Integral Type Curves for Advanced Decline Curve Analysis
- J.P. Spivey (S.A. Holditch and Assocs. Inc.) | J.M. Gatens (S.A. Holditch and Assocs. Inc.) | M.E. Semmelbeck (S.A. Holditch and Assocs. Inc.) | W.J. Lee (S.A. Holditch and Assocs. Inc.)
- Document ID
- Society of Petroleum Engineers
- SPE Mid-Continent Gas Symposium, 13-14 April, Amarillo, Texas
- Publication Date
- Document Type
- Conference Paper
- 1992. Society of Petroleum Engineers
- 5.6.3 Pressure Transient Testing, 5.6.4 Drillstem/Well Testing, 5.2.1 Phase Behavior and PVT Measurements, 4.3.4 Scale, 5.6.1 Open hole/cased hole log analysis, 4.1.2 Separation and Treating, 4.1.5 Processing Equipment
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This paper introduces a new family of type curves for advanced decline Curve analysis. The new type Curves are obtained by combining the dimensionless production rate and the dimensionless cumulative production on a single log-log scale. The new type curve offers two significant advantages: 1) observed cumulative production data is much smoother than observed production rate data, making a match easier to obtain with the new type curve; and 2) simultaneously matching both rate and cumulative production provides more confidence in the selection of the correct early- and late-time stems. Plotting functions are presented to allow the new curves to be used for both oil and gas wells produced at either constant or varying flowing bottomhole pressure. Use of tie new type curves is demonstrated for both simulated and field data.
In 1973, Fetkovich proposed a dimensionless rate-time type curve for decline curve analysis of wells producing at constant bottomhole pressure. These type curves, shown in Fig. 1, were developed for slightly compressible liquids. These type curves combined analytical solutions to the flow equation in the transient region with empirical decline curve equations in the pseudo-steady state region.
The analysis procedure provided estimates of formation permeability, k, and drainage radius, re, instead of the traditional decline curve analysis parameters qi and Di. This approach to decline curve analysis, now commonly referred to as "advanced decline curve analysis", has become widely used as a tool for formation evaluation and reserves estimation. Fetkovich et al. presented several case studies of the use of advanced decline curve analysis.
Bourdet, et al. introduced the use of derivative type curves for transient well test analysis in 1983. By multiplying the, pressure derivative by the time, (or equivalently, by taking the derivative of pressure with respect to the natural log of time), they were able to display both the pressure and pressure derivative type curves on a single set of axes. They pointed out that a simultaneous match of the pressure and pressure derivative type curves provides a more reliable interpretation of pressure transient test data than a match of the pressure type Curve alone. Because of this advantage, recent pressure transient analysis papers have routinely included both pressure and pressure derivative type curves.
The pressure derivative type curve suffers from at least one minor disadvantage in that the process of taking the derivative from measured data amplifies any noise inherent in the data. For this reason, Blasingame, Johnston, and Lee suggested using the pressure integral rather than the pressure derivative . This procedure has the advantage of reducing rather than increasing any noise in the data.
Production data often contains much more noise than pressure transient test data, making application of rate derivative type curves of little value. However, rate integral, or cumulative, type curves, can reduce the effect of this noise and make analysis of production data more reliable.
This paper presents cumulative type curves for wells producing a single phase fluid, from a finite, radial reservoir, at constant flowing bottomhole pressure. In addition, plotting functions are presented to allow the new type curves to be used with gas wells and with oil or gas wells producing at varying bottomhole pressures. In principle, the concept of the combination rate and cumulative type curve may be extended to hydraulically fractured wells, to wells in dual porosity systems,, or to wells in arbitrarily shaped drainage areas.
Review of Fetkovich Decline Curves
Fetkovich developed his type curves by combining an analytical solution to the flow equation, describing transient flow, with empirical decline curve equations describing pseudo-steady state or boundary dominated flow.
The transient portion of tile Fetkovich type curve is based on an analytical solution to the radial flow equation for slightly compressible liquids with a Constant pressure inner boundary and a no flow oiler boundary.
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