A Method of Calculating the Distribution of Temperature in Flowing Gas Wells

Abstract

Published in Petroleum Transactions, AIME, Volume 210, 1957, pages 169–176. Introduction Although one of the primary variables in the calculation of the flowing bottom-hole pressure in gas wells from surface measurements is the temperature at any point and its distribution in the flow-string, only few experimental data are available in the literature and little attention has been given to analysis of the problem. Virtually all of the recently published methods of calculating flowing bottom-hole pressures depend on the assumption that either the temperature is constant at some average value or that the variation is linear with depth. The purposes of this work are to analyze the problem theoretically and to verify the analysis by comparison with experimental data so that practical problems in the analysis of the behavior of gas wells can be solved with greater accuracy, reliability, and ease. Mathematical Outline of Problem Assuming that:The mass velocity and chemical composition of the gas stream are constant and in normal gas well operations, the change in linear velocity in the entire flow-string is trivial,The product of the density and heat capacity of the gas is constant,No horizontal temperature gradient exists in the gas stream,Net flow of heat by conduction within the formation and in the gas stream in the vertical direction is trivial in magnitude and can be neglected,The regional vertical geothermal gradient is constant, andThe temperature of the gas entering the borehole is constant, and equal to that of the reservoir, a set of two simultaneous, linear partial differential equations with appropriate boundary conditions was derived to describe the temperature distribution in the gas stream and the surrounding formation. These equations were solved by operational techniques for the distribution of temperature in the gas stream. The resulting integrals were evaluated numerically on an IBM 604 at the Machine Accounting Div. of the Railroad Commission of Texas.