Joint inversion of NMR and SIP data to estimate pore size distribution of geomaterials

Abstract

There are growing interests in using geophysical tools to characterize the microstructure of geomaterials because of the non-invasive nature and the applicability in field. In these applications, multiple types of geophysical data sets are usually processed separately, which may be inadequate to constrain the key feature of target variables. Therefore, simultaneous processing of multiple data sets could potentially improve the resolution. In this study, we propose a method to estimate pore size distribution by joint inversion of nuclear magnetic resonance (NMR) T 2 relaxation and spectral induced polarization (SIP) spectra. The petrophysical relation between NMR T 2 relaxation time and SIP relaxation time is incorporated in a nonlinear least squares problem formulation, which is solved using Gauss-Newton method. The joint inversion scheme is applied to a synthetic sample and a Berea sandstone sample. The jointly estimated pore size distributions are very close to the true model and results from other experimental method. Even when the knowledge of the petrophysical models of the sample is incomplete, the joint inversion can still capture the main features of the pore size distribution of the samples, including the general shape and relative peak positions of the distribution curves. It is also found from the numerical example that the surface relaxivity of the sample could be extracted with the joint inversion of NMR and SIP data if the diffusion coefficient of the ions in the electrical double layer is known. Comparing to individual inversions, the joint inversion could improve the resolution of the estimated pore size distribution because of the addition of extra data sets. The proposed approach might constitute a first step towards a comprehensive joint inversion that can extract the full pore geometry information of a geomaterial from NMR and SIP data.

Enhanced pore space analysis by use of <i>μ</i>-CT, MIP, NMR, and SIP

“…It is assumed that the recorded spectra result from a superposition of polarization processes characterized by different relaxation times. This approach has been adopted to generate synthetic spectra of electrical conductivity from distributions of grain sizes (e.g., Revil and Florsch, 2010) or pore sizes (e.g., Niu and Zhang, 2017).…”

“…We go a step further and directly compare the pore size distributions derived from the different methods. Procedures to derive pore size distributions from induced polarization (IP) data have been proposed only recently Revil et al, 2014;Niu and Zhang 2017;Zhang et al, 2017).…”

“…Each method provides the pore size distribution in a limited range of resolution. It is not our intention to combine the data of the different methods in a joint inversion to get a more reliable pore size distribution as proposed by Niu and Zhang (2017). We prefer to compare the resulting pore size distributions to each other to get two different pore radius distributions, one for the pore body radius and one for the pore throat radius.…”

Role of Pore and Pore‐Throat Distributions in Controlling Permeability in Heterogeneous Mineral Dissolution and Precipitation Scenarios

“…Pore and pore‐throat size distributions can be obtained through a variety of methods including laboratory and 2‐D and 3‐D imaging methods (e.g., Beckingham et al, ; Niu & Zhang, ; Xiao et al, ; Xiong et al, ; Zhang et al, ). Common laboratory methods include mercury injection capillary pressure (MICP) and low‐field nuclear magnetic resonance.…”

“…Pore-to-core-scale reactive transport and resulting changes in individual pores, pore throats, and the greater pore network are easily simulated in pore network models, requiring only pore and pore-throat size distributions and pore connectivity to develop the model. Pore and pore-throat size distributions can be obtained through a variety of methods including laboratory and 2-D and 3-D imaging methods (e.g., Beckingham et al, 2013;Niu & Zhang, 2017;Xiao et al, 2017;Xiong et al, 2016;Zhang et al, 2017). Common laboratory methods include mercury injection capillary pressure (MICP) and low-field nuclear magnetic resonance.…”