Probabilistic Uncertainty Quantification

An encapsulation of the team’s beliefs about models, parameters and their ranges, quality of measurement data, and quality of simulation model, within a probabilistic or Bayesian framework which can generate accurate and validated probabilistic cumulative distribution curves (S curves) for quantities of interest at times of interest, which can then be represented by a suitable set of simulation runs.

Statistical Benefits of proxy models

In the oil and gas industry, proxy models are crucial for probabilistic uncertainty quantification of reservoirs with calibration against history. Markov Chain Monte Carlo (MCMC) methods cannot realistically be applied directly with lengthy reservoir simulations, and even fast proxy models with MCMC can fail dramatically to represent the full range of uncertainty.

Application of the latest Hamiltonian MCMC techniques, together with an efficient implementation of proxy models, can lead to a more reliable and validated probabilistic uncertainty quantification. These methods have been validated against high dimensional problems with known anaytical solutions.

Markov Chain Monte Carlo

Combination of:

  • Hamiltonian methods (NUTS)

  • Differential methods (DREAM)

  • Random walk

Proxy models

Uses multiple proxy models with the latest Gaussian Process techniques, including:

  • Polynomial averaging

  • Matern correlation functions

  • Optimisation of Restricted Maximum Likelihood (REML)

Workflow

EssRisk calculates the S curve from the proxy model, and then samples it to generate new simulation runs. In this way the proxy S curve and the simulation S curve converge, and the engineer can easily choose P10, P50 and P90 models to represent the uncertainty.

Features

  • Pre and post processing

    • Links to geomodelling

    • Creating of tables

    • Rock properties

    • Rel perm tables

    • Derive complex NPV calculations

    • Interface to third party software

  • Simulator interfaces

    • Eclipse

    • CMG

    • Echelon

    • Sensor

    • PSim

    • tNavigator