Znd. Eng. Chem. Res. 1991,30,255-259
255
Prediction of the Solubility of Hydrogen in Naphtha Reformate Using the Modified UNIFAC Group Contribution Method Mohamed A. Fahim**+and Amal S.Elkilani Department of Chemical Engineering, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait
The solubility of hydrogen in the naphtha reformate cut (423-473 K)was estimated by using the UNIFAC group contribution method. Functional group concentrations, estimated from analytical data, and interactions parameters, predicted in this work, were used to provide reasonable estimates of hydrogen solubility. The predicted solubility data were compared favorably with experimental values obtained by the pulse response technique using gas chromatography within 10% error.
,
Introduction Hydrogen solubility is a major factor in the design of naphtha and crude oil processes. Hydrogenation reactions take place to increase the hydrogen-to-carbon ratio of the fuel. Thus, reliable estimates of hydrogen solubilities in naphtha are necessary. The UNIFAC group contribution method can be used for predicting hydrogen solubilities in hydrocarbons with activity coefficient calculations (Fredenslund et al., 1977). Antunes and Tassios (1983) used the modified UNIFAC model for prediction of Henry's constants for methane, nitrogen, and oxygen in alkane solvents and in water. It was concluded that good results including a successful description of the temperature dependency of Henry's constants were obtained with a typical accuracy of *lo%. Sander et al. (1983) predicted the solubility of some gases of industrial importance such as hydrogen, methane, oxygen, and carbon dioxide in pure solvents and solvent mixtures. The method was applicable at low pressures and low solubilities and to both polar and nonpolar solvents. In order to apply the UNIFAC model for the prediction of hydrogen solubility in naphtha reformate, the functional groups present in naphtha have to be identified first. Then the interaction parameters between these groups and hydrogen have to be determined experimentally. These interaction parameters can be used later for solubility predictions. Although there are some interaction parameters that were obtained by Hartounian and Allen (1988) between hydrogen and some main groups, new interaction parameters are predicted in this work as a function of temperature and are used to apply the modified UNIFAC method for solubility predictions. Experimental solubility values must be available in order to compare them with the predicted solubilities. The pulse response technique was used for the determination of the solubility of gases in liquids. Yow and Smith (1983) developed the dynamic pulse method for measuring the solubility of nitrogen, propane, and carbon dioxide in ethylene glycol. Mousa (1984) used the same method to determine the solubility of nitrogen and hydrogen in nitrobenzene and olive oil. The calculation procedure was based on the first moment analysis. First moment analysis has the shortcoming that the weighting factor, t", puts a large weight on the tailing portion of the peak. Fahim and Wakao (1982) reviewed parameter estimation techniques by using tracer response measurements. In the present work, the pulse technique is used to determine the solubility of hydrogen in ethylenebenzene, hexadecane, and
'
Present address: Department of Chemical and Biochemical Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9. * To whom correspondence should be addressed. 0888-5885/91/2630-0255$02.50/0
Table I. Physical Properties of the Naphtha Reformate Cut Measured at 313 K bp range, K 423-473 density, kg/m3 864.2 viscosity, kg/ ( m s ) 7.005 x 104 surface tension, N/m 0.0261
naphtha reformate cut (423-473 K)by using the real time analysis technique. The experimental solubility data obtained by using the pulse technique are compared with those predicted from the modified UNIFAC model. Experimental Section 1. Naphtha Reformate Analysis. The composition of the naphtha reformate cut (423-473 K)was determined by PIANO analyzer Model 412A supplied by Chrompack. It is a gas chromatograph that can identify paraffins, isoparaffins, aromatics, naphthenes, and olefins (PIANO). The separation of these components is carried out by three standard columns, OV-275,OV-101,and molecular sieve 13X. The FID detector was used with an air flow rate of 0.05 X m3/s and hydrogen flow rate of 5 X m3/s. The helium carrier gas flow rate was 5 X m3/s. Each column has a certain temperature program to separate one class of hydrocarbons, paraffins for example, and trap the others until all paraffins come out. The temperature program for the second column is then started and at the same moment naphthenes enter the column from the trap and so on until all hydrocarbons are separated. The apparatus has a built-in calibration for quantitative and qualitative analyses. The physical properties of the naphtha reformate are listed in Table I. 2. Measurement of the Hydrogen Solubility by the Pulse Technique. The hydrogen solubility measurements in naphtha and in solvents, which are required for the determination of interaction parameters, were carried out by using the pulse technique through a Varian Vista 6000 gas chromatograph. The experimental apparatus used in this work is shown in Figure 1. The gas chromatograph was connected with a six-way valve with a 1-mL sample loop. Nitrogen carrier gas was used at different flow rates m3/s. The column was ranging from 2.5 X to 5 X a copper tube of 0.0036 m inside diameter and 0.6 m long. The packing material was solid inert particles of red firebrick of 70-80-mesh size. A liquid loading, which is defined as the initial ratio of weight of liquid to weight of liquid plus solid, of 0.5 was used. The response signal was recorded and analyzed by using the liquid loaded column, while the input signal was recorded by using a column, with the same dimensions, packed with the solid material only. The maximum experimental temperature used was 328 K, in order to avoid any volatilization of the naphtha cut during the runs. C 1991 American Chemical Society
256 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991
naphtha and hydrogen must be available as a function of temperature. Two modifications of UNIFAC have been used in this work. The first modification expresses the interaction parameters as a linear function of temperature according to
1
an, = A,,
+ B,,(T
- 273.15)
(6)
The second modification, proposed by Kikic et al. (1980), is concerned with the combinatorial activity coefficient according to the following expression In
-yF
= (In $ J / x i
+ 1- q i / x i = 1
U
Figure 1. Experimental apparatus for the pulse technique. 1, nitrogen cylinder; 2, hydrogen cylinder; 3, needle valve; 4, rotameters; 5, flow regulater;6, pressure guage; 7, six-way valve; 8, flowmeters; 9, reference column; 10, tested column; 11, Varian 6000 GC.
Prediction of the Hydrogen Solubility by t h e Modified UNIFAC Group Contribution Method At equilibrium, the gas-phase hydrogen fugacity and liquid-phase fugacity can be equated, thus, as
f h , = fft,
(1)
Since this work was done under atmospheric pressure, the gas phase was assumed ideal, and consequently, the fugacity coefficient was assumed unity. The gas-phase fugacity was estimated by using the equation
f 8, = YHZp
(2)
In eq 2, P is the total pressure and yH2is the mole fraction of hydrogen in the gas phase, which is considered to be equal to unity for nonvolatile liquids. Liquid-phase nonideality was determined by using activity coefficient calculations. The fugacity of hydrogen in a solvent can be written as
f k, = XH,YH&
(3)
where x H 2 and YH, are the mole fraction and activity coefficient of hydrogen in the solvent under study while f OH, represents the property of a hypothetical pure liquid whenever the temperature is greater than the critical temperature of the gas. f i cannot be determined experimentally (Wilhelm, 1985,1986). So the expression may be changed into estimating Henry’s law constant for a reference solvent as follows: (4) where -y& is the infinite dilution activity coefficient of hydrogen in the reference solvent and HH is Henry’s law constant of hydrogen in the reference sohent. Use of a reference solvent is required since the standard-state fugacity for hydrogen in naphtha is not available. Propanol was used as a reference solvent in this work. Equations 1-4 are used to obtain the mole fraction of hydrogen in the solvent under study (5) The UNIFAC group contribution method has been applied to predict the activity coefficients. The model deals with functional groups present in the components. Therefore, application of UNIFAC needs naphtha reformate group concentrations, and consequently, all the interaction parameters between the groups present in
-Zqi((ln 2
#i)/Oi
+ 1 - #i/OJ
(7)
where
+i= J
and Oi
= XiQi/EXjQj j
The UNIFAC parameter tables published to date do not contain parameters for the interaction between hydrogen and groups present in naphtha as a function of temperature. Therefore, it has been necessary to estimate such parameters. From experimental solubility data for a certain system such as hydrogen in hexadecane, xH,.in eq 5 is known. The Henry’s law constant of hydrogen in the reference solvent (propanol), H H z , r , was given by Sander i ~then , ~ be) ~calcu~ ~ et al., (1983). The ratio ( ~ ~ , / ~ fcan lated from eq 5. To estimate the interaction parameters, between hydrogen and CH3group, an initial guess was first assumed. The error involved in that guess can be estimated by first calculating (-yHn/-y&r)cdc from modified UNIFAC and comparing it with the corresponding ratio ~ , , ~ )experimentally. ~ ~ ~ The following of ( ~ ~ ~ / - y obtained objective function was used to minimize the errors in the estimation of UNIFAC interaction parameters
where n is the number of data points and -yH, is the activity coefficient of hydrogen calculated by using modified UNIFAC. By using the new predicted interaction parameters, the hydrogen solubility in naphtha can be calculated from eq 5. The activity coefficient YH, was calculated by modified UNIFAC for the functional group concentrations present in naphtha. These group concentrations were calculated from PIANO analysis. Results and Discussion 1. Determination of Group Concentration in Naphtha. The naphtha reformate cut (423-473 K) was used in this work. It was analyzed in PIANO Model 412A by using a certain temperature program for the PNA mode. Table I1 shows all the components present in the chromatogram along with their concentrations in mole percent. The main objective of carrying out the analysis of this naphtha cut is to identify its functional groups. A cut of 423-473 K was used to avoid volatilization during the experiments. Table I11 shows the concentration of all UNIFAC main groups and subgroups present in each component in
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 257 Table 11. PNA Analysis for Nauhtha Reformate component mol % n-pentane 0.0617 n-octane 0.0171 n-nonane 1.0939 n-decane 0.5985 benzene 1.3649 toluene 4.2478 ethylbenzene 9.3368 o-xylene 4.0792 isopropylbenzene 21.6093 n-propylbenzene 6.9202 1,3,5-trimethylbenzene 23.3110 1,2,3,44etramethylbenzene 27.0126 methylcyclohexane 0.0655 ethylcyclohexane 0.2815
0.30
~~~
o T=XK w
0.250.20 -
T=31X
DT='J9& A
T=m
0.15 -
0.0
1 .o
2.0
3.0
4.0
RECIPROCRL OF FLOWRRTE, s . 1 6 ~ , ' % 1 0 ~ ~
naphtha. Since the content of naphthenes in naphtha was < O S mol 90,the cyclic CH, group was treated as the paraffinic group in the estimation of the interaction parameters. The only three main groups present in naphtha were found to be CH,, ACH, and ACCH,. 2. Comparison between Predicted and Measured Solubilities. As discussed before, hydrogen solubility data must be available experimentally to compare them with the predicted values to show the applicability of the UNIFAC model. Hydrogen solubility was measured in this work by using the pulse technique. The solubilities of hydrogen in hexadecane and in ethylbenzene were carried out to estimate the interaction parameters. When a pulse of hydrogen is injected to a column packed with the liquid, a certain response concentration profile Ci&(t) is produced. The transfer function, which is defined in eq 9, can be obtained by the real time analysis technique (Fahim and Wakao, 1982). Henry's law constant can be calculated from this equation:
where C L, is the calculated concentration profile for the response signal and C is the experimental concentration profile for the input signal. C was calculated by using the Fourier series. Q is the gas flow rate, and VGand VL are the volumes of the gas and the liquid in the column, respectively. Floating s values range from 0.1 to 0.2 s-l. H is Henry's constant (defined as H = CG/CL), which can be expressed also in pressure units as HH by using the relation HH2= HRT(Ns/ VL) where N s is the number of moles of solvent in the column. In fitting the experimental data to calculate H in eq g, the root-mean-square error
kxp
Figure 2. H,/hexadecane system plotted for eq 9 at different temperatures.
between C :\p and c :Lc over the entire domain is evaluated by the following equation (Fahim and Wakao, 1982):
The optimum deviation, e, should be less than 0.05. A plot of -(ln F(s))versus 1/Q according to eq 9 is shown in Figure 2 for hydrogen in hexadecane. The amount of hexadecane loaded in the column was 0.0165 mol. The Henry's constant could be calculated from the slope s(VG
+~L/H).
The accuracy of the pulse technique for the determination of Henry's constant has been tested by comparing the experimental and published data for H2in hexadecane (Ying et al., 1988). The results of this comparison are given in Table IV. It is seen from this table that the maximum percent error was 4.15% , which shows reasonable agreement between the dynamic pulse technique and the static method used by Ying et al. (1988). The solubility of hydrogen in hexadecane was then calculated from this Henry's constant, and eqs 5-8 were used in estimating the interaction parameters uH2,CH, and uCH ,HZ as explained before. The same procedure was repeated !or the H2-ethylbenzene system to determine the uH2,ACH, uACH,HZ, uHZ,ACCH2, and uACCH~,I;I~interaction parameters. All Henry's constants determined for these two systems are listed in Table V along with some relevant hydrogen-paraffins and hydrogen-aromatics solubility data available in the literature (Wilhelm and Battino, 1973). The values of the new interaction parameters are given in Table VI. The same experimental procedure for solubility measurements was carried out for hydrogen in naphtha. The
Table 111. Molar Concentration of Functional Groups per Mole of Naphtha Reformate comuonent CHn CH, CH ACH ACCH, n-pentane 0.001 23 0.00185 n-octane 0.000 34 0.001 03 n-nonane 0.02188 0.076 57 n-decane 0.011 97 0.047 88 benzene 0.081 89 toluene 0.212 39 ethylbenzene 0.093 37 0.466 84 0.093 37 o-xylene 0.163 17 0.432 19 isopropylbenzene 1.080 50 n-propylbenzene 0.069 20 0.069 20 0.34601 0.06920 1,3,S-trimethylbenzene 0.699 33 1,2,3,44etramethylbenzene 0.540 25 methylcyclohexane 0.00064 0.009 27 0.000 66 ethylcyclohexane 0.016 89 0.002 82 0.002 82
ACCHi
ACCH
0.042 48 0.081 58 0.21609 0.699 33 1.080 50
258 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 Table IV. Comparison between Experimental and Published Data (Ying et al., 1988) for the Determination of Henry's Law Constant of H2 in Hexadecane temp, K exptl lit. 90 dev 1097 -2.8 300 1129 999 t4.1 313 960 986 -0.4 325 990 881 to.l 350 880 Table V. Hydrogen Solubility Data in Hydrocarbons at 1 atm Used in This Work component temp, K Hw,, atm ref 1129 this work hexadecane 300 this work 960 313 this work 989 325 this work 880 350 this work 2404 ethylbenzene 300 this work 2221 313 this work 2031 323 this work 1783 328 Wilhelm and Battino (1973) 1584 n-hexane 298 Wilhelm and Battino (1973) 1458 n- heptane 298 1461 Wilhelm and Battino (1973) n-octane 298 1445 Wilhelm and Battino (1973) n-nonane 298 3876 Wilhelm and Battino (1973) benzene 298 Wilhelm and Battino (1973) 3154 toluene 298 Wilhelm and Battino (1973) 2408 xylene 298
LO
50
70
60
TIME
80
90
,5
Figure 3. Comparison between predicted and experimental response concentration profiles for the Hz/naphtha system a t T = 300 L/s. K and Q = 2.5 X
m 0 Predicted
Table VI. New UNIFAC Interaction Parameters for Equation 6 an,
aH.,.CHI --..---,. 'CHn,H*
an,.Acn aAcn.nz anp,Accnz aAccn23nt
Am -307.4 740.4 -103.9 748.4 -260.2 907.8
Bnm
0.8996 -0.4789 0.6931 0.4788 -0.6850 -0.6135
Table VII. Henry's Law Constant for Hydrogen in Naphtha Reformate temp, K exptl predicted % dev 300 1552 1730 11.5 308 1522 1687 10.9 318 1507 1636 8.6 1588 7.3 328 1480
amount of naphtha inside the column was 0.026 16 mol. Figure 3 shows the variation between C and C::lc for a selected sample of response peaks, which demonstrates the lowest root-mean-square error reached. The Henry's law constants were determined a t different temperatures (300-328 K),and the results are shown in Table VII. Finally, the solubility of hydrogen in naphtha was predicted from eq 5 using the new predicted interaction parameters and all the group concentrations listed in Table I11 for activity coefficient (YH ) calculations. Table VI1 shows these predicted values dong with the experimental Henry's constants and the resulting percent deviations. It is clear that the UNIFAC approach for estimating the hydrogen solubility in naphtha was successfully applied within 10% error. Comparison between predicted and experimental values of Henry's constant as a function of temperature is shown in Figure 4.
:iP
Summary The hydrogen solubility in naphtha reformate was predicted by using the modified UNIFAC group contribution method. The hydrogen group concentration in naphtha was determined experimentally. New UNIFAC interaction parameters were estimated as a function of temperature. The predicted solubilities of hydrogen in
IO"
3.0
3.2 1000/TEMP
,
3.4 K-l
Figure 4. Temperature dependency of Henry's constant for the Hz/naphtha system.
naphtha reformate were compared with those values obtained experimentally by the pulse technique. It was found that hydrogen solubilities could be reasonably predicted by using modified UNIFAC within 10% error.
Acknowledgment This project has been supported by Kuwait University under Grant EC028. We gratefully acknowledge this financial support. We thank Kuwait National Petroleum Company (KNPC) for supplying the reformate samples.
Nomenclature a,: modified UNIFAC interaction parameter between groups m and n C &(t): normalized concentration profile calculated for the response peak C :i ( t ) : experimental normalized concentration profile for t t e response peak C:J t ) : experimental normalized concentration profile for the in ut peak g2, fH2: E fugacity of H2in the gas phase and the liquid phase, respectively f &: hypothetical liquid-state fugacity of H2 HH2: Henry's law constant of hydrogen, atm H H ~ ,Henry's ~: law constant for hydrogen in reference solvent, atm P: total pressure, atm
259
Ind. Eng. Chem. Res. 1991,30, 259-264 Q: carrier gas flow rate, m3/s qi: UNIFAC surface area parameter for group i
r; UNIFAC group volume parameter for group i s: floating value of transfer function, s-l V,: volume of gas in the column, m3 V,: volume of liquid in the column, m3 xH2: mole fraction ofHz in the liquid phase y H 2 : mole fraction of Hz in the gas phase ys: activity coefficient of hydrogen y ,*: activity coefficient of hydrogen at infinite dilution in the reference solvent t: root-mean-squareerror 7: mean residence time, s Registry No.
HZ,1333-74-0.
Literature Cited Antunes, C.; Tassios, D. Modified UNIFAC Model for the Prediction of Henry’s Constants. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 457-462. Fahim, M. A.; Wakao, N. Parameter Estimation from Tracer Response Measurements. Chem. Eng. J . 1982,25, 1-8. Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria using UNIFAC; Elsevier: Amsterdam, 1977.
Hartounian, H.; Allen, D. T. Group Contribution Methods for Coal-Derived Liquids. Fuel 1988, 67, 1609-1614. Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, A. On the Combinatorial Part of the UNIFAC and UNIQUAC Models. Can. J. Chem. Eng. 1980,58, 253-258. Mousa, A. H. N. Prediction of Henry’s Constant by Gas Chromatography. J . Chem. Eng. Jpn. 1984, 17, 206-208. Sander, B. 0.;Jorgensen, S. S.;Rasmussen, P. Gas Solubility Calculations. I. UNIFAC. Fluid Phase Equilib. 1983,11,105-125. Wilhelm, E. Precision Methods for the Determination of the Solubility of Gases in Liquids. CRC Crit. Rev. Anal. Chem. 1985,16 (2), 129-175.
Wilhelm, E. Dilute Solutions of Gases in Liquids. Fluid Phase Equilib. 1986, 27, 233-261. Wilhelm, E.; Battino, R. Thermodynamic Functions of the Solubilities of Gases in Liquids at 25 OC. Chem. Rev. 1973, 73, 1-9. Ying, H.; Yingnian, X.; Prausnitz, J. M. Molecular Thermodynamics of Gas Solubility (I) Henry’s Constants of Gases in Nonpolar Solvents. J. Chem. Ind. Eng. 1988, 3, 144-184. Yow, J.; Smith, J. M. Chromatographic Determination of Solubilities of Gases in Liquids. Lat. Am. J . Chem. Eng. Appl. Chem. 1983, 13, 185-197.
Received for review February 26, 1990 Revised manuscript received June 22, 1990 Accepted July 18, 1990
Low-Pressure Nitrogen Suspensions Terry
W.Motes,* Lawrence C.Faulkner, and Charles A. Hodge
Chemical Development Department, National Fertilizer & Environmental Research Center, Tennessee Valley Authority, Muscle Shoals, Alabama 35660-1010
High-analysis low-pressure nitrogen (LPN) suspensions can be produced by sparging gaseous ammonia into a urea-ammonium nitrate (UAN) solution and then adding fluid clay. LPN suspensions contain more inexpensive ammonia nitrogen and have about the same salt-out temperature as lower nitrogen content UAN solutions. LPN suspensions have higher nitrogen concentrations but vapor pressures comparable to low-pressure aqua ammonia solutions, as well as better suspending properties for cold blending with other fertilizer materials. The optimum composition of a 38% nitrogen LPN solution with a salt-out temperature of about 32 O F and a vapor pressure of about 5 lb/(in.2 g) at 104 O F is about 8% ammonia, with the remaining nitrogen being 48% urea nitrogen and 52% ammonium nitrate nitrogen. Different fertilizer grades of two- and three-component blends can be made by using LPN suspensions. Fertilizer blends with higher nitrogen content are most cost effective. Low-pressure aqua ammonia solution and urea-ammonium nitrate (UAN) solution fertilizers are widely used in the United States. Both products can be handled and applied by using conventional application equipment that is generally available to the farmer. Also, both products can be cold blended with other fertilizer materials, such as monoammonium phosphate (MAP) solution or suspension and potassium chloride, to produce custom-formulated NP or NPK fertilizers. However, cold blending with UAN solution or aqua ammonia usually requires addition of a suspending agent, such as attapulgite clay, during the cold-blending operation to keep the KC1 from settling out (Cole et al., 1984). Another disadvantage of these nitrogen solutions is that both must be limited in grade or nitrogen content to attain the desired salt-out temperature or vapor pressure. UAN solution generally contains 32% nitrogen with a specific ratio of urea to ammonium nitrate to control the physical properties of the solution such as the salt-out temperature. The salt-out temperature usually is controlled at about 32 O F . Lowpressure aqua ammonia solutions usually are limited in concentration to about 25% nitrogen so that the vapor pressure does not exceed about 5 1b/(inv2g) at 104 OF. Higher concentrated aqua ammonia solutions would have
higher vapor pressures, and specialized equipment would be required for storage, handling, and application. Low-pressure nitrogen (LPN) suspensions can be produced by sparging anhydrous ammonia into a UAN solution and adding fluid clay (attapulgite clay dispersed in water). A less dilute fluid clay can be made by using urea to make up to a 16-0-0-30C grade. The addition of ammonia to the UAN solution increases the nitrogen content, making a more concentrated product with a less expensive source of nitrogen, as compared to urea or ammonium nitrate (AN). The addition of ammonia also can maintain the salt-out temperature of the more concentrated product at about the same level as that of the lower grade 32-0-0 UAN solution. Fluid clay is best added after the ammonia because the sparging of a gas into a suspension reduces its viscosity (TVA, 1978). When making blends, the viscosity of a suspension needs to be high enough to keep added components such as KC1 suspended. LPN suspensions also have an advantage compared with aqua ammonia solution or UAN solution because LPN suspensions contain clay, which could eliminate the need for adding clay during cold blending with other fertilizer materials. Tests were conducted by NFERC researchers to evaluate production of LPN suspensions. First, tests were made
This article not subject to U S . Copyright. Published 1991 by the American Chemical Society
