Polymer flooding velocity

In the case of polymer flooding with a sharpening front, polymer concentration jumps from zero (its initial value) to its injection concentration Ciq. D, in Eq. 2.88 becomes Dp. In this case, the high polymer concentration solution flushes the initial zero polymer concentration solution. As discussed in Section 2.5 on types of fronts, there is a concentration shock. Corresponding to this concentration shock, there is a saturation shock from S p to Swi. The specific velocity of this saturation shock, (vd )as > is... 

To include the velocity change in polymer flooding, we have to consider the velocity-dependent viscosity in the Darcy equation 5.45. For the power-law viscosity model, the polymer viscosity is defined by Eq. 5.3, and the shear rate is defined by Eq. 5.23. Then Eq. 5.45 becomes... 

In these cases, the oil viscosity is reduced by 25 times to such a low value as 0.2 mPa s. We suspect that the velocity effect could be the dominant effect. Even if the velocity effect is important, it certainly can be reduced or eliminated when polymer is added in the surfactant slug in surfactant-polymer flooding. 

From fractional flow analysis (taking polymer flooding as an example in Fignre 9.7), the displacement front velocity is... 

FIGURE 9.7 Schematic of frontal displacement velocities in polymer flooding at different initial oil saturations. 

The product f-F is usually referred to in chromatography of column flow as the retardation factor, Fr (Giddings, 1965). In a polymer flood, there are therefore two competing effects on the retardation factor adsorption, tending to make Fr> 1, and velocity enhancement, which tends to make Fr< 1. Note that if Fr = 1, then it is probable that there are no adsorption or excluded-volume effects however, it could be that they fortuitously cancel. 

This modified water mobility provides the link between the pressure equation, from which the flows are calculated (i.e. velocities, and UJ, and the polymer transport equation (Equation 8.13). It is this feedback that is the important feature of polymer flooding the presence of polymer changes the flows which in turn results in the polymer being transported into different regions of the reservoir compared with the transport of an inert tracer which has no feedback effect on the water mobility. 

Two flood fronts form in this case because S i>S f. The saturation profile is similar to Fig. 3.34 and is characterize by a flood front with saturation S f, an oil bank where the water saturation is constant, and a polymer flood front with saturation 5 3. Table 5.20 presents saturations and fractional flows corresponding to each saturation. Velocities of the three distinct banks calculated from Eqs. 3.142 and 3.143 are also included. Oil recovery during a continuous polymer flood is computed by tracking the three regions as they are displaced through the linear system and then making a material balance as described in Sec. 3.2.7,... 

The drive water is moving faster than the saturations in die polymer bank and gradually overtakes the polymer bank. The drive water arrives at the end of the linear system at the same time as the polymer flood front, x. Fig. 5.59 shows the path traced by the rear of the polymer bank. The location of the rear of the polymer slug is almost a linear function of time for this example. Thus, for this case, the rear of the polymer slug appears to travel at a constant velocity. Fig, 5.59 also shows the waterflood front, oil bank, polymer flood front, and paths of selected saturations in the polymer slug. Saturations in the drive-water region are discussed later. 

A 36- X Ij -in. cylindrical tube was packed with 6,000-md Nevada sand, saturated with brine and driven to connate water saturation of 16.8 percent by 34 cp oil. Subsequent brine injection resulted in the (normal waterflood) oil recovery curve shown in Fig. 15. Two polymer floods were then performed on the same system, in both cases starting with the initial connate water saturation. The floods were run with a superficial velocity of about 1/8 ft/D. Fig. 15 shows the oil recovery curves obtained from these two polymer floods. Prior to the first polymer flood, polymer had not contacted the sand so that adsorption can be presumed active during the flood. The second flood was performed using the same sand pack so that adsorption was minimal or absent. The slightly higher recovery in flood No. 2 probably reflects this lesser adsorption. 

Conduct core flood tests with the polymer solution at different injection rates. Measure the pressure drop, Ap, corresponding to each injection rate (velocity u). The core permeability and porosity are measured before the core flood tests. 

All symbols have their usual meaning and only more important ones are defined here. Cj is the concentration of component j in the aqueous phase (e.g. polymer, tracer, etc.). The viscosity of the aqueous phase, rj, may depend on polymer or ionic concentrations, temperature, etc. Dj is the dispersion of component j in the aqueous phase Rj and qj are the source/sink terms for component j through chemical reaction and injection/production respectively. Polymer adsorption, as described by the Vj term in Equation 8.34, may feed back onto the mobility term in Equation 8.37 through permeability reduction as discussed above. In addition to the polymer/tracer transport equation above, a pressure equation must be solved (Bondor etai, 1972 Vela etai, 1974 Naiki, 1979 Scott etal, 1987), in order to find the velocity fields for each of the phases present, i.e. aqueous, oleic and micellar (if there is a surfactant present). This pressure equation will be rather more complex than that described earlier in this chapter (Equation 8.12). However, the overall idea is very similar except that when compressibility is included the pressure equation becomes parabolic rather than elliptic (as it is in Equation 8.12). This is discussed in detail elsewhere (Aziz and Settari, 1979 Peaceman, 1977). Various forms of the pressure equation for polymer and more general chemical flood simulators are presented in a number of references (Zeito, 1968 Bondor etal, 1972 Vela etal, 1974 Todd and Chase, 1979 Scott etal, 1987). 

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