Hydraulically fractured well productivity greatly depends on fracture conductivity, which itself is dictated by proppant transport and placement. To guide engineering design and evaluate performance of proppant placement, a full understanding of the underlying physics and robust numerical models are needed. This paper introduces a continuum approach for simulating the transport of multiple fluids and proppant particles within hydraulic fractures. To achieve computational efficiency, this proppant model is developed based on the assumption of multi-component single phase flow and captures proppant settling, hindering effects, proppant bed erosion and transport. Inter-particle stresses and collision are not numerically calculated but represented through empirical correlations to include the effects of particle clustering and hindered-settling. This model couples the fluid phase and particle phase through the slip velocity, which is governed by particle settling, particle-particle interaction and fluid-particle drag forces. The presented proppant model is validated by comparing numerical results with experimental data. With the calibrated simulation, the modeling capabilities on fracturing treatment design are demonstrated through sensitivity analysis. As illustrated in this study, this coupled three-dimensional model is capable of simulating proppant placement with various fracturing fluids and a wide range of commercialized proppants. This model can be broadly applied to improve fracturing design in various formations, including tight sandstone, shale, coal bed methane and carbonate reservoirs.
For hydrocarbon production from tight formations, hydraulically fractured wells usually provide an initial high production rate, which drops rapidly within a few months after reaching the peak value. Eventually, unexpected low recovery efficiency occurs. This unfavorable production decline has been commonly reported for various plays, such as the Vaca Muerta shale, the Barnett Shale, and the Permian Basin (Hryb et al., 2014; Baihly et al., 2015; Huang and Ghassemi, 2015; Xu et al., 2019).
In stimulated reservoirs, the mechanical properties of proppant particles and their coverage within the developed fracture network govern the extent of conductive reservoir volume and production performance (Warpinski, 2010; Cohen et al., 2013; Huang et al., 2015; Shiozawa and McClure, 2016; Su et al., 2017; Wang and Elsworth, 2018; Huang et al., 2019; Su et al., 2019). Proppant transport and placement has been identified as a key mechanism to explain this unfavorable behavior. Upon injection, hydraulic fractures can propagate several hundred meters away from the slurry inlets. However, due to the density difference between solid particles and the carrying fluid, sand particles tend to fall and form an immobile proppant bank at the bottom of the developed fracture (Kern et al., 1959; Patankar et al., 2002; Wang et al., 2003; Mack et al., 2014). The irregular geometry and wall roughness of the fractures can cause particle jamming and bridging, which could prevent proppant from moving to the fracture tip and entering reactivated natural fractures (Liu and Sharma, 2005; Tong and Mohanty, 2016; Raterman et al., 2017; Ray et al., 2017). Therefore, only limited fracture surface area can be covered with proppant. Premature closure is always observed for the open regions filled with no or few proppant particles (Warpinski, 2010; Raterman et al., 2017; Wang and Elsworth, 2018; Huang et al., 2019). Only stimulated regions in the vicinity of a wellbore can be filled with enough proppant and unremittingly contribute to long-term production (Cohen et al., 2013; Huang et al., 2015; Barree et al., 2017; Wang and Elsworth, 2020). To enhance fracturing efficiency and overall production, both researchers and operators have searched for engineering solutions to mitigate these observed challenges on proppant transport and distribution. So far, a variety of fracturing fluid and proppants have been manufactured and used to improve proppant transport (Montgomery et al., 2013; Liang et al., 2016; Huang et al., 2018; Ba Geri et al., 2019; Xu et al., 2019). To guide engineering design and evaluate performance, a full understanding of the underlying physics and robust numerical models are necessary.