Based on simulations of a previously published hydraulic fracturing experiment performed by Casas et al. (2006), this paper presents the performance assessment of the famous analytical fracture 2D-models (PKN and KGD) and a 3D numerical model (FDM program FLAC3D of the ITASCA Inc.). Strain-softening models are used in the FLAC3D to describe the fracture creation and propagation as well as to present the material softening properties (permeability, tensile strength, cohesion, friction and dilation angel) as functions of the plastic strain. The results show that the numerical simulator has a much better performance and produces more reliable results than the analytical fracture models. However, numerical models have limitations and thus potential for further development.


Hydraulic fracturing is a high cost operation that, if successful, can significantly benefit the profitability of well operation. The effectiveness of hydraulic fracturing is in most cases directly dependent upon the fracture geometry created in a layered reservoir. However, there is no existing reliable method to accurately measure fracture geometry, especially the fracture width, during and after hydraulic fracturing treatments. Hence, the modelling of the hydraulic fracturing process is very important for a successful application of the fracturing treatment.

The most commonly used analytical models are the PKN model (named after Perkins & Kern 1961 and Nordgren 1972) and the KGD model (named after Khristianovich & Zheltov 1955 and Geertsma & de Klerk 1969). Both models rely on hypotheses, are 2D models and mostly suitable for simple conditions.

Numerical methods like Finite Element Method (FEM), Boundary Element Method (BEM), Finite Difference Method (FDM) and Distinct Element Method (DEM) are theoretically more advanced, more diversified and more accurate. 3D numerical models have the advantage of describing the actual fracture initiation and propagation as function of time. They can handle random spatial variations in elastic properties, rock strength, pore pressure, stress, strain, deformation and material heterogeneity. Fully 3D simulators are necessary, especially for deviated wells because of the complexity of stress state and the fracture geometry around an inclined borehole.

Most numerical simulators do not consider hydro-mechanical interactions, but simulate geohydraulic or geomechanical processes. The FDM program FLAC3D is a specific three dimensional simulator for thermo-hydro-mechanical (THM) coupled processes in rock formations and offers a wide range of capability in solving complex problems in Geomechanics. The main object of this paper is to compare the results from the FLAC3D with the results obtained from the experiment performed by Casas et al. (2006). Secondly, a similar comparison is done with the results from the analytical models.


Casas et al. (2006) performed a hydraulic fracturing test on a large block (0.762 × 0.762 × 0.9144 m3) of Colton sandstone with a high elasticity modulus and a low permeability. A centralized 0.0381m diameter hole was drilled along the entire height of the block and each end of the borehole was sealed with alloy steel. A central portion of the borehole (0.3048 m) was isolated and opened for fracture initiation.

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