Mixture behavior prediction

This paper reviews the experiences of the oil industry in regard to asphaltene flocculation and presents justifications and a descriptive account for the development of two different models for this phenomenon. In one of the models we consider the asphaltenes to be dissolved in the oil in a true liquid state and dwell upon statistical thermodynamic techniques of multicomponent mixtures to predict their phase behavior. In the other model we consider asphaltenes to exist in oil in a colloidal state, as minute suspended particles, and utilize colloidal science techniques to predict their phase behavior. Experimental work over the last 40 years suggests that asphaltenes possess a wide molecular weight distribution and they may exist in both colloidal and dissolved states in the crude oil. 

The real problem with equations of state is in the accurate prediction of mixture behavior. This is somewhat analogous to... 

In spite of their widespread use, surfactant mixtures are fundamentally not well understood at a molecular level. For speciLc applications, such mixtures are often chosen based on experience empirical evidence, ortrial and error research. A comprehensive, predictive, moleculartheory would thus advance our understanding of surfactant mixture behavior. Such a theory would also facilitate the design and optimization of new surfactant mixtures by reducing the experimentation necessary to identify suitable mixtures and optimize their performance (Shiloach and Blankschtein, 1998a). 

An interesting investigation of the ternary mixture H2S + C02+CH4 was performed by Ng et al. (1985). Although much of this study was at temperatures below those of interest in acid gas injection, it provides data useful for testing phase-behavior prediction models. The multiphase equilibrium that Ng et al. observed for this mixture, including multiple critical points for a mixture of fixed composition, should be of interest to all engineers working with such mixtures. It demonstrates that the equilibria can be complex, even for relatively simple systems. 

The theory and conditions for phase equilibrium are well established. If more than one phase is present, then the chemical potential of a component is the same in all phases present. As chemical potential is linked functionally to the concepts of fugacity and activity, models for phase behavior prediction and correlation based on chemical potentials, fugacities, and activities have been developed. Historically, phase equilibrium calculations for hydrocarbon mixtures have been fragmented with liquid-vapor, liquid-liquid, and other phase equilibrium calculations, subject to separate and diverse treatments depending on the temperature, pressure, and component properties. Many of these methods and approaches arose to meet specific needs in the chemical process industries. Poling, Prausnitz,... 

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. 

In Chapter 10 we consider vapor-liquid equilibria in mixtures. For such calculations it is important to have the correct pure component vapor pressures if the mixture behavior is to be predicted correctly. Therefore, for equation-of-state calculations involving polar fluids, the PRSV equation will be used. 

Figure 10.3-13 Vapor-liquid equilibria of the acetone-water binary mixture described by the Peng-Robinson equation of state and the van der Waals one-fluid mixing rules. The solid lines result from the value of the binary parameter xy being fit to the data at 298 K. The dotted lines are the highly nonideal (and unrealistic) behavior predicted by setting k j = 0.

Although the VDW one-fluid mixing rules yield reasonably accurate predictions of mixture behavior for molecules which are not greatly dissimilar, the cases of evaluation of the unlike interaction parameters, (Ty and ij, where i /, from the data may be compensatory in an empirical way. 

The modified VDW one-fluid mixing rules for ( X> Cx and Sx in Equations 6, 7, and 16 were used to determine the ability of this formulation of the conformal solution model for predicting mixture behavior. The following relations were used for cry, ey, and Sy where i /,... 

Finding an appropriate mixed solvent system should not be done on a strictly trial and error basis. It should be examined systematically based on the binary solubility behavior of the solute in solvents of interest. It is important to remember that the mixed solvent system with the solute present must be miscible at the conditions of interest. The observed maximum in the solubility of solutes in mixtures is predicted by Scatchard-Hildebrand theory. Looking at Eq. (1.50) we see that when the solubility parameter of the solvent is the same as that of the subcooled liquid solute, the activity coefficient will be 1. This is the minimum value of the activity coefficient possible employing this relation. When the activity coefficient is equal to 1, the solubility of the solute is at a maximum. This then tells us that by picking two solvents with solubility parameters that are greater than and less than the solubility parameter of the solute, we can prepare a solvent mixture in which the solubility will be a maximum. As an example, let us look at the solute anthracene. Its solubility parameter is 9.9 (cal/cm ). Looking at Table 1.8, which lists solubility parameters for a number of common solvents, we see that ethanol and toluene have solubility parameters that bracket the value of anthracene. If we define a mean solubility parameter by the relation... 

The phase behavior predictions for the reaction mixture were made via the Peng-Robinson equation of state and ChemCAD process simulation software. The calculation method was shown to be accurate to within 10% compared to data from Schneider [20], Olds et al. [21], and Poetmann and Katz [22], Table 1 shows the estimated critical properties for various systems. 

Prediction of Mixture Behavior from Single-Component Data... 

Over the last 10 years or so, a great deal of work has been devoted to the study of critical phenomena in binary micellar solutions and multicomponent microemulsions systems [19]. The aim of these investigations in surfactant solutions was to point out differences if they existed between these critical points and the liquid-gas critical points of a pure compound. The main questions to be considered were (1) Why did the observed critical exponents not always follow the universal behavior predicted by the renormalization group theory of critical phenomena and (2) Was the order of magnitude of the critical amplitudes comparable to that found in mixtures of small molecules The systems presented in this chapter exhibit several lines of critical points. Among them, one involves inverse microemulsions and another, sponge phases. The origin of these phase separations and their critical behavior are discussed next. 

In the second case, the effect of the solvent on copolymerization kinetics is much more complicated. Since the polarity of the reacting medium would vary as a function of the comonomer feed ratios, the monomer reactivity ratios would no longer be constant for a given copolymerization system. To model such behavior, it would be first necessary to select an appropriate base model for the copolymerization, depending on the chemical structure of the monomers. It would then be necessary to replace the constant reactivity ratios in this model by functions of the composition of the comonomer mixture. These functions would need to relate the reactivity ratios to the solvent polarity, and then the solvent polarity to the comonomer feed composition. The overall copolymerization kinetics would therefore be very complicated, and it is difficult to suggest a general kinetic model to describe these systems. However, it is obvious that such solvent effects would cause deviations fi om the behavior predicted by their appropriate base model and might therefore account for the deviation of some copolymerization systems from the terminal model composition equation. 

Particularly when polar groups are present in liquid mixtures, azeotropes are often formed. For the design of separation processes like distillation, the knowledge of the azeotropic composition at different thermodynamic conditions is of critical importance. In this context, molecular simulation offers a powerful route to predict azeotropic behavior in mixtures. The prediction of the vapor-liquid equilibrium of the mixture CO2 + C2H6 is presented here as an example. 

Vrabec et al. [41] predicted the vapor-liquid equilibrium of the mixture CO2 + C2H6 for three different isotherms. The azeotropic behavior of this mixture was predicted using the Lorentz-Berthelot combining mle (12), i.e., relying exclusively on pure substance models without considering any experimental binary data. The quality of the predicted data is clearly superior to the Peng-Robinson EOS with the... 

This equation improves the liquid density prediction, but still cannol describe volumetric behavior around the critical point because of fundamental reason that will be discussed later. There are thousands of cubic equations of states, and many noncubic equations. The non cubic equations such as the Benedict-Webb-Rubin equation (1942) ant its modification by Starling (1973) have a large number of constants they describe accurately the volumetric behavior of pure substances But for hydrocarbon mixtures and crude oils, because of mixing rub complexities, they may not be suitable (Katz and Firoozabadi, 1978) Cubic equations with more than two constants also may not improv the volumetric behavior prediction of complex reservoir fluids. In fact most of the cubic equations have the same accuracy for phase-behavio prediction of complex hydrocarbon systems the simpler equation often do better. Therefore, the discussion will be limited to the Peng... 

The assymetric activity coefficient behavior of non-ideal mixtures is predictable. 

The MFLG model describes the vapor/liquid critical point (v = 1), v/l equilibrium data and isotherms of pure components such as -pentane and other n-alkanes quite well (Fig. 7) while polymers also fall within the scope of the model. Since linear polyethylene and M-alkanes consist of identical repeat units it has been assumed that, in a first approximation, the parameters for n-alkane/polyethylene mixtures can be set equal to zero [55]. This assumption proved to be too simplistic since the locations predicted for spinodal curves were found to be only in qualitative agreement with the measured curves and locations of miscibility gaps. However, Fig. 8 illustrates that values for mixture parameters can be found that provide a fair description of the measured LCM behavior and its pressure dependence for the system n-alkane/linear polyethylene [56, 57]. The predictive power of the procedure is considerable, as is witnessed by Fig. 9 in which the location of cloud points in pressure-temperature-composition space for -octane/n-nonane/ linear PE mixtures is predicted remarkably well in terms of the nearby spinodals. 

Particles can have quite a variety of geometries, but they should be of approximately the same dimension in all directions (equiaxed). For effective reinforcement, the particles should be small and evenly distributed throughout the matrix. Furthermore, the volume fraction of the two phases influences the behavior mechanical properties are enhanced with increasing particulate content. Two mathematical expressions have been formulated for the dependence of the elastic modulus on the volume fraction of the constituent phases for a two-phase composite. These rule-of-mixtures equations predict that the elastic modulus should fall between an upper bound represented by... 

Figuer4.21 shows experimental liquid-liquid equilibria data for the binary mixtures water/phenol (solid squares) and methanol/hexane (solid circles). Here xi is the mole fraction of water and methanol, respectively. Notice that while both systems show the basic behavior predicted by our theory, only the second system also exhibits the symmetry around x = 0.5. Nevertheless, the solid lines are theoretical results, which where obtained using... 

To predict the octane numbers of more complex mixtures, non-linear models are necessary the behavior of a component i in these mixtures depends on its hydrocarbon environment. 

The aroma of fmit, the taste of candy, and the texture of bread are examples of flavor perception. In each case, physical and chemical stmctures ia these foods stimulate receptors ia the nose and mouth. Impulses from these receptors are then processed iato perceptions of flavor by the brain. Attention, emotion, memory, cognition, and other brain functions combine with these perceptions to cause behavior, eg, a sense of pleasure, a memory, an idea, a fantasy, a purchase. These are psychological processes and as such have all the complexities of the human mind. Flavor characterization attempts to define what causes flavor and to determine if human response to flavor can be predicted. The ways ia which simple flavor active substances, flavorants, produce perceptions are described both ia terms of the physiology, ie, transduction, and psychophysics, ie, dose-response relationships, of flavor (1,2). Progress has been made ia understanding how perceptions of simple flavorants are processed iato hedonic behavior, ie, degree of liking, or concept formation, eg, crispy or umami (savory) (3,4). However, it is unclear how complex mixtures of flavorants are perceived or what behavior they cause. Flavor characterization involves the chemical measurement of iadividual flavorants and the use of sensory tests to determine their impact on behavior. 

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