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.

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