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This paper presents a theory for frequency-dependent electroosmosis. It is shown that for a closed capillary the electroosmosis frequency-dependent ratio of DeltaV/DeltaP is constant with increasing frequency until inertial effects become prevalent, at which time DeltaV/DeltaP starts to decrease with increasing frequency. The frequency response of the electroosmosis coupling coefficient is shown to be dependent on the capillary radius. As the capillary radius is made smaller, inertial effects start to occur at higher frequencies. As part of this paper, frequency-dependent electroosmosis is compared to frequency-dependent streaming potentials. In this comparison it is shown that inertial effects start to become more prevalent at higher frequencies for the closed capillary frequency-dependent electroosmosis case than for the frequency-dependent streaming potential case in the same capillary. It is also shown that this difference is due to a second viscosity (transverse) wave that emanates from the velocity zero within the capillary for the electroosmosis case. The second viscosity wave superposes with the viscosity wave that emanates from wall of the capillary to effectively reduce the hydraulic radius of the capillary. Data are presented for a 0.127-mm capillary to support the findings in this paper.

[1] Streaming potentials and zeta potentials were measured at equilibrium conditions, while at elevated temperatures of 23°-200°C and pressures of 20 MPa, on intact rock samples of Fontainebleau Sandstone, Berea Sandstone, and Westerly Granite using the oscillatory data collection method. The streaming potential coupling coefficient for Fontainebleau Sandstone decreased in magnitude from 195 nV/Pa at 23°C to 33 nV/Pa at 160°C before rising to 41 nV/Pa at 200°C. The Berea Sandstone coupling coefficient decreased in magnitude from 100 nV/Pa at 23°C to 23 nV/Pa at 160°C and then increased in magnitude to 100 nV/Pa at 200°C. The Westerly Granite coupling coefficient increased in magnitude from 23 nV/Pa at 40°C to 68 nV/Pa to 120°C, then decreased in magnitude to 43 nV/Pa at 160°C, and then increased in magnitude to 50 nV/Pa at 200°C. The zeta potential for all three samples increased in magnitude with increasing temperature, during these equilibrium experiments, which did not mirror the coupling coefficient responses. The temperature dependence of the zeta potential provides indications of possible chemistry changes occurring within sample, such as pH, ionic concentration, and ionic composition. These experiments confirm that knowledge of rock/solution chemistry is important for modeling coupling coefficients and zeta potentials. Results of the experimental work are compared to a model that predicts zeta potential variation with temperature, and reasonable correlations are obtained.

[1] The variation of streaming potentials (voltage/pressure cross-coupling coefficient) with temperature is examined with particular emphasis on the effect of temperature on zeta potentials. The variation of streaming potential with temperature cannot be explained solely by the known temperature dependence of water viscosity, permittivity, and conductivity; the change of zeta potential with temperature must also be included. Many previous experimental studies show that the magnitude of the zeta potential increases with temperature. It was found in this study that the increase is controlled primarily by the surface charge density. These changes are influenced by the absorption properties of the surface and thus the surface charge, which in turn affects the Stern layer charge and properties of the electrical double layer. It is found that the slope of the temperature versus zeta potential curve is controlled by the change in enthalpy of the surface reactions. It was also found that viscosity is the most dominant term in the coupling coefficient, but changes in the conductivity model used to determine zeta potentials can also affect streaming potential coupling coefficient results. For the cases studied, the temperaturedependent zeta potential is determined by the temperature-dependent behavior of the Debye-Hückel parameter, 4%; the diffuse layer of electrical double layer (EDL), 6%; and the surface charge, 90%. The Revil and Glover model was able to account for much of the change in the surface charge density caused by changes in temperature.

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