Design of Fractionating Columns

d2 = density of vapor, pounds per cubic foot dl = density of liquid, pounds per cubic foot. PRACTICAL. APPLICATION TO ENTRAINMENT. Although the value ...
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Design of Fractionating Columns I. Entrainment and Capacity MOTTSOUDERS, JR.,AND GEORGEGRANGER BROWN,University of Michigan, Ann Arbor, Mich.

T

HE capacity of a frac-

crease in entrainment from that Entrainment in fractionating columns affects tionating column may be plate as c o m p a r e d w i t h t h e the color of the product and the plate eficiency, limited by the maximum plate below. and limits the maximum vapor velocity that quantity of liquid that can be An a b r u p t d e c r e a s e in enwill give satisfactory operation. Using a theop a s s e d d o w n w a r d or by the trainment and corresponding inretical equation and empirically derired conmaximum quantity of vapor that crease in liquid overflow from can be passed upward, per unit a plate m a y be c a u s e d by an stants, a n expression is obtained f o r the maxitime, without u p s e t t i n g t h e increase i n s p a c i n g b e t w e e n mum allowable vapor velocity in a column which n o r m a l f u n c t i o n i n g of the that plate and the plate above. is dependent upon the quantity of entrainment column. The liquid capacity is Similarly, a t the point of introthat can be tolerated according to operating determined by the capacity of duction of an intermediate cold conditions. Values of the constants to be used the weirs and downspouts; but, reflux, there is an increase in if the resistance to the flow of the liquid overflow owing to the f o r determining the capacity of columns for vapor through the plates exceeds decreased entrainment c a u s e d different types of services under ordinary operatthe available head of liquid beby the decrease in velocity of ing conditions are suggested. The effects of tween plates, the normal flow of vapor rising from that plate. intermediate rejlux, the ratio of liquid overflow to l i q u i d is interrupted and the As compared with the normal vapor rising in the column, plate spacing, and column is said to “prime.” The o p e r a t i o n of introducing a l l reflux at the top of the column, vapor capacity is usually below allowable entrainment are discussed so that the the priming point and is limited the use of intermediate cold remaximum vapor velociiy for satisfactory operaflux thus serves to decrease the largely by the quantity of enof fractionating columns under various tion vapor v e l o c i t y , entrainment, trainment that may be tolerated. conditions may be estimated in a fairly satisand liquid overflow of a column For this reason if the column is factory manner. above the point of introduction of good mechanical design and of the intermediate reflux and has adequate liquid capacity, vapor capacity a i limited b y entrainment is the controlling to increase the liquid load a t the plate where the intermediate reflux is introduced. factor determining column capacity. For this reason the probable entertainment in various parts of the column should be considered in calculating the ENTRAINMENT sizes of weirs and downspouts. I n a fractionating column, entrainment signifies the upward The function of a plate is to change the composition of the displacement of liquid particles, from plate to plate, caused vapor rising through the plate. This in turn depends upon by the dynamic action of the vapor. Entrainment may be the fact that there is a difference in composition between the defined as the quantity of liquid carried upward from plate liquid and vapor leaving the plate. Entrainment of liquid to plate by the vapor per unit of time, but possesses little particles in the vapor stream diminishes the effective differquantitative significance unless expressed as a ratio, such ence in composition between the vapor and liquid and deas the quantity of entrained liquid to the quantity of vapor creases the change in composition of the total material (dry rising from a plate per unit of time ( E / V ) or as the ratio of vapor and entrainment) rising through the plate. For these entrained liquid carried upward by the vapor to liquid over- reasons entrainment is a n important factor in limiting the flow from the plate (EIL). fractionating efficiency of a plate. The effects of entrainment in fractionating equipment are largely the impairment of color, loss of liquid overhead as in FACTORSDETERMININGENTRAINMENT oil absorbers, increase in the quantity of liquid flowing from Entrainment may be regarded as the result of two distinct plate to plate due to abrupt changes in vapor load, and deeffects of the flowing vapor, the actual carrying of droplets crease in plate efficiency. The effect of entrainment on color is most important in by the rising vapor and the throwing of liquid particles by flash jugs or chambers without fractionating plates since a the dynamic action of vapor jets. The first effect is a funcsmall quantity of dark residual material may have a rela- tion of the mass velocity of the vapor, the densities of the tively large effect on the overhead material. I n fractionat- liquid and vapor, and the diameter of the particle which in ing columns where several plates separate bottoms and turn is influenced by the surface tension of the liquid, density overhead, the effect of entrainment on color is less important of the vapor, and agglomeration of individual particles into since each plate acts as an entrainment separator, and the larger masses. The entrainment produced by the throwing dark material is progressively diluted by the liquid overflowing of liquid particles is a function of the kinetic energy of the vapor jets, which, in turn, depends upon the density and the from plate to plate. By a material balance it is clear that the liquid overflow linear velocity of escape of the vapor, and is closely related to the spacing between plates. from a plate must be equal the sum of the quantities-vapor, Because of the complex nature of relationships between liquid entrained from the plate below, and liquid overflow from the plate above-less the vapor and entrainment these numerous variables and the limited amount of quantitacarried to the plate above. Therefore the liquid overflow tive data at present available, it is necessary to adopt e l e from a plate is increased by an amount equal to the de- mentary simple relationships between the most important 98

INDUSTRIAL AND ENGINEERING CHEMISTRY

January, 1934

99

TABLEI. OPERATING CONDITIONS OF COMMERCIAL FRACTIONATINQ COLUMNS GENERAL DESCRIPTION Commercial alcohol-water column Commercial presaure distillate rerun column Commercial vacuum column, gas oil overhead Commercial natural gasoline stabilizer Commercial natural ea8 absorber Commercial natural Pas abaorber

COLUMN PRES SUR^ Lb./sq. in. abs. 20 55 0.96"

155 190 465

C b m h e r c i a natural gas absorber Commercial vacuum column, gas oil overhead a 50 mm. b 10 mm. C 20 mm. d 33 mm.

465 0.632d

variables in order to arrive a t a practical solution. I n the following treatment it; is assumed that the mass velocity of vapor upwards through the free space of the column controls the quantity of entrainment in the same manner as the upward mass velocity of any fluid is able to suspend solid or liquid particles, depending upon their density and size.

THEORETICAL SUSPENDING VELOCITY The upward velocity of a fluid required to suspend a body in the fluid stream may be determined from the resistance of the body to the moving fluid and the force of gravity on the body. ,'The resistance of a sphere in a moving fluid is given by the expression (5):

where F , = total force on drop K , k = constants which must be evaluated empirically p = viscosity of fluid D = diameter of particle dz = density of fluid v = linear velocity of fluid relative to drop I n a fractionating column the first term on the right may be neglected, since the viscosity of the vapor is small (0.01 to 0.001 centipoise), so that:

The force of gravity (less buoyancy) on a spherical particle, (3)

where dl g

= =

density of particle acceleration of gravity

When the force of gravity is equal to the resistance t o the moving vapor, the particle remains suspended,

and the suspending velocity,

(4)

If D and k are constants:

v =

linear velocity of vapor, feet per second

Since mass velocity of the vapor W = 3600 vdz in pounds per square foot per hour, W = C[dZ(di - dz)]'/l

(6)

PLATE SPACINQ Inches 12 12 16 16 21 21

24 30

OBSD. C IN SURFACE TENSIONOB MASSVELOCITY LIQUIDON PLAT^ EQUATION Dunee/cm. Lb./ft. X 10-I 60 41 260 235 13 8.9 430 23 15.6 385 9 6.17 400 .. .. .. .. 400 595 630

..

24

16: 4

060 550 635 440 690

where C = a factor depending upon conditions d2 = density of vapor, pounds per cubic foot dl = density of liquid, pounds per cubic foot

PRACTICAL APPLICATION TO ENTRAINMENT Although the value of C in the above derivation is 3600

$$,

Equation 6 is used to include the effects of other variables than the theoretical suspending velocity, which are incorporated in the factor C. The range of sizes of the liquid particles (D) which compose the entrained liquid is a n indeterminate variable. Particle sizes probably are related to the surface tension of the liquid on the plate, since the dispersion of the spray produced by a bursting bubble appears to vary inversely with the surface tension of the film. Increase in density of the vapor also a p pears to promote atomization (3). The tendency for individual particles to coalesce into larger drops which are less readily entrained may be influenced by surface tension, and spacing between plates, or time, which may have a bearing on the probability of collisions between particles. I n addition to the carrying of droplets by the rising vapor, entrainment is produced by the jet action of the vapor caused by the contraction of the path of flow through the bubble caps and vapor-liquid mixture on the plate. The throwing of droplets by vapor jets is related to the density and velocity of the vapor flowing through the slots in the bubble caps and the depth of the "liquid seal." I n general, the penetration of droplets thrown by a jet decreases, and the dispersion increases with increase of the density of the vapor (3). With other conditions constant (velocities, densities, surface tension, etc.), it appears that the entrainment due t o the throwing of droplets should be influenced largely by the distance between plates. Increasing the velocity of the vapor through a column not only tends to increase the height to which droplets may be thrown but also decreases the free space above the vaporliquid mixture on the plate. This effect is due to the vaporlift action of the flowing vapor which raises the froth level as the velocity is increased. For these reasons if the limiting vapor velocity causing entrainment is to be expressed by a simple equation such as 6 , factor C will depend upon surface tension, distance between plates, and the nature of the materials or service conditions. The numerical values to be used for C in Equation 6 can be best determined in an empirical manner. Table I presents operating conditions of a number of commercial fractionating columns operating a t approximately the maximum vapor load compatible with satisfactory products. The operating data include conditions from 0.192 pound per square inch (10 mm. of mercury) to 465 pounds per square inch (0.013 to 32 atmospheres) total pressure, 12 to 30 inches plate spacing, and materials from lubricating oils to natural gasoline. I n each case the value of factor C corresponding to the maximum capacity of the column has been calculated by means of Equation 6.

INDUSTRIAL AND ENGINEERING CHEMISTRY

100

I n Figure 1 the values of C thus obtained from fractionating columns are plotted against the center-to-center distance between the bubble plates. Points where the surface tension pounds per of the liquid on the plates is above 12.7 X foot (20 dynes per cm.) (plotted as circles) define the solid curve; points where the surface tension is less than 20 dynes suggest the location of the dotted curve for surface tension of 6.85 x 10-4 pounds per foot (10 dynes per cm.). The computed values of C for the gas absorbers 702. (Table I) are uniformly lower than c 2 600 for the fractionat8 ing columns. It is possible that part of j 5m9 this difference may be due t o s u r f a c e g 400 9 tension conditions, but these data are -3x 72 d,l not available. Any iwc = 11 entrainment in absorbers r e s u l t s in d; D E N S - " d,-is5 I c u F T . the loss of absorbent oil and contamination of the dry gas; IO 2~ 25 30 35 for this reason, if D PLATES CENTER TO CENTER--INCH(~ for no other, absorbFIGURE 1. EFFECT OF PLATE SPACING ers are operated with much lower mass velocity (1) than other fractionating columns in which limited entrainment can be tolerated. Since the values of factor C expressed in Figure 1 are based on data obtained from the upper or fractionating sections of petroleum columns, these values of C should be modified when applied to gas absorbers and probably require modification when applied to columns or parts of columns which are in different services, such as stripping columns. &o, since Figure 1 represents average maximum operating limits, a factor of safety should be applied to these values of C when they are used for design purposes. Figure 2 is a chart for evaluating the allowable mass velocity of the vapor in a column from the liquid and vapor densities and the value of C obtained from Figure 1, a graphical solution for Equation 6. For example, in a topping column with gasoline overhead, dzis 0.094 and dl is 39.55 pounds per cubic foot, so that dz (dl - dz) is 3.7. With plates spaced a t 24 inches, C (from Figure 1) is 640,. and (from Figure 2) W , the allowable mass velocity of the vapor, is 1200 pounds per square foot of column cross-sectional area, per hour. All material comprising the vapor stream (including products, internal reflux, fixed gases, and steam) should be included when calculating the density of the vapor and the vapor load of the column.

,

BC.0.

= M A 5 5 V E L O C l T I - L B S / S O 'T/HIR. C O N S T A N T , DEPLI?, N G ON DISTANCE B E T W E E N P L A T L S OF L I O V I D - _ B S . / C u

D E N S I T Y OF YIPOR

:'1;.T1 I5 STANCE

FT

1

BETWEEN

QUANTITYOF ENTRAISMENT Data on the quantity of entrainment are meager. I n a semiplant vacuum column with 30-inch plate spacing on a straw oil vapor-liquid system a t 10 mm. and a t 20 mm. total pressure, entrainment was estimated colorimetrically by the use of a nonvolatile dye in the feed t o the column. Although, by plotting quantity of entrainment against mass velocity of the vapor, there was considerable scattering of the points, it was possible to draw a representative curve for each operating pressure. Chillas and Weir (8) reported the quantity of entrainment as a function of the superficial linear velocity of the vapor for an air-water system a t atmospheric temperature and pressure with plates spaced 16 inches center to center, using a constant

lr0I. 26, No. 1

ratio of liquid to vapor. Comparable data on other systems with various plate spacings and reflux ratios are much needed. Comparison between data on the quantity of entrainment obtained under conditions of different liquid and vapor densities, and in different apparatus with different spacing between plates, requires a general equation prope'rly evaluating the effect of these variables. The data of Chillas and Weir on the air-water system and the vacuum column data on the straw oil system were compared using the velocities obtained from the constant, C, corresponding to the different plate spacings (Figure 1) as the basis of the comparison. In Figure 3 quantity of entrainment, expressed as gallons at plate temperature of entrained liquid per pound of dry vapor, is plotted against the ratio of the observed mass velocity to the mass velocity calculated from Equation 6 and Figure 1. Since the quantity of liquid flowing across the plate varied with the mass velocity of the vapor (constant liquid-vapor ratio), the data on the two different systems were also plotted (Figure 4) as gallons of liquid entrained per gallon of liquid overflow against the ratio of observed mass velocity to mass velocity calculated by Equation 6 and Figure 1. Both Figures 3 and 4 show reasonably satisfactory correlation within the limits of accuracy of the experimental data and variations in the mechanical details of the apparatus. More experimental work is required to indicate the effect of vapor-liquid ratio and quantity of liquid flowing across the plate, in order to establish a wholly satisfactory basis of correlation.

01

02

05

,

2

5

10

20

d2(d,-d2)

FIGURE2. CHARTFOR EVALUATING ALLOW~BLE MASS VELOCITY OF THE VAPORIN A COLUMN FROM THE LIQUID AND VAPORDENSITIES, AND THE VALUEOF C FROM FIGURE 1

Although this discussion deals exclusively with plate fractionating columns, it is well to indicate that much greater entrainment may be expected in other types of equipment which do not contain plates or other types of entrainment separating devices. The actual entrainment in a flash chamber of a cracking plant (chamber free of any entrainment separating device) is represented in Figure 3 by the circled point which indicates more than twice the entrainment observed in a plate fractionating tower. The vapor-liquid mixture in this case entered the large chamber through a single pipe at high velocity, and the large kinetic energy of this stream was an important factor in increasing the entrainment over that of a plate column, although the stream was directed against the lower end of the side of the chamber.

ENTRAINMENT AND PLATE EFFICIENCY Defining plate efficiency as the ratio of the actual change in composition of the wet vapor passing through the plate to the change that would take place were the vapor leaving the plate in equilibrium with the liquid overflowing from the plate:

January, 1 9 3 i

I T D U S T R I A L -4UD E N G I N E E R I K G C H E h l I S T K 1

-4d

R A T I O - M L O C I T Y OBSERVED TO VEL CITY CALCD BY E a . 6 W = C [dJd

RATIO-VELOCITY

FIGURE 3 FIGURES

3

4ND

4.

EFFECT OF

\-4POR

(7) where yn

=

Y,+~=

I< 2,

=

=

inole fraxtioii of a component in mixmre of vapor anti entrained liquid rising from plate n mole fraction of the same component in the mixture of vapor and entrained liquid from plate below plat'e n equilibrium constant (4)-i, e., the ratio between mole fraction in dry vapor and mole fraction in liquid under equilibrium condition3 mole fraction of same component in liquid overflowing from plate n

From a inaterial balance around plate n, assuming L and V t o be constant:

to plate per unit of time 1- = total nioles of mixture of vapor and entrained liquid rising from plate t o plate - = mole fraction of same component in liquid overflowing from plate above

whereL

where T"

E

= total nioles of liquid overflowing from plate

T7 = V' + E (10) total moles of dry vapor rising from plate to plate per unit of time = total moles of entrained liquid carried with dry vapor from plate to plate

VELOCITY OU

101

OBSERVED TO VE CITY CALU).BY E P . 6 W-C[d,U, - -4% .

FIGURE 4 Q U ~ \ T I T YO F E U T R I I \ J f E N T

nhere f = a factor nhich iepresnts the degree of approach towaid equilibrium betn een dry vapor and liquid overflow leaving the plate, and is dependent upon a large number of variables including the mechanical design of the plate T h e symbol, f , should not be confused with plate efficiency as defined b y Equation 7 . Therefore

T'y,

+ Exn

= T"j K x , = x1,[VKj'-

E(Kf - l)]

and from Equations S and 12, VY,+ 1 xn[VKf - E(Kf - 1) I - L(xn - I - xu)

(12) (13)

Combining Equations 9 and 13,

F~~plates above the feed plate, Lx,-i Vy, - D X D D = V - L where D = total moles of withdrawTn from column above plate n ZD = mole fraction in composite overhead materials

=

Under actual conditions when equilibrium between liquid and d r y vapor m a y not be attained, t h e actual mole fraction of t h e component in t h e d r y vapor may be expressed b y t h e equation:

A similar derivation for plates below the feed plate,

+

where Lx, - = Vyn B ~ B B = L - V B = total moles of materials u-ithdrawn from column below plate n xg = mole fraction of same component in composite materials drawn below plate n leads to t h e equation:

102

INDUSTRIAL AND ENGINEERING CHEMISTRY

Thus the general equation for the effect of entrainment on plate efficiency becomes: K(1 e = l K

-fl

-3 2"

+ E5 (Kf - 1)

(1

L - 7)

- pL

Vol. 26. No. I

This is found to be the case, and the relative maximum vapor velocities or capacities from actual plant operation for different services are indicated on Figures 3 and 4. These relative velocities are for average conditions and are subject to variations in liquid-vapor ratio, mechanical design, and other factors which may control entrainment or the allowable quantity of entrainment. It has been assumed in the application of Equation 21 and Figure 5 that E/V is independent of L / V . Actually there is

where x p = composite mole fraction in products withdrawn either (a) above plate n for plates above feed plate or (b) below plate n for plates below feed plate Equation 17 may be simplified for special conditions, such

as: Equilibrium plate with total reflux: f = 1, and V / L = 1 e = l-E/V

(18)

Total reflux and no entrainment:

Top plate of a column where the reflux has the same composition as the overhead distillate-i. e., xn - = yn: 1 - E/V e = (20) E + EV ( K - Kf)+ 1 - UKf - 1) V L And for a top plate which is an equilibrium plate-i. e., f = 1: 1-v e = Using Equation 21 for the equilibrium top plate of a column and the straw-oil curve of Figure 3 for the quantity of entrainment to compute E / V for different relative vapor velocities, Figure 5 was constructed giving plate efficiency as a function of relative mass vapor velocity for various values of L/V. From Figure 5 it is clear that plate efficiency may be maintained constant with a greater mass velocity (greater entrainment) if the value for L/V (ratio of liquid overflow to vapor) is increased accordingly, and if E/V is substantially independent of L/V. The ratio L/V (liquid to vapor) in gas absorbers is much lower than in fractionating columns, usually about 0.2 in high-pressure absorbers. Under such conditions high vapor velocities might cause large decreases in plate efficiency. This is possibly another reason for the lower vapor velocities used in gas absorbers.

COLUMNCAPACITYDETERMINED BY ALLOWABLE ENTRAINMENT The relationship between plate efficiency, liquid-vapor ratio ( L / V ) , and relative mass velocity of the vapor as plotted in Figure 5 indicates that the probable maximum vapor load or capacity for satisfactory operation as based on plate efficiency varies more or less directly with the liquid-vapor ratio, L / V . Therefore it is to be expected that fractionating equipment may be operated satisfactorily a t higher capacities when the ratio of liquid to vapor ( L / V ) is larger. Thus, greater mass velocity might be tolerated in the stripping sections of stabilizers or steam strippers than in the rectifying sections of the same columns. Similarly, the permissible mass velocity would be greater a t the top of a topping column than at plates immediately above the feed plate, and the upper part of a topping column would be operated with greater mass velocity of the vapor than the upper or rectifying part of a column for stripping natural gasoline from absorbent oil.

RATIO- VCLWTY

OBSERVCD TO VE CITY CUR w-c[d&,-dJ~

BY EO. e

FIGURE 5. EFFECTOF VAPORVELOCITYON EFFICIENCY OF TOP EQUILIBRIUX PLATE

some evidence that E/V may increase with increasing values for L / V . If this effect is appreciable, i t will tend to minimize the differences in maximum capacity for the different services. The allowable quantity of entrainment may be limited by considerations other than plate efficiency, such as color impairment of overhead or loss of liquid in vapors, and may vary from point to point in a single column. As has been pointed out, the introduction of cold intermediate reflux decreases the entrainment and vapor load in the column above its point of introduction as compared with the introduction of all of the reflux a t the top of the column. The allowable entrainment a t the top of the column is usually the factor controlling the capacity of the column rather than the entrainment a t some lower part, such as below the point of introduction of intermediate reflux, because the entrainment in the top part of the column controls the quality of the overhead product. For this reason the removal of heat from the column a t an intermediate point, as by the introduction of cold intermediate reflux, increases the capacity of the column although a t a loss in effectiveness of fractionation. If overhead side streams are removed from the column below the point of introduction of cold intermediate reflux, the effect of entrainment on such side streams must be considered, as the allowable entrainment below such side stream may be the factor limiting column capacity. If cold intermediate reflux is not used, the allowable entrainment a t the top is usually the controlling factor even when side streams are removed, because the maximum vapor load in such a column is usually just below the top plates.

103

Phase Equilibria in Hydrocarbon Systems I. Methods and Apparatus BRLIXLI. SAGEAIW WILLIAMN. Lactry, California Institute of Technology, Pasadeoa, Calif.

A

KXVOWLEIXE OS tlii: behavior Of coindex drocarbon systems under equilibrium conditions cornsponaingtotiiosefollnl~in iiIlder. ground peiroleurn reservoirs is of p r i m a r y i n i p o r t a n c e to t!ir petroleum proditction tcclitiolw

Apparatus arid methodv for studies of phase quilibria in hydrocarbon mixtures at pressures up to 200 atmospheres in the temperature range from 20" to looy (2. are described. The ddn obtaimd permit lhe prediction of the density, camposition,, an,d relalire mass of each phase present lohen ,,liz.are ofuny total is brought to equilibrium at any set of temperalure and pressure conditions wifhin the rurtge studied. Subseiiuent arlicles of lhis series icill presenl dalafor 60th simple and complr:?rnidnrcs. ~~

\.ls~suitlnie?iTOF ENTERING hf.4TElilALs

llelatively rlonvolatile liquids w w m e a s u r e d by weighing a suitable container before and after pouring tlie sample into t,lhe equilibrium vessel. The latter was then closed and congist. The simpler exnmples of netted for If the liquid such systeiiis are also of interest froln tilc jrlii.clg scie,,tific ljoil,t a pure of volatile i,imracter, a portion of it was of view. ilistilled into the equilibriuni Tlie ai111of t,liis rvork n a i to vessel f r o m a weighed confollow the behavior of gaseous and liquid p1iai;es prcaent in taiiier. I'olatile complex liquids equilibrium at timperatiircs rmgiiig Sboiu 20" to 100" C. were i:oaied to a sufliciently low temlxrature to be handled (68'P. to 212' F.) and at preisiires from I to 2%) :stinosp!ieres by tibe inetliotl i i s c d for notivolatile liquids. Gases entering t i l e system were. measured Og willidraarving (approximately 15 to :joO() pounds per aquzrc incii absolute). constant volunle and nptjng I n order to ascertain completely the state of the system, from a calilratetl reservoir measurements of the density, voluine, an11composition of encli the resulting drop i n pressure. The sample bomb cOtitalNng of the pliases present ware required. These tncaiurements the gas supply was heated in a rlietliylene glycol bath to a were made over a series of temperatures, pressures, and total sufficiently high temperature to insure complete vaporizacompositions in order that tlip effect of these variables miolil. tion. That the temperature used was high enough could he verified by d e t e r !)I: determined. mination of the dew The equilibriuni point of the gas at method uscd in this the pressure eltistwork resolved itself ing in the sample into the following bomb, as described steps: the measurebelow. T h e pa8 ment of the amount was then admitted, of an original liquid through heated tubphase placed in an ing l i n e s , t o t h e equilibrium vessel, reservoir bomb in a the measurement of d i e t h y l e n e glycol a series of quantities bath carefully therof gaseous materinl mostatrd at 100.0' m d their quant.itaC. The reservoir tive compression was so calibrated into the e q u i l i b that the quantity of r i u m vessel, the gas in it was !mown attainment of for any given pree e q u i l i h r i u m , rand sureup to a maxithe determination mum of a h o u t 20 of the state of the atmospheres. The system after each c a l i b r a t i o n was a d d i t i o n o f maF K X ~1.E C o i r ~ ~ e s sAKD o ~ CONTHOL PANBL made for each gas terial.