Physical Explanation of Non-Linear Derivatives in Diagnostic Fracture Injection Test Analysis

Abstract

Abstract Over the past few years several authors have attempted to explain various non-linear pressure-time derivative behaviors observed in diagnostic fracture injection tests (DFIT's) using mathematical theories and application of conventional pressure transient theory. While based in solid math, these authors have, in some cases, ignored the physical processes that drive the observed pressure behavior. This paper seeks to explain the mechanical and physical processes that can occur during the fracture extension and closure process of a DFIT, with a minimum of equations or abstract mathematics. Two major sources of non-linear (non-ideal) leakoff behavior are addressed. They have been variously termed "pressure dependent leakoff" (PDL), and "variable compliance leakoff" (also known as height recession, transverse storage, variable storage, and by other names). Both of these pressure-time derivative signatures can be caused by multiple mechanisms, but really represent simple and fundamental changes in the rate of pressure decay during fracture closure. This paper explains the assumptions leading to the ideal linear derivative model, and the real processes that can lead to the observed deviations from this ideal model. It is hoped that an explanation of the physical mechanisms represented by these tests will lead to a better understanding of the failure conditions of the rock mass, and character of the induced fracture system. Correct interpretation of these tests is critical to design of effective stimulation treatments and to developing an understanding of the post-frac production characteristics of the well.