Semisteady-State Productivity of a Well in a Rectangular Reservoir Producing at Constant Rate or Constant Pressure
- Jacques Hagoort (Hagoort & Associates BV)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2011
- Document Type
- Journal Paper
- 677 - 686
- 2011. Society of Petroleum Engineers
- 5.5 Reservoir Simulation
- Shape factor, Constant-Rate depletion, Semisteady-State, Constant-pressure depletion, Productivity Index
- 2 in the last 30 days
- 636 since 2007
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In this work, we present two exact analytical formulas for the semisteady-state (SSS) productivity index (PI) of an arbitrarily positioned well in a closed, rectangular reservoir: one for production at a constant rate and one for production at a constant pressure. They are based on exact analytical solutions for the long-time well-pressure and well-rate responses obtained by means of Fourier transformation. The formulas are relatively simple and can be implemented in a standard spreadsheet program. Constant-rate and constant-pressure dimensionless PIs and associated shape factors are presented for a wide range of dimensionless well radii, well locations, and aspect ratios. Constant-pressure PIs are always lower than constant-rate PIs. The difference depends on dimensionless well radius and aspect ratio and can be as much as 20% for very large aspect ratios. We illustrate the new formulas by an example calculation of the SSS production rate of a vertical and a horizontal well in a box-shaped gas reservoir.
The PDF file includes an associated discussion by Jing Lu of The Petroleum Institute.
|File Size||1 MB||Number of Pages||12|
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