Performance analysis of linearization schemes for modelling multi-phase flow in porous media

Area of Science:

• Petroleum Engineering
• Computational Science
• Geosciences

Background:

• Reservoir simulation is vital for understanding fluid flow in porous media and optimizing field development.
• Strong geological heterogeneity presents challenges for traditional discretization methods in reservoir simulation.
• Accurate and efficient nonlinear solvers are critical for reducing uncertainties in reservoir characterization.

Purpose of the Study:

• To comprehensively assess and compare numerical linearization techniques for reservoir simulation.
• To evaluate the performance of finite difference central (FDC), finite forward difference (FDF), and operator-based linearization (OBL) methods.
• To guide the selection of linearization techniques for enhancing nonlinear solver accuracy and efficiency.

Main Methods:

• Numerical linearization techniques including FDC, FDF, and OBL were examined.
• Methods were rigorously analyzed based on accuracy, computational efficiency, and adaptability.
• Performance was evaluated for fluid flow problems in porous media with strong heterogeneity.

Main Results:

• FDC offers higher accuracy for complex, heterogeneous reservoirs but exhibits slower convergence.
• OBL demonstrates superior computational efficiency and rapid convergence, suitable for resource-limited or simpler scenarios.
• FDF provides a balance between precision and speed, dependent on derivative estimation step size.

Conclusions:

• Each linearization method (FDC, FDF, OBL) presents unique trade-offs between accuracy and computational efficiency.
• The choice of linearization technique should align with reservoir complexity, computational resources, and desired accuracy.
• Optimizing linearization methods is key to improving nonlinear solvers in reservoir simulation for better field development.