Scaling Laws and Fokker--Planck Equations for 3-Dimensional Porous Media with Fractal Mesoscale

2005 ◽  
Vol 4 (4) ◽  
pp. 1233-1244 ◽  
Author(s):  
Moongyu Park ◽  
Natalie Kleinfelter ◽  
John H. Cushman
Keyword(s):  
Porous Media ◽  
Scaling Laws ◽  
3 Dimensional ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals CO2 Convective Dissolution in Oil-Saturated Unconsolidated Porous Media at Reservoir Conditions

Energies ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 233
Author(s):  
Widuramina Amarasinghe ◽  
Ingebret Fjelde ◽  
Nils Giske ◽  
Ying Guo
Keyword(s):  
Porous Media ◽  
Crude Oil ◽  
Water Solution ◽  
Co2 Storage ◽  
Bromothymol Blue ◽  
Power Relationship ◽  
Dimensionless Time ◽  
3 Dimensional ◽  
Reservoir Conditions ◽  
Unconsolidated Porous Media

During CO2 storage, CO2 plume mixes with the water and oil present at the reservoir, initiated by diffusion followed by a density gradient that leads to a convective flow. Studies are available where CO2 convective mixing have been studied in water phase but limited in oil phase. This study was conducted to reach this gap, and experiments were conducted in a vertically packed 3-dimensional column with oil-saturated unconsolidated porous media at 100 bar and 50 °C (representative of reservoir pressure and temperature conditions). N-Decane and crude oil were used as oils, and glass beads as porous media. A bromothymol blue water solution-filled sapphire cell connected at the bottom of the column was used to monitor the CO2 breakthrough. With the increase of the Rayleigh number, the CO2 transport rate in n-decane was found to increase as a function of a second order polynomial. Ra number vs. dimensionless time τ had a power relationship in the form of Ra = c×τ−n. The overall pressure decay was faster in n-decane compared to crude oil for similar permeability (4 D), and the crude oil had a breakthrough time three times slower than in n-decane. The results were compared with similar experiments that have been carried out using water.

scholarly journals Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180131 ◽  
Author(s):  
Luca Giuggioli ◽  
Zohar Neu
Keyword(s):  
Langevin Equation ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Delay Systems ◽  
Langevin Equations ◽  
Delayed Systems ◽  
Temporal Features ◽  
Fokker Planck Equations ◽  
Random Fluctuations ◽  
Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n  = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

Modified Fokker-Planck equations

1978 ◽  
Vol 36 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Glenn T. Evans
Keyword(s):  
Fokker Planck Equations ◽  
Fokker Planck
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