Phase pressure saturation formulation

To get rid of some of these shortcomings in the numerical solution of the three-phase isothermal flow problems, so-called global (reduced) pressure - saturations formulation is widely used. This approach was first proposed in [8] for modeling of isothermal two-phase flow, and then generalized to the isothermal three-phase case. The idea of the reduced pressure approach is to replace the three-phase flow with the flow of some fluid which motion is described by the Darcy s law. 

Abstract A newly developed numerical simulator of two-phase flow using three-dimensional finite element method is presented in this paper. It is described that the fundamental simultaneous equations, the deduction to implicit pressure explicit saturation formulation and their finite element discretization method. Furthermore, its practical application to the numerical simulation project of predicting Horonobe natural gas product is also introduced. 

If we can assume that always both fluids are present, or, that by regularization, we replace domains with vanishing phases by low saturation domains, we can stay with the pressure pressure formulation which does not degenerate in this case. This approach has the advantage that boimdary conditions can be set for the phase pressures and phase fluxes. Moreover, the definition of interface conditions between porous layers of different characteristics is much simpler It is sufficient to assume continuity of phase pressures and phase fluxes, whereas in the saturation-based cases, the continuity of the capillary pressure has to be bought by a jump in the basic variable, which complicates the numerical schemes. 

Equation (2.53), known as the Kelvin equation, reveals that the vapor pressure, P , decreases with increasing interface curvature. So far, we have assumed that the substrate is liquid-wet or that the new phase forms as a bubble. For a droplet or when gas is the wetting phase, the effect of curvature on saturation pressure is formulated shortly. When the radius of a bubble or droplet becomes very small (say r < 10 cm, for a pure substance), the interfacial tension may become a function of the radius (Defay and Prigogine, 1966). However, the derivation of Eq. (2.53) was not based on the assumption of the interfacial tension being independent of r. 

We can conclude that the stability of static foam in porous media depends on the medium permeability and wetting-phase saturation (i.e., through the capillary pressure) in addition to the surfactant formulation. More importantly, these effects can be quantified once the conjoining/disjoining pressure isotherm is known either experimentally (8) or theoretically (9). Our focus... 

Divisek et al. presented a similar two-phase, two-dimensional model of DMFC. Two-phase flow and capillary effects in backing layers were considered using a quantitatively different but qualitatively similar function of capillary pressure vs liquid saturation. In practice, this capillary pressure function must be experimentally obtained for realistic DMFC backing materials in a methanol solution. Note that methanol in the anode solution significantly alters the interfacial tension characteristics. In addition, Divisek et al. developed detailed, multistep reaction models for both ORR and methanol oxidation as well as used the Stefan—Maxwell formulation for gas diffusion. Murgia et al. described a one-dimensional, two-phase, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymer membrane for a liquid-feed DMFC. 

Volatilization and vapor phase transport are important processes in the dissipation of even the so-called nonvolatile pesticides, such as the chlorinated hydrocarbons. The vapor pressure or the vapor saturation density is therefore an important parameter to assess the persistence of the pesticide. Much work was done very early in the era of the (persistent) pesticides. Table 8.3 shows the vapor pressure and water solubility of some important chlorinated pesticides and contaminants in pesticide formulations. 

Abstract To better understand the coupling of thermal (T), hydraulic (H) and mechanical (M) processes (T-H-M processes) and their influence on the system behaviour, models allowing T-H-M coupling are developed. These models allow simulations in the near-field of the system. Such a model has been developed within the simulator RockFlow/RockMech. This paper concentrates on the thermal and hydraulic processes. For those processes, the material parameters and state variables are highly non-linear and mostly functions of temperature, saturation and pressure. This paper shows how these dependencies are formulated mathematically and are implemented into RockFlow/RockMech. The implementation allows phase changes between the fluid phases (gas and liquid) to occur explicitly. The model allows the simulation of very low permeability clays with high capillary pressures. An example for code validation is shown, where low permeability clay is desaturated, lastly, current work on the calculations performed in the near field study (BMTl) of the DECOY ALEX III project is outlined. 

A formulation removing both possible degeneracies has been introduced by [5]. This formulation has as its basic variables the wetting phase saturation and a so called global pressure p with values between pg and p . Furthermore, it introduces a global velocity. 

The limits of existence of water in a thermodynamically stable liquid state extend from the triple point, at which it is in equilibrium with ice I, the solid state of water under ordinary pressures, to the critical point, at which the distinction between liquid and vapour phases vanishes. The former limit, the triple point, is at 0.01 °C (Ft = 273.16 K) and Tj = 0.61166 kPa. The latter limit, the critical point, is at 374.93 °C (Tc = 647.096 K) and = 22.064 MPa. Liquid water also exists in a meta-stable sub-cooled state, theoretically down to the glass transition point, 139 K, but experimentally to 232 K (—41 °C) before spontaneous nucleation and freezing sets in. Liquid water is at equilibrium with water vapour along the so-called saturation curve, Pc(T), where / a is the vapour pressure, but it exists as a liquid also at higher external pressures. Wagner and Pruss (2002) reported the lAPWS 1995 formulation... 

The thermodynamics of semi-volatile phase partitioning for atmospheric OA mixtures has been extensively treated in the literature [17, 18, 39, 40] and will only briefly be reviewed here. We express the effective saturation concentration (C ) of an organic compound by converting its saturation vapor pressure into mass concentration units and multiplying by the appropriate activity coefficient for the organic mixture (this is the inverse of the partitioning coefficient used in some formulations = 1/C ). The general effect of a solution is to lower the... 

Scaling theory can be used to design microemulsions for important applications such as enhanced oil recovery. The salinities of brines in oil reservoirs range from potable to saturated at elevated temperature and pressure. When a reservoir of high salinity has been flooded previously with fresh water, the brine salinity can also vary greatly within the reservoir. To find a suitable surfactant requires a laborious search for a formulation with the correct optimal salinity for each reservoir. Thus (see Fig. 16.8), there has been a desire to find a surfactant that would form three phases over the broadest range of salinities and have ultralow interfacial tensions for those phases at the same time. However, there are thermodynamic limits on the extent to which these goals can be simultaneously met. 

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