Fractional model equation for anomalous diffusion

Metzler, Ralf; Glöckle, W.; Nonnenmacher, T. F.

doi:10.1016/0378-4371(94)90064-7

Cited by 424 publications

(231 citation statements)

References 11 publications

Supporting

Mentioning

222

Contrasting

Unclassified

Order By: Relevance

“…Analogously, in quantum gravity one could interpret the fractional diffusion equation with α = 1 as a diffusion equation on a fractal spacetime; this is the case of QEG, for instance, where α = 1 and spacetime does have fractal properties. The introduction of a nontrivial measure weight v(x) in position space further changes the background geometry and topology, as happened in some first attempts to generalize the diffusion equation to fractals [74][75][76].…”

Section: A Solution Scheme and Probabilistic Interpretation For S =mentioning

confidence: 99%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

View full text Add to dashboard Cite

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples, and the most general spectral-dimension profile of multifractional spaces is constructed.

show abstract

Section: A Solution Scheme and Probabilistic Interpretation For S =mentioning

confidence: 99%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

View full text Add to dashboard Cite

show abstract

“…Based on the same approach given by Metzler et al [9], the fractional form of differential equation for the transfer of fluid from matrix to fracture under restricted flow condition (the matrix response is slower) can be written as:…”

Section: þmentioning

confidence: 99%

“…Applying the same approach used by Metzler et al [9], based on the concepts of fractal geometry and FC, the dimension-less FFD model in naturally fractured reservoirs can be written as:…”

Section: þmentioning

confidence: 99%

“…In fractally fractured reservoirs, history of flow and nonlocality are pivotal in all stages of production. Metzler et al [9] applied a fractional derivative approach to fractal model to incorporate the memory.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, in the last two decade petroleum engineering has been impressed by FC. Several authors used the concept of FC to describe the complexity of diffusion process in porous media [9][10][11]. These researchers developed a mathematical model to define the response of oil reservoirs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

Razminia

Machado

2014

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

show abstract

Some Applications of Fractional Calculus to Polymer Science

Douglas¹

1997

Advances in Chemical Physics

View full text Add to dashboard Cite

Fractional model equation for anomalous diffusion

Cited by 424 publications

References 11 publications

Diffusion in multiscale spacetimes

Diffusion in multiscale spacetimes

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

Some Applications of Fractional Calculus to Polymer Science

Contact Info

Product

Resources

About