley
46 9
2.6
50.3
1.7
47.2
2.8
47.2
1.7
51.8
0.8
47.6
2.1
49.8 49.2
1.5 1.1
46.3
3.2
49.1
0.7
48.5
1.5
60.0 48.7 50.4
3.9 1.6 3.4
48.6 54.7
1.7 3.9
Petrographic data were available for only a few coals in this study, hence this important factor could not be considered in the development of the equation for the estimation of expansion. PRECISION OF VERTICAL EXPANSION OVEN TESTS
The precision reported in Table I for the vertical expansion oven is less than it actually should be because the effect of the differences in bulk density between two tests has not been considered. Insufficient data exist for determining the true effect of bulk density on the maximum pressure, but the data available show that small differences in bulk density exert less effect on the maximum pressure than the experimental error. Thirty-six tests on 16 coals or blende described in Table I V were used to determine the precision of this oven. The 80% limits are usually used when studying coke qualities; these limits seem more applicable here and are used instead of the 95% limits given in Table I. On the 80% basis, four out of five differences between duplicate tests will be 0.97 pound per square inch or less. The principal purpose of testing coals in the vertical expansion oven is to determine the maximum pressure they exert on the oven aalls. A large number of tests on the same coal cannot be made so as to approach closely the true expansion pressure; hence it is necessary to know how many tests should be made such that the error is not more than a given number of pounds per square inch. Where the standard deviation, u, of a test is known, the standard deviation of the mean, urn,of a number of tests may be estimated by using the simple relation
om =
dk, where
N equals the number of tests used in the average: If the degree of duplicability is arbitrarily set, the number of tests required for this precision can also be calculated from this equation. Using this equation in conjunction with standard tables of the area under a normal curve, Tables V and VI were prepared. In Table V, the degrees of duplicability for various numbers of tests on the aame coal or coal blend are given. Three tests will be necessary, euch that in nine out of ten cases the best average will not be more
tests on the same sample. Similarly, it would require four tests for the same range in pounds per square inch, if the probability of being right was increased from nine out of ten to 95 out of 100 cases. The probabilities in the heading of Table V can be interpreted to read 9 out of 10,95 out of 100,97.5 out of 100 instead of 8 out of 10,9 out of 10, and 95 out of 100, because one of the two tests that range more than the given amount from the mean shows a pressure lower than the given deviation and it could not cause oven damage. Therefore, the probabilities actually are greater than Rtated in the table when only the positive deviations are considered. Table VI gives the probabilities in chances per 1000 cases of the observed pressure not exceeding given limits. If three tests result in an average pressure of 1.5 pounds per square inch, 500 out of 1000 such averages of three tests would be less than 1.5 pounds per square inch, 457 would range from 1.5 to 2.0 pounds per square inch; however, only one in 1500 tests would exceed 2.5 pounds per square inch. Thus, if a wall force of 2.0 pounds per square inch is accepted as the maximum allowable for a safe coking coal and n coal gave a value of 1.5 pounds per square inch when three tests in the vertical expansion oven were averaged, then this coal would be classified as safe for coking in 957 out of 1000 cases. RELATION OF WALL PRESSURE TO INTERNAL GAS PRESSURE
The internal gas pressure in the vertical expansion oven is highly correlated with the wall pressure as shown by the correlation coefficient of 0.95 for 26 tests. The relation is shown graphically in Figure 8. The wall pressure is measured by means of the movable wall and the internal gas pressure is measured by a gage attached to a i/s-inch iron pipe inserted near the geometric center of the coking charge. As the plastic layers meet in the center of the oven, the internal gas pressure and the wall pressure rise to a maximum. It is reasonable to expect that these two pressures are related because they are both measures of the gas pressure within the double plastic layer. At first this relation does not seem of much value because it is necessary to make the test to obtain the gas pressure, but the apparatus could be simplified by eliminating the movable wall apparatus and measuring the gas pressure only. The relation between the wall and gas pressures depends on the geometry of the system. Moving the wall back decreases the wall force and gas pressure, but the gas pressure quickly attains its foimer value, whereas the wall force does not. Gas pressures of 9.0 pounds per square inch were obtained in several tests, but because the wall pressure exreeded the limit -
TABLEV. DUPLICABILITY FOR VARIOUSNUMBERSOF TESW No. of Tests on One Coal
TABLE VI.
Range from Average Pressure in Lb./Sq. In. Which Will Not Be Exceeded in 9 out of 10 cases 95 out of 100 casea 8 out of 10 cases 10.64 1 0 .82 10.98 1 0 .45 10.58 10.69 10.37 10.48 10.57 10.32 10.41 k0.49 10.28 10.36 1.0.43 &0.26 1 0 .33 10.39
CHANCESPER 1000 OF OBSERVEDPRESSURE NOT EXCEEDING LIMITSGIVENBELOW
Observed Average Maximum Pressure, Lb./Sq. In. 1.5 1.5 1.5 2.0 2.0 2.0
No. of Tests 1 2 3 1 2 3
1.6 579 614 633
... ... ...
Limits, Lb./Sq. In. 1.8 2.0 2.3 726 841 945 805 924 989 849 957 997 726 ... ... 805 ... 849
...
... ...
2.5 977 998 999.7 841 924 957
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INDUSTRIAL AND ENGINEERING CHEMISTRY
of the oven, the movable wall was allowed to move back. This probably increased the volume of the charge and lessened the area of contact of the movable wall and the retort. The best straight line probably does not pass through the origin because about 0.5 pound per square inch of wall pressure is applied a t the start of the test before internal gas pressure in the center of the oven is present. Wall pressures corresponding t o 9.0 pounds of gas pressure were 4.2 and 4.3 pounds per square inch. Based on the above assumption, these values are too small because of the lessened area of contact, and they were not used in obtaining the results in Figure 8. The best straight line is broken above 8.0 pounds gas pressure and extrapolation to 9.0 pounds Beems justified. 4 n approximation method is now available to determine the maximum wall pressure when that pressure is beyond the limit of the apparatus and the movable vall is allowed to move back. ACKNOWLEDG,MENT
The writers acknowledge indebtedness to the following members of the staff of the Central Experiment Station, Bureau of Mines, Pittsburgh, Pa. : J. T. McCartney, physicist, supervised many of the sole-heated oven tests described in this report and gave many helpful suggestions regarding interpretation of results and preparation of the manuscript; R. E. Brewer, chemical engineer, supervised the work on plasticity: and H JI. Cooper, chemist, supervised the chemical analyses. LITERATURE CITED
(1) huvil, H. S., Davis, J. D., and hIcCaitney, J. T., C . S. Bur. Mines, Rept. Invest. 3451 (1939). (2) Brewer, R. E., IND. ESG.CHEM.,36, 1165-8 (1944). (3) Brewer, R. E., U. 5.Bur. >lines, BdL. 445, 130-53 (1942).
Vol. 43, No. 12
(4) Brewer, It. E., and Triff,3. E., I m . ENG.CHEM.,ANAL.ED., 11, 242-7 (1939). (5) Brown, W. T., Blast Furnace Steel Plant. 30, 67-71, 219-23. 226 (1942). (6) Ibid., 30, 1137-45, 1255-63 (1942). (7) Ezekiel, M., “Methods of Correlation Analysis,” New York, John Wiley & Sons, 1941.
(8) Fieldner, A. C., and Rice, W. E., U. P. Bur. Mines, InfoTorm. C k . 7241, 56-7 (1943). (9) Isenberg, Pi., and Jackman, H. W.,“Investigation of Beckley
Seam Coal Blended with Wheelvright Coal for Use in the production of Metallurgical Coke,” East Chicago, Ind., Inland Steel Co., 1945. (10) L o w y , H. H., and Junge, C. O., Jr., “Statistical Study of the Precision of Methods for Analysis of Coal and Coke,” Am. SOC.Testing Materials, Proc. 42, 16 pp., June 1942. (11) McCartney, J. T., and Davis, J. D., U. S. Bur. Mines, Rept. Invest. 3644 (1942). (12) Piaugle, B. W., Davis, J. D., hfcCartney, J. T., and Wilson, J. E., Ibid., 4285 (1948). (13) Peters, C. C., and Van Voorhis, W. R., “Statistical Procedures
and Their Mathematical Bases,” Sew York, MaGraw-Hill Book Co., 1940. (14) Reynolds, D. A., and Holmes, C. R., U. S. Bur. Mines, Tech. Paper 685 (1945). (15) Sapozhnikov, L. M., Coke Smokeless-Fuel Age, 1, 27-9 (June 1939), 58-60 (July 1939), correction 131 (September 1939). (16) Soth, G. C., and Russell, C. C., Trans. Am. Inst. illiniw M e t . Engrs., Coal Div., 157 (1944). (17) Walker, H. hl., “Elementary Statistical Methods,” New York, Henry Holt and Co., Inc., 1943. (18) Wilson, P. J., Jr., and Wells, J. H., “Coal, Coke, and Coal Chemicals,” pp. 74-95, Kew York. RfcGraw-Hill Book Co., 1950. (19) Worthing. A. G., and Geffner, J., “Treatment of Experimental Data,” New York, John Wiley & Sons, 1943.
RECEIVED January 5 , 1951. Presented before the Division of Gas and Fuel Chemistry at the 118th Meeting of the Aw%xc.m CHEMICAL SOCIETY, Chicago, Ill.
Styrene-Ethylbenzene-Diethylene Glvcol Svstem d
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TERNARY SATURATION-EQUILIBRIUM DIAGRAM RI. G. BOOBAR, P. 21. BERSCHKER’, R. T. STRUCIP, S. A. HERBERT3, S. L. GRUVER, AND C. R. ICINNEY The Pennsylz‘ariia State College, State College, Pa. Solvent extraction is proposed as a method for recovering the readily polymerizable, heat-sensitive, unsaturated
compounds found in pyrolytic tars produced by the manufactured gas industry, which are usually lost when conventional tar processing methods are used. Because of inherent difficulties in working with tars of unknown composition, styrene and ethylbenzene were chosen to simulate the types of compounds that might appear in a narrow boiling fraction of tar. This separation is also of interest in the manufacture of styrene from ethylbenzene. Of the large number of solvents tested, diethylene glycol was found to be the most selective for styrene. Consequently, the saturation-equilibrium data for the system styrene-ethylbenzene-diethylene glycol were obtained and a ternary diagram was constructed. It would appear that eleven theoretical extraction stages would be required to effect an increase in the concentration of styrene from 10% in the feed to 90% in the solventfree extract phase.
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YROLYTIC tars, particularly those produced by the manufactured gas industry, contain readily polymerizable unsaturates which are loet when convent.ional tar processing methods of thermal dehydration and batch distillation are used. If these tars were first fractionated cold by means of solvents ( 1 ) and the fractions then extracted with other solvents selective for unsaturates, it might be possible to avoid thermal losses of useful products. Owing to inherent difficulties in working with solvent fractions of unknown composition, an investigation of the selective extraction of mixtures of known composition was begun. Styrene and ethylbenzene were chosen as representative examples of both heat-sensitive unsaturated hydrocarbons and the saturated hydrocarbons t o be found in a narrow boiling fraction of tars. The selection of a suitable solvent involved testing over 100 solvents and solvent-water mixtures. Among these, diethylene glycol appears t o be most selective for styrene. 1
Present address, Cities Service Co., Merchantville, N. J. Consolidation Coal Go., Library, Pa. Present address, Purdue University, West Lafayette, Ind.
* Present address, Pittsburgh 3
