Experimental Measurement of Frequency-Dependent Permeability and Streaming Potential of Sandstones

Abstract

Hydraulic flow, electrical flow and the passage of elastic waves through porous media are all linked by electrokinetic processes. In its simplest form, the passage of elastic waves through the porous medium causes fluid to flow through that medium and that flow gives rise to an electrical streaming potential and electrical counter-current. These processes are frequency-dependent and governed by coupling coefficients which are themselves frequency-dependent. The link between fluid pressure and fluid flow is described by dynamic permeability, which is characterised by the hydraulic coupling coefficient (C hp). The link between fluid pressure and electrical streaming potential is characterised by the streaming potential coefficient (C sp). While the steady-state values of such coefficients are well studied and understood, their frequency dependence is not. Previous work has been confined to unconsolidated and disaggregated materials such as sands, gravels and soils. In this work, we present an apparatus for measuring the hydraulic and streaming potential coefficients of high porosity, high permeability consolidated porous media as a function of frequency. The apparatus operates in the range 1 Hz to 2 kHz with a sample of 10 mm diameter and 5-30 mm in length. The full design and validation of the apparatus are described together with the experimental protocol it uses. Initial data are presented for three samples of Boise sandstone, which present as dispersive media with the critical transition frequency of 918.3 ± 99.4 Hz. The in-phase and in-quadrature components of the measured hydraulic and streaming potential coefficients have been compared to the Debye-type dispersion model as well as theoretical models based on bundles of capillary tubes and porous media. Initial results indicate that the dynamic permeability data present an extremely good fit to the capillary bundle and Debye-type dispersion models, while the streaming potential coefficient presents an extremely good fit to all of the models up to the critical transition frequency, but diverges at higher frequencies. The streaming potential coefficient data are best fitted by the Pride model and its Walker and Glover simplification. Characteristic pore size values calculated from the measured critical transition frequency fell within 1.73% of independent measures of this parameter, while the values calculated directly from the Packard model showed an underestimation by about 12%.

Uncoupling electrokinetic flow solutions

“…Periodically driven electrokinetics have seen some interesting laboratory applications , Peng et al 2019), including oscillatory streaming potential (Reppert et al 2001, Tardif et al 2011, Jouniaux and Bordes 2012, Glover et al 2012ab;2020a) and electroosmosis (Reppert and Morgan 2002). In oscillatory systems, the coupling coefficient dependence on frequency becomes important (Reppert et al 2001).…”

“…This type of analytical solution (with appropriate physical dimensions and boundary conditions) could be used to fit to laboratory experimental data (e.g., Peng et al 2019, Glover et al 2020ab). Using the analytical solution illustrated in the previous figures, Figure 8 illustrates solutions for three values of α D for the electroosmosis problem (applied voltage) and the streaming potential problem (applied pressure) through time at x D = 0 (left edges of plots in Figures 6 and 7).…”