Pressure-temperature-concentration phase vapor-liquid equilibrium

Data on the total vapor pressure of amine solutions as a function of temperature and amine concentration are necessary for the design of stripping columns and reboilers. Such data are presented in Figure 2-56 for MEA solutions, 2-57 for DEA solutions, 2-58 for DGA solutions, 2-59 for TEA solutions, 2-60 for DIPA solutions, and 2-61 for MDEA solutions. These charts can be used to determine the boiling point of an amine solution as a function of concentration and pressure however, they do not show the composition of the vapor phase. Vapor-liquid equilibrium composition charts for MEA and DGA solutions at selected pressures are given in Chapter 3. Additional data on amine solution vapor-liquid equilibrium can usually be obtained from the manufacturers. 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

The solution requires the concentration of the heptane and toluene in the vapor phase. Assuming that the composition of the liquid does not change as it evaporates (the quantity is large), the vapor composition is computed using standard vapor-liquid equilibrium calculations. Assuming that Raoult s and Dalton s laws apply to this system under these conditions, the vapor composition is determined directly from the saturation vapor pressures of the pure components. Himmelblau6 provided the following data at the specified temperature ... 

Prediction of the hydrate phase on a laboratory scale is analogous (in vapor-liquid equilibrium) to the prediction of the liquid phase concentration given only the vapor phase concentration, temperature, and pressure. Predictions of either the liquid phase or the hydrate phase are unacceptable because all experimental errors are transferred to prediction of the unmeasured phase. 

The most commonly encountered coexisting phases in industrial practice are vapor and liquid, although liquid/liquid, vaporlsolid, and liquid/solid systems are also found. In this chapter we first discuss the nature of equilibrium, and then consider two rules that give the lumiber of independent variables required to detemiine equilibrium states. There follows in Sec. 10.3 a qualitative discussion of vapor/liquid phase behavior. In Sec. 10.4 we introduce tlie two simplest fomiulations that allow calculation of temperatures, pressures, and phase compositions for systems in vaporlliquid equilibrium. The first, known as Raoult s law, is valid only for systems at low to moderate pressures and in general only for systems comprised of chemically similar species. The second, known as Henry s law, is valid for any species present at low concentration, but as presented here is also limited to systems at low to moderate pressures. A modification of Raoult s law that removes the restriction to chemically similar species is treated in Sec. 10.5. Finally in Sec. 10.6 calculations based on equilibrium ratios or K-values are considered. The treatment of vapor/liquid equilibrium is developed further in Chaps. 12 and 14. 

Lyophilization (Freeze Drying) Lyophilization is most frequently used for heat-labile dosage forms that are unstable in aqueous formulation. The principle of lyophilization can be seen by reference to the phase equilibrium diagram for water (Fig. 15). Water at atmospheric pressure and ambient temperatures is stable in its liquid phase at lOO C the liquid phase attains an equilibrium with its vapor phase. Above 100 C water is stable in its vapor phase. At atmospheric pressures and 0 C the solid (ice) and liquid phases of water are in equilibrium with each other. At vacuum pressures a temperature (the eutectic point) can be reached where the three phases, solid, liquid, and vapor are all in equilibrium with each other. At even lower temperatures and pressures the solid phase comes into equilibrium with the liquid phase. The significance of this is that an aqueous solution can be concentrated by evaporation (sublimation) at low pressures without any necessity for significant heat input. 

The system of equations (21.19)-(21.21) is solved numerically. As a result, the changes in time of water and methanol concentrations in a drop, temperature and radius of drops are determined. Thermo-physical properties of gas and liquid phases involved in equations can be determined by methods given in [9]. Calculations were carried out for various pressures, initial temperatures of the drop and gas, and initial concentrations of methanol in the inhibitor solution. The composition of gas used in calculations depends on p, T and should be determined in advance from the equations of vapor-liquid equilibrium. Thus, for p = 8 MPa and T = 313 °K, the following composition is obtained (molar fractions) N2 = 0.81 CO2 = 0.22 CH4 = 96.97 CzHg = 1.74 CjHg = 0.16 i - C4 = 0.07 n - C4 = 0.03. 

The ideal gas law characterizes the relationship between pressure, temperature, and volume for gases. Both the Clausius-Clapeyron and Antoine equations characterize the vapor-liquid equilibrium of pure components and mixtures. At atmospheric pressure and ambient temperature, water is a liquid but an equilibrium exists with its vapor phase concentration—its vapor pressure. The vapor pressure is a function of temperature. The formula for the Clausius-Clapeyron equation is ... 

When the vapor concentration becomes constant at equilibrium, vapor pressure also becomes constant. The partial pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature is the equilibrium vapor pressure of the substance at that temperature. 

The relationship between the concentration of acid gas in an amine solution and its partial pressure in the gas phase at equilibtium is probably the most important item of data required for the design of treating plants. The relationship may be referred to as gas solubiliiy or vapor-liquid equilibrium (VLE). The concentration in the liquid phase is normally reported as moles acid gas per mole of amine (mole/mole or mol/mol). Since this value varies with the partial pressure (or more precisely with the fugacity) of the acid gas, temperature, type of amine, amine concentration in the solution, and nature and concentration of other components in the solution, the amount of data required to cover all possible conditions is enor-... 

The equilibrium conversion can be calculated from knowledge of the free energy, together with physical properties to account for vapor and liquid-phase nonidealities. The equilibrium conversion can be changed by appropriate changes to the reactor temperature, pressure and concentration. The general trends for reaction equilibrium are summarized in Figure 6.8. 

Gas-liquid relationships, in the geochemical sense, should be considered liquid-solid-gas interactions in the subsurface. The subsurface gas phase is composed of a mixture of gases with various properties, usually found in the free pore spaces of the solid phase. Processes involved in the gas-liquid and gas-solid interface interactions are controlled by factors such as vapor pressure-volatilization, adsorption, solubility, pressure, and temperature. The solubility of a pure gas in a closed system containing water reaches an equilibrium concentration at a constant pressure and temperature. A gas-liquid equilibrium may be described by a partition coefficient, relative volatilization and Henry s law. 

In the example with aniline, the aniline vapor was provided by the equilibrium vapor liquid aniline. Vapor-phase intercalation can be done with compounds that are gases at room temperature and ambient pressure. The most common gas used for intercalation reactions is ammonia. Ammonia intercalation can be accomplished by exposing a host to the vapor generated by a concentrated aqueous ammonia solution. This multi-component vapor containing NH3(g), IfeOQj),... 

Enthalpy-concentration charts are particularly useful for two-component systems in which vapor and liquid phases are in equilibrium. The Gibbs phase rule (Equation 6.2-1) specifies that such a system has (2 -I- 2 - 2) = 2 degrees of freedom. If as before we fix the system pressure, then specifying only one more intensive variable—the system temperature, or the mass or mole fraction of either component in either phase—fixes the values of all other intensive variables in both phases. An H-x diagram for the ammonia-water system at 1 atm is shown in Figure 8.5-2. 

In gas absorption operations the equilibrium of interest is that between a relatively nonvolatile absorbing liquid (solvent) and a solute gas (usually the pollutant). As described earlier, the solute is ordinarily removed from a relatively large amount of a carrier gas that does not dissolve in the absorbing liquid. Temperature, pressure, and the concentration of solute in one phase are independently variable. The equilibrium relationship of importance is a plot (or data) of x, the mole fraction of solute in the liquid, against y, the mole fraction in the vapor in equilibrium with x. For cases that follow Henry s law, Henry s law constant m, can be defined by the equation... 

Many industrial separation processes are based on phase equilibria. By this we mean that the various components of the mixtures present in the (vapor, liquid, solid) phases are in equilibriinn. This is a dynamic equilibriinn and equal mnnbers of components are being transferred continuously from one phase to the other thus the concentrations at equilibriinn do not change. To design the separation processes in industry, e.g., finding the height and number of trays of a distillation column, we need to know the concentrations at equilibrium at any temperature and pressure. 

Consider first the schematic P-T and P-x diagrams for the naphthalene-ethylene system. Figure 3.18b depicts the solubility behavior of naphthalene in supercritical ethylene at a temperature greater than the UCEP temperature. Solid-gas equilibria exist at low pressures until the three-phase SLV line is intersected. The equilibrium vapor, liquid, and solid phases are depicted as points on the horizontal tie line at pressure Pj. As the pressure is further increased a vapor-liquid envelope is observed for overall mixture concentrations less than Xl- A mixture critical point is observed for this vapor-liquid envelope, as described earlier. If the overall mixture composition is greater than Xl, then solid-gas equilibria are observed as the pressure is increased above Pj. 

Shown in figure 3.18c is a solubility isotherm at a temperature, Tb, that is less than the previous temperature, Tj, but still higher than the UCEP temperature. The solubility behavior at T is similar to the behavior in figure 3.18b. But at T, the three-phase SLV line is intersected at a higher pressure, closer to the UCEP pressure. Hence, the vapor-liquid envelope has diminished in size and the solid-gas equilibrium curve is shifted toward higher solvent concentrations. As a result, the solid-gas curve is now much closer to the vapor branch of the vapor-liquid envelope. 

The rate of evaporation is constant at any given temperature, and the rate of condensation increases with the increasing concentration of molecules in the vapor phase. A state of dynamic equilibrium, in which the rate of a forward process is exactly balanced by the rate of the reverse process, is reached when the rates of condensation and evaporation become equal (Figure 11.34). The equilibrium vapor pressure is the vapor pressure measured when a dynamic equilibrium exists between condensation and evaporation. We often use the simpler term vapor pressure when we talk about the equilibrium vapor pressure of a liquid. This practice is acceptable as long as we know the meaning of the abbreviated term. 

Existing methods of technological calculations of the inhibition process [65] are based on the assumption that there exists a thermodynamic balance between liquid (inhibitor) and gas (natural gas) phases. Application of this method allows to determine equilibrium values of concentration of water vapor and inhibitor in a gas at given values of pressure, temperature, inhibitor s mass concentration in the solution, composition of gas, and specific flow rate of inhibitor required for given temperature decrease of hydrate formation ... 

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