A Semi-Analytical Model for Estimation of Hydraulic Fracture Height Growth Calibrated with Field Data

Abstract The vertical growth of hydraulic fractures in layered formations has been a topic of interest amongst researchers because of its critical influence on well performance. The analytical solution to the fracture vertical growth in layered formations is primarily based on force balance amongst various formation layers of segments that the vertical fracture intersects. The pressure associated with fluid movement in the vertical direction in a hydraulic fracture is generally ignored in most semi-analytical solutions to height-growth problems, especially if the vertical growth occurs at a slow pace. For a slow advancing vertical fracture, the tips are be assumed to be near stationary, and the assumption is termed as equilibrium-height model. The model was first conceptualized for a simple 3-layered problem and later extended to multi-layered applications. The available literature shows model-derived solution for simple cases but lack in-depth study of real-world examples, which in doing so could highlight some of the model limitations. The semi-analytical model presented in the study, was first benchmarked by replicating the data published in the existing literature, and then applied to the field cases to compare its output with the observed data. Unlike the typical approach taken in the literature where the location of one of the tips of the fracture is assigned and the position of other tip is determined, the current model determines the most suitable position for a fracture of given height and stress profile. Additionally, new features were added to the model when evaluating the field cases. These include, incorporating calculation procedures that provide accurate fracture placement for given conditions, handling layered property inputs up to 100 layers, and the ability to include variable fracture pressure as opposed to a constant pressure approach. The model was applied on several cases from the field, four of which are presented here. The analysis showed that there is a close agreement between the predicted and the observed fracture heights. The hybrid feature of the model with inclusion of non-uniform pressure drop profile in the fracture, also helped in calibrating a case where a mismatch was observed. It was concluded that this model can predict fracture height growth with reasonable accuracy for cases with low injection rates where low viscosity fluid is used and requires calibration in cases where high net pressures are expected. The newly developed model is simple to program and can assist in making quick estimates of fracture vertical growth in vertical wells with low-rate fracture stimulation treatments.