Thermal Regime Modelled For Drilling And Producing In Permafrost
Authors: Taylor A.E. 
Published: March 2010

Abstract
The importance of the transient thermal disturbance which develops around wellbores during drilling or production operations has long been recognized. This paper describes a numerical model developed to simulate the transient thermal regime in situations involving cylindrical symmetry. It has been designed to include a phase change with latent heat and hence is especially applicable in geophysical problems of the petroleum industry in permafrost regions.
The program has met success in duplicating annual temperature logs taken over 9 years at a Mackenzie Delta well. Hypothelical examples of drilling and production in permafrost areas are presented and compared to similar activity in more temperate regions. The use of an insulating annulus to reduce thawing in these cases is modelled.

Introduction
Knowledge of the transient thermal regime in problems involving cylindrical symmetry is important in many physical applications. The basic problem is represented by the heating and cooling of a large body by a cylinder imbedded internally. A computer program, developed to solve the problem numerically has been designed especially to model the disturbed transient regime where a phase change with latent heat occurs. The program has been used in other publications (Taylor, 1978a, b) to produce a suite of tables of temperatures and radial heat flow in problems involving a phase boundary. These tables provide an "off-the-shelf' solution to many geothermal problems.
This paper outlines the program and illustrates the breadth of its applicability in a variety of situations of interest to the petroleum community. Emphasis will be placed on the thermal features peculiar to a permafrost environment. The numerical solution is applied to a study of the disturbance to the geothermal regime resulting from the drilling of and production from petroleum wells, although it is equally applicable to investigations of the thermal regime around buried pipelines and underground tunnels or drifts.

Previous Studies
The literature contains a number of solutions to the transient heat flow problem in cylindrical symmetry. Carslaw and Jaeger (1959) develop analytic solutions to many thermal problems in cylindrical geometry, but rarely are these in closed form, Ingersoll el 01. (1954) approximate analytic solutions for a wide variety of problems. Jaeger (1956) develops analytic solutions for temperatures within a region of single-phase material surrounding a cylindrical source at times during a disturbance and for temperatures within the source region after the cessation of the disturbance. Such integral solutions are evaluated directly or through series expansions and a set of tables produced. Ritchie and Sakakura (1956) use asymptotic expansions to solve the heat conduction equation for various boundary conditions. Jessop (1963, 1966) calculates numerical values of the integrals in the heat flow equation for single-phase media and produces tables from which heat loss from a cylindrical source for various times can be calculated.
A number of authors have studied such problems and the application to geophysical situations. Bullard (1947) calculates the time for the disturbance due to drilling a borehole to dissipate.