Slant Model

This model simulates the pressure response in a slanted well (wellbore enters the reservoir at an angle) within a rectangular-shaped reservoir with anisotropic heterogenities (differences in permeability in the x, y, and z directions), or dual porosity characteristics. The anisotropy is handled using a conformal mapping procedure that adjusts the boundary sizes accordingly to mimic the effect of increased or decreased permeability in each direction. The slanted well is oriented based on the inclination angle (s) and azimuth angle (q) and may be at any location within the reservoir.

This model supports infinite, no-flow, and constant pressure boundaries. Note that the effective wellbore length (Le) defines the wellbore area open to fluid flow. Thus, classical configurations like a well near a sealing fault, or a constant pressure boundary near intersecting faults can be easily modeled.

At very early times, the cylindrical source solution is used, which is followed by Green’s function solutions for horizontal wells as developed by Thompson et al. (1991). No-flow boundaries are modeled using the method of images. The result is superposed in time based on the rate history provided. Note that the dual porosity model provided is based on pseudo-steady state interporosity flow. The following flow regimes can be handled by this model:

  • Wellbore storage
  • Vertical radial flow
  • Linear horizontal flow
  • Elliptical flow
  • Horizontal radial flow
  • Boundary effects
  • Pseudo-steady state flow

Due to the additional complexity of a slanted wellbore, the solution method requires that the wellbore be split up into specified number of segments (Nw). Increasing the number of segments will result in higher precision in the solution, but with slower computational performance. A value of 100 segments is recommended as it handles most situations adequately.

References

"Efficient Algorithms for Computing the Bounded Reservoir Horizontal Well Pressure Responses", L.G. Thompson, J.L. Manrique and T.A. Jelmert, Paper SPE 21827 presented at 1991 Rocky Mountain Regional Meeting and Low-Permeability Reservoirs Symposium, Denver, CO, April 15 - 17.