A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.

Area of Science:

• Reservoir Engineering
• Computational Geoscience
• Numerical Optimization

Background:

• History matching is crucial for calibrating reservoir models to dynamic behavior, involving inverse problem-solving.
• Objective functions, often Bayesian-based, quantify misfit between predicted and measured reservoir data.
• Efficient optimization is key to minimizing these objective functions for accurate reservoir characterization.

Purpose of the Study:

• To introduce and evaluate a novel Hybrid method for history matching in reservoir modeling.
• To combine Finite Difference and Stochastic Gradient methods for enhanced inverse problem-solving.
• To demonstrate the accuracy and computational efficiency of the proposed optimization technique.

Main Methods:

• Developed a Hybrid method integrating Finite Difference and Stochastic Gradient approaches.
• Formulated an objective function based on a Bayesian approach for reservoir model calibration.
• Iteratively updated reservoir parameters using a combined gradient, replacing stochastic components with finite difference values.

Main Results:

• The Hybrid method efficiently and accurately optimizes the objective function in reservoir models.
• Numerical simulations confirm the method's accuracy and computational effectiveness.
• The approach successfully addresses the inverse problem of history matching.

Conclusions:

• The Hybrid method offers a significant advancement in reservoir model history matching.
• This technique provides an accurate and computationally efficient solution for inverse problems.
• The study validates the Hybrid method's applicability through numerical simulations.