Analysis of Rate Dependence in Transient Linear Flow in Tight Gas Wells

Abstract

Many tight gas wells (permeability less than 0.1 md) exhibit linear flow through their transient period. This transient period may last for years in some cases. It has been learned that this behavior differs in many ways from radial flow behavior. This paper reports another import difference between linear flow and radial flow - rate sensitivity. It has been shown and accepted for years that real gas pseudo-pressure can be used to apply analytical solutions to transient radial flow. However, it has been noticed that analytical solutions can be in serious error when applied to transient linear flow. Specifically, the slope of the departs from the analytical value as the flow rates or degree of drawdown become higher. This paper demonstrates the rate/drawdown sensitivity of transient linear flow. Then a correction factor is presented which corrects the slope of the plot and improves the accuracy of and OGIP, as calculated from production/pressure performance. Introduction Many wells in tight gas reservoirs have long-term performance which exhibit only linear flow, not radial flow, during the transient period. Wells have been observed which stay in the transient linear flow regime for several years. Some of these wells have hydraulic fractures and some do not. It is usually not practical to analyze tight gas wells with build-up tests, but long term production and pressure data can be used for analysis. Previous papers have presented methods of analysis1–5. The analysis of these wells comes from plotting vs. and observing the slope,, and the end of the straight line, tesr (end of the transient linear flow period). From these values, and OGIP can be calculated. The equations for this analysis are given in Table 1. The value of permeability can be calculated if the value of Ac can be estimated. For example, Ac can be estimated for a hydraulic fracture of known fracture length. However, in some tight gas wells there is no hydraulic fracture and linear flow probably occurs because of a natural fracture system. The value of can be thought of as a flow capacity for these wells. The drawdown/rate dependency of this analysis is quite different than analysis of radial flow. This difference was demonstrated with reservoir simulation. Then a correction method was developed to improve the accuracy of analysis of transient linear flow. Solutions for Radial Flow It has long been accepted that radial flow transient solutions can be approximated by analytical solutions, in terms of m(p), regardless of flow rate. Constant rate solutions have been emphasized, but it can also be shown that constant pwf flow can also be approximated by analytical solutions, regardless of the level of drawdown. Figs. 1 and 2 demonstrate this point. These figures show the results of simulated transient radial flow for a wide variety of rate and drawdown values. Specifically, note that all the semi-log straight line slopes are parallel to the analytical solutions in Figs. 1 and 2. This means that when permeability is calculated from the semi-log straight line slope, it will tend to be accurate. However, it was found that this is not true for linear flow. Effect of Drawdown on Transient Linear Flow (Constant pwf) A plot of vs. gives a straight line with slope for the analytical solution. The slope of this plot can be used to calculate the value of. The equation for this is shown in Table 1.

New and Improved Methods for Performing Rate-Transient Analysis of Shale Gas Reservoirs

“…In this method, Equation (12) is used. • Method 4: Ibrahim and Wattenbarger (2005;2006) approach is used. Time is used for linear flow analysis, not corrected pseudo-time, and slippage is not incorporated into pseudo-pressure.…”

“…x k , where f x is fracture half-length and is permeability, or k cm A k , where A cm is contacted matrix surface area, calculated from linear flow analysis for constant pressure production (Ibrahim and Wattenbarger, 2005;2006;Nobakht et al, 2010;Nobakht and Clarkson, 2011a). Ibrahim and Wattenbarger (2005;2006) proposed to multiply f x k obtained using the slope of square root-time plot by an empirically-obtained correction factor, CP f , under constant flowing pressure condition:…”

“…Ibrahim and Wattenbarger (2005;2006) proposed to multiply f x k obtained using the slope of square root-time plot by an empirically-obtained correction factor, CP f , under constant flowing pressure condition:…”

Simplified Forecasting of Tight/Shale-Gas Production in Linear Flow

“…It should also be mentioned that although Eq. 8 has been modified in the literature for calculating the duration of linear flow (Ibrahim and Wattenbarger 2006;Nobakht and Clarkson 2011), Eq. 8 worked reasonably well for the cases used in this study.…”

Well test, rate transient analysis and reservoir simulation for characterizing multi-fractured unconventional oil and gas reservoirs

“…For constant production rate in gas wells, the following equations have been proposed (Ibrahim et al 2006):…”