A new formulation of immiscible compressible two-phase flow in porous media

A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008).     

Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure

A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986).     

An existence result for nonisothermal immiscible incompressible 2‐phase flow in heterogeneous porous media

In the present article, we study the temperature effects on two‐phase immiscible incompressible flow through a porous medium. The mathematical model is given by a coupled system of 2‐phase flow equations and an energy balance equation. The model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy‐Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation; ie, the saturation of one phase, the pressure of the second phase, and the temperature are primary unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we show the existence of weak solutions with the help of an appropriate regularization and a time discretization. We use suitable test functions to obtain a priori estimates. We prove a new compactness result to pass to the limit in nonlinear terms.     

Elucidating Sequence and Structural Determinants of Carbohydrate Esterases for Complete Deacetylation of Substituted Xylans

Acetylated glucuronoxylan is one of the most common types of hemicellulose in nature. The structure is formed by a β-(1→4)-linked D-xylopyranosyl (Xylp) backbone that can be substituted with an acetyl group at O-2 and O-3 positions, and α-(1→2)-linked 4-O-methylglucopyranosyluronic acid (MeGlcpA). Acetyl xylan esterases (AcXE) that target mono- or doubly acetylated Xylp are well characterized; however, the previously studied AcXE from Flavobacterium johnsoniae (FjoAcXE) was the first to remove the acetyl group from 2-O-MeGlcpA-3-O-acetyl-substituted Xylp units, yet structural characteristics of these enzymes remain unspecified. Here, six homologs of FjoAcXE were produced and three crystal structures of the enzymes were solved. Two of them are complex structures, one with bound MeGlcpA and another with acetate. All homologs were confirmed to release acetate from 2-O-MeGlcpA-3-O-acetyl-substituted xylan, and the crystal structures point to key structural elements that might serve as defining features of this unclassified carbohydrate esterase family. Enzymes comprised two domains: N-terminal CBM domain and a C-terminal SGNH domain. In FjoAcXE and all studied homologs, the sequence motif around the catalytic serine is Gly-Asn-Ser-Ile (GNSI), which differs from other SGNH hydrolases. Binding by the MeGlcpA-Xylp ligand is directed by positively charged and highly conserved residues at the interface of the CBM and SGNH domains of the enzyme.     

The Influence of Polysaccharides/TiO2 on the Model Membranes of Dipalmitoylphosphatidylglycerol and Bacterial Lipids

The aim of the study was to determine the bactericidal properties of popular medical, pharmaceutical, and cosmetic ingredients, namely chitosan (Ch), hyaluronic acid (HA), and titanium dioxide (TiO₂). The characteristics presented in this paper are based on the Langmuir monolayer studies of the model biological membranes formed on subphases with these compounds or their mixtures. To prepare the Langmuir film, 1,2-dipalmitoyl-sn-glycero-3-phospho-rac-(1-glycerol) (DPPG) phospholipid, which is the component of most bacterial membranes, as well as biological material-lipids isolated from bacteria Escherichia coli and Staphylococcus aureus were used. The analysis of the surface pressure-mean molecular area (π-A) isotherms, compression modulus as a function of surface pressure, C_S⁻¹ = f(π), relative surface pressure as a function of time, π/π₀ = f(t), hysteresis loops, as well as structure visualized using a Brewster angle microscope (BAM) shows clearly that Ch, HA, and TiO₂ have antibacterial properties. Ch and TiO₂ mostly affect S. aureus monolayer structure during compression. They can enhance the permeability of biological membranes leading to the bacteria cell death. In turn, HA has a greater impact on the thickness of E. coli film.     

Backward emitted protons in interactions of neutrinos with nuclei in photoemulsion

Backward emitted protons with momentump>0.3 GeV/c in interactions of neutrino in the energy range 10–200 GeV with photoemulsion nuclei were investigated. Energy spectrum slope parameter of backward protons was measured to beT ₀=48.9±7.9 MeV. TheA-dependence power index of relative mean yield of backward protons was found to bea=0.68±0.12. A drop in the mean yield of backward protons at the four momentum squared over ～15 (GeV/c)² (the neutrino energy over ～50 GeV) was observed.     

Homogenization results for a coupled system modelling immiscible compressible two-phase flow in porous media by the concept of global pressure

A model for immiscible compressible two-phase flow in heterogeneous porous media is considered. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation) equation with rapidly oscillating porosity function and absolute permeability tensor. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of two-scale convergence.