Implementation of Fracture Calibration Equations for Pressure Dependent Leakoff

Abstract Nolte originally developed a pressure decline analysis method to provide an estimate of the fluid efficiency, closure pressure, fracture geometry and leakoff coefficient. The Nolte method of pressure decline analysis has become a standard for fracture calibration in the industry. Implementation of a proper calibration test is critical for the successful design and evaluation of hydraulic fracturing treatments. Although Nolte's original work has many simplifying assumptions regarding fracture closure (e.g., constant leakoff coefficient, no spurt, no fracture growth after shut-in, constant compliance, etc.) it still provides the foundation for the basic first order parameters affecting pressure decline behavior. The assumption of pressure independent fluid loss may have an adverse affect on the pressure decline analysis if leakoff is controlled by the filtrate viscosity and/or reservoir compressibility and mobility effects or fissure opening effects. An improved procedure is presented for identifying and implementing pressure dependent leakoff. This methodology is formulated from the generalized Nolte G function approach utilizing a dimensionless pressure function based on the original work of Castillo for a pressure dependent leakoff coefficient and Barree for naturally fractured reservoirs. The procedure first makes use of the standard Nolte analysis to identify the presence of pressure dependent leakoff, and then establishes the appropriate leak-off pressure dependent parameters by matching the pressure decline behavior. Deviation of the measured data from the dimensionless pressure function versus Nolte G time indicates closure. The methodology also utilizes the first derivative and pressure superposition derivative to help identify and quantify closure. Guidelines are presented to identify cases where pressure dependent leakoff should be considered. Implications of neglecting pressure dependent leakoff or using a pressure dependent leakoff coefficient improperly are addressed. The governing equations and field examples are presented for clarity.