Wellbore production rates can be significantly influenced by the frictional pressure drop in long inclined or horizontal wells, particularly in high permeability reservoirs with small pressure drawdown. In this paper, a steady-state model is presented which couples the Darcy flow into perforations from the reservoir with the frictional flow in the wellbore.
Reservoir-perforation behaviour is modelled by flow into discrete well perforations within a homogeneous, anisotropic reservoir bounded by infinite parallel planes. By considering the flow into individual perforations, the importance of adjacent boundaries, well inclination, perforation density, perforation phasing and crushed zone damage can be studied. Wellbore flow, specified as either single or multiphase, accounts for the pressure drop along the wellbore due to well inclination, pipe friction and perforation inflow.
To enable flexible wellbore design, the well is partitioned into segments each with its own inclination, length, and number of perforations. Perforation distributions can be user-defined or optimized through various optimization strategies; for example, maximization of wellrate, or uniformity of specific inflow. The model described in the paper has been implemented in software and is currently being used as a design tool.
In the past few years several papers have reported on the importance of wellbore pressure drop in long horizontal and inclined wells. This pressure drop can be significant when compared with the drawdown for highly productive completions, where it can adversely affect wellbore inflow. Some control of wellbore inflow is possible through the use of perforated wellbores. Perforation design, which is central to this paper, can assist in maximizing well productivity or delaying water or gas breakthrough times.
The simplest models used to study wellbore flow are semi-analytical and aim to predict the importance of pressure drop on the inflow performance of a well. More computationally intensive models discretize the well, and simulate the continuous variation of wellbore fluid rates and properties. Ihara et al. developed such a model based on air-water flow loop experiments measuring the pressure drop due to the injection of both phases. Simpler pressure drop calculations have been included in conventional reservoir simulators, but generally lack the detailed physics of perforation inflow which can be included in specialized models.
The model described here extends the perforated wellbore model developed by Landman and Goldthorpe, which couples the frictional pressure drop along the wellbore with Darcy behaviour in an infinite isotropic homogeneous reservoir.