The effect of closure stress on fracture conductivity has been well documented by laboratory measurement. Common industry practice for estimating closure stress on proppant in the field is to subtract flowing bottomhole pressure from the estimated in-situ stress of the pay interval fractured. This paper proposes that the closure stress on proppant in a fracture can be significantly higher than common estimations due to the influence of the bounding layers and the elastic response of the formation acting on the proppant. In this paper we will review past literature on fracture propagation, fracture conductivity and proppant placement and demonstrate the impact that increased proppant stress due to bounding layers can have on fracture conductivity and ultimately production.
Many papers have been written on the subject of fracture propagation. The term "closure pressure" or "closure stress" has been used in these papers primarily in the context of calculating fracture net pressure or excess pressure.1,2 These parameters, and others, are used in calculating the fracture geometry during a fracture treatment.3,4 Accurate measurements of closure stress for individual intervals are especially important for predicting fracture height growth and, hence, fracture geometry with fracturing models.
Procedures for the measurement of closure stress are also well documented in the literature.5,6,7 These procedures describe the pumping of fluid into a formation to create a hydraulic fracture followed by the monitoring of wellbore pressure. The shape of the pressure fall-off curve can then be used to determine the closure pressure or horizontal stress acting across the plane of the vertical fracture. This procedure is best performed with a small amount of fluid and may be used on both pay and boundary intervals. By definition, the closure pressure determined through these mini-frac corresponds to the pressure in the fracture as it closes to a width of essentially zero.
During hydraulic fracturing the reservoir rock is pushed apart by a fluid at pressure. The introduction of proppant with the fracturing fluid results in the fracture being propped open to some width after the fracturing fluid pressure is released. The reservoir rock can thus only partially rebound from the maximum open state caused by the fracturing fluid. As such, the closure pressure on the proppant is higher than that exhibited in the above described test since the fracture width is greater than zero. It is this extra stress, above the closure stress of the pay interval, which increases the stress on the proppant and reduces the propped fracture conductivity below values as estimated by current methods. The elastic mechanics of the above process are described in the later "Mechanics of Closure" section.
To examine the magnitude of the excess closure stress on the proppant, a parametric study of fracture width versus net pressure was performed using a pseudo three-dimensional (P3D) fracture model8. The model data was constructed to represent a simple three layer system with equal higher stress levels in the layers above and below a lower stressed pay interval. The effect of stress differential, between the pay and bounding intervals, the thickness of the pay interval and the Young's Modulus of the layers was investigated through numerous simulations. The P3D model was applied to this problem because it was convenient to use, though care had to be taken to consistently extract the response data (excess closure stress as a function of confining stress and modulus contrast).
The results of all simulations were interpolated to allow calculation of fracture conductivity (using 20/40 Ottawa sand) for any specific pay interval configuration. The results indicate that for larger Young's modulus values (greater than 4 million psi) and smaller pay thickness (less than 60 feet) the bounding layer stresses have a significant effect on the closure stress on proppant. The combined effect of the increase in closure stress felt by the proppant translates to reductions of over 50% in estimated fracture conductivity.