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The viscosity of silica nanoparticle dispersions in permeable media

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  • 1. The Viscosity of Silica Nanoparticle Dispersions in Permeable Media Cigdem Metin, Roger T. Bonnecaze, and Quoc P. Nguyen, University of Texas at Austin Summary The potential application of nanoparticle dispersions as forma- tion-stimulation agents, contrast agents, or simply as tracers in the upstream oil and gas industry requires knowledge of the flow properties of these nanoparticles. The modeling of nanoparticle transport in hydrocarbon reservoirs requires a comprehensive understanding of the rheological behavior of these nanofluids. Silica nanoparticles have been commonly used because of their low-cost fabrication and cost-effective surface modification. The aqueous silica-nanoparticle dispersions show Newtonian behavior under steady shear measurements controlled by a rheometer, as discussed by Metin et al. (2011b). The viscosity of nanoparticle dispersions depends strongly on the particle concentration, and that this correlation can be depicted by a unified rheological model (Metin et al. 2011b). In addition, during flow in permeable media, the variation of shear associated with complex pore mor- phology and the interactions between the nanoparticles and tortuous flow channels can affect the viscosity of nanoparticle dis- persion. The latter is particularly important if the concentration of nanoparticles in dispersion may change because of nanoparticle adsorption on mineral/fluid and oil/water interfaces or by mechan- ical trapping of nanoparticles. In this paper, the flow of silica- nanoparticle dispersions through different permeable media is investigated. The rheological behaviors of the dispersions are compared with those determined by use of a rheometer. We estab- lished a correlation between the nanoparticle concentration and dispersion viscosity in porous media for various nanoparticle sizes. The effects of pore structure and shear rate are also studied. We have confirmed that the concept of effective maximum pack- ing fraction can be applied to describe the viscosity of aqueous nanoparticle dispersions in both bulk flow and flow in porous media with high permeability and regular pore structures, but not at low permeability because of mechanical trapping. Our work provides new insight to engineering nanoparticle rheology for subsurface applications. Introduction The transport of colloids in porous media is a well-established research area. Extensive work has been performed to model col- loidal transport in subsurface environments with applications in groundwater contamination and treatment (Biggs et al. 2003; Sen et al. 2004). Zhang et al. (2011) provided an overview of the recent developments in the application of nanotechnology for res- ervoir engineering and improved oil recovery (IOR). The authors categorized the use of nanoparticles in IOR and reservoir engi- neering into nanoparticle stabilized foams/emulsions as mobility- and conformance-control agents; nanoparticle dispersions as carriers for chemicals and sensors into reservoirs; and image- enhancing agents for improved formation evaluation. As an exam- ple for these applications, paramagnetic nanoparticles could eval- uate fluid saturations by the use of magnetic fields and the measurement of the response when delivered to the target forma- tion. Nanoparticle-stabilized shear-thinning emulsions/foams could be used as drilling and stimulation fluids to block pore entry and prevent formation damage. LeCoanet et al. (2004) studied the mobility of nanomaterials such as silica, fullerol, clusters of fullerene or C60, and single- wall carbon nanotubes in porous media composed of spherical glass beads. They measured the concentration of nanomaterials in the effluent by use of an ultraviolet/visible spectrophotometer. They found that these nanomaterials could travel 10 to 14 m in a sandy aquifer where the velocity of ground water is approximately 9 m/d. Hydrodynamic conditions have an important effect on col- loid retention at the air/water interface in a microchannel, and the Derjaguin and Landau, Verwey and Overbeek (DLVO) theory is inadequate to describe the experimental results (Lazouskaya et al. 2006). Non-DLVO interactions such as hydration, steric, and hydrodynamic potentials must be included to better understand the colloid-air/water interface interactions (Lazouskaya and Jin 2008). Rodriguez et al. (2009) studied the migration of surface- modified nanoparticles in sedimentary rocks. The authors ob- served that polyethylene glycol-modified silica nanoparticles could be transported through sedimentary rocks. The retention mechanism for these nanoparticles was identified as reversible adsorption on the pore wall because of adsorption by van der Waals attraction between particles and minerals on the pore walls and desorption governed by Brownian diffusion of nanoparticles. The authors argued that the apparent viscosity measured during the flow of nanoparticle dispersions was smaller than that meas- ured at the rheometer because of a possible slippage at the pore walls. Caldelas et al. (2011) furthered the study of Rodriguez et al. (2009) to investigate the factors governing the propagation of nanoparticles in porous media. They confirmed the findings of Rodriguez et al. (2009) on the retention mechanism and showed that the nanoparticles could travel several meters in porous media. Ju et al. (2006) proposed a mathematical model for the migration and adsorption of hydrophilic nanoparticles through porous media in the presence of oil. They evaluated the change in porosity, abso- lute permeability, and relative permeability after coreflooding with hydrophilic nanoparticles. Oil recovery increased by 9.3% when 2 vol% hydrophilic nanoparticles were added to water. The numerical results showed that nanoparticles were retained in the pores (adsorbed on the pore walls) and the absolute permeability and po- rosity decreased. Relative permeability to oil increased, whereas rel- ative permeability to water decreased after injecting nanoparticles. Gu et al. (2007) investigated the flow of hydrophobic nanoparticles through porous media and proposed a slip velocity model for capil- lary flow and a slip boundary condition. The authors experimentally observed that hydrophobic nanoparticles could adsorb on porous walls, which changed the contact angle from preferentially water- wet to preferentially oil-wet. The coreflood experiments showed that effective permeability of water increased by 47% after hydro- phobic nanoparticle suspensions were injected. Sun et al. (2006) reported that the motion of nanoparticles in the laminar flow was mainly Brownian, and that the deposition of nanoparticles was inde- pendent of flow velocity. In this sense, smaller particles deposited more easily on the wall surface than larger ones. However, most previous studies of nanoparticle mobility in porous media have not taken into account the correlation between nanoparticle retention and the rheological behavior of nanopar- ticle dispersions. The latter is rarely found in the literature. In this work, the rheology of silica-nanoparticle dispersions is studied systematically, beginning with a high-permeability pack of spher- ical glass beads and followed by the effect of pore structure with Copyright VC 2013 Society of Petroleum Engineers This paper (SPE 157056) was accepted for presentation at the SPE International Oilfield Nanotechnology Conference and Exhibition, Noordwijk, the Netherlands, 12–14 June 2012, and revised for publication. Original manuscript received for review 24 October 2012. Revised manuscript received for review 17 February 2013. Paper peer approved 3 June 2013. August 2013 SPE Reservoir Evaluation & Engineering 327
  • 2. high-permeability sandpacks. The effect of pore morphology and permeability is then further investigated with sandstone and lime- stone cores. The viscosity of nanoparticle dispersions in these media is compared with that determined from bulk rheology measurements (Metin et al. 2011b). This comparison is to validate the application of our new rheological model for nanoparticle-dis- persion flow in porous media. This study brings new insight to the understanding of the transport mechanism of nanoparticles in sub- surface systems. Materials and Methods The material under study is an aqueous dispersion of silica nano- particles. The mean diameters of the primary particles are 5 and 25 nm; they have unmodified surfaces. The particles are monodis- persed in aqueous solution. The shape of silica nanoparticles is spherical, as determined by images of a scanning transmission electron microscope. The silica nanoparticles are electrostatically stabilized in an aqueous medium with a zeta potential of approxi- mately À45 mV at pH ¼ 9. Stock solutions containing 16 to 41 wt% silica nanoparticles were diluted with deionized (DI) water up to a desired silica concentration. In the absence of electrolytes, the silica nanoparticles were well dispersed and did not aggregate as determined by size measurements. The materials used to prepare the unconsolidated permeable media were glass beads of 100- to 140-mesh size (0.10 to 0.15 mm), purchased from Potters Industry Incorporated. The sand used was Ottowa quartz sand of size 100 to 140 mesh (0.10 to 0.15 mm). Berea sandstone and limestone were the consolidated permeable media studied in this work. The glass beads and sand were cleaned with distilled water, dried in an oven set at 100 C for a couple of days, and sieved by use of several meshes stacked on top of each other (ranging from 40 to 170) for 20 minutes under the agitation of a Ro-Tap sieve shaker. The grains collected at 100 to 140 mesh were used to pack the glass. A flow adapter and glass column of 2.5-cm diameter and 30-cm length were pur- chased from Kimble Chase for the preparation of both the glass- bead packs and sandpacks. Glass columns 4.8 cm in diameter by Kimble Chase were used to store the fluid that was to be injected. An Isco pump delivered mineral oil to the glass column displacing the injected fluid to the permeable media. The pressure drop across the permeable media was measured with differential-pres- sure transducers connected in parallel to the inlet and outlet. Low (0- to 1-psid) and midrange (0- to 10-psid) transducers were pur- chased from Cole-Parmer and Rosemount Incorporated, respec- tively. A bleeding line was connected to the pressure transducer to displace any air bubbles trapped in the tubes before each experiment started. The effluent was collected in a fraction collec- tor in 15-cm3 plastic centrifuge tubes. A schematic of the flow loop is presented in Fig. 1. An epoxy-coated core was also used to study the flow of nanoparticles in permeable media. Cores of 2.5- cm diameter and 15-cm length were drilled from large blocks of clean sandstone and limestone and then dried in an oven set at 100 C for a couple of days. The dried cores were then coated with epoxy in a 1.5-in.-diameter polycarbonate tubing, and the epoxy was cured for 24 hours. The glass-bead pack, sandpack, and epoxy-coated cores were put under vacuum and saturated with DI water. The pore volume (PV) was calculated from the difference in weight of saturated and dry glass-bead pack or sandpack or core. The saturated porous medium was then connected to the flow loop, and a tracer test of 0.05 wt% NaCl was conducted. The concentration of NaCl in the effluent was analyzed by a conductivity probe. The normalized effluent concentration (Cnorm) in Eq. 1 is presented as a function of injected PVs, Cnorm ¼ C À Cres Cinj À Cres ; ð1Þ where C is the concentration of the tracer or nanoparticle in the effluent, Cres is the concentration in the resident fluid, and Cinj is the concentration in the injected fluid. From the concentration of NaCl in the effluent, the PV was calculated and compared with that determined on the basis of the mass-balance method. The permeability k was determined by use of Darcy’s law. Then, 20 PV of DI water was injected to clean the tracer from the permeable media. Once the conductivity of the effluent reached that of the DI water, injection of nanoparticle dis- persion was started. The concentration of the nanoparticles in the effluent was determined by use of a calibration curve built by an ultraviolet/visible spectrophotometer. The data from pressure transducers was collected with LabVIEW. (Note that this proce- dure was not applied for the Berea core because the injection of low-salinity water causes swelling of clay, as further discussed later in this paper.) The permeability of the sandstone core was determined by use of air. . . . . . . . . . . . . . . . . . . . . . . . . . Mineral Oil Pump Accumulator Sand Pack Fraction Collector Bleeding column Pressure Transducer Mineral Oil Pump Accumulator Sand Pack Fraction Collector Bleeding column Pressure Transducer Fig. 1—A schematic of the experimental setup for the determination of nanoparticle viscosity in porous media. 328 August 2013 SPE Reservoir Evaluation Engineering
  • 3. Darcy’s law was also used to determine the viscosity of nano- particle dispersion over a wide range of flow rates. The flow rates were set on the pump to 150 cm3 /hr  50% and 100% and 400 cm3 /hr  50%, 70%, and 90%. However, the actual flow rates were determined by use of a graduated glass test tube at the frac- tion collector and measuring the time required to fill 4 cm3 of liq- uid. The use of different flow rates is to verify if all the nanoparticle dispersions exhibit Newtonian behavior. Results and Discussion Table 1 shows the measured porosity and brine permeability of the unconsolidated (glass-bead pack and sandpack) and consoli- dated (sandstone and limestone cores) media. The mass-balance- based and tracer methods gave almost the same porosity value for all the media. The grain size of the glass beads and the sand was similar (100 to 140 mesh); therefore, it is not surprising that the permeability of the sandpack was also found to be approximately 7 darcies, with a porosity of 43%. For the limestone core, the perme- ability was calculated to be 54 md with a porosity of 25%. The sandstone had an air permeability of 500 md. However, this value decreased to 12.1 md during the tracer test because the concentra- tion of NaCl in the injected liquid was much lower than the critical concentration required to inhibit clay swelling (Civan 2007). The dimensions of the porous media studied are also given in Table 1. Flow of Nanoparticle Dispersions in Unconsolidated Porous Media. Fig. 2 shows the respective effluent concentration pro- files for the tracer and the 1 wt% 5-nm unmodified-nanoparticle dispersion in the glass-bead pack. It appears from the shape of the normalized concentration profile in Fig. 2 that the dispersivity of the pack is small. The two profiles collapse on the same trend, indicating insignificant retention of nanoparticles in the glass- bead pack. This result is consistent with our recent findings of the interaction of unmodified and surface-modified silica nanopar- ticles with mineral surfaces (Metin et al. 2012). On the basis of batch adsorption experiments with the silica nanoparticles onto quartz and calcite surfaces, we concluded that significant adsorp- tion of unmodified silica nanoparticles on quartz and calcite surfa- ces was not observed under the experimental conditions studied. For all nanoparticle concentrations used in the bead-pack flow experiment, the pressure drop reached a constant value once the effluent nanoparticle concentration was equal to the injected con- centration. This steady-state pressure drop was used to calculate the viscosity of the nanoparticle dispersion. The results are shown in Fig. 3 for 1, 10, and 16 wt% 5-nm and 35 wt% 25-nm unmodi- fied-nanoparticle dispersions. The pressure drop increased linearly with the flow rate in accordance with Darcy’s law, confirming Newtonian behavior of the dispersions over the range of nanopar- ticle concentration. For the sandpack, only the flow of 1, 16.17 wt% 5 nm and 35 wt% 25 nm unmodified nanoparticle dispersions were studied. The pressure drop as a function of volumetric flow rate for these three nanoparticle dispersions is shown in Fig. 4. Note that the same linear dependency of pressure drop on flow rate was observed as was shown for the glass-bead pack. For both glass- bead pack and sandpack, the permeability after cleaning the packs stayed the same as it was before the injection of nanoparticles. Flow of Nanoparticle Dispersions in Consolidated Porous Media. A limestone core with properties shown in Table 1 was used as a consolidated permeable medium to study the effect of permeability on the rheology of nanoparticle dispersions. The re- spective pressure drops for steady flow of water with and without 1 wt% 5-nm particles at different flow rates are shown in Fig. 5, and they are similar to those observed in the unconsolidated media discussed previously (Figs. 3 and 4). After these two experiments, the core was flooded with 4 wt% NaCl solution for more than 20 PV before determining its permeability again. The original permeability of 54 md was not changed regardless of the TABLE 1—PROPERTIES OF POROUS MEDIA STUDIED Porous Media Permeability* (darcies) Porosity (%) Diameter (cm) Length (cm) Glass-bead pack 7.0 40.3 2.50 18.0 Sandpack 6.7 43.5 2.50 17.3 Limestone 0.054 24.9 2.45 15.2 Sandstone 0.105† 12.6 2.49 14.6 * Permeability to brine at 0.05 wt% NaCl; † permeability to brine at 3 wt% NaCl. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Pore Volumes NormalizedConcentration Tracer Nanoparticle Fig. 2—Normalized effluent concentration vs. cumulative injected PVs for tracer (NaCl) and nanoparticle dispersion in flow through the glass-bead pack. 0 0.5 1 1.5 2 2.5 0 100 200 300 400 Flow rate (ml/hr) ΔΔP(psi) 1 wt% 5 nm Unmodified 10 wt% 5 nm Unmodified 16 wt% 5 nm Unmodified 35 wt% 25 nm Unmodified Fig. 3—Pressure drop across the glass-bead pack vs. flow rate for 5-nm and 25-nm unmodified-nanoparticle dispersions with different nanoparticle concentrations. 0 0.5 1 1.5 2 2.5 0 100 200 300 400 Flow rate (ml/hr) ΔP(psi) 1 wt% 5 nm Unmodified 16.17 wt% 5 nm Unmodified 35 wt% 25 nm Unmodified Fig. 4—Pressure drop across the sandpack vs. flow rate for 5- nm and 25-nm unmodified-nanoparticle dispersions with differ- ent nanoparticle concentrations. August 2013 SPE Reservoir Evaluation Engineering 329
  • 4. salinity of the injection fluids, indicating a trace amount of swel- ling clay minerals in this limestone core. On the basis of our bulk rheology experiments (Metin et al. 2011b), it was found that at a given particle size and concentra- tion, silica-nanoparticle dispersions exhibit a Newtonian behavior within the shear-rate range studied (1 to 200 seconds–1 ) (Metin et al. 2011b). This range of shear rate covers what was used in the coreflood experiments in this work, according to the following correlation between the average velocity and the equivalent shear rate for flow in porous media (Lake 1989), _ceq ¼ 4v e 8k 1=2 ; ð2Þ where v is the average velocity, _ceq is the equivalent shear rate in permeable media, e is the porosity, and k is the permeability. Permeability is a function of grain size and shape. In this study, we investigated the effect of pore structure through the variation of permeability from 54 to 7,000 md with unconsolidated (i.e., spher- ical-glass-bead pack to sandpack) and consolidated (i.e., Berea sandstone and limestone) porous media. The Newtonian behavior of the silica-nanoparticle dispersions observed in our bulk rheol- ogy experiments is still valid for these porous media, regardless of the variation of permeability and matrix consolidation. In other words, the viscosity of the silica-nanoparticle dispersion is not de- pendent on the shear rates for the range of flow rates used in this work and for the given permeability and nanoparticle concentra- tion. However, the bulk viscosity of nanoparticle dispersion is a strong function of particle concentration and size. This relation- ship can be predicted by our scaled viscosity model (Metin et al. 2011b), which is derived from the volume fraction of nanopar- ticles, /, and an effective maximum packing fraction, /eff max: gr ¼ 1 þ 0:75 / ð/eff max À /Þ #2 : ð3Þ In our previous study (Metin et al. 2011b), we showed that the effect of particle size and the electrical double layer on the viscos- ity of unmodified-silica-nanoparticle dispersions is significant. Eq. 3 was obtained by modifying the empirical model proposed by Chong et al. (1971). The authors investigated the dependence of viscosity of highly concentrated suspensions on solid concen- trations by use of an orifice viscometer. On the basis of experi- mental data, an empirical equation that correlates the relative viscosities of suspensions as a function of solids concentrations and particle-size distributions was proposed. In our study, the effective-maximum-packing-fraction concept was incorporated into the viscosity model proposed by Chong et al. (1971) and the correlation between /eff max and /max was given. The correlation between /eff max and /max was based on a simple cubic packing of spherical particles with an electrical double layer (Metin et al. 2011b): /eff max ¼ /max 1 1 þ A jÀ1 a 3 ; ð4Þ where jÀ1 is the Debye length, a is the silica-nanoparticle radius, and A is a constant. The correlation between A and the particle size is given by Metin et al. (2011b). The effect of particle radius could be clearly seen in Eq. 4: As particle size increases, /eff max approaches the hard sphere maximum packing fraction, /max. The conceptual models proposed for the electrostatically stabi- lized silica-nanoparticle dispersions are presented schematically in Fig. 6. A simple cubic packing of particles is assumed in this study because the largest nanoparticle concentration used is less than 25 vol% and the nanoparticles are well dispersed in water. In this study, the viscosity ratio gr of the nanoparticle disper- sions flowing through porous media is calculated from the ratio of the slopes shown in Figs. 3, 4, and 5, divided by that from water runs. Then, the effective maximum packing fraction /eff max was cal- culated by use of Eq. 4 (Metin et al. 2011b). We previously showed that the reduced volume fraction of silica nanoparticles /=/eff max captures the effect of size and surface type on the viscos- ity, and the proposed model predicts well the viscosity of aqueous dispersion of silica particles whose sizes range from 5 to 500 nm (Metin et al. 2011b). Therefore, we used the same method to com- pare the viscosity of nanoparticle dispersions obtained in this study with that from bulk rheology measurements. The results are pre- sented in Fig. 7. The symbols in gray scale are those obtained from bulk rheology measurements (Metin et al. 2011b), and the symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 Flow rate (ml/hr) ΔP(psi) 1 wt% 5 nm Unmodified Water Fig. 5—Pressure drop as a function of flow rate for 1 wt% 5-nm unmodified-nanoparticle dispersion and water. κ 2a - - -- - - - - - -- - - - - - -- - - - - - -- - - -- - - - - –1–1 Fig. 6—Schematic view of the proposed model of effective max- imum packing fraction for unmodified silica particles. 0 5 10 15 20 25 0 50 100 150 200 Time (min) ΔP(psi) Tracer-0.05 wt% NaCl 1 wt% 5 nm Unmodified Fig. 7—Viscosity ratio as a function of volume fraction of silica nanoparticles of various sizes (5, 8, 25, and 75 nm) and two dif- ferent surface types (unmodified and sulfonate-coated), as adapted from Metin et al. (2011b). The volume fractions are nor- malized to the corresponding effective maximum packing frac- tion. All the data collapsed onto a single curve that is well- represented by our unified model. The results obtained from glass-bead pack and sandpack and limestone follow the same curve as bulk rheology data. 330 August 2013 SPE Reservoir Evaluation Engineering
  • 5. in color are those calculated from the flow-through-porous-media experiments. The unified model proposed (Metin et al. 2011b) was able to collapse all the data from the bulk rheology measurements and flow-in-porous-media experiments onto a single curve. However, the retention of nanoparticles can influence the interpretation of the rheological behavior of the nanoparticle dis- persion in porous media if it induces a significant variation of par- ticle concentration in flow. This effect could be demonstrated on a low-permeability rock, such as the sandstone studied in this work. The pressure drops during the injection of 0.05 wt% NaCl solu- tion for 4 hours followed by 1 wt% 5-nm-particle dispersion are shown in Fig. 8. For the brine injection, the pressure drop increases sharply in the first 20 minutes and then much more grad- ually. The pressure drop after 4 hours is approximately 20 psi, which is significantly higher than the expected value of 2.3 psi for 105 md at 20 cm3 /hr. Note that the permeability of 105 md was determined by use of a 3 wt% NaCl solution. This salt concentra- tion is sufficiently higher than the critical concentration, approxi- mately 1.5 wt% NaCl (Civan 2007), below which significant swelling of clay occurs. Therefore, the higher pressure drop dur- ing the injection of 0.05 wt% NaCl solution is caused by the clay- swelling-induced reduction of the sandstone core permeability from 105 to 12 md. As a consequence, when the injection of 1 wt% 5-nm unmodified-nanoparticle dispersion started, the pres- sure drop across the core increased sharply (Fig. 7). The injection of the nanoparticle dispersion is stopped after 60 minutes because the pressure drop reached the maximum of the transducer. Very little effluent was produced, which indicated that nanoparticles had been trapped mechanically and plugged the core. The filtra- tion of nanoparticles can induce a large gradient of nanoparticle concentration in flow, which in turn influences the rheological behavior of flow, according to Eq. 3. The interplay between nano- particle retention and rheological variation determines the mobil- ity of nanoparticles in porous media. In our corefloods, the measured pressure drop was affected by the variation of fluid vis- cosity because of the particle-concentration gradient and the mod- ification of medium permeability as a result of filtration and clay swelling. The rheological model can be used to separate these two effects because it was found that in the absence of nanoparticle retention, our model can accurately predict the viscosity of the dispersion over a wide range of nanoparticle concentration. This helps improve the interpretation of coreflood experiments in terms of filtration associated with clay swelling. Main Conclusions The transport properties of nanoparticle dispersions were studied in unconsolidated (glass-bead pack and sandpack) and consoli- dated (limestone and sandstone cores) porous media. Unmodified nanoparticles did not show any significant retention in high-per- meability glass-bead pack and sandpack as well as limestone core, because the tracer and nanoparticle showed the same efflu- ent concentration profiles. The nanoparticle dispersions studied exhibit a Newtonian behavior. The viscosity of unmodified nano- particles in porous media was in good agreement with that deter- mined by use of a rheometer. The viscosity depends strongly on the particle concentration, and this relationship can be described with a scaled rheological model. On the basis of our model and experimental results, the effect of slippage at the pore walls that may cause a detectable difference in viscosity between rheometer and porous media, as reported by Rodriguez et al. (2009), was not observed in our work. We established a correlation between the nanoparticle concen- tration and dispersion viscosity in porous media for various nano- particle sizes. The pore structure did not show any observable effect on the viscosity for high-permeability media, such as glass- bead packs and sandpacks. For lower-permeability limestone, the measured viscosity of nanoparticle dispersion also agrees well with the model for 1 wt% nanoparticle concentration. However, nanoparticles were retained in the sandstone core as a conse- quence of clay swelling. This effect and its interaction with the dynamic viscosity of nanoparticle dispersion will be further inves- tigated in our future work. Nomenclature a ¼ silica-nanoparticle radius, L, nm A ¼ model parameter, dimensionless C ¼ concentration of nanoparticle or tracer, m/L3 , g/cm3 Cinj ¼ concentration in the injected fluid, m/L3 , g/cm3 Cnorm ¼ normalized effluent concentration, m/L3 , g/cm3 Cres ¼ concentration in the resident fluid, m/L3 , g/cm3 e ¼ porosity, L3 /L3 , dimesionless f ¼ volume fraction of nanoparticles, L3 /L3 , dimensionless feff max ¼ effective maximum packing fraction, L3 /L3 , dimensionless geq ¼ equivalent shear-rate in porous media, 1/t, 1/s k ¼ permeability, L2 , m2 k-1 ¼ Debye length, L, nm v ¼ average velocity, L/t, m/s hr ¼ viscosity ratio, dimensionless Acknowledgments This work is supported by the Advanced Energy Consortium, through contract BEG08-020. We would like to thank 3M 0 2 4 6 8 10 12 14 16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Reduced Volume Fraction of Nanoparticles ( φ/φmax eff ) ViscosityRatio(η//η0 ) 5 nm Unmodified 8 nm Unmodified 25 nm Unmodified 75 nm Unmodified 5 nm Modified 8 nm Modified 25 nm Modified 75 nm Modified proposed model 5 nm Unmodified-Glass bead pack 25 nm Unmodified-Glass bead pack 5 nm Unmodified-Sand pack 25 nm Unmodified-Sand pack 5 nm Unmodified-Limestone Fig. 8—Pressure-drop profile in time for a tracer (0.05 wt% NaCl) and 1 wt% 5-nm unmodified-nanoparticle dispersion flowing through sandstone core. August 2013 SPE Reservoir Evaluation Engineering 331
  • 6. Company, particularly Jimmie Baran, for providing the nanopar- ticles and for scientific discussions. We would also like to acknowledge great help from Wenjun Liu, Monet Motiee, and Tianyu Li for their contributions to the experiments. References Biggs, M.J., Humby, S.J., Buts, A., et al. 2003. Explicit Numerical Simu- lation of Suspension Flow with Deposition in Porous Media: Influence of Local Flow Field Variation on Deposition Processes Predicted by Trajectory Methods. Chem. Eng. Sci. 58 (7): 1271–1288. http:// dx.doi.org/10.1016/S0009-2509(02)00555-9. Caldelas, F., Murphy, M., Huh, C., et al. 2011. Factors Governing Dis- tance of Nanoparticle Propagation in Porous Media. Paper SPE 142305 paper presented at SPE Production and Operations Sympo- sium, Oklahoma City, Oklahoma, 27–29 March. http://dx.doi.org/ 10.2118/142305-MS. Chong, J.S., Christiansen, E.B. and Baer, A.D. 1971. Rheology of Concen- trated Suspensions. J. Appl. Polym. 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Paper SPE 124418 presented at the SPE Annual Technical Conference and Exhi- bition, New Orleans, Louisiana, 4–7 October. http://dx.doi.org/ 10.2118/124418-MS. Sen, T.K., Shanbhag, S. and Khilar, K.C. 2004. Subsurface Colloids in Groundwater Contamination: A Mathematical Model. Colloid Surface A 232 (1): 29–38. http://dx.doi.org/10.1016/j.colsurfa.2003.10.004. Sun, L., Lin, J-Z. and Bao, F-B. 2006. Numerical Simulation on the Depo- sition of Nanoparticles Under Laminar Conditions. J. Hydrodyn. 18 (6): 676–680. http://dx.doi.org/10.1016/S1001-6058(07)60006-7. Zhang, T., Espinosa, D.A., Yoon, K. Y., et al. 2011. Engineered Nanopar- ticles as Harsh-Condition Emulsion and Foam Stabilizers and as Novel Sensors. Paper OTC 21212 presented at the Offshore Technology Con- ference, Houston, Texas, 2–5 May. Cigdem Omurlu Metin holds a PhD degree in petroleum engi- neering from the University of Texas at Austin. Her graduate research focused on characterization of the flow of surface- modified silica nanoparticles in porous media (dispersion stabil- ity, adsorption of nanoparticles onto mineral surfaces and oil/ water interface, aggregation kinetics, rheology of stable dis- persions and nanoparticle gels). After earning the PhD degree, Metin joined Shell. Upon completion of a Health, Safety, Secu- rity and the Environment assignment with the Global Rig Startup Team, she began her current assignment in a deep- water development project as a production technologist. Roger T. Bonnecaze holds a PhD degree in chemical engineer- ing from the California Institute of Technology, Pasadena. He joined the faculty at the University of Texas at Austin in 1993 and served as the chair of the McKetta Department of Chemical Engineering from 2005 to 2013. Bonnecaze is the William and Bettye Nowlin Chair in Engineering and Director of the National Science Foundation NASCENT Engineering Research Center on Nanomanufacturing. His research program focuses on the design and characterization of complex fluids as rheological additives and the development of manufacturing systems for nanoenabled electronic, health, security, and energy devices. Quoc P. Nguyen holds a PhD degree in petroleum engineering from Delft University of Technology, the Netherlands. He joined the faculty of the University of Texas at Austin in 2005. Nguyen is the Foundation CMG Industrial Research Chair in innovative hydrocarbon recovery. His current research program is focused on advanced gas and chemical enhanced-oil-recovery methods in (low-permeability, high-salinity, high-temperature) hydrocarbon formations, improved production of unconven- tional resources (oil sand, shale oil, and gas), and engineering of complex fluids (foam, emulsion, polymer gel, and nanopar- ticle dispersions) for subsurface conformance control. 332 August 2013 SPE Reservoir Evaluation Engineering

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