Polymer fluids, data from

Table 5.3 summarizes some polymer retention data from displacement experiments for partially hydrolyzed polyacrylamides. Retention varies from 35 to about 1,000 Ibm/acre-ft over a wide range of fluid and rock properties. Information on converting retention values from pounds per acre-foot to micrograms per gram of rock is given as a footnote in Table 5.3. Several trends are present in the limited amount of retention data in the literature. Fig. 5.22 shows the variation of polymer retention with brine permeability at ROS. The retention at low permeabilities is large and is probably a result of excessive mechanical entrapment of polymer molecules in small pores. Another possible explanation is high clay content. Polymer concentration appears to have little effect on retention for the data shown in Fig. 5.22. The weak concentration dependence in Fig. 5.22 is reinforced by data from Shah for the retention of partially hydrolyzed polyacrylamide on Berea core material shown in Fig. 5.23. Retention at 50 ppm polymer concentration is 77% of the retention at 1,070 ppm.

FIGURE 7.12 Schematic of the dual-layer spinneret and its flow channels for bore fluid as well as polymer solutions. (Data from D.F. Li, T.S. Chung, R. Wang, and Y. Liu, J. Memb. ScL, 198, 211-223, 2002.)... 

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

All the data from testing to these categories can be used to compare fluids and/or polymers and to... 

Fig. 6. Determination of the critical protein concentration. (A) Plot of protein in the supernatant fluid after quantitatively sedimenting polymer from a polymerized solution of tubules and tubulin at steady state. The critical concentration, Ko, is determined from the value of the y axis intercept, and the fraction of active protein, y, from the slope. (B) The conventionally used experimental method for estimating the critical concentration. Note that the x axis intercept is actually Ko/y, instead of Kj,. Interpretation of the slope from such plots requires knowledge of the ratio of polymer weight concentradon to turbidity (given here as a). Data from experiments such as those in A may be used in conjunction with this plot to obtain the cridcal concentration, and this can serve as an internal test for self-consistency of the data.

Figure 12. The fragility parameter as a function of the inverse number 1 /M of united atom groups in single chains for constant pressure (P = 1 atm 0.101325 MPa) F-F and F-S polymer fluids. For a given M, the parameter is determined as the slope of ScT/( isl/k ) versus hT = T — Tq)/Tq over the temperature range between Tg and Tj. A single data point denoted by refers to high molar mass F-S polymer fluid at a pressure of P = 240 atm (24.3 MPa). (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005 American Chemical Society.)...

Equations of state derived from statisticai thermodynamics arise from proper con-figurationai partition functions formuiated in the spirit of moiecuiar modeis. A comprehensive review of equations of state, inciuding the historicai aspects, is provided in Chapter 6. Therefore, we touch briefly in oniy a few points. Lennard-Jones and Devonshire [1937] developed the cell model of simple liquids, Prigogine et al. [1957] generalized it to polymer fluids, and Simha and Somcynsky [1969] modified Pri-gogine s cell model, allowing for more disorder in the system by lattice imperfections or holes. Their equations of state have been compared successfully with PVT data on polymers [Rodgers, 1993]. 

Correlation Between Steady-Shear and Oscillatory Data. The viscosity function is by far the most widely used and the easiest viscometric function determined experimentally. For dilute polymer solutions dynamic measurements are often preferred over steady-shear normal stress measurements for the determination of fluid elasticity at low deformation rates. The relationship between viscous and elastic properties of polymer liquids is of great interest to polymer rheologists. In recent years, several models have been proposed to predict fluid elasticity from shear viscosity data. 

The uniaxial extensiometers described so far are suitable for use with viscous materials only. They cannot, for example, be used to measure the steady extensional viscosity of such commercially important polymers as nylons and polyesters used in the textile industry, and which may have shear viscosities as low as 100 Pa sec at processing temperatures. As a consequence, other techniques are needed but these invariably involve nonuniform stretching. Here one cannot require that the stress or the stretch rate be constant. Also, the material is usually not in a virgin (stress-free) state to begin with. One can therefore not obtain the extensional viscosity directly from these measurements. Nonetheless, data from properly designed non-uniform stretching experiments can be profitably analyzed with the help of rheological constitutive equations. In addition, such data provide a simple measure of resistance that polymeric fluids offer to extensional deformation. 

Inelastic neutron scattering is used for the smdy of transmission or absorption neutron energy spectra, particularly the side-group motion in polymers. All data reported so far for polymers have been concerned with symmetric top molecules. Three spectrometries are available at present (1) slow neutron spectrometry, which studies slow neutron excitation functions with continuous-energy neutron sources (2) fast neutron spectrometry, which smdies the spectra of neutrons produced in nuclear reaction and (3) monoenergetic slow neutron spectrometry, which smdies the spectra of neutrons corresponding to the inelastic scattering from atoms in solids or fluids. 

For Newtonian fluids, flie pressure measured at the bottom of the pressure hole Pm is the same as the true pressure p at the wall. For a viscoelastic fluid, on the other hand, the pressure (p + T22)m measured at the bottom of the pressure hole is always lower than the true pressure (p-t-T22) at the wall, no matter how small the hole is. This pressure difference arises because the elastic forces tend to pull the fluid away from the hole and results in the pressure hole error Ph = (p + T22)m (p + 22)- This effect is illustrated in Figure 2.13. The possible sources of error in tiie measurement have been considered by Higashitani and Lodge [73] along with a review of published data. The effect of Ph has been well substantiated for polymer solutions but the same is not the case for polymer melts with or without fillers. 

FIG. 17-4. Plot of log flc against volume fraction of polymer, for data of Fig. 17-3 in the transition zone. Curve drawn from equation 13 with parameters as shown. Reproduced, by permission, from Molecular Fluids, edited by R. Balian and G. Weill, Gordon and Breach, London, copyright 1976. 

The correlations represented by Eqs. 5.26a through 5.26e can be extended to interpolate for polymer concentrations between 1,000 and 2,000 ppm by use of a correlation based on the modified Blake-Kozeny model for the flow of non-Newtonian fluids. 62 Eq. 5.27 is an expression for A bk derived from the Blake-Kozeny model. Note that all parameters are either properties of the porous medium or rheological measurements. Eq. 5.27 underestimates A/ by about 50%. However, Hejri et al. 6 were able to correlate pBK and A for the unconsolidated sandpack data with Eq. 5.28. Eqs. 5.27 and 5.28, along with Eq. 5.24, predict polymer mobility for polymer concentrations ranging from l.,000 to 2,000 ppm within about 7%. 

This unusual effect is a property of only a few select water-soluble polymers, among which are the extensive family of acrylamide polymers and copofymers. The exact flow mechanism which causes this resistance factor has not been established but it does appear to be a complex combination of several factors. Although polymer solutions are generally highly non-Newtonian, this is not the only factor. The resistance factor is substantially constant over normal field fluid advance rates as shown in Fig. 2, which also shows the slope line and range of the viscosity-shear rate data from 4.8 to 960 sec determined with a Fann viscometer. Since the shear... 

Fluid entry profiling, pressure transient work, and polymer quality laboratory results were consistent. The data from each of these measurements individually and in combination with each other added to the interpretation of the processes active. The fact that similar conclusions as to polymer... 

Fractional flow curves presented in Figure 3 were derived from relative permeability experiments and represent both waterflood and polymer flood data. Apparent fluid viscosity for the polymer flood curve is 22.0 cp as calculated using 750 ppm of American Cyanamid Cyanatrol 970. These curves show that the increased viscosity of the polymer solution displaces the fractional flow curve to higher water saturations at a given fractional flow of oil, illustrating the potential for additional oil recovery. Using a laboratory measured adsorption value of 0.058 lbs. polymer/bbl pore volume and a S. of 0.54 (water-oil ratio of 25) for the polymer curve, the fractional flow predictive method was used to calculate that an incremental 3.83 MBO (10.1% OOIP) could be recovered within the polymer flood area. 

---