Journal of Canadian Petroleum Technology
Volume 48,
Number 4,
April 2009,
64-71
Abstract
This paper extends the capacity of the current sand production models by
eliminating the influence of artificial conditions and numerical mesh on
localization and deformation response in the sanding model. Past studies
indicate strong size effects when using classical elastoplastic models.
To rectify this deficiency, a fracture energy regularization method is
implemented in the numerical model.The model incorporates both the
geomechanical aspects (e.g. rock elastoplastic deformation and rock
disaggregation), as well as the transport aspects (e.g. the role of seepage on
rock deformation and solid release). The model employs a Mohr-Coulomb flow
theory of elastoplasticity with friction hardening/cohesion softening. Emphasis
is given on calibration procedure and validation of the enriched model through
back analysis of triaxial and uniaxial compression tests. Next, the model is
used to compare the numerical predictions with laboratory data on sand
production. The comparison incorporates the stress and deformation, as well as
the sand volume.
The calibration study shows that friction hardening and cohesion softening can
satisfactorily reproduce numerically the weak sandstone response to various
loading conditions. Further, computation results of strain softening material
illustrates that a fracture energy regularization strategy enables the model to
exhibit mesh invariance of the energy dissipation.
Introduction
Sand production involves two distinct stages. These are: 1) mechanical
degradation of the intact sandstone rock to loose particles by the stress
concentration around the wellbore; and 2) the transport of the loose particles
by hydrodynamic forces to the wellbore. An effective sand production model must
be adequately equipped with the tools that simulate the phenomena associated
with both degradation and seepage forces. One such model is discussed in this
paper with an emphasis on modelling of the degradation process and a detailed
description of the elastoplastic modelcalibration.
As it has been discussed in the literature, rock mechanical degradation is
related to the development of micro-cracks as failure localizes in narrow bands
at post-peak strength. Development of the micro-cracks violates the continuum
mechanics assumption leading to spurious influence of the numerical mesh on the
formation response(1-7). This mesh dependency is separate from the
small numerical error, which should tend to zero with mesh refinement. As a
result of the mesh dependency, the numerical model looses its objectivity and
needs to be rectified.
Recognition of the deficiencies of the standard continuum theory in the
modelling of deformation discontinuity has led to the development of various
enrichment methods. De Borst(8) compared the performance of several
of these techniques. The common approach in all these methods is the
introduction of some sort of length scale that must be built into the
constitutive model.
Mesh independence for localization problems can be obtained in a pragmatic
fashion by scaling the softening rate in inverse proportion to the element
size. This approach was described by Crook et al.(7) and is based on
the work of Pietruszczak and Mroz(5) and Bazant and
Oh(6). The basic idea in this method is that fracture energy, which
is the energy dissipated due to the formation of micro-cracks, must not differ
for numerical meshes of various size.
© 2009. Petroleum Society of Canada (now Society of Petroleum Engineers)
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History
- Original manuscript received:
3 April 2007
- Meeting paper published:
12 June 2007
- Revised manuscript received:
19 February 2009
- Manuscript approved:
2 March 2009
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