Mathematical modeling of thermal stabilization of vertical wells on high performance computing systems

TL;DR

This paper presents a numerical simulation approach for thermal stabilization of oil and gas wells using vertical freezing columns, employing finite element methods and high performance computing to solve complex nonlinear parabolic equations.

Contribution

It introduces a mathematical model and numerical implementation for thermal stabilization of wells, utilizing mesh refinement and high performance computing for large-scale simulations.

Findings

Effective modeling of phase transitions from water to ice.

Successful implementation of finite element method with mesh refinement.

Demonstrated scalability on high performance computing systems.

Abstract

Temperature stabilization of oil and gas wells is used to ensure stability and prevent deformation of a subgrade estuary zone. In this work, we consider the numerical simulation of thermal stabilization using vertical seasonal freezing columns. A mathematical model of such problems is described by a time-dependent temperature equation with phase transitions from water to ice. The resulting equation is a standard nonlinear parabolic equation. Numerical implementation is based on the finite element method using the package Fenics. After standard purely implicit approximation in time and simple linearization, we obtain a system of linear algebraic equations. Because the size of freezing columns are substantially less than the size of the modeled area, we obtain mesh refinement near columns. Due to this, we get a large system of equations which are solved using high performance computing systems.