Vol. 29
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2011-03-25
A Multiplicative Regularized Gauss-Newton Algorithm and Its Application to the Joint Inversion of Induction Logging and Near-Borehole Pressure Measurements
By
Progress In Electromagnetics Research B, Vol. 29, 105-138, 2011
Abstract
Due to the ill-posed nature of nonlinear inverse problems of borehole geophysics, a parameterization approach is necessary when the available measurement data are limited and measurements are only carried out from sparse transmitter-receiver positions (limited data diversity). A potential remedy is the joint inversion of multi-physics measurements. A parametric inversion approach has desirable attributes for multi-physics measurements with different resolutions. It provides a flexible framework to put the sensitivities of multi-physics multi-resolution measurements on equal footing. In addition, the number of unknown model parameters to be inverted is rendered tractable with parameterization. Consequently, a Gauss-Newton based inversion algorithm taking advantage of the Hessian information can be advantageously employed over inversion approaches that rely only on gradient information. We describe a new dual-physics parametric joint-inversion algorithm to estimate near-borehole fluid permeability and porosity distributions of rock formations from fluid-flow and electromagnetic measurements. In order to accommodate the cases in which the measurements are redundant or lack sensitivity with respect to certain model parameters causing nonuniqueness of the inverted solution, the objective functional to be minimized is regularized with a penalty term. One of the central aspects of this approach is the determination of the regularization parameter. The latter must be chosen in such a way that the relative importance of the misfit between measured and predicted data and the penalty term are effectively balanced over the course of minimization. We propose a new method of adaptively choosing the regularization parameter within a Gauss-Newton method based joint-inversion algorithm using a multiplicative regularization strategy. The multiplicative regularization method is tested against additive regularization in joint-inversion problems involving wireline formation tester transient pressure and induction-frequency electromagnetic logging measurements. The multiplicative regularization method delivers improved convergence rates over additive regularization for all investigated problems. Inversions of relatively more noise-contaminated measurements benefit more from multiplicative regularization.
Citation
Faruk Omer Alpak, Tarek Habashy, Aria Abubakar, Carlos Torres-Verdin, and Kamy Sepehrnoori, "A Multiplicative Regularized Gauss-Newton Algorithm and Its Application to the Joint Inversion of Induction Logging and Near-Borehole Pressure Measurements," Progress In Electromagnetics Research B, Vol. 29, 105-138, 2011.
doi:10.2528/PIERB10090502
References

1. Abubakar, A., P. M. van den Berg, and S. Y. Semenov, "Two- and three-dimensional algorithms for microwave imaging and inverse scattering," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 2, 209-231, 2003.
doi:10.1163/156939303322235798

2. Alpak, F. O., "Algorithms for numerical modeling and inversion of multi-phase fluid-flow and electromagnetic measurements," Ph.D. Dissertation, Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 2005.

3. Alpak, F. O., T. M. Habashy, C. Torres-Verdín, and E. B. Dus-san V., "Joint inversion of transient-pressure and time-lapse electromagnetic logging measurements," Petrophysics, Vol. 45, No. 3, 251-267, 2004.

4. Archie, G. E., "The electrical resistivity log as an aid in determining some reservoir characteristics," Trans. AIME, Vol. 146, 54-62, 1942.

5. Aziz, K. and A. Settari, Petroleum Reservoir Simulation, Applied Science Publishers , London, 1979.

6. Druskin, V., L. Knizhnerman, and P. Lee, "New spectral Lanczos decomposition method for induction modeling in arbitrary 3D geometry," Geophysics, Vol. 64, 701-706, 1999.
doi:10.1190/1.1444579

7. Epov, M., I. Yeltsov, A. Kashevarov, A. Sobolev, and V. Ulyanov, "Time evolution of the near borehole zone in sandstone reservoir through the time-lapse data of high-frequency electromagnetic logging," Proceedings of the 43rd Annual Logging Symposium: Society of Well Log Analysts, Vol. 1--10, Paper ZZ, 1-10, Oiso, Japan, Jun. 2--5, 2002.

8. Gill, P. E., W. Murray, and M. H. Wright, Practical Optimization, Academic Press, London, 1981.

9. Habashy, T. M. and A. Abubakar and A. Abubakar, "A general framework for constraint minimization for the inversion of electromagnetic measurements," Progress In Electromagnetics Research, 265-312, 2004.
doi:10.2528/PIER03100702

10. Hunka, J. F., T. D. Barber, R. A. Rosthal, G. N. Minerbo, E. A. Head, A. Q. Howard, G. A. Hazen, and R. N. Chandler, "A new resistivity measurement system for deep formation imaging and high-resolution formation evaluation," Proceedings of the Annual Technical Conference and Exhibition: Society of Petroleum Engineers, 295-307, Paper SPE 20559, New Orleans, Lousiana, Sep. 23--26, 1990.

11. Moskow, S., V. Druskin, T. Habashy, P. Lee, and S. Davydycheva, "A finite difference scheme for elliptic equations with rough coefficients using a Cartesian grid nonconforming to interfaces," SIAM Journal on Numerical Analysis, Vol. 36, No. 2, 442-464, 1999.
doi:10.1137/S0036142997318541

12. Pop, J., R. Badry, C. Morris, D. Wilkinson, P. Tottrup, and J. Jonas, "Vertical interference testing with a wireline-conveyed straddle-packer tool," Transactions of the Annual Technical Conference and Exhibition: Society of Petroleum Engineers, 665-680, Paper SPE 26481, Houston, Texas, Oct. 3--6, 1993.

13. Ramakrishnan, T. S. and D. J. Wilkinson, "Formation producibility and fractional flow curves from radial resistivity variation caused by drilling fluid invasion," Physics of Fluids, Vol. 9, No. 4, 833-844, 1997.
doi:10.1063/1.869483

14. Ramakrishnan, T. S. and D. J. Wilkinson, "Water-cut and fractional flow logs from array-induction measurements," SPE Reservoir Evaluation and Engineering, Vol. 2, No. 1, 85-94, 1999.
doi:10.2118/54673-PA

15. Scharf, L. L., Statistical Signal Processing, Detection, Estimation and Time Series Analysis, Addison-Wesley, Massachusetts, 1991.

16. Semmelbeck, M. E., J. T. Dewan, and S. A. Holditch, "Invasion-based method for estimating permeability from logs," Proceedings of the Annual Technical Conference and Exhibition: Society of Petroleum Engineers, 517-531, Paper SPE 30581, Dallas, Texas, Oct. 22--25, 1995.

17. Tobola, D. P. and S. A. Holditch, "Determination of reservoir permeability from repeated induction logging," SPE Formation Evaluation, 20-26, Mar. 1991.

18. Van Den Berg, P. M. and A. Abubakar, "Contrast source inversion method: State of art," Progress In Electromagnetics Research, Vol. 34, 189-218, 2001.
doi:10.2528/PIER01061103

19. Van Den Berg, P. M., A. Abubakar, and J. T. Fokkema, "Multiplicative regularization for contrast profile inversion," Radio Science, Vol. 38, No. 2, 23.1-23.10, 2003.
doi:10.1029/2001RS002555

20. Yao, C. Y. and S. A. Holditch, "Reservoir permeability estimation from time-lapse log data," SPE Formation Evaluation, 69-74, Jun. 1996.

21. Wu, J., C. Torres-Verdín, M. A. Proett, K. Sepehrnoori, and D. Belanger, "Inversion of multi-phase petrophysical properties using pumpout sampling data acquired with a wireline formation tester," Proceedings of the Annual Technical Conference and Exhibition: Society of Petroleum Engineers, Paper SPE 77345, San Antonio, Texas, Sep. 29--Oct. 2, 2002.

22. Zeybek, M., T. S. Ramakrishnan, S. S. Al-Otaibi, S. P. Salamy, and F. J. Kuchuk, "Estimating multiphase flow properties using pressure and flowline water-cut data from dual-packer formation tester interval tests and openhole array resistivity measurements," Proceedings of the Annual Technical Conference and Exhibition: Society of Petroleum Engineers, Paper SPE 71568, New Orleans, Lousiana, Sep. 30--Oct. 3, 2001.

23. Zhang, J.-H., Q. Hu, and Z.-H. Liu, "Estimation of true formation resistivity and water saturation with a time-lapse induction logging method," The Log Analyst, Vol. 40, No. 2, 138-148, 1999.

24. Alpak, F. O., C. Torres-Verdín, and T. M. Habashy, "Joint inversion of pressure and DC resistivity measurements acquired with in-situ permanent sensors: A numerical study," Geophysics, Vol. 69, No. 5, 1173-1191, 2004.
doi:10.1190/1.1801935

25. Alpak, F. O., C. Torres-Verdín, and T. M. Habashy, "Petrophysical inversion of borehole array-induction logs: Part I --- Numerical examples," Geophysics, Vol. 71, No. 4, F101-F119, 2006.
doi:10.1190/1.2213358

26. Torres-Verdín, C., F. O. Alpak, and T. M. Habashy, "Petrophysical inversion of borehole array-induction logs: Part II --- Field data examples," Geophysics, Vol. 71, No. 5, G261-G268, 2006.
doi:10.1190/1.2335633

27. Alpak, F. O., C. Torres-Verdín, and T. M. Habashy, "Estimation of in-situ petrophysical properties from wireline formation tester and induction logging measurements: A joint inversion approach," Journal of Petroleum Science and Engineering, Vol. 63, No. 1--4, 1-17, 2008.
doi:10.1016/j.petrol.2008.05.007