Dynamic data driven simulations in stochastic environments

To improve the predictions in dynamic data driven simulations (DDDAS) for subsurface problems, we propose the permeability update based on observed measurements. Based on measurement errors and a priori information about the permeability field, such as covariance of permeability field and its values at the measurement locations, the permeability field is sampled. This sampling problem is highly nonlinear and Markov chain Monte Carlo (MCMC) method is used. We show that using the sampled realizations of the permeability field, the predictions can be significantly improved and the uncertainties can be assessed for this highly nonlinear problem.