The flow of homogeneous fluids through porous media: analogies with other physical problems

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development

Perspectives on biological growth and remodeling

Degradation of alkanes is a widespread phenomenon in nature, and numerous microorganisms, both prokaryotic and eukaryotic, capable of utilizing these substrates as a carbon and energy source have been isolated and characterized. In this review, we summarize recent advances in the understanding of bacterial metabolism of long-chain n-alkanes. Bacterial strategies for accessing these highly hydrophobic substrates are presented, along with systems for their enzymatic degradation and conversion into products of potential industrial value. We further summarize the current knowledge on the regulation of bacterial long-chain n-alkane metabolism and survey progress in understanding bacterial pathways for utilization of n-alkanes under anaerobic conditions.

Bacterial metabolism of long-chain n-alkanes.

Wax formation in oil pipelines: A critical review

The heat equation also shows what a PDE is in general: We are given some kind of relationship between a function u(x,t) and/or its partial derivatives. In the one dimensional case this can be partial derivatives in time t or in space x. The problem is to find functions u(x,t) which satisfy the given relationship and sometimes satisfy additional conditions (initital value conditions or boundary conditions).

The One-Dimensional Heat Equation

In this paper we review a series of mathematical models formulated for the flow of waxy crude oils, that is, of mineral oils with a high content of paraffinic hydrocarbons (with the generic name of waxes) which may be dissolved or segregated as solid crystals at sufficiently low temperatures. The flow takes place in a laboratory test loop. The crystals have a tendency to form aggregates, producing a gel-like structure. The resulting product can be modeled as a Bingham fluid, but its rheological parameters (yield stress and viscosity) depend on the amount and state of the segregated phase, whose evolution is in turn influenced by the flow. Of course temperature plays a key role. Wax can form a solid deposit at the pipe wall, reducing the pipe radius and this phenomenon is also taken into account. The models presented have a different degree of complexity, depending on which phenomena they include. In presenting each of them we discuss their expected range of validity.

https://web.math.unifi.it/users/fusi/ricerca/2004_Meccanica-waxy-survey.pdf

Mathematical Models for Waxy Crude Oils

http://web.math.unifi.it/users/primicer/coldagitato.pdf

Modelling wax diffusion in crude oils: The cold finger device

In this paper we present a novel approach for modelling the lubrication flow of a Bingham fluid in a channel whose amplitude is non uniform. The novelty consists in deriving the rigid plug equation using an integral approach based on Newton’s second law, where the unyielded part is treated as an evolving non material volume. Such an approach leads to an integro-differential equation for the pressure that can be solved with an iterative procedure. We prove that a true unyielded plug exists even when the maximum width variation is not “small” and we find constraints on the amplitude of the channel that prevent the plug from “breaking”. We also extend our model to the case of a pressure-dependent viscosity.

Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach

The mechanical behavior of a mixture composed by an elastic solid and a fluid that exchange mass is investigated. Both the liquid flow and the solid deformation depend on how the solid phase has in...

Mathematical Modeling of a Solid–Liquid Mixture with Mass Exchange Between Constituents

In this paper we will present a model for the flow of a waxy crude oil in a test loop, taking into account deposition mechanisms due to the high content of paraffin. We will analyse the flow in a non-isothermal condition considering the main rheological parameters depending on the radial coordinate of the pipe. We will formulate the related mathematical problem, which will turn out to be a free boundary problem, and perform a quasi-steady approximation for some of the equations involved. For such approximated problem well posedness is proved.

/pdf/on-the-stationary-flow-of-a-waxy-crude-oil-with-deposition-1jp2b6zaji.pdf

Lorenzo Fusi

Papers

Mathematical Models for Waxy Crude Oils

Modelling wax diffusion in crude oils: The cold finger device

Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach

Mathematical Modeling of a Solid–Liquid Mixture with Mass Exchange Between Constituents

On the stationary flow of a waxy crude oil with deposition mechanisms