Pressure Transient Analysis in an Elongated Linear Flow System
- Christine Ehlig-Economides (U. of Alaska) | Michael J. Economides (U. of Alaska)
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- December 1985
- Document Type
- Journal Paper
- 839 - 847
- 1985. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 5.1.1 Exploration, Development, Structural Geology, 4.1.2 Separation and Treating, 5.1.2 Faults and Fracture Characterisation, 2 Well Completion, 2.4.3 Sand/Solids Control, 5.6.3 Pressure Transient Testing, 5.9.2 Geothermal Resources, 5.6.4 Drillstem/Well Testing
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Prominent examples of linear flow behavior in-the well test Prominent examples of linear flow behavior in-the well test literature describe flow within or to a fracture penetrated by a producing well. The characteristic pressure transients generally producing well. The characteristic pressure transients generally are exhibited in the early portion of a well test and are followed by infinite-acting radial flow behavior and/or boundary effects. In contrast, if a formation is of a predominantly linear shape, linear flow is expected to develop in late time. In this paper, analyses of interference, drawdown, and buildup tests that are applicable to linear flow systems are described theoretically and illustrated by practical examples. The necessary equations for the analyses are provided for testing oil, gas, and geothermal steam wells. In elongated linear flow systems, the pressure transient behavior associated with linear flow occurs late in the drawdown or buildup test. The type curves provided in this work show that this pressure behavior is distinguishable from conventional well tests, pressure behavior is distinguishable from conventional well tests, particularly in interference tests. particularly in interference tests. Introduction
Interest in linear flow geometry was limited for a long time to water influx applications. Miller I provided solutions for pressure distributions in semi-infinite- or finite-length linear pressure distributions in semi-infinite- or finite-length linear aquifers assuming water influx into the oil zone at a constant flow rate. Ehlig-Economides et al. 2 and Ehlig-Economides and Economides recently developed methods for analyzing geothermal well tests in a predominantly linear flow system. This work was motivated by the presence of parallel linear faults that are predominant in geothermal regions, such as the one shown in Fig. 1. Methods for interference analysis and for drawdown testing of geothermal steam wells were presented. Linear flow geometry currently is cited as a fairly common occurrence in low-permeability gas fields. Kohlhaas et al. provided a case study of linear flow behavior for a gas well completed in a channel-like reservoir and equations for analyzing the linear flow portion of drawdown and buildup tests. Stright and Gordon examined rate-decline behavior in gas wells in the Piceance basin in northwest Colorado that exhibited apparent linear flow behavior. In one case, the well penetrated a fracture in a low-permeability marine sand in which a number of long, natural fractures were present and appeared to be related to extensive faulting in the area. In another case, the well was completed in a long, narrow sand body shown by outcrops in the same area. A recent paper by Nutakki and Mattar provided solutions for drawdown vs. time for linear flow geometry. The solutions are identical to the work done by Ehlig-Economides and Economides for geothermal steam wells. However, the method of analysis, which made use of a "pseudoskin" factor, was distinctly different. In this paper, the previous methods of interference and drawdown analysis for geothermal wells in a linear flow system are reintroduced with additional coefficients for oil- and gas-well testing. In another paper, the drawdown behavior of fractured wells in the predominantly linear flow system is presented in detail.
In Fig. 1, the geological map from a geothermal region shows linear faults running parallel for several hundred feet. If the regional faults provide impermeable boundaries to flow, then a particular well may drain a volume best described as a long, narrow particular well may drain a volume best described as a long, narrow channel. In Fig. 2, schematics of several types of depositional environments show possible oil- and gas-reservoir geometries that would result in predominantly linear flow. These formations, which generally are long, narrow shapes, may be the results of river meander point bars, oxbow lakes, river channels, or tectonic breccias. The model used for this work employs the diffusivity equation, which requires assumptions concerning the formation and fluid properties, such as homogeneous and isotropic formation, horizontal monophasic Darcy flow, fluid of small and constant compressibility, and constant viscosity. The boundary conditions and appropriate dimensionless variables are defined separately for interference analysis and for drawdown/buildup analysis.
For interference analysis, the active well is located at the center of a rectangular cylinder of infinite length and is approximated by a planar source, as depicted in Fig. 3. The cross section of the cylinder is assumed to be a rectangle with height h and width b. The planar source boundary condition for the linear flow model is analogous to the vertical line source for horizontal radial flow. For drawdown analysis, a model incorporating wellbore storage and skin is required, as will be discussed later in this paper.
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