Petroleum Science

, Volume 8, Issue 1, pp 63–69 | Cite as

A novel steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs

Article

Abstract

It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional (3-D) flow into two-dimensions (2-D). This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs. Firstly, the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir. Then, using the fundamental solution and the Simpson integral formula, the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section. Two case-studies are given in the paper, the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data, indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.

Key words

Horizontal well point-source function bottom water driver gas reservoir steady-state productivity 

References

  1. Anklam E G and Wiggins M L. Horizontal-well productivity and wellbore pressure behavior incorporating wellbore hydraulics. Paper SPE 72361 presented at the SPE Production Operations Symposium, 16-19 April 2005, Oklahoma City, OklahomaGoogle Scholar
  2. Babu D K and Odeh A S. Productivity of a horizontal well. SPE Reservoir Engineering. 1989. 4(4): 417–421CrossRefGoogle Scholar
  3. Babu D K and Odeh A S. Productivity of a horizontal well: Appendices A and B. Paper SPE 18334 presented at the SPE Annual Technical Conference and Exhibition, 2–5 October 1988, Houston, TexasGoogle Scholar
  4. Borisov J P. Oil production using horizontal and multiple deviation wells. The R & D Translation Company, Bartlesville, Oklahoma, 1984Google Scholar
  5. Billiter T, Lee J and Chase R. Dimensionless inflow-performance-relationship curve for unfractured horizontal gas wells. Paper SPE 72361 presented at the SPE Eastern Regional Meeting, 17–19 October 2001, Canton, OhioGoogle Scholar
  6. Caralaw H S and Jaeger J C. Conduction of heat in solids. Oxford University Press. 1946. 353–386.Google Scholar
  7. Chen W, Zhu D and Hill A D. A comprehensive model of multilateral well deliverability. Paper SPE 64751 presented at the International Oil and Gas Conference and Exhibition in China, 7–10 November 2000, Beijing, ChinaGoogle Scholar
  8. Giger F M, Reiss L H and Jourdan A P. The reservoir engineering aspects of horizontal drilling. Paper SPE 13024 presented at the 59th Annual Technical Conference and Exhibition, 16–19 September 1984, Houston, TexasGoogle Scholar
  9. Giger F M. Horizontal wells production techniques in heterogeneous reservoirs. Paper SPE 13710 presented at the Middle East Oil Technical Conference and Exhibition, 11–14 March 1985, BahrainGoogle Scholar
  10. Gradshteyn I S and Ryzhik I M. Table of Integrals, Series and Products (Seventh edition). Academic Press Inc., San Diego, CA., California, U.S.A, 46–49, 2007Google Scholar
  11. Gringarten A C and Ramey H J. The use of source and Green’s functions in solving unsteady-flow problems in reservoirs. SPE Jounral 1973. 5(13): 285–296 (Paper SPE 3818)CrossRefGoogle Scholar
  12. Helmy M W and Wattenbarger R A. Simplified productivity equations for horizontal wells producing at constant rate and constant pressure. Paper SPE 49090 presented at the SPE Annual Technical Conference and Exhibition, 27–30 September 1998, New Orleans, LouisianaGoogle Scholar
  13. Joshi S D. Augmentation of well productivity using slant and horizontal wells. Journal of Petroleum Technology. 1988. 6(40): 729–739 (Paper SPE 15375)CrossRefGoogle Scholar
  14. Karcher B J and Giger F M. Some practical formulas to predict horizontal well behavior. Paper SPE 15430 presented at the SPE Annual Technical Conference and Exhibition, 5–8 October 1986, New Orleans, LouisianaGoogle Scholar
  15. Kong X Y. Advanced Mechanics of Fluids in Porous Media. Hefei: Science and Technology University Press. 1999: 103–125 (in Chinese)Google Scholar
  16. Larsen L. Productivity computations for multilateral, branched and other generalized and extended well concepts. Paper SPE 36754 presented at the SPE Annual Technical Conference and Exhibition, 6–9 October 1996, Denver, ColoradoGoogle Scholar
  17. Lu J. An analytical solution of steady-state flow equation for the productivity of a horizontal well. Petroleum Exploration and Development. 1993. 20(Supplement): 135–140 (in Chinese)Google Scholar
  18. Lu J. New productivity formulae of horizontal wells. Journal of Canadian Petroleum Technology. 2001. 40(10): 55–67CrossRefGoogle Scholar
  19. Lu J, Lin T, Rogers R, et al. A mathematical model of horizontal wells pressure drawdown and buildup. Journal of Canadian Petroleum Technology. 2002. 41(10): 45–57CrossRefGoogle Scholar
  20. Lu J, Lin T, Rogers R, et al. A supplemental discussion of productivity formulae of horizontal wells. Journal of Canadian Petroleum Technology. 2003. 42(10): 23–27Google Scholar
  21. Merkulov V P. Le debit des puits devies et horizontaux. Neft. Khoz. 1958. 1(6): 51–56.Google Scholar
  22. Reiss L H. Production from horizontal wells after five years. Journal of Petroleum Technology. 1987. 39(11): 1411–1416 (Paper SPE14338)CrossRefGoogle Scholar
  23. Renard G and Dupuy J M. Formation damage effects on horizontal-well flow efficiency. Journal of Petroleum Technology. 1991. 7(43): 786–789 (Paper SPE 19414)CrossRefGoogle Scholar
  24. Zwillinger D. Standard Mathematical Tables and Formulae. New York: CRC Press. 1996. 103–104Google Scholar

Copyright information

© China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.State Key Laboratory of Oil and Gas Reservoir Geology and ExploitationSouthwest Petroleum UniversityChengdu, SichuanChina
  2. 2.School of ScienceSouthwest Petroleum UniversityChengdu, SichuanChina

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