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Percolation in Porous Media

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Encyclopedia of Complexity and Systems Science

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Definition of the Subject

Porous media are important in many areas including hydrocarbon reservoir engineering, hydrology and environmental engineering. They are alsoimportant in, for example, fuel cells, many industrial process and biological systems (lungs, bones, capillary networks and termite nests are allbiological examples). Understanding the structure of porous media and the physics of fluid flow in porous media is of great interest. For example,choosing the efficient recovery techniques by reservoir engineers requires understanding of how different fluids and the porous media interact atdifferent scales by simulating the fluid flow in the reservoir under variety of conditions. The exchange and transport of reagents in fuels cells governstheir efficiency. Percolation theory which describes the connectivity of a system mathematically [22,100] has also many important applications from the spread ofdiseases and forest fires to the connectivity of geological entities (e.?g.,...

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Abbreviations

Anisotropy:

There is anisotropy when the global physical property of the system is direction dependent.

Breakthrough time:

The time for convection of a single phase passive tracer between an injection well and a production well.

Connectivity:

The fraction of occupied sites belonging to the percolating clusters i.?e. represents the strength of the percolating cluster.

Continuum percolation:

Percolation on continuum spaces with randomly distributed geometrical objects where there is no lattice at all.

Capillary dominated flow:

A flow regime in which the only dominant driving force is due to capillarity.

Fracture:

Any discontinuity within a rock mass which developed as a response to stress.

Field scale:

This represents large scale heterogeneities at reservoir level or the kilometer scale.

Finite size scaling:

A scaling law within percolation theory which deals with the effects of the finite boundaries.

Invasion percolation:

Another kind of percolation theory appropriate for describing the structure and amounts of two immiscible fluids at breakthrough.

Modeling:

Describing physical phenomena under nature's law in some mathematical relations, e.?g. governing fluid flow, to better understand the system and to predict its behavior.

Porous media:

A medium consists of rock grains and disordered void spaces of approximately 10–100?µm across usually occupied by oil, water and gas in a typical hydrocarbon reservoir and characterized by porosity and permeability.

Pore scale:

This represents pore throat level or the micron scale.

Permeability:

The “conductance” of the rock to fluid flow determined from Darcy's Law that the flow rate is proportion to the applied pressure gradient and inversely proportional to the fluid viscosity, the constant of proportionality is the permeability.

Percolation threshold:

A particular value of occupancy probability at which one large cluster spans the whole region.

Simulation:

Numerical model for solution to the mathematical equations which be able to predict the physical behavior of the system.

Uncertainty:

The estimated amount or percentage by which an observed or calculated value may differ from the true value.

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Authors and Affiliations

  1. Imperial College London, London, UK

    Peter King

  2. Sharif University of Technology, Tehran, Iran

    Mohsen Masihi

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  1. Peter King
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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King, P., Masihi, M. (2009). Percolation in Porous Media. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_389

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