On displacement of viscous liquid in a system of parallel tubes

TL;DR

This paper presents an explicitly solvable quasi 1D model for viscous liquid displacement in parallel tubes, using a fixed point algorithm to recover reservoir geometry and analyzing solution stability across different functional classes.

Contribution

It introduces a novel explicit model for oil displacement in parallel tubes and a fixed point method for reservoir geometry recovery, with stability analysis.

Findings

Model provides explicit solutions for viscous displacement.

Fixed point algorithm effectively recovers reservoir geometry.

Stability varies across different functional classes.

Abstract

An explicitly solvable quasi 1D model of oil displacement is studied. The problem of recovering of the reservoir geometry is solved by means of a fixed point algorithm. The stability of solution is studied in various functional classes.