Apparatus for Accurate, Rapid Determinations of the Solubilities of Gases in Liquids at Elevated Temperatures Peter M. Cukor and John M. Prausnitz* Department of Chemical Engineering, University of California, Berkeley, Calif. 94720
An apparatus has been developed for measuring the solubilities of gases in liquids at pressures in the vicinity of 1 atm over the temperature range 25-200°C. Equilibrium compositions are determined from the total gas pressure and from a material balance. With careful operation, this apparatus can yield solubilities accurate to about 1%.
Thermodynamic properties of gases dissolved in liquids are often required in the design and operation of industrial processes, particularly in the petroleum industry. For many systems of commercial interest solubility data have been reported a t temperatures near 25°C ; however, numerous industrial processes operate at higher temperatures. Unfortunately, few measurements of gas solubilities a t elevated temperatures appear in the literature. Scarcity of gas-solubility data a t higher temperatures is due, in part, to experimental difficulties in measuring the pressure of a gas in equilibrium with a volatile solvent. We describe here a new apparatus for determining the solubilities of gases in liquids with speed and accuracy. The apparatus may be operated a t temperatures ranging from 25 to 200OC. The solubility apparatus shown in Figure 1 is similar t o that described by Dymond and Hildebrand (1967) for solubility measurements a t ambient temperatures. The central part of t'he apparatus consists of two bulbs, A and B, having volumes of approximately 280 and 120 cc, respectively. The bulbs are connected directly by a 1/4-in. tube and also b y a side arm, C, which cont'ains a metal-inglass plunger. The plunger, operated magnetically, pumps the liquid from A through the side arm to B. Two glass valves in C reduce the backflow of liquid into A. The volumes between stopcock GI and mark b and between mark b and the stopcock a t D were determined by weighing wat'er displaced from these volumes. The dotted line represents a thermostated bath whose temperature is controlled to better than 10.05OC. The bath fluid is a silicone oil, Dow Corning 200 Fluid, 100 cSt viscosity. This liquid is satisfactory for the temperature range 25-200OC. Capillary tubing, H , leads to flask E which cont'ains the pure solvent. E can be removed from the system to facilitate filling by means of two ball and socket joint connections. (All ball joints in the apparatus are fitted with Viton O-rings t o eliminate contamination of the solvent wit'h grease. All high-vacuum stopcocks through which the solvent passes are made of Teflon and are manufactured by either Westglass Corp. or Fischer and Porter Co.) Flask I serves as a reservoir of fresh solvent, and can easily be removed for weighing during operation. Gas buret J is naterjacketed and contains three chambers each having a volume of approximately 40 em3 and four chambers of approximately 638
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10 cm3 volume each. A 10-cm3calibrated buret, K, is used to balance the pressure inside the gas buret with atmospheric pressure transmitted through open tube L. 1Ianometer R4, 80 cm high, is used during the filling of the buret to indicate when the gas pressure is about 1 atm. hlercury for displacing gas pressure is about 1 atm. Mercury for displacing gas from the buret is stored in reservoir R. Pressure M e a s u r e m e n t
T h e accuracy of our solubility measurements depends on accurate measurement of t'he equilibriu'm pressure in bulb B. Both the undissolved solute gas and the solvent vapor cont,ribute to this pressure. It is, therefore, necessary to measure the pressure with a device whose temperature is a t least' as large as t,hat of the solvent in the thermostated bath; if vapor from bulb B is cooled below its dew point, some of the solvent vapor condenses inside the pressure-measuring device, thereby invalidating the results of the experiment. Our pressure-measuring equipment , manufactured by Texas Instruments, Inc., is shown in Figure 2. H o t vapors from B are conducted along quartz capillary tubing P, which is wrapped with nichrome heating wire and several layers of asbestos tape. The tube temperature is approximately 235°C. This t'ube leads to a fused-quartz Bourdon tube enclosed in a Vycor envelope. This high-temperature pressure capsule is mounted in a furnace whose temperature is coiit,rolled a t 235°C. -1 light beam, reflected off a platinum mirror att,ached to the end of the I3ourdon tube, st'rikes a pair of matched photocells located in the null detector. When the vapor is conducted into the Bourdon t,ube, the tube deflects, unbalancing the null detector. The null-detector error signal activates a servo-operated pressure controller which raises or lowers the pressure in the Vycor envelope surrounding the Bourdon t'ube. Since the deflection of the tube is proportional t o t'he difference in pressure across the tube, as t'he pressure outside the tube approaches the pressure inside the tube, the deflection approaches zero. The two outputs of the controller are in parallel and hence the pressure read by the precision pressure gauge is the same as that which balances the high-temperature l3ourdoii tube. The pressure supply to the controller is dry nitrogen; hence, there is no problem with condensation when measuring this balancing pressure.
S
AR
Figure 1 .
M
Solubility apparatus
VENT SOLUBILITY APPARATUS
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VENT PRECISION PRESSURE GAGE
4 REG U LATO R FILTER
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HIGH TEMP E R ATURE CAPSULE
HEATER
l l O V AC
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PROPORT I ONAL TEM PER AT URE CONTROLLER
Figure 2.
Measurement of pressure on condensable gases
The precision pressure gauge operation is similar t o that of the high-temperature null detector. The nitrogen output from the pressure controller is conducted into a second fusedquartz Bourdoii t,ube. This capsule is maintained a t 44OC. The envelope of the capsule is evacuated t o less than 1 p . Photocells mounted on a turntable sense deflections of t’he Bourdon tube using a n optical system as discussed above and send an error signal t o a servo amplifier. The amplifier output activates a motor which rotates the turntable until a null condition is reached. The angle of rotation of the turntable from the iiull position is read oi1-a digit’al counter to 1 part in
100,000. Calibration of the pressure readings is achieved using a dead-weight gauge. This method for pressure measurement is accurate to within 10.002% of the full-scale rating of each.of the pressure capsules used, which in our syst’em was 1000 Torr. Hence our pressure measurements are accurate to within 1 0 . 0 4 Torr. An advantage of this pressure-measuring system is that the volume of the high-temperature Bourdon tube is only 0.5 cm3; therefore the “dead apace” is held to a minimum. Furt,her, the controller operation is automatic and as a result the gas pressure may be observed continuously until the Ind. Eng. Chem. Fundam., Vol. 10, No. 4, 1971
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pressure remains constant, indicating that equilibrium has been attained. Procedure
Valves 1 and 4 in Figure 2 are opened and the photocells in the null detector are positioned such that the error signal as read on a microammeter is zero. Valves 1 and 4 are then closed, valves 2 and 3 are opened, and the entire apparatus is evacuated. Mercury from reservoir R is allowed to flow into the gas buret until the menisci in both tubes are level with the calibration marks and the calibrated tube is about half full of mercury. Purified gas enters the buret through taps S and T until the pressure indicated b y manometer M is about 1 atm. The mercury height in tube K is adjusted until the gas pressure is exactly atmospheric and the number of moles of gas in the buret is calculated. Purified solvent in E is degassed by repeatedly freezing in liquid NZ, pumping on the frozen solvent, melting the solid, and refreezing. Unless the solvent is completely degassed solubility measurements will be highly inaccurate. The solvents used in this work were so involatile that it was necessary to heat the liquid in order to drive i t through tube H into A. Sufficient solvent is added to bring the liquid level substantially above the calibration mark b. Stopcock Gz is tightly closed and the solvent is circulated until it has cooled to the bath temperature. The bath temperature may be set a t any point where the solvent densit,y is vel1 known. Stopcock G3 is closed and GI and Gd are opened allowing the solvent to flow into flask I until t'he meniscus in A is level with the calibration mark b . GI, Gq, and G j are closed, Gs and Gg are opened, and the flask is removed and weighed to within 0.001 g. The bath temperature is raised to the highest value for which a solubility measurement is t o be made. The solvent in A has now expanded. Flask I is attached, the space between taps G7 and GI is evacuated, and solvent is again removed from A until the meniscus is level with the mark at b. I is again removed and weighed t o calculate t'he quantity of solvent remaining in A. (As t'he temperature of the bath is decreased during a given run, fresh solvent from I is added to A to maintain the liquid level at. b. Each time solvent is added the flask is weighed and the number of moles of solvent in A is calculated.) Gas from the buret is sloivly added t o B b y pushing on the gas with mercury from reservoir R. As the gas pressure in B approaches 1 at'm, as read on the precision pressure gauge, the gas is shut off and the mercury height in K is again adjusted urit'il the pressure of the gas remaining in the buret is equal to atmospheric pressure. The number of moles of gas added is then calculated from the difference between the initial and final buret readings. The motor is turned on and the solvent is circulated from A into B at a rate of about 5 cm3of liquid/sec.. I n this manner no bubbles of gas form in the liquid in A. The pressure i n B is monitored periodically until a constant value is obtained. For the systems studied here equilibrium was attained in 2 hr or less. More gas is added and the system is reequilibrated so as t o check the first measurement for the attainment' of equilibrium. For very soluble gases this procedure also serves t o test the applicability of Henry's law. The bath temperature is then lowered to the next desired point, solvent from I is forced into A by heating the flask until the liquid level is a t b, and the liquid is circulated until equilibrium is attained. Solubility measurements a t various temperat'ures may only be made b y going dowirvard from t'he highest temperature desired. This results from the 640 Ind.
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C
Figure 3. Solubility of methane in n-hexadecane at 1 atm partial pressure
necessity of maintaining the solvent level at b so that the gas volume is always known. Once the liquid in A comes into contact with gaseous solute it must never be removed from the apparatus until a set of solubility determinations has been made. This results from the strong dependence of solubiljty on the pressure. Since there is only one volume calibration mark (at b) , corrections for gasified liquid removed from B cannot be made accurately. Hence i t is necessary t o add pure, degassed solvent from I at a series of decreasing temperatures. Typical Results
The solubility (mole fraction) of methane in n-hexadecane at 1 a t m partial pressure is shown in Figure 3. Detailed results and a discussion of solubilities for nine systems over the same temperature range are given by Cukor (1971) and Cukor and Prausnitz (1971). Acknowledgment
We especially wish to express our gratitude to Locke Yow for his diligence and skill in constructing the solubility apparatus and to Reginald Powell for his observations regarding the operation of the high-temperature Bourdon tube. Keith Xiller and R. G. Linford assisted in the design of the apparatus. Literature Cited
Cukor. P. A I .I Dissertation, University of California, Berkeley, Calif., 1971: Cukor, P. M., Prausnitz, J. M.,submitted for publication in J . Phys. Chem.
Dymond, J., Hildebrand, J. H., IXD.ENG.CHEM.,FUNDAM. 6, 130 (1967).
RECEIVED for review March 4, 1971 ACCEPTEDJuly 12, 1971 The authors are grateful to the donors of the Petroleum Research Fund and to the National Science Foundation for financial support.
