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Gamma phi method

Gamma-Phi Method for Vapor-Liquid Phase Equilibrium... [Pg.7]

In this method we choose FFF 1 for the components in the vapor (a), but we use one of FFF 2-5 for the components in the liquid ( 3). Therefore, we have four general versions of the gamma-phi method however, at low pressures FFF 2-5 are all equivalent, and we have this one general form ... [Pg.424]

The gamma-phi method has served as the traditional way for solving low-pressme vapor-hquid equilibrimn problems. The elimination of pressure (and hence volmne) from the representation of one phase considerably simplifies the calculations relative to the phi-phi method, though the calculations generally still involve trial-and-error... [Pg.424]

For this low-pressure VLB situation, we choose the gamma-phi method (10.1.4), using fugacity coefficients for the vapor phase and activity coefficients for the liquid phase. In particular, we choose FFF 1 for the vapor and since we are considering only low pressures, any one of FFF 2-5 for the liquid at low pressures, FFF 2-5 are all the same. Then, the gamma-phi equations take the form... [Pg.432]

Figure 11.2 Algorithm for using the gamma-phi method to solve multicomponent bubble-T problems in vapor-liquid equilibrium situations at low pressures [3]... Figure 11.2 Algorithm for using the gamma-phi method to solve multicomponent bubble-T problems in vapor-liquid equilibrium situations at low pressures [3]...
The methods presented in previous sections can be combined to attack multiphase equilibrium problems. To illustrate, we combine the gamma-phi method wi the gamma-gamma method to solve three-phase, vapor-liquid-liquid problems. We again choose to pose these problems as analogies to isothermal flash calculations, as in 11.1.5. Then such problems are well-posed when we have specified values for T independent properties, where T is given by (9.1.12) with S = 0,... [Pg.493]

Gas solubility usually refers to the liquid-phase mole fraction x, that occurs in a VLB situation in which the system temperature T is above the critical temperature of the pure solute (T > Tcil but below the critical temperature of at least one other component (T < Tg ). An example is CO2 dissolved in a carbonated beverage. These situations can be described using either a phi-phi or a gamma-phi approach the gamma-phi method is the traditional approach. [Pg.543]

Therefore for a known concentration x( = 1 - x ) of solute dissolved in the liquid, (12.2.11) can be used to estimate the amount by which the pure-solvent freezing point decreases (AT). (In contrast, boiling point elevations are usually determined from the gamma-phi method, using the Lewis-Randall rule for the solvent and the solute-free Henry s law for the solute.)... [Pg.547]

First, we discuss the phi-phi approach to enthalpies, then we describe the gamma-phi method. [Pg.559]

Gamma-phi method. Instead of phi-phi, we might choose to solve the VLB problem for a flash unit using the gamma-phi method. Then the energy balance (12.4.6) should be written in terms of residual enthalpies for the vapor and excess enthalpies for the liquid. The vapor product enthalpies would still be obtained from the form used in (12.4.8), but liquid phase enthalpies would now be computed by... [Pg.561]

This is a general form of the steady-state energy balance for flash calculations based on the gamma-phi method. Simplifications may occur, depending on the temperatures of the feed and product streams. For example, for an isothermal flash (12.4.16) reduces to... [Pg.561]

This equation is sometimes referred to as the gamma-phi method because it uses the fugacity coefficient... [Pg.424]

For the analytical equations, there are two methods to compute the vapour-liquid equilibrium for systems. The equation of state method (also known as the direct or phi-phi method) uses an equation of state to describe both the liquid and vapour phase properties, whereas the activity coefficient method (also known as the gamma-phi approach) describes the liquid phase via an activity coefficient model and the vapour phase via an equation of state. Recently, there have also been modified equation of state methods that have an activity coefficient model built into the mixing mles. These methods can be both correlative and predictive. The predictive methods rely on the use of group contribution methods for the activity coefficient models such as UNIFAC and ASOG. Recently, there have also been attempts to develop group contribution methods for the equation of state method, e.g. PRSK. " For a detailed history on the development of equations of state and their applications, as well as activity coefficient models, refer to Wei and Sadus, Sandler and Walas. ... [Pg.270]

The gamma-phi and gamma-gamma methods involve activity coefficients, which measure how component fugacities in a real mixture deviate from those in an ideal solution. Many kinds of ideal solutions are available, and yet all have one common attribute every ideal solution has each fugacity linear in its mole fraction. [Pg.428]

Figure 11.6 Double Rachford-Rice algorithm for using the combined gamma-phi and gamma-gamma methods to solve multicomponent (C > 3) vapor-Uquid-Uquid equilibrium problems. This method fails for binary mixtures (C = 2). Figure 11.6 Double Rachford-Rice algorithm for using the combined gamma-phi and gamma-gamma methods to solve multicomponent (C > 3) vapor-Uquid-Uquid equilibrium problems. This method fails for binary mixtures (C = 2).
Cheng, Y.S., Yu, C.C., Tu, K.W. (1994). Intercomparison of activity size distributions of thoron progeny by alpha-and gamma-counting methods. Health Phys. 66, 72-79. [Pg.157]

P. Marmey, M.C. Porte-Durrieu, C. Baquey, PVDF multifilament yarns grafted with polystyrene induced by gamma-irradiation Influence of the grafting parameters on the mechanical properties, Nucl. Instrum. Methods Phys. Res. B 208 (2003) 429-435. [Pg.405]

R.J. Rasmussen, W.S. Fanselow, H.W. Lefevre, M.S. Chmelik, J.C. Overley, A.P. Brown, G.E. Sieger and R.M.S. Schofield, Average atomic number of heterogeneous mixtures from the ratio of gamma to fast-neutron attenuation, Nucl. Instrum. Methods Phys. Res. Sec. A, 124(4) (1997) 611-614. [Pg.154]

Dogue ILJ, Mermilliod N, Foerch R. Grafting of acrylic acid onto polypropylene— Comparison of two pretreatments gamma-irradiation and argon plasma. Nucl Instrum Methods Phys Res B 1995 105(l-4) 164-7. [Pg.40]

Chmielewski, A.G., Chmielewska, D.K., Michalik, J., and Sampa, M.H. 2007. Prospects and challenges in apphcation of gamma, electron and ion beams in processing of nanomaterials. Nucl. Instrum. Methods Phys. Res. B 265 339-346. [Pg.477]

Bertrand GHV, Hamel M, Normand S, Sguerra F (2015) Pulse shape discrimination between (fast or thermal) neutrons and gamma rays with plastic scintillators state of the art. Nucl Instmm Methods Phys Res Sect A Accelerators Spectrometers Detectors Assoc Equip 776 114-128... [Pg.728]

Yanagida T, Roh T, Takahashi H, Hirakuri S, Kokubun M, Makishima K et al (2007) Improvement of ceramic YAG(Ce) scintillators to (YGd)3Al50i2(Ce) for gamma-ray detectors. Nucl Instrum Methods Phys Res Sect A Accelerators Spectrometers Detectors Assoc Equip 579 23-26... [Pg.730]

Simpkin, D.J., A general solution to the shielding of medical X and gamma rays by the NRCP report No. 49 methods, Health Phys., 52, 431, 1987. [Pg.601]

Mahlous, M., Tahtat, D., Benamer, S., and Nacer Khodja, A. 2007. Gamma irradiation-aided chitin/chitosan extraction from prawn shells. Nucl Instrum Methods Phys Res B. 265 414—417. [Pg.21]

Parus JL, Raab W, Donohue D, Deron S (1987) Analysis of Pu containing materials by gamma spectrometry. Inorg Chim Acta 140 283-284 Parus JL, Raab W, Swietly H, Cappis J, Deron S (1992) On the capability of isotope dilution alpha spectrometry in the determination of plutonium concentration. Nucl Instrum Methods Phys Res A 312 278 Parus J, Kierzek J, Raab W, Donohue DL (2003) J Radioanal Nucl Chem 258 123 Parvin D (2007) In JAEA-IAEA workshop on advanced safeguards technology for the future nuclear fuel cycle, Tokai-mura... [Pg.3012]

FIG U RE 1.21 High-resolution gamma spectrum of a UF,5 cylinder containing low-enriched manium (4.4% of acquired during a period of 3.8 h. The photons emitted from the sample at different energy ranges (a) 80-240 keV, (b) 500-950 keV, and (c) 1160-1380 keV. (From Croft, S. et al., Nucl. Instrum. Methods Phys. Res. A, 698,192, 2013. With permission.)... [Pg.48]

Croft, S., Swinhoe, M.T., and Miller, K.A. (2013). Alpha particle induced gamma yields in uranium hexafluoride, Nucl. Instrum. Methods Phys. Res. A 698, 192-195. [Pg.61]


See other pages where Gamma phi method is mentioned: [Pg.421]    [Pg.424]    [Pg.424]    [Pg.425]    [Pg.425]    [Pg.470]    [Pg.486]    [Pg.559]    [Pg.639]    [Pg.421]    [Pg.424]    [Pg.424]    [Pg.425]    [Pg.425]    [Pg.470]    [Pg.486]    [Pg.559]    [Pg.639]    [Pg.478]    [Pg.479]    [Pg.486]    [Pg.519]    [Pg.520]    [Pg.56]    [Pg.328]    [Pg.3012]    [Pg.138]    [Pg.203]   
See also in sourсe #XX -- [ Pg.432 , Pg.470 ]




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