Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff

Abstract

Abstract Nolte developed an analysis of the pressure decline following a fracturing treatment to provide an estimate of fluid efficiency, fluid loss coefficient, and fracture geometry. This analysis has become an industry standard for evaluating and improving the design of fracturing treatments. The derivations by Nolte assume the leakoff coefficient is a pressure independent constant. This assumption is valid when leakoff is controlled by a compressible filter cake. In cases where leakoff is primarily controlled by filtrate viscosity, by an incompressible filter cake, or by reservoir permeability and compressibility, the leakoff coefficient is pressure dependent, and, therefore, declines during the closure period. Under these circumstances, direct application of the Nolte technique may not be appropriate, and could cause an optimistic estimate of fluid efficiency and leakoff coefficient. This paper introduces a new plot for fracture pressure decline analysis that determines the pressure parameters (ISIP, Pc, P*) required in the Nolte leakoff calculations. The derivative of this plot may be used to identify the extension period, the closure period, and to assess the influence of pressure dependent leakoff on fracture pressure decline. In order to account for pressure dependent leakoff, equations are presented where the leakoff coefficient is treated as a mathematical variable. The equations describe simple linear relations applicable to the fracture closure period. When these relations are plotted on Cartesian coordinates, the closure period is recognized by a straight line with slope proportional to the leakoff coefficient. As shown in the examples, this modified approach is easily applied and provides new insight to the fracture closure period. Introduction The methodology currently used in fracture pressure decline analysis employs type-curve matching to determine a match pressure (P*) that is proportional to the leakoff coefficient. Data used in the curve match must correspond to the closure period. This period is usually interpreted as the "linear" region of a square-root of time plot or as the half-slope region of a log-log plot. Analysis of the square root plot or the log-log plot, however, is often inconclusive. To aid identification of the closure period, the closure pressure is usually determined prior to a calibration treatment from a stress test (e.g. pump-in flow-back test). A new plot is introduced that has the unique advantage of providing all of the pressure variables (ISIP, Pc, P*) required in decline analysis. This plot is more easily applied than the Nolte type curves, and is superior to the square-root of time plot because it uses a more precise relationship between decline pressure and time. When the derivative of this plot is graphed against time, fracture extension after shut-in, fracture closure, and pressure dependent leakoff can be observed. This plot enhances interpretation and identification of the closure period. However, by no means should use of this plot replace stress tests. When analysis of the derivative plot indicates a dependence of leakoff rate on pressure, a technique is presented to account for a declining leakoff coefficient during closure. P. 273^