Phase behavior prediction

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. 

For the substituted polysilylenes, (SiRR ) , the coupling constant can be varied systematically by changing the side groups (this change affects e and Vd via the backbone polarizability) or the solvent (this change affects Vj) via the London dispersion forces e is expected to be only weakly solvent dependent for nonpolar systems). Therefore, in principle, the three distinct phase behaviors predicted by the theory may be observed by judicious choice of polymer-solvent pairs. 

The experimental results in Figure 2 and Table II clearly show three qualitatively different behaviors an abrupt order-disorder transition a relatively rapid continuous transition and a gradual, smooth ordering of the polymer backbone. These observations are qualitatively identical to the three possible phase behaviors predicted by the theory. Moreover, a degree of quantitative understanding can be obtained. 

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,... 

Consider now the phase behavior predicted by Equation 9 for the elements of the S matrix. For simplicity, we assume the background contribution provided by S Is weak compared to S, and we concen-... 

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. 

Anthamatten M (2007) Phase behavior predictions for polymer blends containing reversibly associating endgroups. J Polym Sci Polym Phys 45(24) 3285-3299... 

The first relations have already been proposed by Margules (95MAR1) more than one eentury ago, and later on they have appeared many others, e.g. the equations by Van Laar, Wohl, Seatehard-Hammer, Carlson-Colbum etc. some of them were modified in mareh of time. At present, several newer ones beeame popular because of their easy application to the deseription of multieomponent systems and for the phase behavior prediction methods based on knowledge of binary data. 

For illustration, the phase behavior predicted by the H-W theory for an SI diblock copolymer at 150°C is given in Fig. 6. In obtaining Fig. 6 we used the following expressions for an interaction parameter a having the units of mol/cm given by [39] ... 

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

The behavior predicted by this equation is illustrated in Fig. 16-33 with N = 80. Xp = (Evtp/L)/[il — )(p K -i- )] is the dimensionless duration of the feed step and is equal to the amount of solute fed to the column divided by tne sorption capacity. Thus, at Xp = 1, the column has been supplied with an amount of solute equal to the station-aiy phase capacity. The graph shows the transition from a case where complete saturation of the bed occurs before elution Xp= 1) to incomplete saturation as Xp is progressively reduced. The lower cui ves with Xp < 0.4 are seen to be neany Gaussian and centered at a dimensionless time - (1 — Xp/2). Thus, as Xp 0, the response cui ve approaches a Gaussian centered at Ti = 1. 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

The performance of demulsifiers can be predicted by the relationship between the film pressure of the demulsifier and the normalized area and the solvent properties of the demulsifier [1632]. The surfactant activity of the demulsifier is dependent on the bulk phase behavior of the chemical when dispersed in the crude oil emulsions. This behavior can be monitored by determining the demulsifier pressure-area isotherms for adsorption at the crude oil-water interface. 

Based on the above, we can develop an "adaptive" Gauss-Newton method for parameter estimation with equality constraints whereby the set of active constraints (which are all equalities) is updated at each iteration. An example is provided in Chapter 14 where we examine the estimation of binary interactions parameters in cubic equations of state subject to predicting the correct phase behavior (i.e., avoiding erroneous two-phase split predictions under certain conditions). 

Given an EoS, the objective of the parameter estimation problem is to compute optimal values for the interaction parameter vector, k, in a statistically correct and computationally efficient manner. Those values are expected to enhance the correlational ability of the EoS without compromising its ability to predict the correct phase behavior. 

If the correct phase behavior i.e. absence of erroneous liquid phase splits is predicted by the EoS then the overall fit should be examined and it should be judged whether it is "excellent". If the fit is simply acceptable rather than "excellent", then the previously computed LS parameter estimates should suffice. This was found to be the case for the n-pentane-acetone and the methane-acetone systems presented later in this chapter. 

If incorrect phase behavior is predicted by the EOS then constrained least squares (CLS) estimation should be performed and new parameter estimates be obtained. Subsequently, the phase behavior should be computed again and if the fit is found to be acceptable for the intended applications, then the CLS estimates should suffice. This was found to be the case for the carbon dioxide-n-hexane system presented later in this chapter. 

As seen from the figure, the stability function does not become negative at any pressure when the hydrogen sulfide mole fraction lies anywhere between 0 and 1. The phase diagram calculations at 311.5 K are shown in Figure 14.11. As seen, the correct phase behavior is now predicted by the EoS. 

Care should be exercised in using the coefficients from Table 4.14 to predict two-liquid phase behavior under subcooled conditions. The coefficients in Table 4.14 were determined from vapor-liquid equilibrium data at saturated conditions. 

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. 

One major question of interest is how much asphaltene will flocculate out under certain conditions. Since the system under study consist generally of a mixture of oil, aromatics, resins, and asphaltenes it may be possible to consider each of the constituents of this system as a continuous or discrete mixture (depending on the number of its components) interacting with each other as pseudo-pure-components. The theory of continuous mixtures (24), and the statistical mechanical theory of monomer/polymer solutions, and the theory of colloidal aggregations and solutions are utilized in our laboratories to analyze and predict the phase behavior and other properties of this system. 

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