Strain constrictive

Soo and Radke (11) confirmed that the transient permeability reduction observed by McAuliffe (9) mainly arises from the retention of drops in pores, which they termed as straining capture of the oil droplets. They also observed that droplets smaller than pore throats were captured in crevices or pockets and sometimes on the surface of the porous medium. They concluded, on the basis of their experiments in sand packs and visual glass micromodel observations, that stable OAV emulsions do not flow in the porous medium as a continuum viscous liquid, nor do they flow by squeezing through pore constrictions, but rather by the capture of the oil droplets with subsequent permeability reduction. They used deep-bed filtration principles (i2, 13) to model this phenomenon, which is discussed in detail later in this chapter. 

Straining capture refers to the condition that results when a particle lodges in a pore throat of size smaller than its own. The rate of capture is directly proportional to the velocity. Re-entrainment of strained droplets occurs either by squeezing of droplets through pore constrictions due to locally high pressures or by breakup of the oil droplets. 

Filtration Model. A model based on deep-bed filtration principles was proposed by Soo and Radke (12), who suggested that the emulsion droplets are not only retarded, but they are also captured in the pore constrictions. These droplets are captured in the porous medium by two types of capture mechanisms straining and interception. These were discussed earlier and are shown schematically in Figure 22. Straining capture occurs when an emulsion droplet gets trapped in a pore constriction of size smaller than its own diameter. Emulsion droplets can also attach themselves onto the rock surface and pore walls due to van der Waals, electrical, gravitational, and hydrodynamic forces. This mode of capture is denoted as interception. Capture of emulsion droplets reduces the effective pore diameter, diverts flow to the larger pores, and thereby effectively reduces permeability. 

Waxman There is a nagging issue of the apparently different results from different laboratories. One does an experiment as simple as cutting the sciatic nerve and looking for neuropathic hyperexcitability, but the results are very different from different laboratories. It is often because of different strains of rats or mice and different operators a chronic constriction injury in one lab may involve a tighter suture than in another laboratory, or there may be polymorphisms that hold some clues for us. It is important for us as investigators to look at the disparities and see whether we can even use them as tools. 

As regards deformation, let all lines in the material that are initially straight and parallel to x remain so, and let them approach each other by a small cylindrically symmetrical constriction, elongating along x. Let strain rates be designated e x, etc. then = a fixed value Cq, uniform... 

If two polymorphs are strongly bonded at a planar interface and subjected to a constriction stress field about the interface s normal as the constriction axis, for the strain to be uniform the compressive stress profile must be exponential. Within a few nanometers of the interface, stress gradients and diffusion of material become noticeable. Equation (12.6) applies and Figure 13.3 illustrates the results. 

For plane strain, if the two polymorphs deformed without diffusion, would need to equal -I- tr x)/2 but if self-diffusion occurs, this stress condition no longer leads to plane strain. Where cylindrical constriction requires a simple exponential profile of compressive stress, plane-strain deformation at an interface requires a more complicated curve. 

The preceding statements describe behavior in a condition of cylindrical symmetry about one direction (x), uniformity in all planes normal to x, and no strain along all lines normal to x. In a condition of uniform constriction (strain rate = an arbitrary rate eo along all lines normal to x), any variation in viscosity due to variation in composition will give rise to a fifth effect as in eqn. (15.6). 

If two materials meeting at an interface are subjected simultaneously to change of temperature and to a constrictive strain, can these influences be adjusted in such a way that no change of phase occurs ... 

Specifically, let phase g be the higher viscosity, lower-volume phase. Then, starting from an equilibrium condition, raising the overall pressure on the system will tend to make h convert to g. On the other hand, imposing a uniform constrictive strain rate will tend to make g convert to h, as in Chapter 13. If the two tendencies balance each other, an interesting condition will exist it is this condition that we wish to explore. 

If two phases with viscosities and Nf, are constricted at the same radial strain rate Cq, the driving stress differences in the two phases are 6eoAg and 6e()Nf. If the stress states have a common stress the two magnitudes of will differ by 6eo(Ng — Nf,). If is, for example, Ag/lO, the order of... 

The simplest applications of eqn. (12.7) are to situations with cylindrical symmetry. Let be the direction of the symmetry axis and let the situation be uniform in all respects in transverse directions x, and x then d a/dxf = d a/dx = 0. Also, if is taken to lie in the mn plane, then 2 Ues in the In plane and d a/dal = 0. There remain just two contributions to the transverse strain rate e , a contribution from constrictive change of shape and a contribution from self-dilfusion along the axis. 

Two examples follow. First, let the transverse compression vary harmonically along m then the constrictive strain rate also varies harmonically. Where is a maximum, d a Jdx is also a maximum and the two contributions to reinforce each other both vary harmonically and are in phase. Second, let the sample consist of two polymorphs of different viscosities as in Chapter 13 then a uniform constrictive strain rate leads to nonuniform transverse compression. Profiles of are exponential in such a way that where (t is less than its remote value, d a Jdx is greater than its remote value. The two contributions to e vary antipathetically and can add up to a constant sum at all points along the cylindroid axis x. ... 

In the elastic range, the Poisson s ratio, Vei = —/, can be used to relate the amplitude of transverse constriction with axial strain. The volume strain depends on this material coefficient by = (1 — 2vei)e - Similarly, for nonlinear materials, the tangent Poisson s ratio Vt = —d i/d 3 may be introduced at large strain, so that coefficient is also obtained from the instantaneous slope of the volume strain versus axial strain from (1 — 2vt ) = d v/d 3. In this paper, the latter slope will be called dilatation rate (or damage rate ) and denoted by the variable A. 

A mechanical analogue of this model is obtained by series combinations of a spring and a dashpot (a vessel whose outlet contains a flow constriction over which the pressure drop is proportional to flow rate), as shown schematically in Figure 1.19. If the individual strain rates of the spring and the dashpot respectively are yi and y2, then the total strain rate y is given by the sum of these two components ... 

Straining. This is the simplest of the collection mechanisms and occurs when the particle diameter is larger th the constriction through vdiich the fluid flow streamlines pass. The grain size plays an in ortant role in this mechanism as narrower passages are found with smaller grained collection media. 

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