Frequency-dependent streaming potential of Ottawa sand

摘要

The scientific literature is almost devoid of frequency-dependent electrokinetic measurements on geological materials. An apparatus that allows the measurement of the streaming potential coupling coefficient of unconsolidated and disaggregated materials such as sands, gravels, and soils has been designed, constructed, and tested. The apparatus, which uses an electromagnetic drive, operates in the range 1 Hz to 1 kHz and has a 25.4 mm diameter sample chamber for samples up to 150 mm long. We have made streaming potential coupling coefficient measurements on samples of Ottawa sand as a function of frequency. The results have been analyzed using critically and variably damped second-order vibrational mechanics models as well as the theoretical models of Packard for capillary tubes and Pride for porous media. The best fit was provided by an underdamped second-order model with a damping factor of 0.8561 (R = 0.993). Transition frequencies were derived from the two vibrational models and the Pride model either by fitting the model to the data or directly from the model, giving 230, 273, and 256.58 Hz, respectively. These values are in good agreement with the transition frequency expected for a sand with an independently obtained effective pore radius of 6.76 x th~(-5) m from laser diffraction grain size measurements. The Packard model also agrees extremely well with the experimental data (R~2 = 0.987) directly providing a value of the equivalent capillary radius of 6.75 x 10~(-5) m that coincides within experimental errors with the independently obtained effective pore radius measurements.