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Anna Nissen: Data-driven uncertainty quantification for transport problems in structured porous media

Tid: To 2017-10-19 kl 14.15 - 15.00

Plats: Room F11, Lindstedtsvägen 22, våningsplan 2, F-huset, KTH Campus.

Medverkande: Anna Nissen, KTH

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Abstract:

Many subsurface reservoirs of interest in practical applications such as CO2 storage, petroleum engineering or thermal energy extraction are highly heterogeneous with complex geological structures such as channels, fractures and faults. In addition, lack of experimental data as well as the infeasibility to represent all structural features relevant to describing flow and transport makes mathematical models of these reservoirs subject to significant geological uncertainty. A meaningful mathematical model should therefore be able to accurately represent the most important sources of uncertainty. In addition, stochastic methods for flow and transport simulations of channelized reservoirs must be able to represent non-smooth material properties, such as sharp permeability transitions between channels and surrounding matrix. Traditional two-point statistics methods perform poorly in representing these features, but methods relying on multiple-point statistics can be used to represent channels within a stochastic framework.

In this work we consider a multiple-point statistics framework using kernel transformations to accurately represent structured porous media. Training images of heterogeneous media or empirical data can be used as a basis for the stochastic representation of permeability. Stochastic quadrature rules specifically tailored to the data are then constructed using the generalized polynomial chaos method based on empirical moments.

We apply the uncertainty quantification framework to a setting where heterogeneity and uncertainty are present and crucial for the outcome: a vertical equilibrium model of CO2 migration. CO2 is injected into a brine-filled heterogeneous (channelized) reservoir, in which it migrates through gravity and background flow over many years. The CO2 migration is described by a nonlinear conservation law, discretized in space with a finite volume method and a Godunov flux function for robust shock-capturing.