Multilevel Monte Carlo methods for computing failure probability of porous media flow systems

• We study improvements of the standard and multilevel Monte Carlo method for point evaluation of the cumulative distribution function (failure probability) applied to porous media two-phase flow simulations with uncertain permeability. To illustrate the methods, we study an injection scenario where we consider sweep efficiency of the injected phase as quantity of interest and seek the probability that this quantity of interest is smaller than a critical value. In the sampling procedure, we use computable error bounds on the sweep efficiency functional to identify small subsets of realizations to solve highest accuracy by means of what we call selective refinement. We quantify the performance gains possible by using selective refinement in combination with both the standard and multilevel Monte Carlo method. We also identify issues in the process of practical implementation of the methods. We conclude that significant savings in computational cost are possible for failure probability estimation in a realistic setting using the selective refinement technique, both in combination with standard and multilevel Monte Carlo.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Geovetenskap och miljövetenskap -- Oceanografi, hydrologi och vattenresurser (hsv//swe)

NATURAL SCIENCES  -- Earth and Related Environmental Sciences -- Oceanography, Hydrology and Water Resources (hsv//eng)

Keyword

CDF estimation

Failure probability

Porous media flow simulation

Multilevel Monte Carlo

Selective refinement

Selective refinement

Publication and Content Type

ref (subject category)

art (subject category)