Temperature Calculations for Wells Which Are Completed Through Permafrost
Authors: Howell E. P. , Seth M. S. , Perkins T. K. 
Published: December 2007

This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by who the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
The thermal behavior of a flowing well that is completed through permafrost is of considerable interest when designing insulated wells and when predicting produced fluid temperatures. In this paper, studies of several aspects of heat transfer are described. The energy balance within the wellbore involves measured PVT data and enthalpy calculations for both gas and liquid phases. The energy change in the flow string is balanced with the heat loss to the formation. Heat transfer by conduction in the permafrost and by conduction, convection and permafrost and by conduction, convection and radiation in the annuli around the flow string are considered. The effects of eccentric tubing and casing strings and the heat transfer involved when there is metal-to-metal contact were also investigated.
A mathematical simulation of the above system consists of a numerical description of convection in the flow string, conduction in the soil, and permafrost melting which occurs in the permafrost region. Space dependent latent heat as well as changes in thermal properties of the thawed and frozen regions are properties of the thawed and frozen regions are included. The coupled equations were solved using successive overrelaxation techniques in the formation. A considerable savings in computer time is realized by approximating behavior in the flow string as a series of steady-state conditions. Thawing behavior as well as refreezing of a shut-in well after drilling has been investigated. Actual field examples are presented which show agreement between observed and Computed temperature profiles. profiles

Introduction
Discovery of oil in arctic regions has led to a number of new engineering problems now under active study by oil companies. Much attention has been focused on permafrost and its influence on drilling and completion practices. Nearly all studies concerning permafrost influence are closely related to calculations of heat transfer to the permafrost, for it is the thawing or refreezing of permafrost that leads to its influence on the well. In addition, surface temperatures of flowing streams must be determined so that surface facilities can be adequately designed.
In this paper we will discuss a method for calculating heat transfer in a well completed through permafrost. In particular, we will consider the energy balance within the wellbore and show how commonly available PVT data and engineering correlations can be utilized in the heat transfer calculation. Heat transfer mechanisms from the wellbore and within the earth will also be discussed. Fig. 1 illustrates the complexity of the situation under consideration.