Perrys handbook for chemical engineering

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EMBED for wordpress. Want more? Advanced embedding details, examples, and help! Lilehy, Robert C. The maximum possible fluid velocity is the speed of sound, reached at the exit. A converging subsonic nozzle can therefore deliver a constant flow rate into a region of variable pressure. Combination of Eqs. Here, discharge pressure. This throttling process produces Ws isentropic no shaft work, and in the absence of heat transfer, Eq.

The process therefore occurs at con- where Ws is the actual shaft work. By Eqs. Throttling of a wet vapor to a sufficiently low sion in a turbine with that of an isentropic expansion for the same pressure causes the liquid to evaporate and the vapor to become intake conditions and the same discharge pressure. The isentropic superheated.

This results in a considerable temperature drop because path is the dashed vertical line from point 1 at intake pressure P1 to of the evaporation of liquid.

The irreversible path solid line starts at point 1 and ter- If a saturated liquid is throttled to a lower pressure, some of the liq- minates at point 2 on the isobar for P2. The process is adiabatic, and uid vaporizes or flashes, producing a mixture of saturated liquid and irreversibilities cause the path to be directed toward increasing saturated vapor at the lower pressure. Again, the large temperature entropy.

The greater the irreversiblity, the farther point 2 lies to the drop results from evaporation of liquid. Turbines Expanders High-velocity streams from nozzles imping- Compression Processes Compressors, pumps, fans, blowers, ing on blades attached to a rotating shaft form a turbine or expander and vacuum pumps are all devices designed to bring about pressure through which vapor or gas flows in a steady-state expansion process increases.

Their energy requirements for steady-state operation are of which converts internal energy of a high-pressure stream into shaft interest here. Compression of gases may be accomplished in rotating work.

The motive force may be provided by steam turbine or by a equipment high-volume flow or for high pressures in cylinders with high-pressure gas expander. The energy equations are the same; indeed, In any properly designed turbine, heat transfer and changes in based on the same assumptions, they are the same as for turbines or potential and kinetic eneregy are negligible.

Equation there- expanders. Thus, Eqs. In Eq. How- ever, if the fluid expands reversibly and adiabatically, i.

The compression process is shown on an HS diagram in Fig. The LNG 2 arrives by ship, stored as saturated liquid at K and 1.

The saturated-vapor LNG so produced is compressed adiabatically to 20 bar, using the work pro- duced by the heat engine to supply part of the compression work.

Estimate the work to be supplied from an external source. The equations that apply to Carnot engines can be found in any thermo- dynamics text. The equation for work gives Liquids are moved by pumps, usually by rotating equipment.

How- This is the reversible work of a Carnot engine. The assumption is that the actual ever, application of Eq. The The enthalpy and entropy of saturated vapor at K and 1. Interpolation in Table Combining this with Eq. A total-system because of chemical reactions even in a closed system.

However, no such generally valid relation is known, and the connection must be established experimentally for every specific system. Once an apportioning solution properties in the parent equation are related linearly in the recipe is adopted, the assigned property values are quite logically algebraic sense. This equation may also be written pressure, and composition. Equation , which defines a partial molar property, provides The following are mathematical identities: a general means by which partial-property values may be determined.

However, for a binary solution an alternative method is useful. For multicomponent solu- The first of these equations is merely a special case of Eq. Known as the summabil- appropriate. Thus a in equations of state as applied to mixtures are related to composition solution property apportioned according to the recipe of Eq. The partial molar second virial coefficient is by definition Equation applied to the definitions of Eqs.

The sim- limit of zero pressure, and provides a conceptual basis upon which to plest result is build the structure of solution thermodynamics. An analogous expression follows from Eq. In combi- Comparison with Eq. How- constant-composition solution there exists a parallel relationship for ever, the chemical potential exhibits certain unfortunate characteris- the partial properties of the species in solution.

All terms in this equation have units of moles; moreover, the enthalpy rather than the entropy appears on the right in which a new property fi replaces the pressure P. This equation side. Subtraction of Eq. Thus, residual properties. The ideal solution is similarly useful as a standard to which real solution behavior may be compared.

The ideal solution is there- from Eq. An equation analogous to the ideal gas expression, Eq. Because it is not a partial property, it is identified by a cir- written as cumflex rather than an overbar. Thus the fugacity of species i in an ideal gas mixture is equal yield to its partial pressure.

For the special case of species i in an ideal A more comprehensive generalized correlation results from Eqs. Division of By Eq. For an ideal solution, each excess property is zero, Ideal solution behavior is often approximated by solutions com- and for this special case the equations reduce to those shown in the prised of molecules not too different in size and of the same chemical third column of Table Thus, a mixture of isomers conforms very closely to ideal solu- Property changes of mixing and excess properties are easily calcu- tion behavior.

So do mixtures of adjacent members of a homologous lated one from the other. The most common property changes of mix- series. These properties are ference between the actual property value of a solution and the value identical to the corresponding excess properties. Moreover, they are it would have as an ideal solution at the same T, P, and composition. This definition is analo- gous to the definition of a residual property as given by Eq. Of the four fundamental property relations shown in the second col- However, excess properties have no meaning for pure species, umn of Table , only Eq.

Partial molar excess properties M i useful supplementary thermodynamic properties. An alternative form follows by introduction of the fugacity coef- ficient given by Eq. The result is listed as Eq. Applications are usually to liquids. The summability relation therefore applies, and tion for an excess property [Eq.

In view of Eq. In the simplest case of a gas properties are developed in much the same way as those for residual mixture for which the virial equation [Eq. For the special case of an ideal solution, Eq. For a binary system these equations imposed. Equation is the fundamental excess-property rela- reduce to tion. An alternative form follows by introduction of the activity coeffi- P cient as given by Eq. This result is listed as Eq. RT The following equations are in complete analogy to those for resid- ual properties.

Each equation of the upper left quadrant is a b special case of Eq. These are shown Symbols without subscripts represent mixture properties, and I is in the lower right quadrant. The equations of Table store an enor- given by Eq. However, by inspection one can Application of Eq. The simplest proce- These are the van Laar equations. McGraw-Hill, New York ]. Although providing great flexibility Symp. When all parameters are zero, and intermolecular forces.

Introduced by G. Wilson [J. However, all parameters are of data, but they are adequate for most engineering purposes. More- found from data for binary in contrast to multicomponent systems, over, they are implicitly generalizable to multicomponent systems and this makes parameter determination for the local composition without the introduction of any parameters beyond those required to models a task of manageable proportions. In these equations ri a relative molecular volume and qi a rel- qj xj ative molecular surface area are pure-species parameters.

The criteria for phase and chemical reaction equilibria are less obvious. The inequality applies to all incremental changes toward the equilib- If a closed PVT system of uniform T and P, either homogeneous or rium state, whereas the equality holds at the equilibrium state where heterogeneous, is in thermal and mechanical equilibrium with its sur- change is reversible. Particularly important is fixing T and t t state. The masses of constant T and P proceed in a direction such that the total Gibbs the phases are not phase rule variables, because they have nothing to energy of the system decreases.

Thus the equilibrium state of a closed do with the intensive state of the system. At the equilibrium state, differential variations may potentials or fugacities as functions of T, P, and the phase composi- occur in the system at constant T and P without producing a change in tions, the phase rule variables: Gt.

This is the meaning of the equilibrium criterion 1. Equation for each independent chemical reaction, giv- This equation may be applied to a closed, nonreactive, two-phase ing r equations system. The 1. Write formation reactions from the elements for each chemical change in the Gibbs energy of the two-phase system is the sum of compound present in the system.

When each total-system property is expressed by an 2. This usu- If the two-phase system is at equilibrium, then application of Eq. More than one such set is often possible, but all sets num- i i ber r and are equivalent. T and y1, or P and x1, or x1 and y1, etc. Thus for equilibrium at a This is the criterion of two-phase equilibrium.

It is readily generalized particular T and P, this state if possible at all exists only at one liquid and one to multiple phases by successive application to pairs of phases. The vapor composition. Once the 2 degrees of freedom are used up, no further spec- general result is ification is possible that would restrict the phase rule variables.

Three possible pairs of equations may result, depending on how the combination of equations is effected. Any pair of the following prevail, the criteria of Eqs. This number of independent variables is given by the phase mole fractions in an equilibrium mixture of these five chemical species, pro- rule, and it is called the number of degrees of freedom of the system. It vided nothing else is arbitrarily set. Thus it cannot simultaneously be required is the number of variables that may be arbitrarily specified and that that the system be prepared from specified amounts of particular constituent must be so specified in order to fix the intensive state of a system at species.

For this The meaning of completely determined is that both the intensive and isothermal change of state from saturated liquid at Pisat to liquid at extensive states of the system are fixed; not only are T, P, and the pressure P, Eq. Thus there are 2N indepen- obtained when evaluation of the integral is based on the assumption dent variables, and application of the phase rule shows that exactly N that Vi is constant at the value for saturated liquid Vil: of these variables must be fixed to establish the intensive state of the system.

The remaining N variables are then subject to calculation, Equation may now be written as provided that sufficient information is available to allow determina- tion of all necessary thermodynamic properties. Identifying superscripts l and v are omitted here with the understand- The N equations represented by Eq.

Applications of Eq. The fugacity fi of pure compressed liquid i must be evaluated at the For the systems of interest here, this factor is always very close to T and P of the equilibrium mixture. This is done in two steps. Nevertheless, it is useful as a stan- dard of comparison. Real solution behavior is reflected by fisat fiv fil values of activity coefficients that differ from unity. Process Des. Fun- dam. Rasmussen, Ind. Calculation here is sios, Ind.

C , Eqs. A , B , and C yield the values listed in the table on the following page. Equations and The range of applicability of the original UNIFAC model has been then become greatly extended and its reliability enhanced.

Its most recent revision and extension is treated by Wittig, Lohmann, and Gmehling [Ind. Not only do they provide a wide temperature range of applicability, but also they allow corre- b. With x1 an unknown, the lation of various kinds of property data, including phase equilibria, activity coefficients cannot be immediately calculated. However, an iteration infinite dilution activity coefficients, and excess properties. The most scheme based on Eqs. C , results are listed in the accompany- model is provided by Gmehling et al.

Both papers contain extensive literature citations. An iteration scheme or a solve routine with starting values for the unknowns is The UNIFAC model has also been combined with the predictive required. The procedure is table. Again, an iteration most completely described with background literature citations by scheme or a solve routine with starting values for the unknowns is required.

For Horstmann et al. Azeotrope calculations: As noted in Example 1a, only a single degree of freedom exists for this special case. Given T, correlations. Similarly, given P, one finds the azeotropic composition and temperature. Shown in the accompanying table are calculated Bi azeotropic states for a temperature of 46! C and for a pressure of Defining these residuals as Given values are italic; calculated results are boldface.

Given here is a brief description of the treatment of data left is effectively zero, and the preceding equation becomes taken for binary systems under isothermal conditions. A more com- prehensive development is given by Van Ness [J. Experi- sistency with respect to this equation. A simple summability relation analogous to Eq.

Thus Eq. This is the result obtained when represented by Eq. When they do not, derived values of the activity coefficients by Eqs. With experimental error usually concen- experimental values are given by differentiation of Eq. It has no thermodynamic content, but may make for computational Equations and are applicable to species 2, desig- convenience through elimination of one set of mole fractions in favor nated the solvent, but not to the solute, for which an alternative of the other.

However, the effect of P on a liquid-phase fugacity, given by a Poynting factor, is very small and for practical pur- yi poses may usually be neglected. For the solute, this equation takes the place of Eqs. The flash calculation is a very common application of VLE. P, but of composition. Thus, Eq. Determine lations, both special cases of Eq. The present treatment is applicable to both.

Three segments are evident. The very steep one on Equation here becomes the left rs is characteristic of liquids. B and C of Example 3. In the unlikely event that the sum is For pure species i, Eq. If not, then successive trials eas- written as ily lead to this value. More elegant solution procedures can of course be employed. These points then represent saturated liquid and vapor phases in equilib- rium at temperature T. Moreover, it is most satisfactory for Expressions for Z iv and Zil come from Eqs.

As defined Each line includes three segments as described for the isotherm of by Eq. Because these points for a given line are for the same composition, they do not rep- The remaining equation-of-state parameters, given by Eqs. This pressure is the phase equilibrium pressure, and the composition for The eight equations through may be solved for the the dashed line is that of the equilibrium vapor.

Perhaps more useful is the reverse calculation whereby an equation- In the absence of a theory to prescribe the composition depen- of-state parameter is evaluated from a known vapor pressure. A common combining rule is given by Eq. The general mole fraction variable xi is used here because application is to both liquid and vapor mixtures. Because Zil and Ziv depend on qi, an iterative procedure is mixture parameters solely from parameters for the pure constituent indicated, with a starting value for qi from a generalized correlation as species.

They find application primarily for mixtures comprised of given by Eqs. For mixtures the presumption is that the equation of state has Useful in the application of cubic equations of state to mixtures exactly the same form as when written for pure species. Equations are partial equation-of-state parameters.

Here, these parameters, and therefore definitions are b and a T , are functions of composition. Liquid and vapor mixtures in equilibrium in general have different compositions. They are displaced from each other because the equation- of-state parameters are different for the two compositions.

Parameter q is defined in relation to parameters a and b by Eq. Although more complex, the same basic principle applies as for FIG. The solid line is for a pure-species VLE. Thus, specification of N at the same P as shown , they represent phases in equilibrium. The extensive literature on this subject is reviewed by Valderrama [Ind.

In this case only the first two terms on the right Eq. The key relations are Eq. C , both VLE data and the excess-property analog of Eq. DATA Ser. A, Sel. Data Mixtures, 67 ] and excess enthalpy data [Morris et al. The VLE data are well correlated by the Margules equa- tions. As noted in connection with Eq. Thus, we have from the VLE data at More generally, for a Extrapolations based on the same data to still higher temperatures can be The stoichiometric numbers provide relations among the changes expected to become progressively less accurate.

The Equation is the basic expression of material balance for a UNIQUAC equation is suitable, and therefore prediction is possible closed system in which r chemical reactions occur.

It is not an equilibrium relation, but — ]. The reaction coordinate has [Fluid Phase Equilib. Data for LLE are collected in a three-part set compiled by meaning that reaction j has proceeded to such an extent that the Sorensen and Arlt [Liquid-Liquid Equilibrium Data Collection, change in mole number of each reactant and product is equal to its Chemistry Data Series, vol.

Main — ]. With activity coeffi- For a system in which just a single reaction occurrs, Eq. A standard state of species i is its real or hypotheti- composition variables. Then, for fixed temperature Eqs. The standard heat of reaction position, i. Equation this equation into Eq. Convenience suggests set- often taken as unity.

This problem has not been solved for the general case. Two courses The activities in Eq. The standard states are always at the equilibrium temperature. Data 11, supp. See also Sec. Reaction rate increases with increasing T, but because the reac- increasing T; for an exothermic reaction, it is negative and Kj decreases tion is exothermic the equilibrium conversion decreases with increasing T. A with increasing T. Carrero-Mantilla and M. Llano- Because the standard state pressure is constant, Eq.

For these dT conditions we determine the fractional conversion of benzene to cyclohexane. Integration of these equations from reference temperature T0 usually A feed stream containing 3 mol H2 for each 1 mol C6H6 is the basis of calcu- lation, and for this single reaction, Eq. Assume first that the equilibrium mixture is an ideal gas, and apply Eq.

Combining this equation with Eqs. However, in the case of an ideal solu- tion Eq. Note that Tc and Pc for hydrogen are effective values as calculated by Eqs. C6H12 In addition, the fugacity is eliminated—in are determined from the Soave-Redlich-Kwong equation of state. In no case are favor of the fugacity coefficient by Eq. With these these calculated conversions significantly divergent. A more direct procedure and one suitable for Combination with Eq.

There are N equilibrium equa- i on conservation of the total number of atoms of each element in a sys- tions [Eqs.

Let subscript k identify a particular material balance equations [Eqs.