J . Phys. Chem. 1984,88, 2398-2404
2398
Investigation of the Gas-Solid Joule-Thomson Effect for Argon-, Nitrogen-, and Carbon Dioxide-Carbon Powder Aerosol Systems Thomas R. Rybolt* Department of Chemistry, The University of Tennessee at Chattanooga, Chattanooga, Tennessee 37402
and Robert A. Pierotti School of Chemistry, The Georgia Institute of Technology, Atlanta, Georgia 30332 (Received: June 27, 1983; In Final Form: November 1, 1983)
An apparatus was constructed to disperse a fine powder in a flowing gas and measure the thermal changes associated with a pressure drop across a glass orifice. The gas-solid Joule-Thomson effect was examined for 12 different gas-solid systems at a temperature of 302 K, a downstream pressure of 120 kPa, pressure drops across the orifice from 5 to 45 kPa, flow rates from 2 to 14 mmol/s, and aerosol concentrations from 0 to 16 g of powder/mol of gas. The gaseous component included either argon, nitrogen, or carbon dioxide and the particulate component included either Mexican Graphite (26 m2/g), Nuchar S-C (903 m2/g), Nuchar S-A (1661 mZ/g),or Super Sorb (3169 m2/g) carbon powder. A significant enhancement of the JouleThomson cooling effect was found for gas-porous carbon systems relative to a pure gas. The dependence of the magnitude of this effect on the gas-gas and gas-solid interactions was predicted from a virial equation of state based on statistical thermodynamic considerations. Gas-solid virial coefficients and their temperature derivatives were used in conjunction with the theoretical model as modified by heat-transport effects to assess the reliability of theory in predicting the experimentally determined gas-solid Joule-Thomson coefficients.
Introduction During the period from 1852 to 1862 a series of experiments were carried out by James Prescott Joule and William Thomson (Lord Kelvin) in which they measured the temperature changes associated with the expansion of various gases through a porous plug or a throttle From an applied standpoint, much of the interest in this effect is due to practical application in the liquefaction of gas and in cryogenic coolers." Joule-Thomson data on pure and mixed gases also provide a sensitive measure of the reliability of various empirical equations of state and can be used to calculate various other thermodynamic quantities.' From a theoretical standpoint, the Joule-Thomson experiment is important because it provides information which can be used to examine the nature of the intermolecular forces operative among gase~.~,~ A number of theoretical and experimental studies have been made on multicomponent gas systems, including work by Strakey,' Ng,l0 Ahlert," Gustafsson,'* and many others. Despite the prior studies on gas mixtures, there has been no previous work on determining the Joule-Thomson coefficient for a gas-solid dispersion. If a fine powder is dispersed into a gas, then the resultant solid aerosol may be considered to be a new fluid with unique thermodynamic properties. The solid particles may be formally considered to be giant molecules and thus they make up one component of a multicomponent mixture.13 The possibility of (1) J. P. Joule and W. Thomson, Philos. Trans. R. SOC.London, 144,321 (1854). (2) J. P. Joule and W. Thomson, Philos. Trans. R. SOC.London, 7, 127 (1856). (3) J. P. Joule and W. Thomson, Philos. Trans. R. SOC.London,152,579 (1862). (4) R. W. Johnson, S . C. Collins, and J. L. Smith, Jr., Adu. Cryog. Eng., 16, 171 (1971). ( 5 ) R. V. Annable, Appl. Opr., 17, 2739 (1978). (6) K. C. Cheng and J. Ou,Can. J . Chem. Eng., 56, 31 (1978). (7) J. P. Strakey, C. 0. Bennett, and B. F. Dodge, AIChE J . , 20, 803 ( 1974). (8) V. P. S. Nain and R. A. Aziz, Can. J . Chem., 54, 2617 (1976). (9) L. Rodriguerz, AIChE J., 24, 5 5 5 (1978). (10) H. J. Ng and A. E. Mather, J . Chem. Eng. Data, 21, 291 (1976). (11) R. C. Ahlert and L. A. Wenzel, AICHE J., 15, 256 (1969). (12) 0. Gustafsson, Ark. Fys., 40, 481 (1970).
0022-3654/84/2088-2398$01.50/0
using a gas-solid dispersion has not been considered prior to the current work, and there have been no previous studies of the gas-solid Joule-Thomson effect. In the current work, thermodynamic modeling of a gas-solid dispersion is accomplished by considering the gas-gas and gas-solid interactions which are present because of van der Waals forces. A virial equation of state associated with a gas-solid aerosol is used to predict the dependence of the magnitude of the gas-solid Joule-Thomson effect on gas and gas-solid virial coefficients. The purpose of this investigation is to determine the magnitude of the gas-solid Joule-Thomson effect for 12 different aerosol systems and compare these experimental results with the theoretical predictions.
Theory W i a l Model. The Joule-Thomson Coefficient, pm, corresponds to the change in temperature associated with a change in pressure at constant enthalpy, (dT/dP),. The Joule-Thomson coefficient may be related to the molar volume of a gas by where cpis the molar heat capacity, Tis the temperature, and P is the pressure. Using the virial equation of state for a pure gas, one may rewrite 1 as14
where B2* is the second gas virial coefficient, B2s/ is the temperature derivative of the second gas virial coefficient, B3gis the third gas virial coefficient, B3gl is the temperature derivative of the third gas virial coefficient, etc. The limiting value of the Joule-Thomson coefficient as the pressure goes to zero is written as
where
cpois the zero-pressure value of the molar heat capacity.I5
(13) R. B. Evans 111, G. M. Watson, and E. A. Mason, J . Chem. Phys., 35,2076 (1961). (14) T. R. Rybolt, J . Chem. Educ., 58, 620 (1981). (15) J. Q.Hirschfelder, C. F. Curtis, and R. B. Bird, "Molecular Theory of Gases and Liquids", Wiley, New York, 1964.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88. No. 11, 1984 2399
Gas-Solid Joule-Thomson Effect In order to develop an expression for the Joule-Thomson coefficient of a gas-solid dispersion it is first desirable to derive a virial equation of state for an aerosol. A correct statistical mechanical treatment will of necessity include the gas-gas interactions as manifest in deviations from gas ideality and the gassolid interactions as manifest in physical adsorption. Utilizing the ensemble method of Gibbs,16J7we have presented elsewhere a derivation of the virial equation of state for a solid powder dispersed in a gas.ls,lg The theoretical treatment uses the grand partition function and is based on the following assumptions: the system of interest is a two-component fluid phase composed of a molecular gaseous component and a particulate component where the solid particles are formally treated as giant molecules, the molecular component is an imperfect gas capable of interacting with the particulate component and itself through dispersion forces, and the particulate component is dilute enough to exclude particle-particle interaction. The virial equation of state for a gas-solid dispersion is
PV/RT = 1
+ (B2, - wBZs)(P/RT) +
(B3g - BZg2 - 4B3s
+ 2B2,B2s))(P/RTl2 + ... (4)
where R is the gas constant, w is the mass of solid dispersed in 1 mol of gas molecules, Bi,is the ith gas-solid viriall coefficient where i = 2, 3, 4, ..., and is the constant-pressure heat capacity for a gas-solid dispersion. In the region of low surface coverage = wCS1where is the heat one may approximmae cgs capacity of 1 mol of gas and C,’ is the heat capacity of 1 g of solid. Solvin eq 4 for V, substituting the resultant equation into eq 1 , and simplifying gives
e, +
c,
= KTB2,’ - BZg) + @zs - TB2,’)l + (P/RT)((TB3,’ - 2TB2,B2,‘ - 2B3, 2B2,2) w(2B3, 4BzoB2, - TB3,’ - 2TB,,BZ,’ - 2TB2glB2,)J ... ( 5 )
CLgscgs
+
+
+
+
where pgsis the gas-solid Joule-Thomson coefficient and Bi,’is the temperature derivative of the ith gas-solid virial coefficient. The limiting value of the gas-solid Joule-Thomson coefficient where the pressure goes to zero is written as llgSO~g’gs0 =
(TB2,’
- B2g) + @2s
- TBZ,‘)
(6)
where is the zero-pressure limit of the molar heat capacity. Transport Considerations. In the ideal Joule-Thomson experiment a steady stream of gas flows through a constriction under adiabatic conditions and the temperature change is given by AT,, = pgAP
(7)
where ATjT is the change in temperature arising from the Joule-Thomson effect, AP is the pressure drop across the constriction, and @, is the Joule-Thomson coefficient for a gas. The actual experiment is complicated by heat leaks. Thermal variations along the flow tube are induced by jet kinetic cooling in the region of the orifice and Joule-Thomson cooling in the lower pressure region beyond the orifice. The effects of heat transfer into the cooler regions of the flow tube alter the ideal relation indicated in eq 7. Due to jet kinetic cooling in the region of the orifice, the gas stream is cooler than the surroundings, and so there may be a heat leak.20,21 Because of the experimental design, the constriction in the flow tube is not an extended capillary, but more like an orifice in a thin plate. Thus, the surface area around the orifice (16) T. L. Hill, ’Introduction to Statistical Thermodynamics”, AddisonWesley, Reading, MA, 1960. (17) T. L. Hill, ”Statistical Mechanics”, McGraw-Hill, New York, 1956. (18) R. A. Pierotti and T. R. Rybolt, J . Chem. Phys., in press. (19) T. R, Rybolt, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA, 1981. (20) G. Pocock, and C. J. Wormald, J . Chem. Soc., Faraday Tram. 1,71, 705 (1975). (21) J. S. Rowlinson, “The International Encyclopedia of Physical Chemistry and Chemical Physics”, Vol. 5, Pergamon Press, New York, 1969, Topic 10, pp 112-20.
Figure 1. Flow behavior of a gas. Circles represent experimental data for nitrogen, oxygen, argon, and carbon dioxide. Solid line is based 00 linear regression fit where slope is 1.66.
across which heat flow could occur was very small. It was found that the net warming of the gaseous fluid stream in the vicinity of the orifice was negligible in this experiment. A more significant heat leak arises because gas downstream of the orifice is cooled due to the Joule-Thomson effect. The result of this heat leak is to cause the measured AT to be smaller than that expected for an isenthalpic Joule-Thomson experiment. The change in temperature of a flowing gaseous fluid due to a transfer of heat from warmer surroundings is given as20
where AThl is the temperature change due to a heat leak, dqldt is the heat transfer per unit time, f,is the molar flow, and is the molar heat capacity of a gas. Both radiative and conductive heat transfer per unit time can be modeled by22323dqldt = +gATd where is a constant which depends on the mode of heat transfer and the total surface area across which heat is transferred and ATd is the thermal difference between lower and higher temperature regions. It was observed experimentally (Figure 1) that the fluid flow for a pure gas could be effectively modeled as
e,
+,
where AP is the pressure drop across the orifice, P2 is the pressure on the downstream side of the orifice, M is the molar weight of gas, T1 is the temperature of the gas stream upstream from the orifice, and k, = 1.66 (g mol K)’l2/(atm s) is the constant for the gas. For an aerosol it was found that the flow of the gas component could be modeled by eq 9 where the constant k,, is specific to the type of gas-solid mixture and loading conditions, Le., amount of powder dispersed into flowing gas stream. This empirical equation is analogous to the equation used to model the flow through an orifice in a thin plate.20J4 For a heat leak which arises because of Joule-Thomson cooling in a flowing gas AT,, is given by eq 8, dg/dt is given by +,ATjT, f,is given by eq 9, and ATjT is given by eq 7 . Combining these four equations, one obtains for the heat leak
(22) A. I. Brown and S. M. Marco, ‘Introduction to Heat Transfer”, 3rd ed., McGraw-Hill, New York, 1958, pp 26-33, 49-61. (23) M. N. Saha and B. N. Srivastava, “A Treatise on Heat”, 2nd ed., Indian Press, Allahabad, India, 1935, pp 334, 573-4. (24) E. Ower and R. C. Pankhurst, “The Measurement of Air Flow”, 5th ed., Pergamon Press, Elmsford, NY, 1977.
2400 The Journal of Physical Chemistry, Vol. 88, No. 11, 1984
where the constant 9, is an empirical constant. An analogous equation can be written for the heat leak in a flowing aerosol where the parameters &, p,,, k,,, and CgSare used to represent a gassolid system. Thermal Equations. The temperature change of the gas is given by AT = AT,, - AThl + ATin (11) where ATi, is the initial temperature difference across the orifice found by extrapolating AP to zero. This term, ATin,is a constant which serves only to shift the origin of the AT vs. AP curve. Replacing AT,, by eq 7 and AThlby eq 10 gives
If the values of d,, M , T , k,, @, and P2 are known, then a series of AT and AP pairs can be used to find the best fit of pg and ATi,. An equation analogous to eq 12 can be written to describe the thermal effects operative in the flow of a gas-solid dispersion where the temperature change in a dusty gas, AT, is given by
In the region of low pressure the gas-solid Joule-Thomson coefficient is approximated by
If w is not maintained at a constant value, then wgS will not be a constant. However, even if w and AP are varied independently as AT is measured, B2s- TB28/is a constant for a given gas-solid system. Equation 14 can be substituted into eq 13 to give ~
( A T - ATi,)Cg',,Z
O
s
=
n
9 ,kg,P21/2 s(Mn'/2Apl/2
-
(15)
z
where 0, = BZs- TB2,' and 0, = TB2i - B2,. Given the values of ,1Q M, T, k,,, @., C,', P2, and @, then a series of values of AT, AP, and w can be used to find the best fit of 0, and ATi,,. Once the values of 0, and 0, are obtained, then p,, can be predicted a t any loading w.
Experimental Section Materials. The gases used in this work included argon, carbon dioxide, helium, nitrogen, and oxygen; these gases had a minimum reported mole percent purity of 99.8, 99.8,99.998,99.6, and 99.7, respectively. The heat capacities of these gases a t 101 kPa and 300 K are as follows (J/(mol K)): Ar, 20.8; C02, 37.1; He, 20.8; N2, 29.1; and 02,29.4.25 Carbon dioxide was obtained from Matheson. The other gases were supplied by M & A Welding Co., Atlanta. The powders used in the current work included Mexican Graphite (No. 25 Lubricating Graphite from the United States Graphite Co.), Nuchar S-C, Nuchar S-A (provided by Dr. Kornegay of Westvaco Chemical Division), and Super Sorb (provided by Dr. Thomas OGrady of Amoco Research). These powders were selected to span a range of surface area and porosity. The Nuchar S-C powder was filtered through a 177-um sieve to remove larger particles which clogged the glass orifice during aerosol flow. According to information supplied by Amoco, the Super Sorb particles ranged up to 103 pm in diameter, 96% of the particles were smaller than 19 pm, 66% were smaller than 3.8 pm, 54% were smaller than 2.7 gm, and 25% were smaller ( 2 5 ) F. D. Rossini, Ed., "Tables of Selected Values of Chemical Properties", National Bureau of Standards, Washington, DC, 1952, Natl. Bur. Stand. (US.), Circ. No. 500.
Rybolt and Pierotti
RECULAIOR
OUTLET VALVE
ImEr VALVE
FILIER
Figure 2. Schema of gas-solid Joule-Thomson apparatus
than 1.1 pm. According to WestvBco, the Nuchar S-C and S-A powders averaged 95-100% smaller than 149 pm, 85-95% smaller than 74 pm, and 65-85% smaller than 44 pm. The bulk densities of Super Sorb, Nuchar S-A, and Nuchar S-C powders were 0.35, 0.40 f 0.02, and 0.45 f 0.03 g/cm3. The powders were degassed to remove water prior to placing them in the aerosol generator. The nitrogen BET surface areas were 26, 903, 1661, and 3169 m2/g for Mexican Graphite (MG), Nuchar S-C (SC), Nuchar S-A (SA), and Super Sorb (SS), respectively. Pore size distributions were determined. The pore volumes for pores in the 2-60-nm range were 0.118, 0.572, 0.925, and 0.797 cm3/g for MG, SC, SA, and SS, respectively. Using a DSC-18 PerkinElmer differential scanning calorimeter we found the heat capacities of Mexican Graphite, Nuchar S-C, Nuchar S-A, and Super Sorb to be 0.77 f 0.02,0.87 f 0.09, 0.93 f 0.05, and 0.88 f 0.1 1 J/(g K) at 29 OC. The heat capacity of graphite has been reported as 0.73 J/g K) at 30 oC.26 Apparatus. A scheme of the gas-solid Joule-Thomson apparatus is shown in Figure 2. With this apparatus it is possible to disperse a fine powder into a gas stream, flow the resultant mixture through an orifice, measure the absolute pressure and temperature of the flowing aerosol, measure the pressure drop and temperature change across the orifice, filter out the solid powder, and determine the flow rate of the gas. The portion of the apparatus which required temperature control was placed inside a thermostated box. The aerosol generator consisted of a metal chamber containing a rotating powder container, retaining partition, and pickup valve?' The bulk of the powder was retained behind a metal partition, while a thin layer of powder was carried under the pickup valve. Powder was entrained and deagglomerated by gas passing upward through the multiple small-diameter passages in the pickup valve. The aerosol generator was mounted on a cylindrical base which was bolted to the bottom of the thermostated box. A variablespeed motor was used to rotate the powder container. The interior chamber pressure was maintained with the use of rotating seals. The flow system was designed to flow a gas-solid mixture through a glass constriction, filter out and collect the particulate solid, and monitor the flow rate of the gas. Gas was flowed through a inlet valve and thermally equilibrated prior to entering the aerosol generator. The gas-solid mixture after leaving the aerosol generator was flowed through a glass constriction tube (6-mm i.d. and 9.4-mm 0.d. with a 1-mm i.d. orifice). Branches off the central tube were 10 cm before and after the constriction. Powder filters using medium-porosity fritted glass disks were placed at each of these side tubes. After flowing through the constriction tube the gas-solid aerosol flowed into a filter bag to remove the solid. The gas flowed through the filter bag through an outlet valve to a wet test meter to determine the flow rate. The (26) C. L. Mantell, "Carbon and Graphite Handbook", Wiley-Interscience, New York, 1968, p 28. (27) E. Y . H. Keng and C. Orr, Jr., "Heat Transfer to a Gas Containing a Cloud of Particles", Final Report NASA Grant No. NSG-273-62, Georgia Institute of Technology Atlanta, GA, 1969.
Gas-Solid Joule-Thomson Effect collector bottle with attached filter bag could be removed from the collector tube and weighed before and after powder flow to determine the mass of powder transferred. A Model 90H-300 MKS Baratron capacitance manometer head was used to measure the pressure difference across the glass orifice. The high-pressure and low-pressure sides of the capacitance head were connected to the upstream and downstream filters, respectively. A Bourdon gauge was used to measure the pressure downstream of the orifice relative to atmospheric pressure. Atmospheric pressure was determined with a mercury barometer. Twelve copper-constantan thermocouples were used in these measurements. One of the thermocouples was placed in a water-ice bath and used as a reference. Eight of the thermocouples could be used in conjunction with a reference thermocouple to determine absolute temperatures. Three of these thermocouples could be used with the remaining three thermocouples to determine differential temperatures. A Keithley 155 microvoltmeter was used to measure the potential between selected thermocouples. The output from the microvoltmeter was recorded on a strip chart recorder. The main thermocouples of interest were thermocouples 1 and 2, which were placed in the middle of the glass flow tube 6.3 cm upstream and downstream of the orifice, respectively. Other thermocouples were placed throughout the apparatus to make sure that the interior of the thermostated box had reached thermal equilibrium. The thermocouples were calibrated against a Leeds and Northrup Model 8163-C NBS traceable four-lead platinum resistance thermometer. A fifth-order polynomial was used to calculate the temperature from the thermocouple potential. The results were consistent among all the thermocouples and the calculated temperatures agreed with the platinum resistance temperatures within fO.O1 from 252 to 310 K. Operation. The gas and gas-solid Joule-Thomson data were taken in a temperature range of 298-303 K. The inlet and exit valves were adjusted to give the desired values of P2 and AP. The downstream pressure, P2, was held fairly constant at about 125 kPa while AP was adjusted to some value between 2 and 42 kPa. The primary experimental data for each gas system included measurements of P2, AP, T I ,AT, andf,. After data were taken at one value of AP,the gas flow was halted and then started again at the next desired value of AP. A series of measurements were made over a range of AP values. The initial procedure which was used for a solid aerosol was the same as for a pure gas. After the gas flowed for about 15 min and the data were obtained for the pure gas, the aerosol generator was started. While a gas-powder mixture was flowing, the measurements of AT, T 1 ,P2, AP, and f,were repeated. In addition, the average concentration of the aerosol, w , was calculated from the mass of powder transported to the collector and moles of gas flowed through the flowmeter during the time interval that the aerosol generator was operating. The aerosol concentration was found to depend on the flow rate of the gas. Since the flow rate is determined by the pressure drop across the orifice, the aerosol concentration varied as AP was changed. For a given gas-solid system a series of measurements were made over a range of AP values. Results Experimental Joule-Thomson data were obtained for helium, nitrogen, oxygen, argon, and carbon dioxide. These data included measurements of AP, AT, P2, and T I . These experimental JouleThomson data can be used in conjunction with the molecular weights and heat capacities of the gases and the flow constant k, = 1.66 to obtain the Joule-Thomson coefficients. Since eq 12 describes the thermal effects associated with a pressure drop in a flowing gas system, it is used to analyze the experimental data. Equation 12 may be rewritten as
where
The Journal of Physical Chemistry, Vol. 88, No. 11, 1984 2401 TABLE I: Results of Gas Joule-Thomson Analysis *K9
gas He Nz 0 2
Ar CO2
T1, K 298.3 298.0 298.1 298.1 298.4
P2,
atm 1.224 1.230 1.230 1.235 1.233
atm1I2 s K/J 0.905 1.705 1.807 2.845 1.675
AT,,, K -0.006 -0.024
MK,
K/atm -0.060 0.21 0.26 0.38 1.15
I:$ -0.014
o.06t t
-1
I
Y
Y
0.0
0.1
0.2
0.3
0.4
0.5
AP (ATM) Figure 3. Joule-Thornson results for nitrogen where circled points are experimental data and solid line is empirical fit based on eq 12 using parameters given in Table I. A linear relationship is obtained between p,AP - T and AP1I2 where the slope of the line is given by p,Q,\k,, and the intercept is given by AT,,. Within a given set of gas data, T I and P2 vary only slightly; therefore, \k, is a constant. If the heat-leak constant, 4,. is known, then p, can be determined from the slope. For a given set of gas data, values of T I and P2 are calculated and k, to calculate and used with the appropriate values of M, V?*. A value for p, is selected and used with AP, AT data to generate a set of psAP - AT vs. AP1I2data pairs. A linear regression fit is used to find the slope (p&,\k,) and intercept (AT,,). The slope is used with 4, and V?, to calculate fi,. The selection is incremented and the preceding process repeated. This process is continued until the selected value and calculated value of the gas Joule-Thomson coefficient are in agreement. The difference between these two quantities diverges as one moves in either direction from the correct value of the Joule-Thomson coefficient, The results of the preceding computations for five different gases are reported in Table I. A selection of the system heat-leak constant, 4, = 0.060 J/(s K), was made by requiring the argon data to give the expected Joule-Thomson coefficient of 0.38 K/atm. For the remaining gases, the Joule-Thomson coefficients were calculated by using the same value of the heat-leak constant. Comparisons of the expected results for pJT(K/atm) at 101 kPa and 300 K (-0.062 for He,280.22 for N2,200.27 for 02,29 0.38 for Ar,30and 1.10 for C 0 2 l ) and the observed results reveal a good correlation of the data. The consistency of Joule-Thomson coefficients obtained for these five gases confirms the validity of the thermal-transport considerations developed earlier. Figure 3 shows the nitrogen ATvs. AP experimental data and the best-fit curve through these data. This curve is based on eq 12 and the
c,,
(28) D.T. Mage, Can. J. Chem. Eng., 42, 2911 (1965). (29) R. D. McCarty and L. A. Weber, NES Tech. Note, No. 384 (1971). (30) A. Michels, R. J. Lunbeck, and G. J. Wolkers, Appl. Sci. Res. Sect. A , 2, 345 (1951). (31) E. W. Washburn, Editor-in-Chief,"International Critical Tables", Vol. V, Maple Press, New York, 1929, p 145.
2402 The Journal of Physical Chemistry, Vol. 88, No. 11, 1984
Rybolt and Pierotti
TABLE I 1 Results of Gas-Solid Joule-Thomson Analysis
k,,, gas-solid system Ar-MG Ar-SA Ar-SA Ar-SS Nz-MG NZ-SC N2-SA Nz-SS COZ-MG
c0,-sc COz-SA co2-ss
Ti, K
Pz, atm
(g mol K)'12/ (atm s)
302.0 302.0 301.7 302.3 302.3 302.5 301.5 302.5 299.8 302.4 302.5 302.4
1.252 1.239 1.255 1.252 1.242 1.237 1.241 1.259 1.249 1.237 1.245 1.270
1.78 1.56 1.72 1.75 1.75 1.56 1.76 1.58 1.86 1.77 1.87 1.87
constants summarized in Table I. The square root of AP dependence introduces curvature into the ATvs. AP plots and ATin causes a vertical displacement relative to 0. Experimental Joule-Thomson data were obtained for 12 gassolid systems. The gaseous component was either argon, nitrogen, or carbon dioxide. The particulate component was either Mexican Graphite (MG), Nuchar S-C(SC), Nuchar S-A (SA), or Super Sorb (SS). Two sets of data were taken for each gas-solid system including values of w, AP, AT, Pa,T I ,and f,. One set of data was obtained from measurements made when the aerosol generator was not operating and thus represents pure gas flow. For all of these data the loading factor, mass of powder dispersed per mole of gas, w, is zero. The second set of data was obtained from measurements made when the aerosol generator was operating and thus represents gas-powder flow. Gas and gas-powder flows were alternated for a range of AP values. In the flow rate, low AP region where fn < 3.0 X mol/s or AP < 10 kPa it was not possible to obtain a sufficient dispersion of powder to make the analyses of gas-solid flow practical. A loading of less than 3 g/mol was found to be too small to be acceptable for the gas-solid analysis, because AT for the gas-solid was too similar to AT for the gas to make a clear distinction between the two conditions. The concentration of the solid aerosol varied among the gas-solid data because the magnitude of the loading depended on AP and the flow rate. Also, the loading varied because the effectiveness of dispersing a powder among the various gas-solid systems was inherently different. The aerosol concentration ranged from 3 to 16 g of powder/mol of gas. The gas data which were taken interspersed with the gas-solid data provided a check to ensure that there were no changes due to the presence of powder coating the flow system. All the gas data were grouped into three sets including data for argon (37 points), nitrogen (40 points), and carbon dioxide (49 points). These data sets which included values for AP,AT, Pz, and T I were analyzed by using the pure-gas procedure which was described previously. The same value of 4g = 0.060 J/(s K) was found to provide satisfactory fit of the gas data which were taken in a powder-coated system. The gas Joule-Thomson coefficients were found to be 0.37,0.19, and 1.05 K/atm for argon, nitrogen, and carbon dioxide, respectively. The respective ATi, values were 0.002, -0.002, and 0.009 K. Despite the fact that the flow system was coated with powder when the data were taken and that the data were obtained over a period of several months, the agreement with the expected results and the previous experimental pure-gas results is good. The experimental values of AT and AP obtained for pure nitrogen, nitrogen-Mexican Graphite, nitrogen-nuchar S-C, and nitrogen-Super Sorb are shown in Figure 4. It is clear that the addition of the low surface area graphite powder attenuates the gas Joule-Thomson effect. However, the dispersion of porous powders into a gas is observed to greatly enhance the JouleThomson effect. The treatment employed for the gas-solid data was based on eq 15. Since the aerosol loading was not constant, the gas-solid data could not be fitted to a single curve as was the
A,
ATim K
cm3/g
SD of ,f3,
-0.014 0.035 -0.005 0.024 -0.020 0.01 1 0.010 0.013 -0.044 0.104 0.067 0.049
0.3 15.4 18.0 25.8 0.5 18.8 17.7 28.7 2.1 83.7 108.5 193.2
5.31 2.60 3.17 1.97 3.37 0.53 2.94 0.82 5.86 1.32 2.61 19.2
L
J
I
I
I
I
I
I
0.0
0.1
0.2
0.3
0.4
0.5
AP (ATM) Figure 4. Gas-solid Joule-Thomson data for pure nitrogen (circles), nitrogen-Mexican Graphite (triangles),nitrogen-Nuchar S-C (squares), and nitrogen-Super Sorb (hexagons).
case for the gas data. However, ,f3, should be a constant for a given gas-solid system at one temperature. Therefore, an iterative procedure involving the adjustable parameter ATi,,was utilized to find the minimum standard deviation of 0,for a given gassolid system. The relevant parameters involved in calculating 0,include M , c , C,', T I ,P2, AT, w, AT,,, k &, and &. The heat capacities of the solids were determineds'from differential scanning calorimeter studies and found to be 0.77 J/(g K) for the graphite powder and 0.89 J/(g K) for the averaged value of the porous powders. The temperature, pressure, and aerosol loading parameters were determined during each set of gas-solid experiments. The flow constants were determined by fitting the experimental data to eq 9, the flow equation. 0,values of 78, 63, and 403 cm'/mol were calculated for argon, nitrogen, and carbon dioxide, respectively. Equation 15 was used in conjunction with the available experimental data to calculate values of p, for each gas-solid system at each value of AP for which data were available. Using 4gs= 0.060 J/(s K) we selected the value of ATinto give the minimum standard deviation of 0,values for each gas-solid system. The results of these calculations are given in Table 11. All three gas-Mexican Graphite systems resulted in an attenuation of the cooling effect relative to the pure gas. For these three systems the value of ATi, was selected to be the same as that for pure gas, and because of the small magnitude of the effect considerable scatter in the data was observed. The values obtained for (3, could be roughly divided into five groups. The use of Mexican Graphite resulted in a reduction of the cooling relative to the pure gas and gave small values of &, close to zero. Argon and nitrogen used with either Nuchar S-C or Nuchar S-A resulted in a value of p, in the range of 15-20
The Journal of Physical Chemistry, Vol. 88, No. 11, 1984 2403
Gas-Solid Joule-Thomson Effect
TABLE III: Estimates of p, Based on Gas-Solid Chromatoerachv Data 0.20 g h o l
0.2
0.0
0.4
gas-solid system Ar-MG Ar-SC Ar-SA Ar-SS Nz-MG N2-K Nz-SA Nz-SS C02-MG
0.8
0.6
co*-sc COZ-SA coz-ss
1.0
AP (ATMI Figure 5. Predicted dependence of the carbon dioxide-powder isenthalpic Joule-Thomson effect as the type of powder is varied.
T11 K 302.0 302.0 301.7 302.3 302.3 302.5 301.5 302.5 299.8 302.4 302.5 302.4
P,,
cm3/g 0.16 35.5 21.8 40.7 0.15
41.7 23.9 46.9 2.04 1488 814 859
4s10,
kJ/mol 9.6 16.1 13.1
13.2 9.2 17.6 13.9 14.1 17.3 30.3 27.4 23.1
w = 20 g/mol the Joule-Thomson effect for C02-SS is about 7 times greater than for pure COz. For the C02-graphite system, the adiabatic Joule-Thomson effect is decreased relative to the pure gas. This attenuation of the Joule-Thomson effect is not due to a negative gassolid interaction because @, must be positive for the temperature at which data were taken. However, if @, is approximately zero, the primary effect of adding powder to a gas is to increase the heat capacity of the gas-powder fluid relative to the pure gas. As eq 17 shows, an increase in the heat capacity will cause a decrease in the Joule-Thomson coefficient. The effect of changing the gaseous component and varying the loading in the gas-Super Sorb system in shown in Figure 6. The COz has a much stronger interaction with the solid than argon or nitrogen and thus produces a much larger cooling effect.
Discussion
-
2
0'
I
I
I
I
5
10
15
20
25
o (g/mol) Figure 6. Predicted dependence of the argon-Super Sorb, nitrogen-Super Sorb, and carbon dioxide-Super Sorb isenthalpic Joule-Thomson coefficients as the concentration of the aerosol is changed.
cm3/g. Argon or nitrogen with Super Sorb gave a value of @, around 25-30 cm3/g. Carbon dioxide with Nuchar S-C and Nuchar S-A gave results of 84 and 108 cm3/g. The largest effect was observed for carbon dioxide and Super Sorb with @, equal to 193 cm3/g. On the basis of the uncertainty of the primary data and a propagation of error analysis the gas-porous carbon values of P, may have an experimental uncertainty of up to 15%. Once 8, and PK are known, the adiabatic gas-solid JouleThomson coefficient can be calculated from wgs
--
@B -k
CK+ WC,'
(17)
for any aerosol loading, w . Figures 5 and 6 are based on eq 17 and thus assume an adiabatic experiment with no heat leaks. The effect of maintaining the loading constant, but varying the type of powder, is shown in Figure 5 . For the C02-porous powder systems which have strong gas-solid interactions, the adiabatic Joule-Thomson effect is increased relative to the pure gas. For
The effectiveness of the powders in producing a gas-solid Joule-Thomson cooling effect may be ordered as S S > SA SC > MG. The effectiveness of the gases in producing a gas-solid Joule-Thomson cooling effect may be ordered as C 0 2 > N2 Ar. Basically, these results correlate with the surface area of the powders and the expected strength of the gas-solid interaction. A direct comparison of the theoretical predictions and the experimental results found for the gas-solid Joule-Thomson effect requires an independent measurement of the second gassolid virial coefficient and its temperature dependence for each of the 12 gas-solid systems which had been studied. Gas-solid chromatography was used to determine values of B2, between 265 and 325 K for each of these s y s t e m ~ . ' ~ JFrom ~ gas-solid chromatography measurements the temperature dependences of the second gas-solid virial coefficients were determined, and it was found that In BZsvs. 1 / T was linear. As shown in Table I11 values of @, were calculated from the gas-solid chromatography dataI9J2 at the same temperatures of the corresponding Joule-Thomson measurements. Also given in Table I11 are the calculated values of the isosteric heats, qsto,which provide a measure of the enthalpy associated with desorption. A comparison of the values of P, obtained from the gas-solid Joule-Thomson (gsJT) experiments (Table 11) and the values of @, obtained from the gas-solid chromatography (GSC) experiments (Table 111) reveals that the former values are always less than the latter values. Values of the experimental gsJT and expected GSC Joule-Thomson coefficients can be calculated at any aerosol concentration by using eq 17. The predicted GSC Joule-Thomson coefficients increase as the loading, w, is increased, and they follow a pattern similar to the one observed for the gsJT Joule-Thomson coefficients (Figure 6). The most striking difference between pgsvs. w calculated from GSC and gsJT data is found in the C02-porous powder systems where clKSfor GSC increases very rapidly as the loading is increased. For the COz-SC, COz-SA, and COz-SS systems with w = 10 g/mol, pKsis predicted from GSC data to be 33.7, 18.8, and 19.8 K/atm, whereas pKscalculated from gsJT data is 2.7, (32) T. R. Rybolt and R. A. Pierotti, AZChE J., in press.
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The Journal of Physical Chemistry, Vol. 88, No. 11, 1984
Rybolt and Pierotti the isosteric heat since the gas-solid systems are in the region of low coverage. Therefore, it is expected that the logarithms of &(gsJT)/P,(GSC) will be linearly proportional to the isosteric heats of gas-porous carbon systems. Using the data from Tables I1 and 111, we constructed Figure 7. Figure 7 shows the suggested linear relation. An additional consideration is that higher order virial coefficients may be required to correctly predict values of pgs even at these temperatures and coverages.
qi+ (KJ/mol) Figure 7. Dependence of In (P,(gsJT)/P,(GSC)}on the isosteric heat for nine gas-solid systems where the type of solid and gas is designated as follows: SC, triangle; SA, circle; SS,square; Ar, point, N2,line, and C02 cross.
3.3, and 5.1 K/atm. Smaller discrepancies are observed for the argon-porous carbon and nitrogen-porous carbon systems. For example, for Ar-SC, Ar-SA, and Ar-SS systems with w = 10 g/mol, p g Sis predicted from GSC data to be 1.5, 1.0, and 1.7 K/atm, whereas p ,calculated from gsJT data is 0.79,0.88, and 1.2 K/atm. For t i e gas-graphite systems, the difficulty of accurately measuring the small values of AT observed in the Joule-Thomson experiments and the resultant scatter in &(gsJT) values means that the values of P,(GSC) fall within the range of uncertainty of P,(gsJT). The apparent discrepancies between these two methods may be reconciled by considering the influence of the gas-solid interaction energy on the kinetics of desorption. The Joule-Thomson coefficient, as defined, is an equilibrium thermodynamic property. In a Joule-Thomson experiment for a pure gas, the flowing gas reaches equilibrium just beyond the orifice. Because the molecules are weakly interacting through the van der Waals forces, there is no significant barrier to prevent the rapid attainment of equilibrium. However, the gassolid interaction energies are 10-20 times as strong as the pure-gas interaction energies. For the gas-powder systems, especially the porous powders, there is an energetic barrier to the desorption process. Thus, as the gas-solid aerosol flows past the downstream thermocouple, the equilibrium distribution of adsorbed and desorbed gas molecules may not have been attained. Therefore, the observed AT is smaller than the expected value based on equilibrium measurements such as those made with gas-solid chromatography. On the basis of an Arrhenius type relation, the rate of desorption should be dependent on the exponential of the energy of activation of desorption. If the attenuation of the expected GSC JouleThomson coefficient is due to the time required for desorption in the actual gassolid Joule-Thomson experiment, then the ratio of P,(gsJT)/&(GSC) should be related td the rate of desorption. The energy of activation for desorption can be approximated by
Conclusion The magnitude of the gas-solid Joule-Thomson effect was found to depend on the surface area and pore structure of the solid, the heat capacity of the particulate and gaseous components, the gas-gas and gas-solid interaction potentials, the operating temperature and pressure, and the concentration of the particulate component relative to the gas. A low surface area powder, such as a graphitic carbon, caused an attenuation of the cooling effect found in a pure gas, because the addition of the powder increased the heat capacity of the fluid. For a large surface area powder, the magnitude of the total gas-solid interaction was sufficient to overcome the attenuating effect of the increased heat capacity. In future studies of the gassolid Joule-Thomson effect, it would be useful to construct an apparatus which allows the following: a continuous flow of an aerosol gas, permitting recycling of the gas and powder in a closed system; pressures and pressure drops up to several hundred atmospheres; a variation of the orifice size to enable the flow rate and pressure drop to be independently varied; a conontinuous monitoring of the aerosol concentration and the ability to sample the particulate concentration without interrupting the aerosol flow; an aerosol generator in which the concentration of the aerosol produced could be easily varied; and a flow system thermostated precisely over a wide range of temperatures. Since the current work is the first study involving the gas-solid Joule-Thomson effect, it is desirable to obtain Joule-Thomson data for a variety of gassolid systems over a range of temperatures and pressures. Also, it would be useful to monitor the temperature of an aerosol along a considerable length of tube on the downstream side of the orifice. Temperature variation with position and hence time might be used study to the kineic effects of desorption. The refinement and continued study of the gas-solid Joule-Thomson experiment is of both theoretical and applied interest and should provide a novel approach which could be used to obtain information regarding the following: the unique thermodynamic properties associated with an aerosol fluid; the gassolid interaction potentials; the behavior of a condensed fluid in pores; the kinetics of desorption; the surface area and three-dimensional structure of particulate solids; and the use of an aerosol fluid in applied thermodynamic cycles.33 Registry No. Ar, 7440-37-1;N2, 7727-37-9;CO,, 124-38-9;graphite, 7782-42-5; supersorb, 7440-44-0. (33) R. A. Pierotti and T. R. Rybolt, U S . Patent 4321 799, 1982.
