Ensemble Data Assimilation Applied to Geological Reservoir Models

Ensemble Data Assimilation Applied to Geological Reservoir Models offers an in-depth examination of ensemble-based data assimilation methods for numerical modeling of geological reservoirs. Grounded in a Bayesian framework, the book emphasizes the integration of prior geological knowledge with dynamic data to enhance model predictions. A central focus is on iterative ensemble smoothers, particularly the Ensemble Smoother with Multiple Data Assimilation (ES-MDA), which has demonstrated effectiveness in real-world applications. The methods are presented with a balance of theoretical rigor and practical insights, featuring pseudo-codes and case studies to bridge theory and practice. This book is intended for researchers, students, and practitioners involved in reservoir characterization and management in diverse applications, including hydrocarbon production, groundwater hydrology, carbon capture and storage, and geothermal energy.

Keywords: Data assimilation, history matching, reservoir models, ensemble Kalman filter, ensemble smoother with multiple data assimilation

Author: Alexandre A. Emerick

Publisher: Petrobras

Year: 2025

ISBN: 978-6588763292

Open Access

Contents

1. Introduction

Geological Reservoirs
Reservoir Models
Uncertainty
Forward Problem
Inverse Problem
Bayesian Viewpoint
Ensembles

2. Bayesian Formulation of the Data Assimilation Problem

Introduction
Model Likelihood
Maximum a Posteriori
Data Assimilation as a Sampling Problem
Normalized Objective Function

3. Optimization Methods for Data Assimilation

Introduction
Derivative-Based Methods
Stochastic Optimization Methods
Other Derivative-Free Optimization Methods
Methods Based on Proxy Modeling
Sensitivity Analysis
Parametrization

4. Ensemble Kalman Filter

Introduction
Kalman Filter
Ensemble Kalman Filter

5. Ensemble Smoother with Multiple Data Assimilation

Introduction
Ensemble Smoother
Ensemble Smoother with Multiple Data Assimilation

6. Iterative Ensemble Smoothers

Introduction
Ensemble Randomized Maximum Likelihood
Subspace Iterative Ensemble Smoother

7. Sampling Errors and Rank Deficiency

Introduction
Rank Deficiency
Spurious Correlations
Covariance Inflation
Localization

8. Computational Implementation of the Analysis

Introduction
Analysis in Matrix Form
Inversion
Matrix Multiplications

9. Practical Aspects and Field Examples

Introduction
Parametrization
Observed Data
Results Evaluation
Field Examples
Representative Models

A. Elements of Linear Algebra

B. Elements of Linear Inverse Problems

C. Elements of Probability and Geostatistics

D. Brief Literature Review

Intended Audience

This book is aimed at researchers, students, and practitioners involved in:

Reservoir characterization and history matching
Geological modeling
Subsurface monitoring and forecasting
Data assimilation in energy and environmental systems

Citation

If you use this book in your research or teaching, please cite it as:

Emerick, A. A. (2025). Ensemble Data Assimilation Applied to Geological Reservoir Models. Petrobras. ISBN: 978-6588763292.

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