This paper presents new performance type curves for hydraulically fractured wells. The new curves are similar to the Fetkovitch curves for decline curve analysis, but have been developed specifically for fractured wells with linear flow instead of conventional wells with radial flow. Hydraulically fractured wells exhibit different flow regimes than conventional wells, including a skin-dominated period during clean-up, bilinear flow, linear flow, pseudo-radial flow, and boundary- or interference-affected flow. The type curves were constructed in Laplace domain for constant reservoir properties, and were then inverted numerically. The effect of varying reservoir properties was incorporated using an average compressibility determined from material balance.
The type curve methodology provides a new tool for the reservoir engineer to perform rapid analysis of reservoir properties (kh), fracture effectiveness (Xf), and well drainage area (A) for fractured wells. The impact of skin on performance is considered, along with the effect of reservoir geometry (alternative length-to-width ratios) that enable these type curves to be used on lenticular formations. The type curves also include variable compressibility and viscosity that are missing in prior work. More than 1000 tight gas wells in the Green River and Piceance basins have been analyzed using the type curves, and relevant examples from these two basins are presented.
Rate-time decline curve extrapolation is one of the most frequently used tools in the petroleum industry. In the classical formulation by Arps, based on work dating back to 1908, these curves were purely empirical, and the methodology was generally limited to exponential and hyperbolic decline curve analysis. Although not generally recognized in the industry, a sound theoretical basis for exponential decline curves was presented in 1937 by Muskat, whose solution of the rate equation for a closed circular reservoir with constant rock and fluid properties consisted of a series of exponential functions of time. After the second and subsequent terms decay, the first term leads to the usual exponential decline. Other investigators found that changes in fluid properties (non-constant compressibility and viscosity) could cause a hyperbolic decline, as could gravity drainage. The introduction of log-log performance type curves by Fetkovitch in 1973 greatly simplified the selection of the appropriate hyperbolic decline exponent, and made decline curve analysis easier and faster.
The majority of the work performed prior to 1968 involved radial flow cases. Even when a fractured well was considered, it was usually handled as an equivalent radial flow case with improved productivity index or increased effective wellbore radius. The recognition that different flow regimes could develop grew out of pressure transient analysis of fractured wells. As stimulation treatments grew larger, and progressively lower permeability reservoirs were exploited, linear flow during well tests was recognized by MilIheim and Cichowicz in 1968. The complete transition from linear flow to pseudo-radial flow during well tests was presented by Gringarten and Ramey in 1974 for infinite conductivity and uniform flux fractures, and by Cinco-Ley, et al. in 1978 for finite conductivity fractures. In 1979, Kucuk and Brigham derived the pressure and rate response for an infinite conductivity fracture in an infinite reservoir using elliptical flow considerations. Because these works were primarily focused on pressure transient response rather than production rate analysis, they are not readily usable for estimating alternate recovery, future gas rates, or well drainage.
Other investigators used simulators to evaluate production rate and transient tests for vertically fractured wells. Locke and Sawyer simulated type curves for an infinite conductivity fracture in infinite and closed reservoirs.