Mobilization of trapped

The very low interfacial tensions reported for many crude oil-caustic systems should permit substantial reduction of residual oil saturation by the mobilization of trapped oil. We have discussed earlier that crude oil-caustic tension is low initially where reactants meet at a fresh interface but the interfacial tension increases as reaction products diffuse into the bulk phases. The technique of determining micellar aggregate size distributions could be used to study the diffusion of the reaction products into the aqueous phase. 

The conditions required for prevention of trapping are compared with those required for mobilization of trapped blobs of residual nonwetting phase. It is estimated that mobilization of trapped blobs is about five times more difficult to achieve than prevention of trapping. For low interfacial tension systems, buoyancy forces may sometimes have significant influence on the microscopic mechanism of displacement in reservoir rock. 

Mobilization of trapped nonwetting phase Laboratory studies show that trapped residual oil can be recovered if the pressure difference due to viscous flow is sufficient to overcome capillary forces so that trapped blobs, or at least parts of blobs, are mobilized (2-4). If the ratio of viscous to capillary forces is raised sufficiently, almost complete recovery of residual oil can be achieved. For packs of very coarse sand, Leverett (8) reported data which showed indications t)f slightly improved recovery efficiency for capillary numbers (,j.n this case, of the form yv/a( )) as low as 10". In the present work, some of the systems in which trapping was measured were later subjected to high flow rate in an attempt to measure the capillary number required for mobilization of trapped nonwetting phase so that results could be compared with capillary numbers for trapping. 

Comparison of entrapment and mobilization The foregoing result can be used to provide a comparison of the conditions required for prevention of entrapment with those required for mobilization of trapped liquid. Movement of a trapped blob involves drainage at the leading edge of the blob and imbibition at the rear (see Figure 14). For a completely wetted random sphere pack, the pressure drop required for mobilization, AP, is given by the difference between drainage and imbibition displacement pressures (3,12,13). At 70% water saturation, these pressures are 6.7a/R... 

Confined environments can be used to alter the selectivity of a reaction by influencing the orientation of the reactants, altering the mobility of trapped molecules, facilitating one reaction pathway, or selectively stabilizing the products [124]. 

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

Interactions in the stationary phase employing a porous stationary phase or support must also involve the mobile phase trapped in a static form inside the pores. It follows that the diffusivity of the solute in the stationary phase (Ds) will be similar to that in the mobile phase (Dm). Thus, to a first approximation, it can be assumed that Ds = coDm, where (co) is a constant probably close to unity. Thus, equation... 

One could assume that this characteristic behavior of the mobility of the polymers is also reflected by the typical relaxation times r of the driven chains. Indeed, in Fig. 28 we show the relaxation time T2, determined from the condition g2( Z2) = - g/3 in dependence on the field B evidently, while for B < B t2 is nearly constant (or rises very slowly), for B > Be it grows dramatically. This result, as well as the characteristic variation of with B (cf. Figs. 27(a-c)), may be explained, at least phenomenologically, if the motion of a polymer chain through the host matrix is considered as consisting of (i) nearly free drift from one obstacle to another, and (ii) a period of trapping, r, of the molecule at the next obstacle. If the mean distance between obstacles is denoted by ( and the time needed by the chain to travel this distance is /, then - (/ t + /), whereby from Eq. (57) / = /Vq — k T/ DqBN). This gives a somewhat better approximation for the drift velocity... 

Chemical processes work either to change the mobility of a displacing fluid like water, or to reduce the capillary trapping of oil in the rock matrix pores. Reducing the mobility of water, for example by adding polymers, helps to prevent fingering, in which the less viscous water bypasses the oil and... 

Concerning the nature of electronic traps for this class of ladder polymers, we would like to recall the experimental facts. On comparing the results of LPPP to those of poly(para-phenylene vinylene) (PPV) [38] it must be noted that the appearance of the maximum current at 167 K, for heating rates between 0.06 K/s and 0.25 K/s, can be attributed to monomolecular kinetics with non-retrapping traps [26]. In PPV the density of trap states is evaluated on the basis of a multiple trapping model [38], leading to a trap density which is comparable to the density of monomer units and very low mobilities of 10-8 cm2 V-1 s l. These values for PPV have to be compared to trap densities of 0.0002 and 0.00003 traps per monomer unit in the LPPP. As a consequence of the low trap densities, high mobility values of 0.1 cm2 V-1 s-1 for the LPPPs are obtained [39]. 

Figures 12-17 and 12-18 show the temperature dependencies of the mobility in a hopping system with a Gaussian DOS of variance <7=0.065 eV as a function of the relative concentration c of traps of average depth ,=0.25 eV and as a function of the trap depth E, at a fixed concentration < =0.03, respectively. For c=0...

Figure 12-22. The dependence of the mobility on trap concentration. The width of the DOS was 0.065 eV, the...

Figures 12-12 and 12-13 document that trap-free SCL-conduction can, in fact, also be observed in the case of electron transport. Data in Figure 12-12 were obtained for a single layer of polystyrene with a CF -substituted vinylquateiphenyl chain copolymer, sandwiched between an ITO anode and a calcium cathode and given that oxidation and reduction potentials of the material majority curriers can only be electrons. Data analysis in terms of Eq. (12.5) yields an electron mobility of 8xl0 ycm2 V 1 s . The rather low value is due to the dilution of the charge carrying moiety. The obvious reason why in this case no trap-limited SCL conduction is observed is that the ClVquatciphenyl. substituent is not susceptible to chemical oxidation.

Figure 12-17. The icmperalurc dependencies of Ihe mobility simulated lor <7=0.065 eV for different concentrations of traps. The Irap deplh was 0.25 eV and Ihe field 2x10s V cm 1. The dashed line corresponds to the absence of trap (Kef. 72 ).

Eq. (12.14) is recovered. The presence of traps lowers ihe mobility as expected. The essential message of Figures 12-17 and 12-18 is that, to a first order approximation, Eq. (12.14) maintains the icmperalurc dependency of the mobility if one replaces the disorder parameter by an effective disorder parameter ocJj or, equivalently, an effective width of the DOS that depends on both the concentration and the depth of the traps. Deviations from the behavior predicted by Eq. (12.14) become important for ,>0.3 eV, notably at lower temperatures. It is noteworthy, though, that the T- oo intercepts of p(7), if plotted as In p versus 7 2, vary by no more than a factor of 2 upon varying trap depth and concentration. 

The variation of o,.jj with trap depth is presented in Figure 12-19. The effect of traps on the mobility, reflected in an increase of acjj, becomes noticeable only above a certain critical trap depth that depends on concentration. Above that critical value, a2,.), increases approximately linearly with ,. Figure 12-20 shows complementary information concerning the effect of the trap concentration on a,. at constant trap depth. The data reproduces as a family of parallel straight lines on a (Pr/jlo)2 versus In c plot. Their intersection with the ov)jla— 1 tine indicates the critical concentration c, of traps of depth , needed to effect the mobility (see Fig. 12-21). 

The effect of traps on charge carrier motion does not become noticeable until the trap concentration reaches a threshold value. One can define a critical concentration Ci/2 at which the mobility has decreased to one half of the value of the trap-free system. Eq. (12.19) predicts that. ... 

However, although it allowed a correct description of the current-voltage characteristics, this model presents several inconsistencies. The main one concerns the mechanism of trap-free transport. As noted by Wu and Conwell [1191, the MTR model assumes a transport in delocalized levels, which is at variance with the low trap-free mobility found in 6T and DH6T (0.04 cm2 V-1 s l). Next, the estimated concentrations of traps are rather high as compared to the total density of molecules in the materials (see Table 14-4). Finally, recent measurements on single ciystals [15, 80, 81] show that the trap-free mobility of 6T could be at least ten times higher than that given in Table 14-4. 

---