The Determination of Minimum Tested Volume from the Deconvolution of Well Test Pressure Transients

Abstract

Radius of investigation and tested volume are important results of well test analysis which can make or break future field development. Currently, their evaluation is either approximate or relies on a complete analysis of the transient pressure response using an appropriate model. A new method is proposed that uses the deconvolved derivative response to determine a minimum tested volume. It is accurate and does not rely on further transient analysis. The method can be applied to any oil or gas well test. It is simple and only requires input of data that is known at the time of testing. Furthermore, if the uncertainty in the deconvolution is quantified, then the uncertainty in tested volume is also defined. Field examples of both oil and gas well tests are presented which demonstrate how tested volume is easily calculated. Radius of investigation is calculated from the tested volume by making assumptions about the reservoir geometry. The method relies on a good deconvolution algorithm which can also compute the error bars in the derivative response. Recent advances in deconvolution algorithms have enabled the use of this simple but powerful new method to accurately calculate tested volume without the need for complex transient analysis. Introduction In the last thirty years, there have been many advances in well test analysis (Earlougher 1, 1977, Gringarten 2, 2007) of which deconvolution is probably the most recent. In the context of the analysis of pressure transients recorded during the testing or production of a well, deconvolution is the extraction of an equivalent single rate pressure response from the actual well response which is usually a continuous variation in rate and pressure. Within its known limitations (Levitan 3, 2004), it is a powerful technique because it allows the engineer to see the transient response of the well and reservoir without the complexity of the effects of superposition. Furthermore, the deconvolved response applies to the entire duration of the test rather than the duration of any particular constant rate period within the test (usually a build-up). A well test analysis work flow starts with the diagnosis of the transient response using a log-log plot of the pressure change and derivative response. Flow regimes are identified and an appropriate model selected. Often the models are analytical and they describe the pressure response of the well producing at constant rate for a given set of model parameters. The principle of superposition is then used to convert the constant rate response into the response due to the actual rates at which the well flowed. The resulting pressure history simulation is then compared with the observed data on a variety of plots. The parameters of the model are adjusted manually or automatically using regression techniques (Levenberg-Marquardt 4,5) until the best fit between the model simulation and the observed pressure response is obtained. If a numerical model is selected, a similar process is used but without the constraints of linearity that are imposed by the use of analytical models and superposition (Houze 6,7 et al, 2002, 2007).

Radius of Investigation for Reserve Estimation from Pressure Transient Well Tests

“…Recently, Whittle and Gringarten (2008) suggested using the intersection as shown in Fig. 7 for calculating the radius of investigation from derivative curve.…”

“…Therefore, if a unit slope on the derivative plot due to a no-flow boundary condition is available, one should use either Eq. 12 (Whittle and Gringarten, 2008) or Eq. 13, particularly with noise derivatives.…”

Calculation Model of Drainage Radius of Single-Layer/Multi-Layer Commingled Gas Production Wells in a Closed Constant-Volume Gas Reservoir and Its Application

“…Daungkaew et al [4] derived a calculation formula of the radius of investigation of a vertical well in a homogeneous reservoir with a closed boundary. Whittle and Gringarten [5] suggested that the radius of investigation can be calculated using the intersection of the unit slope representing pseudo-steady flow and the horizontal slope corresponding to infinite radial flow on the pressure derivative curve. By considering oil production, reservoir thickness and pressure gauge resolution, Kuchuk [6] proposed a calculation formula of the radius of investigation of a radial cylindrical oil reservoir.…”

An Integrated Approach to Well Test Analysis - Use of Numerical Simulation for Complex Reservoir Systems

“…Then the deterministic (volumetric) estimates of hydrocarboninitially-in-place based on the resulting geometry (from the numerical simulation) are compared with estimates of minimum tested volumes derived using the method of Whittle et al, 2008. In the end it is shown that for single-phase systems with small pressure drops, the simple 2D numerical simulator can aid in the reduction of geological uncertainty thereby solving a complex problem through relatively simpler means.…”

“…Top structure isochore map used for numerical simulation showing the active fault used for fault seal sensitivity.MINIMUM TESTED VOLUME Using the method suggested byWhittle et al (2008), the minimum tested volume during the test is estimated.…”