Numerical inversion of laplace transforms in the solution of transient flow problems with discontinuities

Proceedings - SPE Annual Technical Conference and Exhibition

Volumn 6, Issue , 2008, Pages 3696-3710

  Al Ajmi, N ^a   Ahmadi, M ^b   Ozkan, E ^a   Kazemi, H ^a  

^a Department of Geology and Geological Engineering   (United States)

^b Norwest Questa Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECONVOLUTION; FUNCTIONS; TIME DOMAIN ANALYSIS; TRANSIENT ANALYSIS;

CONTINUOUS FUNCTIONS; DECONVOLUTION ALGORITHM; DIFFERENTIABLE FUNCTIONS; DISCONTINUOUS FUNCTIONS; LAPLACE TRANSFORMATIONS; NUMERICAL INVERSION OF LAPLACE TRANSFORM; PIECEWISE-CONTINUOUS; PRESSURE TRANSIENT ANALYSIS;

LAPLACE TRANSFORMS;

EID: 58849092836     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2118/116255-ms     Document Type: Conference Paper

References (28)

1. Abate, J. and Valkó, P. P. 2004. Multi-Precision Laplace Transform Inversion. Computers Math. Applic. 48: 629-636.
2. Bellman, R., Kalaba, R. E., and Lockett, J. A. 1966. Numerical Inversion of Laplace Transform: Applications to Biology, Economics, Engineering, and Physics. American Elsevier Publishing Co. Inc., New York, NY.
3. Chen, C. C. and Raghavan, R. 1996. An Approach to Handle Discontinuities by the Stehfest Algorithm. SPEJ (Dec): 363.
4. rd Ed. McGraw-Hill, Inc. New York.
5. Coats, K. H., Rapoport, L. A., McCord, J. R., and Drews, W. P. 1964. Determination of Aquifer Influence Functions from Field Data. JPT (Dec): 1417-1424.
6. Cohen, A. M. 2007. Numerical Methods for Laplace Transform Inversion. Springer Science+Business Media LLC. New York.
7. Correa, A. C. and Ramey, H. J. Jr. 1986. Combined Effects of Shut-in and Production: Solution with a New Inner Boundary Condition. Paper SPE 15579 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA. 5-8 Oct.
8. Crump, K. S. 1976. Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation. J. ACM 233: 89-96.
9. Duhamel, J. M. C. 1833. Mémoire sur la méthode générale relative au mouvement de la chaleur dans les corps solides polongé dans les milieux dont la température varie avec le temps. J. de Ec Polyt. (Paris) 14: 20-77.
10. Fetkovich, M. J. and Vienot, M. E. 1984. Rate Normalization of Buildup Pressure by Using Afterflow Data. JPT (Dec): 2211-2224.
11. Gaver, D. P. 1966. Observing Stochastic Process and Approximate Transform Inversions. Oper. Res. 14, 3: 459.
12. Ilk, D., Valkó, P. P., and Blasingame, T. A. 2005. Deconvolution of Variable-Rate Reservoir Performance Data Using B-Splines. Paper SPE 95571 presented at the SPE Annual Technical Conference and Exhibition. Dallas, TX. 9-12 Oct.
13. Iseger, P. D. 2006. Numerical Transform Inversion Using Gaussian Quadrature. Probability in the Engineering and Informational Sciences, 20. 1-44.
14. Kryzhniy V.V. 2004. High-resolution exponential analysis via regularized numerical inversion of Laplace transforms. J. Comp. Phys., Vol. 199/2, 618-630
15. Kryzhniy, V. V. 2006. Numerical Inversion of the Laplace Transform: Analysis via Regularized Analytic Continuation. http://laplacetransform.org/.
16. Kuchuk, F. J., Carter, R. G., and Ayesteran, L. 1990. Deconvolution of Wellbore Pressure and Flow Rate. SPEFE (March): 53-59.
17. Lamm, P. K. 2000. A Survey of Regularization Methods for First-Kind Volterra Equations. Surveys on Solution Methods for Inverse Problems, ed. D. Colton, H. W. Engl, A. Louis, J. R. McLaughlin, W. Rundell. Springer, Vienna and New York: 53-82.
18. LePage, W. R. 1961. Complex Variables and the Laplace Transform for Engineers. McGraw-Hill Inc. New York.
19. Levitan, M. M. 2003. Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests. Paper SPE 84290 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO. 5-8 Oct.
20. Meunier, D., Wittmann, M. J., and Stewart, G. 1985. Interpretation of Pressure Buildup Test Using In-Situ Measurement of Afterflow. JPT (Jan.): 143-152.
21. Onur, M. and Reynolds, A. C. 1998. Numerical Laplace Transformation of Sampled Data for Well-Test Analysis. SPEREE (June): 268-277.
22. Ozkan, E. and Raghavan, R. 1997. Some Strategies to Apply the Stehfest Algorithm for a Tabulated Set of Numbers. SPE Journal. 2 (Sept.): 363-372.
23. Roumboutsos, A. and Stewart, G. 1988. A Direct Deconvolution or Convolution Algorithm for Well-Test Analysis. Paper SPE 18157 presented at the SPE Annual Technical Conference and Exhibition. Houston, TX. 2-5 Oct.
24. Stehfest, H. 1970. Numerical Inversion of Laplace Transforms. Communications, ACM 13 (1): 47-49.
25. Talbot, A. 1979. The Accurate Numerical Inversion of Laplace Transforms, J. Inst. Maths. Applies., 23: 97-120.
26. Valkó, P. P. and Abate, J. 2004. Comparison of Sequence Accelerators for the Gaver Method of Numerical Laplace Transforms Inversions. International Journal for Numerical Methods in Engineering. 60: 979-993.
27. van Everdingen, A. F. and Hurst, W. 1953. The Application of the LaPlace Transformation to Flow Problems in Reservoirs, Trans. AIME 198: 171-176.
28. Von Schroeter, T., Hollaender, F., and Gringarten, A. C. 2004. Deconvolution of Well-Test Data as a Nonlinear Total Least-Squares Problem. SPEJ (Sept.): 375-390.