Spectral element based numerical solvers are developed to simulate electrokinetically driven flows for micro-fluidic applications. Based on these numerical solvers, basic phenomena and devices for electrokinetic applications in micro and nano flows are systematically studied. As a first application, flow and species transport control in a grooved micro-channel using local electrokinetic forces are studied. Locally applied electric fields, zeta potential patterned grooved surfaces, and geometry are manipulated to control mixed electroosmotic/pressure driven flow in the grooved micro-channel. The controlled flow pattern enables entrapment and release of prescribed amounts of scalar species in the grooves. As another application, hydrodynamic/ electrokinetic focusing in a micro-channel is studied. External electric field, flow rate of pressure driven flow, and geometry in the micro-channel are manipulated to obtain the focusing point, which led to determination of the electrophoretic mobility and (relative) concentration of dilute mixtures. This technique can be used to identify and detect species in dilute mixtures.

Single-probe formation testers have been used since the 1950s to measure pore pressure and estimate mobility in fluid-bearing formations penetrated by a well. They are widely used in the oil and gas industry, with tens of measurements often made in every newly drilled well as part of the formation evaluation program. Each measurement consists of placing the tool in the wellbore in direct contact with the face of the formation, extracting a small amount of fluid (from 1 to 50 cc) from the rock and analyzing the fluid pressure response of the system. Pressure interpretation is based on models that assume that temperature within the formation tester flowline remains constant during the tool operation. However, formation pressure measurement involves relatively fast volume and pressure changes within the flowline, which result in temperature changes. These temperature changes are modeled semi-analytically and their effect on pressure transients is analyzed. Temperature variations are accounted for by describing the pressure and temperature dependence of fluid density in the continuity equation, and that temperature varies with both space and time. It is considered here that once a temperature change is imposed on the system, the primary mechanism of thermal transport to achieve equilibrium is conduction. Including temperature in the analysis requires taking into account flowline geometry, and well environmental conditions during the measurement-- namely, wellbore temperature and type of drilling fluid in the wellbore, all of which are immaterial in the isothermal analysis. Arguably, pressure behavior during formation tester measurements could be influenced by several factors. All previous studies related to formation testers assume perfect tool performance and provide explanations to pressure behaviors from the reservoir point of view (e.g., Stewart and Witmmann, 1979; Phelps et al., 1984; Proett and Chin, 1996, etc.). The approach followed here is diametrically opposite. The formation is considered `perfect' from the point of view of pressure measurement, and physical phenomena (thermal transients) that may affect the measured pressure signal are studied. The focus is to understand fundamental aspects of the tool performance that can be studied analytically while minimizing, as much as possible, external parameters that add uncertainty. This dissertation was motivated by inconsistencies observed between the pressure behavior in field measurements and existing (isothermal) theory. For instance, false buildups, buildup overshoots and long time required to reach pressure equilibration, have puzzled those involved in the interpretation of formation tester pressure transients for many years. These behaviors can be reproduced in pressure computations when accounting for temperature variations. The focus of this dissertation is on modeling the tool capability to sense pressure transients associated with recompression of formation fluids several inches away from the wellbore, accounting for temperature variations during the measurement. This is relevant because it is desirable to characterize formation properties beyond the region affected by drilling mud filtrate invasion. In practice, a discrepancy is often observed between formation mobility obtained from drawdown, which depends mostly on formation properties near the wellbore, and mobility obtained from the analysis of late-time buildup pressure, which in theory depends on formation properties farther from the wellbore (Moran and Finklea, 1962). This dissertation examines the influence of late-time tool storage effects caused by thermal equilibration of the flowline fluid on the pressure equilibration and buildup mobility interpretation. It was found that in some cases such late-time storage effects could exhibit a behavior that resembles that expected from spherical flow, that is, the flow regime characteristic of single-probe formation testers; and could therefore invalidate mobility determined by isothermal transient pressure analysis. Formation tester flowline and probe design, test parameters (rate and volume), and environmental conditions during the measurement, mostly type of drilling fluid and wellbore temperature, are important variables in determining the magnitude of late-time storage effects, and hence the tool capability to detect a deep formation signal (spherical flow). Temperature variations affecting late-buildup pressure transients were observed to be more pronounced (listed in order of importance): as wellbore temperature increases; drilling fluid is oil-based mud; flowline with large radius components (e.g. > 1 cm); large flowline volume; small probe radius (< 1 cm); and, large drawdown rate. Temperature effects on the late-buildup also tend to be more significant when mobility is in the 0.1 to 10 md/cp range, that is for those formations more likely, in theory, to exhibit spherical flow regime during buildup. / text