Improved numerical inverse Laplace transformation to improve the accuracy of type curve for analyzing well testing data

Kim, Song Chol; Song, Yong Il; Han, Chol Gwang

doi:10.1007/s11600-021-00585-7

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Artykuł - szczegóły

Czasopismo

Acta Geophysica

2021 | Vol. 69, no. 3 | 919--930

Tytuł artykułu

Improved numerical inverse Laplace transformation to improve the accuracy of type curve for analyzing well testing data

Autorzy

Kim, Song Chol , Song, Yong Il , Han, Chol Gwang

Wybrane pełne teksty z tego czasopisma

https://www.springer.com/journal/11600

Warianty tytułu

Języki publikacji

Abstrakty

Analyzing well-testing data by the type-curve matching is a modern well-testing analysis method and is widely used in the petroleum and gas industry. By improving accuracy of type curve, we can get more accurate results from analyzing welltesting data, which provide a scientifc base for development of oil, gas and water resources. By solving percolation equations, we can obtain type curves. The Laplace transformation methods are often used to solve them. In this paper, we improve the accuracy of type curve by improving the numerical inverse Laplace transformation (NILT) based on infinite series. We combine the NILT based on infinite series with Levin convergence acceleration and determine necessary parameters through numerical experiments to improve accuracy and speed. To verify this method, we compare the improved method with the Stehfest method using some functions such as trigonometric function. Type curves for analysis of well-testing data for the homogeneous reservoir with elastic outer boundary and a dual porosity reservoir are plotted and compared by using the improved numerical inversion and the Stehfest numerical inversion, respectively. These results show that type curves plotted by the improved method are less in vibration and fuctuation than ones plotted by the Stehfest method.

Słowa kluczowe

numeryczna odwrotna transformacja Laplace'a pompowanie próbne

numerical inverse Laplace transformation well testing type curves convergence acceleration Stehfest infinite series

Wydawca

Czasopismo

Acta Geophysica

Rocznik

2021

Tom

Vol. 69, no. 3

Strony

919--930

Opis fizyczny

Bibliogr. 59 poz.

Twórcy

autor

Kim, Song Chol

Faculty of Mining Engineering, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea, ksc71821@star-co.net.kp

autor

Song, Yong Il

Faculty of Mining Engineering, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea

autor

Han, Chol Gwang

Faculty of Mining Engineering, Kim Chaek University of Technology, Pyongyang, Democratic People’s Republic of Korea

Bibliografia

1. Agarwal RG (1980) A new method to account for producing time effects when drawdown type curves are used to analyze pressure buildup and other test data. SPE Paper 9289, In: presented at SPE-AIME 55th Annual Technical Conference, Dallas, Texas, 1980. Sept. 21–24
2. Agarwal RG, Al-Hussainy R, Ramey HJ Jr (1970) An Investigation of wellbore storage and skin effect in unsteady liquid flow: I—analytical treatment. SPE J 10(3):279–290
3. Bourdet D (1983) Anew set of type curves simplifies well test analysis. Well Oil 196:95–106
4. Bourdet D, Gringarten AC (1980) Determination of fissure volume and block size in fractured reservoirs by type-curve analysis. In: SPE Paper 9293, presented at the 1980 annual technical conference and exhibition, Dallas, 1980. Sept. 21–24
5. Bourdet, D., Alagoa, A., Ayoub, J.A., Pirard, Y.M., 1984. New type curves aid analysis of fissured zone well tests. World Oil pp. 111–124
6. Crump KS (1976) Numerical inversion of Laplace transforms using a Fourier series approximation. J ACM 233:89–96
7. D’Amore L, Laccetti G, Murli A (1999a) An implementation of a Fourier series method for the numerical inversion of the Laplace transform. ACM Trans Math Softw 25(3):279–305
8. D’Amore L, Laccetti G, Murli A (1999b) Algorithm 796: A Fortran software package for the numerical inversion of the Laplace transform based on a Fourier series method. ACM Trans Math Softw 25(3):306–315
9. Dejam M, Hassanzadeh H, Chen Z (2018) Semi-analytical solution for pressure transient analysis of a hydraulically fractured vertical well in a bounded dual-porosity reservoir. J Hydrol 565:289–301
10. Dewandel B, Lanini S, Lachassagne P, Maréchal J-C (2018) A generic analytical solution for modelling pumping tests in wells intersecting fractures. J Hydrol 559:89–99. https://doi.org/10.1016/j.jhydrol.2018.02.013
11. Dubner H, Abate J (1968) Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. J ACM 15:115–123. https://doi.org/10.1145/321439.321446
12. Durbin F (1974) Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. Computer 17:371–376
13. Earlougher RC Jr, Kersch KM (1974) Analysis of short-time transient test data by type-curve matching. J Pet Technol 26(7):793–800
14. Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer, Dordrecht
15. Feng Q, Zhan H (2018) Constant-head test at a partially penetrating well in an aquifer-aquitard system. J Hydrol. https://doi.org/10.1016/j.jhydrol.2018.12.018
16. Gringarten AC, Ramey HJ, Raghavan R (1974) Unsteady-state pressure distributions created by a well with a single infinite-conductivity vertical fracture. Soc Pet Eng J 14(4):347–360
17. Gringarten AC, Ramey HJ, Raghavan R (1975) Applied pressure analysis for fractured wells. Pet Technol 27:887–892
18. Gringarten AC, Bourdet DP, Landel PA, Kniazeff VJ (1979) A comparison between different skin and wellbore storage type-curves for early-time transient analysis. In: Paper SPE 8205 Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 1979. September 23–26
19. Hsu JT, Dranoff JS (1987) Numerical inversion of certain Laplace transforms by the direct application of fast Fourier transform (FF’T) algorithm. Comput and Chem Eng 11:101–110
20. HwangWuLu CR-YM-J (1994) A technique for increasing the accuracy of the FFT-based method of numerical inversion of Laplace transforms. Comput Math Appl 27(7):23–29
21. Iseger PD (2006) Numerical transform inversion using Gaussian quadrature. Probab Eng Inf Sci 20:1–44
22. Ji J, Yao Y, Huang S, Ma X, Zhang S, Zhang F (2017) Analytical model for production performance analysis of multi-fractured horizontal well in tight oil reservoirs. J Pet Sci Eng. https://doi.org/10.1016/j.petrol.2017.08.037
23. Ke X, Guo D, Zhao Y, Zeng X, Xue L (2017) Analytical model to simulate production of tight reservoirs with discrete fracture network using multi-linear flow. J Pet Sci Eng. https://doi.org/10.1016/j.petrol.2017.01.007
24. Levin D (1973) Development of non-linear transformations for improving convergence of sequences. Internat J Comput Math B3:371–388
25. Levin D (1975) Numerical inversion of the Laplace transform by accelerating the convergence of Bromwich’s integral. J Comp Appl Math 1:247–250
26. Li S, Zhang D, Zheng P, Gui Q (2017) Similar structure of solution for triple media shale gas reservoir. J Petrol Sci Eng. https://doi.org/10.1016/j.petrol.2017.02.008
27. Li S, Zhao C, Zheng P, Gui Q (2019) Analysis of oil and gas flow characteristics in the reservoir with the elastic outer boundary. J Pet Sci Eng 175:280–285. https://doi.org/10.1016/j.petrol.2018.12.042
28. Liao X, Shen P (2002) Modern analysis of well-testing. Petroleum Engineering Publisher (in Chinese)
29. Lu B-x, Wang Z-z, Wang Y-j, Liu X (2002) Voltage response analysis for fault transmission line. J North China Electric Power Univ 29(2):31–33 ((in Chinese))
30. Luo W, Wang L (2014) A novel semi-analytical model for horizontal fractures with non-Darcy flow. J Petrol Sci Eng 122:166–172. https://doi.org/10.1016/j.petrol.2014.07.006
31. Mishra V (2014) Review of numerical inversion of Laplace transforms using Fourier analysis, fast Fourier transform and orthogonal polynomials. Math Eng Sci Aerospace 5:239–261
32. Peller W (1971) An introduction to probability theory and its application, 2nd edn. Wiley, New York
33. Piessens R (1982) Inversion of the Laplace transforms. Comput J 25:278–282
34. Ren Z, Wu X, Han G, Liu L, Wu X, Zhang G, Lin H, Zhang J, Zhang X (2017) Transient pressure behavior of multi-stage fractured horizontal wells in stress sensitive tight oil reservoirs. J Petrol Sci Eng. https://doi.org/10.1016/j.petrol.2017.07.073
35. Schapery RA (1962) Approximate methods of transform inversion for viscoelastic stress analysis. In: Proceedings of the 4th US national congress applied mechanics, New York; 1075–85
36. Sedghi MM, Zhan H (2018) Flow to a well in an unconfined-fractured and leaky wedge-shaped aquifer system. J Hydrol 567:605–625. https://doi.org/10.1016/j.jhydrol.2018.10.043
37. Shan H-n (1999) Study on the method for numerical inversion of Laplace transforms. Num Calc Comput Appl 3:231–235
38. Stehfest H (1970) Numerical inversion of Laplace transform. Commun ACM 13(1):47–49
39. Sun H-D, Liu Y-w, Shi Y (2013) A well test model for composite reservoir with resistance force on interface. Open Pet Eng J 6:43–48
40. Takuya O (2000) Numerical inversion of the Laplace transform using a continuous Euler transformation. Kyoto Univ Res Inf Repos 1145:188–193
41. Talbot A (1979) The accurate numerical inversion of Laplace transforms. IMA J Appl Math 23:97–120. https://doi.org/10.1093/imamat/23.1.97
42. Tan X-h, Li X-p (2014) Transient flow model and pressure dynamic features of tree-shaped fractal reservoirs. J Hydrodynam 26(4):654–663
43. Van Everdingen AF, Hurst W (1949) The application of the Laplace transformation to flow problems in reservoirs. Trans AIME 186:305–324
44. Wang L, Xue L (2018) A Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers. J Hydrol 567:712–720. https://doi.org/10.1016/j.jhydrol.2018.06.027
45. Wang Q, Zhan H (2015) On different numerical inverse Laplace methods for solute transport problems. Adv Water Resour 75:80–92. https://doi.org/10.1016/j.advwatres.2014.11.001
46. Wang J, Jia A, Wei Y, Qi Y, Dai Y (2018) Laplace-domain multiwell convolution for simulating pressure interference response of multiple fractured horizontal wells by use of modified Stehfest algorithm. J Petrol Sci Eng. https://doi.org/10.1016/j.petrol.2017.11.074
47. Warren JE, Root PJ (1963) The behavior of naturally fractured reservoirs. Soc Pet Eng J 3:245–255
48. Weeks WT (1966) Numerical inversion of Laplace transforms using Laguerre functions. J ACM 13:419–429. https://doi.org/10.1145/321341.321351
49. Wu Z, Cui C, Lv G, Bing S, Cao G (2019) A multi-linear transient pressure model for multistage fractured horizontal well in tight oil reservoirs with considering threshold pressure gradient and stress sensitivity. J Petrol Sci Eng. https://doi.org/10.1016/j.petrol.2018.08.078
50. Wynn P (1956) On a device for computing the em(Sn) transformation. Math Tables and Aids to Comp 10:91–96
51. Wynn P (1966) Transformations to accelerate the convergence of Fourier series. In: MRC technical report 673
52. Xia W-w, Li S-c, Gu D-d (2015) The similar structure method for solving the radial seepage model of fractal composite reservoir with double-porosity. Am J Appl Math Stat 3(2):80–85. https://doi.org/10.12691/ajams-3-2-7
53. Yonemoto A, Hisakado T, Okumura K (2003) Accuracy improvement of the FFT-based numerical inversion of Laplace transforms. IEE Proc-Circuits Dev Syst 150(5):399–404
54. Zakian V (1969) Numerical inversion of Laplace transforms. Electron Lett 1:120–121. https://doi.org/10.1049/el:19690090
55. Zeng J, Wang X, Guo J, Zeng F, Zhang Q (2018) Composite linear flow model for multi-fractured horizontal well in tight sand reservoirs with the threshold pressure gradient. J Pet Sci Eng 165:890–912. https://doi.org/10.1016/j.petrol.2017.12.095
56. Zhang L, Guo J, Liu Q (2010) A well test model for stress-sensitive and heterogeneous reservoirs with non-uniform thicknesses. Pet Sci 7:524–529
57. Zhao Y-l, Zhang L-h, Zhao J-z, Luo J-x, Zhang B-n (2013) “Triple porosity” modeling of transient well test and rate decline analysis for multi-fractured horizontal well in shale gas reservoirs. J Pet Sci Eng 110:253–262
58. Zhao Y-L, Zhang L-H, Luo J-X, Zhang B-N (2014) Performance of fractured horizontal well with stimulated reservoir volume in unconventional gas reservoir. J Hydrol 512:447–456. https://doi.org/10.1016/j.jhydrol.2014.03.026
59. Zhao Y, Zhang L, Liu Y (2015) Transient pressure analysis of fractured well in bi-zonal gas reservoirs. J Hydrol 524:89–99

Typ dokumentu

Bibliografia

Identyfikatory

DOI

10.1007/s11600-021-00585-7

Identyfikator YADDA

bwmeta1.element.baztech-54d8ed68-aa42-40c9-85b9-d31e442f3090