Horizontal Model

This model simulates the pressure response in a horizontal well 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 horizontal well is oriented in the x-direction and may be at any location within the reservoir (see figure below), and the 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

References

1. "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.

2. "Determination of Horizontal Permeability Anisotropy from Horizontal Well Tests", M.B. Issaka, K. Zaoral, A.K. Ambastha, L. Mattar, Paper presented at the 2000 SPE Saudi Arabia Section Technical Symposium, Dahran, Saudi Arabia, October 21 - 23.