Pressure saturation boundary

Within the PV region delimited by the two saturation boundary curves, liquid and vapor phases coexist stably at equilibrium. To the right of the vapor saturation curve, only vapor is present to the left of the liquid saturation curve, vapor is absent. Let us imagine inducing isothermal compression in a system composed of pure H2O at T = 350 °C, starting from an initial pressure of 140 bar. The H2O will initially be in the gaseous state up to P < 166 bar. At P = 166 bar, we reach the vapor saturation curve and the liquid phase begins to form. Any further... 

Possibly the most widely employed charts are those of Nelson and Obert [7,2]. These contain graphs of Z as a function of reduced pressure, Py, and reduced temperature, Ty, for 0 < Py < 0.1 and 0.6 < T,- < 2.0 as a small-scale (1x1 in.) inset for 0 < P,. < 1, 0.6 < Ty < 5.0 and for larger ranges. No saturation-boundary curves are given, and the small-scale in.set is difficult to use. In general applications, the author has found the need for a low-pressure/low-temperature chart of "readable accuracy" with an indicated saturation boundary.. Also, some of (he Nelson/Oberl data may not be accurate. 

The uncertainties in the equation of state are 0.2% in density, 3% in heat capacities, 1% in speed of sound, and 0.5% in vapor pressure and saturation densities. The estimated uncertainty in the liquid phase along the saturation boundary is approximately 3%, increasing to 10% at pressures to 100 MPa, and is estimated at 10% in the vapor phase. The estimated uncertainty in the liquid phase is approximately 5% and is estimated as 10% in the vapor phase. 

Since they are thermodynamic variables, specific entropy and specific enthalpy may be regarded as functions of the two variables temperature and pressure. However, pressure is a single-valued function of temperature along the saturated boundary, and so the specific entropy and enthalpy of saturated steam are themselves single-valued functions of temperature. Hence specific enthalpy may be plotted as a singlevalued function of specific entropy in saturated conditions. This has been done in Figure 16.1. 

The explicit formula pxr — I = (1 — Pr)0 for reduced saturation density as a function of reduced pressure is proposed for the entire liquid-vapor saturation boundary. The expression A 1 depends on Pr p 0.35 depends weakly on Pr, corresponding at Pr = 1 to the critical exponent pc. The parameters A and ft can be related to the Pitzer factor o>. Special cases include the power law pr — 1 = C(1 — Tr)0c. . . and the low-pressure vapor equation prx0 = p0Pr The function A — Ac = g(Pr) is found from data to be a universal function for nonpolar substances. If Ac is correlated with o>, the formula takes on the corresponding-states form pr = /o,(Pr, to). This form predicted the density of saturated liquid and vapor with 0.4% and 0.9% accuracy, respectively, for 38 substances. 

Phe smooth curve passing through the critical point and bounding the two-phase liquid-vapor region in a pressure-volume diagram is familiar to every student of thermodynamics. The mathematical description p(P) of this coexistence curve or saturation boundary is the subject of this chapter. 

The numerical value of the exponent ft proves to be quite close to that of the critical exponent 0.35 over the entire range of pressures. Generally the exponent A takes on different values on the vapor and liquid branches of the saturation boundary. The numerical range of X easily can be estimated, using the critical point, the low-pressure vapor, and the low-pressure liquid as reference points. Near the critical point, the vapor-pressure equation is... 

A plot of the saturation boundary in pressure-volume coordinates is shown in Figure 6 for three different values of to. On the scale of this plot, no deviation of the curves (calculated from the corresponding-states model) from the data can be detected. 

The presented TH simulations are essentially simplified ID predictions of the relative humidity by means of calibration of the temperature boundary conditions. The actual geometry, behaviours of the heater, liner and rock, and the deformation of the buffer are not considered. Convection heat transfer and variations of pressure, viscosity of liquid, or liquid density are neglected, and the gas diffusion is of a simple form. The main simulational simplifications are the approximation of the heater adjustment period by a linear time dependence of temperature, and the use of a full saturation boundary condition at the rock surface. 

The vapor-pressure equation given by Grilly [" ] was selected to define the saturation boundary when using (1). 

At high pressures, where n = 0 and 0 = 1, the solid surface is saturated by and the hydriding kinetics are unaltered by changes in pressure. The rate is then controlled by a process occurring within the solid and depends only on temperature, as defined by the Arrhenius term. As fixed by the pressure-independent isotherms beyond the saturation boundary indicated by P, in fig. 14, for the rate-controlling process in the solid phase is 29kJ/mol as determined by Bloch and Mintz (1981). 

Marrucho and Ely developed a saturation boundary based method to evaluate the shape factors that is easily transferable between reference fluids. The method is based on the Frost-Kalkwarf vapour-pressure equation and the Rackett equation " for saturated-liquid densities. Using these relations and eqs 6.30 one finds for the 6 shape factor... 

Water loss in operating an HDR faciUty may result from either increased storage within the body of the reservoir or diffusion into the rock body beyond the periphery of the reservoir (38). When a reservoir is created, the joints which are opened immediately fill with water. Micropores or microcracks may fill much more slowly, however. Figure 11 shows water consumption during an extended pressurization experiment at the HDR faciUty operated by the Los Alamos National Laboratory at Fenton Hill, New Mexico. As the microcracks within the reservoir become saturated, the water consumption at a set pressure declines. It does not go to zero because diffusion at the reservoir boundary can never be completely elirninated. Of course, if a reservoir joint should intersect a natural open fault, water losses may be high under any conditions. 

The term aquifer is used to denote an extensive region of saturated material. There are many types of aquifers. The primary distinction between types involves the boundaries that define the aquifer. An unconfined aquifer, also known as a phraetic or water table aquifer, is assumed to have an upper boundary of saturated soil at a pressure of zero gauge, or atmospheric pressure. A confined aquifer has a low permeabiUty upper boundary that maintains the interstitial water within the aquifer at pressures greater than atmospheric. For both types of aquifers, the lower boundary is frequendy a low permeabihty soil or rock formation. Further distinctions exist. An artesian aquifer is a confined aquifer for which the interstitial water pressure is sufficient to allow the aquifer water entering the monitoring well to rise above the local ground surface. Figure 1 identifies the primary types of aquifers. 

Processing variables that affect the properties of the thermal CVD material include the precursor vapors being used, substrate temperature, precursor vapor temperature gradient above substrate, gas flow pattern and velocity, gas composition and pressure, vapor saturation above substrate, diffusion rate through the boundary layer, substrate material, and impurities in the gases. Eor PECVD, plasma uniformity, plasma properties such as ion and electron temperature and densities, and concurrent energetic particle bombardment during deposition are also important. 

A method of estimating original gas in place using the results of drilling (structural assessment, effective thickness, porosity, gas saturation, pressure, temperature, gas characteristics, and the boundaries of the accumulation). These data may be supplemented by geological or geophysical data on the shape of the reservoir. 

The eoexistence of laumontite and wairakite is common in zone (1). If the saturated water vapor pressure is equal to 0.3 of total pressure (Zeng and Liou, 1982), the temperature for equilibrium reaetion (1—23) and saturated water vapor pressure are estimated to be 170°C and 230 bar, respectively (Liou, 1971b). Zeng and Liou (1982) have shown that yugawaralite is stable at less than 230°C and a total pressure of 500 bar, under the condition of quartz saturation. However, if the activity of Si02 is not unity, the boundary for reactions (1-24) and (1-25) may shift to lower temperatures. Liou (1971a) studied the equilibrium for reaetion (1-26) and showed that the equilibrium... 

The fluid properties and porosity and permeability are determined independently. Boundary and initial conditions are specified for the particular experiment to be considered. With specified multiphase flow functions, the state equations, Eqs. (4.1.28, 4.1.5 and 4.1.6), can be solved for the transient pressure and saturation distributions, p (z,t) and s,(z,t), t= 1, 2. The values for F can then be calculated, which correspond to the measured data Y. 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

The basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

The boundary conditions for the system are (1) that at the surface of the hygroscopic material the partial pressure of water is determined by that of the saturated salt solution (Ps) and (2) that at a characteristic distance from the surface (8) the partial pressure of water vapor is given by the chamber pressure (Pc). 

The boundary conditions are that (1) at the moving boundary ( ) the solution is saturated with salt with a corresponding concentration of water (Cs) and (2) at the disk/atmosphere surface the concentration of water is governed by the equilibrium vapor pressure in the chamber to give a water concentration of C0. 

A realistic boundary condition must account for the solubility of the gas in the mucus layer. Because ambient and most experimental concentrations of pollutant gases are very low, Henry s law (y Hx) can be used to relate the gas- and liquid-phase concentrations of the pollutant gas at equilibrium. Here y is the partial pressure of the pollutant in the gas phase expressed as a mole fraction at a total pressure of 1 atm x is the mole fraction of absorbed gas in the liquid and H is the Henry s law constant. Gases with high solubilities have low H value. When experimental data for solubility in lung fluid are unavailable, the Henry s law constant for the gas in water at 37 C can be used (see Table 7-1). Gas-absorption experiments in airway models lined with water-saturated filter paper gave results for the general sites of uptake of sulfur dioxide... 

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