Migration from plastic packages into their contents. I. The role of mathematical models

1995 ◽  
Vol 350 (1694) ◽  
pp. 379-406 ◽  
Keyword(s):  
Mass Transfer ◽  
Mathematical Models ◽  
Diffusion Coefficients ◽  
Unit Area ◽  
Detailed Examination ◽  
Diffusion Equations ◽  
Legal Regulations ◽  
Successful Model ◽  
Plastic Packages

Materials contained in plastic packages can transfer (migrate) into the contents. In some circumstances, such as packages of food, drink or medicine, the consequences of this migration can be unpleasant or even harmful. Many countries, and the European Community, have adopted legal regulations designed to limit the amount of migration. It is shown, partly by discussing one example in some detail, that certain quantitative criteria in such regulations are unsatisfactory. The reasons include ( a ) improper recognition of the importance of package geometry, ( b ) invalid assumptions about a correspondence between concentrations in the contents and mass transfer per unit area of the package-contents interface and ( c ) failure to account, in an adequate manner, for the inevitable variability between nominally identical package systems. The principal theme of the paper is that these faults could have been, and can be, substantially ameliorated by proper use of mathematical models. Common shortcomings in the previous (but very limited) use of mathematics are exposed partly by detailed examination of a recent research paper. The paper discusses the requirements of a successful model and considers the simplest type, namely diffusion equations with diffusion coefficients that are independent of the concentrations of the migrant in either the plastic or the contents. Particular solutions are chosen to illustrate faults in existing legislation and practice, and because they are thought to be good candidates for testing against data. It is argued that future experiments would be more successful and more useful if they were planned and conducted in teams involving mathematicians.

An Experimental Investigation of Mass Transfer in Tight Dual-Porosity Systems

2021 ◽  
Author(s):  
Saeed Alahmari ◽  
Kristian Jessen
Keyword(s):  
Mass Transfer ◽  
Binary Mixtures ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Gas Injection ◽  
Fluid Exchange ◽  
Fluid System ◽  
Diffusive Mass Transfer ◽  
Displacement Experiments

Abstract During gas injection in ultra-tight fractured reservoirs, molecular diffusion can play a dominant role in the mass transfer process and enhance recovery by extracting oil components from matrix and delaying gas breakthrough. There has been a growing interest from scholars and operators to study the effect of diffusive mass transfer on the potential incremental recovery from CO2 and rich gas injection. However, many fundamental questions pertaining to the physics of multicomponent multiphase flow and transport are still left unanswered. This paper aims to improve the understanding of multicomponent diffusive mass transfer between matrix and fracture blocks through experimental and modeling work. Displacement experiments were carried out using analog fluids and mesoporous medium to effectively isolate and study the relevant physical mechanisms at play. The experiments were performed in packed columns utilizing silica-gel particles that have internal porosity. The particle size is 40-70 micron with highly controlled internal pore size of 6 nm that makes up approximately 50% of the overall porosity. The quaternary analog fluids system consists of Water, Methanol, Isopropanol, and Isooctane, was used because it mimics the phase behavior of CO2, Methane, Butane and Dodecane mixtures at 2,280 psi and 100°C. Our selection of the analog fluid system and porous medium allowed us to investigate matrix-fracture fluid exchange as observed during an enhanced recovery operation in an ultra-tight fractured system. The effluents from these displacement experiments served as the basis for our analysis of diffusive mass transfer. The role of molecular diffusion in the displacement experiments was investigated by first performing separate diffusion experiments to obtain diffusion coefficients for all relevant binary mixtures. Infinite dilution diffusion coefficients were measured for all binary mixtures and then used to model binary and multicomponent diffusion coefficients over the whole composition range. The accuracy of this approach was determined by performing additional binary diffusion experiments over a broader range of compositions. The displacement experiments were simulated using an in-house simulator and excellent agreement was obtained: The extensive experimental/modeling work related to the diffusion coefficients of the analog fluid system was used in interpreting the diffusive mass transfer between the matrix (stagnant) and fracture (flowing) domains via a 1D linear model. The presented work provides new insights into the role of diffusive mass transfer in ultra-tight fractured systems and builds a framework to highlight the critical data needed to effectively characterize and simulate recovery from such complex geological settings.

ROLE OF FLOW AND MASS TRANSFER IN PHOTOBIOREACTOR: FROM BACTERIA LOCOMOTION TO HYDROGEN PRODUCTION

2018 ◽  
Author(s):  
Xun Zhu ◽  
Qiang Liao ◽  
Rong Chen ◽  
Ao Xia ◽  
Chao Zhang ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Hydrogen Production

Organisational aspects of spatial information infrastructure in Poland

2013 ◽  
Vol 62 (1) ◽  
pp. 85-95 ◽  
Author(s):  
Elzbieta Bielecka ◽  
Agnieszka Zwirowicz-Rutkowska
Keyword(s):  
Spatial Information ◽  
Information Infrastructure ◽  
Class Diagram ◽  
Use Case ◽  
Legal Regulations ◽  
Organisational Structure ◽  
Technical Aspects ◽  
Polish Law

Abstract One of the more important elements of spatial information infrastructure is the organisational structure defining the obligations and dependencies between stakeholders that are responsible for the infrastructure. Many SDI practitioners and theoreticians emphasise that its influence on the success or failure of activities undertaken is significantly greater than that of technical aspects. Being aware of the role of the organisational structure in the creating, operating and maintenance of spatial information infrastructure (SII), Polish legislators placed appropriate regulations in the Spatial Information Infrastructure Act, being the transposition of the INSPIRE Directive into Polish Law. The principal spatial information infrastructure stakeholders are discussed in the article and also the scope of cooperation between them. The tasks and relationships between stakeholders are illustrated in UML, in both the use case and the class diagram. Mentioned also are the main problems and obstructions resulting from imprecise legal regulations.

The role of (bio)surfactant sorption in promoting the bioavailability of nutrients localized at the solid-water interface

1999 ◽  
Vol 39 (7) ◽  
pp. 91-98 ◽  
Author(s):  
Ryan N. Jordan ◽  
Eric P. Nichols ◽  
Alfred B. Cunningham
Keyword(s):  
Mass Transfer ◽  
Cell Membrane ◽  
Substrate Concentration ◽  
Water Interface ◽  
Industrial Systems ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Surfactant Sorption

Bioavailability is herein defined as the accessibility of a substrate by a microorganism. Further, bioavailability is governed by (1) the substrate concentration that the cell membrane “sees,” (i.e., the “directly bioavailable” pool) as well as (2) the rate of mass transfer from potentially bioavailable (e.g., nonaqueous) phases to the directly bioavailable (e.g., aqueous) phase. Mechanisms by which sorbed (bio)surfactants influence these two processes are discussed. We propose the hypothesis that the sorption of (bio)surfactants at the solid-liquid interface is partially responsible for the increased bioavailability of surface-bound nutrients, and offer this as a basis for suggesting the development of engineered in-situ bioremediation technologies that take advantage of low (bio)surfactant concentrations. In addition, other industrial systems where bioavailability phenomena should be considered are addressed.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Kolmogorov and classic diffusion equations

1988 ◽  
Vol 53 (6) ◽  
pp. 1181-1197
Author(s):  
Vladimír Kudrna
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Parabolic Type ◽  
Diffusion Equations ◽  
Stochastic Motion ◽  
Energy Component ◽  
Classic Form

The paper presents alternative forms of partial differential equations of the parabolic type used in chemical engineering for description of heat and mass transfer. It points at the substantial difference between the classic form of the equations, following from the differential balances of mass and enthalpy, and the form following from the concept of stochastic motion of particles of mass or energy component. Examples are presented of the processes that may be described by the latter method. The paper also reviews the cases when the two approaches become identical.

Pieces of Mind

2018 ◽  
Author(s):  
Carrie Figdor
Keyword(s):  
Mathematical Models ◽  
Moral Status ◽  
Entire Range ◽  
Fruit Flies ◽  
Literal Interpretation ◽  
Psychological Capacities

Many people accept that chimpanzees, dolphins, and some other animals can think and feel. But these cases are just the tip of a growing iceberg. If biologists are right, fruit flies and plants make decisions, worms and honeybees can be trained, bacteria communicate linguistically, and neurons have preferences. Just how far does cognition go? This book is the first to critically consider this question from the perspective of the entire range of new ascriptions of psychological capacities throughout biology. It is also the first to consider the role of mathematical models and other quantitative forms of evidence in prompting and supporting the new ascriptions. It defends a default literal interpretation of psychological terms across biological domains. It also considers the implications of the literal view for efforts to explain the mind’s place in nature and for traditional ways of distinguishing the superior moral status of humans relative to other living beings.

scholarly journals Catalytic Systems Based on Cp2ZrX2 (X = Cl, H), Organoaluminum Compounds and Perfluorophenylboranes: Role of Zr,Zr- and Zr,Al-Hydride Intermediates in Alkene Dimerization and Oligomerization

Catalysts ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 39
Author(s):  
Lyudmila V. Parfenova ◽  
Pavel V. Kovyazin ◽  
Almira Kh. Bikmeeva ◽  
Eldar R. Palatov
Keyword(s):  
Diffusion Coefficients ◽  
Organoaluminum Compounds ◽  
Zirconium Hydride ◽  
Nmr Studies ◽  
Catalytic Systems ◽  
Selective Formation

The activity and chemoselectivity of the Cp2ZrCl2-XAlBui2 (X = H, Bui) and [Cp2ZrH2]2-ClAlEt2 catalytic systems activated by (Ph3C)[B(C6F5)4] or B(C6F5)3 were studied in reactions with 1-hexene. The activation of the systems by B(C6F5)3 resulted in the selective formation of head-to-tail alkene dimers in up to 93% yields. NMR studies of the reactions of Zr complexes with organoaluminum compounds (OACs) and boron activators showed the formation of Zr,Zr- and Zr,Al-hydride intermediates, for which diffusion coefficients, hydrodynamic radii, and volumes were estimated using the diffusion ordered spectroscopy DOSY. Bis-zirconium hydride clusters of type x[Cp2ZrH2∙Cp2ZrHCl∙ClAlR2]∙yRnAl(C6F5)3−n were found to be the key intermediates of alkene dimerization, whereas cationic Zr,Al-hydrides led to the formation of oligomers.

Laboratory Experiments of Mass Transfer in the London Clay

1988 ◽  
Vol 127 ◽  
Author(s):  
P. J. Bourke ◽  
D. Gilling ◽  
N. L. Jefferies ◽  
D. A. Lever ◽  
T. R. Lineham
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Radioactive Waste ◽  
Mass Transport ◽  
Mathematical Models ◽  
Laboratory Experiments ◽  
Naturally Occurring ◽  
Diffusion And Convection ◽  
Waste Repository ◽  
London Clay

ABSTRACTAqueous phase mass transfer through the rocks surrounding a radioactive waste repository will take place by diffusion and convection. This paper presents a comprehensive set of measurements of the mass transfer characteristics for a single, naturally occurring, clay. These data have been compared with the results predicted by mathematical models of mass transport in porous media, in order to build confidence in these models.

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