On-Line Estimation of Catalyst Activity Profiles in Packed-Bed Reactors Having Catalyst Decay

Ajinkya, M. B.; Ray, W. Harmon; Froment, Gilbert F.

doi:10.1021/i260050a003

Cited by 21 publications

(3 citation statements)

References 2 publications

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“…Markedly improved estimation times and accuracy were obtained, but the basic models were linear and low order. Some nonlinear high-order processes, with direct measurement of a single state variable, have been studied (Lynch and Ramirez, 1975; Ajinkya, Ray, and Froment, 1974; Mehra and Wells, 1971). However, with many complex reactions, the state variables must be inferred from multiple on-line measurements, so that both the state and measurement equations contain appreciable modeling errors.…”

Section: Scopementioning

confidence: 99%

Digital monitorina and estimation of polymerization reactors

Bankoff

1976

AIChE Journal

103

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Section: Scopementioning

confidence: 99%

Digital monitorina and estimation of polymerization reactors

Bankoff

1976

AIChE Journal

103

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“…TWO papers (Ajinkya et al, 1974;Ramirez, and Clough, 1976) have appeared in which the full distributed nature of the problem is treated. In the first paper, only the catalyst activity profile was estimated, while the gas phase concentrations were not estimated but measured.…”

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confidence: 99%

Nonlinear state estimation of packed‐bed tubular reactors

Soliman

Ray

1979

AIChE Journal

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Packed-bed tubular reactors are characterized by nonlinear behavior, limited on-line measurements, and stiff dynamics. Because of the limited number of temperature and composition sensors normally available, state estimation algorithms would be a desirable part of the reactor control system. However, to complicate matters, the thermal transients are usually several orders of magnitude slower than the concentration transients, thus leading to very stiff distributed parameter modeling equations. In spite of a number of reported state estimation studies of this class of problems, a good understanding of the structure of the problem has not conie forth, and the previously published results have important practical limitations. In this note we shall illustrate how recently developed, general, theoretical results ( Soliman and Ray, 1978) can be profitably applied to this problem and help elucidate the structure of these state estimation problems.To illustrate the essential features of the problem, we shall choose to study a simple reactor in which a firstorder, irreversible, exothermic reaction is taking place. We shall assume a pseudohcmogeneous axial dispersion model for the reactor 2. There is the danger that essential features of the problem will be lost through brute force discretization. A theoretical analysis of the full partial differential equations is safer and is to be preferred. 3.There is a similar danger in just setting c = 0 and applying the state estimation theory to the degenerate equations, This procedure usually gives incomplete and sometimes even incorrect results (for example, Haddad and Kokotovic, 1971). In particular, the estimator resulting from setting € = 0 does not allow dynamic estimates of the fast variables ( x i here) or the proper treatment of composition measurements.TWO papers (Ajinkya et al., 1974;Ramirez, and Clough, 1976) have appeared in which the full distributed nature of the problem is treated. In the first paper, only the catalyst activity profile was estimated, while the gas phase concentrations were not estimated but measured. Thus, the problem of two time scales did not arise. In the second paper, state estimation of concentration was attempted using an incorrect algorithm, and rather poor filter performance was reported. A third recent paper describes studies of distributed parameter observers applied to the packed-led estimation problem (Zeitz, 1977) and reports reasonable estimates with sufficient temperature measurements.In contrast to earlier estimation algorithms, our recent results, reported in more generality and mathematical detail elsewhere (Soliman and Ray, 1978), allow the estimation prollem to be decomposed into two time scales with two state estimators, one for the fast variables alone and one for the slow variables. In addition, our results allow, for the first time, the proper inclusion of concentration measurements into the filtering equations for c + 0. To illustrate these results, the resulting state estimator for the packed-led reactor system ( 1) to (6) ...

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“…These derivations required measurement information to be available at every point in the spatial domain, an unrealistic stipulation. Thau [18] [2], applied such a filter to data previously gathered from a packed-bed reactor in order to estimate catalyst decay. They simulated on-line estimation by processing the data in sequential fashion on an off-line computer, and, in estimating carbon deposition, they inferred measurement points and using gas phase composition measurements.…”

Section: Derivation Of the On-line Filtermentioning

confidence: 99%

On-line estimation and identification of a nonlinear, distributed-parameter process: The dehydrogenation of ethylbenzene to form styrene in a tubular, fixed-bed, catalytic reactor

Ramirez

Clough

New Trends in Systems Analysis

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The industrial production of styrene monomer is achieved via the dehydrogenation of ethyl benzene in the presence of steam over a metal oxide catalyst at a temperature around 6OO°C. The goal of this investigation was to develop and demonstrate an online scheme for estimation of process variables and identification of the dehydrogenation reaction parameters using a distributed-parameter, Kalman filter.This technique was first tested by computer simulation and accurately estimated the process states.Reaction parameters were identified well also, although they proved to be more sensitive to process noise than the state variables. A pilot plant and digital computer system were constructed in order to investigate experimentally the on-line identification scheme. The filter proved effective in estimating process variables. As the simulation predicted, the experimental identification of dehydrogenation reaction parameters was sensitive to process noise; however, the identified parameters are shown to be of potential use in optimization of the reactor operating conditions.

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On-Line Estimation of Catalyst Activity Profiles in Packed-Bed Reactors Having Catalyst Decay

Cited by 21 publications

References 2 publications

Digital monitorina and estimation of polymerization reactors

Digital monitorina and estimation of polymerization reactors

Nonlinear state estimation of packed‐bed tubular reactors

On-line estimation and identification of a nonlinear, distributed-parameter process: The dehydrogenation of ethylbenzene to form styrene in a tubular, fixed-bed, catalytic reactor

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