Capillary rise of a liquid between two vertical plates making a small angle.

The penetration of a wetting liquid in the narrow gap between two vertical plates making a small angle is analyzed in the framework of the lubrication approximation. At the beginning of the process, the liquid rises independently at different distances from the line of intersection of the plates except in a small region around this line where the effect of the gravity is negligible. The maximum height of the liquid initially increases as the cubic root of time and is attained at a point that reaches the line of intersection only after a certain time. At later times, the motion of the liquid is confined to a thin layer around the line of intersection whose height increases as the cubic root of time and whose thickness decreases as the inverse of the cubic root of time. The evolution of the liquid surface is computed numerically and compared with the results of a simple experiment

Anisotropic permeabilities evolution of reservoir rocks under pressure: new experimental and numerical approaches

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CO2GeoNet, the unique role of the European scientific body on CO2 geological storage

CO2GeoNet is a Network of Excellence on the geological storage of CO2, initiated by the EC's 6th research framework programme in 2004 and integrating Europe's key research institutes to create a scientific reference body dedicated to the development of CO2 geological storage as a viable option for mitigating climate change. It has gained international recognition through bodies such as CSLF and IEA-GHG. It emerges as the world's largest integrated scientific community on this theme. In 2008, the network has been transformed into a legally registered Association, thus reinforcing its identity as a durable entity engaged for the safe and reliable deployment of CO2 geological storage. CO2GeoNet's activities encompass joint research, training, scientific advice, and information and communication on CO2 geological storage. © 2009 Elsevier Ltd. All rights reserved

Electrohydrodynamic model of vesicle deformation in alternating electric fields

We develop an analytical theory to explain the experimentally-observed morphological transitions of giant vesicles induced by AC electric fields (1). The model treats the inner and suspending media as lossy dielectrics, while the membrane as an ion-impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, and bending stresses exerted on the membrane. Considering a nearly spherical vesicle, the solution to the electrohydrodynamic problem is obtained as a regular perturbation expansion in the excess area. The theory predicts that stationary vesicle deformation depends on field frequency and conductivity conditions. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasi-spherical rest shape. The analysis shows that the evolution towards the stationary vesicle deformation strongly depends on membrane properties such as viscosity. The model can be applied to rationalize the transient and steady deformation of biological cells in electric fields

Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow-Dependent Relative Permeability Scaling

The phenomenology of steady-state two-phase flow in porous media is recorded in SCAL relative permeability diagrams. Conventionally, relative permeabilities are considered to be functions of saturation. Yet, this has been put into challenge by theoretical, numerical and laboratory studies that have revealed a significant dependency on the flow rates. These studies suggest that relative permeability models should include the functional dependence on flow intensities. Just recently a general form of dependence has been inferred, based on extensive simulations with the DeProF model for steady-state two-phase flows in pore networks. The simulations revealed a systematic dependence of the relative permeabilities on the local flow rate intensities that can be described analytically by a universal scaling functional form of the actual independent variables of the process, namely, the capillary number, Ca, and the flow rate ratio, r. In this work, we present the preliminary results of a systematic laboratory study using a high throughput core-flood experimentation setup, whereby SCAL measurements have been taken on a sandstone core across different flow conditions -spanning 6 orders of magnitude on Ca and r. The scope is to provide a preliminary proof-of-concept, to assess the applicability of the model and validate its specificity. The proposed scaling opens new possibilities in improving SCAL protocols and other important applications, e.g. field scale simulators

In-Situ Investigation of Aging Protocol Effect on Relative Permeability Measurements Using High- Throughput Experimentation Methods

International audienceRelative permeabilities are a first-order parameter to consider when describing multiphase flows in porous media. Among many other parameters, the core wettability controls the fluids repartition in the porous media at pore scale, strongly affecting how the fluids can be displaced (i.e., their relative permeabilities). As the initial wettability of cores sampling a reservoir is rarely preserved, classical SCAL measurements (such as relative permeabilities) may not reflect the rock properties at reservoir conditions. This original core wettability may be restored in a process referred as ‘core aging’. It is generally done by injecting the core with the reservoir fluids (brine and crude-oil) to equilibrate the rock surface with respect to the oil and brine components. Here, we investigated the effect of two aging protocols (static and dynamic) on wettability restoration, and characterize the aging using oil/water relative permeabilities measured on the core after aging. The two aging protocols were applied on a set of initially strongly water-wet outcrop sandstone samples (Bentheimer). The relative permeabilities were measured using the steady-state method and a state-of-the-art experimental setup (CAL-X) based on X-ray radiographies. The setup is equipped with an X-ray radiography facility, enabling monitoring of 2D local saturations in real time and thus giving access to fluid flow paths during the flooding. The relative permeability curves of aged samples show clear differences when compared to water-wet relative permeabilities, hence. suggesting that the wettability has been effectively altered. However, the two aging protocols were unable to produce the same results. The dynamic aging has led to an inversion of the original relative permeability curves asymmetry, suggesting a strongly oilwet system, whereas the static aging protocol has altered the wettability to a lesser extent. The differences can be explained by analyzing 2D saturation maps. In the case of dynamic aging we observed a homogeneous distribution of fluid saturation during fractional flow. In contrast, the static protocol results in heterogeneous flow paths, confirming that this protocol did not uniformly alter the wettability of the sample and generates a patchier mixed-wettability system

A New Model to Calculate Three-Phase Relative Permeabilities: Application and Validation for a Sandstone

Three-phase flow in a porous medium is usually described by the Stone model (1970). This model is based on two-phase data and relies on empirical correlations. It is valid only under strong water wettability and recognized as being a poor predictor. The goal of the present study is to develop a mathematical model for three-phase flow avoiding any empirical correlations. In this paper, only strong water-wet and spreading conditions are considered. However the model could be relatively easily extended to oil-wet or even mixed-wet conditions. The model is based on a physically relevant description of phase distribution and flow mechanisms at the pore scale. The porous medium is described as a set of fractal pores, whose linear fractal dimension and size distributions are derived from a mercury intrusion capillary pressure curve. The fluids are allowed to flow together in the same fractal pore, gas in the center, water near the walls and oil in an intermediate phase. The relative permeabilities are evaluated by calculating the flow of each fluid applying Poiseuille's law. The model results are compared to relative permeabilities obtained by history matching of gas injection experiments. The same experiments are also simulated using Stone's model and laboratory measured two-phase data

Potential structures for CO₂ geological storage in the Baltic Sea: Case study offshore Latvia

This study is focused on two structures in the Baltic offshore region (E6 and E7 structures in Latvia) prospective for the geological storage of carbon dioxide (CO 2 ). Their CO 2 storage capacities were estimated recently with different levels of reliability. Petrophysical, geophysical, mineralogical and geochemical parameters of reservoir rocks represented by quartz sandstones of the Deimena Formation of Middle Cambrian in two wells and properties of Silurian and Ordovician cap rocks were additionally studied and interpreted in the present contribution. Extended methodology on rock measurements and estimation of conservative and optimistic storage capacity are presented. Uncertainties and risks of CO2 storage in the offshore structure E6 estimated as the most prospective for CO2 geological storage in the Baltic Region, and the largest among all onshore and offshore structures studied in Latvia, were discussed. We re-estimated the previous optimistic capacity of the E6 structure (265–630 Mt) to 251–602 Mt. Considering fault system within the E6 structure we estimated capacity of two compartments of the reservoir separately (E6-A and E6-B). Estimated by the optimistic approach CO2 storage capacity of the E6-A part was 243–582 Mt (mean 365 Mt) and E6-B part 8–20 Mt (mean 12 Mt). Conservative capacity was 97–233 Mt (mean 146 Mt) in the E6-A, and 4–10 Mt (mean 6 Mt) in the E6-B. The conservative average capacity of the E6-B part was in the same range as this capacity in the E7 structure (6 and 7 Mt respectively). The total capacity of the two structures E6 and E7, estimated using the optimistic approach was on average 411 Mt, and using the conservative approach, 159 Mt