Application of Multi-Step Rate Models in the Stability Analysis of Fixed-Bed Catalytic Reactors — Part I. Development of the Models
TL;DR: In this article, a procedure is developed in which statistical, thermodynamic and kinetic criteria are used to eliminate the unlikely steps gradually, assuming the possibility of all steps to be significant to start with.
About: This article is published in Chemical Engineering Journal.The article was published on 1982-01-01. It has received 2 citations till now.
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TL;DR: In this paper, the dynamics and stability of three gas-phase reactions in fixed-bed reactors are analyzed employing multi-step rate models and single-step Langmuir-Hinshelwood rate equations.
1 citations
Journal Article•
TL;DR: In this paper, the rate data were well represented by a steady state two-stage redox model given by the equation: -r = ((k/sub 1/k/s/sub 2/p/sub E/P/sub O/sub 0.5/S 0.2/S 5/S ) + Nk 1/p 1/s 1/n/sub √ E/p E/E 2/E 0.1/S 2/P 1/E E/sub (nk/Sub 1/S 1/
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28,888 citations
TL;DR: In this article, a detailed study is made of the effect of routine application of rejection criteria to replicate determinations of a single value, especially for triplicate and quadruplicate determinations.
Abstract: If one reading is a long way from the rest in a series of replicate determinations, or if in a least-squares analysis one reading is found to have a much greater residual than the others, there is temptation to reject it as spurious. Numerous criteria for the rejection of outliers have been proposed and discussed during the past 100 years. They seem always to have been regarded as something like significance tests, and attention has been focussed on rejection rates. It is suggested that rejection rules are not significance tests but insurance policies, and attention would be better focussed on error variance. A detailed study is made of the effect of routine application of rejection criteria to replicate determinations of a single value. Determinations in triplicate and quadruplicate are especially considered. Complex patterns of observations are also considered, especially factorial arrangements with high symmetry, and there is a study of the correlations between residuals. Attention is focussed mainly o...
439 citations
193 citations
TL;DR: In this paper, a method for using power transformation weights in least squares analysis to account for inhomogeneity of variance is presented, where the need for this form of weighting is common when, as is illustrated with an example, a linearized kinetic rate expression is analyzed.
Abstract: A method is presented for using power transformation weights in least squares analysis to account for inhomogeneity of variance. The need for this form of weighting is common. In particular, it frequently arises when, as is illustrated with an example, a linearized kinetic rate expression is analyzed.
179 citations
TL;DR: In this article, the differential equations governing the propagation in time of the sensitivity matrix for a mathematical model given by a system of ordinary differential equations are derived and used to perform a statistical sensitivity analysis of models for chemical reactors.
Abstract: The differential equations governing the propagation in time of the sensitivity matrix for a mathematical model given by a system of ordinary differential equations are derived. These equations are used to perform a statistical sensitivity analysis of models for chemical reactors. The behavior of the sensitivities at equilibrium is analyzed. It is shown that the sensitivity equations for linear kinetics may be solved using an analytic representation. The numerical solution of these equations is discussed, and illustrative examples are presented. The lognormal distribution is presented as being representative of errors in rate constants.
115 citations