Mariela Araujo

Capillary rise in porous media

Capillary rise experiments were performed in columns filled with glass beads and Berea sandstones, using visual methods to register the advance of the water front. For the glass-bead-filled columns, early time data is well fitted by the Washburn equation. However in the experiments, the advancing front exceeded the predicted equilibrium height. For large times, an algebraic behavior of the velocity of the front is observed (T. Delker, D. Pengra and P. Wong, Phys. Rev. Lett. 76 (1996) 2902). A model to study the capillary pressure evolution in a regular assembly of spheres is proposed and developed. It is based on a quasi-static advance of the meniscus with a piston-like motion, and allows to estimate the hydraulic equilibrium height, with values very close to those obtained by fitting early time data to a Washburn equation. The change of regime is explained as a transition in the mechanism of advance of the meniscus. On the other hand, only the Washburn regime was observed for the sandstones. The front velocity was fitted to an algebraical form with an exponent close to 0.5, a value expected from the asymptotic limit of the Washburn equation.

P-wave velocity-porosity relations and homogeneity lengths in a realistic deposition model of sedimentary rock

Abstract A realistic model of a porous rock is generated by simulating critical processes in sedimentary rock formation. The simulated processes include deposition of grains in different energy environments, compression with grain rearrangement effects due to the stratigraphic column pressure and cementation. It has been shown that such processes are fundamental in determining the appropriate correlations for the system to exhibit realistic electrical and hydraulic conductivities of sandstones. Here we analyse the theoretical model from the geometrical and acoustic standpoint, determining the relations of the homogenization volumes and sound speed to the resulting porosity of the model. For the quartz cemented contact model we find the correct velocity magnitudes and concavities in the velocity–porosity curves. We also show that using anisotropic rescaling as a compaction stage can lead to inadequate acoustic properties for the rock model, due to the importance of grain rearrangement.

Threshold capillary pressure in capillaries with curved sides

Modeling of fluid flow through permeable media is of great importance in assessing the performance of both hydrocarbon reservoirs and aquifers. In this process, network models based on cylindrical capillaries with circular cross sections are frequently used. This type of capillaries are not able to reproduce interesting physical phenomena observed in the experiments, for example, situations where there is flow by films with the wetting fluid occupying the crevices and wedges of the structure. We present an analysis of the behavior of the capillary pressure of a droplet of non-wetting fluid with an infinite length, inside objects of cylindrical symmetry with curved sides. The calculation is based on a method proposed by Mayer and Stowe and Princen (MS–P). Different capillary geometries are considered, and the behavior of the capillary pressure and transversal fluid saturation as a function of the shape factor is studied. The results found either analytically or numerically, allow to understand the relation between geometry and flow properties, and helps in the building of more realistic pore network models for flow studies at the pore scale.

Liquid-vapor isotherm in a closed single-component system with curved interfaces.

A thermodynamic model to obtain the radius of bubbles or droplets in a single-component system for a given temperature, total volume, and phase distribution is developed. The general formulation of the model includes bubbles or droplets in the form of spheres, truncated spheres on a flat solid surface or inside conical walls. In these three geometries the liquid-vapor curvature radius is positive but in the case of conical walls it can be also negative. States with different dispersed-phase distributions are compared using the total free energy of the system. When the curvature radius is positive, it has a minimum nonvanishing value and the occurrence of the Ostwald ripening is energetically favorable. On the other hand, when the curvature radius is negative, it is energetically more favorable to find the dispersed phase even in the expected single-phase region, and the occurrence of an anti-ripening phenomenon. The PV isotherms obtained from the model and the applicability of the results to the nucleation process are discussed.

Nuclear magnetic relaxation of protons in Venezuelan crude oil

Abstract Venezuelan crude oils of different viscosity were studied by pulsed n.m.r.. Four phases with different microdynamical properties could be distinguished through the measurement of magnetic relaxation times T1 and T2. Their temperature dependence showed the known BPP behaviour with a wide correlation time distribution caused by magnetic dipolar and electron-proton interactions. When the temperature was increased, the transformation from a viscous phase to a more liquid phase could be observed.

Liquid-vapor isotherm in a closed single-component system with droplets or bubbles in smooth crevices.

A thermodynamic model in order to study a single-component system where droplets or bubbles are inside smooth crevices is presented. Liquid-vapor interface curvature radius can change its sign as the droplet or bubble volume change. The results suggest that there is always dispersed phase inside smooth crevices of microscopic dimensions, even in the expected single-phase region. Thus, the occurrence of an anti-ripening phenomenon is predicted from a microscopic point of view; meanwhile the occurrence of a ripening phenomenon is energetically favorable at a macroscopic scale. The relevance of these results on the heterogeneous nucleation process is analyzed.

Flow equations on a fractal structure

Two-phase flow equations are solved on a fractal Bernasconi lattice including capillary and viscous forces. The recursive structure of the lattice allows the use of a renormalization group approach to calculate flow properties, resulting in a much faster method compared to conventional simulations. The interplay between disorder or heterogeneity in local flow conductance and capillary pressure effects is studied as a function of length scale. Flow related quantities such as water cut curves, saturation profiles, and breakthrough times are found to depend on the size of the system and on disorder strength. As disorder increases larger sizes are needed to get good averaging. It is found that this lattice can be used to get a good approximated solution of the two-phase flow equations in complex anisotropic structures, since it grants considering the effect of anisotropy on flow properties, a condition relevant for a variety of industrial applications.

Renormalization approach for the simulation of two-phase flow in porous media

A new method for simulating two-phase flow in porous media using hierarchical lattices is presented. These type of lattices allowed us to perform simulations of very large systems at a very low computational cost. It is shown how flow properties agree with those found using conventional simulations with and without capillary pressure. The interplay between heterogeneity effects and capillary forces is analyzed. It is shown that capillary pressure reduces the irruption time for the case of homogeneous systems while producing the opposite effect when disorder is present.