A Model for Optimizing Proppant Distribution Between Perforations

ABSTRACT Uniform proppant distribution between perforation clusters is one of the goals in hydraulic fracturing operations. However, this can be challenging to achieve, even if limited entry is used to acheive a nearly uniform fluid distribution. Two mechanisms contribute to a non-uniform proppant distribution between perforations. The first is particle settling in the wellbore, which becomes especially important towards the toe of the stage where the flow velocity is lower. The second mechanism is related to proppant inertia, whereby some particles are unable to follow the fluid streamlines and miss the perforation. In this paper, a mathematical model is developed to simulate both of these physical phenomena and is calibrated against available experimental and computational data. The model is then combined with an optimization algorithm to investigate perforation designs leading to nearly uniform proppant distribution between perforations. It is found that it is possible to significantly improve proppant placement by varying perforation orientation along the stage. If the same orientation is required for all perforations, then perforations located in the lower part of the wellbore with azimuths between 110° and 120° lead to more uniform proppant distribution, compared to other cases. INTRODUCTION Many studies have addressed the problem of particle distribution between perforations because this is a critical issue for optimization of hydraulic fracturing treatments. One of the first experimental studies (Gruesbeck and Collins, 1982) investigated the problem of slurry flow in a perforated vertical well, as is typical for conventional hydraulic fracturing treatments. It was observed that particle size and viscosity play a significant role on the resultant amount of proppant leaving through the perforation. With the rise of unconventional resource development as well as computational capabilities, Computational Fluid Dynamic (CFD) models have been used to address the same problem of particle turning into a perforation (Wu and Sharma, 2016; Wu, 2018). What is interesting is that in this study authors observed practically no dependence on particle size and fluid viscosity. A model that is employed in this study for the optimization purposes (see Dontsov (2023)) is able to explain such a contradiction by showing that the parameters used in Gruesbeck and Collins (1982) and Wu and Sharma (2016); Wu (2018) lead to dominance of different particle turning mechanisms, which in turn caused different sensitivities.