Pore system characterization and petrophysical rock classification using a bimodal Gaussian density function.

*(English)*Zbl 1321.86037Summary: This paper introduces a bimodal Gaussian density function to characterize pore-size distributions in terms of incremental pore volume versus logarithmic pore-throat radius. An inverse problem is formulated and solved to reconstruct mercury injection capillary pressure curves by enforcing a bimodal Gaussian pore-size distribution. The bimodal Gaussian model generates six petrophysically interpretable attributes which provide a quantitative basis for petrophysical modeling and rock typing. Correlations between these attributes and their associated petrophysical properties are investigated to verify interpretations. In the field case, the correlation coefficient (\(R^2\)) between absolute permeability, end-point gas relative permeability and the mean value of large pore-throat size mode are 0.93 and 0.715, respectively. Correlation (\(R^2 = 0.613\)) is also observed between critical water saturation and pore volume connected by small pore-throat sizes. Petrophysical modeling based on the bimodal Gaussian pore-size distribution with sufficient core data calibration predicts static and dynamic petrophysical properties that are in agreement with laboratory core measurements. The quantitative pore-system description underlies a new petrophysical rock typing method that combines all relevant pore-system attributes. Verification of the method was performed with field data from two key wells in the Hugoton carbonate gas field, Kansas.

##### Keywords:

bimodal Gaussian density function; inverse problem; pore-size distribution; petrophysical modeling; rock typing
PDF
BibTeX
XML
Cite

\textit{C. Xu} and \textit{C. Torres-Verdín}, Math. Geosci. 45, No. 6, 753--771 (2013; Zbl 1321.86037)

Full Text:
DOI

##### References:

[1] | Archie, GE, Introduction to petrophysics of reservoir rocks, Am Assoc Pet Geol Bull, 34, 943-961, (1950) |

[2] | Basan, PB; Lowden, BD; Whattler, PR; Attard, J, Pore-size data in petrophysics: a perspective on the measurement of pore geometry, No. 122, 47-67, (1997) |

[3] | Buiting, JJM, Upscaling saturation-height technology for arab carbonates for improved transition-zone characterization, SPE Reserv Eval Eng, 14, 11-24, (2011) |

[4] | Burdine, NT, Relative permeability calculations from pore size distribution data, J Pet Technol, 5, 71-78, (1953) |

[5] | Childs, EC; Collis-George, N, The permeability of porous materials, Proc R Soc A, 201, 392-405, (1950) |

[6] | Clerke, EA, Permeability, relative permeability, microscopic displacement efficiency, and pore geometry of M_1 bimodal pore systems in arab D limestone, SPE Journal, 14, 524-531, (2009) |

[7] | Clerke, EA; Mueller, HW; Phillips, EC; Eyvazzadeh, RY; Jones, DH; Ramamoorthy, R; Srivastava, A, Application of thomeer hyperbolas to decode the pore systems, facies, and reservoir properties of the upper jurassic arab D limestone, ghawar field, saudi arabia: a “rosetta stone” approach, GeoArabia, 13, 113-160, (2008) |

[8] | Dubois MK, Byrnes AP, Bhattacharya S, Bohling GC, Doveton JH, Barba RE (2006) Hugoton Asset Management Project (HAMP). Hugoton Geomodel Final Report. KGS Open File Report |

[9] | Gao, B; Wu, JH; Chen, SH; Kwak, H; Funk, J, New method for predicting capillary pressure curves from NMR data in carbonate rocks, Colorado Springs, Colorado, May 14-18 |

[10] | Genty, C; Jensen, JL; Ahr, WM, Distinguishing carbonate reservoir pore facies with nuclear magnetic resonance measurements, Nat Resour Res, 16, 45-54, (2007) |

[11] | Handy, LL; Datta, P, Fluid distributions during immiscible displacements in porous media, SPE Journal, 6, 261-266, (1966) |

[12] | Hidajat, I; Mohanty, KK; Flaum, M; Hirasaki, G, Study of vuggy carbonates using X-ray CT scanner and NMR, SPE Reserv Eval Eng, 7, 365-377, (2004) |

[13] | Huang, DD; Honarpour, MM; Al-Hussainy, R, An improved model for relative permeability and capillary pressure incorporating wettability, Calgary, Canada, September 7-10 |

[14] | Marschall, D; Gardner, JS; Mardon, D; Coates, GR, Method for correlating NMR relaxometry and Mercury injection data, San Francisco, California, United States, September 7-10 |

[15] | Mohanty, KK; Salter, SJ, Multiphase flow in porous media: II. pore-level modeling, New Orleans, Louisiana, September 26-29 |

[16] | Nimmo, JR, Porosity and pore size distribution, No. 3, 295-303, (2004), London |

[17] | Olson, TM; Babcock, JA; Prasad, KVK; Boughton, SD; Wagner, PD; Franklin, MK; Thompson, KA, Reservoir characterization of the giant hugoton gas field, kansas, Am Assoc Pet Geol Bull, 81, 1785-1803, (1997) |

[18] | Peters EJ (2012) Advanced petrophysics—volumes 1 and 2. Greenleaf Book Group, Austin |

[19] | Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes. the art of scientific computing, 3rd edn. Cambridge University Press, New York. Sect. 16.1: Gaussian mixture models and \(k\)-means clustering · Zbl 1132.65001 |

[20] | Spencer, DW, The interpretation of grain size distribution curves of clastic sediments, J Sediment Res, 33, 180-190, (1963) |

[21] | Thomeer, JHM, Introduction of a pore geometrical factor defined by the capillary pressure curve, J Pet Technol, 12, 73-77, (1960) |

[22] | Xu, C; Heidari, Z; Torres-Verdín, C, Rock classification in carbonate reservoirs based on static and dynamic petrophysical properties estimated from conventional well logs, San Antonio, Texas, October 5-9 |

[23] | Xu, C; Torres-Verdín, C, Saturation-height and invasion consistent hydraulic rock typing using multi-well conventional logs, Cartagena, Columbia, June 16-20 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.