Pseudo-component approach

Even if the pseudo-component approach does not fit the whole CPC it is possible to use this model to adjust the branch poor in CO, i.e. that of practical interest, leading to a dispersed phase rich in CO and generating a shadow curve (dotted line in Fig. 14). The interaction parameter resulting from the fitting was [78]... 

In 1974, Stangeland developed a pseudo-component approach to the modelling of conversion kinetics in hydrocrackers. Conceptually, he divided the feed and products into a set of 50°F-wide slices - 100°F to 150°F, 150°F to 200°F, etc. He then built a set of rate expressions for converting higher-boiling slices into lower-boiling slices and linked them with an expression that reflects the fact that heavy hydrocarbons react faster than light ones ... 

Coal-derived liquids, heavy petroleum fractions, vegetable oils and polymers are mixtures that have very large numbers of components. It is practically impossible to identify each component by ordinary chemical analysis. One can no longer use mole fractions of individual components. Traditionally, the pseudo-component approach, or the key component approach, has been used to handle such complex mixtures. 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

Feed analyses in terms of component concentrations are usually not available for complex hydrocarbon mixtures with a final normal boihng point above about 38°C (100°F) (/i-pentane). One method of haudhug such a feed is to break it down into pseudo components (narrow-boihng fractions) and then estimate the mole fraction and value for each such component. Edmister [2nd. Eng. Chem., 47,1685 (1955)] and Maxwell (Data Book on Hydrocarbons, Van Nostrand, Princeton, N.J., 1958) give charts that are useful for this estimation. Once values are available, the calculation proceeds as described above for multicomponent mixtures. Another approach to complex mixtures is to obtain an American Society for Testing and Materials (ASTM) or true-boihng point (TBP) cui ve for the mixture and then use empirical correlations to con-strucl the atmospheric-pressure eqiiihbrium-flash cui ve (EF 0, which can then be corrected to the desired operating pressure. A discussion of this method and the necessary charts are presented in a later subsection entitled Tetroleum and Complex-Mixture Distillation. ... 

To estimate the isomerization rate coefficients, eqn 5.8 is applied to the time required for close approach to the straight-line behavior of the first-order curves. Judging this time to be about 25 minutes for a 90% approach to the steady-state isomer distribution, eqn 5.8 yields k 0.1 min-1. With this value and an isomerization equilibrium constant Kn = 20 at 150°C calculated from thermochemical data [5,6] (with 2-cis and 2-trans pentene lumped into a single pseudo-component), eqns 5.40 give as rough estimates... 

Figure 5 Illustration of pseudo-component characterization of petroleum crude into narrow boiling range compounds . A similar approach is used for estimating specific gravities of pseudo-components ...

To be able to quantitatively describe and predict the aforementioned phenomena and to be able to relate catalyst properties to unit operation performance, a more detailed description of the species involved as well as a better representation of the fundamental processes that are occurring between the bulk fluid and the catalyst surface than that which is currently employed in pseudo-component, lumped parameter, power law models is required. This more fundamental approach to kinetic modelling has been achieved in many other systems where there are only a few components and reactions by using Langmuir-Hinshelwood and/or Eley-Rideal type rate expressions such expressions are usually developed by considering the... 

The approach to constructing adiabatic ARs with temperature is slightly more complicated than isothermal constructions. The energy balance generally does not allow for temperature to obey a linear mixing law, and as a result temperature cannot generally be treated as a pseudo component in the state vector C (which is possible with residence time t). If temperature is to be incorporated, T must usually be introduced into the analysis via an energy balance and treated as an extra parameter in a rate expression, in the form r(C, T). 

Daniel, R.C. and Berg, J.C., Dynamic surface tension of polydisperse surfactant solutions a pseudo-single-component approach, Langmuir, 18, 5074, 2002. 

A new approach for desulfurization kinetics is proposed which is based on a discretization of the GC-AED spectrum. For LGO it was discretisized into 132 pseudo components... 

Heidemann et al also presented a discontinuous method to calculate spinodal curves and critical points using two different versions of the Sanchez-Lacombe equation of state and PC-SAFT. Moreover, Krenz and Heidemann applied the modified Sanchez-Lacombe equation of state to calculate the phase behaviour of polydisperse polymer blends in hydrocarbons. In this analysis the polymer samples were represented by 100 pseudo-components. Taimoori and Panayiotou developed a lattice-fluid model incorporating the classical quasi-chemical approach and applied the model in the framework of continuous thermodynamics to polydisperse polymer solutions and mixtures. The polydispersity of the polymers was expressed by the Wesslau distribution. 

Direct use of (28) to (32) requires choosing a certain number of polymer components that can be used within the calculations. One could, e.g., think of dividing the polymer molecular weight distribution into (not necessarily equally spaced) intervals and choosing the polymer (pseudo)components such that each of them represents one of these intervals (Fig. 15). Depending on the shape of the molecular weight distribution, this approach requires about 5-20 polymer components for representing the phase boundary of the polydisperse system. 

It is not really possible to represent mixture behavior by a pseudo pure component approach. Possibly should separate correlation equation into repulsive and attractive potentials. The repulsive potential could be represented by the hard core potential and only the attractive potential correlated by the pseudocritical approach. 

Crude heavy oils are composed by a large variety of compounds, mostly aromatics and alkylated aromatics with a carbon number from 14 to 25. These heavy aromatic hydrocarbons are very difficult to characterize, the heavier fractions like asphaltenes being impossible to characterize in any way. Because of these complexities, it is very difficult and inaccurate to select one or several pseudo-components to represent the original heavy oil for the purpose of kinetic modelling. A combination of theoretical and experimental methods must be considered to develop a suitable kinetic scheme for heavy oil pyrolysis. The approach followed by Tan et al. 

As is the case with the dififerent solid compounds found in this volume, we will model non-stoichiometry of the hydrates using quasi-chemistry of stmcture elements. This approach, however, presents a munber of difficulties because these hydrates are relatively-complex solids, with at least three main components the anion (which itself is usually complex), the cation and water. In cases where the salt can accept several successive limited hydrates, even the water molecules are not all equivalent in terms of the sites they occupy and the energy of their bond to the lattice. In order to simplify the model, we will use a pseudo-binary approach, considering the hydrated salt to be formed of two main components - one of which is the water involved in the equilibrium in question (p molecules per salt molecule) and the other is the skeletal structure of the salt, involving the anhydrous part, and possibly the n water molecules of inferior hydrates not involved in the equilibrium. 

The actual Russian standards allow presentation of hydrocarbon components of UGC as individual compounds only for C -C hydrocai bons. The rest is described as pseudo-compound C,, although its content may reach 60 % m/m. Apparently, the detailed determination of composition of hydrocarbons C, in UGC allows essentially to raise quality of both its processing and its record. The best method for the determination of heavy hydrocai bons is capillary gas chromatography. Typical approach is based on preliminary sepai ation of UGC samples to gaseous and liquid phases. 

Step 3. Calculate the weight average critical temperature and critical pressure for the remaining heavier components to form a pseudo binary system. (A shortcut approach good for most hydrocarbon systems is to calculate the weight average T only.)... 

Equilibrium data are thus necessary to estimate compositions of both extract and raffinate when the time of extraction is sufficiently long. Phase equilibria have been studied for many ternary systems and the data can be found in the open literature. However, the position of the envelope can be strongly affected by other components of the feed. Furthermore, the envelope line and the tie lines are a function of temperature. Therefore, they should be determined experimentally. The other shapes of the equilibrium line can be found in literature. Equilibria in multi-component mixtures cannot be presented in planar graphs. To deal with such systems lumping of consolutes has been done to describe the system as pseudo-ternary. This can, however, lead to considerable errors in the estimation of the composition of the phases. A more rigorous thermodynamic approach is needed to regress the experimental data on equilibria in these systems. 

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