Ind. Eng. Chem. Res. 2004, 43, 1827-1831
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Application of the Attainable Region Concept to the Oxidative Dehydrogenation of 1-Butene in Inert Porous Membrane Reactors David Milne, David Glasser, Diane Hildebrandt,* and Brendon Hausberger Centre of Material and Process Synthesis, University of the Witwatersrand, Johannesburg, Private Bag 3, WITS 2050, South Africa
The attainable region (AR) concept uses a geometrical procedure to determine the boundaries of the region that include all possible reactor products for a known feed condition. The procedure also allows the choice of reactor(s) and the sequencing of these reactors to maximize the selection of reactor products in terms of predefined objective functions. It is also possible to derive the process operating conditions commensurate with an optimum objective function. The AR concept currently is being applied to industrial applications, and in this paper the concept is used to study the manufacture of butadiene by the oxidative dehydrogenation of 1-butene. Process operating conditions, specifically the partial pressure of oxygen, are reviewed. The reactors discussed in this paper are the fixed-bed reactor and the inert porous membrane reactor. A candidate AR for the system butene-butadiene is proposed. Over the last 15 years, several papers have been published dealing with mapping of the region (the attainable region, AR) within which all of the reactants and products of a chemical reaction lay, assuming known feed conditions.1 In particular, two chemical reaction systems have been studied to determine the boundaries of the candidate AR, the Trambouze and the van der Vusse. These two examples represented reactions of considerable academic and theoretical interest but suffered from the lack of direct applicability to problems of industrial significance. Specifically, there is a general paucity of chemical reaction rates and kinetic data, and in the study of the Trambouze and van der Vusse reactions, assumptions had to be made which, although undeniably useful in mapping of the boundaries of the AR, could not easily be applied to specific chemical reactions. The Trambouze and van der Vusse reactions, however, do possess the advantage of mathematical simplicity coupled with the ability to model a wide range of reactor behavior and resulting reactor configurations. With the publication2 of the reaction rates and kinetic data for the oxidative dehydrogenation (ODH) of nbutanes to butene and butadiene in inert porous membrane reactors (IMRs), it became possible to examine a specific chemical reaction of industrial interest. Te´llez et al.2 developed equations for the rate expressions associated with the ODH of n-butane, the three isomers of butene (1-butene, cis-2-butene, and trans-2-butene), and butadiene. Values of the respective rate constants also were provided. The experiments by Te´llez and his colleagues were conducted in an IMR operating at atmospheric pressure and within a feed temperature range of 748-823 K. In a more recent publication,5 Assabumrungrat et al. compared the performance of a porous membrane reactor with that of a conventional fixed-bed reactor (FBR) in the ODH of n-butane. The porous membrane reactor was used to add oxygen to the hydrocarbons in a controlled manner. Assabumrungrat et al., in developing * To whom correspondence should be addressed. Fax: +27 (11) 717 7557. E-mail:
[email protected].
Figure 1. Reaction scheme for the ODH of butene to butadiene.
their mathematical models, used the kinetic and experimental data developed by Te´llez2-4 and his colleagues. The reaction network for the ODH of butene was postulated2,3 as that in Figure 1. Using the kinetic data developed by Te´llez, the techniques used to identify a candidate AR for a particular chemical reaction1 were applied to the ODH of butene to butadiene. The objective of this research was to establish the operating conditions necessary to maximize the yield of butadiene from a fixed feed of butene and, in so doing, to identify a candidate AR for the system butene-butadiene. The chemical reactions involved in the ODH of butene are as follows:
Oxidation of butene C4H8 + 1/2O2 ) C4H6 + H2O (r7) r7 ) k7PC4H8θ0 C4H8 + 4O2 ) 4CO + 4H2O (r8) r8 ) k8PC4H8λ0 C4H8 + 6O2 ) 4CO2 + 4H2O (r9) r9 ) k9PC4H8λ0 Oxidation of butadiene C4H6 + 7/2O2 ) 4CO + 3H2O (r10) r10 ) k10PC4H6λ0
10.1021/ie0303193 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/13/2004
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C4H6 + 11/2O2 ) 4CO2 + 3H2O (r11) r11 ) k11PC4H6λ0 Oxidation of catalyst sites θ0 ) 2k12PO2/(2k12PO2 + k7PC4H8)
Figure 2. FBR configuration.
λ0 ) 2k13PO2/[2k13PO2 + (8k8 + 12k9)PC4H8 + (7k10 + 11k11)PC4H6] Factors influencing the rate expressions presented by Te´llez et al.2,3 include the partial pressures of butene and butadiene and the selective (θ) and nonselective (λ) oxidation catalyst sites, respectively. The latter two, in turn, are influenced by the partial pressure of oxygen and by the partial pressures of butene and butadiene. The mathematical model created to examine the ODH of butene assumed isothermal conditions and atmospheric pressure. An initial feed of pure butene was used, and the partial pressure of oxygen was varied over the range of 0.25-85 kPa. In the presentation of the results of the mathematical analyses, the mass fraction of carbon in the reactants and products was used because mass fraction variables obey the linear mixing rule. Linear mixing has the additional advantage of providing a greater insight into the characteristics of the AR than is possible through use of the partial pressures of the various components. The mass fractions of carbon in the respective products and reactants are equal to their respective fractions on a carbon molar basis. It was recognized that the addition of oxygen served two purposes: (i) to provide heat by its exothermic reaction with the hydrogen released during the oxidation of butene and butadiene and in so doing to nullify the endothermic dehydrogenation of butene; (ii) to dehydrogenate butene to butadiene. (The dehydrogenation of both butene and butadiene to carbon monoxide and carbon dioxide is an unwanted side effect of the reaction process.) Initially, two scenarios were considered. The first was feeding butene and oxygen, the latter at an initial specified partial pressure, to a stabilized (steady-state) FBR and permitting the reaction to continue until either all of the oxygen or all of the butene was depleted. In the second scenario, using an IMR, the partial pressure of oxygen was maintained at a constant specified level by the addition of fresh oxygen along the length of the IMR. The effect of the reactor size upon the yield of butadiene also was examined in both scenarios. Scenario 1: Depletion of Oxygen in a FBR The reactor configuration for this scenario is shown in Figure 2. All butene and butadiene concentrations are expressed in mass fractions of carbon. At an initial oxygen partial pressure of 85 kPa, the reaction proceeds until all of the oxygen has been depleted. When this occurs, the residual butene and butadiene concentrations are 0.0009 and 0.07, respectively. The other components present upon completion of the reaction, other than butene and butadiene, are carbon monoxide, carbon dioxide, and water. All of the oxygen has been utilized in the oxidation of butene and
Figure 3. Profiles of butene and butadiene at oxygen partial pressures of 15, 25, 45, 65, and 85 kPa in a FBR.
butadiene. The water gas shift reaction, i.e., the reaction of carbon monoxide and hydrogen, was not considered by Te´llez and his colleagues.2,3 If the initial partial pressure of oxygen is increased to 86 kPa, all of the butene and butadiene is oxidized and there is residual oxygen present upon completion of the reaction. At this initial partial pressure of oxygen, the supply of butene is the limiting factor. At oxygen partial pressures of less than 85 kPa, the reaction ceases with oxygen depletion. At an initial oxygen partial pressure of 65 kPa, reaction cessation occurs after a residence time of 20 s (at 45 kPa, cessation occurs after a residence time of 9 s). When the reaction ceases, we are left with butene, butadiene, carbon monoxide, carbon dioxide, and water. At this initial partial pressure of oxygen, the supply of oxygen is the limiting factor. The maximum yield of butadiene, 0.51, occurs at an initial oxygen partial pressure of 65 kPa. The oxygen partial pressure at this stage has been reduced to slightly less than 0.0005 kPa. Residual butene has a concentration marginally in excess of 0.21. Figure 4 shows that the reaction times to attain the maximum yields of butadiene do not exceed 20 s for all oxygen partial pressures, implying that the ODH reaction is a very fast one. Figure 5 shows the residence times and the residual butene concentrations on reaction cessation at the respective oxygen partial pressures. Scenario 2: Replenishment of Oxygen in an IMR The reactor configuration for this scenario is shown in Figure 6. Figure 7 shows the effect of adding oxygen along the length of the reactor to maintain a constant oxygen partial pressure in the stream of reactants and products. Figure 7 also shows that the convex shape of the butene-butadiene profiles decreases with reduced oxygen partial pressure. This trend particularly is notice-
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Figure 4. Residence times for butadiene at oxygen partial pressures of 5, 15, 25, 45, 65, and 85 kPa in a FBR.
Figure 7. Profiles of butene and butadiene at constant oxygen partial pressures from 85 to 0.25 kPa in an IMR.
Figure 5. Residence times for butene at oxygen partial pressures of 15, 25, 45, 65, and 85 kPa in a FBR.
Figure 8. Residence times for butadiene at constant oxygen partial pressures from 85 to 0.25 kPa in an IMR.
Figure 6. IMR configuration.
able at an oxygen (constant) partial pressure of 0.25 kPa when the butene-butadiene profile, in mass balance space, is almost a straight line, although still convex. It is noticeable from Figure 7 that the maximum yield of butadiene increases and the residual butene decreases as the partial pressure of oxygen is reduced. At an oxygen partial pressure of 0.25 kPa, the maximum yield of butadiene is 0.88 with a commensurate low value of butene (less than 0.003). It is concluded that the lower the (constant) oxygen partial pressure in an IMR, the greater is the yield of butadiene and the associated conversion (consumption) of butene. The maximum yield of butadiene at an oxygen partial pressure of 0.25 kPa is 0.88 after a residence time of 248 s (see Figure 8). A detailed analysis of Figure 8 shows that the residence time for the maximum yield of butadiene initially decreases with reduced oxygen partial pressure over the range of 55-85 kPa. Between the range of 40 and 55 kPa, the residence time for the maximum yield of butadiene is practically
Figure 9. Residence times for butene at constant oxygen partial pressures from 85 to 0.25 kPa in an IMR.
constant at 11 s. This represents the minimum residence time for butadiene yields between 0.4 and 0.5. As the (constant) partial pressure of oxygen is reduced below 40 kPa, the residence times for the maximum yield of butadiene gradually increase. For partial pressures of less than 1 kPa, the residence time for the maximum yield of butadiene increases sharply. Figure 9 shows butene residence times for constant values of oxygen partial pressure over the residence
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Figure 10. Profile of butene and butadiene at a very low oxygen partial pressure and in a very large IMR.
Figure 12. Profiles of butene and butadiene at different oxygen partial pressures for an IMR and for a FBR.
Figure 11. Butadiene residence times at a very low oxygen partial pressure and in a very large IMR.
As has already been noted, for an IMR at a constant oxygen partial pressure of 0.25 kPa, the maximum yield of butadiene is 0.88 with a reactor size of 248 s. This represents an achievement of 98% relative to the theoretical maximum butadiene yield of 0.90. For a FBR with an initial oxygen partial pressure of 65 kPa and in which the oxygen is not replenished, the maximum yield of butadiene is 0.51 (see Figure 3). This represents an achievement of 57% relative to the theoretical maximum butadiene yield of 0.90. In Figure 12, for a FBR in which the initial oxygen is depleted through the normal oxidative process, the maximum butadiene yield at 65 kPa is 0.51 at a residual butene value of 0.21. Also shown in Figure 12 are the butene-butadiene profiles for an IMR, in which the original oxygen partial pressures (0.25 and 0.000 001 kPa) are maintained constant through the addition of fresh oxygen along the length of the reactor. At an oxygen partial pressure of 0.25 kPa, the maximum butadiene yield is 0.88 at a residual butene value of less than 0.003. For a very low oxygen partial pressure (i.e., 0.000 001 kPa), the maximum butadiene yield is 0.90 at a butene value infinitesimally close to zero. It is noteworthy that the butene-butadiene profiles considered in Figure 12 (depleted oxygen at 65 kPa and constant oxygen at 0.25 kPa) all lie below the profile for a very low oxygen partial pressure. From an analysis of Figures 3-12, we conclude that the theoretical profile for the maximum butadiene yield at a very low oxygen partial pressure represents the furthermost boundary within which all scenarios so far identified lie. Consequently, we believe that Figure 10 represents a candidate AR for the system butenebutadiene.
time range of 0-300 s. Provided that the reactor is sized accordingly, i.e., the residence time is sufficiently large (approximately 340 s for 0.25 kPa), all of the butene will be depleted. Examination of Figure 7 supports the belief that the maximum yield of butadiene increases with decreasing oxygen partial pressure. Figure 8 shows that the reactor size (residence time) associated with the maximum yield of butadiene falls to a minimum and then increases. This observation begs the question as to what yield of butadiene could be attained at a very low oxygen partial pressure and a reactor of infinite size. This question was answered by defining a very low oxygen partial pressure as 0.000 001 kPa, and the results are shown in Figures 10 and 11. The maximum yield of butadiene at a very low oxygen partial pressure and as the concentration of butene tends to zero is 0.90. The butene-butadiene profile in Figure 10 is convex over its entire length. Figure 11 shows that the residence time at a very low oxygen partial pressure for the total conversion of butene is 5.29 × 107 s. That such a large residence time is required for the total conversion of the butene can be inferred from Figure 8, which shows that the residence time for the maximum yield of butadiene increases almost asymptotically for (constant) oxygen partial pressures of less than 1 kPa.
Effect of the Temperature All of the analyses conducted have been at the datum temperature of 773 K,4 and consequently our candidate AR shown in Figure 10 is applicable only at that temperature. Figure 13 shows the effect of the temperature upon the butene-butadiene profile. Examination of Figure 13 shows that an increase of the reactor temperature from 773 to 823 K raises the maximum theoretical yield of butadiene from 0.90 to
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dence time of 248 s. This yield of butadiene represents 98% of the theoretical quantity from an IMR of very large size with a very low oxygen partial pressure. The reactor configuration for this example was an IMR with a constant oxygen partial pressure of 0.25 kPa (Figure 7). A candidate AR has been identified for the system butene-butadiene at a temperature of 773 K. This candidate AR is shown in Figure 10. It represents an IMR with a (constant) very low oxygen partial pressure and of very large size. This candidate region contains all reactants and products so far identified. Nomenclature
Figure 13. Effect of the temperature upon the theoretical maximum yield of butadiene.
0.96. Decreasing the operating temperature from 773 to 748 K reduces the maximum theoretical yield of butadiene from 0.90 to 0.83. From Figure 13, we conclude that the theoretical maximum yield of butadiene increases with temperature over the range of 723-823 K. Consequently, each of the three profiles shown in Figure 13 represents a candidate AR for the system butene-butadiene at the temperature indicated. Conclusions For initial oxygen partial pressures greater than 45 kPa in a FBR, a higher yield of butadiene can be attained without the addition of fresh oxygen than when the oxygen partial pressure is kept at a constant level in an IMR (Figures 3 and 7). (At an oxygen partial pressure of 85 kPa, the butadiene yield from a FBR is 1% greater than that from an IMR.) For oxygen partial pressures of less than 45 kPa, a higher yield of butadiene can be attained in an IMR when the oxygen partial pressure is kept at a constant level than when it is depleted through normal ODH in a FBR (Figures 3 and 7). The best yield of butadiene identified in this study is 0.88 carbon mass fraction with a corresponding resi-
Eai ) activation energy for species i, kJ/mol ki ) kinetic constant for reaction i, mol/kg‚s Pi ) partial pressure of species i, atm ri ) rate of reaction of reaction i, mol/kg‚s R ) gas constant, 8.314 J/mol‚K T0 ) reference temperature, 773 K T ) feed temperature, K Greek Symbols θ0 ) selective oxidation catalyst site λ0 ) nonselective oxidation catalyst site
Literature Cited (1) Glasser, D.; Hildebrandt, D.; Crowe, C. A Geometric Approach to Steady Flow Reactors: The Attainable Region and Optimisation in Concentration Space. Am. Chem. Soc. 1987, 18031810. (2) Te´llez, C.; Mene´ndez, M.; Santamarı´a, J. Kinetic Study of the Oxidative Dehydrogenation of Butane on V/MgO Catalysts. J. Catal. 1999, 183, 210-221. (3) Te´llez, C.; Mene´ndez, M.; Santamarı´a, J. Simulation of an Inert Membrane Reactor for the Oxidative Dehydrogenation of Butane. Chem. Eng. Sci. 1999, 54, 2917-2925. (4) Te´llez, C.; Mene´ndez, M.; Santamarı´a, J. Oxidative Dehydrogenation of Butane using Membrane Reactors. AIChE J. 1997, 43 (No. 3), 777-784. (5) Assabumrungrat, S.; Rienchalanusarn, T.; Praserthdam, P.; Goto, S. Theoretical Study of the Application of Porous Membrane Reactor to Oxidative Dehydrogenation of n-Butane. Chem. Eng. J. 2002, 85, 69-79.
Received for review April 15, 2003 Revised manuscript received December 2, 2003 Accepted December 2, 2003 IE0303193
