Reduction of thermodynamic data by means of the multiresponse maximum likelihood principle

Abstract

) dtThe system was first partitioned, giving two small loops and one large loop. LOOP 1 consisted of Eqs. III-9,III-10,111-13,III-14 and 111-20 in which Eqs. 111-9 and 111-10 are nonlinear. LOOP 2 was made up of Eqs. 111-18,111-24,111-26,111-30 and 111-31 all of which are linear. Once these blocks were isolated they were collapsed into single nodes leaving one large cycle, LOOP 3, consisting of all of the remaining equations.The constant kz was varied to make the system stiff. Solutions were obtained for k2 = 3 (non-stiff) and for kz = 50 and k2 = lo00 which made LOOP 3 stiff. Eigenvalues were not calculated because stiffness was obtained (and proven) in this manner for Example I. Reduction of Thermodynamic Data by Means of the Multiresponse Maximum Likelihood PrincipleThe statistical behavior of some common parameter estimation methods is investigated by simulation. The methods based on the maximum likelihood principle give the best estimates of parameters in a given model. An analysis of the possibilities for detecting systematic errors by means of the maximum likelihood method showed that this method gives at best the same information as other well known tests.

Thermodynamic consistency of vapor‐liquid equilibrium data at high pressure

“…However, it should be noted that statistical methods that account for errors in the other measured variables can also be used (Kemeny et al, 1982). Given Np experimental data points of the PTxy type, one of the following different objective functions was minimized in order to evaluate the model parameters:…”

Generalized least‐squares parameter estimation from multiequation implicit models

“…Ž . Kemeny et al, 1982. Kemeny et al 1982 examined manýś imilar functions; although they did not conclude that any one of them was markedly better than the others, their work showed that inclusion of weights led to consistently superior results.…”

“…1968 , and of the VLE data-reduction method developed by Ž . Kemeny et al 1982 . The latter authors observed that thé complexity of calculations is ''considerably reduced'' by omitting the determination of the true values of the regressors.…”

“…Although most subsequent work has focused on reduction of Ž . Ž vapor᎐liquid equilibrium VLE measurements Anderson et al, 1978;Kemeny et al, 1982;Rubio et al, 1983;Skjold-. Jørgensen, 1983;Englezos et al, 1991 and on the related problem of assessing the thermodynamic consistency of such Ž .…”

Oxygenate Vapor–Liquid Equilibrium in Gasolines

“…the Reid vapor pressure) of the gasoline -oxygenate mixture is largely determined by the vapor pressure of the oxygenate. It is partly for this reason that largely C 5 result in a very slight increase in the Reid vapor pressure of a gasoline. Higher ethers such as tert-amyl methyl ether (TAME), diisopropyl ether (DIPE), and others, which are less volatile, have little effect on the Reid vapor pressure of the gasoline at the concentrations in which they are used, and may even result in a slight lowering.…”