Emilie Walker

Grain-size to effective pore-size transformation derived from electrokinetic theory

Most permeability models use effective grain size or effective pore size as an input parameter. Until now, an efficacious way of converting between the two has not been available. We propose a simple conversion method for effective grain diameter and effective pore radius using a relationship derived by comparing two independent equations for permeability, based on the electrokinetic properties of porous media. The relationship, which we call the theta function, is not dependent upon a particular geometry and implicitly allows for the widely varying style of microstructures exhibited by porous media by using porosity, cementation exponent, formation factor, and a packing constant. The method is validated using 22 glass bead packs, for which the effective grain diameter is known accurately, and a set of 188 samples from a sand-shale sequence in the North Sea. This validation uses measurements of effective grain size from image analysis, pore size from mercury injection capillary pressure (MICP) measurement...

Permeability models of porous media: Characteristic length scales, scaling constants and time-dependent electrokinetic coupling

Fluidpermeabilityisoneofthemostimportantcharacteristics of a hydrocarbon reservoir, and is described by a number of empirical and theoretical models. We have taken four of the most importantmodels,eachofwhichisderivedfromadifferentphysicalapproach,andhaverewrittentheminagenericformthatimplies a characteristic scale length and scaling constant for each model. The four models have been compared theoretically and using experimental data from 22 bead packs and 188 rock cores from a sand-shale sequence in the U. K. sector of the North Sea. TheKozeny-Carmanmodeldidnotperformwellbecauseittakes no account of the connectedness of the pore network and should no longer be used. The other three models Schwartz, Sen, and JohnsonSSJ;KatzandThompsonKT;andtheRevil,Glover, Pezard,andZamoraRGPZallperformedwellwhenusedwith their respective length scales and scaling constants. Surprisingly,we found that the SSJ and KT models are extremely similar, such that their characteristic scale lengths and scaling constants arealmostidenticaleventhoughtheyarederivedusingextremely different approaches: The SSJ model by weighting the Kozeny-Carman model using the local electrical field, and the KT model by using entry radii from fluid imbibition measurements.Theexperimentallydeterminedscalingconstantsforeach model were found to be cSSJcKT8 /3cRGPZ/3. Use of these models with AC electrokinetic theory has also allowed us to showthatthesescalingconstantsarealsorelatedtotheavaluein the RGPZ model and the m* value in time-dependent electrokinetictheoryandthentoderivearelationshipbetweentheelectrokinetic transition frequency and the RGPZ scale length, which we have validated using experimental data. The practical implication of this work for permeability prediction is that the KT model should be used when fluid imbibition data are available, whereastheRGPZmodelshouldbeusedwhenelectricaldataare available.

A transient method for measuring the DC streaming potential coefficient of porous and fractured rocks

High-quality streaming potential coupling coefficient measurements have been carried out using a newly designed cell with both a steady state methodology and a new pressure transient approach. The pressure transient approach has shown itself to be particularly good at providing high-quality streaming potential coefficient measurements as each transient increase or decrease allows thousands of measurements to be made at different pressures to which a good linear regression can be fitted. Nevertheless, the transient method can be up to 5 times as fast as the conventional measurement approaches because data from all flow rates are taken in the same transient measurement rather than separately. Test measurements have been made on samples of Berea and Boise sandstone as a function of salinity (approximately 18 salinities between 10 -5 mol/dm3 and 2 mol/dm3). The data have also been inverted to obtain the zeta potential. The streaming potential coefficient becomes greater (more negative) for fluids with lower salinities, which is consistent with existing measurements. Our measurements are also consistent with the high-salinity streaming potential coefficient measurements made by Vinogradov et al. (2010). Both the streaming potential coefficient and the zeta potential have also been modeled using the theoretical approach of Glover (2012). This modeling allows the microstructural, electrochemical, and fluid properties of the saturated rock to be taken into account in order to provide a relationship that is unique to each particular rock sample. In all cases, we found that the experimental data were a good match to the theoretical model.

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

Frequency-dependent streaming potential coefficient measurements have been made upon Ottawa sand and glass bead packs using a new apparatus that is based on an electromagnetic drive. The apparatus operates in the range 1 Hz to 1 kHz with samples of 25.4 mm diameter up to 150 mm long. The results have been analysed using theoretical models that are either (i) based upon vibrational mechanics, (ii) treat the geological material as a bundle of capillary tubes, or (iii) treat the material as a porous medium. The best fit was provided by the Pride model and its simplification, which is satisfying as this model was conceived for porous media rather than capillary tube bundles. Values for the transition frequency were derived from each of the models for each sample and were found to be in good agreement with those expected from the independently measured effective pore radius of each material. The fit to the Pride model for all four samples was also found to be consistent with the independently measured steady-state permeability, while the value of the streaming potential coefficient in the low-frequency limit was found to be in good agreement with other steady-state streaming potential coefficient data.

Frequency-Dependent Streaming Potential of Porous Media—Part 1: Experimental Approaches and Apparatus Design

Electrokinetic phenomena link fluid flow and electrical flow in porous and fractured media such that a hydraulic flow will generate an electrical current and vice versa. Such a link is likely to be extremely useful, especially in the development of the electroseismic method. However, surprisingly few experimental measurements have been carried out, particularly as a function of frequency because of their difficulty. Here we have considered six different approaches to make laboratory determinations of the frequency-dependent streaming potential coefficient. In each case, we have analyzed the mechanical, electrical, and other technical difficulties involved in each method. We conclude that the electromagnetic drive is currently the only approach that is practicable, while the piezoelectric drive may be useful for low permeability samples and at specified high frequencies. We have used the electro-magnetic drive approach to design, build, and test an apparatus for measuring the streaming potential coefficient of unconsolidated and disaggregated samples such as sands, gravels, and soils with a diameter of 25.4 mm and lengths between 50 mm and 300 mm.