ABSTRACT
The goal of this work is to study the uncertainty quantification in inverseproblems of miscible flows in heterogeneous porous media in Bayesian framework and propose a permeability update based on observed measurements of spatially sparse tracer concentration at certain times. The Successive Sum of Independent Gaussian Fields method is used to parametrization of the uncertainty in heterogeneous porous media. A two-stageMarkov chain Monte Carlo (MCMC) method is used to solving the inverse problem. For the construction of Markov chains is used the Metropolis-Hastings algorithm based on a random walk sampling process employs an auto-regressive instrumental distribution. The main idea of MCMC is to generate a Markov chain with an equilibrium distribution equal to the posterior distribution of interest. Numerical results are presented for a set sampled realizations of the permeability fields.
Keywords:
Gaussian stochastic field; porous media flow; two-stage MCMC method; tracer
