Dynamic Mode Decomposition for Analyzing Dynamics in Multi-phase Flow in Porous Media

Abstract

For multi-phase flow through multi-scale heterogeneous porous media, such as the pore space of rocks, the interaction between multiple immiscible fluids and an intricate network of pores, creates a wide range of dynamic flow phenomena. At larger scales i.e. scales relevant for practical applications such as carbon sequestration, this interplay of dynamic phenomena is often referred to as "complexity". However, it is important to describe the persistent features of the flow in an adequate manner, to represent the "complexity" of the system. Dynamic mode decomposition (DMD) is a dimensionality reduction algorithm that computes a set of modes associated with fixed oscillatory behaviours. In this work, data is extracted from dynamic two-phase flow experiments and analyzed with DMD. We show that DMD can reproduce the data. Furthermore, not all dynamic modes are required to reproduce key dynamic features; this highlights the important spatial and temporal scales for flow. We show that dynamic mode decomposition was able to identify localized regions important to flow. Overall, DMD is proven as a useful diagnostic tool for complex 4D flow dynamics for multi-phase flow.