Ind. Eng. Chem. Process Des. Dev. 1981,20,401-403
Conclusion A method has been proposed and proven for predicting the effect of KC1, CaC12,CH,OH, and C2H60Hinhibition of pure gas hydrates using existing hydrate parameten and data obtainable in the literature. The extension to other inhibitors and gas mixtures is straightforward. The determination of the inhibitor concentration in the vapor phase in equilibrium with that of the liquid phase is a separate vapor liquid problem of the standard type. Work is proceeding to extending the measurements to simulated natural gases using methanol and glycols as inhibitors. Nomenclature Cmj = Langmuir constant for a j molecule in an m cavity f . = gas phase fugacity of species j = enthalpy, difference between hydrate and water, J/mol AH = hydrate dissociation enthalpy (to water and gas), J/mol P = total pressure, kPa R = gas constant, J/mol K T = temperature, K Av = volume difference between hydrate and water, cm3/mol xi = mole fraction in liquid
hz
Greek Letters yi = activity coefficient of water 8 = fractional occupation of type m cavity by type j molecule pw=
chemical potential
40 1
i = inhibitor 0 = at reference T or P 1 = formation condition without inhibitor Literature Cited Davidson, D. W. ”Water, a Comprehenshre Treatlse”, Vol. 2, F. Franks, Ed.: Plenum Press: New York. 1973; Chapter 3, pp 115-234. Dharmrwardhena. P. B.; Parrlsh, W. R.; S b n , E. D. 2nd. €ng. Chem. Fundam. 1960, 79, 410. Hafemann, D. R.; Miller, S. L. J. phys. Chem. 1969, 73. 1392. Hammerschmldt, E. 0. 2nd. Eng. Chem. 1934. 26, 851. Hammerschmldt, E. G. O// Gas J . May 1939, 66. Holmes, M. J.; Van Winkle, M. Ind. Eng. Chem. 1970, 62, 21. Katz, D. L. J. Pet. Techno/. 1971, 419. Kobayashl. R.: Withrow, H. J.; Williams, 0. B.: Katz, D. L. Roc. Net. Gas A m . Am. 30th Ann. Conf. 1951, 27. Makogon, Y. F. “Hydrates of Natural Gases”, Moscow (1974) Transl. by W. J. Cleslewlcz, Colorado School of Mines, 1977. Menten, P. D. M.S. Thesis, Colorado School of Mines, Dec 1979. Parrlsh, W. R.; Prausnltz, J. M. Ind. Eng. Chem. Process Des. Dev. 1972, 1 1 , 26. Pleroen, A. P.; Korvezee, A. P. Recl. Trav. Chlm. 1962, 87, 898. van der Waals, J. H.; Platteuw, J. D. “Advances In Chemical Physics”, I. Prlgoglne, Ed.: Vol. 11, Intersclence: New York, 1959; Chapter 1. Von Stackelberg, M.; Miiller, A. R. 2. Elektrochem. 1954, 58, 25. Weast, R. C., Ed., ”CRC Handbook of Chemistry and Physics”, 46th ed.; Chemical Rubber Co.: Cleveland. 1965-66. Zerpa, C. 0.: Dharmawardhana, P. B.; Parrish, W. R.; Sloan, E. D. J . Chem. Eng. Data 1979, 24, 26.
Superscripts
Received for review July 7, 1980 Accepted November 25, 1980
p = unoccupied hydrate lattice H = occupied hydrate lattice L = pure liquid
Paula D. Menten William R. Parrish’ E. Dendy Sloan*
Chemical and Petroleum-Refining Engineering Colorado School of Mines Golden, Colorado 80401
Support for this work by NSF Grant ENG 7901662 is gratefully acknowledged.
Subscripts w = water
’Phlilips Petroleum Co.,Bartlesvllle, OK
74003.
Solubility of Isobutene in Sulfuric Acid-fert-Butyl Alcohol-Water Mixtures A critical discussion is made about the available data on the solubility of isobutene in sulfuric acid-tert-butyl alcohol-water mixtures, which is supported by our measurements.. I f the concentration of tert-butyl alcohol is greater than 2 X lo3 mol/m3 the solubility is independent of the concentration of the acid. The corrected data are useful for the design of isobutene absorbers.
Introduction The design of gas-liquid reactors is of great importance in the chemical industry. Available reactor models have to be tested with the aid of suitable data on chemical reactions. However, the system parameters, usually determined from the products generated, are often interrelated and cannot be uniquely determined. One of the most important parameten is the solubility of the gas. Recently the absorption of isobutene in sulfuric acid on an industrial scale has been the subject of many investigations (Deckwer et al., 1975,1977;Deckwer and Puxbaumer, 1975; Deckwer, 1976, 1977; Gehlawat and Sharma, 1968; PopoviE and Deckwer, 1975). Accurate data on the physical solubility of the gas can only be obtained in the kinetic regime of absorption processes with slow chemical reaction (Astarita, 1967), where the liquid phase is everywhere saturated with the absorbed gas. In this regime the absorption rate is independent of the interface area and of the mass transfer coefficient and proportional to the liquid holdup. For a first-order reaction it is given by R = kl*c**el (1)
If the conditions for the kinetic regime are not fullfilled it is not possible to measure the solubility by conventional means, but in the case of electrolyte solutions the solubility can be estimated by the method of van Krevelen and Hoftijzer (1948). This relates the relative solubility c*,/c*, the ratio of the gas solubility in water and in the solution, with the ionic strength I of the solution log
c*w
= hI c*
Assuming total dissociationof the electrolyte,the constant h is composed of contributions referring to the species of positive and negative ions h, and h- and to the species of gas h,. The logarithm of the relative solubility of some nonreactive gases in sulfuric acid as a function of the acid concentration, which is proportional to the ionic strength, is presented in Figure 1. From acid concentrations greater than 4 X lo3 mol/m3 it shows independence of the acid concentration, so that eq 2 is not fullfilled. Contrary to this, Gehlawat and Sharma (1968) as well as Deckwer (1976) have published values of the relative solubilities of 0 1981 American Chemlcal Society
100
:.
-~
r~
70
= hydrogene
I R ~ e l ~ c 19111 hl
0
= 8sobYtene
I OeckwCI
19761
=oxygen@
:Bohr
19101
s
i
1 Bohr I Den0
1913!
I
50 IL
nitrogene
m i benzene d
.=
i
,sobutone
z
2-butene
~~
-. ~~
~
.
-~~~~ - .- . ~~
l
2 X lo3mol/m3 one can easily use the value of the solubility in water-tert-butyl alcohol mixtures. For the range of tert-butyl alcohol concentration 0 < ct > 2 X lo3 mol/m3, we propose to interpolate halflogarithmic between the solubility of the aqueous solutions and the solubility of tert-butyl alcohol mixtures of 2 X lo3 m0i/m3. Acknowledgment The authors gratefully acknowledge financial support of the Landesamt fur Forschung, Nordrhein-Westfalen, West Germany. Nomenclature a’ = interfacial area per unit volume of liquid, m-* cg = gas concentration in the bulk phase, mol/m3
c* = equilibrium gas concentration in liquid phase, mol/m3 c*, = gas solubility in water, mol/m3
h = constant related to the ionic strength, m3 mol h+, h-, h, = components of the constant h, m /mol I = ionic strength, mol/m3 kl = mass transfer coefficient, m kl = first-order rate constant, R = absorption rate, mol mZ3s-l Greek Letters el = liquid phase volume fraction Literature Cited
d
Astarlta, G. “Mass Transfer with Chemlcal Reactbns”,Eteevkr: Amsterdem, 1967; Chapter 2, p 28. Bohr, C. I.phys. Chem. 1910, 72,47. Danckwerts, P. 8. “Gas Uquld Reactions", McQlaw-HIH: New York, 1970; Chapter 6, p 160. Deckwer, W. D.; PopoviE, M.; Allenbach, U. Reect. K b t . Catal. Left.1975, 3,449. Dedcwer, W. D.;Puxbawner, H. H. Chem. Ing. Tech. 1975, 47, 183. Deckwer, W. D.; Puxbaumer, H. H. Chem. Ing. Tech. 1975, 47, 809. Deckwer, W. D. J. CY”. €ng. LMta 1978, 21, 175. Deckwer, W. D.; Albnbach, U.; Bretschnekler, H. Chem. €ng. So/. 1977,
32,43. Deckwer, W. D. Chem. €ng. Scl. 1977, 32,51. Deckwer, W. D.; Albnbach, U.; Bretschneider, H.J.; PopoviE, M.; Puxbaumer, H. H. Chem. Ing. Tech. 1977, 49, 575. Deno, N. C.; Perluolo, C. J. Am. Chem. Soc. 1957, 79, 1345. Frledrich, A.; Warnecke, H.J.; Langemann, H. Chem. Ing. Tech. 1981, In press. Qehlawat, J. K.; Sharma, M. M. Chem. €ng. Scl. 1988, 23, 1173. van Krevelen, D. W.; HoftiJzer,P. J. Chhnb et IndusMe: Numero Speclele di XXIe Congres International de Chimb IndwtrIeHe, Bruxelles Sept 1948, p 168; chkn.I d . 1948, 60, 65. de Llgny, C. L.; Aifenaar, M. Recl. Trav. Chem. 1987, 86, 1182. Puetschl, P.; AmHe, R. F. J . phys. Chem. 1988, 70, 716. PopovlcE, M.;Deckwer, W. D. Chem. Eng. Scl. 1975, 30.913.
Znstitut fiir Technische Chemie und Chemische Verfahrenstechnik
Uniuersitat-Gesamthochschule
A. Friedrich’ H. Warnecke H. Langemann*
Paderborn, West Germany Received for reuiew October 19, 1980 Accepted December 15, 1980
’ Umweltbundesamt, 1000 Berlin, West Germany.
