An Improved Method for Calculating Bottomhole Pressures in Flowing Gas Wells With Liquid Present

Abstract

Summary. A method is presented for calculating bottomhole pressures (BHP's) from wellhead measurements in flowing gas wells with liquid present in the well stream. This method, a modification of existing methods, is based on including the contribution of entrained liquid to gravitational gradients. The study also includes evaluation of effective roughness factors evident from actual flowing pressure data. The proposed method was tested vs. both a two-phase flow model developed by Govier and Fogarasi and currently applied methods based on dry-gas wells. The method was also tested with Govier and Fogarasi's data from 94 flowing wells and with data from 50 wells from the public files of the Texas Railroad Commission. The new method compared favorably with the two-phase flow model and was superior to currently applied methods. Introduction Several methods currently exist for calculating BHP's in gas wells. This information is used for reservoir analysis and on completion reports submitted to state regulatory bodies. The method used by most state agencies, such as the Texas Railroad Commission, is based on a procedure detailed in U.S. Bureau of Mines Monograph by Rawlins and Schellhardt and is often referred to as the average T and z method because of the assumptions inherent in its derivation. The method usually does not include compensation for liquids in the flow stream. While this method is adequate for wells producing from less than 4,000 or 5,000 ft [1220 or 1525 m] in depth. it does not perform well for most deep, high-temperature, high-pressure gas wells. When such wells produce at low gas/liquid ratios, the method is even less reliable. The aim of this paper is to develop a simple method for calculating BHP's in gas wells that takes into account condensate and water production. Cullender and Smiths method, developed for dry-gas wells, is generally believed to be the most accurate hand-held calculator method to calculate BHPS. This method was therefore chosen as the basic model for this paper. Several modifications have been made to the method to take into account condensate and water production. These adjustments treat the gas/liquid system as a pseudo-homogeneous mixture. The improved method has been tested vs. Both the average T and z method without adjustment for entrained liquids and a two-phase flow model developed by Govier and Fogarasi. The Govier and Fogarasi method is a modification of a method originally developed by Wallis and was designed specifically for gas-condensate wells. Govier and Fogarasi showed that it had lower errors than the two-phase flow models of Duns and Ros, Hughmark, and Wallis. No attempt was made to compare the results of the proposed new method with other two-phase flow correlations because the Govier and Fogarasi model should be among the best for gas-condensate wells and because our primary intention in this work was to develop a simple calculator method for these calculations. From the outset of this project, it was decided that the chosen method must be capable of being programmed on a Hewlett-Packard HP-41 CV hand-held calculator or equivalent. This constraint limited the eventual candidates for the proposed method to those developed for single-phase flow. Most of the two-phase flow models either could not be programmed into the limited memory of the HP41 CV or would require impractical run times for general use. The program that was developed is presented in the Appendix. Two data sets are included in this paper: one from the Govier and Fogarasi paper and the second from the public files of the Texas Railroad Commission. The latter data set was necessary because the average T and z method used by the Railroad Commission requires that static BHP (BHSP) be calculated before flowing BHP (BHFP) is calculated. The Govier and Fogarasi paper does not include the data needed to calculate BHSP, hence the need for a second data set. Cullender-Smith Method The Cullender-Smith Method involves a numerical integration technique for calculating both BHSP's and BHFP'S. Because it takes into account both variations in temperature and compressibility factor with depth, it is a more accurate method than the average T and z method used by the Railroad Commission and others. Again, this theoretical improvement makes little difference at less than 4,000 or 5,000 ft [1220 or 1525 m] in depth, but it does make a significant difference in deep, high-pressure, high-temperature gas wells drilled so often today. If it is assumed that flow is steady state and kinetic energy effects are neglected, the mechanical -energy-balance equation can be expressed as follows: ................(1) where ptf = tubinghead flowing pressure, pwf = BHFP, T = temperature, z = gas compressibility factor, fm = Moody friction factor, q = volumetric flow rate, d = pipe ID, g = gas specific gravity, L = length of flow string, and D = true vertical depth. This equation is solved with a two-step numerical integration. This procedure, described by Ikoku, involves iterative calculations based on dividing the wellbore into two parts. SPEPE P. 643^