1、Retrospective Theses and Dissertations1991Phase equilibrium simulation and its application incrystallization processesWeixin SongIowa State UniversityFollow this and additional works at: http:/lib.dr.iastate.edu/rtdPart of the Chemical Engineering CommonsThis Dissertation is brought to you for free
2、and open access by Iowa State University Digital Repository. It has been accepted for inclusion inRetrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, pleasecontact digirepiastate.edu.Recommended CitationSong, Weixin
3、, “Phase equilibrium simulation and its application in crystallization processes “ (1991). Retrospective Theses andDissertations. 10069.http:/lib.dr.iastate.edu/rtd/10069INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original
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8、. Contact UMI directly to order. University Microfilms International A Bell 2. Concentrating fruit juices (food industry); 3. Purifying organic chemicals (pharmaceutical industry). Basic techniques used are as follows: a solution is cooled to below its freezing point and pure ice is formed, concentr
9、ating the solution. Depending on the degree of concentration the process may result in precipitation of dissolved salts. The advantage of the freezing concentration technique is that it is an energy-saving process. The energy involved in freezing one pound of water is of the order of 150 BTU, for bo
10、iling is of the order of 1,000 BTU. Furthermore, corrosion problems are minimized since it operates at low temperatures. As an example, CBI Freeze Technologies, Inc., Plainfield, 111., developed the first FC unit for treating hazardous wastewater in early April, 1988. The process is capable of treat
11、ing aqueous wastes containing reactive ions, metals, and organics with 1 - 10 wt% solids. The wastewater is precooled to the freezing point. The ice in the concentrated slurry is separated 2 and melted to produce pure water. The remaining liquor is either recycled for more ice formation or removed a
12、s a concentrated stream. If concentration is such that it becomes supersaturated in its solutes, provision is made to cause crystallization to take place separately from the ice formation. The thermodynamic basis of those crystallization processes is the phase equilib rium. Since the phase diagrams
13、of multicomponent systems are usually not available and experimental determination is extremely tedious, a computer simulation scheme is employed. It is based on the thermodynamic theory that states that the Gibbs free energy of the system at equilibrium is at its minimum value. From the above discu
14、ssion, it is clear that an accurate thermodynamic model for predicting the Gibbs free energy of the system and an effective mathematical procedure for finding the minimum of the Gibbs free energy is necessary so that the computer simulation of the system phase equilibrium can be carried out. The lit
15、er ature review of the thermodynamic models and the phase equilibrium computation algorithms is given below. Review Of the Thermodynamic Model for Gibbs Free Energy and Activity Coefficient Of Concentrated Electrolyte Solutions The peculiarities of strong electrolyte solutions were a major puzzle to
16、 physical chemists in the first two decades of this century. In 1923 Debye and Huckel proposed their solution theory and obtained the simple limiting law that resolved the primary puzzle (see Appendix A.). The complete Debye-Huckel model is useful up to ionic strength of 0.1 m with one adjustable pa
17、rameter. An empirical linear form in ionic strength can be added and the modified model can obtain good representation up to 3 2 m with two adjustable parameters. It was not until the last two decades, owing to the development of molecular ther modynamics, that the prediction of thermodynamic proper
18、ties of mixed electrolyte solutions at high concentrations became possible. Among those, the following four models have gained success in different applications: The extended Pitzers model (Virial form) (Pitzer, 1973); The NRTL model of Cruz and Renon (Cruz and Renon, 1978); The NRTL model of Chen (
19、Chen et al., 1982); The UNIQUAC model of Sander (Sander et al., 1986a,b). Generally speaking, all solution models assume certain forms of excess Gibbs free energy. The thermodynamic properties of the solution can then be obtained from derivatives of the excess Gibbs free energy. The excess Gibbs fre
20、e energy of the electrolyte solutions is usually assumed to be the summation of the excess Gibbs free energy of different contributions: 1. Long-range interactions; 2. Short-range interactions; 3. The concentration dependence of dielectric constants. The four models mentioned above also can be calle
21、d primitive models because they all use an extended Debye-Huckel model to express long-range interactions. The different contributions of these four models are compared in Table 1. The equation of state model (a nonprimitive model), will be discussed later. Table 1: Comparison of different models Mo
22、del Long-range Short-range Dielectric constant Pitzer Extended DH (Pitzer, 1973) Extended DH Virial No Renon NRTL Debye-McAulay (Earned and Owen,1958) No No Chen Sander (Fowler and Guggenheim, 1956) Extended DH as Pitzer Extended DH (Sander et al., 1986a) NRTL UNIQUAC Pitzers Model Since Pitzer and
23、his coworkers proposed the extended virial model in 1973, it has been applied to predict various thermodynamic properties of electrolyte systems. The simple analytical form of the equation gives a quantitative representation of all reliable and available activity and osmotic coefficient data of stro
24、ng electrolytes. The accuracy is usually good up to 6 molality. The model can be readily extended to complex electrolyte mixtures using binary and common-ion ternary parameters. Pitzer (1979) compiled an extensive database for the 25C binary and ternary model parameters. The first-order temperature
25、derivatives of the binary parameters were also listed for many systems. However, the model assumes complete dissociation of the solute, water as the major solvent. Two extensions of the Pitzers model have been made by Beutier and Renon (1978) and Chen et al. (1979) for the calculation of vapor-liqui
26、d equilibrium involving molecular solutes. Some problems have been discovered in determining density with this model. Fitting density data of the CaCl2, NaCl and their mixture, Kumar et al. (1983) 5 found that fit for CaCl2 was distinctly inferior. This problem has also been observed in fitting the
27、activity coefficients of CaCl2 above 5 molal (Phutela and Pitzer, 1983). This is due to the fact that the hydration sphere of the ion is changing in the concentration range above 1 m. There is no simple way this can be accommodated in the theory. Actually, Pitzer did not distinguish the hard-core ef
28、fect and the hydration effect that made the model very empirical. Despite some limitations, Pitzers model remains the most widely used. Harvie and Weare (1980) applied Pitzers model to the prediction of mineral solubilities in natural waters at 25C with great success. Following their work, a series
29、of articles have been published that predict mineral solubilities within temperature ranges of - 54 to 250C and at pressures up to 1 kbar (Harvie, Moller and Weare, 1984; Felmy and Weare, 1986; Pabalan and Pitzer, 1987; Moller, 1988; Greenberg and Moller, 1989; Spencer, Moller and Weare, 1990; Monni
30、n, 1990). Monnin (1989) applied Pitzers model to calculate density and partial molal volumes of natural waters. The author concluded that the Pitzer model gave good accuracy at moderate concentration using only the binary parameters. The accuracy decreased at higher concentration because ternary par
31、ameters could not be obtained with reasonable confidence and therefore were not used. The Pitzer model has also been used to calculate the activity coefficients of the supersaturated solutions (Sohnel, Garside and Jancic, 1977; Sohnel and Garside, 1979) with the assumption that there is no discontin
32、uity in water activity between the saturation and the supersaturation region. These applications demonstrated the capability of the Pitzer model. It is proba bly the most suitable model for engineers dealing with aqueous electrolyte solutions. 6 NRTL (Non-Random Two Liquid) Model All parameters in t
33、he Pitzers model are empirical. Binary parameters are em pirical functions of ionic strength and ternary parameters are necessary at high con centration and for mixtures. Since Pitzers model is based on a virial expansion, it is subject to all the limitations of a virial model. Pitzers equation cann
34、ot be used for a mixed solvent system because its parameters are unknown functions of solvent composition. To apply the thermodynamic model to a mixed solvent and a system involving molecular species, another approach was proposed based on the NRTL model of nonelectrolyte solutions (Cruz and Renon,
35、1979; Chen et al., 1982). Although both models use the NRTL approach for short-range interactions, the difference between the work of the two is that different assumptions were used. Cruz and Renon assumed the complete solvation of all solutes; Chen et al. adopted Bron-steds principle of specific in
36、teraction, which states that there would be specific inter actions only between ions of the opposite sign (like-ion repulsion), and the distribution of anions and cations around a neutral molecule is such that the net charge is zero. As for long-range interactions, Chen used the same extended Debye-
37、Huckel model as Pitzer did. Cruz and Renon followed the extension of Debye-Huckel model made by Fowler and Guggenheim (1956), and considered the concentration depen dence of the dielectric constant. The concentration dependence of the dielectric constant is expressed as Born or Debye and McAulay the
38、ory (Harned and Owen, 1958). The comparison of Pitzer equation to Chens NRTL and modified Cruz and Renons NRTL was given by Ball and Renon (1985). In both single electrolyte and mixture cases (single solvent water), best fit was achieved with Pitzers model (trun cated with only binary parameters use
39、d). Both NRTL models gave similar accuracy. The advantage of NRTL models, however, is that they are more flexible and easy to handle mixed solvents and systems including molecules as well as ions. Chen and coworkers have applied Chens NRTL model to calculate the phase equilibrium of amino acids (Che
40、n et al., 1989) and antibiotics (Zhu et al., 1990) with success. In 1989, Liu et al. (1989a,b) proposed an activity coefficient model for electrolyte solutions, which goes beyond previous models because it is based on a theoretically improved combination of the Debye-Huckel theory and the local-comp
41、osition (NRTL) concept. Recall that all the models consider the long-range and short-range interac tions independent of each other. The new model gives appropriate attention to the effect of the short-range interaction on long-range interaction and vice versa. The parameters are ion-specific, not el
42、ectrolyte-specific. The unique feature of the Liu et al.s model is their modification of the Debye-Huckel expression. The Debye-Huckel expression used in previous models gives the interactions between each central ion and all the other ions in the solution. The Debye-Huckel expression of Liu et al.
43、gives only the interactions between each central ion and ions outside the first coordi nation shell. The interactions of ions inside the first coordinate shell are considered in the NRTL expression (see Figure 1). The dielectric constant, D, of the solution is assumed to be a function of the water m
44、ole fraction D = 31.65 + 46.65a;ti) The disadvantage of NRTL model is that the parameters are not in linear form. 8 O Boundary of the first coordination shell Figure 1: Long-range and short-range interaction in Liu et al. model This leads to some difficulties in data treatment. The parameters are ge
45、nerally strongly correlated; the initial values may influence the final correlation; and mul tiple roots exist. Therefore there is some uncertainty about the best values of the parameters. UNIQUAC (Universal Quasi Chemical Theory) Model An interesting fact drawn from the above discussion of the diff
46、erent kind of models is that the major distinction between them is the way short-range interactions are handled, which is related to the interactions within the non-electrolyte system. The basis of the virial or NRTL idea is really taken from non-electrolyte VLE (Vapor-9 Liquid Equilibrium) predicti
47、ons. All the successful VLE models can be incorporated into the electrolyte system in a suitable way. In 1986, Sander et al. (1986a) proposed the UNIQUAC model. The excess Gibbs function is assumed to be the sum of two contributions, the Debye-Huckel type for long-range and modified UNIQUAC for shor
48、t-range interactions. The Debye-Huckel equation was generalized to handle mixed solvents. The application to the VLE and SLE (A“ Mg H2O phase equilibrium) yields good results (Sander et al., 1986b). The extension of the UNIQUAC model has been made by Rennotte et al. (1988, 1989). The Debye-McAulay t
49、heory was added and a new correlation of the concentration dependence of dielectric constant is proposed: A + DiuY with A 2/3(Dw jDqj), is a constant and Dw is dielectric constant of pure water. Equation of State for Electrolyte Solutions The most recently published thermodynamic model for aqueous electrolyte so lutions containing multiple salts is an equation of state model by Jin and Donohue (1991). Unlike the previous models, this equation of state model uses only one ad justable parameter for each ion that must be determined from all available bi
