The Estimation Of Physical Properties

In this book, the various estimation methods are correlations of experimental data. The best are based on theory, with empirical corrections for the theory's defects. Others, including those stemming from the law of corresponding states, are based on generalizations that are partly empirical but nevertheless have application to a remarkably wide range of properties. Totally empirical correlations are useful only when applied to situations very similar to those used to establish the correlations.

The text includes many numerical examples to illustrate the estimation methods, especially those that are recommended. Almost all of them are designed to explain the calculation procedure for a single property. However, most engineering design problems require estimation of several properties; the error in each contributes to the overall result, but some individual errors are more important that others. Fortunately, the result is often adequate for engineering purposes, in spite of the large measure of empiricism incorporated in so many of the estimation procedures and in spite of the potential for inconsistencies when different models are used for different properties.

As an example, consider the case of a chemist who has synthesized a new compound (chemical formula CCl2F2) that boils at -20.5°C at atmospheric pressure. Using only this information, is it possible to obtain a useful prediction of whether or not the substance has the thermodynamic properties that might make it a practical refrigerant?

Figure 1-2 shows portions of a Mollier diagram developed by prediction methods described in later chapters. The dashed curves and points are obtained from estimates of liquid and vapor heat capacities, critical properties, vapor pressure, en-

Mollier Diagram Methane

Enthalpy, J/g

FIGURE 1-2 Mollier diagram for dichlorodifluoro-methane. The solid lines represent measured data. Dashed lines and points represent results obtained by estimation methods when only the chemical formula and the normal boiling temperature are known.

Enthalpy, J/g

FIGURE 1-2 Mollier diagram for dichlorodifluoro-methane. The solid lines represent measured data. Dashed lines and points represent results obtained by estimation methods when only the chemical formula and the normal boiling temperature are known.

1.8 CHAPTER ONE

thalpy of vaporization, and pressure corrections to ideal-gas enthalpies and entropies. The substance is, of course, a well-known refrigerant, and its known properties are shown by the solid curves. While environmental concerns no longer permit use of CCl2F2, it nevertheless serves as a good example of building a full description from very little information.

For a standard refrigeration cycle operating between 48.9 and -6.7°C, the evaporator and condenser pressures are estimated to be 2.4 and 12.4 bar, vs. the known values 2.4 and 11.9 bar. The estimate of the heat absorption in the evaporator checks closely, and the estimated volumetric vapor rate to the compressor also shows good agreement: 2.39 versus 2.45 m3/hr per kW of refrigeration. (This number indicates the size of the compressor.) Constant-entropy lines are not shown in Fig. 1-2, but it is found that the constant-entropy line through the point for the low-pressure vapor essentially coincides with the saturated vapor curve. The estimated coefficient of performance (ratio of refrigeration rate to isentropic compression power) is estimated to be 3.8; the value obtained from the data is 3.5. This is not a very good check, but it is nevertheless remarkable because the only data used for the estimate were the normal boiling point and the chemical formula.

Most estimation methods require parameters that are characteristic of single pure components or of constituents of a mixture of interest. The more important of these are considered in Chap. 2.

The thermodynamic properties of ideal gases, such as enthalpies and Gibbs energies of formation and heat capacities, are covered in Chap. 3. Chapter 4 describes the PVT properties of pure fluids with the corresponding-states principle, equations of state, and methods restricted to liquids. Chapter 5 extends the methods of Chap. 4 to mixtures with the introduction of mixing and combining rules as well as the special effects of interactions between different components. Chapter 6 covers other thermodynamic properties such as enthalpy, entropy, free energies and heat capacities of real fluids from equations of state and correlations for liquids. It also introduces partial properties and discusses the estimation of true vapor-liquid critical points.

Chapter 7 discusses vapor pressures and enthalpies of vaporization of pure substances. Chapter 8 presents techniques for estimation and correlation of phase equilibria in mixtures. Chapters 9 to 11 describe estimation methods for viscosity, thermal conductivity, and diffusion coefficients. Surface tension is considered briefly in Chap. 12.

The literature searched was voluminous, and the lists of references following each chapter represent but a fraction of the material examined. Of the many estimation methods available, in most cases only a few were selected for detailed discussion. These were selected on the basis of their generality, accuracy, and availability of required input data. Tests of all methods were often more extensive than those suggested by the abbreviated tables comparing experimental with estimated values. However, no comparison is adequate to indicate expected errors for new compounds. The average errors given in the comparison tables represent but a crude overall evaluation; the inapplicability of a method for a few compounds may so increase the average error as to distort judgment of the method's merit, although efforts have been made to minimize such distortion.

Many estimation methods are of such complexity that a computer is required. This is less of a handicap than it once was, since computers and efficient computer programs have become widely available. Electronic desk computers, which have become so popular in recent years, have made the more complex correlations practical. However, accuracy is not necessarily enhanced by greater complexity.

The scope of the book is inevitably limited. The properties discussed were selected arbitrarily because they are believed to be of wide interest, especially to

THE ESTIMATION OF PHYSICAL PROPERTIES 1.9

chemical engineers. Electrical properties are not included, nor are the properties of salts, metals, or alloys or chemical properties other than some thermodynamically derived properties such as enthalpy and the Gibbs energy of formation.

This book is intended to provide estimation methods for a limited number of physical properties of fluids. Hopefully, the need for such estimates, and for a book of this kind, may diminish as more experimental values become available and as the continually developing molecular theory advances beyond its present incomplete state. In the meantime, estimation methods are essential for most process-design calculations and for many other purposes in engineering and applied science.

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