New Methods for Determining Formation Properties from Stabilized and Unstabilized Gas-Well-Test Data

Abstract

In this paper, new explicit analytical equations for stabilized and transient deliverability coefficients in terms of formation/fluid parameters are presented. These equations are derived for fully and partially penetrating vertical wells and for fully penetrating horizontal wells. The proposed equations use the relationship between the empirical (Rawlins and Schellhardt) deliverability equation and rigorous (or Forechheimer's) deliverability equations for both stabilized and unstabilized (transient) flow conditions. Based on these new equations, we also present new methods for determining not only the performance coefficients, but also formation parameters from stabilized and transient gas deliver ability data. Unlike the existing methods, our new methods do not require geometric mean of pressure or rate data. This is a distinct advantage of the methods presented in this paper over the existing methods because determination of geometric mean of pressure or rate data may be quite difficult, and the mean value is quite sensitive to the measurement errors in such data. Thus, the methods given in this paper should prove very useful for determining formation parameters accurately from deliverability tests in vertical and horizontal wells. The accuracy and applicability of the methods given in this study are verified by analyzing two test data published previously in the literature. Results are compared with those obtained from the existing methods in the literature and indicate that combination of our new methods with the Hinchman-Kazemi-Poettmann method for isochronal test types provides more information about the formation and reliable deliverability forecasting. Introduction Analyzing well-test data obtained from gas wells is of great importance to natural gas industry. Multipoint tests for gas wells, in general, can be divided into two groups; "stabilized" and "unstabilized" flow tests. The conventional backpressure tests for stabilized flow conditions and isochronal tests for unstabilized flow conditions are designed primarily to determine deliverability of gas wells. Transient data from these multipoint tests are often not considered for determining formation parameters (e.g, permeability-thickness product, non-Darcy flow coefficient, and skin factor). Thus, one of the main objectives of this work is to develop methods to determine deliverability characteristics of gas wells from transient data. As is well known, the deliverability characteristics of gas wells can be described by either the empirical U.S. Bureau of Mines (USBM) back-pressure equation developed by Rawlins and Schellhardt1, or the more general (i.e., theoretically more exact) equation known as the Forchheimer equation.2,3 Rawlins and Schellhardt's1 equation is given by Equation (1) where C and n are constants empirically derived from a log-log plot of the pressure squared differences vs. gas flow rate (qsc) data. C in Eq. 1 is called the stabilized-performance coefficient and, in general, depends on the flowing time. It becomes constant at long times. Taking the logarithm of both sides of Eq. 1, we find that a log-log plot of (Equation) vs qsc will be a straigt line with a slope of 1/n where 0.5 = n =1. When turbulent flow becomes important, the value of n becomes smaller than 1 and reaches the value of 0.5 for complete turbulence.

Effect of the Wellbore Conditions on the Performance of Underground Gas-Storage Reservoirs

“…7 Other equations for determining the C constant may be derived from various other inflow performance relationships. 8,9 The n constant in Eq.1 is known as the turbulent factor and ranges between 0.5 and 1, where at a value of 0.5 the flow of fluid in the reservoir is totally turbulent, and at a value of 1 the flow is totally laminar. The wellbore performance may be determined by using any wellbore flow equations.…”

Analytical and numerical solutions on the response of pore pressure to cyclic atmospheric loading: with application to Horonobe underground research laboratory, Japan

“…The objective of their work is to evaluate the permeability of non-fractured reservoirs, i.e., essentially, distributed permeability from the pore space. Satman et al (2000) presented an explicit analytical method for determining formation parameters accurately from deliverability tests in vertical and horizontal wells by using the relationship between the empirical (Rawlins and Schellhardt) deliverability equation and rigorous (or Forechheimer's) deliverability equations for both stabilized and unstabilized (transient) flow conditions. Silin and Tsang (2001) proposed a method to estimate the formation hydraulic properties in the vicinity of wellbore without interrupting the operations by using regular pumping rate-pumping pressure data.…”