A simple geometric model of sedimentary rock to connect transfer and acoustic properties
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ORIGINAL PAPER
A simple geometric model of sedimentary rock to connect transfer and acoustic properties Gabor Korvin & Klavdia Oleschko & Abdulazeez Abdulraheem
Received: 13 April 2012 / Accepted: 25 January 2013 # Saudi Society for Geosciences 2013
Abstract A simple rock model is presented which reproduces the measured hydraulic and electric transport properties of sedimentary rocks and connects these properties with each other, as well as with the acoustic propagation velocities and elastic moduli. The model has four geometric parameters (average coordination number Z of the pores, average pore radius r, average distance between nearest pores d, and average throat radius δ) which can be directly determined from the measured porosity Φ, hydraulic permeability k, and cementation exponent m of the rock via simple analytic expressions. Inversion examples are presented for published sandstone data, and for cores taken from Saudi Arabian, Upper Jurassic and Permian carbonate reservoirs. For sandstone, the inversion works perfectly; for carbonates, the derived rock model shows order-of-magnitude agreement with the structure seen in thin sections. Inverting the equations, we express the transfer properties Φ, k, and m as functions of r, d, δ, and Z. Formulae are derived for the bulk density Db, formation factor F, and P-wave velocity in terms of the proposed geometrical parameters.
G. Korvin (*) Earth Sciences Department and Reservoir Characterization Research Group, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia e-mail: [email protected] K. Oleschko Centro de Geociencias, Universidad Nacional Autónoma de México (UNAM), Km. 15.5 Carretera Querétaro-San Luis Potosí, C. P. 76230, Juriquilla, Querétaro, Mexico e-mail: [email protected] A. Abdulraheem Petroleum Engineering Department, King Fahd University, Dhahran, Saudi Arabia e-mail: [email protected]
Keywords Digital rock physics . Petrophysics . Pore-space model . Rock physics . Pore structure inversion
Introduction The most exciting recent development in petrophysics has been the emergence of digital rock physics (Andrä et al 2012; Arns et al 2004; Boylan et al, 2002; Dong 2007; Dong et al. 2008; Dvorkin et al. 2009, 2011; Kalam et al. 2011; Kayser and Ziauddin 2006; Keehm 2003; Knackstedt et al. 2007, 2009a, b, c; Peng et al. 2012; Rassenfoss 2011; Saenger et al. Sok et al. 2009; Sorbie and Skauge 2011; Touati et al. 2009; Zhang and Knackstedt 1995, etc.). In digital rock physics (DPR), one reconstructs the pore space of a small (less than 1 cm3) piece of rock by computerized X-ray tomography, digitizes the pore space, and then “numerically simulates various physical processes to obtain such macroscopic rock properties as permeability, electric conductivity and elastic moduli” (direct quote from Andrä et al. 2012). What is not always emphasized in DPR literature (see, however, Dvorkin et al. 2011) is that the tiny fragment of rock selected for analysis must be a statistically representative realization of all possible random rock
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