HEAT TRANSFER IN THE RADIANT SECTION OF PETROLEUM HEATERS (part2): 1 - 2 - 3 - 4

*In a bank of three or more rows of tubes a = 1.0, and A_cp = aA_cp'

It may be seen from Table III that in practically every case the equation presented in this paper correlates the test data better than the empirical equation even though the furnace tests used to determine the constants of the empirical equation are included in the present data. The maximum deviation has been reduced from 335 to 16%. These facts are perhaps best illustrated by Figures Nos. 9 and 10, which show the spread of the data using both methods of correlation. Inasmuch as the data represent plant tests, it is suspected that the larger deviations may be due to inaccuracies in the data and not to any fundamental fault in the radiant equation. It is significant that using the theoretical equation the greatest deviations are not confined to any one furnace but seem to be well distributed. Again, furnace No. 4, the worst case, shows deviations of -11% and -12% and +14%, indicating that the data on this one furnace are probably less reliable than the average. Actually, the temperature of the gases leaving the radiant section of this furnace was determined at only two points instead of by a complete traverse. Since in many cases it is difficult to judge exactly the accuracy of the plant data, no attempt has been made to segregate and give more weight to the better data. The number of tests available for this study is hardly large enough for a rigid statistical analysis, but for some generalizations are justified. For instance, considering the data in their entirety, Figures Nos. 10 and 12(A) indicate that the deviations between the observed and the calculated heat absorption occur in a random manner and are not peculiar to any one fiurnace, even though the ratio of effective refractory to effective cold surface, ( A_r / aA_cp ), varied fourteen-fold for the furnaces investigated.
Figure 11 (B) (C) (D) and Figure 12 (B) (C) (D) are given in order to permit visualizing the effect of some of the variables on the results obtained by the two correlations.
The effect of excess air is shown in Figures 11 (B) and 12 (B). It should be remembered that although the percentage of excess air varied less than 10% to more than 170%, other factors may likewise have been varying at the same time. In general, the empirical equation appears to predict correctly the heat absorption by the oil in the radiant section in the excess air range from 10% to 80%, the more usual commercial range. Above 80% it predicts heat absorptions which are 10% to 13% too high. Over this range, 10% to 170%, the theoretical equation shows no significant trend. As previously pointed out, the use of an air-fuel ratio is open to criticism and the trend may be due to this factor.
Figures 11 (C) and 12 (C) classify the data according to average radiant rate based on circumferential tube surface, B.t.u. per hour per sq. ft. In those furnaces with a double row of radiant tubes, the rate has been taken as the average first row rate. Here, again, the theoretical equation shows no significant trend over the range 3,000 to 51,000 B.t.u. per hour per sq. ft. The empirical equation shows signs of breaking down at rates below 4,000 and predicts radiant section heat absorption 10% in excess of the true figure at that point. Only two tests are available at rates between 3,000 and 4,000 but they confirm the trend and indicate that the heat absorbed by the oil, as calculated by the empirical equation, may be almost 40% high in this range.
Figures 11 (D) and 12 (D) give another indication of the range of the furnace data, but have significance only in that they give an indication of the theoretical flame temperature. These figures show that over the wide range of t'_{f '} the pseudo-theoretical flame temperature, the deviations have no definite trend. It is obvious, therefore, that petroleum heaters can be designed by means of the new equation for fuels of widely different heating values as a low pseudo-flame temperature may mean either a fuel of low grade, or a high heating value fuel degraded with excess air or recirculated inert gas. Since most of these tests have been made with very similar fuels, the trend shown in Figure 11 (D) is probably due to the composite effect of rate and excess air discussed above.

<-- page 1 -- page 3 -->