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Characterizing flow in oil reservoir rock using SPH: absolute permeability

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Abstract

In this paper, a three-dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale fluid flow in porous rock is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including flows related to permeable rock for both groundwater and petroleum reservoir research. While previous approaches to such problems using SPH have involved the use of idealized pore geometries (cylinder/sphere packs etc), in this paper we detail the characterization of flow in models with geometries taken from 3D X-ray microtomographic imaging of actual porous rock; specifically 25.12 % porosity dolomite. This particular rock type has been well characterized experimentally and described in the literature, thus providing a practical ‘real world’ means of verification of SPH that will be key to its acceptance by industry as a viable alternative to traditional reservoir modeling tools. The true advantages of SPH are realized when adding the complexity of multiple fluid phases, however, the accuracy of SPH for single phase flow is, as yet, under developed in the literature and will be the primary focus of this paper. Flow in reservoir rock will typically occur in the range of low Reynolds numbers, making the enforcement of no-slip boundary conditions an important factor in simulation. To this end, we detail the development of a new, robust, and numerically efficient method for implementing no-slip boundary conditions in SPH that can handle the degree of complexity of boundary surfaces, characteristic of an actual permeable rock sample. A study of the effect of particle density is carried out and simulation results for absolute permeability are presented and compared to those from experimentation showing good agreement and validating the method for such applications.

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Notes

  1. Note, if multiple mineral phases are present, different corresponding boundary phases could be assigned if the effect of each on flow characteristics were expected to be distinguishably different.

  2. i.e. the positioning of in-flow and out-flow pore throats would need to match one another perfectly as in a unit cell (see [44, 65, 67, 71]) for such conditions to be applicable.

  3. Note, given the model geometry used in the numerical tests, i.e. Fig. 3, \(F_d\) was determined as the force from any particle within the bounds of the rock sample only, to avoid any disparities that may otherwise arise from the inclusion of additional supply volume particle forces.

  4. Note, local sub-block porosity of 33.71 % could have been used, however, global porosity is more useful given that multiple sub-blocks of different local porosity will be used in the next section.

  5. Note, increasing particle density, increases numerical expense so, while model (or physical) time to convergence was reduced, actual execution (or wall clock) time was still greater.

  6. Note, Zhu et al. [44] suggest that \(\sim \)15 particles throat\(^{-1}\) are necessary to achieve accurate flow profiles though porous media, consistent with the findings here.

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Acknowledgments

The authors would like to acknowledge the Schlumberger-Doll Research Center and Saudi Aramco for their joint financial support of this research. Additional thanks to Schlumberger-Doll Research for providing the X-ray \(\upmu \)CT data used in this work.

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Authors and Affiliations

  1. College of Science, Technology and Engineering, James Cook University, Douglas, Townsville, QLD, 4811, Australia

    David W. Holmes

  2. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    John R. Williams

  3. Department of Mathematics and Modeling, Schlumberger-Doll Research Center, 1 Hampshire Street, Cambridge, MA, 02139-1578, USA

    Peter Tilke

  4. School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, Brisbane, QLD, 4072, Australia

    Christopher R. Leonardi

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  1. David W. Holmes
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Correspondence to David W. Holmes.

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Holmes, D.W., Williams, J.R., Tilke, P. et al. Characterizing flow in oil reservoir rock using SPH: absolute permeability. Comp. Part. Mech. 3, 141–154 (2016). https://doi.org/10.1007/s40571-015-0038-7

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