I n d . E n g . Chem. Res. 1988,27, 718-721
718
Table 11. Rigorous Simulation (Feed Composition, 11 mol %
Ethanol) tray T,O F
206.88 203.18 198.44 194.17 190.93 188.70 193.24 192.94 192.12 190.43 187.59 184.22 181.42
0 1 2 3 4 5 6 7 8 9 10 11 12
n 0.0100 0.0191 0.0342 0.0528 0.0719 0.0893 0.0578 0.0594 0.0643 0.0755 0.0996 0.1428 0.2027
y 0.0417 0.0950 0.1613 0.2300 0.2920 0.3433 0.3452 0.3483 0.3555 0.3706 0.3973 0.4341 0.4738
L , mol/h 878.05 1232.95 1228.06 1224.37 1222.25 1221.34 207.88 206.83 206.79 206.73 206.80 207.36 208.59
V , mol/h 354.88 350.01 346.33 344.20 343.29 329.83 328.80 328.74 328.69 328.69 329.31 330.54 332.03
were moved up to tray 8, a lower reflux ratio could be used to make the same separation with the same number of total trays in the column. The operating line in this case would be closer to the equilibrium line and the liquid composition on tray 5 would be lower. The higher tray 5 liquid composition (that results when a nonoptimum feed tray is used) should give a high tray 5 vapor composition entering the rectifying section. But, tray 5 vapor composition will not be high if the tray efficiency is low. A component balance around the entire rectifying section shows that x 6 must decrease as y s decreases. Therefore, reducing tray efficiency reduces y5, which reduces x 6 . At some efficiency, x 6 can become less than x 5 . The appropriate criteria to use in a rating program with efficiencies of less than 100% are (1)x N F + ~> 0 and (2) xNF+2
’
xNF+l.
In these examples, Murphree tray efficiencies defined on the basis of the vapor phase have been used, and the tray-to-tray calculations have been performed from the bottom to the top of the column. A similar reversal in the vapor concentration profile could be observed if liquid tray efficiencies were used and the calculations were made from the top to the bottom. This reversal would occur when switching from the rectifying to the stripping operating line prematurely. Murphree tray efficiency has been studied in this paper because it is the most widely used efficiency. Similar results would be expected if other tray efficiencies were
utilized, such as those proposed by Holland, Hausen, and Standart (summarized by King (1971)). If overall column efficiencies were used, the phenomenon of concentration profile inversion will not be seen. Conclusion The phenomenon of composition inversion can occur in distillation rating programs when tray efficiencies of less than 100% are used. The rating program must be modfied to permit a one-tray decrease in liquid composition on the tray above the feed tray. Nomenclature E = tray efficiency F = feed flow, mol/h L = liquid flow, mol/h N T = total number of trays N F = feed tray QR = reboiler duty, 106Btu/h RR = reflux ratio T = temperature, O F V = vapor flow, mol/h xb = bottoms composition xd = distillate composition x, = nth tray liquid composition XNF = liquid composition on feed tray y n = nth tray vapor composition z = feed composition Literature Cited Buckley, P. S.; Luyben, W. L.; Cox, R. K. Chem. Eng. Prog. 1978, June, 49. Buckley, P. S.; Luyben, W. L.; Shunta, J. P. Design of Distillation Column Control Systems; Instrument Society of America: New York, 1985. King, C. J. Separation Processes; McGraw-Hill: New York, 1971.
Cristian A. Muhrer, Michael A. Collura William L. Luyben* Chemical Process Modekng and Control Research Center Department of Chemical Engineering Lehigh University Bethlehem, Pennsylvania 18015 Received for review December 23, 1986 Revised manuscript received October 14, 1987 Accepted December 23, 1987
Wet Oxidation Catalyzed by Ruthenium Supported on Cerium( IV) Oxides The activity of precious metal catalysts in the wet oxidation of organic compounds was investigated. Ruthenium was the most active catalyst among the precious metals examined, and cerium(1V) oxide was the most effective support. T h e Ru/Ce catalyst rivaled homogeneous copper catalyst, which is used in the practical wastewater treatment, for the oxidation of n-propyl alcohol, n-butyl alcohol, phenol, acetamide, poly(propy1ene glycol), and acetic acid. In addition, it was especially effective for the oxidation of some compounds with high oxygen content such as poly(ethy1ene glycol), ethylene glycol, formaldehyde, and formic acid. The most general and widely used process for wastewater purification is biological treatment. However, it cannot be applied to the purification of highly contaminated wastewaters or wastewaters containing toxic materials to microorganisms. These wastewaters can be purified by wet oxidation. Organic pollutants in wastewaters are oxidized to carbon dioxide and water under oxygen pressure a t high temperatures, e.g., 423-573 K. The process 0888-5885/88/2627-0~18$01.50/0
has been applied successfully to the treatment of wastewaters discharged from petroleum and petrochemical industries (Tagashira et al., 1976) and to the treatment of pulp and paper mill wastes (Teletzke, 1964). However, the relatively severe operative conditions require high installation and running costs. Therefore, it is desirable to develop catalysts that can be used under milder conditions. The most practical and the most active catalyst is homo@ 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 719 geneous copper salts (Tagashira et al., 1976; Imamura et al., 1982a). An additional process, however, is necessary to recover toxic copper ion after use. In order to eliminate this step, attempts have been made to develop active heterogeneous catalysts. However, the data on active heterogeneous catalysts seem to be meager (Katzer et al., 1976). We have investigated the development of various catalysts (Imamura et al., 1982b,c) and found that manganese-cerium composite oxide exhibited much higher activity than homogeneous copper catalysts (Imamura et al., 1985, 1986, 1987). However, our investigations have not covered precious metals. As precious metal catalysts are highly effective in vapor-phase combustion, the possibility still remains to improve the activity of manganese-cerium catalyst by combining it with precious metals. It is necessary, however, to know the catalytic action of precious metals in wet oxidation before using them as promoters for manganese-cerium catalyst. This paper deals with the catalytic activity of precious metals, especially ruthenium, in the wet oxidation of some organic compounds. Experimental Section Commercial n-propyl alcohol, n-butyl alcohol, phenol, acetamide, acetic acid, poly(propy1ene glycol) with an average molecular weight of 1000 (PPG-1000), poly(ethylene glycol) with an average molecular weight of 200 (PEG-200),ethylene glycol, formic acid, and formaldehyde were used without further purification. Cerium(IV) oxide was obtained by precipitating aqueous cerium(II1) nitrate and calcinating the resultant precipitate a t 723 K for 3 h in air. NaY zeolite was provided by Toso Co. Other supports (7-A1203,ZrOz, and TiOJ were used as obtained commercially. The BET surface area of the supports after loading of precious metals was measured by a conventional gas adsorption apparatus with a glass vacuum line using nitrogen as an absorbate. Ruthenium(II1) chloride, rhodium(II1) nitrate, palladium(I1) nitrate, iridium(II1) chloride, and hydrogen hexachloroplatinate(IV) were used for the preparation of supported precious metal catalysts. The supported catalysts were prepared as follows. A known amount of precious metal salts (5 wt % loading as metal on the supports) and an excess amount of formaldehyde over precious metals were dissolved in deionized water in the presence of dispersed supports, and the solution was heated to 363 K. Sodium hydroxide (3 N) was added until the pH of the solution was 12, and the solution was kept standing for 1 h with stirring. After the solution was cooled to room temperature, the resultant precipitate was filtered and was washed several times with water until the pH of the solution was below 9. I t was dried a t 373 K overnight and was calcined a t 723 K for 3 h in air. Manganese-cerium composite catalyst with an equimolar composition [Mn/Ce (1/1)]was obtained by coprecipitation from a mixed aqueous solution of manganese(I1) nitrate and cerium(II1) nitrate followed by calcination at 723 K in air (Imamura et al., 1985). Copper(I1) nitrate was used as a homogeneous copper catalyst. Reactions were carried out by using a 270-mL autoclave equipped with a sample injector and a valve for sampling under a pressure of oxygen (1.0 MPa) and nitrogen (2.0 MPa). A reactant solution (2000 ppm as total organic carbon) was injected into the autoclave under a pressure of nitrogen at the reaction temperature. The solution was stirred by a magnetic agitator, and the constancy of the rate of reaction with the change of agitation speed showed that the reactions were not controlled by diffusion of oxygen into the liquid phase. A t appropriate time intervals,
Table I. Wet Oxidation of PEG-ZOO' catalystb ATOC,' % catalystb 9.4 Ir/Ce Ru/Ce 100.0 Pd/Ce Rh/Ce 100.0 CU(NO&~ Pt/Ce 100.0 Mn/Ce (1/1)
ATOC,' % 74.8 49.7 12.3 43.8
O473 K;pH 5.1-5.4; [TOCIo = 2000 ppm; [Cat] = 1 2 mM (total metal concentration); [O,] = 1.0 MPa; [N,] = 2.0 MPa. bPrecious metal = 5 wt % on CeOz. cPercentage decrease in TOC after 1 h. Homogeneous catalyst. Table 11. Effect of Supports on the Activity of Ruthenium in the Wet Oxidation of PEG-ZOO" support m2/g ATOC,' % CeO, 135.7 100.0 Y-Al203 138.5 68.1 NaY zeolite 509.8 54.6 ZrOz 15.2 36.3 3.8 33.8 Ti02
O473 K;pH 5.4;[TOCIo = 2000 ppm; Ru = 5 wt %; [Cat] = [Ru] [O,]= 1.0 MPa; [N,] = 2.0 MPa. bSurface area measured after loading of Ru. CAfterl h. = 1 mM;
an aliquot of the reaction mixture was withdrawn and was submitted to analysis of total organic carbon (TOC). The TOC was determined by using Sumitomo 12N TOC analyzer. The ESCA spectra and X-ray diffraction pattern of the catalyst were obtained by the use of a Shimadzu ESCA 750 spectrophotometer and a Rigaku Denki Geigerflex 2012 X-ray analyzer, respectively. A shimadzu GC-3BT gas chromatograph was used for the analysis of carbon monoxide. The column packing consisted of molecular sieve 5A (1.3 m) plus Celite 545 (1.7 m), and the column temperature was 363 K. I t was confirmed that ruthenium was not eluted from the Ru/Ce catalyst on the basis of the analysis of ruthenium ion after reaction (Banks and O'Laughlin, 1957). Results a n d Discussion Poly(ethy1ene glycol) was selected as a neutral model reactant (Imamura et al., 1986),and the activity of precious metals supported on cerium(IV) oxide was investigated at 473 K (Table I). Activities of Ru, Pt, and Rh were much higher than that of homogeneous copper catalyst; oxidation by the former resulted in the complete removal of TOC after 1h, whereas only 12.3% TOC was removed by the latter. Moreover, they had an even higher activity than the Mn/Ce (1/1)catalyst. As Ru showed the highest activity among the three active catalysts (ATOC at 45 min: 99.1% for Ru, 95.7% for Pt, and 82.8% for Rh), the effect of the supports on the activity of Ru was investigated, and the result is shown in Table 11. Although the BET surface area differed remarkably depending upon the kind of supports and, therefore, evaluation of the inherent catalytic activity was difficult, cerium(1V) oxide seemed to be the most effective support for practical purposes. Therefore, Ru catalyst supported on cerium(1V) oxide (5 wt % or 8.2 mol % loading of Ru as metal on CeO,) was used in the following experiments. This catalyst was designated as Ru/Ce. Figure 1shows X-ray diffraction patterns of the Ru/Ce. In addition to the well-resolved pattern due to CeO,, small peaks were observed a t 20 of 35.0' and 54.4' which corresponded to those due to RuO, (McClune, 1980). No diffraction pattern due to Ru metal was observed. Table I11 exhibits the results of ESCA analysis of the catalyst. The BE of Ru 3d3,~(281.0 eV) was about 1eV higher than that for Ru metal and coincided with that for RuOz (Kim and Winograd, 1974). Both X-ray and ESCA analyses
720 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 I
0
I
" I _
"423 K; [TOClo = 2000 ppm; [Cat] = 12 mM (total metal concentration); [O,] = 1.0 MPa; [N,] = 2.0 MPa. bAfter 1 h; ATOC without catalyst was 24.9%. = 5 wt 7' on CeO,. dUnder Nz atmosphere.
~
30
40 50 60 28 (CuKa) Figure 1. X-ray diffraction pattern of the Ru/Ce catalyst: (0) CeO,; ( 0 )RuO,. 20
Table V. Wet Oxidation Catalvzed bv Ru/Ce and C u .( N 0 A " ATOC,~% reactant DH Ru/Cec Cu(NO& PEG-200 5.4 48.3 9.1 ethylene glycol 4.8 98.0 6.2 formic acid 1.9 100.0 64.7 2.8 62.7 3.6 40.9 5.6 7.0 formaldehyde 4.3 96.4 24.1 9.3 97.8 4.3 23.1d
Table 111. ESCA Data of the Ru/Ce Catalyst binding energy, eV surface of Ce 3d5/, Ru 3psi2 Ru 3d3/, Ru," mol 7'0 before Ar etching 882.7 463.0 281.0 8.0 after Ar etching 882.8 462.8 280.9 5.4 "Determined by the comparison of the peak areas of Ce 3d,/, and Ru 3p3,,.
Table IV. Wet Oxidation Catalyzed by Ru/Ce and Cu(NOd2" ATOC,~% reactant Ru/Cec Cu(NOnh n-propyl alcohol 47.2 28.3 n-butyl alcohol 27.8 40.1 phenol 94.8 93.5 acetamide 51.6 18.1 PPG-1000 54.3 29.5 acetic acid 44.5d 32.6' "473 K; pH 5.0-6.0; [TOClo = 2000 ppm; [Cat] = 12 mM (total metal concentration); [O,] = 1.0 MPa; [N,] = 2.0 MPa. *After 1h. 'Ru = 5 wt % on CeO,. d p H 2.7. e p H 2.5.
suggested that Ru was in the form of Ru02. The content of Ru on the surface of CeOzwas calculated by comparison of the peak areas of Ce 3d612and Ru 3P3p instead of the peak area of Ru 3d3~2which could not be measured accurately due to the presence of the nearby C Is peak (285 eV). The surface Ru content was found to be 8.0 mol % , and it decreased to 5.4 mol % after 5 min of Ar etching. If Ru02covers the surface of Ce02in a thin layer, e.g., two or three layers, it would be completely eliminated by 5 min of Ar etching. The fact that 5.4 mol % Ru still remained after Ar etching shows that RuO, did not coat the surface of Ce02in a thin layer but aggregated in the form of island on the surface of CeO,. The activity of the Ru/Ce was compared with that of homogeneous copper catalyst in the oxidation of several organic compounds (Table IV). Although Mn/Ce (1/1) was much more active than copper catalysts, comparison was based upon the activity of the latter from the consideration that they are practically used in the purification of industrial wastewaters. Ru/Ce showed almost the same activity as the copper catalyst for the oxidation of the compounds listed in Table IV. Although acetic acid was not decomposed completely both by the Ru/Ce and the copper catalysts, it was found that complete removal of acetic acid was attained by Mn/Ce (1/1)under the same reaction condition. This fact together with the previous
result that the Mn/Ce composite catalysts had much higher activity than copper catalyst for the oxidation of various compounds (Imamura et al., 1986) shows that the Ru/Ce catalyst is inferior to the Mn/Ce catalysts for the treatment of wastewaters containing various pollutants. However, poly(ethy1ene glycol) was decomposed much faster by Ru/Ce than by Mn/Ce (1/1)as is shown in Table I, which indicates that Ru/Ce has selectivity toward reactants. As poly(ethy1ene glycol) produces ethylene glycol, formaldehyde, and formic acid (Imamura et al., 19811, reactivity of these compounds toward the Ru/Ce and the copper catalysts was investigated a t 423 K (Table V). It is seen that Ru/Ce had much higher activity for these compounds than the copper catalyst. As all these compounds were decomposed by Ru/Ce faster than poly(ethylene glycol), the rate-determining step is not the decomposition of these intermediates but the decomposition of poly(ethy1ene glycol) itself. Reactivity of formic acid depended remarkably on pH; it was readily decomposed in the acidic region, whereas scarce decomposition occurred above pH 5. This shows that formate ion is less reactive than formic acid, the pK, of formic acid being 3.75. The same phenomenon was observed in the case of acetic acid; ATOC's after 1h at 473 K were 19.4% at pH 6.9 and 44.5% a t pH 2.7 in the oxidation catalyzed by Ru/Ce. As formaldehyde was decomposed readily irrespective of the pH of the solution, it is clear that formaldehyde was converted directly to carbon dioxide and water without formation of formic acid as an intermediate. Carbon monoxide was not detected in the vapor phase. Decomposition of formaldehyde did not proceed so much in the absence of oxygen. In conclusion, Ru/Ce showed a moderate catalytic activity comparable to copper ion for the oxidation of ordinary compounds. However, it is highly active toward poly(ethy1ene glycol) or some low molecular weight compounds with a high content of oxygen such as formaldehyde, ethylene glycol, or formic acid. It can be a selective catalyst for the decomposition of formaldehyde which has attracted attention recently due to its high carcinogenic toxicity. In addition, the results presented here indicate the high possibility of Ru to be used as a promoter for the Mn/Ce composite catalysts.
Acknowledgment We thank Kazunori Utani for his assistance and encouragement in carrying out this work. Registry No. PEG, 25322-68-3; PPG, 25322-69-4; Ru, 744018-8; Rh, 7440-16-6; P t , 7440-06-4; Ir, 7439-88-5; Pd, 7440-05-3; Cu, 7440-50-8; Mn, 7439-96-5; CeO,, 1306-38-3; ZrOz, 1314-23-4; TiO,, 13463-67-7; HO(CH,),CH,, 71-23-8; HO(CH&CH3, 71-36-3;
Ind. Eng. Chem. Res. 1988,27, 721-723 CBHSOH, 108-95-2; H3CCONH2, 60-35-5; H&C02H, 64-19-7; HO(CHz),OH, 107-21-1; HCOZH, 64-18-6; HCHO, 50-00-0.
Literature Cited Banks, V. C.; O’Laughlin, J. W. Anal. Chem. 1957,29, 1412-1417. Imamura, S.;Tonomura, Y.; Kawabata, N.; Kitao, T. Bull. Chem. SOC.Jpn. 1981,54, 1548-1553. Imamura, S.;Sakai, T.; Ikuyama, T. Sekiyu Galzkaishi 1982a, 25, 74-80. Imamura, S.; Hirano, A.: Kawabata, N. Ind. Eng. Chem. Prod. Res. Dev. 198213, 21, 570-575. Imamura. S.: Kinunaka.. H.:. Kawabata. N. Bull. Chem. SOC.J m . 1982c,’55, 3679-3680. Imamura, S.; Doi, A.; Ishida, S. Ind. Eng. Chem. Prod. Res. Deu. 1985, 24, 75-82. Imamura, S.; Nakamura, M.; Kawabata, N.; Yoshida, J.; Ishida, S. Ind. Eng. Chem. Prod. Res. Dev. 1986, 25, 34-37. Imamura, S.: Nishimura, H.: Ishida, S . Sekivu Gakkaishi 1987.30, 199-202. Katzer. 3. R.: Ficke. H. H.: Sadana. A. J. Water Pollut. Control Fed. 1976, 48, 920-933.
72 1
Kim, K. S.; Winograd, N. J . Catal. 1974, 35, 66-72. McClune, W. F. “Powder Diffraction File”. Sets 21-22, 1980, p 375; International Centre for Diffraction Data, Pittsburgh, PA. Tagashira, Y.; Takagi, H.; Inagaki, K. Japanese Patent 75 106862, 1976; Chem. Abstr. 1976,84, 79359. 1964960p33-38. Teletzke, G. H. ‘Kyoto Institute of Technology. t Chubu University. Seiichiro Imamura,*t Ikumi Fukuda,? Shingo Ishida’ Department of Chemistry Kyoto Institute of Technology Matsugasaki, Sakyo-ku, Kyoto 606, Japan and Department of Industrial Chemistry Chubu University Matsumto-cho 1200, Kasugai 487, Japan
Received for review May 1, 1987 Accepted December 29, 1987
Cramer’s Rule and Partial Thermodynamic Properties: A Revisit A simple method which formalizes the computation of partial thermodynamic properties for a single substance is presented. The method utilizes the matrix representation of the total differentials of U, A , G, H, S, and V and Cramer’s rule for solving sets of linear equations to generate the required partial derivatives. This approach allows any one of the 336 partial thermodynamic properties to be calculated in a systematic and simple way, and thus this approach lends itself to implementation on a digital computer. T h e evaluation of determinants for the case when the partial derivative of a n energy term is taken with respect t o another energy term involves significant algebraic manipulation although the technique is the same for all partial derivatives. Two examples are given to illustrate the procedure outlined in the paper. Expressions relating the first partial derivatives of thermodynamic functions to measurable quantities are well established. For a pure substance, eight common thermodynamic variables exist, i.e., U, A, G , H,S , P, T, V, and there are possible 8 X 7 X 6 = 336 first partial derivatives. Bridgman (1914,1925) has devised a system in which these derivatives can be related to measurable quantities involving V, T, and P, their mutual derivatives, Le., a and p, the heat capacity, C,, and the entropy, S . The introduction of the entropy does not pose any difficulties since it can be conveniently calculated from the heat capacity and volumetric data. Thus, he introduced 45 relationships, better known as the Bridgman relationships, for calculating the more desirable thermodynamic functions and their partial derivatives. From these relationships one can then calculate any other partial derivative. Later work by Lerman (1937) presents a method similar to that devised by Bridgman but redefined in such a manner so as to permit the resolution of the 45 forms into a few, more basic forms. Tobolsky (1942) presents another systematic method of obtaining these derivatives which is applicable to any set of independent variables. A more rigorous approach is given by Shaw (1935) which introduces the method of the Jacobian transformations, and a short overview of this technique can be found in Sandler (1977). Here we present a method by Erben (1973) which formalizes the Jacobian transformations in a simpler concept which is easier to understand and to our knowledge is not available in the literature. There is a synergism between the method of the Jacobian transformations and the method we describe below which is not immediate. However, we do not intend to demonstrate this is this communication. This method is outlined below together with two examples to illustrate the technique. Let xl, x2, and x , be three variables related by the following set of linearly independent algebraic equations: 0888-5885/88/2627-0721$01.50/0
Since there are three variables and two equations describing the system, we can only solve two of them in terms of the third one. Suppose we want to solve for x1 and x 2 in terms of x,; we can rearrange eq 1and 2 in the following manner: 2x1 + x 2 = -x3 (3) Xi
+ 3x2 = 4 x 3
(4)
or in matrix notation
where A is the square matrix premultiplying the vector x = [xl x2IT(T = transpose). A well-known method for the solution of linear algebraic equations is Cramer’s rule (cited in Wylie (1966)): The mechanics of this method are as follows: First find the determinant of A, det A = [ (2)(3) - (1)(1)] = 5. Then move vector b to the column for which the solution is desired, e.g., xl, and form matrix Al as follows:
where det Al = [(-1)(3) - (-4)(1)] = 1. The solution for x1 is then expressed by x ~ / x ,= det A,/det A =
y5
Similarly the solution for x2 can be found by substituting vector b in lieu of the second column, giving x 2 / x 3 = det A2/det A = 0 1988 American Chemical Society
-y5
