Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects

We consider the two-phase flow through a dual-porosity medium, characterized by a period of heterogeneity ω, a ratio of global permeabilities ∈_K, and a ratio of the order of capillary forces ∈_c. The limit when ω tends to zero at different values of ∈_K and ∈_c gives four classes of global behavior, differing by the type of elementary flows at the one-cell level. We propose a diagram of their predominance. A macro-scale model is constructed by formal homogenization techniques for one of these classes; it shows a nonlinear kinetic relationship for the averaged capillary pressure functions, and leads to a decomposition for the effective phase permeability tensors. A capillary relaxation time is explicitly determined. This revised version was published online in August 2006 with corrections to the Cover Date.     

Long-term observations of the electric field vertical component in Lake Baikal (preliminary results)

A deep-water station is constructed for measuring the vertical component of the electric field on the surface-bottom base. A long-term experiment of measuring the vertical component in Lake Baikal is carried out. The measured signal fully reflects (due to the absence of the telluric component) variations in total flows in the range of periods from a few hours to tens of days. The coefficient of internal turbulent friction is estimated from the divergence between theoretical and experimental periods of the inertial flow. The detection of spectral maximums corresponding to variation periods of the hard component of solar radiation is the most important result of the present study. Possibly, this fact is direct evidence for the global electric circuit closure under suitable regional conditions.     

Method of negative saturations for flow with variable number of phases in porous media: extension to three-phase multi-component case

Various EOR methods lead to the appearance of specific macroscopic surfaces called interfaces of phase transition (IPT) such that the number of phases on two sides of an IPT is different, and fluids separated by an IPT are in non-equilibrium. Therefore, the flow equations are also different on two sides of an IPT and cannot be deduced from each other by a continuous degeneration, which imposes difficulties in numerical modelling. To describe such systems, we developed a new conceptual mathematical method based on the replacement of the real single-phase fluid by an imaginary multi-phase multi-component continuum having fictitious properties. As the result, the fluid over all zones becomes multi-phase and can be described by uniform multi-phase hydro- and thermodynamic equations, which allows applying the direct numerical simulation. The equivalence principle determines the physical properties of the fictitious multi-phase fluid, as well as the structure of the uniform multi-phase equations. It also proves that the saturation of each phase becomes an extended function negative or higher than unity in non-equilibrium zones, which becomes the efficient method of tracking the interfaces, the number of phases at any point, and their degree of disequilibrium. The method was developed in [1, 2] for the two-phase case. In the present paper, the new version of the method is developed for the three-phase case with gravity, diffusion, and capillarity. We have obtained the new equivalent uniform multi-phase equations which contain additional non-classical terms responsible for the diffusion and gravity across an IPT. The comparison with classical method is presented. The presentation is illustrated by several examples of simulation by means of the code developed by the research group; their concern: EOR by miscible methods and CO ₂ bubble raising in aquifer.