Model thermodynamic data errors

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

All of the information obtained in this research area depends upon indirect evidence through the use of nonisotopic carriers or normalized data in the form of ratios. These are subject to error but the trends and insights that have been obtained are very useful to the description of the behavior of plutonium in the environment. Better thermodynamic data in the range of environmental concentrations would be helpful in further quantification of chemical species, as would phenomenalogical descriptions of the behavior of plutonium in reasonably good models of the environment. 

For these reasons, the thermodynamic data on which a model is based vary considerably in quality. At the minimum, data error limits the resolution of a geochemical model. The energetic differences among groups of silicates, such as the clay minerals, is commonly smaller than the error implicit in estimating mineral stability. A clay mineralogist, therefore, might find less useful information in the results of a model than expected. 

Most importantly, has the modeler conceptualized the reaction process correctly The modeler defines a reaction process on the basis of a concept of how the process occurs in nature. Many times the apparent failure of a calculation indicates a flawed concept of how the reaction occurs rather than error in a chemical analysis or the thermodynamic data. The failed calculation, in this case, is more useful than a successful one because it points out a basic error in the modeler s understanding. 

Using our experimental activity data for Na20 in glass, we have modeled the effect of a typical combustion gas mixture on alkali vaporization ( ). For this purpose we have acquired, and adapted to our computers, a code known as SOLGASMIX (7 ) which is unique in its ability to deal with non-ideal solution multicomponent heterogeneous equilibria. Previous attempts to model this type of problem have been limited to ideal solution assumptions ( ). As is demonstrated in Table III, if solution non-ideality is neglected, drastic errors result in the prediction of alkali vapor transport processes. Table III and Figure 21 summarize the predicted alkali species partial pressures. The thermodynamic data base was constructed mainly from the JANAF (36) compilation. Additional details of this study will be presented elsewhere. 

It appears that the largest source of error in these comparisons is the analytical data. The next largest source of error seems to be the adequacy of activity coefficients and stability constants used in the model and last is the reliability of the field Eh measurement. Close inspection of Figure 3 shows a slight bias of calculated Eh values towards more oxidizing potentials. Fe(III) complexes are quite strong and it is likely that some important complexes, possibly FeHSO " (5 4,5 5), should be included in the chemical model, but the thermodynamic data are not reliable enough to justify its use. 

Standard Deviations. In order to evaluate the effect on the modeling calculations of errors in the analytical input data, propagated standard deviations are now computed for a subset of the solid phase activity products considered in the model. Arrangements have also been made to enter and output standard deviations for thermodynamic data. 

A clear understanding of the limits of applicability of geochemical models and of the uncertainties and potential errors in the analytical and thermodynamic data is essential to the correct use of SOLMINEQ.88 and the interpretation of the results. These limits can be primarily divided into four different groups, which are errors and uncertainties in the physical parameters the chemical analysis and in the thermodynamic data and extrapolation of the equations and formulas beyond their range of applicability. 

The thermodynamic parameters for the formation of several metal-cyanide complexes, among others those of Ni(CN)4 , have been determined using pH-metric and calorimetric methods at 10, 25 and 40°C. In case of nickel(II), the thermodynamic data were determined by titration of Ni(C104)2 solutions with NaCN solutions. The ionic strength of the solutions were 1 < 0.02 M in all cases. The Debye-Huckel equation, related to the SIT model, was used to correct the formation constants to thermodynamic constants valid at 7 = 0. Since previous experiments indicated that the dependence of A,77° in the ionic strength in dilute aqueous solutions is small compared to the experimental error, the measured heats of reaction (A,77 = - 189.1 kJ mol at 10°C A,77 ,= -183.7 kJ mol at 40 C) were taken to be valid at 7 = 0, but the uncertainties were estimated in this review as 2.0 kJ moT. From the values of A,77 , as a function of temperature, average A,C° values were calculated. 

The estimation of f from Stokes law when the bead is similar in size to a solvent molecule represents a dubious application of a classical equation derived for a continuous medium to a molecular phenomenon. The value used for f above could be considerably in error. Hence the real test of whether or not it is justifiable to neglect the second term in Eq. (19) is to be sought in experiment. It should be remarked also that the Kirkwood-Riseman theory, including their theory of viscosity to be discussed below, has been developed on the assumption that the hydrodynamics of the molecule, like its thermodynamic interactions, are equivalent to those of a cloud distribution of independent beads. A better approximation to the actual molecule would consist of a cylinder of roughly uniform cross section bent irregularly into a random, tortuous configuration. The accuracy with which the cloud model represents the behavior of the real polymer chain can be decided at present only from analysis of experimental data. 

Even if we make the stringent assumption that errors in the measurement of each variable ( >,. , M.2,...,N, j=l,2,...,R) are independently and identically distributed (i.i.d.) normally with zero mean and constant variance, it is rather difficult to establish the exact distribution of the error term e, in Equation 2.35. This is particularly true when the expression is highly nonlinear. For example, this situation arises in the estimation of parameters for nonlinear thermodynamic models and in the treatment of potentiometric titration data (Sutton and MacGregor. 1977 Sachs. 1976 Englezos et al., 1990a, 1990b). 

The first step in building a solubility model in Aspen Properties is to define the solute as a new component in two instances, one for the solid phase and the other for the liquid phase. Acetylsalicylic acid is used as a convenient basis for new drug molecules in the Aspen template, because it includes data for all of the necessary thermodynamic methods to satisfy the simulation engine and avoid run time errors. 

Results in Table I illustrate some of the strengths and weaknesses of the ST2, MCY and CF models. All models, except the MCY model, accurately predict the internal energy, -U. Constant volume heat capacity, Cv, is accurately predicted by each model for which data is available. The ST2 and MCY models overpredict the dipole moment, u, while the CF model prediction is identical with the value for bulk water. The ratio PV/NkT at a liquid density of unity is tremendously in error for the MCY model, while both the ST2 and CF models predictions are reasonable. This large error using the MCY model suggests that it will not, in general, simulate thermodynamic properties of water accurately (29). Values of the self-diffusion coefficient, D, for each of the water models except the CF model agree fairly well with the value for bulk water. 

The esterification of TPA with EG is a reaction between two bifunctional molecules which leads to a number of reactions occurring simultaneously. To simplify the evaluation of experimental data, model compounds have been used for kinetic and thermodynamic investigations [18-21], Reimschuessel and coworkers studied esterification by using EG with benzoic acid and TPA with 2-(2-methoxyethoxy) ethanol as model systems [19-21], The data for the temperature dependency of the equilibrium constants, AT, = K,(T), given in the original publications are affected by printing errors. The corrected equations are summarized in Table 2.3. 

It must always be remembered that optimisation is not an exact science and, therefore, it is sometimes difficult to define confidence limits in the final optimised values for the coefficients used in the thermodynamic models. The final outcome is at least dependent on the number of experimental measurements, their accuracy and the ability to differentiate between random and systematic errors. Concepts of quality can, therefore, be difficult to define. It is the author s experience that it is quite possible to have at least two versions of an optimised diagram with quite different underlying thermodynamic properties. This may be because only experimental enthalpy data were available and different entropy fiinctions were chosen for the different phases. Also one of the versions may have rejected certain experimental measurements which the other version accepted. This emphasises the fact that judgement plays a vital role in the optimisation process and the use of optimising codes as black boxes is dangerous. 

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