Title: Chebyshev Spectral Collocation Method for
Leakoff in Hydraulic Fracturing
Author(s): M. Sanchez, D. Lin and J.-C. Roegiers, The
University of Oklahoma
Presentation: 8th International Conference on
Computer Methods and Advances in Geomechanics
Location: West Virginia USA
Date: 1994
Abstract: The behavior of a non-Newtonian fracturing
fluid flowing through a hydraulically-induced fracture in a
rock is simulated considering the flow of a viscoelastic,
incompressible fluid in a channel with parallel walls,
driven by steady uniform suction through the porous channel
wall. The Harnoy constitutive equation is used to model the
viscoelastic fluid behavior. The solution of the governing
differential equation is constructed numerically by
implementing a family of spatial discretization formulae
based on polynomial expansions. It is found that the
velocity profiles flatten as the amount of elasticity, as
measured by the Deborah number (De), increases. The skin
friction in the walls also increases with De. The numerical
results for the velocity profiles agree well with a first
order perturbation solution up to around De = 0.15. Loss of
convergence occurs at different points depending upon the
mesh size and upon the suction Reynolds number.
