ENGINEERING AND PROCESS DEVELOPMENT sample saturated with brine/resistance of quantitg of brine of same size and shape as bulk volume of sample I;i = Brownell’s friction factor factor PR. = Brownell’s Reynolds nunihcr factor f = friction factor gc = conversion factor, 32.17 pounds mass X foot/pounds force X square second G, = superficial mass velocity, pounds mass/square foot x second 120 = Kozeny constant, dimensionless 121 = dimensionless, geometrical constant in laminar term of flow equation kz = dimensionless, geometrical constant in turbulence term of flow equation LB = over-all length of porous media, feet L E = effective length of flow path, feet m = hydraulic radius, feet M = molecular weight of a gas P or Pj = pressure, pounds force/square foot absolute R = gas constant: 1543 pound: force X cubic feet/squar& foot X pound mole R. T = absolute temperature, R. Y, = superficial velocity, feetjsecond V E = effective velocity in pore structures, feet/second X = fractional porosity z = compressibility factor of a gas CY = coefficient of laminar term of flow equation, feet-’ P = coefficient of turbulence term of flow equation, feet-‘ 6 = dimensionless constant relating hydraulic radius and effective diameter E = roughness dimension of a pipe, feet p = viscosity, pounds mass/(foot)(second) p = fluid density, pounds mass/cubic feet (1) Archie, G . E., Trans. Am. Inst. Mining M e t . Etagrs., 146, 54 (1942). (2) Bakhmeteff, B. A., and Feodoroff, N. V., Trans. A m . Soc. Mech. E’ngrs., 59, A-97 (1937).
(4) Bicher, L. B., and Kats, D. L., Trans. A m . Inst. Mining M d , Rngrs., 155,246 (1944). (5) Brownell, L. E., Dombrowski, H. S., and Dickey, C. A., Chem. Eng.Progr., 46,415 (1950). (6) Brownell, L. E., and Kata, D. L.. Ibid.,43, 537 (1947). (7) Carlson, A. J., and Eastman, J. E., A m . Inst. il4ining M e t . Engrs., Tech. Publs., 1196 (,\lay1940). ( 8 ) Carman, P. C., Trans. I n s t . Chena. Enyrs. (London), 15, 150 (1937). (9) Ibid.,16, 168 (1938). (IO) Dallavalle, J. XI., “AIicromeritics,” Kew York, Pitman Publishing Co., 1943. (11) Ergun, S., Chem. Eng. Progr., 48, 89 (1952). (12) Fancher, G. H., and Len%, J. A., IXD.ENR. CHEM.,25, 1139 (1933). (13) Green, L., and Duwea, P., J . AppZ. N e c h o n i c s , 18, 39 (1951). (14) Grunberp, I>.,and Nissan, A. €I.,J . I n s t . Petroleum Technol., 29, 192 (1943). (15) Handbook of Chemist1.g arid Physics, 24th ed., Cleveland, Ohio, Chem. Rubber Publishing Co.. 1941. (16) International Critical Tables, Vol.-V, p. 2 , Sew I-ork, LicGIawHill Book Co., 1929. (17) Kozeny, J., Ber. Wien. Aknd., 136a. 271 fl927). (18) Martin, J. J., Ph.D. thesis, Carnegie Institute of Technulogy, 1948. (19) Nichels, A., and Gibson, R. O., Proc. Rou. Soc. (London), A134, 288 (1931). (20) Muskat, M., “Physical Principlesof Oil Pioduction,” Sew Yoi k, McGraw-Hill Book Co.. 1949. (21) Perry, J. H., “Chemical Engineers’ Handbook,” 3rd ed., Scw York, McGraw-HillBook Co., 1950. (22) Sullivan, R. R., and Hertel, K. I>., “Advances in Colloid Science,” Vol. I, New Pork, Interscience Publishers, 1942. (23) Wyllie, M. R. J., and Rose, W. D., J . PetroZeum Technol., 2, 105 (1950). (24) Wyllie, bl. R. J., and Spangler, 11. B., Gulf Research a n d Development Co., Research Project 4-G-l, Rept. 15 (i\Iaich 19,1951). (25) Young, J. TV., and Pot, R., Petroleum Engr., 22B, 50 (.Janualy 1950).
(3) Barrer, R. E., “Diffusion in and through Solids,” London, Cambridge University Press, 1941.
RErEIvm) for review June 30, 19.52.
5
literature Cited
ACCEPTED August 8 , 1953.
Radiation-Conduction Correction for eratwre Measurements in Mot Gases W. E. WEST, JR.,
AND
J. W. WESTWATER
University o f Illinois, Urbana, 111.
A
C C C R h T E measurement of the temperature of a hot g a ~i q a problem beset with difficulties. Consider the common case of a hot gas flowing through a duct. A number of possible temperature measuring devices could be used, but objections ran be cited for each. If some sort of radiation meter is sighted through a peep-lioic, it “sees” the duct walls as well as the gas. The durt nalls cannot be a t the gas temperature unless the outside of the duct is provided with perfect insulation. Usually the duct is losing heat to the surroundings, and the duct temperature and gas temperature are different. Thus the pyrometer may give readings that are in error, possibly by several hundred degrees (6). One radiation scheme does give good accuracy; this is the line-reversal method which consists essentially of measuring the radiation emitted by a salt suspcnded in the hot gas. This method is suitable for flames only and is so inconvenient to use that it is rarely seen in industry. If a thermometer or similar probe device is inserted into the gas stream, it will have a radiation error, because the probe can see
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the cool duct ~aalls. Thtw \\ill I N > :i contluction error also (tlie so-ralled fin effect) cawed i)y the, flair of heat along the probe to the duct u-all. Two methods of attacking the p i oblem are possible. Onr consists of trying different design&of temperature measuring ilc~vices until one is found that produc~,-a dirert reading of the true gas temperature. A large body of litciature deals Hith thii appioach. Some of the methods use shiolci
