Calculation of Bottom-Hole Pressure in Gas Wells

Publisher Website
Google Scholar
Abstract
A simple, fact and accurate method for computing flowing and static bottom-hole pressures in gas wells is presented. The method employs any of the well known methods for numerical integration and the Newton-Raphson iteration scheme. The proposed method may he easily programed for digital computers or it may be used for hand calculations. The method is superior to previously proposed methods in accuracy and rate of convergence. Accuracy of the method depends mainly on the type of integration scheme and input data. Several integration schemes are evaluated here for use with this method. Introduction: The basic equation for flow in a vertical pipe and hydrostatic head are well known and are reviewed in a recent manual published by the Oil & Gas Conservation Board of Alberta and in a series of papers published by the author. Only the most general form of these equations used for practical calculations will be presented here. This form of the equations was first proposed by Cullender and Smith. For static bottom-hole calculation we have, ........................................(1) and for flowing bottom-hole pressure, ........................................(2) The usual procedure in bottom-hole calculations is to (1 ) assume a value of p, (2) compute the right-hand side of Eq. 1 or 2 depending on the type of calculation being performed (static or flowing) and (3) check to see if the computed value of the integral is equal to the known left-hand side of the equation. If the two sides of the equation are not equal within a certain allowable tolerance, the calculations are repeated with a new estimate of ps. The numerical method used for evaluating the integral is usually either the trapezoidal rule or Simpson's rule. Proposed Method: A method is proposed here for performing bottom-hole pressure calculations so that a minimum number of iterations is required. The method could be used with any numerical integration scheme. Rewrite Eq. 1 or 2 in the following form,........................................(3) in this equation, K. y and, hence, 0 take on different values depending on the problem being considered. For the static case, ........................................(4)

This publication has 0 references indexed in Scilit: