Correction. Flash Calculations for the Continuous or Semicontinuous Mixtures Using and Equation of State

Abstract

Sir: Kvaalen's remarks contain two misconceptions regarding my paper. The first is that the paragraph in question refers to the Deming method. While that method is mentioned, the subject of the paragraph is methods that are similar but not identical with Deming's.The second and more important is the interpretation of the phrase "linear Constraints". I agree that my paper is ambiguous on this point. As Kvaalen shows, the various methods can give different parameter estimates for constrainta that would normally be considered linear. However, as stated in my paper and covered in detail by the authors to whom I referred (e.g., Reilly and Patino-Leal, 1981), the maximum likelihood method treats both the measured variables, z, and the parameters, 8, as estimates to be adjusted in the optimization procedure. Therefore, in this case the constraints must be linear with respect to both z and 8, i.e.where A, B, and c are constant matrices. Kvaalen's example does not satisfy this requirement.His example does, however, illustrate the main point of my paper, which was that one should regard the output of any parameter estimation method with healthy skep-f(z,e) = o = AZ + Be + c ticism. It is true that computing time should not be overly emphasized, but the fact that the maximum likelihood fit gives a lower sum of squares does not mean that the maximum likelihood fit is "correct" or that the Deming method "does not work". It is clear from his figure that the (hypothetical) data and/or the model are suspect, as are the assumptions implicit in the maximum likelihood approach. I would not put much faith in the parameter estimates produced by either method in this case. If, on the other hand, the (hypothetical) experimentalist had spent less time on the computer but had obtained more precise data covering a wider range of conditions (and had derived the true theoretical relationship between x and y ) the difference in the parameter estimates would have been insignificant. Literature CitedRellly, P. M.; Patlndeal, H. Technometrlca 1981, 23(3), 221.

Thermodynamics of semicontinuous n-alcohol/ultra-low sulfur diesel blends

“…The vapor-liquid equilibrium and molar balance equations were developed in terms of the carbon number, following Cotterman and Prausnitz [10] and Lage [24]. Basically, several constant-pressure flash separators were connected inseries such that the liquid phase of one flash was the feed to the following flash which operates at a different temperature (Fig.…”

“…The continuous and semi-continuous thermodynamics, which are built on a distribution function relating the composition of a blend with a specific property, have been successfully used to model complex fuels such as ULSD [10][11][12][13][14], allowing, for instance, to model the distillation curves of some fuels. This approach can be coupled with a group-contribution method to evaluate the phase equilibrium of mixtures with a large number of different chemical species.…”

Application of Gaussian quadrature method to characterize heavy ends of hydrocarbon fluids for modeling wax precipitation

“…Another advantage is the definition of C 7 þ heavier into a series of pseudocomponents based on statistical reasoning and the model parameters used to describe molar distribution [17]. A continuous description can also be used directly in EOS [18][19][20][21][22].…”

“…For our purpose, we sought mathematical simplicity. A useful distribution function for that purpose is the gamma distribution, the one suggested by Cotterman [19][20][21].…”

A Novel Kinetic Model for Complex Reaction Systems in Molecular Level: Part 1. Monte Carlo Simulation of Feedstock

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