November 1951
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
In general, punched-card methods will probably not reduce greatly the time spent by the chemical engineer on distillation problems. He will continue to do all the thinking. However, he can get from machine methoda much additional information which will be useful in improving both operation and design but which does not justify the time now required by manual methods. ACKNOWLEDGMENT The writera wish to thank the chemical engineering staff of The Daw Chemical Co. for advice ahd d t a n c e , R. N. Shiraa of the Shell Development Co. for helpful suggestiona, and Helen Hecox, Oakland, Calif., and Paul W, Fullerton, Jr., N8w York, of the International Business Machinee Corp., for technical aasistance. NOMENCLATURE
-
D rate of removal of distillate, moles per hour F feed rate, moles per hour H = heat content of vapor, calorie8 per mole ( h 0 at 25’ C. H = AHVat25’C.) AH, latent heat of vaponzatjon, calories per mole K equilibrium conitant L = liquid rate, rectifying section, moles per hour L’ = liquid rate, stripping section moles per hour total heat content of liquid-vapor mixture, calories per Q 3
--
mole constant in E uation 6, mole er cent T = temperature le-centi axe = constant in liquation 5, rn% per cent V = vapor rate, rectifying section, moles per hour V‘ = vapor rate,stri pmg section, moles per hour W = rate of removafof bottoms product, moles per hour = heat loss er theoretical plate, calorie8 per hour = total numLr of components in mixture = liquid heat content, calories per mole r = ratio of li uid composition to that in product v = z,, liquid composition. mole per cent, leaving nth plate y, vapor composition, mole per cent, leaving nth plate I = total composition, liquid plus vapor, mole per cent S
3
u
{
-
+e,
Subscripts = compoaition of distillate liquid compoaition of liouor leaving nth plate from bottom xn xd
7 Qt
2471
= compoeition of bottoms liquid = component number = n for feed plate = number of tray above which feed ie introduced total heat content of feed
-
LITERATURE CITED (1) Bubb, F. W., Nisle, R. Q., and Carpenter, P. G., Petroleum Tram.Am. I m t . Mining Met.Engra., 189, 143 (1950). (2) Donnell, J. W., and Turbin, R., Petroleum Refiner, 29, No. 10, 108 (1950). (3) Eckert, W. J., J. Chem. Edumtion, 24,54 (1947). (4) Eckert, W. J., “Punched Card Methods in Scientific Computation,” New York. Columbia University Preas, 1946. (5) Go&, 0. W., and Calvert, J. F., Am. Inst. Elec. Engrs., Tech. Pope* 50-15 (1950). (6) Grosch. H. J., Proaeedinga of Scientific Computation Forum, 1848, International Business Machinee Corp., Endicott, N. Y., 1950. (7) King, G. W., J. Chern. Education, 24,61 (1947). (8) Krawitz, E., Proaeedinga of Seminar on Industrial Cornputation, September 1950, International Bdneas Machines Corp., Endicott, N. Y., 1951. (9) Lewis, W. L., and Matheson, G. L., IND.ENP.CFI~M., 24, 494 (1932).
(IO) Opler, A., and Heitz, R. G., Proceedings of Seminar on Industrial Computation, September 1950, International Businesr Machines Corp., Endicott. N. Y., 1951. (11) Row, A., and Williams, T. J., IND.ENQ.CHEIM., 42,2494 (1950). (12) Rose, A., Williams, T. J., and Dye, W. S., Proceedings of Seminar on Industrial Computation, September 1950, International Busineas Maphinee Corp.. Endicott, N. Y.. 1951.
Scarborough, J. B., “Numerical Mathematical Analyah,” Baltimore, Johns Hopkins Presa, 1930. (14) Sherman, J., and Ewell, R. B., J . C h m . Phys., 46,641 (1942). (16) Stull, D. R., The Dow Chemical Co., Midland, Mich., personal communication. (16) Thiele, E. W., and Geddee, R. L., IND. ENP. CHEM.,25, a89 (13)
(1933). (17) (18) (19)
Thomson, G. W., Chem.Rem., 48, 1 (1946). Uitti, K.D., Pelvokmm ReJlnw,29, 130 (1950). Von Neumann, J., and Goldstine, H. H., Bull. Am. Mafh. Soo., 53, 1021 (1947).
Whittaker, E.T., and Robinson, G., “ C a l ~ u lof~ sObservations,” London, Blackie and Son, 1924. (21) Wilaon, E. B., Jr., Chsm. Rms., 27.17 (1940). Racman Maroh 21, 1961. (20)
Evaluation of Performance Factors of Fuel-Oxidant Mixtures STUART R. BRINKLEY, JR.
U. S. Bmeoa of Mines, Pittsbargh, fa. The computation of flame temperature, the analysis of power plant cycles, and related scientific and technical problems in the field of flame and combuetion require a knowledge of the thermodynamic properties of the products of combustion reactions. In order to perform the necessary calculations efficiently on automatic equipment, systematic, easily programed, computational routines are required. Generally applicable methods appropriate for application to automatic equipment are described for the computation of the thermodynamic properties of combustion gases. The results of such computation are the equivalent, in numerical form, of a Mollier chart for each fueloxidant mixture. The application of these results, employing automatic computationalequipment, to the calculationof flame temperatures and fuel performance parameters is described.
F
OR the theoretical description of power plants deriving their energy from the cornbustion of a fuel, it is necessary to solve t o an appropriate degree of precision a hydrodynamic problem requiring for ite solution a knowledge of the thermodynamic properties of the working fluid composed of the products of the combustion reaction. It is uaually a good approximation to assume that the properties of the combustion gas are determined by the conditions of thermal equilibrium, and thus it ia possible to employ the methods of classical thermodynamics for their computation. The thermodynamic properties of fuel gases are also of considerable importance, since they form the basis for the design of appropriate means for their effective utiliation. The specilication of the operating conditions to produce a gas for use as an intermediate in a chemical process, such as the synthesis of liquid fuels, may be based upon a study of the variation of the composition of the synthesis gas with changes in the various proceea variablee.
Vol. 43, No. 11
INDUSTRIAL A N D ENGINEERING CHEMISTRY
2472
Although there exist a large number of important scientific and technical applications of the data that can be obtained from the systematic determination of the thermodynamic properties of combustion gases, such applications have been handicapped by the extremely tedious and time-consuming computational methods required. The development of large-scale automatic computational equipment makes feasible the initiation of a systematic program for determining the thermodynamic properties of combustion gases and for applying such data to specific problems of scientific and technical importance. For a long time there has been a need for systematic and economical methods for the calculation of the thermodynamic properties of systems of many constituents, and this need is emphasized by the application of automatic computational equipment. In this paper methods are briefly described that have been routinely employed in this laboratory for the calculation of the equilibrium composition of multicomponent gas mixtures and the evaluation of the thermodynamic properties of the equilibrium mixture. The application of automatic computational equipment to these calculations is discussed. It is possible to utilize punched card equipment in a variety of applications of the results of these calculations to determine performance characteristics of particular fuel-oxidant systems. These methods are illustrated by a discussion of the evaluation of the specific impulse of a rocket propellent.
(3)
resulting in the formation of the dependent constituents from components only. The mass action laws for chemical equilibrium can be put into the form
where K , is the thermodynamic equilibrium constant, a function of temperature only (it is assumed here that the gas mixture obeys the ideal gas law), for the chemical reaction 3 leading to the formation from components only of the ith dependent constituent. Equation 1 comprises a set of linear equations equal in number to the number of components of the system (usually, but not necessarily, equal to the number of different elements of the system). Equation 4 comprisee a set of nonlinear equations equal in number to the number of dependent constituents of the system. Together, the two sets are sufficient to determine completely the composition at equilibrium of a multicomponent gas mixture. For fuel-rich carbon, hydrogen, oxygen, nitrogen systems, an appropriate choice of components is j = CO, Hz,H20,N2
with the dependent constituents,
i = CO,,
CARD PROGRAMED ELECTRONIC CALCULATOR
This laboratory is equipped with punched card equipment designated a card programed electronic calculator, supplied by the International Business Machines Corp. This equipment provides automatic computational facilities of moderate speed and very considerable flexibility. It consists of an electronic calculator, controlled by a punched card reader, and supplemented by a moderate amount of internal storage and by printed page and punched card output. The manner in which the equipment is used is determined by the manner in which a set of control panels is wired. By an appropriate choice of control panel circuits, it is possible to operate the equipment as a general purpose digital computer. Alternatively, it is possible to design special control panel circuits making possible the efficient utilization of the equipment as a special purpose computer for the rapid solution of a particular problem. Specific methods will be given for the application of the IBM card programed electronic calculator to the calculation of the thermodynamic properties of combustion gases and the evaluation of the performance characteristics of fuel-oxidant systems.
02,
Fj
=
(1)
0
where
0, OH, H, NO, N, NHI, CH,
For fuel-lean carbon, hydrogen, oxygen, nitrogen systems, an a p propriate choice of components is j = COz,H20,Op, N2
with the dependent constituents,
i
=
CO, Hz,O, OH, H, NO, N
The simultaneous solution of Equations 1 and 4 is most conveniently carried out by an iterative method. If an approximate set of values of the mole fractions of the components, z J ,is selected, Equation 4 permits the calculation of the mole fractions of the dependent constituents, x 2 . The resulting set satisfies Equation 1 if the correct values of X, were selected. If the function F,does not vanish, an improved set of values of xi is obtained by application of the Newton-Raphson method (19). If the function F , is expanded in a Taylor series about the approximate set of values of r J ,with neglect of derivatives of second and higher orders, a set of linear equations results
CALCULATION OF EQUILIBRIUM COMPOSITION OF COMBUSTION GASES
A systematic procedure for determining the equilibrium composition of multicomponent gas mixtures has been described in detail elsewhere (9, 3, 6, 7, 11). The conditions for thermodynamic equilibrium can be stated in a form that is particularly appropriate for routine calculation. The conservation of each element by the system requires that
K ~ ( T ) P ~ - ~ ~ ~ x , ~ ~ I (4)
XI
where the rth and ( r are related by
+ 1)th approximations to the composition
z9(r+1)
= zJ(r)[I
(6)
which can easily be solved for the fractional corrections, hi('), to the rth approximation to the mole fractions, xi, of the components. The superscript r denotes that the quantity is to be evaluated with the rth approximation to the composition of the system. The coefficients of Equation 5 are given explicitly by
i
and where x i and xi are the mole fractions in the equilibrium mixture of the ith dependent constituent and j t h component, respectively; q j is the mole fraction of the j t h component in the hypothetical stoichiometrically equivalent mixture consisting of components only; uij are the coefficients of the chemical reactions
+ hJ(r)]
Vi) =
= p i Vj'
- Ujjl
U
