A Systematic Method for Applying Fracturing Pressure Decline: Part I
Authors: Nolte K. G. , Mack M. G. , Lie W. L. 
Published: December 2007

Abstract
Although the basic analysis of decline data has become a standard tool for improved fracturing, an extension to current practice is necessary because the assumptions of the basic analysis are seldom met in practice. Some of these assumptions are that fluid loss depends on t and is independent of pressure, fracture area and closure pressure are constant, and that the fluid is incompressible. Deviations from most of these assumptions have been considered previously, but not in a manner which provides a systematic methodology for application.
The purpose of this two part paper is to provide a systematic methodology for the analysis and application of pressure decline data following a calibration fracture. A comprehensive review, systematic assessment of assumptions, and an application methodology are provided to ensure consistent and reasonably accurate results from the decline analysis, or to offer guidelines when the analysis may be inaccurate.
The proposed method is based on consideration of the slope at strategic locations on the G-plot for pressure decline, in conjunction with normally available information for the fluid and reservoir, standard well logs, pressure diagnostics, and treatment design improvements.
The analysis divides naturally into two portions, and the number of topics considered exceeds the limitations of a single paper, so it is presented in two parts. In the first part (this paper), considerations which can be quantified mostly analytically, and verified by numerical simulation, are discussed. These include spurt loss, pressure-dependent fluid loss (without stress sensitive fissures), compressible fluids, and poroelastic stress changes. These considerations are generally found to either not be significant to the decline analysis, or to be amenable to well-defined corrections. Part I also includes a review of the basic decline analysis, diagnostics for violating the basic assumptions, and the definition of the proposed method of application. The conclusions for Part I are provided at the end of each section.
Part II (SPE 26136) assesses effects for which analytic solutions are insufficient. Numerical simulations are used to provide guidelines for the decline analysis. These effects include height growth, stress-sensitive fissures, and fracture penetration and recession during the decline. These considerations are more significant than those considered in Part I, and are the primary requirements for use of a systematic approach. Part II also includes an overall assessment of the proposed method of decline analysis, as well as its limitations, i.e., the conclusions of Parts I and II.
Although pressure decline analysis is emphasized, a large part of the analysis (particularly in Part I) is also applicable to the injection part of a treatment. The analytic solutions are represented in terms of dimensionless variables for broad application.
The fracture simulator used for this study includes height growth, fluid temperature and compressibility, general models of fluid loss, poroelasticity, and both height and length recession during closure (with lateral-elastic coupling). A more detailed description of the simulator is provided in Part II.