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@inproceedings{Westbroek:2016:10.3997/2214-4609.201601856,
author = {Westbroek, MJE and King, PR and Vvedensky, DD},
doi = {10.3997/2214-4609.201601856},
title = {Path Integral Method for Flow through Random Porous Media},
url = {http://dx.doi.org/10.3997/2214-4609.201601856},
year = {2016}
}

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TY - CPAPER
AB - One of the key problems in modelling flow in oil reservoirs is our lack of precise knowledge of the variations in flow properties across the field. At best we can infer the statistics of these variations from field observations. The challenge is to determine the statistics of the flow itself (flow rates, pressures etc.) from the statistics of the permeability variations. Conventional simulations are computationally very expensive unless smart sampling techniques or surrogate models are used. In this paper we demonstrate the use of a path integral formulation for this problem. To demonstrate how this methods works, we start with the one dimensional Darcy flow problem: q(x)=-K(x)dp(x)/dx where p(x) is the pressure, q(x) is the flow rate and K(x) is the rock permeability. The randomness of the porous medium is modelled by regarding K as a stochastic quantity which is assumed to follow Gaussian statistics. Because of the randomly varying rock structure, there is a variety of conceivable pressure realisations p(x). The path integral Z is an integral over all realisations with an appropriate probability measure. Once Z is evaluated, either analytically, or by standard Monte Carlo methods, any observable of interest, including pressure correlations can be easily obtained.
AU - Westbroek,MJE
AU - King,PR
AU - Vvedensky,DD
DO - 10.3997/2214-4609.201601856
PY - 2016///
TI - Path Integral Method for Flow through Random Porous Media
UR - http://dx.doi.org/10.3997/2214-4609.201601856
ER -

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