### Abstract

Estimating the probability of rare events is an extremely challenging task. For example, estimating the probability of leakage of CO2 from a saline aquifer using a direct Monte-Carlo approach would in general require a number of simulations proportional to the inverse of the rare event probability. Since it is likely that any action will require a probability of failure of less than $10^{-6}$, requiring $10^7$ to $10^8$ simulations, it is understandable that few such studies have been published. In this paper, we propose a means of simulating such rare events using a multilevel splitting algorithm called subset simulation (SS)[Au and Beck, 2001]. SS is an iterative algorithm that introduces intermediate events which are easier to sample from, and then iteratively samples within each constrained region in the probability space until the rare event threshold is reached. We show results for a standard benchmark for CO2 leakage through a leaky well [Class et al., 2009]. In this test case, CO2 is injected into a deep aquifer, then spreads within the aquifer and, upon reaching an abandoned well, it rises to a shallower aquifer. We show that subset simulation is an effective algorithm for estimating the probability of rare events with significant computational advantages over a direct Monte-Carlo approach. The SS algorithm relies on two parameters that have to be adjusted at the start of the simulation; we show the effect of these parameters on the quality of estimated rare event probabilities and propose guidelines on how to select these parameters.

Original language | English |
---|---|

Title of host publication | 14th European Conference on the Mathematics of Oil Recovery 2014 (ECMOR XIV) |

Publisher | EAGE Publishing BV |

ISBN (Print) | 9781634391689 |

DOIs | |

Publication status | Published - 8 Sep 2014 |

Event | 14th European Conference on the Mathematics of Oil Recovery 2014 - Catania, Italy Duration: 8 Sep 2014 → 11 Sep 2014 |

### Conference

Conference | 14th European Conference on the Mathematics of Oil Recovery 2014 |
---|---|

Abbreviated title | ECMOR 2014 |

Country | Italy |

City | Catania |

Period | 8/09/14 → 11/09/14 |

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geotechnical Engineering and Engineering Geology
- Energy Engineering and Power Technology

## Fingerprint Dive into the research topics of 'Estimating the probability of CO2 leakage using rare event simulation'. Together they form a unique fingerprint.

## Cite this

Elsheikh, A. H., Oladyshkin, S., Nowak, W., & Christie, M. (2014). Estimating the probability of CO2 leakage using rare event simulation. In

*14th European Conference on the Mathematics of Oil Recovery 2014 (ECMOR XIV)*EAGE Publishing BV. https://doi.org/10.3997/2214-4609.20141876