Performance of Vapor-Lift Pump under Vacuum

In the first place an experimental vapor lift was constructed from a pipe of 0.5-inch nominal bore, elevating to a net height of 18 feet with 10-foot ...
0 downloads 0 Views 1MB Size
Download PDF
Performance of Vapor-Lift Pump under Vacuum N. R. MUKHERJEEI AND H. R. C. PRA’IT2 B.X. Plastics, Ltd., Branthum Works, Nr. Munningtree, Essex, England

I

apparently because the heat A n experimental vapor-lift pump based on a pipe of transfer rate is extremely low 1-inch nominal bore has been installed and operated under tinuous distillation pressures of 2 to 10 inches of mercury absolute. Using to liquids in natural convecplants comprising two or dipentene as the test liquid it was found that the rate of more stills in series, it is fretion in narrow tubes. On lift was a function of the steam pressure in the heating quently necessary to provide some occasions, h o w e v e r , jacket and of the temperature of the inlet liquid; there means for the transfer of success was achieved, genwere critical values below and above which the performthe bottom product from erally after heating for some ance fell off. The rate of lift increased with the relative one still to the feed point hours, and it was then possubmergence and with the pressure on the system. A n of the next in the series. sible to keep the lifter operatattempt has been made to give a theoretical explanation of When the throughput is coming indefinitely. The rate the mechanism of the vapor lifter. The quantity of liquid paratively large, as for exof lift was very low, of the elevated appears to be determined by a balance between the ample, in the petroleuni order of 5 gallons per hour, energy input and the three major energy losses due to acindustry, this is best accomand the installation was thereceleration of the vapor-liquid mixture, friction, and slipplished by means of centrifufore not considered satisfacpage of liquid relative to the vapor. Owing to lack of data gal pumps. Cases often tory for the present purpose. for these losses in the “slug-flow” region, however, it was arise, however-for example, Based on this experience, not possible to explain the performance quantitatively. in pilot plants and in full scale a larger installation was plants in which the materials designed and constructed, undergoing treatment are comparatively expensive and the using a pipe of 1-inch nominal bore, and making provision for throughput is comparatively low-where the amount to be transcondensing the separated vapor at the head of the lift and for ferred is of the order of a few hundred gallons per hour or less. separate measurement of the liquid and condensate quantities. The use of centrifugal pumps for such quantities is not satisA considerable number of tests were carried out with this appafactory and an alternative means of pumping becomes necessary. ratus and it was proved that vapor-lift pumps were suitable for the purpose in view. Plunger pumps are frequently used for this purpose, but with most designs vaporization takes place from the surface of the The experimental installation was set up for purely practical reasons, to ascertain the suitability of the vapor-lift pump for a plunger a t each stroke as it leaves the stuffing box, resulting in considerable losses. If the liquid being pumped has strong solspecific purpose. At the time, however, i t was realized that, from vent properties it may not be possible to lubricate the pumps satisthe theoretical point of view, more valuable data could be obfitctorily, and excessive wear may occur. The latter objection tained by the incorporation of certain modifications to allow also applies to small rotary positive displacement pumps. temperatures and pressures to be determined at a number of A problem of this nature arose in a plant which was being points in the rising pipe. Unfortunately, time did not permit designed for the distillation of terpene hydrocarbons. In this this, but it was found that useful information relating to the case there was the additional complication that the plant was to mechanism of the lifter could be derived indirectly from the data operate under vacuum, and it was thought that a device someobtained on the apparatus as described. These results were conwhat similar to the air-lift pump but using vapor instead of sidered to be of general value to designers, and are therefore compressed air would achieve the desired result. The action offered subject to the above reservation. would be very similar to that occurring in water-tube boilers and natural circulation evaporators in which circulation takes place LITERATURE SURVEY owing to the boiling of the liquid in the tubes. At the time No references could be found in the literature dealing specifinothing could be found in the literature dealing specifically with cally with the vapor-lift pump, but the related problemof the airthis problem, but shortly afterwards in an article describing II lift pump has been dealt with in same detail by Purchas (&?), benzene plant installed by The Midland Tar Distillers ( 1 ) Owens (9$), Swindin (H), and Martin (91). it was mentioned that vapor lifts were used to elevate the bottoms The subject of the flow of water 9temperatures close to the of each still to the feed point of the next. The original idea was boiling point was fist dealt with by Rateau (94), who showed due to the Societe des fitablissements Barbet, Paris, which had that the flow of water through a nozzle can be calculated by means successfully installed ta number of vapor lifts operating a t atmosof the temperature-entropy diagram, and that for any given initial pheric pressure. This firm, however, had had no experience in saturation pressure there is a critical throat pressure for which the operation of this device under vacuum, and it was therefore the flow is a maximum. Bottomley ( 4 ) extended Rateau’s decided to set up an experimental installation. thermodynamic expressions and made several measurements of In the first place an experimental vapor lift was constructed the rate of flow of saturated water through nozzles. The measfrom a pipe of O.Mnch nominal bore, elevating to a net height ured flows were actually four to five times greater than those of 18 feet with 10.foot submergence and a steam jacket 3 feet calculated theoretically, provided that the static head was long on the lowest portion of the rising pipe. Using dipentene sufficient to prevent the entrainment of steam. This effect as the test liquid a t an absolute pressure of about 2 inches of was attributed to the delay in vaporization resulting from the mercury it was extremely difficult to start the lifter working, increase in internal pressure of very small bubbles due to surface 1 Present addrass, University of Washington. Seattle 5, Wash. tension forces. Bottomley also formulated expressions for the Present addresa 7 Letcomb Ave. Abingdon, Berks, England. S T H E design of con-

1883

INDUSTRIAL AND ENGINEERING CHEMISTRY

1884

flow of boiling water inside pipes, and made several measureinents which were in satisfactory agreement with theory. Benjamin and Miller (2) measured the rate of flow of boiling water through shzrp-edged orifices and found that no critical state existed, the flows corresponding closely with those calculated by the usual formula for "cold" water. Finally, Burnell (6) reported data for the flow of saturated water through nozzles, which were i n very satisfactory agreement with those of Bottomley. He also determined the rate of flow through pipes of various lengths and diameters, in some cases preceded by a nozzle, and found that the flow was generally greater (up to double) than the calculated value. This effect, which was much less evident with the higher upstream pressures and longer lengths of pipe, was attributed to slippage of the water relative to the steam bubbles.

D, VAPOR ~ l q U l D

-,SEPARATOR

circulation rates. Iiirschbaum, Krana, and Starck ( 2 1 , 1 2 ) experimented with an evaporator with a single external heating tube with an inside di:tmeter of 40 mm. and a heated length of 1.97 meters. The measured circulation rate was plotted it6 a function of the evaporation rate. Foust,' Baker, and Badger (10)investigated the circulation rates and heat transfer roefficients in a basket-type natural circulation evaporator with 31 tubes, each 2.5 inches in outside diameter and 48 inches high. The pressure drop in a single-tube forced circulation evaporiitor was investigated by Boarts, Badger, and Meisenburg (S),while McAdams, Woods, and Heroman (18,19) measured the pressure drop in a horizontal tube evaporator with I-inch tubes during the Vaporization of water and benzene. Dittus and Hildebrand (9) gave a method for the calculation of the pressure drop of oilvapor mixtures flowing through furnace coils, and Davidson et nl. (8) carried out experiments on the vaporization of water flowing through pancake coils mounted against the back wall of a furnace.

SIGHT GLASS

K. REMOVABLE SECTION OF

"Ym

A. FEED VESSEL

STEAM JA KETS

"E: NUMBERS IN CIRCLES REFER TO B.S.S. WMINAL PIPE SlZES IN INCH.

THEORY O F OPERATION

The most obvious basis of design for a vapor lift is obtained by assuming equality of the weights of liquid in the descending and of liquid-vapor mixture in the ascending limb. This may be expressed by means of the following equation:

iTEAM EJECTOR H.

-

Vol. 42, No. 9

'

STEAM

180 Lghq. In

igure 1. Arrangement of Experimental Vapor Lift Installation

Some attention has been given to the question of circulation rate in water tube boilers. Lewis and Robertson (14) made an analysis of this problem on the same lines as the above, in which they neglected the effect of hydrostatic pressure on the boiling point of the water, and of slippage, and assumed the absorption of heat to be uniform throughout the length of the tube. This method has been developed further by Brunt (6),Markson, Ftavese, and Humphries (% andIRoddatis ), and Lokshin (26). In the discussion after the second paper, Rowand gave some data for the circulation rates in a boiler operating at 1350 pounds per square inch, and showed that they were in satisfactory agreement with the calculated values. Data have been given by Schmidt, Behringer, and Schurig ( 2 8 ) for the velocity of steam relative to a stationary column of water. Measurements were carried out in a special apparatus, and also in a model watertube boiler, which was used in addition to measure circulation rates and heat-transfer coefficients. The relative velocity data were plotted against the densities of the steam-water mixtures, and the question of a general correlation involving dimensionless groups was also discumed. Finally, data are available from a number of sources for the performance of natural circulation evaporators. The earlier work on this subject was concerned only with over-all heat transfer coeffirients, but Linden and Montillon (16) in their experiments with an inclined tube evaporator also measured

Plh, = Pmhi (1) As pointed out by Swindin (27), however, this equation gives the total height to which a liquid will rise in a tube when no flow is taking place. When flow occurs, the height lifted is less, because it is necessary to take into account the following losses of energy:

Entrance loss into downcomer of lifter Friction loss in downcomer and riser pipes Exit loss a t top of rising main Loss due to slip age Loss due to acceferation of liquid in the zone of vapor formation In the case of the air-lift pump these losses were thoroughly investigated by Swindin (87), who showed that the acceleration loss can be reduced considerably by means of foot pieces specially designed to prolong the period of aeration. The operation of a vapor lift, although basically the same, is different in that the vapor is not admitted in a predetermined zone. Thus, on passing through the jacketed section the liquid is heated, but owing to the effect of hydrostatic head, vaporization does not necessarily take place in this region. On rising, the liquid reaches a cross section where the total pressure is equal to the vapor pressure and vaporization starts. Between this point and the top of the lift the pressure gradually falls and the quantity of vapor increases. This flashing results in a lowering of the temperature, until a t the top it will be the same as that of the saturated liquid under the pressure on the system, providing that a delay in vaporization does not occur, as in the case of the flow of boiling water through orifices (2,7). (In an actual case, however, the vapor is slightly superheated.) Theoretically, above the point of initial boiling the conditions must be calculated by an application of the tot8al energy balance equation, which may conveniently be written in the following form: dZ

+ dE + pdv + udp +

=

9. dQ = dE $. pdv - d F

dQ 4- dW,,

(2)

(3)

Assuming that no external work is done by the fluid, and that conditions in the rising pipe above the steam jacket are adiabatic, dZ

+ vdp + UdU 9c + dF

= 0

(4)

Substituting the value of the friction loss, for flow through a vertical pipe, this becomes

I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY

September 1950

CWVC No.

Stcorn Pnuure

0

I

0

2

75Lbl In 90,194 100 s t

Symbol

In Equation 5 the third term refers to the energy loss due to acceleration of the vapor-liquid mixture and the last to the loas due to friction. The energy input to the system which overcomes these losses and at the same time elevates the mixture by the amount given by the first term results from the expansion of the fiuid mixture and is given by the second term in this equation. For ease of computation Equation 6 may be expressed in the following form, suitable for stepwise calculation:

- zz) 1 1 + 4f 2gD

.".U

0

3

0

4

1,

I

5

6

110 12s 150

*, I ,

(%)* 1 + ( p , - p*) + a U L

This equation is applied in practice, starting from the point a t which vaporization first occurs, which is referred to hereafter as the point of initial boiling (P.I.B.). To find the position of the point of initial boiling the Bernoulli equation may be applied between this point and the level of liquid in the feed vessel. Assuming the velocity in this v e m l to be mro, this equation may be written as follows: (7)

where 2' is the distance of the point of initial boiling below the static liquid level in the feed vessel and subscripts f and o refnr to the feed vessel and the point of initial boiling, respectively. In deriving this equation it is assumed that the specific volumes of the liquid before and after heating are the =me. However, in most c w s the kinetic energy and the friction loss terms can be neglected, 80 that the value of 2' is given closely by the difference between the vapor pressure of the heated liquid and the pressure on the system. The method of calculation represented by Equations 5 and 6 is basically the same as that developed by Lewis and Robertson and others (14)for the calculation of circulation rates in water-tube boilers. EXPERIMENTAL WORK

Description of Installation. The apparatus used in the present work is shown in Figure 1. I t consists of a feed vessel, A, 3 feet in diameter and 2 feet 9 inches long on the strai ht, fitted with a multitubular reflux condenser, B, 9 inches in & m e t e r and 4 feet long, and a steam coil. From the bottom of this vessel the vapor lift was connected; this consisted of a pipe of 1-inch nominal bore aasing finst horizontally then vertically downwards. At the kwest point it turned through 180.', passing vertically upwards for 34 feet 3 inches to the vapor-liquid separator, D . The lowest portion of the rising ipe was steam-jacketed with %inch pipe in three 2 feet, and 1 foot long, respectively, starting from sections, 3 the bottom. *he heating medium waa 180 pounds per square inch steam controlled by two */&rich globe valves in series. A Spirax float trap waa fitted because it had previous1 been found that the steam pressure could not be accurate& controlled with a vapor expansion trap. The li uid issuing from separator D , which consisted of a horisont3 length of i e 0 inches in inside diameter and 7.75 inches Ion4 with we&$-on ends, passed to a sight glass,and to liquid receiver E. This vessel was 15 inches in inside diameter and 2 feet high and was fitted with a level lass and graduated scale. The vapor passed to the multitubufar condenser, F, 9 inches in diameter and 3 feet 2 inches between tube plates, and the condensate waa collected in vessel B,which was 13 inches in inside diameter and 3 feet 2 inches long, also fitted with a level glass. The bottom outlets on the two receivers were connected through cocks and a U-seal back to kettle A, so that the lifter could operate under steady-state conditions until it was desired to carry out measurements. The venta from receiver E and condensers B and F passed to a Mirrlees Wataon two-stage steam jet ejector, HI the pressure on the system being measured by means of a Negretti and Zambra absolute pressure gage, J . The rising pipe together with the heating jacket and the 3footlong vertical section of vapor pipe above the vapor-liquid

Lt

lsaS

U

INLET

Figure 2.

LIQUID TEMPERATURE,

%.

Effeot of Inlet Liquid Temperature on Rate of Lift

Seriscl C Total lift, 84 feet 3 inahta Submergenee, 44.6% Abwlute manum on nyntern. 2 inches H g Length orstjaaket, S feat

se arator was insulated with 1-inch thickness of magnesiaasgestos sectional lagging. In order to find the effect of reducing the height of the lifter, a section of pipe 4 feet 9 inches long waa fitted between flanges at K. For one set of runs this was removed, thus lowenng the vapor-liquid se arator. The pipes connectin this with receiver E and con&nser F were made correspon8in ly shorter. Material #sed. By-product dipentene (&limonene) was used for the testa, aa this material waa typical of those which it waa desired to handle. The specific gravity a t 15' C./15' C. was 0.856 and the boiling range at 760 mm. of mercury pressure was 175' to 182' C. Method of 0peratio.i. The ejector pump was first started up and controlled until the desired vacuum wm obtained. The water was turned on to the two condensers and the liquid in kettle A waa brought to the desired temperature as indicated on the dial thermometer. The steam valve leading to the bottom jacket waa then opened to bring the lifter into operation quickly, the pressure being allowed to rise to a value 50 to 100% greater than that desired. After a short time, pumping started and 5 to 6 minutes later the steam pressure waa lowered to the desired value and maintained constant. After running continuously for 0.5 to 0.75 hour the cocks beneath receivers E and G were shut and the times required to fill 6 inches of receiver E and 3.5 inches of receiver G were measured with a stop watch. Under each set of conditions two to three readings were taken and the mean was tabulated.

Results. In all, 138 runs were carried out; the results are recorded in Tables I to 111. Four series of tests were carried out to investigate the effect of relative submergence, of variation of steam pressure in the jacket, and of temperature of the liquid entering the lifter. The results are given in Table I and plotted in Figures 2 to 6. Series A to C were carried out with a total lift of 34 feet 3 inches with three different values of the Submergence, while series D was carried out with 29 feet 6 inches lift and 15 feet 3 inches submergence. (The submergence is defined as the height of the li uid in t h i feed vessel above the bottom of the steam jacket. Tge relative submergence is the ratio of this to the height of the inlet to the vapor-liquid separator above the bottom of the steam jacket, expressed as a ercentaee.) In all cases the absolute preaeure was maintainef at 2.0 inches of mercury. The effect of the inlet liquid temperature on the rate of lift for series C is shown in Figure 2, and the effect of jacket steam pressure for the same series is shown in Figure 3. In Figure 4 the quantity lifted is plotted against the percentage of vapor at the top of the lifter, while Figures 5 and 6 show the effect of submergence. In Figure

INDUSTRIAL AND ENGINEERING CHEMISTRY

1886

Vol. 42, No. 9

I)

k

W m

%

m d

10 0

h a

September 1950

I N D U S T R I A L A N D ENGINEERING CHEMISTRY

1887

1888

INDUSTRIAL 4 N D ENGINEERING CHEMISTRY r

Vol. 42. No. 9

6, series D was probably not comparable with the remainder, because the height of the lifter was less and slippage losses may have been relatively lower.

g

Further tests were carried out (series E) to determine the effect of variation of absolute pressure on the system; the results are given in Table I1 and plotted in Figure 7, while the effect of varying the length of the steam heating jacket is given in Table I11 (series F).

^^

EXAMINATION OF RESULTS

d

w

Heat Input. I n order to obtain a more complete understanding of the method of operation of the vapor lifter, the heat input and the temperature of the liquid leaving the heating zone were calculated, assuming that no vaporization occurred in this region. In the first place, however, it was necessary to obtain values of the specific heat and the latent heat of vaporization of dipentene. No data could bc found for the former, but values have been reported of 0.380 for camphene at 35' C. and 0.411 for turpentine at 0" C. Inasmuch as all these substances are isomers, they would be expected to have specific, heats of the same order, and a value of 0 40 was therefore assumed for dipentene. The latent heat of vaporization was assumed to be 69.5 pound centigrade units per pound, the value reported in the literature for limonene. In the first place the temperature drop of the liquid passing through the unhgged downcomer (approximately 16-foot total length) was calculated. It was assumed that the heat loss occurred by convection and radiation to air at 25" C., the emissivity of the pipe being taken as 0.80. The resulting temperature drops are included in Table I, and the inlet liquid temperature t o the heating jacket was obtained by subtracting this temperature drop from the temperature of liquid in the kettle. By a heat balance across the rising pipe, assuming equilibrium to occur in the vaporliquid separator, the heat input is equal to the sensible heat required to raise the total quantity of liquid and vapor lifted from inlet temperature to the temperature corresponding to the saturation pressure at the head, together with the latent heat of vaporization of the condensate and with heat losses from the rising pipe. The first two quantities were calculated assuming the thermal properties given above. An approximate estimate was made of the heat loss from the rising pipe, taking the thermal conductivity of the lagging to be 0.04 p.c.u./ (hour)(sq. foot)(' C.)(foot). The value thus calculated was 460 P.C.U. per hour in the case of series A to C. Although the true value may have been somewhat higher owing to imperfections in the lagging, the effect on the final calculated liquor temperature would be comparatively small. Finally, the total heat input in the

September 1950

INDUSTRIAL AND ENGINEERING CHEMISTRY

heating zone was obtained by adding the above three heat quantities, and the temperature of the liquid a t this point was calculated. The results are included in Table I together with the vapor pressure of the heated liquid. With the exception of runs A30 and B30, in all cases the vapor pressure of the liquid leaving the heating zone was lower than the total p re S R U r e 4 .e., the p r e s s u r e on t h e STEAM PRESSURE IN system together with JACKET, Lt&.ln. (gage) the hydrostatic head -at this point, showFigure.7. Effect of Jacket Steam Pressure on Rate of Lift ing th%t vaporization did not occur in the Seriea C Total lift, 84 feet 3 inchea jacketed section. In Submergence, 44.6% Abwlute prensum on system, 2 inchorder confirm the Hg heat quant,ities calrubn g t h of steam jacket, 3 feet lated above, attempts were made to measure the steam condensate rate. The results obtained in this manner were invariably high, however, a fact which may possibly be attributed to wetness of the entering steam. Heat Transfer Coefficients. The over-all heat transfer coefficients in the jacketed section of the rising pipe were calculated from the heat inputs and the logarithmic means of the temperature differences at the top and bottom of the jacket. Corrections were not made for the resistance of the condensing steam film and the metal wall, because the accuracy was doubted, owing to the indirect nature of the measurements. In any case, failure to make this correction would result in an error no greater than 10 to 30% in the majority of cases. The results are included in Tables I to I11 and are plotted against the rate of flow in Figure 8 for series A to D. As in practically all cases vaporization d'd not occur in the heating section, it was anticipated that the heat transfer coefficients could be correlated by the usual equation for heat transfer to liquids in forced convection inside pipes, as for evaporators operating with high liquid velocities in the tubes (3, 1 7 ) . The coefficients for series D, in which the total height IiAed was lower, appeared to lie on a line about 45% above that used to represent series A to C, but in both cases the results were correlated best by lines of slope of about 0.8, as was expected. The line shown in Figure 8 for series A to C i s represented by the following equation:

tube evaporators (3, 18, 19). The type of liquid used, the pressure under which the system was studied, and the type of equipment in the case of the forced-circulation vertical-tube evaporators are different from those of the present evperiment; therefore correlation of data obtained from these two types of experiments is not attempted. For the same submergence and inlet liquid temperature, U increases with At, reaches a maximum, and decreases again. As expected, the more the temperature of the inlet liquid the less is the value of At a t which U is maximum. For the same inlet liquid temperature but different submergence, the value of At at which U is maximum remains practically the same (variation as seen in Figure 9 is supposed to be within experimental error, owing to indirect nature of measurement). It follows therefore that the submergence has practically no effect on the heat transfer coeffirient in the heating sertion, provided the point of initial boiling is above the heating zone all the time-Le., the heating jacket is sufficiently below the static level of t,he liquid in the lifter tube.

3

s

U = 229uO.8

(8)

The value of the constant in Equation 8, calculated from Colburn's proposed correlation ( 7 ) for forced convection, assuming the viscosity and thermal conductivity to be the same as for turpentine, was 72.5. Consequently, the heat transfer coefficients obtained in the present work for series A to C were three times the expected value and were still higher in the case of series D. The reason for this discrepancy is discussed below. In Figure 9, the curves obtained by plotting the heat transfer coefficient, U ,against the temperature difference, At, between the temperature of the steam in the heater jacket and the average temperature of the liquid in the heating section of the lifter tube, are of the same nature as those of forced circulation verticnl-

1889

Symbol c L:

Curve Number

Inlet Liq

0

I

Temp.,%. 54

A

2 3 4 5

60 68 76 85

e 0

A

"a VAPOR Figure 4.

AT TOP OF LIFT Variation of Rate of Lift with Vapor Generation

Series C Total lift, 34 feet 3 inches Submergence, 44.6% Length of steam jacket, 3 feet

Comparison with Theory. Attempts were made by stepwise application of Equation 6 to calculate the total height to which the liquid would rise in the case of a few typical runs. The method of calculation is shown below in detail for run A7. CALCULATION OF THEORETICAL HEIQHTLIFTEDFOR Rcx A7. The rate of lift ma# 57.2 gallons per hour-Le., 460 ouiids per hour or 19.5 pounds per second (square foot), the ins& diameter of the pipe being 1.096 inch. u = 0.39 foot per second. The estimated heat loss from the lagging was 460 P.C.U. per hour, correspouding to a drop in temperature of thr liquid of 460 2.5' C. Assuming this heat loss t o be tiis9 X 0.80 X 0.40 tributed evenly throughout the height of the rising pip(. abovr the heating jacket, it was estimated from a reliminary trial that the temperature drop was 0.8' C. below an81.7" C. above thrb point of initial boiling. Hence temperature at point of initial boiling = (103.6 - 0.8)= 102.8" C. Therefore vapor pressure a t point of iiiitial boiling = 76.0 mm. and excess pressure = (76 51) = 25 mm., correspoiidin to 1.4 foot head of liquid. %e lecting friction and other losses, the point of initial boiling was $13.5 - 1.4) = 12.1 fwt above the bottom of the heater iaakpt, -- -- - -. Also, assuming the viscosity of the liquid to be 0.5 c y . , __ Dup - ' ' 0 g ~ ~ x 0 ~ ~ $ 4 5 0 =' 2 5300. Therefore f (for rough

-

I

M

pipes) = 0.010.

1890

INDUSTRIAL A N D ENGINEERING CHEMISTRY TABLE V.

Vol. 42, No. 9

COMPARISON OF CALCULATED A N D ACTUAL LIFTS FOR THREE TYPICAL RUNS

(Submergence 13.5 feet. Total actual lift 34.25 feet) Amount Lifted Gal./ Hour 27.7 57.2

Run NO.

A1 A7 A12

SUBMERGENCE

Figure 5 . Effect of Submergence on Rate of Lift Absolute pressure on system, 2 inches Hg Length of steam jacket, 3 feet

Owing to lack of data for "slug" flow, this value was assumed for purposes of illustration to hold throughout the zone of vaporization, The sum of the calculated inlet friction and acceleration losses for the pipe between the feed vessel and the point of initial boiling was 0.025-foot head, confirming the accuracy of the above calculation of the position of the point of initial boiling. The height of the rising pipe above the point of initial boiling was then calculated in steps, starting from the temperature a t the point of initial boiling and finishing at the saturation temperature corresponding to the pressure on the system. These calculations are given in Table IV.

TABLE IV. CALCULATIONS Point No. t

1

"e.

102 8

it., c.

0

Vapor pressure,

77

rn "1

vi;&'

pressure, lb./sq. inch lOOzb % v Y c c;!. feet/lb. vd,'cu. feetilh. us;., cu, feet/lb. AZO6,feet (Id

1.488

...

... 0.02 ...

2 (:)*& ] . . .

2gcD A Z / , feet

...

2 102 0 0 8

3 100 2 8

4

5

6

97 5 1

94 8 5

92 9 1

62 5

55

50

75

70

1.450 0.46 36.8 0,189 0.105 0.35

1.353 1.210 1.063 2.94 4 89 1.61 49.0 39.2 43.5 1.30 2.42 0.651 1.86 0.420 0.976 14.9 3,59 12.3 ZAZO = 4 4 . 2 feet

..

0.966 5.25 53.5 2.83 2.62 13.1

1.029

1 457

9.92

18.8

0.34

1.50 2,.46 3 54 ..ZAZ = 8.5feet

0 7

3.47

51.1

70

Vapor 4.30 5.25 10.4

P.I.B., Feet 12.1 12.1 10.3

Total Calcd. Lift, F e e t Excl. Incl. friction friction 84.9 47.7 15866..36 2304..63

trate the application of Equation 6. The results of these calculations for three runs are given in Table V. Runs A7 and A12 are of interest because the amounts lifted were of the same order, although the proportion of vapor formed in the second was almost double that in the first. The effect of friction was very much greater in the case of run A12, owing to the higher velocity at the outlet. This illustrates the reason why in general there are two values of the heat input for any quantity lifted. In attempting to apply this method of calculation to runs in which the rate of lift was greater than about 100 gallons per hour it was found that the height, AZ, of the steps became negative; the acceleration loss became greater than the energy input given by the expansion term. Because such high rates of lift were obtained experimentally, the reason for the discrepancy was investigated. The one source of loss which is not taken into account in the above calculation is the loss due to slippage of the vapor relative to the liquid. In two-phase flow slippage results in an increase in the vapor and a reduction in the liquid velocities for any given throughput, so that the proportion of the crosssectional area of the pipe that is filled with liquid is greater. Consequently, the average density of the mixture is increased and the specific volume reduced by slippage. The effect of slippage may therefore be introduced into Equation 6 if data are available giving the actual specific volume of the mixture under the conditions existing in the section. The effect of a reduction in the specific volume can be either to increase or reduce the calculated height of a step according to conditions. Thus at high rates of lift, if slippage is neglected, the acceleration loss is apparently greater than the energy input, but if slippage is taken into account, then obviously the acceleration loss is reduced and a positive instead of a negative value is obtained for AZ. On the other hand, the height is reduced owing to the presence of the term vav. in the denominator of the first term. Again, however, the effect of slippage on the friction loss is to reduce this, owing to the lower velocity which results, so that the value of AZ is

a Last three steps corrected for temperature drop of 1.7' C. resiilting from heat losses. b % vapor = 2 ! At = 0.575At.

L

_ _ ( p in mm. Hg). 0.001MP (1 Z) VI. e From Equation 6, neglecting frjction term. j From Equation 6. including friction term. cyy =

d u = zuv

+ -

Hence, allowing for the height of 12.1 feet below the point of initial boiling, the total calculated height of the rising pipe above the bottom of the heating jacket is 56.3 feet neglecting friction, or 20.6 feet allowing for the friction loss. Owing to lack of data no correction was made for slippage loss and the friction factor was assumed to be the same throughout as that calculated for the liquid at the point of initial boiling. This value is almost certainly high but was used merelv t,o illus-

5

36

Figure 6.

40

44

48

52

SUBMERGENCE

Effect of Submergence on Hate of Lift

INDUSTRIAL AND ENGINEERING CHEMISTRY

September 1950

$, w

1-

0 .

A A

o x fy, l -

12 I ----% ----%

Total Lift, Ft. 34.25 34.25

Submet= hM Lq. Scam P r e s gcnccq, Temp%. Lt$q.In.,g

Vapor Vapor

~h, ~h,pressure pressure

60 100 68 29.50 SI4 66 Quantity Llfted Vs. Rcsrun

42.3

446

I

-

ABXKUTE PRESSURE ON SYSTEM, NCH Hg

Figure 7. Effect of Absolute Pressure on System on Rate of Lift

increased. The effect of slippage is complex and cannot be estimated without a knowledge of the exact conditions prevailing. Data have been given by Schmidt, Behringer, and Sahurig (9&) for the velocity of steam bubbles relative to a stationary column of water, and of air relative to water in motion. When the average density was greater than about 0.8 the effect of water circulation velocity was probably negligible. This probably corresponded to the disperse flow region, but in two-phase flow it is well known that three clearly defined regions occur:

1891

vapor lift is partially vaporized and the boil-up of this still can therefore be reduced by an amount corresponding to the vapor entering in the feed, provided that the height of the stripping section is increased slightly. However, if it is necessary to cool the liquid entering the lifter below saturation temperature as in the present work, the sensible heat removed will be lost unless it can be recovered in a heat exchanger. DISCUSSION

It is apparent from the foregoing results that the mechanism of the vapor-lift pump is very complicated, inasmuch as the rate of lift depends on the balance between the energy input term, Jvdp, and the energy losses due to acceleration, slippage, and friction. When the rate of lift is comparatively low and the proportion of vapor small, the effect of increasing the steam pressure and hence the rate of heat transfer is to increase the rate of lift. As may be seen from Figure 4, the increase in lift may sometimes be accompanied by a decrease in the proportion of vapor formed, although the total heat transferred is greater. As the proportion of vapor increases, however, the velocity at the top of the lifter becomes very high and the friction losses increase rapidly, 80 that the rate of lift reaches a maximum and then decreases as the heat transfer is further increased. Kirschbaum et a2. (11) obtained a similar result in their experiments with a natural circulation evaporator. In Figure 5 of their paper they plotted the rate of circulation of the liquid as a function of the rate of evaporation and obtained curves similar in form to those of Figure 4 of the present work; the liquid circulation rate increased very rapidly up to a maximum and then fell off as the rate of evaporation was increased.

Region of disperse flow in which small bubbles of vapor are dispersed in the liquid. Region of slug flow or coalescence in which the small bubbles coalesce into large ones which ultimately OCCUDY _ - the whole cross section of the piie. Climbinn film region in which the liauid travels as a thin film UP the wan, the motion being maintaiied by the friction of the high velocity core of vapor passing up the center. At the lower densities the relative velocity appeared to be a complicated function of the flow rates of both liquid and gas.

This probably corresponded to the slug flow region, where conditions would be expected to be complex, because a t any particular cross section liquid alone is present at some times, and vapor with a liquid film on the walls a t others. In addition, there is a lack of data regarding frictional pressure drop in pipes in this region, as the data of Lockhart and Martinelli (IS)are stated specifically to refer only to the region of disperse flow. Consequently, the problem of calculating analytically the performance of a vaporlift pump is complicated and cannot be carried out accurately with the data at present available. Thermal EBciency of Vapor-Lift Pump. The efficiency of the lift was calculated by comparing the actual energy input in terms of heat added in the jacketed section to the work done in elevating the liquid. This was found to be very low, generally less than O.l%, although if the heat input for vaporization alone was considered the efficiency was increased. Thus the lower curves of Figures 10 and 11 show that the efficiency on this basis was 0.35% for series C and 0.17% for series D. The low efficiency of the lifter would be anticipated from the Carnot principle, because the difference between the temperatures after heating and after expansion is comparatively small. However, the main application of the vapor-lift pump would appear to be the feeding of distillation columns, and an examination of the operating diagram for a typical column shows that this heat i s not entirely lost: The feed to the still which is being fed by the

RATE OF LIFT, GAh/HR. Figure 8. Derived Over-all Heat Transfer Coefficient for Heater Jacket

The effect of inlet liquid temperature on the rate of lift is rather surprising, for it might be expected that this would merely involve an additional heat transfer problem quite independent of the question of pumping. However, i t was found in the first experiments that the lifter appeared to be unstable when the liquid entered at the saturation temperature corresponding to the pressure on the system. The effect of inlet liquid temperature is shown clearly in Figures 2 to 4, and a method of plotting which further illustrates this effect is shown in Figures 10 and 11. I n the latter the heat required for vaporhation per gallon of liquid lifted is plotted as a function of the rate of lift. Two limiting curves are obtained, the lower one showing that the heat required for vaporization is directly proportional t o the rate of lift. The upper curve corresponds to the reduction in rate of lift as the heat input is increased beyond a certain poi"$ this reduction is due to the rapid increase in frictional losses. The effect of liquid temperature is to vary the point a t which crossover occurs from the lower to the upper curve, and there is an optimum temperature for which the rate of lift reaches a maximum.

Vol. 42, No, 9

INDUSTRIAL AND ENGINEERING CHEMISTRY

1892

1

.

'

Note: Numbers ' in 'CirLles refer Inlet Lia. Temp&.

' 4 4400 0

L-

230

A t , %. Figure 9. Effect of Temperature Difference on Over-all Heat Transfer Coefficient

This pulsation will cause rapid pressure changes in the heating zone and it is probable that incipient vaporization takes place in the stagnant liquid film on the wall when the pressure reaches a minimum. These vapor bubbles will recondense as soon as the pressure rises, but they would be expected to cause the heat transfer coefficient to increase considerably. A similar theory has been proposed by Boarts et al. ( 8 ) in connection with their experiments with a forced circulation evaporator, and they suggest that incipient vaporization followed by collapse of the bubbles in the inner core of the fluid is analogous to dropwise condensation of steam in increasing the heat transfer coefficient. If the inlet liquid enters at too high a temperature, this incipient vaporization will occur in the lower sections of the heating zone and the vapor bubbles may be swept into the downcoming pipe by the flow reversal and result in a lifting effect which is opposed to that in the rising pipe. On the other hand, if the liquid is cooled, incipient Vaporization will occur toward the top of the heating jacket and the flow may reverse again before the bubbles reach the bottom of the rising pipe. This theory at least has the merit of explaining both the effect of liquid inlet temperature and the unexpectedly high heat transfer coefficients. I t is possible also that the effect of relative submergence may be explained in a similar manner, inasmuch as the amount of incipient vaporization occurring in the heating zone would be expected to increase as the submergence is reduced. If this explanation is true, it is possible that raising the heating jacket to a point nearer the point of initial boiling will result in an improved performance in so far as to nullify the effect due to reversal and to enhance the heat transfer Coefficient owing to vaporization occurring at the heating zone, although unfortunately i t has not been possible up to the present to carry out any work on these lines.

A t = Difference between temperature of steam in heater jacket nnd average temperature of liquid in heating section of lifter tube

The effect of relative submergence as shown in Figures 5 and 6 is also not clear. In these plots the curves representing the effect of submergence are shown dashed for series D, because it is probable that the reduction in the total lift from 34 feet 3 inches to 29 feet 6 inches affected the performance apart from the change in the relative submergence, as slippage losses were relatively less As shown above, ljowever, vaporization almost invariably started some considerable distance above the heating jacket owing to the effect of hydrostatic head, and it is not clear why an increase in the length of the zone beneath the point of initial boiling should affect the performance. However, for the same total height of the lifter, an increase in submergence decreases the net height through which the liquid is to be raised, and consequently decreases the slippage loss and friction and therefore increases the rate of lift. A useful fact emerges from these results, because they suggest that the rate of lift should be controlled by means of a valve located in the liquid inlet line in order to vary the effective submergence rather than the steam pressure. The mechanism of the vapor lifter is not clear, but the pulsating nature of the flow due to slugging may be at least partially responsible for the above phenomena. This pulsation was very noticeable on the flow recorder charts before the flowmeters were fully damped. With the larger lifter the flow appeared to diminish sharply and then rise rapidly to the original value once in every 4 minutes. Although it was not proved, it is possible that an actual reversal in flow takes place momentarily. This may in fact be anticipated from the calculations described above, inasmuch as when the rate of lift exceeds about 100 gallons per hour the energy loss due to acceleration is greater than the energy input. When vaporization is just about to occur in order to form a fresh slug of liquid, this energy may be absorbed by a reversal for a short period until the effect of slippage allows the flow to return in the normal direction.

20 60 100 140 QUANTITY LIFTED (incl vapor condensate), Gadhr.

Figure 10. Variation of Heat Input for Vaporization with Quantity Lifted Series A t o

C

The results of the experiments given in Table I1 are of interest because the rate of lift was found t o increase considerably with pressure. The conditions under the different pressures are not strictly comparable, because the saturation temperature of the liquid increases with pressure and consequently the relative subcooling of the inlet liquid also increases. The heat transfer coefficient appeared to increase to extremely high values, hlthough the vapor pressure of the heated liquid in all cases was lower than the total pressure (including hydrostatic head) at the top of the

INDUSTRIAL AND ENGINEERING CHEMISTRY

September 1950

9

heating section. However, at the higher pressures the difference was not great and the results indicate that incipient vaporization in the heating zone must have resulted in a considerable reduction in thickness of the laminar film. I n Table I11 the effect of varying the length of the heating jacket is shown, but because the steam pressure was maintained constant the degree of vaporization increased, and the reduction in the amount lifted with length of heating jacket was almost certainly due to increased friction. Consequently, i t i s probable that the length of the heating jacket has little effect on the performance, provided that the steam pressure in the jacket is adjusted to give comparable rates of heat transfer.

A

150--I

a I

P

110

.-

I

'' ' I

I

l

l

&Ll

1

1

1

-

0

I Inlet L1q.Temp, "C.54

A

60

0

68

c3 A

76 85

-

-

-

QUANTITY LIFTED (incl. wpor condenrotr), Gouhc

Figure 11. Variation of Heat Input for Vaporization with Quantity Lifted Qeriea D

DESCRIPTION OF FULLSCALE VAPOR-LIFT INSTALLATION.To illustrate the practical a plication of the above results, a descrip tion is given of an instahtion of two vapor-lift pumps in a commercial distillation plant, The snialler of these is based on a pipe of 1-inch nominal bore and the quantity pumped is comparatively small. The design, therefore, was very similar to that used in the present experimental work. The second was required to ump 80 to 100grallons per hour of a terpene mixture with a bo& point of 100 C. under a pressure of 6 inches of mercury to a net feight of 28.5 feet, the pressure at the top being 4.5 inches The difference in pressures is due to remure drop of niercur through d e acking of the distillation columns; tge controlled pt.easure on t i e condenser vents was 3.0 inches of mercury absoUte. The arrangement adopted is shown diagrammatically in Fi ure 12. The li uid to be umped is taken from the inlet to the ca!audria of the xrst still, and passed through a jacketed serpentine cooler, B, with a cocurrent flow of coolin water designed to reduce the temperature to 70' C. The liquirflevel in the calandria of the first still is controlled by a differential liquid level controller, E, of the averaging type, which operates a control valve situated beyond the orifice plate after the cooler. The flow is measured by means of a differential mercury-type How indicator-transmitter, C, whic*his necessarily located beneath the orifice plate in order to keep the impulse lines full of liquid. The flow 18 transmitted to a recciver-recorder on the maill vontrol panel. Because the height to be lifted was grwter than that used in any of the present experiments, with a consequent possibility of greater friction and sli age losses, and it was desired to provide a margin of about 1 0 0 g o n the quantity lifted to enable satisfactory control to be obtained, it was decided to base the lifter on a 1.5-inch bore pipe. In order to ohtain the required submergence without elevating the stills excessivrly, a hollow pile 13 inches in diameter was sunk to bedrock, a second tube 8 inches in inside diameter was placed inside, and the annulus was filled with cement. By this means the lifter was lowered 10 feet below ground level, giving a submer ence of 20 feet, or allowin for the differenw in pressures at t i e inlet and outlet of the fifter, 22.1 feet (45.6%). The jacketed section was 4 feet long tirid was supplied with steam at a pressure of 170 pounds per square inch gage through a l/Anch globe valve, the conderisate passing to a small Hoat trap. A vapor-liquid separator R ~ Sfitted a t the head of the risin pilie, as shown a t Gin Figure 12. Thi*is 8 inches in diameter an2

.

*

1893

Fi ure 12. Diagrammatic Arrangement of fapor Lift Pump in Distillation Plant contains an upper impingement baffle and a second base coverin the lower halt. The latter is provided with two orifices designef to pass the liquid continuous1 at a rate corres pnding to the average rate of pumping. A cLarance is rovifed in the vertical plane between the two baffles, so that t i e upper surface of the ower one will act as a weir if the orifices plug. By this means an approximately constant rate of feed to the second still, H, is maintained. The inleta to this still are provided with a system of cocks as shown, to enable the va or to be admitted to the feed position above the liquid inlet. T i e vent, F,is fitted to prevent airlocking fiqom occurring in the orifice line and a by-pass, D , is provided across the cooler and orifice pipe for use when starting up, When the plant was first started up difficulties were encountered because the Iareer lifter surged violently, giving anextremely high rate of flow of liquid for about 2 minutes and then stopping entirelv for about 5 minutes while fresh liquid was heated. Under th&e conditions the second still did not operate satisfactorily and in ltny case the rate of pumping was somewhat less than the rate of feed to the first still. It was then found that if the setting of the control valve, which was a 1-inch valve of the logarithmic veeport type, was altkred so that it was only about 20 to 25% open, the lifter would start almost inimediately to operate smoothly. Under these conditions the system h a l l came. to equilibrium with the control valve about 15% open. 8 n opening the valve further the rate of lift increased rapidly, but a point was reached where instability was likely to set in. -4 similar oscillating flow has been re orted by Ledinegg (13) under certain conditions with a La d o n t forced circulation boiler; this was overcome by fitting nozzles a t the inlet end of the steam tubes. The control valve was later replaced by one of 0.5-inch size, and very little difficulty has since been experienced in starting up. Since this change was made no difficulties have occurred with either of the lifters, and the installation him proved to be a complete ~UCCPJS. CONCLUSIONS

A vapor-lift pump will operate mtisfwtorily under VYCUM as low as 2 inches of mercury absolute. The rate of lift increases with the relative submergence and possibly also with reduction in the net height lifted. A critical value exists for the steam pressure in the heater jacket and hence for the rate of heat transfer, the rate of lift falling off with higher or lower pressures. This effect is explained by the rapid increase in the energy loss due to friction as the proportion of vapor generated is increased.

INDUSTRIAL AND ENGINEERING CHEMISTRY

1894

Contrary to expectations, the inlet liquid temperature appears to have a profound effect on the performance, as there is a critical value below or above which the rate of lift diminishes. This critical temperature was lower than the saturation temperature corresponding to the pressure on the system. It is not clear whether this effect would occur with lifters operating under comparatively high presaures. When operating under a pressure of 2 inches of mercury it was found that vapor formation generally did not occur until the liquid had reached a point considerably above the top of the heating zone. This effect is due to the relatively large influence of the hydrostatic head when operating undLr low pressures and it becomes less as the pressure on the system is increased. The over-all heat transfer coefficient in the heating zone was found to vary as the 0.8 exponent of the liquid velocity, except for isolated runs in which the heat transfer rate was so large that Vaporization occurred in the jacketed section. Correction was not made for the resistances of the condensing steam film and of the pipe wall, because these were relatively small. The experimental coefficients were about three times those calculated from the usual correlation for heat transfer to a liquid in forced convection in a pipe. This is explained as being due to incipient vaporization occurring in the stagnant liquid film caused by pressure variations resulting from the pulsating nature of the flow. With increasing pressure on the system, the rates of lift were found to increase when the steam pressures and inlet liquid temperatures were maintained constant. The heat transfer coefficients increased very rapidly with pressure, no doubt because of an increase in the degree of incipient vaporization in the heating zone. I n order to control the rate of lift, the control valve should be located in the liquid-inlet line to the lifter and not in the steaminlet line. ACKNOWLEDGMENT

Thanks are due to the directors of B.X.Plastics, Ltd., for permission to publish this work. Acknowledgment is also due to the directors of the SociBt6 des fitablissements Barbet, Paris, and to Midland Tar Distillers, Ltd., for providing information on the operation of vapor-lift pumps under atmospheric pressure. Thanks are also due to J. F. Sebald, chief engineer of the Feed Water Heater Engineering Division, Worthington Pump and Machinery Corporation, for much valuable advice in the preparation of this paper, and also for suggesting the method of plotting used in Figures 10 and 11. NOMENCLATURE

a

=

cross-sectional area of pipe, sq. feet

D = pipe diameter, feet E -

F

f go

h. ht

L M P

Q s

T

internal energy, foot lb./lb. mechanical energy converted into heat by friction, foot lb./lb. = friction factor = gravitational conversion factor, (Ib. mass)(foot)/(lb. force)(sec.*) = submergence measured from surface of inlet liquid to bottom of’steam jacket, feet = total lift from bottom of steam jacket to vapor-liquid separator, feet = latent heat of vaporization, p.c.u./lb. = molecular weight = pressure, lb./sq. foot = energy equivalent of heat added by external source, foot Ib./lb. = specific heat, p.c.u./(lb.)( C.) = temperature, K.

=

difference between temperature of steam and average temperature of liquid in heating section, C. U = over-all heat transfer coefficient, p.c.u./(hr.)(sq. ft.) (“C.) u = velocity, feet/second u = specific volume, cu. feet/lb. uaV. = average specific volume over increment of height, cu. feet/lb. Wex.= external work done by fluid, foot Ib./lb. w = mass flow rate, Ib./second 5 = weight fraction of vapor formed 2 = height, feet pt = density of liquid entering lifter, Ih./cu. foot pm = average density of mixture of liquid and \ apor in rising pipe, Ib./cu. foot At

=

SUBSCRIPTS av. =

1 v

average

= liquid = vapor

LITERATURE CITED

(1)finon., Ind. Chemist, 22,206 (1946). (2) Benjamin, M. W., and Miller, J. G., T r a m . Am. SOC.Mech. Eltgrs., 63,419 (1941). (3) Boarts, R. M., Badger, R. L., and Meisenburg, S. J., Trans. Am. Inst. Chem. Engrs., 33, 363 (1937); IND.ENO. CHEM.. 29,912 (1937). (4) Bottomley, W. T.,Trans. North East Coast Inst. Engrs. R. Shipbuilders, 53,65 (1936-37). (5) Brunt, J. V.,Trans. A m . SOC.Mech. Engrs., 63,339 (1941). (6) Burnell, J. G.,J. Inst. Engineers, Australia, 18,1 (1947);E7~gginew, 164,572 (1947),abridged version. (7) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29, 174 (1933). (8) Davidson, W. F., Hardie, P. H., Humphries, C. G. R., Markson, A. A., Mumford, A. K., and Ravese, T., Trans. A m . &c. Mech. Engrs., 65,553 (1943). (9) Dittus, F. W., and Hildebrand, A..Ibid., 64,185 (1942). (10) Foust, A. S., Baker, E. M., and Badger, W. L., Trans. A m . Ittat. Chem. Engrs., 35, 45 (1939). (11) Kirschbaum, E., Chem. Fabrik, 10,337 (1937). (12) Kirschbaum, E.,Kranz, B., and Starck, D., Forsch. Gebirte I?&genieurw., B6, Forschvngsheft 375, 1-8 (1935). (13) Ledinegg, M., Maschineabau und Wlirmewirtschaft, 3,49 (1948); Engineers’ Digest, 10,85 (1949). (14)Lewis, W.Y.,and Robertson, 9. A., Proc. Inst. Mech. Engrs., 143,147 (1940). (15) Linden, C. M., and Montillon, G. H., Trans. A m . Inst. Cliem. Engrs., 24, 120 (1930). (16)Lockhart, R. W., and Martinelli, R. C., Chem. Eng. Pwgress, 45, 39 (1949). (17) Logan, L. A., Fregen, N., and Badger, W. L., IND.ENG.CHEM., 26, 1044 (1934). (18) McAdams, W. H., “Heat Transmission,” 2nd ed., Chagt. X, New York, McGraw-Hill Book Co., 1942. (19) McAdams, W.H., Woods, W. K., and Heroman, L. C., T r a m . Am. SOC.Mech. Engrs., 64,193 (1942). (20) Markson, A. A.,Ravese, T., and Humphries, C. G. R.. ILid. 64,275(1942). (21) Martin, S.C.,IND.ENG.CHEM.,19, 1346 (1927). (22) Owens, J. S., Engineering, 112,458 (Sept. 23,1921). (23) Purchas, A.W., Proc. Znst. Mech. Engrs., 613 (November 1917). (24) Rateau, Ann. mines, ( 6 ) 1,45 (1902). (25) Roddatis, K.F.,and Lokshin, V. A., Zzwest. Vsesogwz. TrpEoiekh. Znst., 15, No.4/5,16 (1946). (26) Schmidt, E., Behringer, P., and Schurig, W.,Forsch. Gcbiefe Ingenieurw:, B5,Forschungsheft 365 (1934). (27) Swindin, N.,Proc. Chcm. Eng. G ~ o u p10, , 116 (1928).

O

O

Vol. 42, No. 9

RECErVED

August 2, 1948