The Application of a Thermal Network Analyzer Program to Pipe Flow and Wellbore Heat Transfer
Authors: Lea James F. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 50th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Dallas, Texas, Sept. 28-Oct. 1, 1975. 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 whom 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 discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
Complex heat transfer problems common to the petroleum industry have often been attacked by the development of finite difference computer solutions to the equations peculiar to the problem. Example solutions are presented here to heat flow problem. Example solutions are presented here to heat flow problems arising from flow in a pipe, circulating mud columns, and problems arising from flow in a pipe, circulating mud columns, and oil production through permafrost. Each of the solutions was obtained by generating input for one multi-purpose thermal network computer program. Network heat flow programs have been previously used in problems dealing with conduction in irregular geometries as well as modeling heat sources, convection, radiation and in general, combined modes of heat transfer. A method is presented here for modeling temperature distributions in flowing fluids which is used in the example problems. In addition, several other problems are discussed which may be approached with this type of problems are discussed which may be approached with this type of program. program

Introduction
Examples of computer models using finite difference techniques to solve heat flow problems can be easily found in the literature, as well as analytical techniques requiring simplifying assumptions. This article demonstrates the use of a general network heat flow program and how it can be applied to various problems common to the petroleum industry. Although tedious to problems common to the petroleum industry. Although tedious to input, the use of this type of program can often give information on a particular problem in a matter of hours while the development of a complete finite difference model can take weeks or months.
PROGRAM INPUT PROGRAM INPUT The method of analysis used by the program is outlined in Appendix A. The user, however, needs only to be able to calculate the appropriate values for capacitances and resistors and input them in a manner so that they are connected to represent a physically realistic problem. The values of resistors to be used physically realistic problem. The values of resistors to be used to represent convection and conduction may be found in most texts containing a discussion of electrical analogy to heat flow. The expressions in Table 1 are repeated for convenience.