Viscosity ratio correction

Note that the isothermal fully developed friction coefficients in the laminar, turbulent, and transition regions can be obtained easily from h qs. 8-79, 8-80, and 8-81, respectively, by setting the exponent on the viscosity ratio correction to unity (i.e, with m - 0). 

Core flood tests were used to compare polymer flood only and alkaline-polymer performance. To model in situ oil/water viscosity ratio correctly, the operator mixed the crude oil with kerosene at a ratio of 100 26. Single-, double-, and triple-column tests were conducted. In the single-column tests, polymer flood increased sweep efficiency over waterflood by 5.6 to 9.77%, and AP flood increased by 13.7 to 19.3%. On average, AP outperformed polymer flood by 8.8%. In the double- and triple-column tests, AP recovery factors were about 18 to 20% higher than waterflood recovery factors. Half of the incremental recovery came from the low permeability column. 

Much the most usual method of estimating branching is from the intrinsic viscosity ratio g1, defined in Eq. (4.2). In addition to the intrinsic viscosity of the sample, its (viscosity-average) MW must also be known, so that the denominator of the fraction (4.2) can be found. It is usual to use the light scattering technique for this, assuming that Afw = or if any information on the MWD is available, a correction may be applied to M . Recently it has become common to combine GPC measurements with those of viscosity see Subsection 9.2.4. 

If the tube wall is corrected here for the viscosity ratio < ), then ... 

We have already shown visual evidence in Chap. 2 (Fig. 2 15), that this is the correct time scale for the relaxation process. Further quantitative evidence is offered in Fig. 8 3. In this figure is plotted the measured deformation from Fig. 2 15, specified in terms of the dimensionless parameter Df = L — B)/ L + B) where L is the length of the drop and B is its breadth at the equator. It can be seen that when time is scaled with t, the deformation curves for the two different viscosity ratio fluids are reduced approximately to a single curve. 

It is to be remembered that the quantitative results obtained by Bates for the osmotic pressure of 10ns and molecules rest on the assumption that the conductivity-viscosity ratio gives a sensibly correct measure of the ionisation 1 That is, he considers assumptions 2 and 3 as both invalid, and illustrates it by the data already quoted at length in the case of KC1 All the values of m and ttu which have been given rest on the truth of the conductivity method If the conductivity method were shown to be unsound, these values would of course lose their significance It is therefore very necessary—especially in view of G N Lewis s work already alluded to—to examine more closely the conductivity method of determining y The arguments m its favour are cited bnefly by Bates as follows —... 

Preliminary estimates of the coefficients are obtained from Eq. (12.32) omitting the correction for viscosity ratio ... 

Diabatic friction factors are obtained in the usual manner by applying a viscosity- or temperature-ratio correction. For heating of water at bulk temperatures below 200°F (93.3°C), the following correction to Eq. 11.20 has been suggested [195] ... 

Conkie and Savic (C5) proposed a correction factor for the presence of a boundary layer by introducing a velocity factor K defined as the ratio of the true interfacial velocity and potential-theory velocity, and dependent on the Reynolds number and viscosity ratio (Fig. 9). In their view, the boundary... 

Equation (Il.b.l) has been applied to systems at concentrations up to 2N, Reid and Sherwood, 1966 (45). In many cases the product (PgVg) is close to unity, as is the viscosity ratio (Ur/uab) so that equation (Il.b.l) provides an activity correction to the diffusion coefficient at infinite dilution, hence... 

Another method to avoid complex calculations is to use an effective viscosity to be used in the Newtonian equation in order to predict output for a non-Newtonian fluid. This method was proposed by Booy [132]. A drawback of this method is that it only corrects the pressure how term. As a result, the method does not work at small pressure gradients. The effective viscosity ratio has to be obtained from a graph. The ratio can be approximated by taking the effective viscosity ratio equal to the power law index. However, the latter approximation will be considerably less accurate than Eq. 7.291. 

If the polymer application is for viscosity control, then the simple model may be a 2-D areal or simple layered five-spot pattern the well locations will be known, and any faults that are known should be included using transmissibility modifiers. In this areal system, the key features in the calculation are that the oil viscosity is correct and reasonable estimates of the reservoir relative permeabilities are available. For a heterogeneity control flood, a multilayer cross-section similar to the eight-layer system described in Chapter 8 may be selected. Here, the most important factor is to get the layering structure and layer permeabilities correct, especially the permeability contrast between the high-permeability layer(s) and the position of this layer. The value of the kjk ratio may also be very important in this type of polymer flood, but it may be sufficient to know that it is > 0.05 for example (see Chapter 8). In such an application, the mobility ratio may be close to... 

Eqs. 179 and 180 indicate that the shear rate at the die wall has a correction due to the non-Newtonian character of the viscosity. This correction on the shear rate is called the Weissenberg-Rabinowitch correction. The shear stress itself may also need to be corrected so as to account for pressure losses due to elastic effects at the die entrance and exit. This correction is known as the Bagley correction. The Bagley correction can be obtained by repeating the pressure drop measurements with different aspect ratio (L/R) dies. The pressure drop vs. L/R plot which results is called a Bagley plot the intercept on the negative L/R axis represents the additional length of fictitious capillary which corresponds to the extra losses. 

The conclusion of the nylon 6/SPS fiber work was that, to obtain correct particle sizing, the viscosity ratio (SPS/PA6) at low shear rates (<100-500/s) should be greater than or equal to 10. Levels of the SPS above -7% showed... 

The specific resistance coefficient for the dust layer Ko was originally denned by Williams et al. [Heat. Piping Air Cond., 12, 259 (1940)], who proposed estimating values of the coefficient by use of the Kozeny-Carman equation [Carman, Trans. Inst. Chem. Fng. (London), 15, 150 (1937)]. In practice, K and Ko are measured directly in filtration experiments. The K and Ko values can be corrected for temperature by multiplying by the ratio of the gas viscosity at the desired condition to the gas viscosity at the original experimental conditions. Values of Ko determined for certain dfists by Williams et al. (op. cit.) are presented in Table 17-5. 

Viscosities of the blends and composites were measured in shear flow with a Gottfert Rheograph 2002 capillary viscosimeter. The shear rate was investigated from 100-10000 s" . The L D ratio of the capillary die was 30 mm 1 mm. Rabinowitch correction was made to the measurements, but Bagley correction was not applied. 

In practice, K and K2 are measured directly in filtration experiments. These values can be corrected for temperature by multiplying by the ratio of the gas viscosity at the desired condition to the gas viscosity at the original experimental condition. 

Table 8. Details of different labelled 12-arm PIP stars (samples 1,2,4 arms of symmetnc diblock of protonated and deuterated PI, respectively)(1) bam = 10 24 cm2 (2) evaluated on the basis of the structural model<3) corrected for the ratio of the viscosities of octane and toluene...

The removal of free silanol groups is important for correct calculation of the ratio of the two monomers in the subsequent coequilibration-step. This step is required in order to generate a copolymer of appropriate viscosity and to separate the functional groups in. the polysiloxane by at least five dialkylsiloxy units. The reason for this necessity is discussed below. 

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