Continuous data assimilation for two-phase flow: analysis and simulations

TL;DR

This paper introduces a new continuous data assimilation algorithm for two-phase flow in reservoir simulation, demonstrating exponential convergence of approximate solutions to reference solutions using coarse mesh observations.

Contribution

The paper presents a novel data assimilation algorithm for two-phase flow that guarantees exponential convergence and effective synchronization with limited domain data.

Findings

Exponential decay of residual error in solutions

Effective synchronization with partial domain data

Numerical validation of convergence and efficiency

Abstract

We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using coarse mesh observations, converge at an exponential rate in time to the corresponding exact reference solution of the two-phase model. More precisely, we obtain a stability estimate which illustrates an exponential decay of the residual error between the reference and approximate solution, until the error hits a threshold depending on the order of data resolution. Numerical computations are included to demonstrate the effectiveness of this approach, as well as variants with data on sub-domains. In particular, we demonstrate numerically that synchronization is achieved for data collected from a small fraction of the domain.