Ice sheet modelling taking account of glacier ice compressibility

A mathematical treatment of the theory of glacier dynamics in relation to subsurface firn thickness, compressibility and the effects of densification. The analysis provides a theoretical basis for investigating heat and mass transfer processes in ice sheets with allowance for compressibility effects. -K.Clayto

Numerical scheme for non-linear model of supercritical fluid extraction from polydisperse ground plant material: Single transport system

© Published under licence by IOP Publishing Ltd.Numerical algorithm is developed for modelling non-linear mass transfer process in supercritical fluid extraction (SFE). The ground raw material is considered as polydisperse, characterized by discrete number of effective particle fractions. Two continuous interacting counterparts separated by permeable membrane are distinguished in plant material build-up. The apoplast plays role of transport channels during extraction, and symplast contains extractable oil. The complete SFE model is non-linear as a result of non-linearity of oil dissolution kinetics. The computational scheme is based on the finite-volume approximation method and Thomas elimination procedure. The resulting system of algebraic equations is solved iteratively. Special attention is paid to polydisperse substrates, when particle scale characteristics of all fractions interact with each other through pore phase concentration on the vessel scale. Stability of the developed algorithm is demonstrated in numerical tests. Special iterative procedure guarantees a monotonic decrease of oil content in individual particles of substrate. It is also shown that in the limit of the so-called shrinking core approach the number of mesh nodes on a particle scale should be increased

MEAN DESCRIPTION OF HEAT-TRANSFER PROCESSES IN FILTRATION IN CRACKED AND POROUS MEDIA.

On the basis of the method of averaging differential equations with rapidly oscillating coefficients, a mean equation describing the heat transfer in a filtering cracked medium is constructed. The effective transfer coefficients are calculated, and compared with experimental data

Bidisperse Shrinking Core Model for Supercritical Fluid Extraction

© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. The broken-and-intact-cell model is conventionally used for interpretation of overall extraction curves (OECs) observed in supercritical fluid extraction (SFE) of ground oilseeds. Another possibility, considered here, assumes that the packed beds of the ground material always contain a significant amount of very small particles, i.e., dust, which control the initial extraction rates. The bidisperse representation of particle ensembles allows accurate description of OECs on the basis of the modified shrinking core model. A simple asymptotic solution has been derived for bidisperse granulometric distributions under typical SFE conditions. Special microscopic observations have been performed to reveal and examine the dust fraction in ground seed substrates

Optimization of supercritical fluid extraction: Polydisperse packed beds and variable flow rates

© 2015 Elsevier B.V. This theoretical study examines variable-in-time flow rates v(t) and different ways of packing polydisperse ensemble of ground particles as controls in supercritical fluid extraction (SFE) to maximize the extraction yield. The so-called packing function χ is introduced to describe the local particle-size distribution in the pack along the extraction vessel. The research is based on the modified shrinking-core (SC) model for the mass transfer inside particles and assumes the pseudo-steady solvent flow in the SFE vessel. It is rigorously proven that for any variable flow rate v(t) and overall particle-size distribution F, the corresponding locally-monodisperse stratified (LMS) packing χ 0 maximizes the current amount of extracted solute, while the appropriate filtration policy extends the domain of efficient particle-size distributions. Sufficient conditions that guarantee a certain extraction degree at a fixed time are deduced and formulated in terms of F-distribution. Being of obvious practical significance for finely ground substrates, optimization is shown to be rather limited for relatively big particles (commonly used in laboratory experiments), and only longer extraction times, higher oil solubility and diffusion rates allow noticeable increase in the extraction yield in this case

Optimization of supercritical fluid extraction: Polydisperse packed beds and variable flow rates

© 2015 Elsevier B.V. This theoretical study examines variable-in-time flow rates v(t) and different ways of packing polydisperse ensemble of ground particles as controls in supercritical fluid extraction (SFE) to maximize the extraction yield. The so-called packing function χ is introduced to describe the local particle-size distribution in the pack along the extraction vessel. The research is based on the modified shrinking-core (SC) model for the mass transfer inside particles and assumes the pseudo-steady solvent flow in the SFE vessel. It is rigorously proven that for any variable flow rate v(t) and overall particle-size distribution F, the corresponding locally-monodisperse stratified (LMS) packing χ 0 maximizes the current amount of extracted solute, while the appropriate filtration policy extends the domain of efficient particle-size distributions. Sufficient conditions that guarantee a certain extraction degree at a fixed time are deduced and formulated in terms of F-distribution. Being of obvious practical significance for finely ground substrates, optimization is shown to be rather limited for relatively big particles (commonly used in laboratory experiments), and only longer extraction times, higher oil solubility and diffusion rates allow noticeable increase in the extraction yield in this case