Pure-fluid phase equilibria

Pure solid + fluid phase equilibrium calculations are challenging but can, in principle, be modeled if the triple point of the pure solid and the enthalpy of fusion are known, the physical state of the solid does not change with temperature and pressure, and a chemical potential model (or equivalent), with known coefficients, for solid constituents is available. These conditions are rarely met even for simple mixtures and it is difficult to generalize multiphase behavior prediction results involving even well-defined solids. The presence of polymorphs, solid-solid transitions, and solid compounds provide additional modeling challenges, for example, ice, gas hydrates, and solid hydrocarbons all have multiple forms. 

For a pure fluid, diffusional equilibrium wfil occur when there is no net driving force for diffusion of material from one phase to the other. This occurs when... 

In the first step, in which the molecules of the fluid come in contact with the adsorbent, an equihbrium is established between the adsorbed fluid and the fluid remaining in the fluid phase. Figures 25-7 through 25-9 show several experimental equihbrium adsorption isotherms for a number of components adsorbed on various adsorbents. Consider Fig. 25-7, in which the concentration of adsorbed gas on the solid is plotted against the equilibrium partial pressure p of the vapor or gas at constant temperature. At 40° C, for example, pure propane vapor at a pressure of 550 mm Hg is in equilibrium with an adsorbate concentration at point P of 0.04 lb adsorbed propane per pound of silica gel. Increasing the pressure of the propane will cause... 

The shaded region is that part of the phase diagram where liquid and vapor phases coexist in equilibrium, somewhat in analogy to the boiling line for a pure fluid. The ordinary liquid state exists on the high-pressure, low-temperature side of the two-phase region, and the ordinary gas state exists on the other side at low pressure and high temperature. As with our earlier example, we can transform any Type I mixture... 

Fig. 12. Evaluation of He-Ar and C02-Ar equilibrium conditions. The concentrations are expressed in mmol/ mol on a water-free basis. As an effect of re-injection, the data points, representative of the original fluid before re-injection, move from an almost complete equilibrium in vapour phase towards to a mixed phase, where equilibrium conditions in a pure liquid phase become more and more important. (From Giggenbach Goguel 1989.)...

Other phenomena can be simply explained by the fact that the critical pressure and temperature for a given mixture is not, as it happens for a pure fluid, the maximum temperature and pressure that allows the coexistence of a vapour and liquid phase in equilibrium. Retrograde condensation phenomena can be easily explained in this way. 

In a binary system more than two fluid phases are possible. For instance a mixture of pentanol and water can split into two liquid phases with a different composition a water-rich liquid phase and a pentanol-rich liquid-phase. If these two liquid phases are in equilibrium with a vapour phase we have a three-phase equilibrium. The existence of two pure solid phases is an often occuring case, but it is also possible that solid solutions or mixed crystals are formed and that solids exists in more than one crystal structure. 

The greatest use of cubic equations of state is for phase equilibrium calculations involving mixtures. The assumption inherent in such calculations is that the same equation of state as is used for the pure fluids can be used for mixtures if we have a satisfactory way to obtain the mixtures parameters. This is most commonly done using the van der Waals one-fluid mixing rules,... 

The phase rule specifies the number of intensive properties of a system that must be set to establish all other intensive properties at fixed values (3), without providing information about how to calculate values for these properties. The field of applied engineering thermodynamics has grown out of the need to assign numerical values to thermodynamic properties within the constraints of the phase rule and fundamental laws. In the engineering disciplines there is a particular demand for physical properties, both for pure fluids and mixtures, and for phase equilibrium data (4,5). 

Equations of State. Equations of state having adjustable parameters are often used to model the pressure—volume—temperature (PVT) behavior of pure fluids and mixtures (1,2). Equations that are cubic in specific volume, such as a van der Waals equation having two adjustable parameters, are the mathematically simplest forms capable of representing the two real volume roots associated with phase equilibrium, or the three roots (vapor, liquid, solid) characteristic of the triple point. 

Figure 14.10 The five types of (fluid + fluid) phase diagrams according to the Scott and van Konynenburg classification. The circles represent the critical points of pure components, while the triangles represent an upper critical solution temperature (u) or a lower critical solution temperature (1). The solid lines represent the (vapor + liquid) equilibrium lines for the pure substances. The dashed lines represent different types of critical loci. (l) [Ar + CH4], (2) [C02 + N20], (3) [C3H8 + H2S],...

In Aspen Plus, solid components are identified as different types. Pure materials with measurable properties such as molecular weight, vapor pressure, and critical temperature and pressure are known as conventional solids and are present in the MIXED substream with other pure components. They can participate in any of the phase or reaction equilibria specified in any unit operation. If the solid phase participates only in reaction equilibrium but not in phase equilibrium (for example, when the solubility in the fluid phase is known to be very low), then it is called a conventional inert solid and is listed in a substream CISOLID. If a solid is not involved in either phase or reaction equilibrium, then it is a nonconventional solid and is assigned to substream NC. Nonconventional solids are defined by attributes rather than molecular properties and can be used for coal, cells, catalysts, bacteria, wood pulp, and other multicomponent solid materials. 

R0sjorde et al studied the phase transition in a pure fluid using non-equilibrium molecular dynamics simulations (NEMD). The NEMD method solves Newton s equations of motion for several thousand particles in an imaginary box see Hafskjold for a review. The particles interacted with a Lennard-Jones-type pair... 

In Figure 3, heat transfer coefficients are shown for n-pentane--C02 at 8.9 MPa and bulk fluid CO2 mole fractions of 0.830 on the liquid side of the LOST, 0.865 precisely at the LOST, and 0.876 on the vapor side. For comparison, we also show results for pure carbon dioxide at the same bulk temperature and pressure. A similar set of results is shown for n-decane--C02 for each of two pressures in Figures 4 and 5. In Figure 4, at 10.4 MPa, the LOST of 325 K occurs at a CO2 mole fraction x of 0.93 0.02 according to our Peng-Robinson fit of the phase equilibrium data. Thus, only the results for x - 0.973 are clearly on the vapor side of the LOST and only those for x - 0.867 are on the liquid side. In Figure 5, for 12.2 MPa, the LOST has shifted slightly to x - 0.91 + 0.02 and T -335 K. Therefore, we expect the data for x - 0.940 to now be on the vapor side. 

In general, any substance that is above the temperature and pressure of its thermodynamic critical point is called a supercritical fluid. A critical point represents a limit of both equilibrium and stability conditions, and is formally delincd as a point where the first, second, and third derivatives of the energy basis function for a system equal zero (or, more precisely, where 9P/9V r = d P/dV T = 0 for a pure compound). In practical terms, a critical point is identifled as a point where two or more coexisting fluid phases become indistinguishable. For a pure compound, the critical point occurs at the limit of vapor-Uquid equilibrium where the densities of the two phases approach each other (Figures la and lb). Above this critical point, no phase transformation is possible and the substance is considered neither a Uquid nor a gas, but a homogeneous, supercritical fluid. The particular conditions (such as pressure and temperature) at which the critical point of a substance is achieved are unique for every substance and are referred to as its critical constants (Table 1). 

In pursuing an accurate thermodynamic description of the three-phase, three-component system, the phase equilibrium compositions can be calculated after pressure and temperature have been fixed, since it is known from the Gibbs phase rule that there are only 2 degrees of freedom. There are five unknown compositions, assuming that the solid is crystalline and pure and that its solubility in the vapor/fluid phase is negligible. Two of these unknown mole fractions are eliminated by the constraints that the mole fractions in each phase sum up to unity. To find these three unknown mole fractions, namely, xi, X3, and y2, only three equilibrium relations are required. 

In pioneering research by Hailing and co-workers, it was demonstrated that the activity of water is a more representative and useful parameter than water concentration for describing enzymatic rates in nonaqueous enzymology. Water activity, or is defined as the fugacity of water contained in a mixture divided by the fugacity of pure water at the mixture s temperature. For a typical nonaqueous enzymatic reaction operated in a closed system, the medium will consist of a solvent (or fluid) phase, an enzyme-contaiifing solid phase, and air headspace above the solvent. As a first approximation, the water transport between the three phases is assumed to be at thermodynamic equilibrium. For such a situation, can be defined in terms of the air headspace properties ... 

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