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
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- 584 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|
Carlslaw, H.S. and Jaeger, J.C. 1959. Conduction of Heat in Solids,second edition. Oxford, UK: Oxford University Press.
Dake, L.P. 1978. Fundamentals of Reservoir Engineering. New YorkCity: Elsevier Scientific Publishing Company.
Dietz, D.N. 1965. Determination of Average Reservoir Pressure From Build-UpSurveys. J Pet Technol 17 (8): 955-959. SPE-1156-PA. http://dx.doi.org/10.2118/1156-PA.
Earlougher, R.C. Jr. 1977. Advances in Well Test Analysis, Vol. 5.Richardson, Texas, USA: SPE.
Gringarten, A.C. 1978. Reservoir Limit Testing for Fractured Wells. PaperSPE 7452 presented at the SPE Annual Fall Technical Conference and Exhibition,Houston, 1-3 October. http://dx.doi.org/10.2118/7452-MS.
Hagoort, J. 1988. Fundamentals of Gas ReservoirEngineering, No. 23. Amsterdam, The Netherlands: Developments in PetroleumScience, Elsevier Science Publishers B.V.
Helmy, M.W. and Wattenbarger, R.A. 1998. New Shape Factors for WellsProduced at Constant Pressure. Paper SPE 39970 presented at the SPE GasTechnology Symposium, Calgary, 15-18 March. http://dx.doi.org/10.2118/39970-MS.
Hovanessian, S.A. 1961. Pressure Studies in Bounded Reservoirs. SPEJ. 1 (4): 223-228. SPE-50-PA. http://dx.doi.org/10.2118/50-PA.
Jolley, L.B.W. 1961. Summation of Series, second revisededition. New York City: Dover Publications.
Muskat, M. 1937. The Flow of Homogeneous Fluids Through Porous Media.New York City: McGraw-Hill Book Co.
Peaceman, D.W. 1990. Discussion of Productivity of a HorizontalWell. SPE Res Eng 5 (2): 252-253. SPE-20306. http://dx.doi.org/10.2118/18298-PA.
Sneddon, I.N. 1995. Fourier Transforms. New York City: DoverPublications.