Determination of Pressure Dependent Leakoff and Its Effect on Fracture Geometry

Abstract

Abstract The effects of natural fissure opening, or pressure dependent leakoff, on the pressure behavior observed during fracturing are significant. Previous work has suggested that this behavior can be identified from pressure diagnostic plots during pumping, or from pressure falloff analysis. However, these techniques lead to ambiguous conclusions regarding the magnitude, and even existence, of pressure dependent leakoff. This paper presents a method of pressure falloff analysis which removes this ambiguity and allows an accurate determination of the magnitude of pressure dependent leakoff. The effects of fracture tip extension and recession, height recession, and transient flow in the fracture are also identified. The effect of pressure dependent fracture compliance, which has not been previously published, is also described. Introduction Post fracture pressure decline during shut-in is often affected by fracture height growth, extension or recession of the fracture tip after shut-in, and pressure dependence of leakoff. These factors can alter the shape of the pressure decline curve. The G-function, which describes fracture pressure decline behavior, was analytically shown to be linear for constant leakoff with a wall-building type of fluid. However, many factors which affect pressure decline behavior can result in non-linearities in the computed G-function. In 1990, Mukherjee et al proposed a method of fracture pressure decline analysis for cases of pressure dependent leakoff, assuming the G-function to be piecewise linear during pressure decline in naturally fractured reservoirs. Methods were presented to derive a very simple exponential relationship between the leakoff coefficient and the rate of pressure decline. The assumptions in this work were influenced by prior findings of Walsh, that natural fissures dilate with increased treatment pressure resulting in an exponential increase in permeability. Warpinski extended this finding to relate net pressure to leakoff coefficient. Though the pressure dependent leakoff analysis resulted in a means to estimate the pressure dependent leakoff function, the method could not be validated because of the lack of a suitable fracture design model capable of using this function to calculate fracture geometry. In this study the method is validated by a fully 3D fracture geometry model. A diagnostic superposition derivative of the analytical G-function is shown to uniquely distinguish between pressure dependent leakoff, fracture height changes, and tip extension and recession. Use of the superposition derivative to analyze fracture treating pressure behavior during pumping has been presented by Ayoub, et al. The correct application of pressure dependent leakoff to fracture geometry calculations substantially alters the resulting fracture size and fluid efficiency. Accurate modeling of this effect can reduce the occurrence of premature screenouts, which are common in the case of pressure dependent leakoff, and improve the overall treatment design. Pressure Dependent Leakoff Naturally fractured reservoirs requiring hydraulic fracture treatments exhibit pressure dependence of the fluid leakoff coefficient. In general, the induced hydraulic fracture propagates perpendicular to the minimum horizontal in-situ stress. The transverse natural fissures are held closed by the action of the maximum horizontal stress. As the treating pressure increases and approaches the maximum horizontal stress, natural fissures dilate resulting in exponential increase in the leakoff coefficient. Conventional fracture pressure decline analysis fails to predict this phenomenon uniquely, especially when fracture height growth or tip extension or recession occurs during fracture closure. P. 85