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Equilibrium Gas-Phase Compositions and Carbon Deposition Boundaries in the CHO-Inert System' Shantllal Mohnot and 6 . G. Kyle" Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
Gas-phase compositions in equilibrium with solid carbon have been calculated over the complete composition range for the system comprised of the elements carbon, hydrogen, oxygen, and nitrogen. The calculations were performed via the free energy minimization technique and cover a range of temperatures from 500 to 1500 K, pressures from 1 to 25 atm, O/H atom ratios from 0.001 to 1000, and N/O atom ratios from 0 to 10. Also, over this range of conditions carbon deposition boundaries were determined. These are presented on triangular coordinates in terms of atom percent of the elements C, H, and 0. Under the conditions studied, nitrogen can be considered inert and the species of major interest are C, CO, COP,H2, H20, CH4,and N2. While the calculations were made with nitrogen as the inert, these results can be applied easily to systems containing the elements C, H, and 0 plus any inert substances. The effect of gas-phase nonideality was studied and found to be negligible.
Introduction Chemically reacting systems comprised of the elements carbon, hydrogen, and oxygen are encountered in many industrial processes. For this very important system, Cairns and Tevebaugh (1964) presented gas-phase compositions in equilibrium with solid carbon and carbon deposition boundaries a t 1 atm and over the temperature range 298 to 1500 K. More recently, Baron et al. (1976) have considered the basic gasification system consisting of water, hydrogen, and oxygen in the presence of excess solid carbon. Their results include gas-phase composition, gas heating value, reactor energy balance, and moles of product per mole of carbon reacted and were obtained over temperatures ranging from 76.4 to 2500 O F , pressures ranging from 1to 100 atm, and H/O atom ratios ranging from 1 to 3. Their study also included equilibrium in the presence of nitrogen for an H/O atom ratio of unity. We have calculated gas-phase compositions in equilibrium with solid carbon and have constructed carbon deposition boundaries for the carbon-hydrogen-oxygennitrogen system for temperatures ranging from 500 to 1500 K, pressures ranging from 1to 25 atm, and N/O atom ratios ranging from 0 to 10. In the CHO system when gas-phase compositions in equilibrium with solid carbon are converted to atom percentages of the constituent elements and plotted on a triangular diagram, the resulting curve is the carbon deposition boundary. Cairns and Tevebaugh (1964) appear to have originated this concept and have discussed extensively its utility for practical design calculations. The reader is referred to their paper for a detailed explanation complete with specific examples; here only a brief explanation is presented. A reacting system comprised of any set of reactants containing only the elements carbon, hydrogen, and oxygen can be represented by a point on a diagram similar to those of Figures 1-4. If this system point lies below the carbon deposition boundary, no carbon will form. If the system point lies above the carbon deposition boundary, carbon will form and the composition of the gas phase on an atom percent basis can be found where a straight line passing through the system point and the apex (100%C) intersects the carbon deposition boundary. The relative amounts of carbon and gas on an atomic basis can then be found by application of the lever arm principle. A wide variety This is Department of Chemical Engineering Contribution No. 54j, the Kansas Agricultural Experiment Station (Project 0946), Kansas State University.
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of problems may be easily solved with this graphical approach. These concepts apply also to CHON systems if it is recognized that the carbon deposition boundary depends on amount of inert as well as temperature and pressure.
Thermodynamic Considerations and Computational Method Cairns and Tevebaugh (1964) have shown that in the CHO system the gas phase in equilibrium with graphite contains the species Ha, CO, C02, CH4, and HzO in significant amounts, and that in such a system there are three degrees of freedom in the phase rule sense. The addition of an inert species to this system merely increases by one the degrees of freedom; thus, for the CHON system four intensive variables must be specified. We have chosen temperature, pressure, O/H atom ratio, and N/O atom ratio as independent variables. The computational method was based on Free Energy minimization as first described by White et al. (1958) with the method of steepest descent applied to a quadratic fit being used to locate the minimum. Examination of the expression for the free energy of the reacting system revealed that the terms containing pressure and total gas-phase moles could be combined into a single term involving their ratio. Although this combination of variables would appear to lessen the degrees of freedom in apparent violation of the phase rule, this is not the case because a quantitative relation between these two variables cannot be determined a priori. Nevertheless, this combination of variables has qualitative utility. Details of the thermodynamic analysis, the computational scheme, the computer program, and extensive results are given by Mohnot (1977). Results and Discussion In the range where our results overlap those of Cairns and Tevebaugh (1964) and Baron et al. (1976), comparisons have shown excellent agreement. Complete results in the form of tables of gas-phase compositions in equilibrium with solid carbon and figures showing carbon deposition boundaries are available as supplementary material; only data sufficient to illustrate trends are presented here. (See the paragraph at the end of the paper regarding supplementary material.) Carbon deposition boundaries plotted on nitrogen-free atom percent triangular coordinates are shown on Figures 14. Figures 1and 2 illustrate the effect of temperature and Figures 0 1978 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 17,No. 3, 1978 271 L
C
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Figure 1. Carbon deposition boundaries for the CHOI system at 1 atm, 7 = 3.762, T as a parameter, K.
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Figure 3. Carbon deposition boundaries for the CHOI system at lo00 K, P = 1 atm, with 7 as a parameter:0, 2,3.76, 10. L
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Figure 2. Carbon deposition boundaries for the CHOI system at 25 atm, 7 = 0.000, T as a parameter, K.
Figure 4. Carbon deposition boundaries for the CHOI system at lo00 K, 7 = 0, with P as a parameter: 1 , 5 , 1 5 , 2 5 .
3 and 4 illustrate the effect of N/O atom ratio and pressure, respectively. The figures show that, in some cases carbon deposition boundaries change only slightly in response to changing conditions; however, this only means that the gasphase atomic percentages are the same and does not imply equal mole percentages of the chemical species. In fact, several cases were observed where carbon deposition boundaries superimposed and as much as 20% difference in these mole fractions was found. As Cairns and Tevebaugh have noted, an increase in temperature causes a shift in the equilibrium gas-phase compositions toward CO and Ha. Thus, carbon deposition boundaries a t high temperature approach straight lines connecting Hz and CO, and gas-phase compositions may be estimated by applying the lever arm rule. At lower temperatures the species CH4, COz, and HzO become increasingly important and carbon deposition boundaries exhibit curvature. It was found that the effects of N/O atom ratio and pressure on carbon deposition boundaries are most pronounced around
1000 K and were small at both lower and higher temperatures. For practical problems it would be reasonable to ignore these effects near the extremes of 500 and 1500 K. Because the effects of pressure and N/O atom ratio can be combined through the use of the ratio of pressure to total gas-phase moles, it is expected that increases in these variables will produce opposite effects. This can be observed from examination of Figures 3 and 4. Also, as expected, the maximum effect of N/O atom ratio is seen at the lowest pressure, and, accordingly, when the N/O atom ratio is zero the maximum effect of pressure is observed. The direction of these effects is determined by LeChatelier’s principle. As can be seen in Figure 4, an increased pressure shifts the gas-phase composition toward more CH4 and COz. Figure 3 shows that an increase in inerts decreases the effective pressure and causes a shift toward CO. The corresponding shift toward Hz does not show on the diagram because as CH4 and Hz are approached the quantity of oxygen, hence the effect of N/O atom ratio, decreases. In this composition range the effect of inerts can be easily de-
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termined from consideration of equilibrium in the simple C-HpCH4 system. Because of the wide range of variables studied, this work should be useful for design purposes where the question of carbon deposition is important or where gas-phase compositions in equilibrium with solid carbon are needed. The results are applicable to systems comprised of any set of reactants containing only the elements carbon, hydrogen, oxygen, and nitrogen or reactants containing only the elements carbon, hydrogen, and oxygen plus any number of inert components. L i t e r a t u r e Cited Baron, R. E., Porter, J. H., Hammond, 0. G., Jr., "Chemical Equilibria in Car-
bon-Hydrogen-Oxygen Systems", MIT Press, Cambridge, Mass., 1976. Cairns, E. J., Tevebaugh. A. D., J. Chem. Eng. Data, 9 (3), 453 (1964). Mohnot, S. M.. M.S. Thesis, Kansas State University, Manhattan, Kansas, 1977. White, W. B., Johnson, S. M., Dantzig, G. B., J. Chem. Phys., 28, 751 (1958).
Received for review March 16,1977 Accepted January 12,1978 Supplementary Material Available: A thermodynamic analysis, the computational scheme, a tabulation of gas-phase compositions in equilibrium with graphite, and carbon deposition boundaries (47 pages). Ordering information is given on any current masthead page.
Economics of Alternative Distillation Configurations for the Separation of Ternary Mixtures Nickos Doukas and Wllliam L. Luyben" Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 180 15
The separation of a ternary mixture into three product streams was studied using four different configurations of distillation columns: (1) removing components sequentially in decreasing order of relative volatility in two conventional columns, (2) removing components in increasing order of relative volatility in two conventional columns, (3) a single column with sidestream product, and (4) a prefractionator column followed by a sidestream column. Economic calculations were performed to determine the optimum scheme. Several values of relative volatilities and feed compositions were explored. A single sidestream column was found to be the most economical when relative volatilities are larger than 3:2:1 and when concentrations of the lightest or heaviest components in the feed are less than 10 mol YO.For higher feed concentration, the prefractionator/sidestream column configuration was found to be more economical than the conventional direct or inverted sequences in most cases.
Introduction Optimum configurations of sequences of distillation columns for separating multicomponent mixtures have been discussed in the literature for many years. King (1971) described the use of N - 1conventional (two product) columns to separate N components into N more-or-less pure product streams. Nishimura and Hiraizumi (1971) discussed optimal patterns of sequences of conventional columns. Petlyuk et al. (1965),in a pioneering paper, suggested several alternative configurations for separating ternary mixtures. One-, two-, and three-column schemes were studied for a low relative volatility system (1.2, 1.1,and 1) with symmetrical amounts of the lightest and heaviest components in the feed and over a range of compositions of the intermediate component. Comparisons were made on the basis of the total amount of vaporization required in all columns a t minimum reflux conditions. Capital costs were not considered. Conventional sidestream columns were also not considered. Stupin and Lockhart (1972) discussed one of the schemes proposed by Petlyuk et al. (1965) for a ternary system with high relative volatilities (9,3, and I), a feed that was an equal molal mixture of three components and 90% product purities. No detailed process engineering calculations or economics were presented. Rathore et al. (1974) studied sequences of N - 1 conventional columns with heat integration. Freshwater et al. (1976)
studied essentially the same problem, with four- and fivecomponent mixtures, considering heat integration and conventional columns. Hendry et al. (1972), Rodrigo et al. (1975), Gomez et al. (1976),and Seader et al. (1977) discussed techniques for optimal design of sequences of conventional separation processes for multicomponent mixtures. Tedder (1975), in a study similar to the present one, examined the separation of ternary mixtures of alkanes. No heat integration was considered, but complex designs with sidestreams and multiple feeds were studied. This study is an extension of the work of Petlyuk et al. (1965). Detailed design and economic calculations were performed for four configurations. A ternary mixture of benzene, toluene, and o-xylene (relative volatilities of (6.7,2.4, and 1)) was studied with small amounts of the lightest component (benzene) in the feed and for small amounts of the heaviest component (0-xylene) in the feed. The other two component compositions were assumed equal. The desired product streams were: (1)benzene with 5% toluene impurity; (2) toluene with 5% benzene and 5% o-xylene impurities; (3) o-xylene with 5% toluene impurity. Heat integration was not studied, nor were feeds with small amounts of the intermediate component considered. The pressure in all columns was assumed to be atmospheric since this gave reasonable operating temperatures for both heat input and heat removal. Ideal trays, saturated liquid feeds and
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