This talk was given for Saudi Company Maaden. Different idea why uncertainty quantification in geology, mine business, reservoir description is important.
2. Our possible contribution to Maโaden
Aluminum, Phosphate and Gold divisions:
1. Mathematical more accurate modeling capabilities
2. Statistical Processes Control
3. Software-based simulation
4. Environmental safety
5. Higher-order non-linear, non-Gaussian stochastic models
of geological risk
6. Simulation of geology โ new frameworks
7. Robust optimization under uncertainty
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3. Introduction
Parameters are affected by uncertainty (because
they are not perfectly known or because they are
intrinsically variable).
Goal: devise effective ways to include, treat and
reduce uncertainty in a mathematical model.
Examples
Subsurface modeling: groundwater flows, contaminant
transport, earthquake simulations, ...
4. Uncertainty Quantification (UQ)
โข Forward UQ: given the input uncertain parameters, quantify the
uncertainty in the output quantities.
โข Global sensitivity analysis: Find out which input random parameters
have the largest influence on the value of interest.
โข Inverse UQ/ Data Assimilation: use available measurements to
reduce input uncertainty.
Optimal Design of Experiments: which measurements to reduce at
most the uncertainty on the random input ?
โข Optimization under uncertainty:
Minimize a given cost functional w.r.t. uncertainty in the input
parameters (Robust Control).
5. Example of UQ and its importance
E. g. 10% uncertainty in permeability => 25% uncertainty in the
pressure and 10% in ore grades.
โข Understanding of uncertainty in the input results in better
estimates of the risk (also uncertain)
โข Uncertainties influence on the optimal design of experiment
โข Usage of UQ and Bayesian formula allows us better estimate
parameters of ore from measurements (inverse problem)
KAUST King Abdullah University of Science and Technology 5
6. Methods for Stochastic Forward problem
โข generalized polynomial chaos
โข stochastic Collocation
โข stochastic Galerkin
โข (quasi) MC and multi-level MC
โข โฆ
Permeability/porosity
coefficient
Right hand side
Mean value of the solution Variance of the solution
Uncertain Input
Uncertain Output
7. Our experience
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Together with Uni Stuttgart: Effective approaches and solution
techniques for conditioning, robust design and control in the subsurface
1. Conditional simulation
2. Experimental design
3. Robust design
4. Robust predictive control
5. Risk assessment and prediction of
extreme events.
Full spectrum of tasks:
(W. Nowak)
percentage of a certain mineral ore in the rock
4000 measurements, 25000^3 nodes
8. Estimation of risk of CO2 leakage
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Benchmark for CO2 leakage through abandoned well
Compute mean and variance of CO2 saturation, mean and variance of CO2 leakage,
failure probabilities for short and long perspective. (S. Oladyshkin)
9. Ensemble Kalman Filter
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Work together with TU Braunschweig: (O. Pajonk)
Uncertainty quantification in dynamical systems
10. Optimal Design of Experiment
1. Decide optimal location for mining
2. Optimize underground sensor network
3. Robust risk management and decision making
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Quan Long, Marco Scavino, Raul Tempone
Impedance tomography design
11. Other applications
1. groundwater quantity and quality management
problems,
2. underground storage of nuclear waste,
3. remediation of contaminated sites,
4. technical or biological systems such as fuel cells, lithium
batteries,
5. help to reduce economical as well as ecological risks in
the oil and gas industries (projects with ARAMCO).
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12. Give better answers on questions
โข How can an optimum field development plan be
identified?
โข How are geological as well as technical uncertainties and
associated risks taken into account?
โข How are development options and risks related?
Focus on the development of advanced optimization
techniques for production, optimization and field
management.
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13. Benefits for Maโaden
1. (+) better prediction accuracy (e. g. of ore grades),
2. (+) more accurate use of big data for risk-analysis,
3. (+) increasingly cost-efficient sampling designs for expensive data,
4. (+) better robust engineering designs,
5. (+) more robust control and increased accuracy in predicting,
extreme events.
(1-5) -> better risk management and more reliable information basis
and decision support for sustainable management of environmental
resources.
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