As described above, the AMPS-modified HPAM has a good salinity tolerance and some resistance to chemical/thermal degradation. Its currently available molecular weight is only 2–4 million (e.g., for SNF’s SAV10), meaning that a high concentration is needed to generate a desired viscosity with a resultant high cost. In order to overcome the limitation, a potential solution is to connect these polymer molecules by adding a low concentration of surface-coated nanoparticles to serve as “linkers” between polymer molecules. As the polymer molecules will be present as “fluffy globules”, connecting two polymer molecules by one molecule’s chain end to another’s chain end, as schematically shown in Figure 4A, will be ideal but generally very difficult (Gbadamosi et al., 2019). As described below, a more practical approach would be to make the nanoparticles serve as linkers between the “fluffy globules”, as conceptually depicted in Figure 4B. Compared with individual polymer globules, a much higher viscosity is expected once the globules are connected by nanoparticles to form long “strings”.

On maintaining high polymer viscosity, a common approach is to add nanoparticles to serve as “linkers” between polymer molecules. Available literature (Zhu et al., 2014), (Hu et al., 2017) suggests that small nanoparticles serve as inter-molecular linkers (which is desirable) but also cause intra-molecular association (which is undesirable). This conceptual picture implies that not only nanoparticles but also the chain elements of another polymer molecule can easily penetrate into a polymer molecule’s “fluffy globule” inner domain, as depicted in Figure 4C (Cao et al., 2018a). Literature data however shows that the size of nanoparticles (∼50–200 nm, usually in slightly aggregated state) (Huh et al., 2019), (Bagaria et al., 2013) is not much smaller than polymer’s hydrodynamic radius (∼100–1,000 nm) (Ghosh and Mohanty, 2020), (Silva et al., 2018). Thus, a rational approach would be to make the nanoparticles serve as linkers between the “fluffy globules” of polymer (Figure 4B), so that the viscosity of the “string” becomes significantly higher than that of the individual globules. To make the particle surface have sufficient repulsion so that it would not penetrate into the polymer’s inner domain, but still allow its attachment to the polymer globule, available literature is critically examined with the above improvement objective in mind.

Cao et al. (Cao et al., 2018a), (Cao et al., 2018b) described their nanoparticle surface coating development to obtain the polymer viscosity increase in some detail, which is reviewed here as a good example of similar research efforts. They applied to silica nanoparticle (diameter = 7–40 nm) different amounts of surface coating of 3-aminopropyl-triethoxy-silane (APTES) to study their effect on the rheology of AMPS-modified poly (acrylamide) (PM). Figure 5A shows the nanoparticle size in DI water at pH = 6, and Figure 5B shows the dependence of zeta potential of the particles on pH (Cao et al., 2018b). In the figures, NS is the nanoparticle as received from vendor (presumably without any surface coating) and for ANS-1, -2 and -4, the mole ratio of APTES to–OH on silica nanoparticle surface are 0.2, 0.5 and 1.5, respectively. Figure 5A shows that, while the nanoparticle size increased with more APTES coating (peak values from 134 to 179 nm for ANS-2 to -4), the “bare” nanoparticle size is larger (peak value ∼240 nm) suggesting that minor aggregation occurred (Cao et al., 2018b). Note that the nanoparticle sizes are quite comparable to the hydrodynamic radius of polymer, as described above. Figure 5B shows that with the APTES coating, the nanoparticle’s surface charge is now positive, making them electrostatically attractive to the negatively charged sulfonate ligands along the polymer chain, so that the nanoparticles can be readily attached to the polymer chain (Cao et al., 2018b). Figure 6A shows that, while the addition of the APTES-coated nanoparticles significantly increased the polymer viscosity, its undesirable dependence on the salinity is still significant (Cao et al., 2018b). On the other hand, the dependence of polymer viscosity on the hardness of brine is much less with the nanoparticles with higher APTES surface density (Figure 6B) (Cao et al., 2018b). In an attempt to improve upon the above APTES-coated silica nanoparticles, Cao et al. (Cao et al., 2019) also developed a coating that additionally includes octyl-triethoxyl-silane (OTES) which is more hydrophobic than APTES, thus allowing the nanoparticle to have both electrostatic and hydrophobic interactions with the polymer chain (Israelachvili, 2011), (Meyer et al., 2006).

Zheng et al. (Zheng et al., 2017) applied to the silica nanoparticle surface two different coatings: hexamethyl-disilazane (HMDS) and hexadecyl-trimethoxy-silane (HDTS) at different mole ratios of the coating material to the -OH on the silica surface. Figure 7A shows the schematics of the HMDS-attached silica nanoparticle, and Figure 7B shows the dependence of the polymer viscosity on the nanoparticle concentration for untreated nanoparticle and HMDA- and HDTS-treated nanoparticles (Zheng et al., 2017). With the HMDS coating, the polymer viscosity improved over the untreated nanoparticle but the HDTS coating did not help. This suggests that the hydrophobic end of the silane attached to the particle plays an important role in linking the nanoparticle to the polymer, and the hydrophobic interactions between them need to be better understood. Figure 8 shows the dependence of the HPAM (MW = 20 million) viscosity on the temperature, for different concentrations of untreated nanoparticles (Zheng et al., 2017). While the viscosity of polymer without nanoparticle addition decreased substantially with temperature increase, the nanoparticle addition not only increased the viscosity but also reduced the temperature-dependent reduction of the polymer viscosity. This compares with the dependence of the viscosity on temperature with the similar addition of “as-received, untreated” nanoparticles, which shows a substantial decrease in viscosity with temperature increase, as shown in Figure 9 (Hu et al., 2017). It is noted that, at almost any salinity, the bare silica nanoparticle is unstable and quickly aggregates. This suggests that the “untreated” nanoparticle has some surface coating that needs to be characterized.

The quantitative assessment on the effects of nanoparticle addition on polymer viscosity is rather difficult because, for a number of studies, the chemical nature of the nanoparticle surface coating is not provided. Overall, with increase in nanoparticle concentration, the polymer viscosity increase is observed, and the reduction in viscosity due to temperature increase is less severe. As described above, the nanoparticle surface coating has a significant effect on polymer viscosity, but the detailed molecular mechanism for the nanoparticle-polymer linkage and the consequent viscosity increase is yet to be determined.

In addition to the study on the effects of various nanoparticles on polymer viscosity, a number of researchers performed oil recovery core flood experiments. The results showed that, with addition of nanoparticles, not only was the viscosity higher than that of nanoparticle-free polymer but also a higher oil recovery was generally observed (Maghzi et al., 2014). When they increased the nanoparticles concentration, a higher oil recovery was attained (Hu et al., 2017).

For a long, single-chain polymer molecule such as HPAM, the chemical and mechanical degradation, i.e., the simple scission of the chain, drastically reduces the polymer molecular weight. This is critically important because the dependence of polymer viscosity on the molecular weight is quite large, as revealed by the Mark-Houwink equation that provides the polymer’s intrinsic viscosity, | η | , in terms of the polymer molecular weight (Jouenne et al., 2019), (Lohne et al., 2017), | η | = a M w b where a and b are polymer-specific constants. The intrinsic viscosity, which is a measure of the hydrodynamic size of polymer molecules, is the dominant parameter for polymer viscosity (Jouenne et al., 2019). An effective method developed to alleviate the oxidizing agent’s attack of the -c-c- bond of the HPAM molecular chain is to attach N-vinyl pyrrolidone (NVP) group along the chain, but then such modification adds cost. An alternate strategy to reduce the impact of the degradation is to connect the smaller polymer molecules with the nanoparticles as the linker, as depicted in Figure 4B. It is important to note that the effects of degradation are relatively less for smaller polymer molecules. The amide groups in the HPAM molecule can associate with silanol groups at the surface of silica, and the degradation tendency can be reduced as observed by Zhu et al. (Zhu et al., 2014). As described above (Cao et al., 2018a), (Cao et al., 2018b), (Cao et al., 2019), the silica nanoparticles functionalized with amino- and other silanes are found to behave much better in improving the chemical/thermal stability of HPAM in harsh conditions, compared with the cases of polymer only or polymer with untreated nanoparticles.

As the polymer degradation mechanisms even without nanoparticle addition are varied and complex, the detailed mechanism on how the nanoparticle helps reduce the degradation is yet to be determined.

Although polymer retention in porous media is also caused by trapping at pore throats and pore crevices, adsorption is the main mechanism that removes polymer from the solution and results in a significant viscosity reduction. The adsorption measurement by the bulk static method is generally greater than that by dynamic flow conditions (Lakatos et al., 1981), but is commonly employed to study the effects of different process parameters, such as the addition of nanoparticles.

Polymer solutions containing nanoparticles have been generally found to have less adsorption compared to polymer-only solutions (Sirk et al., 2009), (Phenrat et al., 2010). The results of static adsorption experiments show that nanoparticles play a major role in polymer adsorption on the rock surface (Cheraghian, 2016). Cheraghian et al. (Cheraghian et al., 2014) studied the effect of silica nanoparticle concentration on the retention reduction of HPAM polymer. Static polymer adsorption experiments were conducted at room temperature by adding crushed sandstone or carbonate rock samples to the polymer solution and stirring until adsorption was complete. Figure 10 shows the polymer adsorption data on sandstone samples with the addition of 2.25 wt% (A24) and 1.8 wt% (A41) nanoparticles; and on carbonate samples with similar addition of nanoparticles (B16 and B52, respectively). It shows that the adsorption in sandstone is much smaller than that in carbonate and that polymer solutions containing more silica nanoparticles have less adsorption. These results clearly show that the nanoparticles served the role of sacrificial adsorption agent.

Another factor that may increase the reservoir oil recovery when using nanoparticle-enhanced polymer flooding is that it can change an oil-wet reservoir to water-wet. It is well documented that oil recovery is affected by the wettability of the reservoir with more oil being recovered from water-wet rocks compared to oil-wet rocks. Extensive research efforts have been made to investigate the effects of “nanofluid” injection for improved oil recovery (Cheraghian and Hendraningrat, 2016a), (Cheraghian and Hendraningrat, 2016b), (Hendraningrat and Torsæter, 2015), (Hendraningrat and Torsæter, 2016). Usually, the alteration of wettability is examined by measurements of interfacial tensions and contact angles. Nanoparticles have been found to reduce the contact angle that polymer solution makes on the rock surface. A higher nanoparticle concentration would be expected to better reduce contact angle; however, the increased nanoparticle concentration may also reduce the stability of fluid because of the aggregation and sedimentation of nanoparticles, which results in a specific threshold of nanoparticle concentration (Cheraghian et al., 2014).

Because the wettability is directly affected by the interfacial tension via the Young’s equation (Berg, 2010), the effect of nanoparticles on interfacial tension between HPAM solution and oil has been studied. El-hoshoudy et al. (El-hoshoudy et al., 2016) studied the effect of silica nanoparticle on the interfacial tension of polymer solution and oil recovery. Flooding experiments were performed with a sandstone core using HPAM with different concentrations of silica (0, 1, 2, 3, and 4 g/L). Figures 11A,B show that with the increase of nanoparticle concentration, the crude oil/brine interfacial tension decreases, and the cumulative oil recovery increases. The interfacial tension reduction is not sufficient enough to mobilize the oil by the capillary-number mechanism, indicating that the increased oil recovery is most likely due to the wettability alteration. It is observed that a concentration threshold appears to exist at ∼2 g/L with a maximum oil recovery there; but the mechanism for synergy between polymer and nanoparticle is not yet known. A pore-level study on the synergy mechanism, similar to that between surfactant and nanoparticle (Xu et al., 2017), is warranted.

Sharma et al. (Sharma et al., 2016) studied the effect of nanoparticles on polymer and surfactant-polymer flooding. Coreflood experiments were carried out at both 30 and 90°C with SiO₂ nanoparticles at 1 wt%. Figure 12 shows the relative permeability curves for brine and oil before and after the nanoparticle-added polymer flooding at 30°C. The addition of 0.1 wt% SiO₂ nanoparticles clearly increased the oil relative permeability while the brine relative permeability was reduced, showing the wettability alteration. They also showed that the nanoparticle addition increased the oil recovery.

Kumar et al. (Kumar et al., 2022) studied the effect of different types of nanoparticles (SiO₂ and GO) and salinities (NaCl and CaCl₂) on the interfacial tensions and contact angles. Figure 13A shows that the crude oil/brine interfacial tension decreases linearly with increasing nanoparticle concentration, when HPAM-SiO₂ is in NaCl brine. Figure 13B shows that the contact angle, measured on a silica plate with the fluids of (a), also decreased for NP concentration from 0.05 to 0.1%. While the decreases for both were relatively minor but showed positive trends.

A magnetic field induces an additional pressure p m a g n e t i c in the ferrofluid (Rosensweig, 1985). The additional pressure has three terms, the magnetostrictive pressure p s , the fluid-magnetic pressure p m , and the magnetic normal pressure p n . p magnetic = p s + p m + p n p s = μ 0 ∫ 0 H v ( ∂ M ∂ v ) H , T dH p m = μ 0 ∫ 0 H MdH p n = 1 2 μ 0 ( n → ⋅ M → ) 2 where μ 0 is the magnetic permeability in vacuum, H is the magnetic field strength, M is the magnetization, χ is the magnetic susceptibility, and n → is the normal direction of the fluid interface. While p s and p m are bulk pressures, p n is an interfacial term that should be added to the Young–Laplace equation at the interface between two fluids.

Even when a uniform external magnetic field H → is applied, the magnetization M → and the magnetic flux density B → is non-uniform at the pore scale because of the contrast of magnetic permeabilities of rock, oil, and brine. As a result, the corresponding magnetic-induced pressure is thus non-uniform in the ferrofluid as the flooding fluid (Prodanovic et al., 2010), (Soares et al., 2014; Wang and Prodanovic, 2017; Wang et al., 2020; Wang et al., 2021), as shown in Figure 14. This non-uniform magnetic pressure leads to deformation of the oil-ferrofluid interface and helps the mobilization of the oil droplet in the pore space. Prodanović et al. developed 2D models based on the level-set method to analyze the equilibrium state of the trapped oil droplets and the corresponding oil saturation change with and without the static magnetic field (Soares et al., 2014), (Wang et al., 2020). They predicted that a static magnetic field improves oil recovery when the magnetic field direction is along the flow direction. However, Wang et al. developed a 3D model based on volume of fluid method and predicted the prohibits the oil recovery when the magnetic field direction is transverse to the flow direction, which is in contrary to their experimental results, hinting the presence of other mechanisms (Wang et al., 2021), (Wang et al., 2020).

Magnetic nanoparticles form temporal micro-structures when exposed to external disturbances of either magnetic fields (Robbes et al., 2011), (Tracy and Crawford, 2013) or shears (Ishida et al., 2021), as shown in Figure 15. These micro-structures can be permanentized by solidifying the fluid (Tracy and Crawford, 2013). These micro-structures can either interact with the oil droplets and apply additional propulsion to the oil droplet, or adhere to the oil droplets and provide additional hydrodynamic forces to the oil droplets (Wang, 2021), (Wang et al., 2021). Either way, the oil droplets may have an increased chance of displacement from the pore.

Wang et al. experimentally demonstrated the EOR effect of a 2.6 mT static magnetic field transverse to the flow direction in a ferrofluid flooding despite of unsuccessful approaches by other researchers, as shown in Figure 16 (Wang et al., 2021), (Wang et al., 2020). They measured the oil saturation in a micromodel during a ferrofluid flooding before and after the application of an external magnetic field. In one experiment, the application of the static magnetic field mobilized 86.2% of the oil that was not mobilized by the ferrofluid flooding alone. They also observed the chaining of oil droplets both in the micromodel and in a Hele Shaw cell.

Whether the mobilization of oil droplets is because of the non-uniform magnetic-induced pressure or the nanoparticle chains is not yet clear. However, presently it appears that the existence of nanoparticle chains could better explain the increased oil recovery when the magnetic field is transverse to the flow direction than the theory where we have uniform suspension of nanoparticles (which was the assumption made in simulation in Figure 14). No matter which mechanism is dominant, the magnetic forces aided mobilization of the trapped oil in a foot-long micromodel when the magnetic field is slowly rotating at a sub-Hertz frequency (Wang et al., 2021).

The increased oil recovery driven by a static magnetic field was also confirmed by Esmaeilnezhad et al. in core flooding (Esmaeilnezhad et al., 2018a). However, they only guessed the oil recovery was caused by an improvement in sweep efficiency without further analysis.

The magnetic field strength around a static magnetic source decreases at the rate of 1 / r 3 , where r is the distance to the magnetic source. Thus, it is pivotal to investigate the mobilization capability of the magnetic forces as a function of the magnetic field strength, especially at low magnetic field strength.

Magnetic materials are attracted to higher magnetic field intensity gradient direction. In a ferrofluid, the body force density f m in a nonlinear magnetization process is (Rosensweig, 1985) f m = − ∇ { μ 0 ∫ 0 H M d H } + μ 0 M ∇ H where M is the magnetization, H is the magnetic field intensity magnitude, and μ 0 is the vacuum magnetic permeability. In the reservoir, the magnetic field is weak and the magnetization is usually assumed linear (Huang et al., 2017), (Wang et al., 2021). Assuming incompressible flow and linear magnetization, the body force is f m = μ 0 M ∇ H

The body force term can be plugged into the Darcy’s equation to study the flow of ferrofluid in porous media.

A static magnetic source, e.g., a magnet, induces a large-scale non-uniform magnetic field and attracts magnetic nanoparticles and ferrofluid to the magnetic source. This effect can be used to manipulate the flooding fluid and improve the volume sweep efficiency, as shown in Figure 17 (Huang et al., 2017).

However, the corresponding magnetic body force decreases at the rate of 1 / r 4 , where r is the distance to the magnetic source. The oil mobilization capability based on the non-uniform magnetic field decreases faster than the capability provided by the other two mechanisms. The impact of the magnetic field strength needs further investigation before field application.

Further, manipulating flooding fluid by magnetic attraction forces requires the magnetic field source (a magnet) being placed in the reservoir. When applied in the field, the magnet needs to be placed in a well that is not flowing. The production planning is thus to be studied.