Hydrodynamic retention

Finally, from the available research into the variety of mechanisms for targetting ophthalmic drugs to specific tissues, means for integrating—both figuratively and literally—combinations of effects are now available [15]. Certainly, the combination of hydrodynamics, retention or sustained release, and diffusional or even active transport can be computed, their influence anticipated, and some specific deficiencies addressed. Nonetheless, many unanticipated interactions may often intrude and still leave the field heavily dependent on empirical assessment. 

Mechanical entrapment occurs when larger polymer molecules cannot pass through smaller pore throats. On the other hand, hydrodynamic retention occurs when the polymer concentration increases at pore entrances, thereby reducing the polymer translational diffusion rate. In severe circumstances when the polymer solution contains microgels, hydrodynamic retention can result in cake formation leading to polymer plugging. 

Polymer retention includes adsorption, mechanical trapping, and hydrodynamic retention. These different mechanisms were discussed by Willhite and Dominguez (1977). Mechanical entrapment and hydrodynamic retention are related and occur only in flow-through porous media. They play no part in free powder/ bulk solution experiments. Retention by mechanical entrapment is viewed as occurring when larger polymer molecules become lodged in narrow flow channels (Willhite and Dominguez, 1977). 

After a steady state is reached in a polymer retention experiment in a core, the total level of retention increases when the fluid flow rate is increased (Chauveteau and Kohler, 1974). This type of rate-dependent retention, called hydrodynamic retention, is not understood as well. Fortunately, it is generally thought to give a small contribution to the total retained material (Sorbie, 1991). 

For the preceding three mechanisms of polymer retention, mechanical entrapment can be avoided by prefiltering or preshearing the polymer or by applying the polymer in a high permeability formation. Hydrodynamic retention is probably not a large contributor in the total retention and can be neglected... 

In most cases, polymer adsorption is considered irreversible that is, it does not decrease as polymer concentration decreases (Szabo, 1979 Lakatos et al., 1979 Gramain and Myard, 1981). The irreversible effect is caused by polymer adsorption on rock. However, this is not exactly true because small amounts of polymer can be removed from porous rock using prolonged exposure to water or brine injection. Usually, however, the rate of release is so small that it is not possible to measure the concentrations accurately. It is thus more accurate to state that the rate of polymer retention is much greater than the rate of polymer removal. Retention also may occur when flow rates are suddenly increased. This process is called hydrodynamic retention, which is reversible (Green and Willhite, 1998). 

The curves are analyzed below on the basis of the effects of the different phenomena possibly governing propagation molecular diffusion and hydrodynamic dispersion, viscous fingering,exclusion chromatography, adsorption and hydrodynamic retention. 

The overall retention of polymers during their propagation through porous media includes both adsorption which is partly reversible as discussed above and a flow-dependent retention, which is usually called hydrodynamic retention and which was found to increase with flow rate and to be reversible if flow rate is decreased (9, 18, 19). However, the presence of microgels could be partly responsible for the hydrodynamic retentions previously observed. 

A more precise description of hydrodynamic retention can be proposed since new results concerning the hydrodynamic behavior of macromolecules in small calibrated membranes in weak deformation regime are available (24). 

It must be noted that such hydrodynamic retention is less likely for semi-rigid polymers like xanthan since their conformation makes more probable their hydrodynamic orientation parallel to the opening axis. 

The hydrodynamic retention previously observed in Berea sandstones (18) was probably induced by the presence of microgels in the xanthan sample used. 

The conditions under which hydrodynamic retention can occur in flow of polymer solutions through porous media have been analyzed, leading to the conclusion that Peclet numbers corresponding to potential retention zones were too low to induce this type of retention. 

In this chapter, all mechanisms that remove polymer from the transported aqueous phase are referred to collectively as retention . A distinction will be made between individual mechanisms—including polymer adsorption, mechanical entrapment and hydrodynamic retention—in the course of this chapter. It is noted that mechanical entrapment is a filtration-like mechanism in which the larger polymer species are thought to be strained out in the smaller pores. Thus, because of the nature of filtration and the resulting pore blocking that must occur, this is not a mechanism that can persist throughout a reservoir formation. In a polymer solution, free from debris (from the... 

In this section, the above polymer retention mechanisms are surveyed. However, polymer adsorption is treated very briefly since it is discussed in much more detail in Sections 5.4 and 5.6 below. A fuller discussion of mechanical entrapment and hydrodynamic retention is given here since these topics are not discussed again after this section. 

Dominguez and Willhite (1977) also noted a flow rate dependence of polymer retention in their floods, but this effect is normally associated with the phenomenon of hydrodynamic retention, which is discussed further in the following section. 

Hydrodynamic retention of polymer is the least well defined and understood retention mechanism. The idea arose from the observation that, after steady state was reached in a polymer retention experiment in a core, the total level of retention changed when the fluid flow rate was adjusted to a new value (Desremaux etai, 1971 Maerker, 1973 Chauveteau and Kohler, 1974 Dominguez and Willhite, 1977). An example of this is shown for a core flood experiment using HPAM from the work of Chauveteau and Kohler (1974) in Figure 5.3. As the flow rate increased from 3m/day to 10.3m/day in this experiment, more polymer was retained from the mobile aqueous phase, as shown by the dip in the polymer effluent concentration. When the flow rate is lowered back to 3 m/day the polymer effluent concentration rises above the input value (400 ppm), denoting a drop in the retained level. This trend of increasing polymer retention with flow rate is consistent with the observations of other workers (Maerker, 1973 Dominguez and Willhite, 1977). For... 

Figure 5.3. The effect of flow rate on the hydrodynamic retention of HPAM (from Chauveteau and Kohler, 1974).

Polymer adsorption at a liquid/solid interface is a very well-established phenomenon and has an enormous associated literature (Lipatov and Sergeeva, 1974 Parfitt and Rochester, 1983). On the evidence from porous medium flow experiments it appears that mechanical entrapment is also a reasonably well-established mechanism for polymer retention in flow through porous media. Hydrodynamic retention is a rate-dependent effect which is rather less well understood. However, this retention mechanism is not a very large contributor to the overall levels of polymer retention in porous media and, although interesting, is probably not a very important effect in field-scale polymer floods. The important point to note is that it must be understood sufficiently well in laboratory floods so that core flood results can be interpreted correctly concerning polymer adsorption and entrapment retention mechanisms. 

Adsorption is a more fundamental property of the polymer-rock surface-solvent system and cannot be avoided in the same way except by trying another polymer. Thus, adsorption is the most important mechanism that should be studied in evaluating a given polymer flood application. Retention via mechanical entrapment should be treated as a screening variable and should be avoided. Hydrodynamic retention is generally small and can be neglected in most practical applications. Because of these views, most of the rest of this chapter will concentrate mainly on adsorption. This approach... 

The general phenomenon of polymer adsorption/retention is discussed in some detail in Chapter 5. In that chapter, the various mechanisms of polymer retention in porous media were reviewed, including surface adsorption, retention/trapping mechanisms and hydrodynamic retention. This section is more concerned with the inclusion of the appropriate mathematical terms in the transport equation and their effects on dynamic displacement effluent profiles, rather than the details of the basic adsorption/retention mechanisms. However, important considerations such as whether the retention is reversible or irreversible, whether the adsorption isotherm is linear or non-linear and whether the process is taken to be at equilibrium or not are of more concern here. These considerations dictate how the transport equations are solved (either analytically or numerically) and how they should be applied to given experimental effluent profile data. 

Retention also may occur when flow rates are suddenly increased after polymer has been injected at a constant rate until a steady-state condition has been attained—i.e., until the effluent coneen-tration has reached the injected concentration. This type of retention, called hydrodynamic retention, is characterized by expulsion of the polymer when the flow rate is reduced suddenly. Thus, it is possible to obtain polymer concentrations in the effluent of linear displacement experiments that are larger than the injected concentration. 39-41 Hydrodynamic retention appears to be reversible because the amount of polymer retained after an increase in flow rate is about the same as the amount of polymer recovered when the rate is reduced. 

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