Summary
History matching and uncertainty quantification are two important research
topics in reservoir simulation currently. In the Bayesian approach, we start
with prior information about a reservoir (e.g., from analog outcrop data) and
update our reservoir models with observations (e.g., from production data or
time-lapse seismic). The goal of this activity is often to generate multiple
models that match the history and use the models to quantify uncertainties in
predictions of reservoir performance. A critical aspect of generating multiple
history-matched models is the sampling algorithm used to generate the models.
Algorithms that have been studied include gradient methods, genetic algorithms,
and the ensemble Kalman filter (EnKF).
This paper investigates the efficiency of three stochastic sampling
algorithms: Hamiltonian Monte Carlo (HMC) algorithm, Particle Swarm
Optimization (PSO) algorithm, and the Neighbourhood Algorithm (NA). HMC is a
Markov chain Monte Carlo (MCMC) technique that uses Hamiltonian dynamics to
achieve larger jumps than are possible with other MCMC techniques. PSO is a
swarm intelligence algorithm that uses similar dynamics to HMC to guide the
search but incorporates acceleration and damping parameters to provide rapid
convergence to possible multiple minima. NA is a sampling technique that uses
the properties of Voronoi cells in high dimensions to achieve multiple
history-matched models.
The algorithms are compared by generating multiple history-matched reservoir
models and comparing the Bayesian credible intervals (p10–p50–p90) produced by
each algorithm. We show that all the algorithms are able to find equivalent
match qualities for this example but that some algorithms are able to find good
fitting models quickly, whereas others are able to find a more diverse set of
models in parameter space. The effects of the different sampling of model
parameter space are compared in terms of the p10–p50–p90 uncertainty envelopes
in forecast oil rate.
These results show that algorithms based on Hamiltonian dynamics and swarm
intelligence concepts have the potential to be effective tools in uncertainty
quantification in the oil industry.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
3 November 2008
- Meeting paper published:
2 February 2009
- Revised manuscript received:
13 March 2009
- Manuscript approved:
19 March 2009
- Published online:
17 November 2009
- Version of record:
12 March 2010
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