Abstract
Diagnostic Fracture Injection Tests (DFIT) are commonly interpreted with G-function derivative plots. In these plots, an upward deviation from linearity is generally attributed to fracture height recession or transverse storage. This interpretation neglects changing fracture compliance during closure. Results presented in this study show that in low permeability formations, an upward deviation of the G-function plot G*dP/dG is caused by a sharp reduction in fracture compliance due to closure. It is not necessary to invoke more complicated explanations such as height recession or transverse storage. The specific shape of the G*dP/dG curve is controlled by factors that affect fracture compliance before and after closure. These factors include the fracture height, fracture stiffness, and the residual aperture (which is affected by the microscopic and macroscopic roughness of the created hydraulic fracture). Wellbore storage broadens the post-closure peak in the G*dP/dG curve. A curve of G*dP/dG that constantly increases during the shut-in period may be caused by wellbore storage, rather than fracture tip extension. In higher permeability formations (with non-zero wellbore storage), the effect of fracture compliance is less important. As a result, changing fracture compliance during closure does not have a significant effect on the pressure transient plots, and closure decreases the rate of pressure decline because it reduces the rate at which fluid can leak off into the matrix. In all cases, as long as a single planar fracture has formed, the best pick for the minimum principal stress is at the deviation from linearity on the G*dP/dG plot, whether or not this departure is concave up or concave down. Closure picks via a tangent to near the peak in G*dP/dG (as is commonly performed) may significantly underestimate the minimum principal stress. These picks should be confirmed with other measurements, such as a subsequent injection period or a pump-in flow-back test. The fact that an extremely sharp upward trend in G*dP/dG is generally not observed in DFIT tests suggests that the actual geometry of the created fracture is rougher and more complex than is typically assumed by standard models.
