Frequency-Dependent Streaming Potential of Porous Media—Part 2: Experimental Measurement of Unconsolidated Materials

Table 2

Summary of results.

Property	Unit	Ottawa sand	Glass beads			Comment
			0. 5 mm	1 mm	2 mm
Steady-state electrokinetic modelling
Measured steady-state streaming potential coupling coefficient, 𝐶𝑠𝑜	V/MPa	0.518±0.155	1.37±0.411	1.61±0.483	1.80±0.54	Value at lowest frequency measured.
Modelled steady-state streaming potential coupling coefficient, 𝐶𝑠𝑜	V/MPa	1.05	1.26	1.57	1.76	Using [16, 17].
Modelled zeta potential, 𝜁	mV	−15.9	−29.6	−29.6	−29.6	Using [16, 17].
pH for electrokinetic modelling	—	6	6.7	6.7	6.7
Transition frequencies
Transition frequency, critically damped 2nd order vibrational model, 𝜔𝑡	Hz	230	234	54	13	Using [22].
Transition frequency, 2nd order model with variable damping, 𝜔𝑡	Hz	748.8	636.9	176.4	41.7	Using [22].
Damping factor, ξ	—	1.5	1.5	1.5	1.5	Using [22].
Transition frequency from the Pride model, 𝜔𝑡	Hz	256.58	213	58.79	13.85	Using [23].
Transition frequency from the Glover and Walker simplification, 𝜔𝑡	Hz	256.58	213.36	57.32	12.61	Using [19].
Predicted effective pore radius
Calculated effective pore radius from independent measurement, 𝑟𝑝	𝜇m	67.6±16.2	70.8±0.70	139±3.41	287±4.03	From Table 1
From the Packard model, equivalent capillary tube radius, 𝑟eff	𝜇m	67.5	72	145	302	Using [6].
From the critically damped 2nd order vibrational model	𝜇m	70.46	69.85	145.41	296.35	Using (12)
From the Pride model	𝜇m	66.71	73.21	139.36	287.11	Using (12)
From the Glover and Walker simplification	𝜇m	66.71	73.15	141.13	300.90	Using (12)
Characteristic length scale, Λ	𝜇m	62.40	67.76	131.45	280.24	Using (10)
Predicted permeabilities
Measured permeability, 𝜅meas	m^2	1.19×10^−10	1.62×10^−10	5.95×10^−10	27.2×10^−10	See text.
Predicted permeability using the RGPZ method, 𝜅RGPZ	m^2	1.22×10^−10	1.52×10^−10	5.80×10^−10	24.8×10^−10	Using [26].
From the critically damped 2nd order vibrational model	m^2	1.33×10^−10	1.48×10^−10	6.32×10^−10	26.4×10^−10	Using (12)
From the Pride model	m^2	1.19×10^−10	1.62×10^−10	5.80×10^−10	24.8×10^−10	Using (12)
From the Glover and Walker simplification	m^2	1.19×10^−10	1.62×10^−10	5.95×10^−10	27.2×10^−10	Using (12)