1. Sand Production Modelled with Darcy Fluid Flow Using Discrete Element Method
M. N. Nwodo, Y. P. Cheng, N. H. Minh
Introduction
• About 70% of the world’s oil reserves are contained in weakly-
consolidated reservoirs; 60% of all petroleum reservoirs in the world
are sandstones. These weakly-consolidated sandstone reservoirs are
liable to sand production which is the erosion of weakened and de-
bonded sandstones by the produced oil fluid (Fig. 1).
fig.1 Sand production.
• For efficient sand management therefore, there has been need for a
reliable study tool to understand the mechanism of sanding
• One method of studying sand production is the use of the widely
recognized Discrete Element Method (DEM), Particle Flow Code
(PFC3D) which represents sands as granular individual elements
bonded together at contact points.
• However, there is limited knowledge of the particle-scale behavior of
the weak sandstone, and the parameters that affect sanding.
• The model in this paper considers horizontal oil well (Fig. 2).
fig. 2 Illustrating horizontal oil well drilling.

2. Aims and Objectives
• This paper aims to investigate the reliability of using PFC3D 3.0 in
understanding the behavior of compacted oil weak sandstone under
stress.
• The following objectives emphasize how the aim is to be achieved:
 An isotropic tri-axial test on a weak oil sandstone sample to calibrate
and validate the PFC3D model.
 Investigation of the effect of Darcy flow on the number bonds failure
in the sample.
 Parametric studies on the effect of confining stresses, fluid flow
pressure on the number of bonds failure in the sample.
 Validate flow rate – permeability relationship to verify Darcy’s fluid
flow law.
Material and Methods
• Computer simulations using PFC3D parallel bond model are utilized.
• Sample adapted from published experimental work. Model geometry
is 10m, 10m height and diameter respectively (Fig. 3).
• Numerical servo-mechanism applied to achieve specified confining
reaction force, therefore, stress.
• The fluid flow network comprised of domains of pores created by
every four neighboring particles (Fig. 4) such that each flow link or
pipe was a face of a tetrahedron.
Fig. 3 Sample geometry Fig. 4 Fluid flow network

3. Results I
• The results from the isotropic tri-axial computer simulation tests are
shown in Figs. 5-7 depicting stress-strain relation (Fig. 5), normalized
stress-strain relation (Fig. 6), and volume-axial strain behavior (Fig.
7). Axial/radial stress is set constant at 1MPa.
Fig. 5 Fig. 6
Fig. 7
Results II
• The results from the computer simulations tests without fluid flow
show the relations between number of produced sands and the
confining stress for the sample model (Fig. 8) and a chosen smaller
model (Fig. 9).
Fig. 8
Fig. 9

4. Results III
• The variation of the number of broken bonds with fluid pressure (Fig. 10), and the rate of the breakage for different fluid pressures (Fig. 11) are
shown. A graph of flow rate against permeability to verify simple Darcy’s fluid flow law is also presented (Fig. 12).
Fig. 10 Fig. 12
Fig. 11

5. Conclusion and Discussion
• Isotropic Tri-axial Test: A steep slope with clear peak strength of the sample (Fig. 5) can be deduced. Data successfully calibrated the 4.4MPa
Uniaxial Compression Strength (UCS) of the chosen sample. The steep slope is probably due to the additional stiffness of parallel bonding. The
observed shape in stress-strain graph (Fig. 5) is similar to stress-strain behavior of 4.5% cementation of drained sample reported in a published
work. The parallel bond model seems to depict the behavior of real cemented sandstones.
• Tests Without Fluid Flow: there seems to be an exponential increasing relationship between the number of sanding and confining stress (Fig. 8) for
the sample model, while observing a curvilinear behavior for the chosen smaller model (Fig. 9). This shows the model’s scale factor effect which is
largely neglected by studies in this research area.
• Tests With Fluid Flow: the presence of hydrodynamic fluid flow induces tensile force in the particle-fluid interaction, and may contribute to tensile
failure of particles within the cavity region during oil production, as shown by the increasing number of broken bonds with fluid pressure (Fig. 10).
• By successfully calibrating the parallel bond model for a weak sandstone sample, the PFC numerical tool seems reliable in studying the
micromechanical behavior of weak oil sandstones. Establishing this confidence at the use of the tool will enable a faster and more economical
means of predicting the sanding behavior of weak sandstones in sandstones reservoir, with the view to properly manage and control sanding for
efficient oil production in such oil reservoirs.
• As a further study, a better understanding of the micromechanical behavior of real weak sandstones is required, including investigations on the
effect of particle crushing on sand production.
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