Phase equilibrium multi component mixtures

When oil and gas are produced simultaneously into a separator a certain amount (mass fraction) of each component (e.g. butane) will be in the vapour phase and the rest in the liquid phase. This can be described using phase diagrams (such as those described in section 4.2) which describe the behaviour of multi-component mixtures at various temperatures and pressures. However to determine how much of each component goes into the gas or liquid phase the equilibrium constants (or equilibrium vapour liquid ratios) K must be known. 

Note that this equation holds for any component in a multi-component mixture. The integral on the right-hand side can only be evaluated if the vapor mole fraction y is known as a function of the mole fraction Xr in the still. Assuming phase equilibrium between liquid and vapor in the still, the vapor mole fraction y x ) is defined by the equilibrium curve. Agitation of the liquid in tire still and low boilup rates tend to improve the validity of this assumption. 

Equilibrium data are thus necessary to estimate compositions of both extract and raffinate when the time of extraction is sufficiently long. Phase equilibria have been studied for many ternary systems and the data can be found in the open literature. However, the position of the envelope can be strongly affected by other components of the feed. Furthermore, the envelope line and the tie lines are a function of temperature. Therefore, they should be determined experimentally. The other shapes of the equilibrium line can be found in literature. Equilibria in multi-component mixtures cannot be presented in planar graphs. To deal with such systems lumping of consolutes has been done to describe the system as pseudo-ternary. This can, however, lead to considerable errors in the estimation of the composition of the phases. A more rigorous thermodynamic approach is needed to regress the experimental data on equilibria in these systems. 

Using different initial concentrations or adsorbent amounts, the relevant concentration range is covered. The method is easily expanded to multi-component mixtures, where the loading is a function of all components present. Drawbacks are the time consuming preparations of the different mixtures and the transferability of the results to packed columns (e.g. uncertainty in phase ratio/porosity). Because of the numerous steps of manual work and the uncertainty when equilibrium is reached, the accuracy is not too high. 

The computer program PROG72 performs equilibrium flash calculations for an ideal multi-component mixture. The program listed determines the moles of each component in the liquid and vapor phases... 

The modified van Laar equation (Black, 1959) extends the applicability of the van Laar equation to many systems, including non-symmetrical and hydrogenbonding binaries. The equation, which is generalized to multi-component mixtures, is expressed in terms of three binary interaction parameters A, and Q (= Cj. These parameters must be determined from binary phase equilibrium data. The modified van Laar equation reduces to the van Laar equation if Q = 0. Refer to the source (Black, 1959) for detailed mathematical formulation of the equation. 

The NRTL equation is one of the more successful equations for representing phase equilibrium data, including liquid-liquid equilibrium. It is applicable to multi-component mixtures, which may include non-symmetrical binaries. It also has built-in temperature dependency over moderate ranges. 

The equation, which is generalized to multi-component mixtures, requires pure component data for the van der Waals area and volume parameters, and r. Additionally, the binary interaction parameters (Uj -Uj and (Wy - are also required and are generally determined from binary phase equilibrium data. Temperature dependency is incorporated in the equation, similar to the Wilson and NRTL equations. The UNIQUAC equation is applicable to many classes of components, including mixtures containing considerably dissimilar molecules, and is also applicable to liquid-liquid equilibrium systems. It can represent temperature dependency over moderate ranges but is not necessarily more accurate than simpler equations in spite of its theoretical foundation. 

The separation of a multi-component mixture into products with different compositions in a multistage process is governed by phase equilibrium relations and energy and material balances. It is not uncommon in simulation studies to require certain column product rates, compositions, or component recoveries to satisfy given specifications with no concern for conditions within the column. Such would be the case when downstream processing of the products is of primary interest. In these instances, one would be concerned only with overall component balances around the column but not necessarily with heat balances or equilibrium relations. Separation would thus be arbitrarily defined, and the problem would be to calculate product rates and compositions. The actual performance of the separation process is analyzed independently in all the following chapters. 

To complete the construction of the Y-X diagram from simulation results, the feed line must be drawn. The intersection with the diagonal of a straight line drawn through the feed composition determines one point on the q-line. One other point is determined by the feed equilibrium vapor and liquid compositions at the feed tray conditions. If the feed is a saturated liquid, the equilibrium liquid composition is the same as the feed composition, and the equilibrium vapor composition is the bubble point composition on the equilibrium curve. In this case the q-line is vertical. For a saturated vapor feed, the equilibrium vapor composition is the same as the feed composition, the equilibrium liquid composition is the dew point composition, and the q-line is horizontal. For a mixed-phase feed, the c/ line slope is determined by the feed thermal condition (Section 5.2.2). Note that, for a multi-component mixture, the feed equilibrium vapor and liquid compositions from the simulation output may not lie exactly on the equilibrium curve because of the discrepancies resulting from lumping the light components in one pseudocomponent. 

Equation (5.56) is fundamental for calculations regarding multi-component mixtures, which are designated in thermodynamics by PVTx systems. From this we can obtain the generalisation of the phase equilibrium condition as follows ... 

Step 7. Identify the root having the lowest value of f2 as the stable one-phase mixture at the proposed T, P, and From Table 8.2 we see that the stable one-phase mixture is root p. Therefore root a, which is our proposed mixture, is not a stable one-phase mixture. Further, Figure 8.18 shows that root a satisfies the requirement on the derivative (8.4.8), so the proposed mixture is not unstable. Hence, it must be metastable it might be observed, but more likely it will split into two phases. To find the compositions of those phases, we would solve the phase-equilibrium problem. Other procedures for identifying stable one-phase mixtures include the tangent-plane method which originates with Gibbs [15] and has been fully developed by Michelsen, especially for multi-component mixtures [16]. 

Head-space gas chromatography is a modem tool for the measurement of vapor pressures in polymer solutions that is highly automated. Solutions need time to equilibrate, as is the case for aU vapor pressure measurements. After equilibration of the solutions, quite a lot of data can be measured continuously with reliable precision. Solvent degassing is not necessary. Measurements require some experience with the equipment to obtain really thermodynamic equilibrium data. Calibration of the equipment with pine solvent vapor pressures may be necessary. HSGC can easily be extended to multi-component mixtures because it determines aU components in the vapor phase separately. 

Also given in Table 3.2 is the residual part of the chemical potential of component. s in a multi-component mixture at specified (T, p, x ). The partial fugacity p of component. s in a mixture, often used in phase equilibrium calculations, is defined by the relation... 

There have been few studies reported in the literature in the area of multi-component adsorption and desorption rate modeling (1, 2,3., 4,5. These have generally employed simplified modeling approaches, and the model predictions have provided qualitative comparisons to the experimental data. The purpose of this study is to develop a comprehensive model for multi-component adsorption kinetics based on the following mechanistic process (1) film diffusion of each species from the fluid phase to the solid surface (2) adsorption on the surface from the solute mixture and (3) diffusion of the individual solute species into the interior of the particle. The model is general in that diffusion rates in both fluid and solid phases are considered, and no restrictions are made regarding adsorption equilibrium relationships. However, diffusional flows due to solute-solute interactions are assumed to be zero in both fluid and solid phases. 

For safety reasons, the cycling operation is interrupted during the weekend. After an interruption, always happening at the end of a discharge phase, several cycles are necessary to join the continuous curve representative of the evolution of the behaviour of the tank. This phenomenon tends to demonstrate the importance of the kinetics of the multi-component adsorption equilibrium in the case of a complex mixture of gas. 

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