Page 13 - Oil and Gas Simulations
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region is stable enough.                      condition, meaning that no fluid flow         A.
   This example model, which is shown         will occur across impervious boundaries       B.
                                              (e.g., between different branches). The
in Figure 2, uses the Subsurface Flow         reservoir is assigned a uniform fluid
Module in the COMSOL Multiphysics®            pressure of 122.45 psi, and the geometry
software to study the underground fluid       is constrained on all external boundaries.
flow and the effects of pumping on the        Loads are placed on the branch
rock. The model reduces the geometry of       boundaries to represent the well support
                                              forces. The well opening, however, is left
FIGURE 4. Simulation results showing the      free to deform in the horizontal direction.
pressure on the floor of the well (contours)
and the deformation of the branch walls          Model results (see Figure 4) give the
(scaled for visibility).                      deformation due to the pressure drop
                                              within the branch and the resulting
a multilateral well to one junction, and      velocity field of the fluid flow. The most
assumes elastic deformation. The domain       critical point in the branch appears to be
surrounding the borehole is represented       just above the junction.
by a poroelastic matrix.
                                                 This gives a clear idea of what is
   Pressure levels at the well boundaries     happening inside the branching junction,
will reveal the structural strength of        showing the full range of pressure and
the junction, prescribed by its depth         displacement. However, this data does not,
and by the pump specifications. Using         on its own, indicate how stable the well
the Poroelasticity interface, the model       is. The results show how pressure changes
describes properties of the surrounding       affect the stress and strain distribution,
production fluid (a hydrocarbon mixture       but to determine whether the borehole is
of oil, gas, and water) such as density,      stable enough without internal casing, a
dynamic viscosity, and compressibility. The   failure criterion is needed.
COMSOL® software simulation solves for
changes in fluid pressure after pumping          The 3D Coulomb criterion incorporates
begins and the resulting changes in stress,   cohesion and friction into an expression
strain, and displacement (see Figure 3),      relating rock failure to the principal
rather than their absolute values.            stresses and fluid pressure within the
                                              reservoir. If the pumping pressure
èWELL STABILITY                               compresses the reservoir enough, the rock
                                              walls will fail. In the simulation, the fail
In this model, geometric boundaries           expression will indicate which regions of
perpendicular to the top and bottom well      the well are within the “danger zone” by
axes are assigned the No flow boundary        accounting for principal stresses in each
                                              direction, the friction angle (a description
                                              of the shear strength of the soil), and
                                              several calibration constants. Plots of the
                                              fail values are shown in Figure 5, where
                                              negative values indicate a higher risk.

                                              èINTERPRETING THE FAIL                        FIGURE 5. COMSOL results showing the
                                              CRITERION                                     fail expression plotted on the branching
                                                                                            junction. A.) red surfaces indicating
                                              As expected, the greatest potential for       negative values (prone to failure) and blue
                                              failure is near the branching junction.       indicating positive values (stable). This plot
                                              The plot maps the well’s vulnerability        is shown for a borehole with no casing
                                              to mechanical failure due to pumping,         (bottom), a borehole with weak casing
                                              indicating for which operating conditions     (middle), and a borehole with medium-
                                              an interior borehole casing is necessary.     strength casing (top). B.) the gradient of
                                                                                            values over the entire branch is shown,
                                                 For the specific pumping operations        indicating how extreme the failure will be
                                              and well properties examined here,            in different regions.
                                              the casing is necessary in each case to
                                              prevent failure of the shaft. For wells
                                              with different pumping specifications,
                                              fluid pressure, stresses in the rock walls,
                                              or even different rock types, the results
                                              may be different. Multiphysics simulation
                                              is a valuable asset in determining the
                                              needs and dangers of many different
                                              multilateral well systems. v

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