Temperature Simulation While Drilling Permafrost
Authors: Pui N.K. , Kljucec N.M. 
Published: March 2010

Abstract
A numerical simulator was developed to study the thermal disturbances around the wellbore while drilling. Calculated results compare favourably with field measurements.
The simulator has been used to predict the location of the thaw front in permafrost and the amount of gas that could be liberated from a gas hydrate zone during drilling operations. The formation temperature distribution was found to be strongly dependent on the inlet mud temperature.

Introduction
Thermal disturbances in permafrost propagate from the wellbore during drilling operations. While drilling the surface hole, warm drilling fluids are in direct contact with the permafrost and during subsequent drilling heat losses through the casing cause thawing of the permafrost. Mathematical modelling of the heat losses from the wellbore during drilling operations will provide data on the location of the thaw front and other isotherms around the wellbore. Data on temperature conditions in the permafrost during drilling operations were required to assess the location of the calculated thaw radius in relation to the degree of hole enlargement, to determine the volumes of gas that could be liberated from a hydrated gas zone during drilling operations and to determine the volume of unfrozen soil for calculating external freezeback pressure behaviour following drilling(1).

Model Description
The governing differential energy equation and the numerical method of solution are summarized in the Appendix. The simulator consists of two distinct portions. One part is to calculate the heat loss or gain between the drilling fluid and the formation surrounding the wellbore; this part of the program takes into account the effect of free convection in the annuli if these are filled with low-viscosity fluid. The heat is assumed to be transferred radially between the drilling fluid and the formation. The other portion of the program is to solve the two-dimensional heat conduction equations that involve a change of state. A variational technique was employed to obtain approximate piece-wise planar temperature solutions to the heat conduction equation at discrete times. A backward difference implicit scheme was used to relate the solution at successive points in time. The resultant non-linear algebraic equations are solved by Newtonian iteration. A detailed description of the method is presented by Wheeler(2).
The effects of heat convection in the formation, drilling fluid invading the formation or formation fluid entering the wellbore are considered insignificant and were neglected in the simulation. The drill bit is assumed to penetrate the formation in a stepwise fashion and the grid interval is assumed to be drilled if more than half of the interval has been penetrated. The viscosity corresponding to the average shear rate is used in calculating the Reynolds and Prandtl numbers.

Case Studies

Simulator Confirmation
In order to check the drilling thermal simulator, data were obtained from a well being drilled in Alberta. The inlet mud and outlet mud temperatures were recorded every hour. A thermistor cable was strapped to the surface casing to monitor the temperature around the casing for the top 600 feet of the formation.