Ind. Eng. Chem. Process Des. Dev. 1981, 20, 399-401
(leading to a higher level of “free” hydroperoxide in the liquid phase) and thus increase the critical catalyst/initial hydrocarbon concentration ratio. This increase in the critical catalyst/initial hydrocarbon concentration ratio with increasing temperature may be noted for Co203catalyzed cumene oxidation (Evmenenko et al., 1972). Similar increases in the “free” hydroperoxide concentration in the liquid phase have caused critical phenomena to occur at higher catalyst/initial hydrocarbon concentration ratios for other liquid-phase hydrocarbon oxidations (Meyer et al., 1965; Mukherjee and Graydon, 1967; Gorokhovatskii, 1973a,b; Neuberg et al., 1975; Mikhalovskii et al., 1976). Conclusions
An expression is developed to relate CCC with an adsorption type constant, A , for liquid-phase hydrocarbon oxidations involving either ROO. free-radical termination both on the catalyst surface and in the liquid phase or ROO. termination just on the catalyst surface. On the complete justification of the validity of eq 13 and the determination of the values of A,, and AH therein one would be able to predict CCC values for different reaction temperatures. Besides, the method permits a plausible insight into the physics and adds to the basic under-
399
standing of the chemistry involved in the CCC phenomenon. L i t e r a t u r e Cited b c h e r k w a , I. V.; Gwokhovatskii, Ye. 8.; Evmenenko, N. P. Klmt. Ketal. 1971, 12, 1437. Evmenenko, N. P.; Gorokhovatskii, Ya. B.; Pylenko, Yu. I. Do&/.Akad. mu& SSSR 1972, 202, 1117. Gorokhovatskii, Ya. 8. Cafal. Proc. Inf. Congr. 5th 1972 1973a, 879. Gorokhovatskli, Ya. B. Klmt. Ketal. 1973b, 14, 83. Gorokhovatskii, Ya. B.; Pyatnitskaya, A. I. Kinet. Ketal. 1972, 13, 1527. Knorre, D. 0.; Chugukina, L. 0.; Emanuel, N. M. 2%. F k . Khlm. 1959, 33, 877. Meyer, C.; Clement. G.; Balaceanu, J. C. Proc. Int. Congr. Catal. 3rd 1984 1965, 1 , 134. Mikhalovskii, S. V.; Gorokhovatskii, Ya. 8.; Evmenenko, N. P. Klmt. Ketal. 1976, 17. 1058. MukherJee, A.; Graydon, W. F. J . fbys. C b m . 1967, 71, 4232. Neuberg, H. J.; Graydon. W. F. J . Catal. 1972, 25, 425. Neubeq, H. J.; Phillips, M. J.; Graydon, W. F. J. Catal. 1976, 38. 33. Robertson, A.; Waters, W. A. J . Chem. Soc. 1948, 1535. Sadana, A.; Katzer, J. R. J . Catal. 19741%35, 140. Sadana, A.; Katzer, J. R. I d . Eng. Ghem. Fundam. 1974b, 13, 127. Sadana, A. Ind. Eng. Chem. proces4Des. Dev. 1979, 18, 50. Varma, G. R.; Graydon, W. F. J. Cats/. 1973, 28, 236. Vreugdenhil, A. D. J. Catal. 1973, 28, 493.
Chemical Engineering Division National Chemical Laboratory Poona 41 1 008,India
Ajit Sadana
Received for review May 29, 1980 Accepted October 28, 1980
Effect of Inhibitors on Hydrate Formation A method is proposed to predict the effect of inhibitors on natural gas hydrate formation conditions. Initiil experimental results indicate that the proposed method is much more accurate than the method which forms the basis for current industrial practive of inhibitor injection into natural gas streams.
Introduction
Gas hydrates are members of a group of compounds called clathrates, which are comprised of guest molecules and host molecules. The host, or water molecules, form a lattice which is stabilized by the inclusion of the guest molecules. Conditions favoring hydrate formation are those of high pressures and low temperatures. One of the two structures (I or 11) is formed by the water and gas, depending on the size of the gas molecule. Gas hydrates can be formed by a pure gas or by a mixture of gases. Davidson (1973) gives an excellent review of the physicochemical aspects of hydrates. The formation of natural gas hydrates was first brought to the attention of the natural gas industry by HammerSchmidt (1934), when he determined that freezing in gas pipelines was not due to ice but to gas hydrates. Recently, hydrates have become of interest due to estimates of large deposita of gas in hydrate form by Makogon (1974) and Katz (1971). In his initial effort, Hammerschmidt (1939) presented a method for determining the effect of inhibitors such as calcium chloride, ethanol, and methanol on hydrate formation conditions. Unfortunately, the compositions of the gases used by Hammerschmidt were not reported. Nevertheless the initial study was the basis for the current industrial standard, as in the GPSA Data Book, for methanol injection to inhibit hydrate formation. This work was undertaken to determine a theoretically sound, yet accurate method for determining hydrate inhibition. A modification is made to the model of Parrish 019&4305/81/1120-0399$01.25/0
and Prausnitz (1972) to incorporate the effects of inhibitors. Thermodynamic Model
Shortly after the crystalline structures of hydrates were determined, van der Waals and Platteuw (1959) developed the basic statistical thermodynamics model used in current three-phase (hydrate-gas-water rich liquid) formation predictions as kwL= pwH - RT In y ~ =, pWB + RT&, In (1 -) ,6 + RT In yg, (1) m
The basic equation may be considered as a modification of Raoult’s law with k@ as the chemical potential of water in the unoccupied hydrate lattice, the summation term resulting from the guest molecule occupation of the lattice, and the final term resulting from the normally small solubility of the guest molecule in liquid water. The activity coefficient of water, yw,is normally taken as 1.0 due to the fact that the water concentration is almost pure when hydrocarbons are the hydrate gases. The number of type m cavities per water molecule in the lattice, v, is a constant. The fraction of type m cavities occupied by a type j gas molecule is given by the formula
where the Langmuir constant, Cmj,is a function of tem0 1981 American Chemlcal Soclety
400
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
I
I
-I"
I 273 15
274 15
275 15 TEMPERATURE ( K )
276 15
277 15
__
Figure 1.
273 15
274 15
275 15
277 15
276 15
TEMPERATURE (K)
Figure 3. I5 10.
- Kakaymhl'r
60 273 15
ma
A-Calculated u s m g Hommschmidt I
70
274 15
275 15
276 15
X Cakubted usrq model eqwm
27715
TEMPERATURE ( K i
Figure 2.
perature, specific to each guest compound and cavity. The second basic equation of the model, proposed by Parrish and Prausnitz is
(3) where Ap (E pw@ - pwH) is related to the volume difference between hydrate and water Au, as determined by the X-ray crystallographic work of von Stackelbergand Mdler (1954) and by the reference Ap(To,Po)and Ah, recently determined by Dharmawardhana et al. in this laboratory (1980). The basic method for finding hydrate dissociation conditions requires that the temperature and pressure be determined which cause the chemical potential difference of eq 3 to match that of eq 1. With an inhibitor such as a salt present in the liquid, only the activity coefficient in eq 1 need be changed to reflect the new activity of the water, because the inhibitor has a low vapor pressure and does not enter the hydrate structure. Experimental and Calculational Results The experimental apparatus, described in detail by Zerpa et al. (1979), consisted of a windowed hydrate formation cell, platinum resistance thermometer, and capacitance pressure gauge. Liquid solutions at the desired inhibitor concentration were loaded into the cell. The 99.86% pure cyclopropane was chosen as the hydrate dormer due to its unique ability to form each structure as a function of temperature, as cited by Hafemann and Miller (1969). After hydrate formation the temperature was slowly increased to allow the hydrates to decompose. The visually determined point of hydrate decomposition over several cycles was taken as the equilibrium point at the temperature and pressure. Further details of the experiments are presented elsewhere (Menten, 1979). Data are presented in Figures 1, 2, and 3 for hydrate inhibition with KC1, CaC12,and CH,OH. The lines of these figures were determined by the model eq 1through 3 with
2L2?415
2 k I 5 2 7 b 2&15 2&l5 TEMPERATURE ( K l
&I5
&15'
Figure 4.
the parameters presented by Parrish and Prausnitz. Differences between the lines only indicate a water activity 9 ~no) effect effect modifying eq 1with the RT In ( ~ term; on the hydrate itself is included. The three equations are then used in the normal manner to obtain hydrate formation conditions. Colligative properties, such as freezing point depression, from the CRC Handbook (1966) were used to estimate the water activity coefficients in the salt solutions. For water activity coefficients in methanol solutions, Wilson equation parameters were obtained from Holmes and Van Winkle (1970). With any of the three inhibitors the lowest water activity coefficient was 0.95, which illustrates the strong effect of a small deviation from unity. For the methanol calculations, a flash was performed to ensure that a negligible amount of methanol was lost to the vapor phase; for these conditions the pure cyclopropane fugacity could be used in eq 2 with no loss in accuracy. Pieroen and Korvezee (1962) use the Gibbs-Helmholtz relation to determine that the isobaric hydrate formation depression, AT, should be constant for small inhibitor concentrations, with the equation RT12 AT z In (1- xi) constant P (4) AH Equation 4 indicates that the inhibitor merely displaces the P-T behavior of the pure binary hydrate, resulting in the parallel nature of the lines of Figures 1through 4. In this study there were insufficient data to conclusively determine if the cyclopropane hydrate transition from structure I and II was affected by the inhibitor's presence. To further test the model, data presented by Kobayashi et al. 1951) for a 15 wt % ethanol solution with pure methane were compared to predictions by the HammerSchmidt method and the method of the present work, as shown in Figure 4. For this system the inhibition method proposed gives an average of eight times the accuracy of the Hammerschmidt method.
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
