Multiscale characterization of effective conductivity of random heterogeneous porous media: multiple versus single realization approaches.

ALEJANDRO OTERO; ALEJANDRO BOSCHAN; COLECCHIO PUA I; NOETINGER B

Valencia

Congreso; InterPore2019 Valencia; 2019

International Society for Porous Media

Most porous natural or synthetic materials possess a multiscale structure that have a major impacton large scale transport properties. In particular, the large scale effective conductivity associated tothermal, electrical or hydraulic fluxes depends on the media microstructure as well as on the spatialscale considered.In this talk, the potential field that solves the up scaling closure problem for a single large realization(4096^2grid blocks) of a 2D media sample (a Log normal with Gaussian or exponential covariance,or binary media of high conductivity contrast of 10^4) is first determined.Then, using two different post treatment of that potential, we calculate two descriptors of the equiv-alent conductivity for any subsample. These descriptors correspond to the evaluation of the viscousdissipation and of the average flow rate in that subsample, both estimators requiring negligible extracost once the full potential has been determined.The probability density function (pdf) of these descriptors are studied as a function of the subsamplesize and are compared with reference pdf determined by directly solving the subsample up-scalingclosure problem by a complete and far more expansive Monte Carlo study. Each descriptor con-verges towards the full sample value if the REV size is smaller that the full sample size. Numericalresults are compared in the asymptotic case to analytical estimations. For log normal media, these es-timations are found to be accurate, even for large input Log k variance. This also happens for binarymedia, except near percolation , where slow convergence to the asymptotic regime is observed.These post-treatment strategies are discussed for the REV determination, as well as for a deeperunderstanding of the convergence of the effective properties distribution to a limiting one.Future work using 3 D cases, power law conductivity distributions and long ranged correlations willbe discussed, as well as applications of such finding to uncertainty quantification.