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only the reactant B can be chemisorbed on the catalyst ... and B are the initial reactants, C is the desired product (of the selective conversion), D is the undesired ...

Theoretical Foundations of Chemical Engineering, Vol. 39, No. 1, 2005, pp. 70–77. Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 1, 2005, pp. 72–79. Original Russian Text Copyright © 2005 by Zagoruiko.

Selective Exothermic Catalytic Reactions in a Reverse Heat Front A. N. Zagoruiko Boreskov Institute of Catalysis, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 5, Novosibirsk, 630090 Russia E-mail: [email protected] Received December 17, 2003

Abstract—A model system of exothermic reactions of selective and complete catalytic conversion is considered. The system comprises the reactions A + m[B] ⇒ C + [ ], C + n[B] ⇒ D + [ ], and B + [ ] ⇒ [B], where A and B are the initial reactants, C is the desired product (of the selective conversion), D is the undesired side product (of the complete conversion), [B] is the reactant B chemisorbed on the catalyst surface, and [ ] is a free catalytic active site. Numerical study of the system of reactions in an adiabatic catalyst bed shows that the yield of the desired product and the specific performance of the catalyst can be significantly increased if the reactions are performed not under steady-state conditions but in unsteady-state modes involving periodic time-separated introduction of the reactants A and B. Of greatest interest is to carry out the process in a reverse heat front propagating upward the flow of the gaseous reaction mixture, since, in this front, the maximal catalyst temperature is much lower and also the conversion selectivity is high.

The search for ways to increase the selectivity of desired reactions in complex systems of reactions is one of the most topical problems in modern catalysis science. Among such systems of reactions are numerous processes of selective catalytic oxidation, hydrogenation, halogenation, and many others. The most complex problems in their optimization are to increase the yield of products of partial conversion and to minimize the formation of side products of deep conversion of initial reactants. As a rule, such problems are solved by developing new highly selective catalysts and optimizing their performance. However, such an approach is far from always giving the required result. A considerable potential of improving the existing catalytic technologies of selective conversion is contained in unsteady-state processes in which the state of a catalyst is purposefully varied with time [1]. A review [2] of experimental studies in this area showed that a periodic change in the composition of the initial reaction mixture can increase the selectivity of many systems of reactions. In particular, by the example of oxidative dehydrogenation of propane into propylene on vanadium catalysts, it was demonstrated [3] that the propylene yield in the case of a cyclic change in the propane-to-oxygen ratio in the initial mixture is higher than that under steady-state conditions and is maximal in the case of separate periodic introduction of the reactants into the catalyst bed. Similar results were also obtained for 1-butene oxidation into butadiene [4] and many other selective catalytic reactions. Attempts were also made to develop industrial technologies based on this principle [5], which, however, were as yet unsuccessful.

The main drawback of the described studies is the lack of due consideration of thermal processes that may take place in an adiabatic catalyst bed under unsteadystate conditions. However, these processes are apparently quite important; furthermore, their effect on the process selectivity and the yield of a desired product may be both beneficial and adverse. PROBLEM FORMULATION Let us consider the simplest model mechanism of a selective reaction that involves the consecutive steps of partial and complete conversion: Ä + v1Ç ⇒ ë, ë + v2Ç ⇒ D, where A and B are the initial reactants, C is the desired product, and D is the side product. Let us assume that only the reactant B can be chemisorbed on the catalyst surface during the catalytic reaction. In this case, the mechanism of the catalytic steps can be represented as (1) Ä + v1[B] ⇒ C + v1[ ], C + v2[B] ⇒ D + v2[ ],

(2)

B + [ ] ⇒ [B], (3) where [B] is the reactant B chemisorbed on the catalyst surface and [ ] is a free catalytic active site. Let us also assume that all steps (1)–(3) are exothermic and their activation energies increase in the order E1 < E2 < E3. The latter means that an increase in temperature not only increases the degree of conversion of the initial reactants, but also decreases the selectivity of

0040-5795/05/3901-0070 © 2005 MAIK “Nauka /Interperiodica”

SELECTIVE EXOTHERMIC CATALYTIC REACTIONS IN A REVERSE HEAT FRONT

the partial conversion, and increases the yield of the products of the deep conversion. Mechanism (1)–(3) also suggests that the selectivity of the partial conversion decreases with an increase in the concentration of the reactant B. These properties, albeit of model character, are nonetheless quite typical of such systems of exothermic reactions as selective oxidation of hydrocarbons (in this case, the reactant A is a hydrocarbon and B is oxygen) and also many others. The purpose of this study was to model reactions (1)–(3) with allowance for the heat release in the reactions and the heat and mass transfer in the adiabatic catalyst bed. MATHEMATICAL MODEL The processes in the catalyst bed were described using the following one-dimensional two-temperature model of an adiabatic bed of a granular catalyst: cat

β i s sp ( c i – c i ) =

∑v

(4)

ij W j ,

j

cat

u∂c i /∂l + β i s sp ( c i – c i ) = 0,

(5)

a∂θ/∂t = – mW 1 – nW 2 + W 3 ,

(6)

uC p ∂T /∂l + αs sp ( T – T cat ) = 0,

(7)

∂T cat ( 1 – ε )γ ---------∂t 2

∂ T cat - + αs sp ( T – T cat ) + = λ eff -----------2 ∂l

∑Q W . j

(8)

j

j

The following boundary conditions were imposed:  T = T inlet  l = 0 ⇒  λ eff ∂T cat /∂l = 0  inlet  ci = ci ,

(9)

 θ ( l ) = θ init t = 0⇒ init  T cat ( l ) = T cat .

(11)

cat

(15)

Since reactions (1) and (2) involving the chemisorbed component generally occur in several steps, the orders m and n of these reactions in θ can, with sufficient accuracy, be assumed to be unity. When constructing the model, we also assumed that the reactions are performed in a plug-flow reactor and are not limited by internal diffusion, and the parameters of the gas flow are quasi-steady-state with respect to the inertial parameters of the catalyst. In addition, for simplicity of the model, it was supposed that the reactions cause no significant changes in the volume and specific heat of the reaction mixture. The set of Eqs. (4)–(15) was solved numerically using an algorithm based on balance difference schemes [6]. The algorithm included two levels of iterations, at the first of which the subset of material balance equations (4)–(6) and (12)–(15) was solved at constant catalyst temperature, and at the second, heat balance equations (7) and (8) were solved by iteration. The model studies were performed at the following values of the model parameters: Q1 = 850 kJ/mol, Q2 = 1250 kJ/mol, Q3 = 2100 kJ/mol, k01 = 1 × 103 s–1, k02 = 5 × 103 s–1, k03 = 5 × 106 s–1, ε = 0.4, u = 0.1 m/s, L = 0.1 m, v1 = 1, v2 = 9, E1 = 75 kJ/mol, E2 = 100 kJ/mol, E3 = 200 kJ/mol, a = 50, γ = 1900 kJ/(m3 ä), and Cp = 1.3 kJ/(nm3 K). The heat- and mass-transfer parameters (α, βi, and λeff) and ssp were determined from standard equations for a fixed bed of a granular catalyst [7] at an equivalent size of catalyst granules of 1.5 mm. Note that the kinetic parameters were chosen quite arbitrarily; however, this was of no decisive importance, since the purpose of this study was to reveal qualitative features. The modes of reactions (1)–(3) were characterized by the following parameters: the degree of conversion of the initial reactant A, out

inlet

the selectivity of the conversion of the reactant A into the desired product C, outlet

The kinetic equations for the rates Wj of the steps were written on the basis of the mass action law: cat m

(12)

cat n

(13)

W 3 = k 3 c B ( 1 – θ ).

k j = k 0 j exp ( – E j /RT cat ).

inlet

(10)

W 2 = k 2 cC θ ,

The temperature dependence of the reaction rate constants was described by the Arrhenius law

X = ( c A – c A )/c A ;

∂T cat - = 0, l = L ⇒ λ eff ---------∂l

W 1 = k 1 cA θ ,

71

(14)

S = cA

inlet

outlet

/ ( cA – cA

);

the yield Y = XS of the desired product C; the maximal temperature Tmax in the catalyst bed. RESULTS Steady-state mode. Initially, steady-state modes were modeled. Figure 1 presents typical heat and concentration profiles along the adiabatic catalyst bed length. The gas and catalyst temperatures are seen to increase downstream because of the heat release in

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ZAGORUIKO Y, %

T, °C

5

2

900

15 1

6

10

3 4

700

2

5

1

0

500

Tmax, °C

X, Y, S, θ

6

4 0.8

5

1100

4 900 0.4

6 3 5

0

0.2

0.4

0.6

0.8

1.0 1/L

Fig. 1. Profiles of (1) the gas temperature T, (2) the catalyst temperature Tcat, (3) the degree of conversion X, (4) the selectivity S, (5) the yield Y of the desired product, and (6) the surface concentration θ of the reactant B along the catalyst bed length in the steady-state mode at inlet cB

inlet cA

= 0.01,

= 0.005, and Tinlet = 500°C.

reactions (1)–(3). The degree X of conversion of the initial reactant A and the yield Y of the desired product C also increase, whereas the selectivity S decreases because of the conversion of the product C in reaction (2) into the products of the deep conversion. The maximal yield of the desired product in the adiabatic catalyst bed is apparently restricted by objective factors. First of all, restrictions are imposed on the initial concentrations of the reactants, since their high values lead to strong bed overheating, which, in turn, stimulates the deep conversion and decreases the conversion selectivity; on the other hand, at low reactant concentrations, the specific performance of the catalyst bed is low. Second, there are restrictions on the gas temperature Tinlet at the inlet of the catalyst bed: on the one hand, Tinlet should be high enough to ensure an appropriate degree of conversion, and on the other, an increase in Tinlet causes an increase in Tmax, which leads to a decrease in the selectivity.

2

3

700

1

500 400

450

500

550 Tinlet, °C

Fig. 2. Yield Y of the desired product and the maximal temperature Tmax in the catalyst bed in the steady-state mode inlet

inlet

versus Tinlet at c A = 1% and c B = (1) 0.10, (2) 0.30, (3) 0.40, (4) 0.50, (5) 0.60, and (6) 0.75%.

Figure 2 presents the results of modeling the process parameters in steady-state modes as functions of the inlet temperature at various initial concentrations of the reactant B. It is seen that the yield of the desired product is maximal when the ratio between the initial concentrations of the reactants A and B is twice as high as the stoichiometric ratio for the desired reaction, with these concentrations being rather low (no more than 1%). An increase in the initial concentration of the reactant A (up to 99%) leads to a small increase in the selectivity, but the total yield of the desired product remains virtually unchanged, since the total conversion is limited by the shortage of the reactant B. A further increase inlet in c B is inexpedient, since it would cause a significant increase in temperature and a decrease in the selectivity. Unsteady-state mode—a forward front. Let us consider an unsteady-state process in which the reactants A and B are introduced separately in different cycles of the process. In this case, in each of the cycles,

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Tcat, °C 1200

73

2

0.8 1 2 3 4 5

800

400

0.6 4

0.4 0.2

1 3

0 θ 0.8

100

150

200 t, s

Fig. 4. (1) Degree of conversion X, (2) the selectivity S, (3) the yield Y of the desired product, and (4) the average surface concentration θ of the reactant B versus time in the forward-front mode. The conditions are as in Fig. 3.

0.4

0 0

50

0

0.2

0.4

0.6

0.8

1.0 1/L

Fig. 3. Profiles of the catalyst temperature Tcat and the surface concentration θ of the reactant B along the catalyst bed length at various moments of time t = (1) 0, (2) 50, (3) 100, (4) 150, and (5) 200 s when the heated initial flow is fed into the cold catalyst bed presaturated with the reactant B (forinlet

ward-front mode) at c A

inlet

= 1, c B

= 0, Tinlet = 500°C,

init T cat

= 20°C, and θinit = 1. The solid and dotted arrows indicate the directions of the front and the gas flow, respectively.

unsteady-state concentration and heat patterns may emerge. Such unsteady-state processes are quite well known. In particular, Kiselev [8] presented a theory of heat fronts of exothermic reactions in adiabatic catalyst beds. In addition, there were studies devoted immediately to exploring such phenomena in processes in which the catalyst state varies with time [9, 10]. Of greatest interest is a cycle in which the reactant A is introduced in the adiabatic catalyst bed whose surface is presaturated with the reactant B. In the case where, into the catalyst bed preheated to a high temperature, a heated gas is also fed, there is quite an intense interaction of the reactant A with the catalyst, which leads to abrupt and strong bed overheating and very low conversion selectivity. Similar phenomena take place when a cold gas is introduced into the heated bed.

A milder mode of reactions (1) and (2) is possible when a heated gas is fed into the cold bed. In this case, the catalyst at the bed inlet begins to be heated because of the heat exchange with the reaction gas flow. With an increase in the catalyst temperature, reactions of the reactant A with the chemisorbed reactant B start to occur on the catalyst surface. These reactions are accompanied by heat release and further catalyst heating. When the catalyst temperature in the reaction zone exceeds the gas flow temperature, the interphase heat exchange ensures gas heating and heat transfer into the bed, where similar processes begin to take place. As a result, there emerge heat and concentration waves propagating in the direction of filtration of the gas flow (a forward front). Figure 3 shows the profiles of the catalyst temperature Tcat and the surface concentration θ of the reactant B along the catalyst bed length at various moments of time after introduction of the heated flow of the reactant A into the cold catalyst bed. It is seen that, early in the cycle, a reaction front forms and then uniformly propagates through the catalyst bed. The front itself is established, since its main parameters (velocity, temperature and concentration gradients along the bed length, maximal temperature, degree of conversion, selectivity, and yield) remain unchanged until the end of the cycle (Fig. 4). Unsteady-state mode—a reverse front [11]. Of considerable interest for the purposes of this study is to perform reactions in a heat front propagating toward the flow of the reaction mixture owing to the heat conduction of the catalyst bed. The theoretical possibility of the emergence of such a front was demonstrated by Kiselev [8]; moreover, there is experimental evidence of its formation in processes in which the catalyst state varies [12].

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ZAGORUIKO Tcat, °C 800

S 1.00

600

0.98

5

4

3 2

400 0.96 200

5

4

3

2 0.94

1

0 θ

Y 0.06

1 0.8 5

4

3

5

2

4

3

2

0.04 0.4 0.02

0 0

0.2

0.4

0.6

0.8

1.0 1/L

0 0

0.2

0.4

0.6

0.8

1.0 1/L

Fig. 5. Profiles of the catalyst temperature Tcat and the surface concentration θ of the reactant B along the catalyst bed length at various moments of time t = (1) 0, (2) 125, (3) 250, inlet

(4) 375, and (5) 500 s in the reverse-front mode at c A inlet cB

=

init T cat

= 20°C, θinit = 1, theat = 1, = 0, Tinlet = 20°C, 250 s, u = 0.1 m/s, and a = 50. The solid and dotted arrows indicate the directions of the front and the gas flow, respectively.

Let us consider an unsteady-state mode that takes place when the cold reaction flow of the reactant A is fed into the cold catalyst bed on whose surface the reactant B is chemisorbed. Let the temperature at the outlet of the catalyst bed be increased by introducing heat flux q to the outlet cross section of the catalyst for time theat. Such catalyst heating can be specified in the process model by replacing boundary condition (10) by the condition 0 < t < t heat ,

l = L ⇒ λ eff ∂T cat /∂l = q.

(16)

In this case, in the outlet part of the bed, with an increase in the catalyst temperature, reactions (1) and (2) begin to occur and heat is released. Because of the heat conduction, the inlet part of the bed is heated, and in this part, these reactions also start to take place and the temperature increases. If the conductive heat influx

Fig. 6. Profiles of the selectivity S and the yield Y of the desired product along the catalyst bed length at various moments of time in the reverse-front mode. The conditions and notation are as in Fig. 5.

and heat release in the reactions in this zone exceed the heat removal from the catalyst to the colder reaction flow, then heat and concentration fronts propagating toward the reaction gas flow (reverse fronts) emerge. A typical structure of a reverse front and changes in its parameters with time are illustrated in Figs. 5 and 6. It is seen that the front itself is established and the heat and concentration waves propagate self-similarly. The reactions occur within quite a narrow moving zone: in the inlet part of the catalyst bed, the reactions do not take place because of low catalyst temperature; and in its outlet part, because of the absence of the reactant B on the catalyst surface. Unlike the forward front, in the reverse front in this reaction zone, the effect of the heat exchange between the gas and the catalyst is opposite to the effect of the heat conduction of the bed and the heat release in the

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process. Therefore, the maximal catalyst temperature in the reverse front is much lower than that in the forward front and, consequently, the process selectivity is higher. Moreover, in the reaction zone, the surface concentration of the reactant B decreases with temperature; this decreases the rate of deep conversion (2) and provides an additional gain in the selectivity. On the other hand, the comparative narrowness of the reaction zone in the reverse front and lower temperatures lead to a certain decrease in the total conversion of the reactant A in comparison with that in the forward front. Apparently, the process parameters in the reverse front and the possibility of its formation depend significantly on the process conditions. First of all, of greatest importance are the heat transfer and heat conduction in the bed, whose rates are governed by the geometric characteristics of catalyst granules and the velocity u of the reaction mixture. A second significant factor is the heat release in the process, which is determined by the heats of reactions and the chemisorption capacity ‡ of the catalyst. The chemisorption capacity a controls such a technologically important parameter as the limiting duration of a reaction cycle. Figure 7 shows the parameters of the reverse front versus u at various a. It is seen that, at high flow velocities and low catalyst capacity, the heat exchange predominates over the heat release and heat conduction; as a result, the processes in the bed decay early in the cycle and no reverse front is formed. An increase in the flow velocity leads to a decrease in the residence time of the reaction mixture in the reaction zone, and this decreases the degree of conversion and simultaneously increases the selectivity (Fig. 7). In turn, because of such behavior, Tmax as a function of u is nonmonotonic and has a maximum in the middle of the flow velocity range (Fig. 7). An increase in the catalyst capacity increases the temperature, the degree of conversion, and the yield of the desired product but somewhat decreases the conversion selectivity. Quite a noticeable effect on the process is exerted by the conductive heat transfer rate. Variation of the thermal conductivity of the bed showed that an increase in λeff causes broadening of the reaction zone, which increases the degree of conversion and the yield of the desired product and decreases the conversion selectivity. As a result, at low λeffλ˝Ù, the maximal temperature in the front increases with an increase in the thermal conductivity. At higher λeffλ˝Ù, when the degree of conversion varies less significantly, an increase in the thermal conductivity decreases Tmax because of more efficient dissipation of the heat released in the process. Along with these factors, an increase in the thermal conductivity also broadens the range of admissible flow velocities at which a reverse front can form. Thus, varying the process parameters (gas velocity, chemisorption capacity, and effective thermal conductivity of the catalyst bed) in the reverse front, one can

Tmax, °C

75

4

800 3 2 600

I 1

400 S, % 100

1

3

2

80

4

~ ~

20

4 1

0 X, %

2 0.04

0.02

3 0.06

0.08

0.10 u, m/s

Fig. 7. Maximal temperature Tmax in the catalyst bed, the degree of conversion X, and the selectivity S in the reverse front versus the linear velocity u of the reaction flow at various chemisorption capacities of the catalyst of a = (1) 20, (2) 30, (3) 40, and (4) 50. Region I is the front decay region.

optimize the ratio between the degree of conversion and the conversion selectivity over quite a wide range. DISCUSSION The comparative characteristics of the steady-state mode and also the unsteady-state modes involving the forward and reverse fronts under comparable condiintel tions ( c A = 1, u = 0.1 m/s, L = 0.1m) are presented in the table. In comparison with the steady-state conditions, in the unsteady-state modes, the degree of conComparative characteristics of process modes Tmax, °C

Xmax, %

S, %

Ymax, %

958

0.5

99.4

0.5

Forward-front

1153

9.9

89.5

8.7

Reverse-front

780

6.4

94.2

6.0

Mode Steady-state

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ZAGORUIKO

version of the initial reactant A is much higher, and so is the yield of the desired product: by factors of 17.4 and 12 for the forward and reverse fronts, respectively. This fact is very important, since this allows one to proportionally increase the specific performance of the catalyst and, thus, improve the cost–performance ratio of the process. An additional beneficial factor is the higher concentration of the desired product in the outlet flow, which can simplify and cheapen the procedure of separation of the product from the reaction mixture. The maximal catalyst temperature in the forward front is quite high; however, it is much lower than the temperatures that could take place in the steady-state process at the same values of the degree of conversion and the selectivity. This is related to the fact that, first, from the total heat release in reactions (1)–(3) in the unsteady-state mode involving the separate introduction of the reactants, the heat release in reaction (3) is actually excluded, since reaction (3) is performed in a separate cycle; and second, a part of the heat released in the reactions is consumed to heat the initially cold catalyst. In the reverse front, along with these factors, the opposite effect of the heat exchange and the heat transfer ensures an additional decrease in the maximal temperature down to even below the temperature in the steady-state process, although the degree of conversion and the yield of the desired product are much higher.

u—linear velocity of the gas flow in the catalyst bed, reduced to normal conditions and to the total cross section of the bed, m/s; Wj—rate of the jth reaction, s–1; X—degree of conversion of the reactant A; Y—yield of the desired product; α—heat-transfer coefficient, kW/(m2 K); βi—mass-transfer coefficient of the ith substance, s–1; γ—volumetric heat capacity of the catalyst, kJ/(nm3 K); ε—fraction of free volume in the catalyst bed; θ—surface concentration of the chemisorbed reactant B; λeff —effective thermal conductivity of the catalyst bed, kW/(m K); νij —stoichiometric coefficients for the gas reactants; v1, v2—stoichiometric coefficients of steps (1) and (2), respectively, with respect to the reactant B. SUBSCRIPTS AND SUPERSCRIPTS i—number of a reactant; init—initial value; inlet—value at the inlet of the catalyst bed; j—number of a reaction.

NOTATION a—chemisorption capacity of the catalyst with respect to the reactant B, nm3 per cubic meter of catalyst bed; Cp—specific heat of the gas, kJ/(nm3 K); c, ccat—mole fractions of the reactants in the gas flow and near the catalyst surface, respectively; Ej—activation energy of the jth reaction, kJ/mol; k, k0—reaction rate constants and preexponential factors, respectively, s–1; L—catalyst bed length, m; l—coordinate along the catalyst bed length, m; m, n—order of steps (1) and (2), respectively, with respect to the surface concentration of the chemisorbed reactant B; Qj —heat of the jth reaction, kJ/mol; q—heat flux in catalyst heating, kW/m2; R—universal gas constant, kJ/(mol K); S—selectivity; ssp—specific geometric surface area of catalyst granules in the bed, m–1; T, Tcat—temperatures of the gas flow and the catalyst, respectively, K; t—time, s;

REFERENCES 1. Matros, Yu.Sh., Kataliticheskie protsessy v nestatsionarnykh usloviyakh (Catalytic Processes under UnsteadyState Conditions), Novosibirsk: Nauka, 1987. 2. Silveston, P.L., Composition Modulation of Catalytic Reactors, Amsterdam: Gordon and Breach Science, 1998. 3. Creaser, D., Andersson, B., Hudgins, R.R., and Silveston, P.L., Transient Study of Oxidative Dehydrogenation of Propane, App. Catal. A: General, 1999, no. 187, pp. 147–160. 4. Ven’yaminov, S.A., Mekhanizmy geterogenno-kataliticheskikh reaktsii okisleniya. Sbornik statei (Mechanisms of Heterogeneous Catalytic Oxidation Reactions: Collection of Papers), Novosibirsk: Inst. Katal., Sib. Otd., Ross. Akad. Nauk, 1993, p. 73. 5. Jackson, S.D., King, F., Shipley, G., and Stitt, E.H., Exothermic Process, US Patent 6291686, 2001. 6. Noskov, A.S., Kiselev, O.V., Drobyshevich, V.I., Yausheva, L.V., and Matros, Yu.N., Analysis of Mathematical Model of Unsteady-State Processes in an Adiabatic Reactor, in Nestatsionarnye protsessy v khimicheskikh reaktorakh. Sbornik statei (Unsteady-State Processes in Chemical Reactors: Collection of Papers), Novosibirsk: Nauka, 1982, p. 56. 7. Aerov, M.E., Todes, O.M., and Narinskii, M.A., Apparaty so statsionarnym zernistym sloem. Gidravlicheskie i teplovye osnovy raboty (Fixed Granular Bed Apparatuses: Hydraulic and Thermal Principles of Operation), Moscow: Khimiya, 1979.

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SELECTIVE EXOTHERMIC CATALYTIC REACTIONS IN A REVERSE HEAT FRONT 8. Kiselev, O.V., Teoreticheskoe issledovanie yavleniya rasprostraneniya teplovykh voln v sloe katalizatora (Theoretical Study of Propagation of Heat Waves in Catalyst Bed), Novosibirsk: Inst. Katal., Sib. Otd., Ross. Akad. Nauk, 1993. 9. Zagoruiko, A.N., Kostenko, O.V., Tsyrul’nikov, P.G., Tomilov, V.N., and Sal’nikov, V.S., Adsorption-Catalytic Removal of Organic Compounds from Waste Gas: Kinetic Study and Process Modeling, Khim. Prom–st., 1997, no. 4, p. 278. 10. Balaev, A.V., Drobyshevich, V.I., Gubaidullin, I.M., and Masagutov, R.M., Study of Wave Processes in Fixed Catalyst Bed Regenerators, in Rasprostranenie teplo-

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vykh voln v geterogennykh sredakh. Sbornik statei (Heat Wave Propagation in Heterogeneous Media: Collection of Particles), Novosibirsk: Nauka, 1988, p. 233. 11. Zagoruiko, A.N. and Tomilov, V.N., Method for Performing Selective Exothermic Catalytic Reactions, RF Patent No. 2002134060, 2002. 12. Kalinkina, L.I., Kisarov, V.M., Igolkina, S.M., Toropkina, G.N., Kvashnina, E.M., Gurevich, I.G., and Faleev, G.A., Catalytic-Adsorption Method Eliminating Styrene from Exhaust Gases, in Unsteady-State Processes in Catalysis: Proceedings of the International Conference, Novosibirsk, Matros, Yu.Sh., Ed., Utrecht: VSP, 1990, p. 525.

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