Test Design for Vertical Permeability Determination from a Conventional Pressure Buildup Test

Abstract

This paper was also presented as SPE 102779 at the 2006 SPE Annual Technical Conference and Exhibition, and as SPE 102820 at the 2006 Russian Oil and Gas Technical Conference and Exhibition. Abstract Vertical permeability magnitude is critical to well trajectory and/or completion design whenever the oil is either overlain by a gas cap or underlain by an aquifer or whenever a slanted or horizontal well is planned. Various authors have provided ways to determine horizontal and vertical permeability from a pressure transient test in a well with a limited entry completion. However, none indicate a test design that will ensure that the vertical permeability can be determined. This paper provides the necessary test design considerations for horizontal and vertical permeability determination from a conventional pressure buildup test. A standard limited entry model for the pressure transient behavior is used to determine timing for the start and end of key flow regimes for the transient interpretation. Equations that can be used to design a test for vertical permeability determination are also used to indicate ranges of reservoir, fluid and well properties that result in a successful test. A quick look analysis procedure enables estimation of horizontal and vertical permeability directly from a log-log diagnostic plot of pressure change and its logarithmic derivative. Examples illustrate test design and interpretation applications and demonstrate that determination of vertical permeability is possible even when wellbore storage masks early radial flow and an overlying gas cap and/or underlying aquifer prevent the appearance of late radial flow. Introduction Because its importance to reservoir management is well known, ways to determine vertical permeability by various mechanisms have been proposed. Single and multiprobe formation tests may provide horizontal and vertical permeability at the time a well is logged in open hole.[1,2,3] Single well vertical interference tests[4] have been proposed for cased hole completions with more than one set of perforations in the same production interval, but these tests are expensive to conduct, and the results can be subject to error in the case of a cement leak. A hybrid approach by Pop, et al.,[5] performs the vertical interference test with a wireline-conveyed straddle-packer tool. Conventional pressure buildup tests offer a third option that has been studied in great detail.[6,7,8] This paper explains how to design a conventional pressure buildup test to ensure determination of horizontal and vertical permeability. Possible test configurations are shown in Fig. 1. The key feature of the test is that only a limited portion of the well is open to flow. Reservoir and well properties are used to determine the length of the open interval and whether it is near the top or bottom of the reservoir, or in the middle. Also important to the test design are the length of the drawdown flow period and whether downhole shut-in is required to minimize the duration of wellbore storage. Interpretation procedures proposed in the past have all required the presence in the transient data of the early radial flow regime and/or the late radial flow regime. Further, these procedures relied on identifying lines on specialized plots. Radial flow lines were identified on a Horner plot, and spherical flow on a plot based on the reciprocal square root of time. Yildiz and Bassiouni9 indicated that the apparent line based on early radial flow is subject to error due to lingering wellbore storage effects. This paper shows that what is essential for unique determination of vertical and horizontal permeability, and damage skin, is the spherical flow regime and evidence of the time of its end. The test design strategy is to ensure the presence of these features in the buildup transient data. A previously reported equation for the end of early radial flow provides a limit on the duration of wellbore storage that can be used to determine when downhole shut-in is required, but this proves to be overly restrictive. A new equation is introduced that relates vertical permeability to the time of the end of spherical flow, which occurs at a different time from the start of late radial flow, and which is apparent even in the presence of a gas cap and/or an aquifer. Equations for the minimum drawdown and buildup durations to ensure a unique interpretation are also provided. Instead of using various specialized plots, this paper proposes a quicklook analysis based on values read off the log-log diagnostic plot of pressure change and its derivative. Pressure buildup data matched on this graph with the correct model provide rigorous estimates for vertical and horizontal permeability, damage skin, and the extrapolated reservoir pressure.