Fluid phase equilibria involving

An important aspect of the design of an acid gas injection scheme is the non-aqueous phase equilibrium. Fluid phase equilibrium involving water, which is also very important, will be discussed in chapter 4 and hydrates in chapter 5. 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

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. 

Adsorption and ion exchange share so many common features in regard to apphcation in batch and fixed-bed processes that they can be grouped together as sorption for a unified treatment. These processes involve the transfer and resulting equilibrium distribution of one or more solutes between a fluid phase and particles. The partitioning of a single solute between fluid and sorbed phases or the selectivity of a sorbent towards multiple solutes makes it possible to separate solutes from a bulk fluid phase or from one another. 

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. 

Optimizing solvents and solvent mixtures can be done empirically or through modeling. An example of the latter involves a single Sanchez-Lacombe lattice fluid equation of state, used to model both phases for a polymer-supercritical fluid-cosolvent system. This method works well over a wide pressure range both volumetric and phase equilibrium properties for a cross-linked poly(dimethyl siloxane) phase in contact with CO2 modified by a number of cosolvents (West et al., 1998). 

Tphe breakthrough curve for a fixed-bed adsorption column may be pre-dieted theoretically from the solution of the appropriate mass-transfer rate equation subject to the boundary conditions imposed by the differential fluid phase mass balance for an element of the column. For molecular sieve adsorbents this problem is complicated by the nonlinearity of the equilibrium isotherm which leads to nonlinearities both in the differential equations and in the boundary conditions. This paper summarizes the principal conclusions reached from a recent numerical solution of this problem (1). The approximations involved in the analysis are realistic for many practical systems, and the validity of the theory is confirmed by comparison with experiment. 

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 potential of supercritical extraction, a separation process in which a gas above its critical temperature is used as a solvent, has been widely recognized in the recent years. The first proposed applications have involved mainly compounds of low volatility, and processes that utilize supercritical fluids for the separation of solids from natural matrices (such as caffeine from coffee beans) are already in industrial operation. The use of supercritical fluids for separation of liquid mixtures, although of wider applicability, has been less well studied as the minimum number of components for any such separation is three (the solvent, and a binary mixture of components to be separated). The experimental study of phase equilibrium in ternary mixtures at high pressures is complicated and theoretical methods to correlate the observed phase behavior are lacking. 

Another possible scenario in the pipeline transport of acid gas is a transition from single-phase to two-phase flow or vice versa. For such a situation, it is veiy difficult to perform a calculation. These calculations, which involve a combination of fluid flow and phase equilibrium, should be performed using available software. 

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. 

The calculations reported in this paper and a related series of publications indicate that it is now quite feasible to obtain reasonably accurate results for phase equilibria in simple fluid mixtures directly from molecular simulation. What is the possible value of such results Clearly, because of the lack of accurate intermolecular potentials optimized for phase equilibrium calculations for most systems of practical interest, the immediate application of molecular simulation techniques as a replacement of the established modelling methods is not possible (or even desirable). For obtaining accurate results, the intermolecular potential parameters must be fitted to experimental results, in much the same way as parameters for equation-of-state or activity coefficient models. This conclusion is supported by other molecular-simulation based predictions of phase equilibria in similar systems (6). However, there is an important difference between the potential parameters in molecular simulation methods and fitted parameters of thermodynamic models. Molecular simulation calculations, such as the ones reported here, involve no approximations beyond those inherent in the potential models. The calculated behavior of a system with assumed intermolecular potentials is exact for any conditions of pressure, temperature or composition. Thus, if a good potential model for a component can be developed, it can be reliably used for predictions in the absence of experimental information. 

Competent design of chemical processes requires accurate knowledge of such process variables as the temperature, pressure, composition and phase of the process contents. Current predictive models for phase equilibria Involving supercritical fluids are limited due to the scarcity of data against which to test them. Phase equilibria data for solids In equilibrium with supercritical solvents are particularly sparse. The purpose of this work Is to expand the data base to facilitate the development of such models with emphasis on the melting point depressions encountered when solid mixtures are contacted with supercritical fluids. 

Adsorption is typically operated as an equilibrium-limited process the adsorbent must be in equilibrium with the surrounding fluid phase to obtain the maximum adsorption. It is also important to consider the various transport processes involved and the rate at which adsorption will occur. The mass transfer mechanism of adsorption typically has four steps (Figure 7.2). 

It is useful to mention another class of problems related to those referred to in the previous paragraphs, but that is not considered here. We do not try to answer the ques- tion of how fast a system will respond to a change in constraints that is, we do not try to study system dynamics. The answers to such problems, depending on the system and its constraints, may involve chemical kinetics, heat or mass transfer, and fluid mechanics, all of which are studied elsewhere. Thus, in the example above, we are interested in the final state of the gas in each cylinder, but not in computing how long a valve of given size must be held open to allow the necessary amount of gas to pass from one cylinder to the other. Similarly, when, in Chapters 10, 11, and 12, we study phase equilibrium and, in Chapter 13, chemical equilibrium, our interest is in the prediction of the equilibrium state, not in how long it will take to achieve this equilibrium state. —... 

The discussion of the previous section was concerned with low-pressure vapor-liquid equilibria and involved the use of activity coefficient models. Here we are interested in high-pressure phase equilibrium in fluids in which both phases are describable by equations of state, that is, the cj -4> method. One example of the type of data we are interested in describing (or predicting) is shown in Fig. 10.3-1 for the ethane-propylene system. There we see the liquid (bubble point) and vapor (dew point) curves for this system at three different isotherms. At each temperature the coexisting vapor and liquid. phases have the same pressure and thus are joined by horizontal tie lines, only one of... 

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