Optimal Catalyst Activity Distribution Research Articles

Optimal feed distribution in isothermal fixed-bed reactors for parallel reactions

The optimal design of isothermal fixed-bed catalytic reactors for maximum outlet yield is studied by considering optimal feed distribution (OFD) along the reactor axis for parallel reactions. The activity distribution in pellets is assumed to have the Dirac delta type and the active location is the same for all pellets. The OFD function is derived analytically, indicating a uniform distribution along the reactor portion starting at the zero of the axial coordinate. The size of the feed distribution portion and the active location in pellets need to be found numerically, but in some particular cases, they can be found also analytically. A comparison of the OFD to the optimal catalyst activity distribution (OCAD), along the reactor axis shows that the OFD can give the same outlet yield as the OCAD does, while the former needs only one type of the Dirac delta catalyst activity distribution for all pellets in the reactor.

Application of optimal catalyst activity distribution theory

The application of the optimal catalyst activity distribution (OCAD) theory to maximize the outlet yield or selectivity of a fixed-bed catalytic reactor is discussed for isothermal parallel reacting systems. It is interesting to find that, unlike the case for the maximum outlet conversion, the local optimization of each pellet does not necessarily give rise to the maximum outlet yield or selectivity. Instead, if the OCAD in pellets is considered globally as a parameter to be optimized with respect to the reactor outlet performance, a higher outlet yield or selectivity can be obtained in some specific situations

Optimal catalyst activity distribution for effectiveness factor, productivity and selectivity maximization in generalized nonisothermal reacting systems with arbitrary kinetics

Abstract Optimal catalyst activity distribution for effectiveness factor, productivity and selectivity maximization in nonisothermal pellets has been determined for generalized reacting systems with arbitrary kinetics. It has been shown that optimal catalyst distribution is a Diracδ(x) function in all cases.

Optimal catalyst activity profiles in pellets: 9. Study of ethylene epoxidation

AbstractThe concept of optimal catalyst activity distribution is studied experimentally for the ethylene epoxidation reaction network on a Ag/α–Al2O3 catalyst in a single‐pellet reactor. The Dirac delta‐type distribution of the catalyst is approximated by a step distribution of narrow width. For a fixed amount of silver, the influence of location and width of the catalytically active layer on the conversion of ethylene and on the selectivity and yield to ethylene oxide is investigated under oxygen‐rich conditions in the temperature range 210–270°C. The results clearly demonstrate that for optimum selectivity and yield to ethylene oxide, the silver catalyst should be placed in a thin layer at the external surface of the pellet.

Optimal catalyst activity distribution in pellets for selectivity maximization in triangular nonisothermal reaction systems: Application to cases of light olefin epoxidation

The solution to the general problem of determining the optimal catalyst activity distribution for maximization of global selectivity in flat, cylindrical, or spherical catalyst pellets for parallel, consecutive, or triangular reaction networks in presented. The analysis considers both isothermal and nonisothermal pellets with no external gradients and is applicable to any type of kinetics with arbitrary numbers of chemical species participating in each reaction step. It is shown that the optimal catalyst distribution is an appropriately chosen Dirac δ function. Physically, this implies that the active catalyst must be deposited in a thin zone at a specific distance from the center of the pellet. Analytical expressions are derived for the optimal catalyst location in terms of the pertinent physicochemical and operating parameters. The analysis is applied to C 2H 4 and C 3H 6 epoxidation on Ag. It is shown that pellets with optimal catalyst distribution result in global selectivities that are substantially higher than those obtained with uniformly activated pellets.

Optimal catalyst acitivity profiles in pellets—VIII. General nonisothermal reacting systems with arbitrary kinetics

The theory of optimal catalyst activity profiles is extended to include the most general case, viz. the case of arbitrary number of reactions with arbitrary kinetics occurring in a nonisothermal catalyst pellet with finite external heat and mass transfer resistances. The catalyst performance index can be any one among effectiveness, selectivity or yield. Similar to previous results obtained for simpler situations, it is shown analytically that, in all cases, the optimal catalyst activity distribution is a Dirac delta function, i.e., for optimum performance, all the active catalyst should be deposited at a specific position within the pellet. This position depends, in general, not only on the physicochemical parameters involved but also on the choice of the catalyst performance index selected for optimization. The proof follows an approach which is different from what has been utilized previously, and is illustrated first for a simpler case, before proceeding to the general case.

Optimal catalyst activity distribution in fixed-bed reactor with catalyst deactivation

In this paper the influence of the active catalyst location in a pellet on fixed-bed catalytic reactor performance is described. The optimal activity distribution as a function of an economic parameter (ratio of product and catalyst costs), Thiele modulus and Damkohler number is estimated.

Optimal catalyst activity distribution and generalized effectiveness factors in pellets: single reactions with arbitrary kinetics

Optimal catalyst activity distribution and generalized effectiveness factors in pellets: single reactions with arbitrary kinetics

Optimal catalyst distribution for selectivity maximization in nonisothermal pellets: The case of parallel reactions

The problem of determining the optimal catalyst activity distribution for selectivity maximization in nonisothermal flat, cylindrical or spherical pellets is solved for the case of parallel reactions with arbitrary kinetics. It is shown that the optimal catalyst distribution is an appropriately chosen Dirac δ-function. Simple analytical expressions are derived for the optimal catalyst location in terms of the pertinent physicochemical parameters. Global pellet selectivities obtained with optimal catalyst profiles are shown to be substantially higher than those obtained with uniformly activated pellets.

Optimal catalyst activity profiles in pellets—VII. The case of arbitrary reaction kinetics with finite external heat and mass transport resistances

The theory of optimal catalyst activity profiles is extended to include the most general case of a nonisothermal catalyst pellet, where an irreversible reaction occurs in the presence of finite external heat and mass transport resistances. Similar to our previous results for related cases, it is again found that the optimal catalyst activity distribution is given by a Dirac delta function; i.e. for optimum performance, all the active catalyst should be deposited at a specific position within the pellet. In some instances, this position is the external surface of the pellet. Some general results are first obtained about the optimal location of the catalyst for an arbitrary rate expression, and are then applied to two specific rate expressions of practical interest—the m-th order kinetics ( m ⩾ 0) and the bimolecular Langmuir—Hinshelwood kinetics. The effects of physico-chemical parameters on the optimal location are analysed in detail. The possibility of enhancing catalytic effectiveness, by choosing the operating variables appropriately, is also discussed.

Optimal catalyst activity distribution and generalized effectiveness factors in pellets: Single reactions with arbitrary kinetics

The problem of optimal catalyst activity distribution in pellets is analysed for single reactions with arbitrary kinetics. It is shown that the effectiveness factor for given catalyst mass is maximized (or the catalyst mass required to obtain a given global reaction rate is minimized) by concentrating all the active catalyst in a specific location in the pellet. The optimum location of the catalyst is expressed in terms of a single dimensionless group. General analytical effectiveness factor expressions are also obtained for arbitrary fixed location of the active component in the pellet in terms of a generalized shape-normalizing Thiele modulus Φ B. These expressions show that η = 1 Φ B 2 for large values of Φ B.

Optimal catalyst distribution for selectivity maximization in pellets: Parallel and consecutive reactions

The general problem of optimal catalyst activity distribution for selectivity maximization in isothermal pellets is analysed and solved analytically for parallel and consecutive reactions. In the case of parallel reactions with arbitrary kinetics, it is shown that selectivity is maximized by concentrating the active catalyst in a specific zone in the flat, cylindrical or spherical pellet. A similar conclusion is reached for the same pellet geometries in the two-dimensional optimization problem of consecutive reactions with arbitrary kinetics of the main reaction and positive-order kinetics of the undesirable reaction. In all cases, the optimum location of the catalyst zone z opt is expressed analytically in terms of a single dimensionless number Ω or Ω* which contains all the pertinent physicochemical parameters. It is shown that the optimal catalyst distribution can give global pellet selectivities dramatically higher than those obtained with uniform or external shell distributions.

Optimal catalyst activity profiles in pellets. 1. The case of negligible external mass transfer resistance

The optimal catalyst activity distribution in an isothermal pellet, in which a bimolecular Langmuir-Hinshelwood reaction occurs under steady state conditions, is determined for the case of negligible external mass transfer resistance. It is shown that the effectiveness factor is maximized by concentrating all the active catalyst in a precise location in the pellet. Analytic expressions for this location, as a function of all the involved physicochemical parameters, are given for three pellet geometries: slab, cylinder, and sphere. Numerical computations are reported to analyze the case where the active catalyst is deposited in a step manner, centered around the optimal location. The effect of the step-width on catalyst effectivenes is investigated in this case. Finally, the sensitivity of the catalyst performance to the step location is studied in order to provide guidelines for practical applications of the results obtained.