Comparison of Pseudo-3D and Fully-3D Simulations of Proppant Transport in Hydraulic Fractures, Including Gravitational Settling, Formation of Proppant Banks, Tip-Screen Out, and Fracture Closure

Abstract

A modeling framework is developed to describe proppant transport (including gravitational settling and tip-screen out) in a hydraulic fracturing simulator that can function as either fully-3D or pseudo-3D. The simulator locally enforces mass balance of fluid and proppant and applies appropriate boundary conditions for mechanical calculations. The simulator uses recently developed constitutive equations that smoothly capture the transition from Poiseuille flow to Darcy flow as the proppant concentration transitions from a dilute mixture to a packed bed. We develop new constitutive relations that enable the model to describe fracture closure against proppant (at either low or high concentration) after the end of injection. We also develop a framework for modeling proppant settling in a pseudo-3D model. The method ensures a continuous solution, which guarantees convergence and accuracy with refinement of the temporal and spatial discretization. The framework allows proppant to settle into a proppant bank at the bottom of the fracture. The proppant bank can grow, remain stationary, or erode, depending on flow conditions. The simulator can describe tip-screen out (TSO) and the tendency for the volumetric flowing fraction of proppant to exceed the volumetric fraction of proppant due to the tendency of proppant to flow at the center of the fracture aperture. Pseudo-3D simulations are compared to the fully-3D simulations for both hydraulic fracturing and long-term production. For hydraulic fracturing, the pseudo-3D simulations are able to substantially reproduce the results from the fully-3D simulations and are far more computationally efficient. The simulation methods are compared using a variety of values for proppant size, fluid viscosity, and proppant density. An optimized proppant schedule is tested in order to improve horizontal proppant placement and prevent excessive tip screen-out. The simulations indicate that because fracture closure can be slow in very low permeability formations, substantial settling occurs after the end of injection, significantly worsening vertical proppant placement. For simulation of long-term production, the pseudo-3D results deviate strongly from the fully-3D simulations, indicating that the pseudo-3D model is not suitable for simulating the production phase, as currently formulated.

The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

“…Unfortunately, the final distributions of proppant grains are virtually impossible to image nowadays, and direct numerical simulations of suspension flows in narrow apertures have just begun to emerge (Shiozawa & McClure, 2016;Tomac & Gutierrez, 2015). In general, the processes of proppant transport and settlement are complex and dependent on a large number of parameters including proppant density, fracking fluid properties, pumping rate, and fracture geometry.…”

“…In general, the processes of proppant transport and settlement are complex and dependent on a large number of parameters including proppant density, fracking fluid properties, pumping rate, and fracture geometry. Unfortunately, the final distributions of proppant grains are virtually impossible to image nowadays, and direct numerical simulations of suspension flows in narrow apertures have just begun to emerge (Shiozawa & McClure, 2016;Tomac & Gutierrez, 2015). The monolayer configuration has been traditionally considered as either difficult or impossible to achieve and treated more of a curiosity rather than technologically relevant scenario (Harrington & Hannah, 1975;Wendorff & Alderman, 1969), however, this view has been challenged in recent works (Brannon et al, 2004;Palisch et al, 2010).…”

A new model for simulating particle transport in a low‐viscosity fluid for fluid‐driven fracturing

“…The dimension reduction strategy can dramatically reduce the element number, which can significantly reduce the computational time. This dimension reduction strategy is inspired by the model proposed by Shiozawa and McClure, but all the physical equations and methods are different. The solving procedure of our model is explained in details as follows based on the flowchart.…”

Bed load proppant transport during slickwater hydraulic fracturing: Insights from comparisons between published laboratory data and correlations for sediment and pipeline slurry transport

“…Industry publications are increasingly adopting the view that bed load transport is a dominant process in slickwater fracturing (Patankar et al, 2002;Wang et al, 2003;Brannon et al, 2005;Woodworth and Miskimins, 2007;Mack et al, 2014). Correlations based on bed load transport have been incorporated into field scale fracturing simulators (Weng et al, 2011;Shiozawa and McClure, 2016). This paper revisits the issue of whether bed load transport plays a significant role at the field scale.…”