Uncertainty Quantification with applications in geology

Web: sri-uq.kaust.edu.sa

Alexander Litvinenko

Our possible contribution to Ma’aden

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 – new frameworks

7. Robust optimization under uncertainty

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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, ...

Uncertainty Quantification (UQ)

• Forward UQ: given the input uncertain parameters, quantify the uncertainty in the output quantities.

• Global sensitivity analysis: Find out which input random parameters have the largest influence on the value of interest.

• 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 ?

• Optimization under uncertainty:

Minimize a given cost functional w.r.t. uncertainty in the input parameters (Robust Control).

Example of UQ and its importance

E. g. 10% uncertainty in permeability => 25% uncertainty in the pressure and 10% in ore grades.

• Understanding of uncertainty in the input results in better estimates of the risk (also uncertain)

• Uncertainties influence on the optimal design of experiment

• 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

Methods for Stochastic Forward problem

• generalized polynomial chaos

• stochastic Collocation

• stochastic Galerkin

• (quasi) MC and multi-level MC

• …

Permeability/porosity coefficient

Right hand side

Mean value of the solution Variance of the solution

Uncertain Input

Uncertain Output

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

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)

Ensemble Kalman Filter

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Work together with TU Braunschweig: (O. Pajonk)

Uncertainty quantification in dynamical systems

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

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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Give better answers on questions

• How can an optimum field development plan be identified?

• How are geological as well as technical uncertainties and associated risks taken into account?

• 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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Benefits for Ma’aden

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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