Deconvolution of well-test data as a nonlinear total least-squares problem

SPE Journal

Volumn 9, Issue 4, 2004, Pages 375-390

  von Schroeter, Thomas ^a   Hollaender, Florian ^b   Gringarten, Alain C ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOREHOLES; CONVERGENCE OF NUMERICAL METHODS; CONVOLUTION; ERROR ANALYSIS; INTEGRAL EQUATIONS; LEAST SQUARES APPROXIMATIONS; NONLINEAR EQUATIONS; PRESSURE DROP; TIME DOMAIN ANALYSIS;

DECONVOLUTION; NONLINEAR TOTAL LEAST SQUARES PROBLEM; REGULARIZATION; WELL TEST ANALYSIS;

OIL WELL TESTING;

EID: 13244268352     PISSN: 1086055X     EISSN: None     Source Type: Journal    
DOI: 10.2118/77688-PA     Document Type: Article

References (41)

1. Hutchinson, T.S. and Sikora, V.J.: "A Generalized Water-Drive Analysis," Trans., AIME (1959) 216, 169.
2. Katz, D.L., Tek, M.R., and Jones, S.C.: "A Generalized Model for Predicting the Performance of Gas Reservoirs Subject to Water Drive," paper SPE 428 presented at the 1962 SPE Annual Meeting, Los Angeles, 7-10 October.
3. Coats, K.H. et al.: "Determination of Aquifer Influence Functions From Field Data," Trans., AIME (1964) 231, 1417.
4. Jargon, J.R. and van Poollen, H.K.: "Unit Response Function From Varying-Rate Data," JPT (August 1965) 965; Trans., AIME, 234.
5. Bostic, J.N., Agarwal, R.G., and Carter, R.D.: "Combined Analysis of Postfracturing Performance and Pressure Buildup Data for Evaluating an MHF Gas Well," JPT (October 1980) 1711.
6. Kučuk, F.J. and Ayestaran, L.: "Analysis of Simultaneously Measured Pressure and Sandface Flow Rate in Transient Well Testing," JPT (February 1985) 323.
7. Thompson, L.G. and Reynolds, A.C.: "Analysis of Variable-Rate Well-Test Pressure Data Using Duhamel's Principle," SPEFE (October 1986) 453.
8. Thompson, L.C., Jones, J.R., and Reynolds, A.C.: "Analysis of Pressure Buildup Data Influenced by Wellbore Phase Redistribution," SPEFE (October 1986) 435.
9. Kuchuk, F.J.: "Applications of Convolution and Deconvolution to Transient Well Tests," SPEFE (December 1990) 375; Trans., AIME, 289.
10. Gajdica, R.J., Wattenbarger, R.A., and Startzman, R.A.: "A New Method of Matching Aquifer Performance and Determining Original Gas in Place," SPERE (August 1988) 985.
11. Roumboutsos, A. and Stewart, G.: "A Direct Deconvolution or Convolution Algorithm for Well Test Analysis," paper SPE 18157 presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, 2-5 October.
12. Mendes, L.C.C., Tygel, M., and Correa, A.C.F.: "A Deconvolution Algorithm for Analysis of Variable Rate Well Test Pressure Data," paper 19815 presented at the 1989 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8-11 October.
13. Kuchuk, F.J., Carter, R.G., and Ayestaran, L.: "Deconvolution of Wellbore Pressure and Flow Rate," SPEFE (March 1990), 53.
14. Bourgeois, M.J. and Horne, R.N.: "Well-Test-Model Recognition with Laplace Space," SPEFE (March 1993) 17.
15. Baygün, B., Kuchuk, F.J., and Arikan, O.: "Deconvolution Under Normalized Autocorrelation Constraints," SPEJ (September 1997) 246.
16. Onur, M. and Reynolds, A.C.: "Numerical Laplace Transformation of Sampled Data for Well-Test Analysis," SPEREE (June 1998) 268.
17. Gilly, P. and Horne, R.N.: "Analysis of Pressure/Flow-Rate Data With the Pressure-History-Recovery Method," SPEREE (August 1999) 314.
18. von Schroeter, T., Hollaender, F., and Gringarten, A.C.: "Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem," paper SPE 71574 presented at the 2001 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October.
19. von Schroeter, T., Hollaender, F., and Gringarten, A.C.: "Analysis of Well Test Data From Permanent Downhole Gauges by Deconvolution," paper SPE 77688 presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September-2 October.
20. Levitan, M.M.: "Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests," paper SPE 84290 presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, 5-8 October.
21. van Everdingen, A.F. and Hurst, W.: "The Application of the Laplace Transformation to Flow Problems in Reservoirs," Trans., AIME (1949) 186, 305.
22. Al-Hussainy, R., Ramey Jr., H.J., and Crawford, P.B.: "The Flow of Real Gas Through Porous Media," JPT (May 1966) 624.
23. Bøe, A., Skjaeveland, S.M., and Whitson, C.H.: "Two-Phase Pressure Test Analysis," SPEFE (December 1989) 604; Trans., AIME, 287.
24. Bourdet, D. et al.: "A New Set of Type Curves Simplifies Well Test Analysis," World Oil (1983) 196, 95.
25. Odeh, A.S. and Jones, L.G.: "Pressure Drawdown Analysis, Variable-Rate Case," JPT (August 1965) 960.
26. Bourdet, D., Ayoub, J.A., and Pirard, Y.M.: "Use of Pressure Derivative in Well-Test Interpretation," SPEFE (June 1989) 293; Trans., AIME, 287.
27. Daungkaew, S., Hollaender, F., and Gringarten, A.C.: "Frequently Asked Questions in Well Test Analysis," paper SPE 63077 presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, 1-4 October.
28. Gringarten, A.C. et al.: "Use of Downhole Permanent Pressure Gauge Data to Diagnose Production Problems in a North Sea Horizontal Well," paper 84470 presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, 5-8 October.
29. Wing, M.G.: A Primer on Integral Equations of the First Kind, Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1991).
30. Golub, G.H., Hansen, P.C., and O'Leary, D.P.: "Tikhonov regularization and Total Least Squares," SIAM J. Matrix Anal. Appl. (1999) 21 185.
31. Percival, D.B. and Walden, A.T.: Spectral Analysis for Physical Applications, Cambridge U. Press, Cambridge, U.K. (1993).
32. Stehfest, H.: "Algorithm 368: Numerical inversion of Laplace transforms," Comm. Assoc. Computing Machine (1970) 13, 47.
33. Dong, C.W.: "A regularization method for the numerical inversion of the Laplace transform," SIAM J. Num. Anal. (1993) 30, 759.
34. Golub, G.H. and van Loan, C.F.: Matrix Computations, third edition, The Johns Hopkins U. Press, Baltimore (1996).
35. Björck, Å.: Numerical Methods for Least Squares Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1996).
36. Press, W.H. et al.: Numerical Recipes in PASCAL. The Art of Scientific Computing, Cambridge U. Press, Cambridge, U.K. (1989).
37. Golub, G.H., Heath, M., and Wahba, G.: "Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter," Technometrics (1979) 21, 215.
38. Hansen, P.C. and O'Leary, D.P.: "The use of the L-curve in the regularization of discrete ill-posed problems," SIAM J. Scientific Computing (1993) 15, 1487.
39. Golub, G.H. and Pereyra, V.: "The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate," SIAM J. Num. Anal. (1973) 10, 413.
40. Stewart, D.E. and Leyk, Z.: "MESCHACH, version 1.2b," (1994) http://www.netlib.org.
41. Agarwal, R.G., Al-Hussainy, R., and Ramey Jr., H.J.: "An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow. I: Analytical Treatment," SPEJ (September 1970) 279; Trans., AIME, 249.