The key parameters of proppant transport in complex fractures

Evaluating essential features of proppant transport at engineering scales combining field measurements with machine learning algorithms

“…1 a) and fracture level (Fig. 1 b), including the particle settling velocity (Gadde et al, 2004;Mack et al, 2014;McCabe et al, 1993;Richardson and Zaki, 1954;Yew and Weng, 2014), the critical velocity to restart the settled proppant (also used as the critical turning velocity in complex fractures) (Cao et al, 2006;Hou, Jiang, Li, Zeng andCheng, 2017a, 2017b;Hou, Jiang, Liu, et al, 2017a, 2017bRakshit Sahai, Miskimins, & Olson, 2014), the flowing layer height (H 1 ) (Hou et al, 2019a(Hou et al, , 2019bNovotny, 1977;Patankar et al, 2002;Jing Wang, Joseph, Patankar, Conway and Barree, 2003) and the equilibrium dune level (EDLthe dune height divided by fracture height) (Alotaibi and Miskimins, 2019). Based on the field pumping schedules, those features are further calculated by employing the Velocity, Settling, Bi-power, and EDL models to yield a group of independent variables, which is one of the inputs for ML models (Table 2).…”

“…where C is the volume fraction of proppant; w is the fracture width, m. For a complex fracture network, the dragging of the carrying fluid is one of the most important motivations to drive the proppant turn into branch fractures (Rakshit Sahai et al, 2014). A minimum flowing rate of the slurry (υ turning ) is required for proppant turning, and is estimated by the proppant restarting condition (Cao et al, 2006;Hou, Jiang, Li, et al, 2017a, 2017b υ turning = 0.05 (…”

“…The particle movements could reflect the proppant transporting by evaluating the ratio between particle and fluid velocities (Hou, Jiang, Li, et al, 2017a, 2017b. The Velocity model is defined as { The proppant is tending to form an equilibrium dune in low-viscosity fluids under constant injection conditions (Hou et al, 2019a(Hou et al, , 2019b, as shown in Fig.…”