Oil and gas production from unconventional reservoirs generally requires hydraulic fracturing within layered reservoirs, which are usually stratified with layers of different mechanical properties. Vertical height growth of hydraulic fractures is one of the critical factors in the success of hydraulic fracturing treatments. Among all the factors, modulus contrast between adjacent layers is generally considered of secondary importance in terms of direct control of fracture height containment. However, arrested fluid-driven fractures at soft layers are often observed in outcrops and hydraulic fracture diagnostics field tests. Furthermore, conventional hydraulic fracturing models generally consider planar fracture propagation in the vertical direction. However, this ideal scenario is rather unsatisfactory and fracture offset at bedding planes was widely observed in experimental testing and outcrops. Once the offset is created, the reduced opening at the offset may result in proppant bridging or plugging and may also act as a barrier for fluid flow, and thus fracture height growth is inhibited compared to a planar fracture.
In order to illustrate the effect of modulus contrast on fracture height containment, this study proposed a new approach, which is based on the effective modulus of a layered reservoir. In this study, two-dimensional finite element models are utilized to evaluate the effective modulus of a layered reservoir, considering the effect of modulus values, fracture tip location, height percentage of each rock layer, layer thickness, layer location, the number of layers, and the mechanical anisotropy. Then, the effect of modulus contrast on fracture height growth is investigated with an analysis of the stress intensity factor, considering the change of effective modulus as the fracture tip propagates from the stiff layer to the soft layer. The results show the effective modulus is mainly dependent on the modulus values, fracture tip location, and height percentage of rock layers. This study empirically derived two types of effective modulus depending on fracture tip location, namely the modified height-weighted mean and the modified height-weighted harmonic average. By combining linear elastic fracture mechanics with the appropriate effective modulus approximations, the results indicate that hydraulic fracture propagation will be inhibited by the soft layer due to a reduced stress intensity factor.
A two-dimensional finite element model was utilized to quantify the physical mechanisms on fracture offset at bedding planes under the in-situ stress condition. The potential of fracture offset at a bedding plane is investigated by examining the distribution of the maximum tensile stress along the top surface of the interface. A new fracture is expected to initiate if the tensile stress exceeds the tensile strength of rocks. The numerical results show that the offset distance is on the order of centimeters. Fracture offset is encouraged by smaller tensile strength of rocks in the bounding layer, lower horizontal confining stress and higher rock stiffness in the bounding layer, weak interface strength, higher pore pressure, lower reservoir depth, and larger fracture toughness.Petroleum and Geosystems Engineerin
