Assessing the Long-Term Risks in Subsurface Carbon Storage Projects: Quantifying the Frequency of Long-term Events #26

In order to quantify the potential impacts of low frequency events over time, SCS projects must consider a large number of events with variable risk profiles. Monte Carlo simulation is often used to model these events in petroleum projects, but as an alternative, the Poisson formula can be used. The formula consists of the two equations shown below:

Equation 1. The Poisson equation provides the probability of n events linked to an event rate λ and time t:

p(n) = ((λt)ne(-λt))/n!

Equation 2. Restated, the equation enables computation of the probability of n events over a 1000-year period:

p(n) = exp[n(ln λt) – λt – gammaLN(n + 1)]

The basis of the Poisson distribution is that the rate of the events is constant over the specified time interval, and that each event is independent. The Figure below presents the Poisson distribution of the probability of zero and one-or-more events over a 1,000-year period given a constant annual frequency of 1% per year. Note that as the probability of zero events decreases over time, the probability of one or more events increases. Also note that this chart contains the probability curves for 1 to 10 events over the 1,000-year period.

In SCS projects, the general model is that risk (the product of consequence and likelihood) is not constant but increases during the injection period as the reservoir pressure increases and then declines after the injection is completed. To accommodate this, the Poisson formula can be applied to the event frequencies for a discreet time interval in order to estimate the chance of zero, one or more, or exactly “N” events for that interval.

The idea that risk increases during injection leads to the concept of Peak Risk. This is a period (or periods) where risk is highest. This could be near the beginning of a project life (induced seismicity), in the middle (highest reservoir pressure) or towards the end (post-injection CO2 migration out of the storage complex). Our next post talks more about the timing and duration of Peak Risks.