Numerical Modeling of Fracture Height Propagation in Multilayer Formations Considering the Plastic Zone and Induced Stress

[Image: see text] Hydraulic fracturing and acid fracturing are very effective stimulation technologies and are widely used in unconventional reservoir development. Fracture height, as an essential parameter to describe the geometric size of a fracture, is not only the input parameter of two-dimensional fracturing models but also the output parameter of three-dimensional fracturing models. Accurate prediction of fracture height growth can effectively avoid some risks. For example, petroleum reservoirs produce a large amount of formation water because wrong fracture height prediction leads to the connection between the oil or gas reservoir and the water layer. Although some fracture height prediction models were developed, few models considered the effects of the plastic zone, induced stress, and heterogeneous multilayer formation and its interaction. Therefore, considering the influence of many factors, an improved fracture-equilibrium-height model was developed in this study. The successive over-relaxation iteration method and the displacement discontinuity method were used to solve the model. We investigated the effects of the geological and engineering factors on fracture height growth by using the model, and some important conclusions were obtained. The higher the fracture height, the larger the plastic zone size, and the more obvious its influence on fracture height propagation. High overlying or underlying in situ stress and fracture toughness and low fluid density played a positive role in limiting the growth of the fracture height. Induced stress caused by fracture 1 could not only inhibit the height growth of fracture 2 but also promote its growth. The model established in this paper could be coupled to a fracturing simulator to provide a more reliable fracture height prediction.