Along with horizontal drilling techniques, multi-stage hydraulic fracturing has improved shale gas production significantly in past decades. In order to understand the mechanism of hydraulic fracturing and improve treatment designs, it is critical to conduct modelling to predict stimulated fractures. In this paper, related physical processes in hydraulic fracturing are firstly discussed and their effects on hydraulic fracturing processes are analysed. Then historical and state of the art numerical models for hydraulic fracturing are reviewed, to highlight the pros and cons of different numerical methods. Next, commercially available software for hydraulic fracturing design are discussed and key features are summarised. Finally, we draw conclusions from the previous discussions in relation to physics, method and applications and provide recommendations for further research.

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Piezocone Penetration Test (CPTu) is widely used in offshore projects to obtain soil parameters, such as the undrained shear strength. Due to depth limitations to perform this test, it is common to obtain data until around 40m when the conductor installation process would require at least double the depth. The present work uses extrapolation techniques based on analytic and heuristic approaches to estimate data beyond the depth domain of CPTu tests. Design of the conductor casing is highly dependent on soil properties, since it serves as a foundation element of the well. Estimation of the soil parameters is based on deepwater CPTu data from Brazilian offshore basins. Three analytical approaches are used in this study (linear and non-linear regressions: second and third degrees). Moreover, Artificial Neural Networks (ANN) (dense, convolutional and recurrent networks) are also employed to predict the soil behavior. Methodologies were applied, validated and compared to evaluate their capability to accurately estimate the undrained shear strength. Python subroutines were developed and applied to sets of homogeneous and heterogeneous data from CPTu tests. The undrained shear strength was estimated beyond the test domain until the depth of interest to the conductor casing design around 80m. For this purpose, both groups of techniques were validated analyzing the efficiency of the fitting process, the associated error and coefficient of determination of each methodology. From that point on, we compared data from analytical methods and the neural networks application, verifying which technique fits better on the datasets. These methods of estimation of soil properties work as an instrument to support the decision-making process in top-hole drilling operations. The datasets analyzed present different levels of soil heterogeneity and performing the extrapolation analysis brings additive information to understand the soil behavior beyond depths reached by CPTu tests. This contributes to the safety and reliability of conductor casing design and installation. To the authors' knowledge, this analysis is rarely performed in the literature.