3D Numerical Simulation of Hydraulic Fracture Closure With Application to Minifracture Analysis
- Hongron Gu (BP Intl. Ltd.) | K.H. Leung (BP Exploration, Europe)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- March 1993
- Document Type
- Journal Paper
- 206 - 255
- 1993. Society of Petroleum Engineers
- 3 Production and Well Operations, 5.6.4 Drillstem/Well Testing, 2.5.1 Fracture design and containment, 2.2.2 Perforating, 4.1.2 Separation and Treating, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation
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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 curveswhen the fracture height retracts from high-stress zones during closure.Application of the simulation results to minifracture analysis isdiscussed.
The success of a hydraulic fracture stimulation depends largely on anaccurate estimate of fluid leakoff during treatment. The average formationleakoff coefficient can be determined by analyzing the pressure-decline datafrom a minifracture treatment. Pressure-decline-analysis methods 14 are basedon a number of simplifying assumptions. The key assumptions are fracturegeometry and a constant fracture area during closure. Despite the simplifyingassumptions, pressure-decline behavior in many field observations is consistentwith that indicated by analysis. Pressure-decline analysis also has beenextended to include pressure-dependent leakoffs and leakoff at the interface oftwo formations. However, the pressure-decline-analysis theory, which is basedon constant area, does not explain some of the observed phenomena when thefracture is inside a formation with stress and permeability contrasts. In suchcases, the fracture may grow into permeability contrasts. In such cases, thefracture may grow into the high-stress zones during propagation and shrink backto the lower-stress zones during closure. Thus, the constant-fracture-areaassumption would be violated. Nolte has discussed the effects offracture-height growth on closure and pressure-decline analysis. In this paper,a 3D numerical simulation of fracture closure is used to study the effects ofin-situ stress and leakoff contrasts on fracture closure and pressure-declinebehavior. The fracture-closure mechanism is discussed first, and theassumptions and outline of a 3D fracture-closure simulator are presented. Thesimulation 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 minifractureanalysis technique for shrinking-height fractures and the general principle ofdeducing stress contrast from pressure-decline data are discussed.
After shut-in during a minifracture treatment, wellbore pressure graduallydecreases as the fluid inside the fracture leaks off into the formation. Thefracture is considered closed when the wellbore pressure drops below theminimum horizontal in-situ stress. pressure drops below the minimum horizontalin-situ stress. When pumping stops, the flow rate inside the fracture reducesquickly, and the fluid pressure distribution becomes more uniform because ofthe reduced friction loss. If leakoff is small, the pressure redistribution mayincrease the fluid pressure near the pressure redistribution may increase thefluid pressure near the fracture tip, and hence increase the stress-intensityfactor. The fracture may continue to propagate. If leakoff is high, thepressure drops quickly and the pressure redistribution may not pressure dropsquickly and the pressure redistribution may not increase pressure greatly nearthe fracture tip. In this case, the fracture growth after shut-in most likelywill be insignificant. Medlin and Masse's laboratory results showed no fracturegrowth after shut-in. If the fracture is inside a formation with uniformin-situ stress, fluid pressure inside the fracture is greater than the minimuminsitu stress over most of the fracture, except for a small region near thefracture tip. Therefore, the fracture most likely will close with a constantarea until the pressure drops to near the in-situ stress. Pressure-decline datafrom some field observations and laboratory tests agree with the prediction ofthe constant-area fracture-closure theory. On the other hand, numericalsimulations with the Pericins-Kern-Nordgren (PKN) model show decreasingfracture penetration during closure. In this simulation, the fracturepenetration in a uniformly stressed pay zone is assumed to be constant duringclosure; this assumption is not verified in this work. If in-situ stresscontrasts exist in the formation (Fig. 1), the fracture may grow into thehigher-stress zones during propagation. After shut-in, the fluid pressure dropsand becomes propagation. After shut-in, the fluid pressure drops and becomesmore uniform. The fluid pressure may drop below the higher in-situ stress, andthe part of the fracture in the high-stress zone most likely will close earlierthan the part in the lower-stress zone. Also, high insitu stress often isrelated 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 themore-permeable pay zone to leak off.
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