Calculation of Bottom-Hole Pressures For Deep, Hot, Sour Gas Wells
Authors: Messer P.H. , Raghavan R. , Ramey H.J. 
Published: December 2007

A somewhat neglected method of calculating bottom-hole pressures, that of Sukkar and Cornell, does not involve trial and error and is very fast for hand calculation; but it does not allow for the severe conditions of modern gas wells. Here the method is refined to extend the pressures and temperatures, to allow for sour gas, and to make results readily accessible for hand calculation.

Introduction
Modem trends in gas well drilling have been toward deep, hot, high-pressure completions. Currently, gas wells are being drilled to depths of about 25,000 ft in the southwestern U. S. As would be expected, bottom-hole pressures for these wells are high (about 16,000 psi), and bottom-hole temperatures are in excess of 400 deg. F. The gas produced from many of these deep wells is sour. To run bottom-hole pressure bombs is costly. and because the sour gas rapidly corrodes wirelines it may also be disastrous.There is often no indication of liquid in these wells, so it is possible to compute bottom-hole pressures from measured wellhead data. Of the many methods of computing bottom-hole pressure, perhaps the best known are
- the method for static and flowing gas columns outlined in the State of Texas backpressure manual, and
- the static and flowing gas column method described by Cullender and Smith.
The static method described in Ref. 1 is the Rzasa and Katz Method II, related to the older Rawlins and Schellhardt method. The flowing method in Ref. 1 is a modification of the static column method, which is based on estimating flowing friction from the Weymouth gas flow equation. Although the static method in Ref. 1 can be used with several depth increments to provide reasonable answers for deep wells, the flowing method is not recommended for deep, high-rate wells. The Cullender and Smith method is based upon a mechanical energy balance and is generally reliable for both static and flowing gas columns. But methods in both Ref. 1 and Ref. 2 involve tedious trial-and-error solutions. The Cullender and Smith method is best solved by computer if many determinations are required. There is a method that does not involve trial and error, however, that is very fast for hand calculations; but surprisingly, this method has received very little attention and use. This paper is based on that technique.A method presented by Fowler, involves integrated values of the gas law deviation factor, Z, with pressure, and is a direct method of calculating static pressure, and is a direct method of calculating static bottom-hole pressure, assuming a constant average temperature. Sukkar and Cornell extended Fowler's analysis and presented a general approach to calculating both static and flowing bottom-hole pressures for pure natural gas. They derived a pressure integral for perfectly vertical pipe by assuming negligible kinetic energy change, steady-state isothermal flow, and no work done by the gas in flow. Sukkar and Cornell evaluated the integral generally in terms of pseudoreduced pressures. The integral contains the pseudoreduced pressures. The integral contains the gas law deviation factor as a function of pressure, but it is assumed that temperature can be treated as an average over the depth range of interest. This is not an important weakness in the method because a depth of interest can be broken into several intervals to provide accuracy. The integral is based on a mechanical provide accuracy. The integral is based on a mechanical energy balance for a flowing column and is essentially identical with the Cullender and Smith result.
JPT
P. 85