3D Numerical Simulation of Hydraulic Fracture Closure With Application to Minifracture Analysis
Authors: Gu Hongron , Leung K.H. 
Published: December 2007

Summary
This paper describes a 3D numerical model for the closure of a planar, nonpropped hydraulic fracture under uniform and layering reservoir conditions. The model simulates "double-slope" minifracture pressure-decline curves when the fracture height retracts from high-stress zones during closure. Application of the simulation results to minifracture analysis is discussed.

Introduction
The success of a hydraulic fracture stimulation depends largely on an accurate estimate of fluid leakoff during treatment. The average formation leakoff coefficient can be determined by analyzing the pressure-decline data from a minifracture treatment. Pressure-decline-analysis methods 14 are based on a number of simplifying assumptions. The key assumptions are fracture geometry and a constant fracture area during closure. Despite the simplifying assumptions, pressure-decline behavior in many field observations is consistent with that indicated by analysis. Pressure-decline analysis also has been extended to include pressure-dependent leakoffs and leakoff at the interface of two formations. However, the pressure-decline-analysis theory, which is based on constant area, does not explain some of the observed phenomena when the fracture is inside a formation with stress and permeability contrasts. In such cases, the fracture may grow into permeability contrasts. In such cases, the fracture may grow into the high-stress zones during propagation and shrink back to the lower-stress zones during closure. Thus, the constant-fracture-area assumption would be violated. Nolte has discussed the effects of fracture-height growth on closure and pressure-decline analysis. In this paper, a 3D numerical simulation of fracture closure is used to study the effects of in-situ stress and leakoff contrasts on fracture closure and pressure-decline behavior. The fracture-closure mechanism is discussed first, and the assumptions and outline of a 3D fracture-closure simulator are presented. The simulation results then are analyzed with the minifracture analysis technique. The different pressure-decline behaviors of a constant-area fracture and ashrinking-height fracture are demonstrated and explained. A minifracture analysis technique for shrinking-height fractures and the general principle of deducing stress contrast from pressure-decline data are discussed.

Fracture-Closure Mechanism
After shut-in during a minifracture treatment, wellbore pressure gradually decreases as the fluid inside the fracture leaks off into the formation. The fracture is considered closed when the wellbore pressure drops below the minimum horizontal in-situ stress. pressure drops below the minimum horizontal in-situ stress. When pumping stops, the flow rate inside the fracture reduces quickly, and the fluid pressure distribution becomes more uniform because of the reduced friction loss. If leakoff is small, the pressure redistribution may increase the fluid pressure near the pressure redistribution may increase the fluid pressure near the fracture tip, and hence increase the stress-intensity factor. The fracture may continue to propagate. If leakoff is high, the pressure drops quickly and the pressure redistribution may not pressure drops quickly and the pressure redistribution may not increase pressure greatly near the fracture tip. In this case, the fracture growth after shut-in most likely will be in significant. Medlin and Masse's laboratory results showed no fracture growth after shut-in. If the fracture is inside a formation with uniform in-situ stress, fluid pressure inside the fracture is greater than the minimum insitu stress over most of the fracture, except for a small region near the fracture tip. Therefore, the fracture most likely will close with a constant area until the pressure drops to near the in-situ stress. Pressure-decline data from some field observations and laboratory tests agree with the prediction of the constant-area fracture-closure theory. On the other hand, numerical simulations with the Pericins-Kern-Nordgren (PKN) model show decreasing fracture penetration during closure. In this simulation, the fracture penetration in a uniformly stressed pay zone is assumed to be constant during closure; this assumption is not verified in this work. If in-situ stress contrasts exist in the formation (Fig. 1), the fracture may grow into the higher-stress zones during propagation. After shut-in, the fluid pressure drops and becomes propagation. After shut-in, the fluid pressure drops and becomes more uniform. The fluid pressure may drop below the higher in-situ stress, and the part of the fracture in the high-stress zone most likely will close earlier than the part in the lower-stress zone. Also, high insitu stress often is related to shale layers, which have a much lower permeability than the pay-zonerock. Therefore, the fluid in this part of the fracture flows back to the more-permeable pay zone to leak off.
JPT
P. 206