Saturated liquids, defined

The constants Cj and C9 are both obtained from Fig. 2-40 Ci, usually from the saturated liquid line and C2, at the higher pressure. Errors should be less than 1 percent for pure hydrocarbons except at reduced temperatures above 0.95 where errors of up to 10 percent may occur. The method can be used for defined mixtures substituting pseiidocritical properties for critical properties. For mixtures, the Technical Data Book—Fehvleum Refining gives a more complex and accurate mixing rule than merely using the pseiidocritical properties. The saturated low pressure value should be obtained from experiment or from prediction procedures discussed in this section for both pure and mixed liquids. 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

What happens at the feed stage depends on the condition of the feed, whether it is subcooled, saturated liquid, partially vaporized, saturated vapor or superheated vapor. To define the condition of the feed, the variable q is introduced, defined as ... 

The thermal quality of the feed is defined as the heat required to raise 1 mole of feed from the feed condition to vapour at the feed plate condition divided by the molar latent heat, and the following values apply q=0 for saturated liquid feed q=l for saturated vapour feed, and q>l for cold feed. The value of q affects the relative liquid and vapour flow rates (L and V) above and (L and V ) below the feed plate, as indicated in Fig. 3.54. 

The isothermal vaporization of pure liquid i represents its transition from saturated liquid to saturated vapor at temperature T and at saturation vapor pressure P8 6. The treatment of this transition is facilitated through use of property changes of vaporization defined by equation 139 ... 

Vapor pressure is one of the most fundamental properties of steam. Figure 1 shows the vapor pressure as a function of temperature for temperatures between the melting point of water and the critical point. This line is called the saturation line. Liquid at the saturation line is called saturated liquid liquid below the saturation line is called subcooled. Similarly, steam at the saturation line is saturated steam steam at higher temperature is superheated. Properties of the liquid and vapor converge at tlie critical point, such that at temperatures above the critical point, there is only one fluid. Along the saturation line, the fraction of the fluid that is vapor is defined by its quality, which ranges from 0 to 100% steam. 

Equation (11.17), which defines the fugacity of pure species i, may integrated for the change of state from saturated liquid to saturated vapor,1 at temperature T and at the vapor pressure PT -... 

The relative volatilities are defined by Eq. (13-33), R m is the minimum reflux ratio, and q describes the thermal condition of the feed (1 for a saturated liquid feed and 0 for a saturated vapor feed). The Zfj values are available from the given feed composition. The 0 is the common root for the top section equations and the bottom section... 

Under conditions below the critical temperature, Tc, of the adsorbate, Vm is assumed equal to the molar volume of the saturated liquid at system temperature. Above Tc the adsorbed phase is ill-defined, and this has led to different approximations been proposed for Vm. Likewise, in the supercritical region the concept of vapor pressure does not exist and Ps in Eq. (2) must be replaced a pseudo-vapor pressure. In the present work we followed the suggestions of Agarwal and Schwarz, and estimated and Vm at temperatures above Tc as follows ... 

It is important to mention here that since it is not possible to estimate the absolute enthalpy of a compound, a reference temperature is generally chosen. Ideally, this reference temperature is such that all the enthalpies under consideration are zero at this temperature. In the absolute sense, unfortunately, different compounds have different molecular motions (and hence different enthalpies) at a given temperature. Hence, the solution lies in choosing a temperature that is sufficiently low so that different compounds may be assumed to have the same enthalpy at the reference point.Kesler-Lee defined the reference state for enthalpies of petroleum fluids as saturated liquid at — 200 °F ( 144 K), and it is reasonable to assume that enthalpies of all the petroleum fractions at this low temperature will be zero. 

Figure 147. Liquid requirements for obtaining saturations 5, defined by the energy consumption curve for different types of mixers...

Figure 148. Liquid requirements for obtaining saturations S, defined by the power consumption curve as a function of the amount of PVP (binder) added to the formulation (also influence of viscosity on liquid requirement, see text) ...

For consistency with later examples in which heat of dilution effects are important, we read all the enthapies from the steam tables, which have a reference state (where H is defined to be zero btu/lb) corresponding to saturated liquid water at its freezing point. In Example 8.4-1 on p498, Geankoplis works a very similar problem in which all enthalpies are calculated using the conditions of the liquor as the reference state. Then (by definition) H in (19) is zero the enthalpy of the feed // differs from that of the liquor just in sensible heat, which can be estimated as (8.4-... 

The SVP of a liquid defines its volatility the higher the SVP, the greater the volatility of the compound. When the SVP is equal to the atmospheric pressure, the liquid boils. The SVP of water at 100°C = 760 mmHg. It is common knowledge that water boils at a lower temperature at high altitude than at sea level. This is because the SVP becomes equal to the reduced atmospheric pressure at high altitude at a temperature of less than 100°C. Of course, air is not always saturated with water vapour. When... 

The essential features of vapor-liquid equilibrium (VLE) behavior are demonstrated by the simplest case isothermal VLE of a binary system at a temperature below the critical temperatures ofboth pure components. Forthis case ( subcritkaT VLE), each pure component has a well-defined vapor-liquid saturation pressure ff, and VLE Is possible for the foil range of liquid and vapor compositions xt and y,. Figure 1.5-1 ffiustrates several types of behavior shown by such systems. In each case, (he upper solid curve ( bubble curve ) represents states of saturated liquid (he lower solid curve ( dew curve ) represents states of saturated vtqtor. 

The thermal condition of die feed stream introduces the need for nn energy balance at die feed stage. The feed may be a subcooled liquid, a saturated liquid, a mixture of liquid and vapor, a saturated vapor, or a superheated vapor. A special term may be defined diet can acoonnt for the thermal condition of the... 

As explained in Fig. 5.7, depicting a series of situations representing different liquid saturations in particulate bulk solids or of agglomerates, distinct distribution models exist which depend on the amount of liquid in the structure. The term liquid saturation is defined as the percentage of total void space that is filled with the liquid. A precondition for cohesiveness of particulate solids due to the presence of liquid is that the liquid wets the solids. Although, depending on the application, other liquids may be used to totally or partially fill the voids between particulate solids, in agglomeration water is most commonly used. 

The latent heat of vaporization per unit mass of a pure substance at a given temperature, X, is defined as the difference in enthalpy between the saturated vapor and saturated liquid at the given temperature, T. Since enthalpy is a thermodynamic function of state, show that X can be evaluated from a known value of X0 at a reference temperature T0 from the equation... 

Saturated Liquid Densities. Precise and consistent data are available from the triple point to the critical point (5). The variables are defined as... 

Enthalpy of Vaporization The enthalpy (heat) of vaporization AHv is defined as the difference of the enthalpies of a unit mole or mass of a saturated vapor and saturated liquid of a pure component i.e., at a temperature (below the critical temperature) ana corresponding vapor pressure. AHy is related to vapor pressure by the thermodynamically exact Clausius-Clapeyron equation ... 

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