CaqSoPh [mol/kg] molality of sodium phenoxide in the

aqueous phasek0

[min±1] pseudo-first order rate constantki [kg2m±2mol±1s±1] second-order rate constant of the

reaction at the interfacemi [kg] mass of the component IT [�C] temperatureV [ml] volume

References

[1] Schwuger, M.-J.; Stickdorn, K.; Schomäcker, R., Chem. Rev. 95 (1995) pp.849±864.

[2] Schubert, K.-V.; Kaler, E., Ber. Bunsenges. Phys. Chem. 100 (1996) pp.190±205.

[3] Kahlweit, M.; Strey, R., Angew. Chem. 97 (1985) pp. 655±669.[4] Kahlweit, M., Tenside Surf. Det. 30 (1993) pp. 83±89.[5] Tjandra, D.; Lade, M.; Wagner, O.; Schomäcker, R., Chem. Eng. Technol.

21 (1998) pp. 66± 670.[6] Brandt, M., Ph. D. Thesis, Technische Universität Braunschweig 1998.[7] Battal, T.; Siswanto, C.; Rathman, J., Langmuir 13 (1997) pp. 6053±6057.

This paper was also published in German in Chem. Ing. Tech. 71 (1999) No. 8, pp.877±881.

_______________________

Computer-Controlled Vibrating TubeDensimeter for Liquid DensityMeasurement in a Wide Temperature andPressure Range

By E. Christian Ihmels, Claudia Aufderhaar, Jürgen Rarey, andJürgen Gmehling*

A density measurement system was developed using avibrating tube densimeter prototype for high temperature andhigh pressure (DMA-HDT). Fully automatic density mea-surements over a large temperature and pressure range wererealized with the help of the specially developed controllingsoftware. Currently, the unit is applicable for temperaturesfrom 298 K to 523 K and pressures from atmospheric pressureup to 100 bar. The estimated total error in the densitymeasurements is �0.0002 g/cm3.

1 Introduction

Accurate knowledge of the PvT properties of purecompounds and mixtures is of great importance in manyfields of research and development as well as in industrialpractice. The densities of fluids as a function of temperature,

pressure and composition are particularly important for thedesign of industrial plants and the dimensioning of pipelinesand pumps. Furthermore, reliable density values are the basisfor the development of correlation equations and equations ofstate. Using equations of state and ideal gas heat capacities it ispossible to calculate phase equilibria and other thermody-namic properties, such as enthalpies, entropies, heat capa-cities, heats of vaporization, etc. All these data are required forsolving material and energy balances required for the designand optimization of chemical processes.

Between 1991 and 1998 a databank for pure componentthermodynamic and transport properties was developed andis presently being continuously updated. This project wassupported by the German Federal Ministry for Research andTechnology (BMBF), FIZ Chemie (Berlin), and DDBSTGmbH (Oldenburg). The database is an extension of theDortmund Data Bank (DDB) for phase equilibria and excessproperties. The main objectives of the pure componentdatabase are the determination of recommended values, thefitting of recommended correlation parameters, and thedevelopment of improved prediction methods. To accomplishthis, the database is thoroughly tested and at the same timedata gaps are filled by our own measurements.

Many sophisticated experimental techniques have beendeveloped in our research group for the measurement of therequired thermophysical data (phase equilibria, excessproperties and pure component properties, such as heatcapacity, vapor pressure, viscosity, density, ...) to the requireddegree of accuracy.

The vibrating tube method [1], which is well known and hasbeen widely applied for 30 years, is used in this work for thedetermination of liquid densities. This method is used inresearch and development as well as for routine industrialmeasurements. In contrast to common commercially availablevibrating tube densimeters, our prototype can be used over awider temperature and pressure range. The prototype wassupplied by ªLabor für Meûtechnik Dr. Hans Stabingerº(Graz, Austria) and is designed for temperatures up to 623 Kand pressures up to 600 bar. With the computer-controlledmeasurement system available it is possible to measure a highnumber of temperature- and pressure-dependent densities ina relatively short time.

2 Experimental Section

The schematic assembly of the density measurement systemdeveloped is shown in Fig. 1. The prototype of a high-pressurehigh-temperature vibrating tube densimeter (DMA-HDT) isthe essential part of the computer-controlled system. TheDMA-HDT system consists of the measurement cell and amodified DMA 5000 control unit. The measurement cellcontains the vibrating tube, the sensor and excitation coils, anelectronic thermostat with cooling circuit (e.g., for air or watercooling), and two temperature sensors. The vibrating periodmeasurement and the temperature control is implemented

Chem. Eng. Technol. 23 (2000) 5, Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2000 0930-7516/00/0505-0409 $ 17.50+.50/0 409

Communications

±

[*] Dipl.-Chem. E. C. Ihmels, Dr. J. Rarey, Prof. Dr. J. Gmehling, Departmentof Industrial Chemistry, Carl von Ossietzky Universität Oldenburg,Postfach 2503, 26111 Oldenburg, Germany; e-mail: Gmehling@tech.-chem.uni-oldenburg.de; Dipl.-Chem. C. Aufderhaar, Bayer AG, Tech-nische Entwicklung, 51368 Leverkusen, Germany.

0930-7516/00/0505-0409 $ 17.50+.50/0

410 Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2000 0930-7516/00/0505-0410 $ 17.50+.50/0 Chem. Eng. Technol. 23 (2000) 5

within the DMA control unit. This control unit is connected toa PC via a serial port (RS232). A target temperature can besent to the control unit and every second the currenttemperature and the vibrating period time can be accessedby the PC.

The vibrating tube unit is connected to a variable volumecell (Ruska dosage pump type 2200-802). The piston of thevariable volume cell can be moved by a stepping motorcontrolled by a PC.

For the pressure measurement a pressure transducer(Druck, model PDCR 911) is used. A multimeter (Keithley,model 2000) with serial port is employed for the transforma-tion of the pressure transducer measurement signal.

The vibrating tube unit can be disconnected from thevariable volume cell with the help of two three-way valves. Inthis mode density measurements at atmospheric pressure arepossible using small amounts of sample.

Figure 1. Schematic diagram of the computer-controlled density measurementunit.

2.1 Measurement Range, Accuracy, and Calibration

The installed Pt100 temperature sensors have a resolutionof �3 mK and an accuracy of �30 mK, while the thermostat hasa stability of �20 mK. The period time is measured with aresolution of 1 ns and lies between 2400 and 2600ms dependingon the density, temperature, and pressure conditions.

The observed reproducibility of the density measurementsat atmospheric pressure and temperatures from 298 K up to373 K is close to �5´10-5 g/cm3. At higher pressures andtemperatures hysteresis effects in the vibrating tube materiallimit the reproducibility to �1´10-4 g/cm3.

The pressure sensor is designed for pressures up to 200 barand the error was estimated after calibration with a pressuregauge to be lower than �0.02 bar.

The accuracy in the density measurement depends on theaccuracy of pressure, temperature, and period time measure-ments as well as on the purity of the reference substances andaccuracy of the reference densities.

For calibration the period time of liquid water and butanewere measured at temperatures from 298 K up to 523 Krespectively 348 K (in 5 K steps) and pressures from

approximately 2 bar above the vapor pressure up to 100 bar(in 10 or 20 bar steps). Moreover, the vacuum signal (density =0 g/cm3) was measured at temperatures from 298 K up to 523K. Then the parameters of a 14-parameter calibrationequation (see Eq. 1) were fitted at the calibration points(temperature, pressure, and period time) to the referencedensities of equations of state [2,3] and the density zero (in avacuum) by linear regression.

The following equation was used to determine the densitiesfrom the measured period time at a given temperature andpressure.1)

� � A� B � �2 (1)

with

A �Pi

ai � Ti �Pj

bj � Pj � c � T � P

and

B �Pi

di � Ti �Pj

ej � Pj � f � T � P

with i = 0, 1, 2, 3 and j = 1, 2

The total error in the density measurement is estimated tobe �0.0002 g/cm3. For the measured liquid densities between0.4 and 1 g/cm3 this leads to relative errors between 0.05 and0.02 %.

Up to now the application of the new measurement unit islimited to conditions up to 100 bar and 523 K. The reason forthis limitations are the valves and supply pipes employed.

2.2 The Control Program

The control program ªDensitas per Motum ± DensityMeasurementº was developed for the density measurementsystem: fully automatic temperature-pressure measurementprograms can be realized with this software. Fig. 2 shows themain window of the program with all current systemparameters as well as the measurement program. The currentversion of the program has an integrated connection to theDortmund Data Bank (DDB) for pure component properties(DDB-PCP). Using Antoine parameters from the DDB,dynamic measurement programs with minimal pressuresslightly above the vapor pressure can be realized automati-cally.

In addition, the software checks measurement conditionsagainst the pure component properties (melting point, normalboiling point, critical properties, ...) and detects possibleproblems (e.g., if the final temperature is above the normalboiling point for measurements at atmospheric pressure).While the measurement program is running, all data can be(optionally) stored in an MS-Access database and/or a text file(Excel-CSV format).

Communications

±

1) List of symbols at the end of the paper.

2.3 Experimental Procedure

Atmospheric pressure measurements require 20 cm3 andhigh pressure measurements 75 to 100 cm3 of the purified anddegassed liquid. The measurement program runs from theminimum temperature to the maximum temperature indefined intervals. At each temperature a preset pressureprogram is executed. The control program sets the targettemperature and pressure and waits for a defined time untilconstant system conditions are reached. After recording andstoring the required values with the specified number ofrepeats the program starts the next measurement. After themaximum pressure has been reached, the pressure is reducedand the next measurement temperature is set.

At the end of the measurement program the temperatureand pressure are decreased to the initial values. A simplifiedscheme of the measurement procedure is shown in Fig. 3.

A temperature-pressure program between 298 and 478 Kwith pressures up to 100 bar with a total of about 400measurement points is realized within five days. Atmosphericpressure measurements in the temperature range between 308and 498 K with 40 experimental values are realized within twodays.

3 Results

Atmospheric pressure measurement programs as well astemperature-pressure programs were carried out using thisequipment. Selected results are presented in Figs. 4±6. Fig. 4shows the results for 1-dodecanol at atmospheric pressure andtemperatures up to 498 K. The excellent agreement withpublished data (exception: Naziev et al., 1990) can be seen inFig. 5, which shows the deviations (Dr � rexp ÿ rDIPPR ) betweenthe experimental values and the published data with the

DIPPR correlation [4] arbitrarily set to zero. At temperaturesabove 440 K the DIPPR correlation shows higher deviationsfrom the experimental values, but it should be rememberedthat the DIPPR parameters were only fitted to data up to 400K and to the critical density. As an example for high pressuremeasurements the results for methanol are shown in Fig. 6together with reference values from Goodwin [9]. Up to 428 Kthe relative deviations are lower then 0.05 %. At highertemperatures the experimental values are much lower thanthe reference values (maximum difference 1 %). The

Chem. Eng. Technol. 23 (2000) 5, Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2000 0930-7516/00/0505-0411 $ 17.50+.50/0 411

Communications

Figure 2. Main window of the density measurement control software.

Figure 3. Simplified scheme of the automatic density measurement procedure.

412 Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2000 0930-7516/00/0505-0412 $ 17.50+.50/0 Chem. Eng. Technol. 23 (2000) 5

observed higher deviations may be caused by convectionstreams between the vibrating tube and the supply pipes. Infuture work this effect will be eliminated by a computer-controlled heating of the supply pipes: initial tests havealready shown the expected improvements. In this wayreliable PvT data can be measured over a wide range oftemperature (from 273 K up to 623 K) and pressure (fromatmospheric pressure up to 600 bar).

Figure 4. Densities of 1-dodecanol at atmospheric pressure.

Figure 5. Deviations in density Dr � rexp ÿ rref from the reference equation for1-dodecanol from Daubert and Danner [4] taken as an arbitrary reference.

Figure 6. Comparison of experimental densities of methanol in the temperaturerange between 298 K and 478 K and pressure range between the vapor pressureand 100 bar with reference values taken from Goodwin [9].

4 Summary and Outlook

With a new high-temperature high-pressure vibrating tubedensimeter prototype a computer-controlled density meas-urement unit was developed. At present, the apparatus isapplicable for liquid density measurements up to 523 K and100 bar. The density measurements are realized fullyautomatically using defined temperature-pressure programs.With respect to accuracy, reliability, and time consumptionthis system represents an optimum for measuring PvTproperties. The system is specialized for the measurement ofpure component densities with the integrated connection tothe DDB pure component properties database. It can also beapplied for density measurements of mixtures (determinationof excess volumes). Currently, the system is being modified toallow measurements at up to 600 bar and temperatures from273 K up to 623 K. Furthermore, compressed supercriticalvapor densities will be measured.

Acknowledgement

The authors would like to thank the ªLabor für MeûtechnikDr. Hans Stabingerº (Graz, Austria) for supplying the DMA-HDT prototype.

Received: December 7, 1998 [K2509]

Symbols used

A, B [±] parameter of the basic vibrating tubeequation

a...f [±] parameter of the extended vibratingtube equation

P [bar] total pressure (1 bar = 100 kPa)T [K] absolute temperaturer [g/cm3] densityt [ms] period time of the vibrating tube

References

[1] Kratky, O.; Leopold, H.; Stabinger, H., Z. Angew. Phys. 27 (1969) pp. 273±277

[2] Pruss, A.; Wagner W., The 1995 IAPWS ± Formulation for theThermodynamic Properties of Ordinary Water Substance for Generaland Scientific Use., personal communication as windows-dynamic linklibrary, Bochum 1997.

[3] Younglove, B. A.; Ely, J. F., J. Phys. Chem. Ref. Data 16 (1987) No. 4, pp.577±798.

[4] Daubert, T. E.; Danner, R. R., Physical and Thermodynamic Properties ofPure Chemicals, Tailor & Francis, Washington D.C. ± Bristol ± London1995.

[5] Garg, S. K.; Banipal, T. S.; Ahluwalia. J. C., J. Chem. Eng. Data 38 (1993)No. 2, pp. 227±230.

[6] Naziev, Ya. M.; Shakhverdiev, A. N.; Akhundov, T. S., Izv. Vyssh. Uchebn.Zaved. Neft Gaz 1 (1990) No. 12, pp. 69±72.

[7] Matsuo, S.; Makita, T., Int. J. Thermophys. 10 (1989) No. 4, pp. 885±897.[8] Hales, J. L.; Ellender, J. H., J. Chem. Thermodyn. 8 (1976) pp. 1177±1184.[9] Goodwin, R. D., J. Phys. Chem. Ref. Data 16 (1987) No. 4, pp. 799±856.

This paper was also published in German in Chem. Ing. Tech. 71 (1999) No. 6, pp.605±609.

Communications