Title: Shearing Motion of Dense Proppant Material
in Hydraulic Fracturing
Author(s): D. Lin and J-C. Roegiers, The University
of Oklahoma
Presentation: 1st NARMS (North American Rock
Mechanics Symposium) -The University of Texas at Austin
Location: Austin, Texas USA
Date: June 1-3, 1994
Abstract: Proppant transport and placement are
critical parts of hydraulic fracturing
treatments. Such particulate flow consists of two
interacting materials i.e., proppants and the carrying
fluid. Two-phase flow mechanics requires specifications of
stresses for each phase, plus a relation expressing the
interaction of both materials. The character of the
interparticle forces in the dilute and dense regions is
essentially different. The constitutive equations for dilute
flow specialize the drag to include Stokes and Faxen forces,
and the lift to accommodate the slip-shear force and the
disturbance-shear force. While in dense proppant flow the
solid fraction is high, it is more difficult for them to
move with respect to one another. In the state where maximum
packing has been reached, the particles are so closely
interlocked that only rigid motion is possible. A locking
phenomenon occurs. Here we review briefly the approach of
Passman, Nunziato, and Bailey (1986) to clarify the origin
of the momentum equations arising in the dense proppant
flow. In addition, the constitutive equations fort he
momentum transfer are formulated to account for the viscous
transfer arising form the highly dense particles. In order
to try to fully understand the problem, we have performed
parameter studies and numerical analyses. To solve the
Poiseuille flow problem in the fracture channel we have used
a spectral method which is known to produce accurate
results. The proppant concentration profiles, shear stress
distribution, and velocity profiles for fluid and proppant
are given. The explanation of the results is provided.
