SPE Reservoir Evaluation & Engineering
Volume 14, Number 6, December 2011, pp. 677-686

SPE-149807-PA

Semisteady-State Productivity of a Well in a Rectangular Reservoir Producing at Constant Rate or Constant Pressure

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DOI  More information 10.2118/149807-PA http://dx.doi.org/10.2118/149807-PA

Citation

  • Hagoort, J. 2011. Semisteady-State Productivity of a Well in a Rectangular Reservoir Producing at Constant Rate or Constant Pressure. SPE Res Eval & Eng  14 (6): 677-686. SPE-149807-PA. http://dx.doi.org/10.2118/149807-PA.

Discipline Categories

  • 1.6.3 Evaluation of Reservoir Behavior/Performance
  • 6.6.5 Well Performance Monitoring, Inflow Performance

Keywords

  • Productivity Index, Shape factor, Semisteady-State, Constant-Rate depletion, Constant-pressure depletion

Summary

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.

© 2011. Society of Petroleum Engineers

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History

  • Original manuscript received: 20 September 2010
  • Revised manuscript received: 21 March 2011
  • Manuscript approved: 24 May 2011
  • Published online: 13 December 2011
  • Version of record: 28 December 2011