Trapping number

Table II. Average catches in 1980 from traps at sites with different number of killed trees in 1979. The damage is recorded within 100 m from the traps. Number of traps in parentheses.

This chapter covers the fundamentals of surfactant flooding, which include microemulsion properties, phase behavior, interfacial tension, capillary desaturation, surfactant adsorption and retention, and relative permeabilities in surfactant flooding. It provides the basic theories for surfactant flooding and presents new concepts and views about capillary number (trapping number), relative permeabilities, two-phase approximation of the microemulsion phase behavior, and interfacial tension. This chapter also presents an experimental study of surfactant flooding in a low-permeability reservoir. 

A new dimensionless number called the trapping number has been defined it includes both gravity and viscous forces (UTCHEM-9.0, 2000). The dependence of residual saturations on interfacial tension is modeled in UTCHEM as a function of the trapping number. This is a formulation necessary to model the combined effect of viscous and buoyancy forces in three dimensions. Buoyancy forces are much less important under enhanced oil recovery conditions than under typical surfactant-enhanced aquifer remediation (SEAR) conditions therefore, it had not been carefully considered under three-dimensional surfactant flooding held conditions. 

For an arbitrary flow angle, the preceding trapping number can be rewritten as... 

Pennell et al. (1996) managed to derive the trapping number defined earlier by applying a force balance on a single trapped nonaqueous phase liquid... 

It can be shown that from the magnitude of the hydraulic and buoyancy forces, IfL the trapping number is... 

Equation 7.119 seems to be consistent with the flow in real life. The explanation may be extended to the difference between Eq. 7.103 and Eq. 7.118 at an arbitrary flow angle. Equation 7.118 appears to model the two-dimensional flow in a homogeneous and isotropic porous media. The trapping numbers for two-dimensional and three-dimensional heterogeneous, anisotropic porous media were also derived in Jin (1995). 

The trapping number defined by Eq. 7.103 for an arbitrary dipping angle is consistent with the conventional Buckley-Leverett fractional flow theory. In the Buckley-Leverett fractional flow equation, the gravity term is multiplied by sina (Leverett, 1941). However, Figure 7.34 shows that the trapped residual saturation predicted by Eq. 7.103 is lower than the experimental data at the same trapping number. This figure compares the relationship between the... 

FIGURE 7.34 Comparison of the relationship of trapped residual saturation versus trapping number (with Nc = up/a = 2.82 X 10 not included in the trapping number). 

In summary, neither Eq. 7.103 nor Eq. 7.118, proposed to calculate the trapping number at an arbitrary dip angle, has been validated by the available experimental data. This is not a purely academic issue (L. W. Lake, personal communication on January 19, 2009) and needs to be investigated further. 

The choice of suitable surfactants and additional chemicals for the decontamination of source zones largely depends on the type of pollutant and the structure of the soil (mainly on adsorption behaviour and hydraulic conductivity). Adsorbed and solid pollutants or very viscous liquid phases cannot be mobilised. Preformed microemulsions, co-solvents or co-surfactants can be favourably used for such contaminations in order to enhance the solubilisation capacity of surfactants. NAPL with low viscosity can easily be mobilised and also effectively solubilised by microemulsion-forming surfactant systems. Mobilisation is usually much more efficient. It is achieved by reducing the interfacial tension between NAPL and water. Droplets of organic liquids, which are trapped in the pore bodies, can more easily be transported through the pore necks at lower interfacial tension (see Fig. 10.2). The onset of mobilisation is determined by the trapping number, which is dependent on... 

At Stirring rate n = 0 (stirring absence) according to the plot of Fig. 44 the valne x 0.37 is obtained, that is lower appreciably than this exponent value for d = 3. Equaling the exponents in the Eqs. (87) and (89), let us obtain for the case without sturing d 1.2. This means, that in the indicated case interfacial polycondensation is realized in the space, intermediate between line (d = 1) and plane (d = 2) unlike volume space (d = 3) in case of intensive sturing. It is clear, that in the first case (d 1.2) contacts particle-trap number will be much less, than in the second case that sharply reduces the reaction rate. 

Let us introduce the differential radial density of traps pL,[Pg.295]

We next illustrate three column experiments using Ottawa sand where little or no mobilization occurred because of the relatively high interfacial tension. Mobilization actually depends on the trapping number [41], which is a dimensionless parameter defined as the magnitude of the vector sum of the buoyancy and viscous forces acting on the trapped... 

Trap numbers 1-8 Tekmar trap numbers 9-11 SUPELCO and trap number 12 Alltech. 

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