A New Rate-Time Type Curve for Analysis of Tight-Gas Linear and Radial Flows

Abstract

Abstract This paper presents a new set of Fetkovich type curves for production data analysis. The set extends early-time flow regime to include near-linear up to pure-linear flow, which are lacking in the original set. The proposed set is general but is particularly suitable for tight-gas wells due to the inclusion of the often-observed pure- and near-linear flow behavior. Theory of cross type curves between rate, cumulative production, and time is presented as well as the methodology of cross type-curve matching. Examples are given to show the applicability of the type curves for tight-gas evaluation. Introduction Tight-gas reservoirs are reservoirs with in situ gas permeability of 0.1 md or less. Tight-gas wells require hydraulic fracturing (often a massive scale) for economic production. The created long fracture coupled with the tight permeability imparts linear flow into an otherwise radial flow pattern for a significant time frame. Linear/near-linear flow has been observed at virtually all major tight-gas fields/basins in US, e.g., Appalachian,1 East Texas,2 San Juan,3 Piceance,4 Uinta,5 Denver,6 and Green River.3,7 Analysis and modeling of such a linear/near-linear flow is extremely important because the economic successfulness of a tight-gas well is determined primarily by the "stimulated" transient-flow phase. A practical method to analyze production data is the type-curve approach; see Agarwal et al.8 for a recent review of pertinent works. Of all the type-curves developed, the rate-time set by Fetkovich9–11 is the most general and simplest to use. Fetkovich9 type-curve is a composite set of theoretical and Arps'12 empirical curves. Concept of apparent well radius/skin13–15 is used to incorporate near-well damage/stimulation effects. The strength of Fetkovich type curves is the easy identification and visualization of transient and boundary effects, benefit by the properly designed rate-time scales in a single graph. Fetkovich type curves, however, lack of linear/near-linear-flow features that are more likely to occur in tight-gas wells. Carter16 presented a set of rate-time type curves designed specifically for gas wells. This set is similar to Fetkovich's9 set in the aspect of plotting scales. All curves, however, are theoretical. Carter type curves, although not as straightforward and general as those of Fetkovich, provide understanding and implicit guidelines to field data analysis. Palacio and Blasingame17 later re-presented Carter's16 curves in terms of Fetkovich's9 plotting variables, and addressed the issues of changing fluid properties and operating conditions. Special type-curves designed for hydraulically fractured wells have also been proposed for various degrees of complexity, e.g., planar/elliptical fracture with infinite/finite-conductivity partially/fully penetrated in an infinite/closed reservoir.8,18–23 Our experience indicates that tight-gas production data (especially that of commercial databases) seldom exhibits sufficient quality/resolution to justify the sole use these specialized type curves. The concept of apparent-well-radius/skin presents the most practical approach and provides a first-level analysis for further detailed study. In view of the above review, the objective of this study is to extend the Fetkovich type curves to linear/near-linear-flow features that are important in tight-gas production data analysis. Approach and Model Our approach follows mainly along the lines of Fetkovich9–11 and Carter.16 Based on Fetkovich,9–11 theoretical models are used to model early-time transient flow while Arps'12 "empirical" equations for late-time boundary-dominated flow. Following Carter,16 linear and radial single-phase flow with well producing at constant bottomhole pressure are considered (Fig. 1). Numerical results are obtained from Laplace space solutions (Appendix A) with Stehfest algorithm24 for numerical inversion. For completeness, Arps' equations are summarized in Table 1. Both theoretical and Arps' solutions are presented in dimensionless space which will be discussed later. It should be emphasized that Arps' model is not completely "empirical. " Under certain conditions, Arps' model does have theoretical basis.9,11