Poor post fracture production has been observed in many wells where the fracture treatment had prematurely screened-out. Further investigation has yielded evidence that the frac sand had been crushed. Sand crushing can be attributed to over stressing the fracture faces during screen-out. During a screen-out the sand is tightly packed into the fracture. When the well is flowed back, proppant crushing can occur as the fracture faces exert a stress on the proppant greater than the expected in-situ horizontal stress.
The following procedures have been recommended to reduce the occurance of crushed frac sand: monitoring of bottom hole pressure, reducing maximum fracture pressures, and the use of intermediate strength proppants.
Crushed frac sand has been produced from many oil and gas wells after hydraulic fracture stimulation treatments. Most of these cases have been explained by poor treatment design or poor frac sand quality. However, there remain many cases for which a feasible explanation of the crushed frac sand has 'jet to be provided. These cases are typically sand-offs where extremely high bottom hole fracture pressure occurred. This paper will put forth the theory that high bottom hole fracture pressure may overstress the fracture face during proppant screen-out and result in fracture closure pressures much greater than the regional in-situ horizontal stress. The high closure stress placed upon the proppant pack results in sand crushing and proppant conductivity orders of magnitude less than design. Field cases are presented in which sand crushing, high closure stress, and high post frac skin factors were observed.
The theory of relating fracture pressure to rock stress and fracture geometry has developed significantly with the advent of hydraulic fracture simulators. 1,2,3. Two basic 2D fracture models are commonly used today. The PKN model uses an elliptical cross sectlon and was developed by Perkins, Kern4 and Nordgren5. The GKD model uses a rectangular cross section and was developed by, among others, Geertsma, de Klerk 6, and Daneshy 7. The PKN model is more appropriate when high net pressures are encountered. This is because the net pressure calculated using the PKN model is higher than other models. The PKN model is also considered more accurate than the GKD model, where the frac height relative to frac length is small1,6.
Equation 1 relates fracture width to net pressure (ΔP f) for both PKN fracture geometry and three dimensional modelling.
Equation (1) Available in Full Paper
In a similar equation Nolte8 relates fracture compliance (Cf) to the average width.
Equation (2) Available in Full Paper
Equations l and 2 indicate that fracture width is proportional to net pressure.
It is important to note that the net pressure is equivalent to the overstress on the rock and is proportional to the fracture width. As a fracture treatment is completed, the net pressure, or overstress, is reduced by fluid leak-off until the proppant in place no longer permits further width reduction. This is called the point of closure. After closure, the proppant pack supports the stress placed upon it by the fracture faces.