- Email: [email protected]
New detection method for determining phase boundaries
253
Fluid Phase Equilibria, 65 (1991) 253-261
Elsevier Science Publishers B.V.. Amsterdam
New detection
method for determining
phase boundaries
Rosa Crovetto * and Robert H. Wood Department (U.S.A.)
of Chemistry
and Biochemistry,
University
of Delaware,
Newark,
DE
19716
(Received November 10, 1990; accepted in final form January 23, 1991)
ABSTRACT Crovetto, R. and Wood, R.H., 1991. New detection method for determining phase boundaries. Fluid Phase Equilibria, 65: 253-261.
Modifications in the electronics and experimental set-up of the vibrating tube densimeter (Wood et al., 1989. Rev. Scientific Instruments, 60(3): 493-494) allowed the development of a new detection method for determining phase transitions. The method uses the sharp drop in the amplitude of vibration of a vibrating tube when phase separation occurs. The new detector should be especially useful at high temperatures and pressures where other methods are more difficult to use. Combining phase equilibria detection with conventional density measurements allows the vibrating tube to be used to explore P, V, T, and x at phase boundaries. The experimental procedure and set up are presented together with results from measurements of the vapor pressure of both water and aqueous NaCl solutions. The reliability and estimated accuracy of this method for determining vapor pressure is about &0.4%.
INTRODUCTION
An accurate knowledge of the phase equilibria boundary of pure components and/or mixtures is not only a matter of fundamental scientific interest. It is very important for tests of proposed equations of state (EOS), pair potentials, mixing rules, etc. It is also of great practical importance for geochemistry, for power generation and for many chemical engineering processes. There are two recent reviews on high pressure PVT data and phase equilibria measurements (Schneider and Deiters, 1986; Holste et al., 1986). * Present address: Department Boulder, CO 80303-0215. 0378-3812/91/$03.50
of Chemistry and Biochemistry, University
0 1991 Elsevier Science Publishers B.V.
of Colorado,
254
We refer the reader to them as a general discussion of the available methods and techniques. The well-known PT vapor-liquid coexistence line of pure water was used to test the behavior of the phase detector and to establish the best experimental procedure to follow. The performance of this new detection method was then assessed with measurements of bubble points for pure water and for sodium chloride solutions. It seems likely that many other kinds of phase separations can also be detected and measured in a similar way.
EXPERIMENTAL
When measuring the densities of aqueous alkali metal salt solutions with the modified vibrating tube densimeter (Majer et al., 1991a), it was observed that the amplitude of the vibration changed when either there was a large change in viscosity of the fluid or the tube contained two phases. For our apparatus, the appearance of a liquid-gas transition in the fluid produced a maximum decrease of about S-10% in the amplitude of the pick-up signal at constant drive power. For ease of observation the amplitude differences between a constant base line and the rectified and amplified pick-up signal was displayed on a strip chart recorder. The schematic representation of the flow circuit used in these measurements is shown in Fig. 1. The basic system, including the vibrating tube densimeter, its housing, and the other auxiliary equipment, were the same as described by Majer et al. (1991b). The original Heise manometer was changed for a more accurate Paroscientific transducer which, when inter-
Fig. 1. Schematic representation of apparatus and set-up A, Constametric HPLC pump; B, 6 cm3 injection loop; C, Paroscientific Digiquartz manometer; D, vibrating tube and its housing; E, and E,, Circle Seal BPR 21 series back pressure regulators; 1, Rheodyne 7010 HPLC six-port injection valve; 2, needle valve for decreasing pressure in the system; 3, pre-pressurising valve.
255
(4 0.10
(b) AA 70 -2
I
i‘
pd
Fig. 2. (a) Schematic representation of a typical time evolution of the pick-up amplitude, A, of the vibrating tube plotted as (A - A”)/Ao = AA/A’, where A0 is an arbitrary constant. In this experiment the needle valve 2 was opened and AA/A0 was followed as a function of time. The noise level, O.l-0.2%, is not shown. The height of the shaded area shows typical amplitude increases after arresting the pressure drop. (b) AA/A0 vs. P, the steady state pressure, for small changes in the amount of fluid in the tube. Note that P increases towards ) withdrawal. For definitions of Pi and Pd, see the left. (- - -) infusion of fluid; (text.
faced with an external frequency counter, could provide automatic pressure data logging. (Alternatively, the fluid pressure could be increased by forcing small amounts of fluid into the system with the pump A.) A T-connection ending in a needle valve, 2, was added after the densimeter’s outlet and before the back pressure regulators. (The needle valve allowed fine control of the system pressure by bleeding small amounts of fluid from the pressurized system.) A phase transition in the fluid can be produced by changing the variables P, T or x individually or in combination. For this apparatus an efficient technique was to maintain constant fluid composition and block temperature and to effect a phase change adjustment by carefully adjusting the pressure. Figure 2(a) shows the variation in the de&meter’s pick-up signal amplitude during experiments in vyhich the needle valve was opened, and a continuous decrease in the fluid pressure resulted. In all cases, there was a sharp drop ( = 10%) in amplitude when a second phase appeared, followed
256
by a gradual rise ( = 25%) to a plateau where only the gas phase was present in the tube. The larger vibrational amplitude of the tube when it was filled with gas was presumably due to the lower viscosity of the gas. In the case of a phase separation, the presumed cause of the drop in amplitude is the presence of two phases. If so, we can infer that the magnitude of the observed decrease in the amplitude is related to the relative quantity of the two phases present. Figure 2(b) shows the amplitude plotted as a function of steady-state pressure for experiments in which small withdrawals or injections of fluid were made to change the fluid pressure, which was then read after re-equilibration ( = 20 min). These experiments show a definite hysteresis effect. When making bubble or dew point measurements it is important to try to keep the newly generated phase as small as possible, especially with mixtures, so as to alter the concentration of the initial phase as little as possible. This is done by halting the pressure drop as soon as a detectable amplitude decrease has been observed (the shaded area in Figs. 2(a) and 2(b). The vibration of the tubing at 140 Hz, with an amplitude of about 0.1 mm, should help equilibration by providing some stirring action, and it may help promote nucleation of bubbles. There are important kinetic and thermal effects in any phase separation experiment. They must be carefully considered and examined, especially when working under nearly static conditions and without proper stirring. These include supersaturation and overheating when condensing, and supercooling and undersaturation when evaporating, which are commonly observed with different techniques. In order to assess the magnitude of these problems in the present apparatus, the reproducibility of the pressure at which phase appearance and disappearance occurred was studied using pure water as a test fluid. A typical run for water started with water flowing in the apparatus at 0.1-0.2 cm3 min-’ and at a pressure of 5-10 bar above its vapor pressure. The flow was stopped and by carefully and slowly opening valve 2, the rate of pressure decrease was adjusted to a desired value, and the amplitude was recorded. At this point, the noise level in the amplitude was about 0.1%. When the amplitude dropped by 1 to 3% (the shaded area in Figs. 2(a) and (b)), valve 2 was closed and the corresponding pressure value was noted. The pressure then slowly increased to a steady-state value in the next lo-20 min. This pressure was reported as the “steady-state” phase boundary pressure for decreasing pressure (Pd) (see Fig. 2(b)). Next, the system pressure was increased by injecting a small volume of fluid with the pump, at a flow rate of less than 0.1 cm3 mm-‘. The pump was stopped when the pick-up signal increased to more than 5 times the noise level. After lo-20 min, the pressure and amplitude generally came to new steady-state values. These pressure
257
adjustments were repeated until the steady-state amplitude was equal to or higher (within the noise level) than the amplitude that was observed earlier just before the appearance of the second phase during the decreasing pressure experiment. This pressure was taken as the “steady-state” pressure for phase disappearance with increasing pressure (Pi) (see Fig. 2(b)). The above procedure was repeated again by injecting a new water sample into the system as before. It was found that Pa was always smaller than the corresponding literature values for the vapor pressure of pure water, PO.The velocity at which the pressure was changed played a very important role in determining Pd.With rapid pressure changes, the difference between Pd and P" increased, presumably owing to the lack of thermal equilibration. With very slow pressure changes (0.2-0.3 bar mm’) the experiments took longer and did not yield higher accuracy. There appeared to be an optimum velocity which could potentially be different for each fluid. In our experiments, values obtained for Pd at near optimum rates were -0.25 to -0.88% smaller than PO.In contrast, Piwas always bigger than Pd,almost always bigger than PO,and less dependent on the velocity of the pressure increase. The observed difference, Pi- PO,varied from -0.2 to 2%. The greater spread in differences between Pi and P" reflects the greater experimental difficulty in measuring Pi.For pure water, the pressure average Pay= (Pd+ Pi)/2gave the best agreement with the best literature values for the vapor pressure of water, P" (Haar et al., 1984). The hysteresis shown in Pig. 2(b) and the resulting difference between Pi and Pd could be caused by temperature changes due to the latent heat of phase change followed by slow thermal equilibration, slow nucleation, and slow bubble dissolution, all of which give rise to effects of opposite sign in Pd and Pi. For water, we measured bubble points as described above, and also one dew point (Table 1). For the dew point, measurements were begun at an initial pressure about 5 bar below the vapor pressure of water at the measured block temperature. As with the bubble point experiments, the pressure of phase appearance, Pi,was determined by slowly increasing the pressure. This was followed by a measurement of the pressure of phase disappearance, Pd,established by slowly decreasing the system pressure. Within the experimental error, the measured dew point and bubble point were equal, but the difference Pi- Pd was somewhat higher than for the bubble point measurements, once again because of increased uncertainty associated with vapor-phase measurements. To measure a solution vapor pressure, a solution of known concentration was introduced into the system using the injection valve 1 with a flow of 0.2-0.3 cm3 min-’ . The measurement procedure from there on was the same
TABLE 1 Measured vapor pressure of pure water T W)
PaV(MPa) a
A (MPa) b
P” (MPa) ’
Sd
325.17 333.57 333.80 341.23 344.56 344.71 e 347.04 349.72 349.73 349.73 349.75 349.75 349.78 349.91 349.93 350.28 350.28 350.28 350.28 350.28 350.28 362.91
12.05 13.44 13.44 14.79 15.44 15.49 15.90 16.60 16.47 16.59 16.58 16.52 16.54 16.56 16.45 16.64 16.65 16.59 16.53 16.52 16.47 19.28
0.01 0.09 0.03 0.04 0.06 0.46 0.01 0.27 0.12 0.29 0.24 0.18 0.16 0.17 0.05 0.19 0.28 0.21 0.21 0.20 0.04 0.01
12.07 13.45 13.49 14.82 15.45 15.48 15.93 16.47 16.47 16.47 16.47 16.47 16.48 16.50 16.51 16.58 16.58 16.58 16.58 16.58 16.58 19.32
-0.17 - 0.07 -0.37 - 0.20 - 0.06 0.07 -0.19 0.79 0.00 0.35 0.67 0.30 0.36 0.36 -0.36 0.37 0.43 0.06 -0.30 - 0.36 - 0.66 - 0.21
aP,” = (Pi
+ Pd)/2. bA=(Pi-Pd)/2. ’ P” = pure water vapor pressure from Steam Tables (Haar et al., 1984). d 6 = lOO(P,” - PO)/PO. e Dew point. All other measurements are bubble points.
as that for water. Each 6 cm3 of injected sample allowed 3 to 4 different measurements of the bubble pressure with fresh solution. The variation of the fluid density with pressure exhibits a discontinuity in the slope with the appearance of a second phase. The period of vibration is related to the density by Ap=K(r2-r;) where p is the density, K is the calibration constant and T is the period of vibration. For detecting a change in the number of phases, measuring the period of oscillation as a function of pressure was not as accurate, reproducible or rapid as measuring the amplitude change with the present apparatus. Sudden irreversible shifts in frequency sometimes occur when the pressure is varied so discontinuities in period vs.. pressure might be observed.
259
Also, experiments using period measurements are much slower because the period of vibration must be averaged over one minute of sampling to achieve the necessary accuracy. As a result the pressure variations must be much slower in order to get representative period readings. The temperature was measured in the block that housed the vibrating tube with a calibrated Bums thermometer (accuracy of about 0.1 K). The constancy of the temperature was fO.O1 K. At 623 K the variation of the vapor pressure of pure water with temperature was about 0.19 bar/O.1 K, so that our temperature imprecision of 0.1 K will translate to about a 0.2% error in the vapor pressure of water. The pressure was measured with a Paroscientific Digiquartz manometer with a manufacturer’s calibration accuracy of 0.01% of full scale (41 MPa). The water used was deionized and degassed. NaCl was Fischer Scientific ACS. Solutions were made by weighing the dried salt and the water. The accuracy in concentration was 0.1% for the 1 mol kg-’ NaCl and 0.03% for the 3 mol kg-’ NaCl solutions, respectively.
RESULTS
Table 1 gives the measurement of vapor pressure for water at different temperatures presented as Pav and A, where A = (Pi - Pd)/2. The vapor pressure of water P” and the deviation of the present measurements from
TABLE 2 Vapor pressure for NaCl(aq) A (MPa) b
P (MPa) ’
0.15 0.02 0.23 0.28 0.17
14.83 14.83 14.83 14.83 14.83
-
0.22 0.10
15.91 15.91
- 0.25 - 0.60
m = 3.0 mol kg-’ 349.97 14.89 349.97 14.79 349.97 14.74 349.97 14.80 349.97 14.77 m = 1.0 mol kg-’ 349.94 15.87 349.97 15.81
0.40 0.27 0.61 0.20 0.41
a P,"=(Pi+ Pd)/2. bA=(Pi-Pd)/2. ’ Literature values for the vapor pressure of the solution at 623.15 K (see text). For 3 mol kg-’ NaCl there is about a 1% scatter in the vapor pressure measured in different laboratories; for 1 mol kg-’ the scatter is about 0.3%. dS=1OO( Pa,- PO)/PO.
260
P” are also given. Our average deviation of a single measurement literature value, calculated as
from the
(2) is 0.32% and the reproducibility of individual measurements is normally around + 0.4% (occasionally + 0.7%). In Table 2 we present the results obtained for the salt solutions at an almost constant temperature, near 623 K. Table 2 gives Pa,, A, the literature value and the corresponding deviation from the literature value. The reproducibility of measurements is about +0.5%. Literature values have been taken from a smooth curve through the results of Bischoff and Pitzer (1989), Olander and Liander (1950), Khaibullin and Borisov (1966) and Valyashko et al. (1986), with more weight given to the more recent compilation of Bischoff and Pitzer. The tables show that the results given by the presented detection method are in good agreement with previous results.
CONCLUSIONS
This new detection method for phase boundaries is quick and reasonably accurate for measuring the vapor pressure of solutions at high temperatures. It can be easily automatized and used for on-line operation. Much faster measurements are possible if accuracies of 2 to 5% are adequate. It is not known yet how close to a critical point a measurement can be taken with reasonable accuracy. Near a critical point the densities and viscosities of both phases will approach each other, equilibration will become very slow, and there will be density fluctuations caused by the vibration of the fluid. Every method for determining phase transition boundaries has different advantages and disadvantages. With this technique, we have all of the advantages of a flow system, allowing one to change the samples under study quickly and easily, and minimize the residence time in the high-temperature zones of the densimeter, reducing the rate of decomposition and corrosion. It is also possible to produce the phase separation at constant temperature and composition by increasing and decreasing the pressure of the system. Finally, the problem of getting a representative sample is avoided and the method is faster than static vapor pressure measurements. However, the overall accuracy is not the best that can be achieved. A disadvantage of the present design is that the internal diameter of the capillary tube leading to the vibrating tubing is small (0.24 mm), leading to
261
potential experimental and safety difficulties associated with the inadvertent formation of a solid phase in the capillaries. Unfortunately, it is nearly impossible to dissolve the plug and clean the thin capillary again. For this reason equilibria involving solids might be studied more conveniently in capillaries of higher internal diameter. When a solution of unknown vapor pressure is being studied, we recommend a quick preliminary run with decreasing pressure to determine roughly the two-phase pressure. There is no theoretical reason why this detector should not work with many kinds of phase equilibria separation.
ACKNOWLEDGMENTS
This work was supported by the National Science Foundation under grant no. CHE8712204. Vladimir Majer participated in the discovery of the amplitude effect. We thank: Sergei N. Lvov for critical discussions and help with literature values for the NaCl(aq) phase equilibria, Charles W. Buzzard and Scott Boyette for help with electronic modifications and interfacing the densimeter to a computer, and Patricia Bunville for help with the manuscript and for producing the figures. REFERENCES Bischoff, J.L. and Pitzer, KS., 1989. Liquid-vapor relations for the system NaCl-H,O: summary of the PVT-x surface from 300’ to 5OO’C. Am. J. Sci., 289: 217-248. Haar, L., Gallagher, T.S. and Kell, G.S., 1984. NBS/NRS Steam Tables: Thermodynamic and transport properties and computer programs for vapor and liquid states of water in SI units. Hemisphere, Washington, DC. Holste, J.C., Hall, K.R., Eubank, P.T. and Marsh, K.N., 1986. High-pressure PVT measurements. Fluid Phase Equilibria, 29: 161-176. Khaibullin, Kh.1. and Borisov, N.M., 1966. Experimental investigation of the thermal properties of aqueous and vapor solutions of sodium and potassium chlorides at phase equilibrium. Teplofiz. Vyso. Temp., 4: 518-521. Majer, V., Hui, L., Crovetto, R. and Wood, R.H., 1991a. Volumetric properties of aqueous electrolyte solutions near the critical temperature of water. I. Densities and apparent molar volumes of NaCl(aq) from 0.0025 to 3.1 mol kg-‘, 604.4 to 725.5 K, and 18.5 to 38.0 MPa. J. Chem. Thermodyn., 23: 213-300. Majer, V., Crovetto, R. and Wood, R.H., 1991b. A new version of vibrating tube flow densimeter for measurements up to 730 K. J. Chem. Thermodyn., in press. Olander, A. and Liander, H., 1950. The phase diagram of sodium chloride and steam above the critical point. Acta Chem. Stand., 4: 1437-1445. Schneider, G.M. and Deiters U.K., 1986. High-pressure phase equilibria: experimental methods. Fluid Phase Equilibria, 29: 145-160. Valyashko, V.M., Dibrov, LA. and Puchkov, L.V., 1986. Thermophysical properties of NaCl-Hz0 system in the wide interval of state parameters. Obzori poteplophizicheskim svoistvam veshestv, 4(60): 1-114.
Fluid Phase Equilibria, 65 (1991) 253-261
Elsevier Science Publishers B.V.. Amsterdam
New detection
method for determining
phase boundaries
Rosa Crovetto * and Robert H. Wood Department (U.S.A.)
of Chemistry
and Biochemistry,
University
of Delaware,
Newark,
DE
19716
(Received November 10, 1990; accepted in final form January 23, 1991)
ABSTRACT Crovetto, R. and Wood, R.H., 1991. New detection method for determining phase boundaries. Fluid Phase Equilibria, 65: 253-261.
Modifications in the electronics and experimental set-up of the vibrating tube densimeter (Wood et al., 1989. Rev. Scientific Instruments, 60(3): 493-494) allowed the development of a new detection method for determining phase transitions. The method uses the sharp drop in the amplitude of vibration of a vibrating tube when phase separation occurs. The new detector should be especially useful at high temperatures and pressures where other methods are more difficult to use. Combining phase equilibria detection with conventional density measurements allows the vibrating tube to be used to explore P, V, T, and x at phase boundaries. The experimental procedure and set up are presented together with results from measurements of the vapor pressure of both water and aqueous NaCl solutions. The reliability and estimated accuracy of this method for determining vapor pressure is about &0.4%.
INTRODUCTION
An accurate knowledge of the phase equilibria boundary of pure components and/or mixtures is not only a matter of fundamental scientific interest. It is very important for tests of proposed equations of state (EOS), pair potentials, mixing rules, etc. It is also of great practical importance for geochemistry, for power generation and for many chemical engineering processes. There are two recent reviews on high pressure PVT data and phase equilibria measurements (Schneider and Deiters, 1986; Holste et al., 1986). * Present address: Department Boulder, CO 80303-0215. 0378-3812/91/$03.50
of Chemistry and Biochemistry, University
0 1991 Elsevier Science Publishers B.V.
of Colorado,
254
We refer the reader to them as a general discussion of the available methods and techniques. The well-known PT vapor-liquid coexistence line of pure water was used to test the behavior of the phase detector and to establish the best experimental procedure to follow. The performance of this new detection method was then assessed with measurements of bubble points for pure water and for sodium chloride solutions. It seems likely that many other kinds of phase separations can also be detected and measured in a similar way.
EXPERIMENTAL
When measuring the densities of aqueous alkali metal salt solutions with the modified vibrating tube densimeter (Majer et al., 1991a), it was observed that the amplitude of the vibration changed when either there was a large change in viscosity of the fluid or the tube contained two phases. For our apparatus, the appearance of a liquid-gas transition in the fluid produced a maximum decrease of about S-10% in the amplitude of the pick-up signal at constant drive power. For ease of observation the amplitude differences between a constant base line and the rectified and amplified pick-up signal was displayed on a strip chart recorder. The schematic representation of the flow circuit used in these measurements is shown in Fig. 1. The basic system, including the vibrating tube densimeter, its housing, and the other auxiliary equipment, were the same as described by Majer et al. (1991b). The original Heise manometer was changed for a more accurate Paroscientific transducer which, when inter-
Fig. 1. Schematic representation of apparatus and set-up A, Constametric HPLC pump; B, 6 cm3 injection loop; C, Paroscientific Digiquartz manometer; D, vibrating tube and its housing; E, and E,, Circle Seal BPR 21 series back pressure regulators; 1, Rheodyne 7010 HPLC six-port injection valve; 2, needle valve for decreasing pressure in the system; 3, pre-pressurising valve.
255
(4 0.10
(b) AA 70 -2
I
i‘
pd
Fig. 2. (a) Schematic representation of a typical time evolution of the pick-up amplitude, A, of the vibrating tube plotted as (A - A”)/Ao = AA/A’, where A0 is an arbitrary constant. In this experiment the needle valve 2 was opened and AA/A0 was followed as a function of time. The noise level, O.l-0.2%, is not shown. The height of the shaded area shows typical amplitude increases after arresting the pressure drop. (b) AA/A0 vs. P, the steady state pressure, for small changes in the amount of fluid in the tube. Note that P increases towards ) withdrawal. For definitions of Pi and Pd, see the left. (- - -) infusion of fluid; (text.
faced with an external frequency counter, could provide automatic pressure data logging. (Alternatively, the fluid pressure could be increased by forcing small amounts of fluid into the system with the pump A.) A T-connection ending in a needle valve, 2, was added after the densimeter’s outlet and before the back pressure regulators. (The needle valve allowed fine control of the system pressure by bleeding small amounts of fluid from the pressurized system.) A phase transition in the fluid can be produced by changing the variables P, T or x individually or in combination. For this apparatus an efficient technique was to maintain constant fluid composition and block temperature and to effect a phase change adjustment by carefully adjusting the pressure. Figure 2(a) shows the variation in the de&meter’s pick-up signal amplitude during experiments in vyhich the needle valve was opened, and a continuous decrease in the fluid pressure resulted. In all cases, there was a sharp drop ( = 10%) in amplitude when a second phase appeared, followed
256
by a gradual rise ( = 25%) to a plateau where only the gas phase was present in the tube. The larger vibrational amplitude of the tube when it was filled with gas was presumably due to the lower viscosity of the gas. In the case of a phase separation, the presumed cause of the drop in amplitude is the presence of two phases. If so, we can infer that the magnitude of the observed decrease in the amplitude is related to the relative quantity of the two phases present. Figure 2(b) shows the amplitude plotted as a function of steady-state pressure for experiments in which small withdrawals or injections of fluid were made to change the fluid pressure, which was then read after re-equilibration ( = 20 min). These experiments show a definite hysteresis effect. When making bubble or dew point measurements it is important to try to keep the newly generated phase as small as possible, especially with mixtures, so as to alter the concentration of the initial phase as little as possible. This is done by halting the pressure drop as soon as a detectable amplitude decrease has been observed (the shaded area in Figs. 2(a) and 2(b). The vibration of the tubing at 140 Hz, with an amplitude of about 0.1 mm, should help equilibration by providing some stirring action, and it may help promote nucleation of bubbles. There are important kinetic and thermal effects in any phase separation experiment. They must be carefully considered and examined, especially when working under nearly static conditions and without proper stirring. These include supersaturation and overheating when condensing, and supercooling and undersaturation when evaporating, which are commonly observed with different techniques. In order to assess the magnitude of these problems in the present apparatus, the reproducibility of the pressure at which phase appearance and disappearance occurred was studied using pure water as a test fluid. A typical run for water started with water flowing in the apparatus at 0.1-0.2 cm3 min-’ and at a pressure of 5-10 bar above its vapor pressure. The flow was stopped and by carefully and slowly opening valve 2, the rate of pressure decrease was adjusted to a desired value, and the amplitude was recorded. At this point, the noise level in the amplitude was about 0.1%. When the amplitude dropped by 1 to 3% (the shaded area in Figs. 2(a) and (b)), valve 2 was closed and the corresponding pressure value was noted. The pressure then slowly increased to a steady-state value in the next lo-20 min. This pressure was reported as the “steady-state” phase boundary pressure for decreasing pressure (Pd) (see Fig. 2(b)). Next, the system pressure was increased by injecting a small volume of fluid with the pump, at a flow rate of less than 0.1 cm3 mm-‘. The pump was stopped when the pick-up signal increased to more than 5 times the noise level. After lo-20 min, the pressure and amplitude generally came to new steady-state values. These pressure
257
adjustments were repeated until the steady-state amplitude was equal to or higher (within the noise level) than the amplitude that was observed earlier just before the appearance of the second phase during the decreasing pressure experiment. This pressure was taken as the “steady-state” pressure for phase disappearance with increasing pressure (Pi) (see Fig. 2(b)). The above procedure was repeated again by injecting a new water sample into the system as before. It was found that Pa was always smaller than the corresponding literature values for the vapor pressure of pure water, PO.The velocity at which the pressure was changed played a very important role in determining Pd.With rapid pressure changes, the difference between Pd and P" increased, presumably owing to the lack of thermal equilibration. With very slow pressure changes (0.2-0.3 bar mm’) the experiments took longer and did not yield higher accuracy. There appeared to be an optimum velocity which could potentially be different for each fluid. In our experiments, values obtained for Pd at near optimum rates were -0.25 to -0.88% smaller than PO.In contrast, Piwas always bigger than Pd,almost always bigger than PO,and less dependent on the velocity of the pressure increase. The observed difference, Pi- PO,varied from -0.2 to 2%. The greater spread in differences between Pi and P" reflects the greater experimental difficulty in measuring Pi.For pure water, the pressure average Pay= (Pd+ Pi)/2gave the best agreement with the best literature values for the vapor pressure of water, P" (Haar et al., 1984). The hysteresis shown in Pig. 2(b) and the resulting difference between Pi and Pd could be caused by temperature changes due to the latent heat of phase change followed by slow thermal equilibration, slow nucleation, and slow bubble dissolution, all of which give rise to effects of opposite sign in Pd and Pi. For water, we measured bubble points as described above, and also one dew point (Table 1). For the dew point, measurements were begun at an initial pressure about 5 bar below the vapor pressure of water at the measured block temperature. As with the bubble point experiments, the pressure of phase appearance, Pi,was determined by slowly increasing the pressure. This was followed by a measurement of the pressure of phase disappearance, Pd,established by slowly decreasing the system pressure. Within the experimental error, the measured dew point and bubble point were equal, but the difference Pi- Pd was somewhat higher than for the bubble point measurements, once again because of increased uncertainty associated with vapor-phase measurements. To measure a solution vapor pressure, a solution of known concentration was introduced into the system using the injection valve 1 with a flow of 0.2-0.3 cm3 min-’ . The measurement procedure from there on was the same
TABLE 1 Measured vapor pressure of pure water T W)
PaV(MPa) a
A (MPa) b
P” (MPa) ’
Sd
325.17 333.57 333.80 341.23 344.56 344.71 e 347.04 349.72 349.73 349.73 349.75 349.75 349.78 349.91 349.93 350.28 350.28 350.28 350.28 350.28 350.28 362.91
12.05 13.44 13.44 14.79 15.44 15.49 15.90 16.60 16.47 16.59 16.58 16.52 16.54 16.56 16.45 16.64 16.65 16.59 16.53 16.52 16.47 19.28
0.01 0.09 0.03 0.04 0.06 0.46 0.01 0.27 0.12 0.29 0.24 0.18 0.16 0.17 0.05 0.19 0.28 0.21 0.21 0.20 0.04 0.01
12.07 13.45 13.49 14.82 15.45 15.48 15.93 16.47 16.47 16.47 16.47 16.47 16.48 16.50 16.51 16.58 16.58 16.58 16.58 16.58 16.58 19.32
-0.17 - 0.07 -0.37 - 0.20 - 0.06 0.07 -0.19 0.79 0.00 0.35 0.67 0.30 0.36 0.36 -0.36 0.37 0.43 0.06 -0.30 - 0.36 - 0.66 - 0.21
aP,” = (Pi
+ Pd)/2. bA=(Pi-Pd)/2. ’ P” = pure water vapor pressure from Steam Tables (Haar et al., 1984). d 6 = lOO(P,” - PO)/PO. e Dew point. All other measurements are bubble points.
as that for water. Each 6 cm3 of injected sample allowed 3 to 4 different measurements of the bubble pressure with fresh solution. The variation of the fluid density with pressure exhibits a discontinuity in the slope with the appearance of a second phase. The period of vibration is related to the density by Ap=K(r2-r;) where p is the density, K is the calibration constant and T is the period of vibration. For detecting a change in the number of phases, measuring the period of oscillation as a function of pressure was not as accurate, reproducible or rapid as measuring the amplitude change with the present apparatus. Sudden irreversible shifts in frequency sometimes occur when the pressure is varied so discontinuities in period vs.. pressure might be observed.
259
Also, experiments using period measurements are much slower because the period of vibration must be averaged over one minute of sampling to achieve the necessary accuracy. As a result the pressure variations must be much slower in order to get representative period readings. The temperature was measured in the block that housed the vibrating tube with a calibrated Bums thermometer (accuracy of about 0.1 K). The constancy of the temperature was fO.O1 K. At 623 K the variation of the vapor pressure of pure water with temperature was about 0.19 bar/O.1 K, so that our temperature imprecision of 0.1 K will translate to about a 0.2% error in the vapor pressure of water. The pressure was measured with a Paroscientific Digiquartz manometer with a manufacturer’s calibration accuracy of 0.01% of full scale (41 MPa). The water used was deionized and degassed. NaCl was Fischer Scientific ACS. Solutions were made by weighing the dried salt and the water. The accuracy in concentration was 0.1% for the 1 mol kg-’ NaCl and 0.03% for the 3 mol kg-’ NaCl solutions, respectively.
RESULTS
Table 1 gives the measurement of vapor pressure for water at different temperatures presented as Pav and A, where A = (Pi - Pd)/2. The vapor pressure of water P” and the deviation of the present measurements from
TABLE 2 Vapor pressure for NaCl(aq) A (MPa) b
P (MPa) ’
0.15 0.02 0.23 0.28 0.17
14.83 14.83 14.83 14.83 14.83
-
0.22 0.10
15.91 15.91
- 0.25 - 0.60
m = 3.0 mol kg-’ 349.97 14.89 349.97 14.79 349.97 14.74 349.97 14.80 349.97 14.77 m = 1.0 mol kg-’ 349.94 15.87 349.97 15.81
0.40 0.27 0.61 0.20 0.41
a P,"=(Pi+ Pd)/2. bA=(Pi-Pd)/2. ’ Literature values for the vapor pressure of the solution at 623.15 K (see text). For 3 mol kg-’ NaCl there is about a 1% scatter in the vapor pressure measured in different laboratories; for 1 mol kg-’ the scatter is about 0.3%. dS=1OO( Pa,- PO)/PO.
260
P” are also given. Our average deviation of a single measurement literature value, calculated as
from the
(2) is 0.32% and the reproducibility of individual measurements is normally around + 0.4% (occasionally + 0.7%). In Table 2 we present the results obtained for the salt solutions at an almost constant temperature, near 623 K. Table 2 gives Pa,, A, the literature value and the corresponding deviation from the literature value. The reproducibility of measurements is about +0.5%. Literature values have been taken from a smooth curve through the results of Bischoff and Pitzer (1989), Olander and Liander (1950), Khaibullin and Borisov (1966) and Valyashko et al. (1986), with more weight given to the more recent compilation of Bischoff and Pitzer. The tables show that the results given by the presented detection method are in good agreement with previous results.
CONCLUSIONS
This new detection method for phase boundaries is quick and reasonably accurate for measuring the vapor pressure of solutions at high temperatures. It can be easily automatized and used for on-line operation. Much faster measurements are possible if accuracies of 2 to 5% are adequate. It is not known yet how close to a critical point a measurement can be taken with reasonable accuracy. Near a critical point the densities and viscosities of both phases will approach each other, equilibration will become very slow, and there will be density fluctuations caused by the vibration of the fluid. Every method for determining phase transition boundaries has different advantages and disadvantages. With this technique, we have all of the advantages of a flow system, allowing one to change the samples under study quickly and easily, and minimize the residence time in the high-temperature zones of the densimeter, reducing the rate of decomposition and corrosion. It is also possible to produce the phase separation at constant temperature and composition by increasing and decreasing the pressure of the system. Finally, the problem of getting a representative sample is avoided and the method is faster than static vapor pressure measurements. However, the overall accuracy is not the best that can be achieved. A disadvantage of the present design is that the internal diameter of the capillary tube leading to the vibrating tubing is small (0.24 mm), leading to
261
potential experimental and safety difficulties associated with the inadvertent formation of a solid phase in the capillaries. Unfortunately, it is nearly impossible to dissolve the plug and clean the thin capillary again. For this reason equilibria involving solids might be studied more conveniently in capillaries of higher internal diameter. When a solution of unknown vapor pressure is being studied, we recommend a quick preliminary run with decreasing pressure to determine roughly the two-phase pressure. There is no theoretical reason why this detector should not work with many kinds of phase equilibria separation.
ACKNOWLEDGMENTS
This work was supported by the National Science Foundation under grant no. CHE8712204. Vladimir Majer participated in the discovery of the amplitude effect. We thank: Sergei N. Lvov for critical discussions and help with literature values for the NaCl(aq) phase equilibria, Charles W. Buzzard and Scott Boyette for help with electronic modifications and interfacing the densimeter to a computer, and Patricia Bunville for help with the manuscript and for producing the figures. REFERENCES Bischoff, J.L. and Pitzer, KS., 1989. Liquid-vapor relations for the system NaCl-H,O: summary of the PVT-x surface from 300’ to 5OO’C. Am. J. Sci., 289: 217-248. Haar, L., Gallagher, T.S. and Kell, G.S., 1984. NBS/NRS Steam Tables: Thermodynamic and transport properties and computer programs for vapor and liquid states of water in SI units. Hemisphere, Washington, DC. Holste, J.C., Hall, K.R., Eubank, P.T. and Marsh, K.N., 1986. High-pressure PVT measurements. Fluid Phase Equilibria, 29: 161-176. Khaibullin, Kh.1. and Borisov, N.M., 1966. Experimental investigation of the thermal properties of aqueous and vapor solutions of sodium and potassium chlorides at phase equilibrium. Teplofiz. Vyso. Temp., 4: 518-521. Majer, V., Hui, L., Crovetto, R. and Wood, R.H., 1991a. Volumetric properties of aqueous electrolyte solutions near the critical temperature of water. I. Densities and apparent molar volumes of NaCl(aq) from 0.0025 to 3.1 mol kg-‘, 604.4 to 725.5 K, and 18.5 to 38.0 MPa. J. Chem. Thermodyn., 23: 213-300. Majer, V., Crovetto, R. and Wood, R.H., 1991b. A new version of vibrating tube flow densimeter for measurements up to 730 K. J. Chem. Thermodyn., in press. Olander, A. and Liander, H., 1950. The phase diagram of sodium chloride and steam above the critical point. Acta Chem. Stand., 4: 1437-1445. Schneider, G.M. and Deiters U.K., 1986. High-pressure phase equilibria: experimental methods. Fluid Phase Equilibria, 29: 145-160. Valyashko, V.M., Dibrov, LA. and Puchkov, L.V., 1986. Thermophysical properties of NaCl-Hz0 system in the wide interval of state parameters. Obzori poteplophizicheskim svoistvam veshestv, 4(60): 1-114.