Probabilistic Distribution Model to Predict Fracture Height

The Hydraulic Fracturing Simulation (HFS) fluid pressure gradient during propagation is almost always less than the rock mass horizontal minimum stress gradient. In models with independent lateral stresses, a fracture will grow more in a direction that requires less "work" needed to extend the fracture and increase its aperture. We study geometry of a fracture where a one-layer single fracture model is present to assess how fractures propagate. We use UDEC™, to model a 2D domain, and our results offer better understandings of fracture geometry. We then provide a probabilistic model to examine which outcomes distribution is more suitable to predict fracture height. We have found that a Log Normal distribution seems more suitable for fracture height outcome values. We then examined our model results with those from other solutions equations—Sneddon, GdK, and PKN—using Monte-Carlo simulation. Our model results show an acceptable agreement with the semianalytic and analytic expressions presented in those classic contributions to the subject of hydraulic fracture propagation. 1. INTRODUCTION Since the early studies of Hydraulic Fracturing Stimulation (HFS), fracture geometry has proven to be a useful and interesting subject to model and predict (Geertsma & Haafkens, 1979; Perkins & Kern, 1961). Although these models, referred to as GdK and PKN, have some limitations in the predictions of fracture heights in 2D, they are widely popular because of their simplicity and practicality. Subsequently, as more high-quality HFS field data became available (Fisher & Warpinski, 2012a, 2012b; Palmer & Kutas, 1991; Stegent et al., 2020; Warpinski, 1985, 2011b, 2011a), research has become more focused on how to verify the prediction accuracy of mathematical and numerical models, concentrating on the geometry of single induced fractures—height, width, aperture. An induced fracture system is a complex phenomenon in HFS, given heterogeneities in stress, elastic properties, and rock mass fabric (bedding, joints, lithological contrasts…). Fractures (joints) can be naturally present in the rock mass, they can be created by injection, or existing fractures can be extended during the HFS operation. Opening of fractures (Mode I) is well-understood, and dilatant shear (Mode II) of appropriately oriented natural fractures can lead to larger stimulated volumes. Putting other factors aside, it is widely accepted that larger area fractures (Modes I and II) within the target formation are desirable (Kim & Moridis, 2015; Soroush et al., 2011). The overall success of HFS, if only higher production or injection rates are considered, is related to the larger surface contact area that the stimulated fracture network affords: the higher the direct surface area created and the larger the stimulated volume, the better the flow outcomes.