Pseudocomponent Properties

Stream properties required for solving material and energy balance equations 

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Figure 1.2 Relationship between pseudocomponent properties and theTBP curve (redraw from [1]).

The direct optimization of a single response formulation modelled by either a normal or pseudocomponent equation is accomplished by the incorporation of the component constraints in the Complex algorithm. Multiresponse optimization to achieve a "balanced" set of property values is possible by the combination of response desirability factors and the Complex algorithm. Examples from the literature are analyzed to demonstrate the utility of these techniques. 

The coefficients of the fourth-order regression equation are calculated by Eq. (3.29) using the property of saturated design matrix. The regression equation in pseudocomponent variables has the form ... 

Apart from the need to fractionate residuum-containing fossil fuels for the measurement and prediction of thermophysical properties, other important problems could be resolved better through the study of residuum pseudocomponents. Two examples in the area of coal liquefaction are the role of... 

If a petroleum mixture is represented by pseudocomponents corresponding to its TBP curve, its properties can be estimated by the same methods that apply to mixtures of chemical species. For instance, the mixture enthalpy and phase behavior can be predicted by the methods discussed in this chapter. 

If T, the TBP temperature, can be expressed as a mathematical function of V, the integral may be evaluated analytically. More commonly, the integration is done based on some curve htting technique. Once the pseudocomponents are generated, their properties are estimated from correlations that are functions of the components boiling points and specihc gravities. 

Before proceeding, we mention sources for a few areas not covered in this chapter. Basic chemical thermodynamics is the subject of Chapter 4. For polymers and their solutions, the Polymer Handbook [1] is an indispensable source, and more on polymer thermophysical properties may be found in two books from AIChE s DIPPR project [2, 3]. The estimation of properties of mixtures described by distillation curves (typically petroleum fractions), or of the pseudocomponents derived from such curves, is covered in the AP7 Technical Data Book [4]. Many molecular data, such as dipole moments and spectroscopic constants, are tabulated in the NIST Chemistry Webbook [5]. 

Fig. 7.9. Contour curves for properties of PIB-PE-PW films, in terms of pseudocomponents, (a) Linear model for elongation, (b) Quadratic model for swelling. The desired characteristics are obtained for compositions similar to those of the 6 mixture (high elongation) and mixture 4 (low swelling).

The results can be seen by going to Components, Petro Characterization, and Results on the Data Browser. Figure 11.15 gives a partial list of the pseudocomponents. Note that each has a normal boiling point, density, molecular weight, and critical properties. 

Special requirements to the refining property make necessary a preliminary step to the design procedure the determination of the set of pseudocomponents specified by their normal bubble temperatures (at 1 atmosphere) in each product, and the determination of admissible concentration of impurity components in each product. 

Continuity of properties of components. A large number of components leads to the fact that dependence of properties of components on their normal bubble temperature is continuous. Therefore, in practice, while designing one deals not with the true components but with pseudocomponents (i.e., with groups of components boiling away in a set interval of temperatures), and the quality of the products is characterized not by their purity but by their refinery inspection properties. 

Figure 8.3 shows a decision tree to help in the choice for the thermodynamic property model. Besides the four factors mentioned earlier, this decision tree takes into account the polarity of the mixture. Another feature of the mixture considered is the existence of pseudocomponents and the possibility of some of the components being electrolyte. The most common electrolyte methods are the Pitzer model and the electrolyte NRTL. 

Stream properties required for solving material and energy balance equations and other process calculations are predicted from component properties. The properties of petroleum pseudocomponents can be estimated from their boiling points and specific gravities. The component properties include the molecular weight, critical constants, acentric factor, heat of formation, ideal gas enthalpy, latent heat, vapor pressure, and transport properties. These are predicted mainly by empirical correlations based on experimental data. Many of these correlations are documented in the American Petroleum Institute Technical Data Book (API, 1983). 

Taking into account that each pseudocomponent is characterized by two properties (its mole fraction X2pj and its molecular weight M pj), n pseudocomponents can reproduce 2n moments of a polymer distribution. This means, that, using only two pseudocomponents, one can exactly reproduce A/ , M, and M. It also means that the mole fractions of the two components have to add to unity (A/ ). Using three pseudocomponents, even two additional moments of the molecular weight distribution can be covered. 

Fig. 16 Solubility of poly(E96.2-co-AA3 g) in ethene. Polymer properties can be found in Table 5. Polymer concentration in the mixture is about 3 wt%. Symbols represent experimental data [61] compared with results form PC-SAFT calculation [43]. Dashed line shows monodisperse calculation using Mn solid line shows monodisperse calculation using M and dotted line shows calculation using two pseudocomponents given in Table 6...

Fig. 17 Solubilities of poly(ethylene-co-acrylic acid) copolymers with different acrylic acid contents in ethene. The polymer concentration is 5 wt%. The properties of the copolymers are given in Table 5. Lines show predictions using PC-SAFT and the pseudocomponents given in Table 6 [43]. Symbols represent experimental data [62] Circles poly(E95.4-co-AA4 g), squares poly(E96,3-co-AA3,7), triangles poly(E96.9-co-AA3.i), diamonds poly(E97 g-C(3-AA2,4)...

The first Eq. (30) is similar to Eq. (29). However, the mixture parachors [P and [P]g are calculated Irom different mixing rules than the linear rules used in Eq. (29). The quadratic mixing rules are also used for the common parachor parameter [P] in the second Eq. (30). The parachors of individual components are correlated with their critical properties. This is especially important in petroleum mixtures containing several pseudocomponents and heavy fractions. 

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