Transport and seismoelectric properties of porous permeable rock : numerical modeling and laboratory measurements

Abstract

The objective of this thesis is to better understand the transport and seismoelectric (SE) properties of porous permeable rock. Accurate information of rock transport properties, together with pore geometry, can aid us to better quantify the frequency dependence of its SE coupling coefficient. With the development of micro-CT (pCT) scanners, microstructure of the sedimentary rock can now be obtained in three dimensions at micron level resolution. Pore scale modeling on the rock 3-D pCT images provides us the ability to obtain different rock properties all at once and without much ambiguity. In this thesis, we build numerical tools to compute a range of transport properties and pore geometry parameters (e.g., porosity, electrical conductivity, hydraulic permeability, pore surface area) on the microstructures from basic physical laws. A staggered-grid finite difference (FD) scheme is used to solve the Laplace equation for electrical conductivity and the Stokes equation for hydraulic conductivity. The Laplace solver can handle different levels of conductivity contrast so that different saturations (gas, oil and brine) can be modeled. A three-phase conductivity model developed on the binary representation of the microstructure, which is based on the geometric average of free electrolyte conductance and surface conductance in the EDL, is illustrated. Two different edge detection methods are applied to recognize surface voxel in a binary image. One is a gradient based, first order differential method and the second one is a connectivity-number-based edge detection (CNED) method. Computations are done for a family of synthetic sand packs - Finney pack with low, medium to high porosities - to provide a benchmark of numerical tools and to compare with analytic solutions. Then, the numerical methods are used to calculate properties of Berea Sandstone 500 (BS500) with 23.6% porosity, whose 3-D microtomograms with 2.8 micron resolution are available. Using the numerical methods, rock porosity, pore surface area, (cont.) electrical conductivity and permeability are calculated.

These are compared with the laboratory measurements made on the same rock. The numerical and laboratory values compare very well. Impact of various aspects of numerical modeling on the accuracy of results are evaluated. It is demonstrated that increasing the sample used in the computation improves the match between the numerical values and laboratory measurements. Reducing the spatial resolution (i.e. increasing grid size), most affects the accuracy of electrical conductivity and hydraulic permeability. Seismoelectric measurements are carried out at 10 kHz - 120 kHz range for the BS500 sample. Both single sine pulse and five-cycle sine burst are adopted as acoustic source wavelets. Streaming potential is collected on freshly cut BS500 cylinder core samples saturated with different brine conductivities under the same experimental condition as the AC measurements. With the transport and geometrical parameters previously obtained from ptCT image and laboratory measurements, the frequency dependent coupling coefficient of BS500 is theoretically calculated using available rock properties. Comparison between the theoretical prediction and the experimental data is found to be promising. This experiment extends our ability to conduct quantitative seismoelectric measurements at frequency ranges applied for field and laboratory acoustic borehole logging.