Adiabatic flash calculations for continuous or semicontinuous mixtures using an equation of state

Chou, Grace F.; Prausnitz, John M.

doi:10.1016/0378-3812(86)80043-7

Cited by 47 publications

(13 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…13 to be the dominant contribution, as conductive effects were relatively small in these simulations. Finally, since all available thermophysical property correlations 25,23 utilize m ␣ , for consistency, two of the primitive variables are now c and X ␣ instead of and the mass fractions,…”

Section: Gas-phase Conservation Equationsmentioning

confidence: 99%

“…For a specified initial PDF, the evolution of the mixture is governed by thermodynamic relationships and/or conservation equations. Moreover, the CT approach was validated by many investigators through successful calculations: ͑i͒ calculations of vapor-liquid equilibrium ͑Rätzsch and Kehlen, 22 Tamim and Hallett 23 ͒, ͑ii͒ computations of liquidliquid equilibrium ͑Rätzsch and Kehlen 22 ͒, ͑iii͒ simulations of polymer solutions ͑Cotterman et al, 18 Rätzsch and Kehlen, 22 Whitson 24 ͒, ͑iv͒ computations of distillation ͑Rätzsch and Kehlen 22 ͒, ͑v͒ flash point calculations ͑Cotter-man et al, 18 Chou and Prausnitz, 25 Whitson 24 ͒, and ͑vi͒ characterization of carbon plus fractions ͑Whitson 24 ͒. Based on the CT approach, Tamim and Hallett 23 and Hallett 26 have developed a model for the evaporation of a single, isolated drop of fuel that is a mixture of very many species.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Direct numerical simulation of a transitional temporal mixing layer laden with multicomponent-fuel evaporating drops using continuous thermodynamics

Clercq

Bellan

2004

Physics of Fluids

View full text Add to dashboard Cite

A model of a temporal three-dimensional mixing layer laden with fuel drops of a liquid containing a large number of species is derived. The fuel model is based on continuous thermodynamics, whereby the composition is statistically described through a distribution function parametrized on the species molar weight. The drop temperature is initially lower than that of the carrier gas, leading to drop heat up and evaporation. The model describing the changes in the multicomponent ͑MC͒ fuel drop composition and in the gas phase composition due to evaporation encompasses only two more conservation equations when compared with the equivalent single-component ͑SC͒ fuel formulation. Single drop results of a MC fuel having a sharply peaked distribution are shown to compare favorably with a validated SC-fuel drop simulation. Then, single drop comparisons are performed between results from MC fuel and a representative SC fuel used as a surrogate of the MC fuel. Further, two mixing layer simulations are conducted with a MC fuel and they are compared to representative SC-fuel simulations conducted elsewhere. Examination of the results shows that although the global layer characteristics are generally similar in the SC and MC situations, the MC layers display a higher momentum-thickness-based Reynolds number at transition. Vorticity analysis shows that the SC layers exhibit larger vortical activity than their MC counterpart. An examination of the drop organization at transition shows more structure and an increased drop-number density for MC simulations in regions of moderate and high strain. These results are primarily attributed to the slower evaporation of MC-fuel drops than of their SC counterpart. This slower evaporation is due to the lower volatility of the higher molar weight species, and also to condensation of already-evaporated species on drops that are transported in regions of different gas composition. The more volatile species released in the gas phase earlier during the drop lifetime reside in the lower stream while intermediary molar weight species, which egress after the drops are entrained in the mixing layer, reside in the mixing layer and form there a very heterogeneous mixture; the heavier species that evaporate later during the drop lifetime tend to reside in regions of high drop number density. This leads to a segregation of species in the gas phase based on the relative evaporation time from the drops. The ensemble-average drop temperature becomes eventually larger/smaller than the initial drop temperature in MC/SC simulations. Neither this species segregation nor the drop temperature variation with respect to the initial temperature or as a function of the mass loading can be captured by the SC-fuel simulations.

show abstract

Section: Gas-phase Conservation Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of a transitional temporal mixing layer laden with multicomponent-fuel evaporating drops using continuous thermodynamics

Clercq

Bellan

2004

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…Although the composition PDF generally depends on many variables, it can be appropriately chosen to depend on one or a restricted number of variables that govern the phenomena under consideration. For example, it has been shown, with validation, that the single-Gamma PDF (SGPDF) depending on the molar mass, m, can represent an entire homologous species class of hydrocarbons (Cotterman et al 1985;Whitson 1983;Rätzsch & Kehlen 1983;Chou & Prausnitz 1986); for other applications, such as the computation of atmospheric hydrocarbon partitioning, the composition PDF was chosen to depend uniquely on the normal boiling point of the species, T b (Harstad 2005). When there is liquid-to-vapour phase change, Cotterman et al (1985) have shown that the same mathematical form of the PDF applies in the gas phase as in the liquid from where the vapour originates.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Clercq

Bellan

2005

J. Fluid Mech.

View full text Add to dashboard Cite

A representation of multicomponent-liquid (MC-liquid) composition as a linear combination of two single-Gamma probability distribution functions (PDFs) is used to describe a large number of MC-liquid drops evaporating in a gas flow. The PDF, called the double-Gamma PDF, depends on the molar mass. The gas-phase conservation equations are written in an Eulerian frame and the drops are described in a Lagrangian frame. Gas conservation equations for mass, momentum, species and energy are combined with differential conservation equations for the first four moments of the gascomposition PDF and coupled to the perfect gas equation of state. Source terms in all conservation equations account for the gas/drop interaction. The drop governing equations encompass differential conservation statements for position, mass, momentum, energy and four moments of the liquid-composition PDF. Simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops colder than the surrounding gas. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. During the layer evolution, the drops heat and evaporate. The results address the layer evolution, and the state of the gas and drops when layers reach a momentum-thickness maximum past the double vortex pairing. Of interest is the influence of the liquid composition on the development of the vortical features of the flow, on the vortical state reached after the second pairing, and on the gas temperature and composition. The MC-liquid simulations are initiated with a single-Gamma PDF composition so as to explore the development of the double-Gamma PDF. Examination of equivalent simulations with n-decane, diesel and three kerosenes as the liquid, permits assessment of the single-species versus the MC-liquid aspect, and of mixture composition specific effects. Global layer growth and global rotational characteristics are unaffected by liquid specificity; however, the global mixing is highly liquid-specific. Also liquidspecific is the evolution of the ensemble-averaged drop characteristics and of the volumetric averages representing the gas composition. Visualized rotational characteristics show that the small-scale vortical activity increases with increased fuel volatility, which is confirmed by analysis of the vorticity budgets. Homogeneous-planeaverage budgets of the vorticity and vorticity-magnitude equations indicate that the stretching and tilting, and momentum-source terms are responsible for the difference among simulations. For all MC liquids, the gas displays a high level of composition heterogeneity, which can directly be traced to the original PDF representing the MC-liquid composition. Under most conditions, the single-Gamma PDF develops into a double-Gamma PDF; however, the extent of this transformation, indicative of vapour condensation onto drops, is not readily parametrized by the liquid volatility, initial carrier-gas temperature or trace vapour in the initial ...

show abstract

“…Multi-component streams are also involved in reactions. Components of 'continuous' mixtures like Crude Oil or Coal or Polymers have been grouped into pseudocomponents for ease of calculations involved in their reactions and separations (Aris and Gavalas 1966;Aris 1989;Glinos and Malone 1984;Chou and Prausnitz 1986;Jacome et al 2005). Lumping philosophy is also used successfully for capturing the essence of complicated mass transfer processes (Sircar and Hufton 2002).…”

Section: Introductionmentioning

confidence: 98%

Multi-component adsorptive separation: use of lumping in PSA process simulation

Mhaskar

Moharir

2011

Adsorption

View full text Add to dashboard Cite

Being a discrete-continuous process, approach to a cyclic steady state in computer simulation of Pressure Swing Adsorption is through iterative procedures and simulation itself is quite computation-intensive. Considering the fact that simulation based design itself is an iterative process, it is imperative that simulation be computationally very efficient and phenomenologically as close to the physics of adsorption-desorption as possible. Utility of lumping the components of a gas mixture into fewer pseudo-components was computationally examined in the simulation of a representative multi-step cycle of a pressure swing based adsorptive separation process applied to natural gas treatment. The actual feed had six components competing for adsorbent sites. Five different lumping alternatives were studied and compared with the simulation results for a full sixcomponent simulation under identical equipment dimensions and operating conditions. Lumping could reduce the number of equations to be solved by more than half and the corresponding reduction in CPU time was about 90%. The six component mixture of Natural Gas was found to be sufficiently represented by two pseudo-components. The predicted recovery (in terms of Methane and Ethane) and quality (in terms of content of higher hydrocarbons) of the raffinate differed by not more than 0.8% and 0.02% respectively. The paper discusses possible heuristics for decision-making regarding appropriate lumping as verified by extensive simulation studies. Nomenclature ACross sectional area of the column, m 2 b i Adsorption equilibrium constant for ith component on the solid surface at the operating temperature, m 3 /moleDiameter of a spherical adsorbent particle or equivalent diameter for a non-spherical particle, m ε External voidage in the bed packed with the adsorbent particles, dimensionless Sphericity factor of the adsorbent particle dtStep size for temporal discretization, s dzStep size for spatial discretization, m L Height of the adsorbent layer packed inside the column, m MW i Molecular weight of ith component, kg/kmole P Absolute Pressure, Pa(a) Q Feed Volumetric feed rate of feed Natural Gas at standard conditions, m 3 /hr at STP conditions q i Average concentration of ith component adsorbed in the volume of adsorbent particles, moles/m 3 solid q imax Maximum monolayer adsorption capacity of ith component on the adsorbent surface, moles/m 3

show abstract

Adiabatic flash calculations for continuous or semicontinuous mixtures using an equation of state

Cited by 47 publications

References 5 publications

Direct numerical simulation of a transitional temporal mixing layer laden with multicomponent-fuel evaporating drops using continuous thermodynamics

Direct numerical simulation of a transitional temporal mixing layer laden with multicomponent-fuel evaporating drops using continuous thermodynamics

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Multi-component adsorptive separation: use of lumping in PSA process simulation

Contact Info

Product

Resources

About