## Abstract

Pore size distributions derived from NMR relaxation time measurements are a common descriptor of the morphology of porous reservoir rock. Typically, they are anchored by experiments performed on a core plug (e.g. mercury intrusion capillary pressure) . The first moment of the distribution (e.g. logarithmic mean) is then often used as a length scale in permeability correlations. When the exact form of the distribution rather than the first moment is of interest, assumptions in the conversion of relaxation-time to pore-size distributions and signal to noise ratios play a critical role. While NMR derived pore size distributions result from a spectral approach, X-ray computed microtomography offers a direct image of the pore space at resolutions down to a few microns. Pore partitioning techniques allow the derivation of pore size distributions free of assumptions like weak coupling, constant surface relaxivity or weak internal gradients and without going through an inverse Laplace transform. Furthermore, the exact geometry and topology of the pore space is known from such a partitioning. In this study, we focus on the form of the relaxation time distributions and their relationship with pore size distributions itself for a large selection of reservoir rock samples acquired by micro Xray-CT imaging. In particular, we use pore partitions to calculate the pore size distribution (PSD) and measure the diffusion coupling between pores during NMR relaxation simulations, separately accounting for bulk and surface relaxation. This allows us to directly compare four different pore size distributions: 1. The PSD based on pore partitioning defined by the pore volume: PSD_{V} . 2. The PSD based on pore partitioning defined by the surface/volume ratio for each pore: PSD_{VS}. 3. The PSD based on pore partitioning, diffusion averaged by carrying out an NMR relaxation simulation, taking relaxation weighted pore coupling into account without involving an inverse Laplace transform: PSD_{dr}. 4. The PSD derived by simulation of NMR relaxation at given noise ratio followed by an inverse Laplace transform: PSD_{ilp}. We compare PSD_{V} and PSD_{SV} to test the agreement between a volume based PSD and a PSD expected from an NMR measurement under ideal conditions of spherical pores, fast diffusion, weak coupling, and zero noise. In considering PSD_{dr} we relax the weak coupling condition and show the coupling effect in a forward model. By comparing PSD_{dr} and PSD_{ilp} we consider the effect of inversion with finite noise on the shape of the distribution. In addition to analysing the shape of NMR derived pore size distributions, we consider the implications of diffusion coupling and bulk relaxation effects on permeability predictions We compare to full scale lattice Boltzmann derived permeabilities for a selection of samples.

Original language | English |
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Publication status | Published - 2008 |

Event | SPWLA 49th Annual Logging Symposium 2008 - Austin, United States Duration: 25 May 2008 → 28 May 2008 |

### Conference

Conference | SPWLA 49th Annual Logging Symposium 2008 |
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Country/Territory | United States |

City | Austin |

Period | 25/05/08 → 28/05/08 |