The Effect of Layered Modulus on Hydraulic-Fracture Modeling and Fracture-Height Containment

Abstract

Summary Oil and gas production from unconventional reservoirs, which are usually stratified with layers having different mechanical properties, generally requires the aid of hydraulic–fracturing technology. Predicting hydraulic–fracture–height growth is one of the critical factors in designing successful hydraulic–fracturing treatments. It has been well–documented that the in–situ–stress contrast between adjacent layers and interface properties are the dominating factors in fracture–height containment, whereas the modulus contrast between adjacent layers is generally considered to be of secondary importance in the direct control of fracture–height containment. However, the arrest of fluid–driven fractures at soft layers is often observed in outcrops and hydraulic–fracture–diagnostic field tests. The objective of this study is to investigate fracture–height containment resulting from the modulus contrast between adjacent layers. To illustrate the effect of modulus contrast on fracture–height containment, this study proposes a new approach that uses the effective modulus of a layered reservoir. We use 2D finite–element models to evaluate the effective modulus of a layered reservoir, considering the effects of modulus values, fracture–tip location, height percentage of each rock layer, 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, taking into account the change of the effective modulus as the fracture tip propagates from the stiff layer to the soft layer. This study shows that the detail of layering does not affect the effective modulus and the only important parameters are fracture–tip locations, modulus values, and the height percentage of each rock layer. In addition, this study empirically derives two approximations of effective moduli depending on fracture–tip locations: the modified height–weighted mean and the modified height–weighted harmonic average. Results from combining linear–elastic fracture mechanics with the effective–modulus approximations show that height growth will be inhibited by the soft layer because of a reduced stress–intensity factor. The effective moduli can be applied to other hydraulic–fracture models to take into account the layering effect. This study also shows that soft layers inhibit hydraulic–fracture–height growth in layered reservoirs. As a result, hydraulic–fracture–height containment within a stratified rock stack can be better evaluated by comparing the modulus contrast between adjacent layers.