InterPore2021

Parametrization of uncertainty for predictive modeling of subsurface flow problems

1 Jun 2021, 20:00

1h

Poster (+) Presentation (MS14) Uncertainty Quantification in Porous Media Poster +

Speakers

Alsadig Ali (Mathematical Sciences Department, The University of Texas at Dallas, Richardson, TX, USA) Marcio Borges (LNCC)

Description

We are concerned with a Bayesian framework for rock characterization consisting of a
preconditioned Markov chain Monte Carlo (MCMC) method in conjunction with a
truncated KL [1] expansion for the parametrization of the underlying uncertainty in
subsurface properties [2]. Reduction of the overall uncertainty in determining reservoir
characteristics can be achieved through the incorporation of static (e.g., measurements
of rock properties at sparse locations) and dynamic data (e.g., saturation values at
sparse locations or production curves) in the characterization framework.

In this work we focus on the generation of conditional random fields, that honor known
values of the permeabilities at given locations (static data). The model problem
considered is the two-phase immiscible displacement with unfavorable viscosity
ratio in a heterogeneous reservoir. Initially we review currently available procedures for
incorporating sparse measurements in truncated KL expansions. We show that they
may produce unwanted inaccuracies in the prediction of subsurface flows. Motivated by
these results we propose a novel, projection-based conditioning procedure that
overcomes the difficulties that have been identified, and show that the new procedure
produces accurate predictions while taking into account sparse measurements of rock
properties.

References

[1] M. Loève, Probability Theory, Springer, Berlin, 1997.
[2] A. Al-Mamun, J. Barber, V. Ginting, F. Pereira, A. Rahunanthan, Contaminant
transport forecasting in the subsurface using a Bayesian framework, Applied
Mathematics and Computation 387 (2020) 124980.