An experimental and numerical systematic study of the growth of the Richtmyer–Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15–1.45. The evolution of the mixing zone following the re-shock is found to be independent of its amplitude at the time of the re-shock and to depend directly on the strength of the re-shock. A linear growth of the mixing zone with time following the passage of the re-shock and before the arrival of the reflected rarefaction wave is found. Moreover, when the mixing zone width is plotted as a function of the distance travelled, the growth slope is found to be independent of the re-shock strength. A comparison of the experimental results with direct numerical simulation calculations reveals that the linear growth rate of the mixing zone is the result of a bubble competition process.

No abstract

Exclusion-diffusion potentials arising from temperature gradients are widely neglected in self-potential (SP) surveys, despite the ubiquitous presence of temperature gradients in subsurface settings such as volcanoes and hot springs, geothermal fields, and oil reservoirs during production via water or steam injection. Likewise, with the exception of borehole SP logging, exclusion-diffusion potentials arising from concentration gradients are also neglected or, at best, it is assumed that the diffusion potential dominates. To better interpret these SP sources requires well-constrained measurements of the various coupling terms. We report measurements of thermoelectric and electrochemical exclusion-diffusion potentials across sandstones saturated with NaCl brine and find that electrode effects can dominate the measured voltage. After correcting for these, we find that Hittorf transport numbers are the same within experimental error regardless of whether ion transport occurs in response to temperature or concentration gradients over the range of NaCl concentration investigated that is typical of natural systems. Diffusion potentials dominate only if the pore throat radius is more than approximately 4000 times larger than the diffuse layer thickness. In fine-grained sandstones with small pore throat diameter, this condition is likely to be met only if the saturating brine is of relatively high salinity; thus, in many cases of interest to earth scientists, exclusion-diffusion potentials will comprise significant contributions from both ionic diffusion through, and ionic exclusion from, the pore space of the rock. However, in coarse-grained sandstones, or sandstones saturated with high-salinity brine, exclusion-diffusion potentials can be described using end-member models in which ionic exclusion is neglected. Exclusion-diffusion potentials in sandstones depend upon pore size and salinity in a complex way: they may be positive, negative, or zero depending upon sandstone rock texture (expressed here by the pore radius r) and salinity.

Summary Spontaneous potential (SP) is routinely measured using wireline tools during reservoir characterization. However, SP signals are also generated during hydrocarbon production, in response to gradients in the water-phase pressure (relative to hydrostatic), chemical composition, and temperature. We use numerical modeling to investigate the likely magnitude of the SP in an oil reservoir during production, and suggest that measurements of SP, using electrodes permanently installed downhole, could be used to detect and monitor water encroaching on a well while it is several tens to hundreds of meters away. We simulate the SP generated during production from a single vertical well, with pressure support provided by water injection. We vary the production rate, and the temperature and salinity of the injected water, to vary the contribution of the different components of the SP signal. We also vary the values of the so-called "coupling coefficients," which relate gradients in fluid potential, salinity, and temperature to gradients in electrical potential. The values of these coupling coefficients at reservoir conditions are poorly constrained. We find that the magnitude of the SP can be large (up to hundreds of mV) and peaks at the location of the moving water front, where there are steep gradients in water saturation and salinity. The signal decays with distance from the front, typically over several tens to hundreds of meters; consequently, the encroaching water can be detected and monitored before it arrives at the production well. Before water breakthrough, the SP at the well is dominated by the electrokinetic and electrochemical components arising from gradients in fluid potential and salinity; thermoelectric potentials only become significant after water breakthrough, because the temperature change associated with the injected water lags behind the water front. The shape of the SP signal measured along the well reflects the geometry of the encroaching waterfront. Our results suggest that SP monitoring during production, using permanently installed downhole electrodes, is a promising method to image moving water fronts. Larger signals will be obtained in low-permeability reservoirs produced at high rate, saturated with formation brine of low salinity, or with brine of a very different salinity from that injected.

The injection of cold water into a hydrocarbon reservoir containing relatively warmer, more saline formation brine may generate self-potential anomalies as a result of electrokinetic, thermoelectric, and=or electrochemical effects. We have numerically assessed the relative contributions of these effects to the overall self-potential signal generated during oil production in a simple hydrocarbon reservoir model. Our aim was to determine if measurements of self-potential at a production well can be used to detect the movement of water toward the well. The coupling coefficients for the electrochemical and thermoelectric potentials are uncertain, so we considered four different models for them. We also investigated the effect of altering the salinities of the formation and injected brines. We found that the electrokinetic potential peaked at the location of the saturation front (reaching values of 0.2 mV even for the most saline brine considered). Moreover, the value at the production well increased as the front approached the well, exceeding the noise level ($ 0.1 mV). Thermoelectric effects gave rise to larger potentials in the reservoir ($10 mV), but values at the well were negligible .0:1 mV ð Þ until after water breakthrough because of the lag in the temperature front relative to the saturation front. Electrochemical potentials were smaller in magnitude than thermoelectric potentials in the reservoir but were measurable > 0:1 mV ð Þat the well because the salinity front was closely associated with the saturation front. When the formation brine was less saline ($1 mol=liter), electrokinetic effects dominated; at higher salinities ($5 mol=liter), electrochemical effects were significant. We concluded that the measurement of self-potential signals in a production well may be used to monitor the movement of water in hydrocarbon reservoirs during production, but further research is required to understand the thermoelectric and electrochemical coupling coefficients in partially saturated porous media.