223
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Bayesian deconvolution of oil well test data using Gaussian processes

, , &
Pages 721-737 | Received 27 Aug 2014, Accepted 25 Jul 2015, Published online: 18 Sep 2015

References

  • A. Acuna, I. Ershaghi, Y.C. Yortsos, P.E. Program, and L. Angeles, Fractal analysis of pressure transients in the geysers geothermal field, Proceedings of the 17th Workshop on Geothermal Reservoir Engineering SGP-TR-141 (1992), pp. 87–93.
  • B. Amizic, L. Spinoulas, R. Molina, and A.K. Katsaggelos, Compressive blind image deconvolution, IEEE T. Image Process. 22 (2013), pp. 3994–4006. doi: 10.1109/TIP.2013.2266100
  • M. Andrecut, Pressure rate deconvolution methods for well test analysis, Mod. Phys. Lett. B 23 (2009), pp. 1027–1051. doi: 10.1142/S0217984909019272
  • J. Bay, Fundamentals of Linear State Space Systems, McGraw-Hill, Stanford, CA, 1999.
  • M.J. Bayarri, J.O. Berger, A. Forte, and G. García-Donato, Criteria for Bayesian model choice with application to variable selection, Ann. Stat. 40 (2012), pp. 1550–1577. doi: 10.1214/12-AOS1013
  • J.M. Bernardo and A.F.M. Smith, Bayesian Theory, Wiley, New York, NY, 1994.
  • N. Bissantz, L. Dümbgen, H. Holzmann, and A. Munk, Non-parametric confidence bands in deconvolution density estimation, J. R. Stat. Soc. B. 69 (2007), pp. 483–506. doi: 10.1111/j.1467-9868.2007.599.x
  • D. Bourdet, Well test analysis: the use of advanced interpretation models, in Handbook of Petroleum Exploration and Production, J. Cubitt, ed., chap. 3, Handbook of Petroleum Exploration and Production, Elsevier, Amsterdam, 2002, p. 416.
  • T.F. Chan and C.K. Wong, Total variation blind deconvolution, IEEE T. Image Process. 7 (1998), pp. 370–375. doi: 10.1109/83.661187
  • J. Chang and Y.C. Yortsos, Pressure-transient analysis of fractal reservoirs, SPE Form. Eval. 5 (1990), p. 631.
  • G. Christakos, Random Field Models in Earth Sciences, Academic Press, Inc., Boston, MA, 1992.
  • J. Christen, C. Fox, D. Pérez-Ruiz, and M. Santana-Cibrian, On optimal direction gibbs sampling, Arxiv preprint (2012) Available at: http://arxiv.org/abs/1205.4062v1.
  • O.O. Duru and R.N. Horne, Simultaneous interpretation of pressure, temperature, and flow-rate data using Bayesian inversion methods, SPE Reser. Eval. Eng. (2011), pp. 225–238.
  • F. Flamenco-Lopez and R. Camacho-Velazquez, Determination of fractal parameters of fracture networks using pressure-transient data, SPE Reservoir Evaluation and Engineering SPE82607, (2003) pp. 39–47.
  • A. Gelman, X. Meng, and H. Stern, Posterior predictive assessment of model fitness via realized discrepancies, Stat. Sinica 6 (1996), pp. 733–807.
  • I.I. Gihman and A.V. Skorohod, The Theory of Stochastic Processes, Vol. 1, Springer, New York, NY, 1979.
  • A. Goldenshluger, On pointwise adaptive nonparametric deconvolution, Bernoulli 5 (1999), pp. 907–925. doi: 10.2307/3318449
  • J. Gregson, F. Heide, M. Hullin, M. Rouf, and W. Heidrich, Stochastic Deconvolution, in 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2013, pp. 1043–1050.
  • A.C. Gringarten, From straight lines to deconvolution: the evolution of the state of the art in well test analysis, SPE102079 (2008), pp. 1–10.
  • J.A. Hoeting, D. Madigan, A.E. Raftery, and C.T. Volinsky, Bayesian model averaging: A tutorial, Stat. Sci. 14 (1999), pp. 382–417. doi: 10.1214/ss/1009212519
  • T. Holsclaw, B. Sansó, H. Lee, D. Higdon, K. Heitmann, U. Alam, and S. Habib, Gaussian process modeling of derivative curves, Techonmetrics 55 (2012), pp. 57–67. doi: 10.1080/00401706.2012.723918
  • D. Ilk, P.P. Valkó, and T.A. Blasingame, A deconvolution method based on cumulative production for continuously measured flowrate and pressure data, SPE111269 (2007), pp. 1–10.
  • T.D. Johnson, Bayesian deconvolution analysis of pulsatile hormone concentration profiles, Biometrics 59 (2003), pp. 650–660. doi: 10.1111/1541-0420.00075
  • I.M. Johnstone, G. Kerkyacharian, D. Picard, and M. Raimondo, Wavelet deconvolution in a periodic setting, J. R. Stat. Soc. B. 66 (2004), pp. 547–573. doi: 10.1111/j.1467-9868.2004.02056.x
  • V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, Sparsity-promoting Bayesian inversion, Inverse Probl. 28 (2012), p. 025005. Available at: http://stacks.iop.org/0266-5611/28/i=2/a=025005. doi: 10.1088/0266-5611/28/2/025005
  • F. Kuchuk, M. Onur, and F. Hollander, Pressure transient formation and well testing convolution, deconvolution and nonlinear estimation, Developments in Petroleum Science, Vol. 57, Elsevier, San Diego, CA, 2010.
  • M.M. Levitan, Practical application of pressure/rate deconvolution to analysis of real well tests, SPE84390 (2005), pp. 1–9.
  • M.M. Levitan, G.E. Crawford, and A. Hardwick, Practical considerations for pressure-rate deconvolution of well-test data, SPE90680 (2006), pp. 35–47.
  • B. Minasny and A.B. McBratney, The Matèrn function as a general model for soil variograms, Geoderma 128 (2005), pp. 192–207. doi: 10.1016/j.geoderma.2005.04.003
  • M. Onur, M. Çnar, D. Ilk, P.P. Valko, T.A. Blasingame, and P. Hegeman, An investigation of recent deconvolution methods for well-test data analysis, SPE 102575 (2008), pp. 226–247.
  • A. Palafox, M. Capistrán, and J. Christen, Effective parameter dimension via Bayesian model selection in the inverse acoustic scattering problem, Math. Probl. Eng. 2014 (2014), p. 427203, Available at: http://dx.doi.org/10.1155/2014/427203. doi: 10.1155/2014/427203
  • C. Rasmussen, Gaussian processes to speed up hybrid monte carlo for expensive Bayesian integrals, in Bayesian Statistics 7, Oxford University Press, 2003.
  • Schlumberger, Well Test Interpretation, Schlumberger testing Services, Schlumberger, 2002.
  • M.A. van de Wiel and K. In Kim, Estimating the false discovery rate using nonparametric deconvolution, Biometrics 63 (2007), pp. 806–815. doi: 10.1111/j.1541-0420.2006.00736.x
  • T.V. von Schroeter, F. Hollaender, A.C. Gringarten, and H. Álzaga Ruiz, Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem, SPE71574 (2001), pp. 1–12.
  • M.J. Wichura, Algorithm as 241: The percentage points of the normal distribution, Appl. Stat. 37 (1988), pp. 477–484. doi: 10.2307/2347330

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.