Abstract
The last decade has seen a revolution in the development of liquid-rich unconventional "shale" plays in the U.S. and of a search for analogous opportunities around the world. The primary driver for this revolution has been the expansion of horizontal drilling with multi-stage hydraulic fracturing to access sufficient reservoir to make these developments highly economic. While significant progress in characterizing these reservoirs and the well completion has been made and continues at a rapid rate, significant challenges remain.
Fundamentals of pressure-transient analysis (PTA) and rate-transient analysis (RTA) for characterizing the reservoirs and completions in these unconventional oil and gas reservoirs are fairly well established yet continue to expand at a significant rate. One shortfall in the state of the current literature related to these evaluation techniques is an over-reliance on the old adage of using pressure analysis for oil reservoirs and using pseudo-pressure and pseudo-time for analyzing pressure and rate data from gas reservoirs. Because of the extremely low permeability seen in these unconventional oil plays, the wellbore pressure and near-well reservoir pressures can see significant changes (4000-8000 psi) in relative short periods of time. Changes in liquid PVT and rock properties can be substantial over such large pressure changes. As such, use of traditional pressure analysis for these unconventional oil reservoirs is in direct violation of the assumptions used in the derivation of the liquid solutions; e.g., single-phase oil of constant viscosity and slight and constant compressibility. Not accounting for these changes in fluid properties can result in significant errors in calculated reservoir and completion parameters.
Within this paper, for the first time, we show that use of an oil-based pseudo-pressure and pseudo-time properly account for these fluid and rock property changes, providing accurate estimates of reservoir and completion parameters for the Bakken and Eagle Ford reservoirs. To properly evaluate the pseudo-time, new expressions for the average reservoir pressure during transient radial and transient linear flow have been derived. In fact, for both radial and linear flow, it is shown that the average reservoir pseudo-pressure (pressure) within the active drainage radius is a unique function of the initial reservoir pressure and the wellbore pressure. For the radial flow problem, this can be taken even further to show that the average pseudo-pressure and, therefore, average reservoir pressure is a constant within the drainage radius for which the log-approximation is valid. These expressions represent significant advancements in the realm of pressure-transient analysis for a number of reasons. First, they allow the direct calculation of pseudo-time rather than through an iterative process, making use of pseudo-time no more ominous than using pseudo-pressure. Second, shut-in of the well for a pressure-buildup test is no longer required to obtain the average reservoir pressure. Third, these expressions provide a theoretical basis for the long held recommendation developed from empirical observation that normal time rather than pseudo-time be used for drawdown analysis for radial gas flow. Synthetic reservoir models are used to generate data to verify the rigor and accuracy of these new relations and analysis methods.
