Evaluation of Silicone Fluids and Resins as CO₂ Thickeners for Enhanced Oil Recovery Using a Computational and Experimental Approach

Abstract

CO₂ thickeners have the potential to be a game changer for enhanced oil recovery, carbon capture utilization and storage, and hydraulic fracturing. Thickener design is challenging due to polymers’ low solubility in supercritical CO₂ (scCO₂) and the difficulty of substantially increasing the viscosity of CO₂. In this contribution, we present a framework to design CO₂ soluble thickeners, combining calculations using a quantum mechanical solvation model with direct laboratory viscosity testing. The conductor-like polarizable continuum model for solvation free-energy calculations was used to determine functional silicone and silsesquioxane solubilities in scCO₂. This method allowed for a fast and efficient identification of CO₂-soluble compounds, revealing silsesquioxanes as more CO₂-philic than linear polydimethylsiloxane (PDMS), the most efficient non-fluorinated thickener know to date. The rolling ball apparatus was used to measure the viscosity of scCO₂ with both PDMS and silicone resins with added silica nanoparticles. Methyl silicone resins were found to be stable and fast to disperse in scCO₂ while having a significant thickening effect. They have a larger effect on the solution viscosity than higher-molecular-weight PDMS and are able to thicken CO₂ even at high temperatures. Silicone resins are thus shown to be promising scCO₂ thickeners, exhibiting enhanced solubility and good rheological properties, while also having a moderate cost and being easily commercially attainable.

Introduction

CO₂ injection is one of the most broadly used enhanced oil recovery (EOR) technologies worldwide. Under reservoir conditions, CO₂ is in the supercritical state (scCO₂) and has a liquid-like density while exhibiting a gas-like viscosity. The significant viscosity gap between oil and the solvent may lead to viscous fingering, channeling the gas, and impairing the areal extension of the injected slug, therefore compromising the macroscopic sweep efficiency.

Water alternating gas (WAG) is the most broadly used method for improving macroscopic sweep efficiency in CO₂ EOR. Nonetheless, injecting different phases could generate problems like water blocking, especially at high water saturations.¹⁻³ The CO₂-rich phase may not contact the oil in smaller pores due to capillary pressure creating a capillary induced bypassing.⁴ While volumetric efficiency is enhanced by higher WAG ratios, reduced WAG ratios or even continuous CO₂ injection can have a positive effect on microscopic efficiency.⁵ In order to obtain both good microscopic and macroscopic sweep efficiency, CO₂ thickeners could be used as a mobility control agent.

Another operational issue observed in various CO₂ EOR projects is injectivity reduction due to changes in relative permeabilities.⁶ Both CO₂ and water injectivities have shown to decrease in WAG and simultaneous water-gas injection. In the Grayburg formation (Permian Basin), a water injectivity loss of up to 90% has been reported.⁷ The loss of injectivity derives in a significant pressure drop around the wellbore, reducing the overall reservoir pressure, and miscibility conditions may be lost. It is possible to reduce injectivity loss effects by increasing the gas slug size in WAG cycles,⁶ and by utilizing thickeners alongside with larger gas slugs, volumetric efficiency could be maintained. Furthermore, water availability or water quality issues can also be of concern in some regions. Enhancement of CO₂ viscosity would allow reducing water utilization and all its related issues while maintaining sweep efficiencies.

An affordable CO₂ thickener solution is today acknowledged as a game-changing technology since it would have profound effects on oil recovery.⁸ Such a mobility control agent would adjust the CO₂-rich solution’s viscosity by simply varying its concentration. By directly increasing the viscosity of the CO₂ phase, mobility control can be obtained regardless of the relative permeability of the rock, fluid saturations, or brine properties. Viscosity enhancement has been attained by using CO₂-soluble surfactants and polymers (with and without co-solvents) and most recently with nanoparticles.

Bae and Irani pioneered CO₂ thickener research by utilizing high-molecular-weight (MW) polydimethylsiloxane (PDMS), with toluene as a co-solvent; this formulation has proven to increase CO₂ viscosity up to 90-fold. A 6, 4, and 2 wt % polymer solution in CO₂ increased its viscosity to 3.48, 1.2, and 0.8 cp, respectively, under reservoir conditions. While thickened CO₂ was shown to improve oil recovery from cores and increase gas viscosity, the co-solvent (toluene) requirement made pilot-testing costs prohibitive.⁹ Silicones have also been used as thickeners for fracturing fluids with utilization of kerosene as a co-solvent.¹⁰ Functional silicones with anthraquinone-2-carboxamide end groups,¹¹ ester, amide, urea functional groups,¹² epoxy-terminated PDMS,¹³ and epoxy ether-based PDMS were tested as thickeners for CO₂-based fluids,^14,15 but all had limited solubility. Branched siloxanes were found to have a higher solubility in scCO₂ than linear silicones.¹² Copolymers based on epoxide heptamethyltrisiloxane and glycidyl phenyl ether also showed to increase CO₂ viscosity.¹⁶

Fluorinated thickeners were successfully developed for CO₂. Formulations such as a fluorinated telechelic ionomer, a tri(semi-fluorinated alkyl) tin fluoride, a surfactant with two twin-tailed fluorinated tails, and a high-MW fluoroacrylate homopolymer have been evaluated.^8,17 Poly (fluoroacrylate-styrene) is a fluorinated compound that was able to increase CO₂ viscosity by 10-fold and 19-fold with under 1 and 1.5 wt % additive concentrations, respectively.¹⁸ A four-armed oligomeric CO₂ thickener containing fluorine was recently developed significantly increasing carbon dioxide’s viscosity.¹⁹ Unfortunately, fluorinated compounds are expensive and carry health and environmental concerns.

Recently, nanoparticles have been used to improve EOR methods. Mixture or chemical EOR with nanoparticles has been utilized in water-based nanofluids as well to enhance their physical properties.²⁰ Shah (2009) dispersed CuO nanoparticles in CO₂ with PDMS as a co-solvent. The formulation obtained had a 2.28 cp viscosity under reservoir conditions and showed significant incremental oil recovery in core floods. They additionally developed a formulation with viscosity-reducing injectants.²¹ Hashemi et al. (2016) used NiO nanoparticles with PDMS as a co-solvent. NiO nanoparticles were able to destabilize asphaltene depositions in porous media, mitigating permeability reduction and achieving a significant improvement in the final oil recovery.²² Jafari et al. (2015) used water as a co-solvent to disperse silica nanoparticles in CO₂. The use of water to disperse the nanoparticles in CO₂ significantly reduced the costs, although oil recovery factor increment was not as significant as in the other formulations. WAG with nanoparticle-saturated CO₂ was also tested with positive results.²³ Recently, computational models on MatLab were used to determine optimal nanoparticle concentration in CO₂ EOR.²⁴ Also, the graphene oxide/P-1-D nanocomposite was used to thicken the gas without the use of co-solvents.²⁵ Nanoparticle dispersions in CO₂ have been mainly studied at the viscometer or core flood level, and further research regarding their long-term stability is required. Lemaire et al. (2021) suggest that while there have been only a few reports of stable nanoparticle dispersion in CO₂, future research in this area with surface-functionalized silica nanoparticles with non-fluorous highly CO₂-philic ligands may be promising.²⁶

Other polymers, such as P-1-D and PVEE,^27,28 have been tested as CO₂ and CO₂-rich gas thickeners. Unfortunately, P-1-D and PVEE polymers, especially at low MWs, lack consensus regarding their ability to thicken CO₂. Contradicting results and failed attempts to reproduce findings have been shown, where low-MW polymers/oligomers were unable to significantly increase CO₂’s viscosity.²⁶ Small associative polymers were suggested²⁹ to be soluble in scCO₂. So far, at a laboratory scale, the best CO₂ thickeners are PDMS, polyFAST, and PFOA for CO₂ mobility and conformance control.³⁰

Unfortunately, in order to significantly increase the viscosity of scCO₂, large-MW polymers are required. As their solubility decreases with increasing MW, considerable amounts of co-solvent are required to dissolve these thickeners, thus making their cost economically prohibitive. Therefore, the design of more soluble and efficient thickeners is essential for the development and implementation of the technology.

Partially cross-linked polymers were tested by Kazantsev et al. as thickeners for different solvents. Various degrees of cross-linking were tested by controlling the content of the cross-linking agent. They found that a partial degree of cross-linking achieved the greatest viscosity increment. This is due to the formation of macromolecular coils occupying the largest volume in solution. They also found that a further increase of cross-linking content in the polymer makes it insoluble.³¹

Gallo and Erdmann studied the implementation of thickened CO₂ combined with a WAG scheme, making the process economically feasible. By injecting the thickened gas within a large slug of CO₂, high volumetric efficiency can be achieved combined with high recovery factors while significantly reducing the costs of thickeners. The same research also showed that the optimal CO₂ viscosity for that study was between 0.3 and 0.5 cp. This was due to the fact that higher viscosity accounted for a higher pressure drop in the reservoir, leading to a loss of miscibility.³² Similar results were reported where compositional reservoir simulation showed that increasing the injected gas viscosity close to that of the oil (0.24 cp) had a significant impact on oil recovery.³³

The design of CO₂-philic additives is complex, time-consuming, and expensive due to the characteristics of this supercritical fluid. Laboratory experiments usually require long periods of experimentation, specialized apparatuses, and the testing of numerous candidates. Many current polymer candidates are custom-made, requiring polymer synthesis, making their development slow, difficult, and costly. Additionally, in some cases, the mechanisms responsible for their solubility are poorly understood.

In this study, we used a quantum mechanical (QM) solvation model to efficiently narrow down the list of thickener candidates, thus significantly reducing the testing time and cost, while having a further understanding of CO₂–polymer interactions and thus determining a more CO₂-philic additive. Viscosity enhancement was later studied using an experimental rolling ball apparatus and contrasted with nanofluids. We found that silicone resins have high CO₂-philicity as well as good viscosity enhancement capabilities.

Materials and Methods

Solubility from Free Energy of Solvation

Implicit or continuous solvent models, where the solvent is represented by a polarizable dielectric continuum and its interaction with the solute is accounted for through the reaction field, offer an excellent trade-off between computing time and accuracy, offering an appealing alternative to explicit models.^34,35 The conductor-like polarizable continuum model (CPCM) partitions the surface in small regions called tesserae, which are assigned partial charges based on the electrostatic potential.³⁶ CPCM is often considered one of the most successful solvation models^37,38 and was used to study isomeric structures, energies, and properties of the substituted silacyclopropylidenoids in various solvents.³⁹

The thermodynamic cycle using the solvation free energy (ΔG_sol), the standard-state free energy of the liquid–vapor equilibrium of component A (ΔG₁^○), and the standard-state free energy of the equilibrium of a given solvent (scCO₂) with liquid A (ΔG₂) is shown in Figure 1.

1

where the standard free energies are represented⁴⁰ as

2

where P_x^● is the equilibrium vapor pressure of X over pure X, P^○ is the pressure of an ideal gas at a 1 M concentration and 298 K, M^○ is the standard-state molarity, M_x is the equilibrium molarity of pure X, S is the solubility in molarity units, R is the gas constant, and T is the absolute temperature. M^○is equal to 1 mol per liter as defined in P^○ in order to simplify the equations. By adding eqs 1 and 2, S can be expressed in terms of ΔG_sol according to⁴¹

3

Figure 1.

Thermodynamic cycle used for solubility calculations.

Using eq 3, the relative solubility of component A with respect to a known component B can be expressed as

4

In this paper, we used linear PDMS as a reference for comparison as it is the most soluble non-fluorinated CO₂ thickener known to date.⁴²

Since the vapor pressure of polymers is usually very low and not always available, using eqs 1–3 it is expedient to express S in terms of ΔG_sol and ΔG₁^○, that is, the free energy of solvation of component X in its liquid, according to

5

where M_x^s is obtained using the component’s X density and its molar mass. Thus, the solubility increment of component A over B can be calculated as

6

QM CPCM Solvation Model

In a continuum model, the influence of the solvent over the solute Hamiltonian (Ĥ) is expressed as

7

where Ĥ° is the solute Hamiltonian in vacuum and V̂ represents the perturbation due to the effect of the solvent. The CPCM model characterizes the solvent as a conductor-like polarizable continuum using its dielectric constant. The surface is discretized with a tessellation scheme where point charges are located in small areas (tesserae). The operator V̂ is written in terms of these apparent polarization charges q_i placed on each tessera i. Considering the conductor-like boundary condition

8

where V is the electrostatic potential due to the solute, V_qi is the electrostatic potential due to the polarization charges, and r⃗ is a point on the surface. The relationship between the vector of the conductor-like polarization charges (q) and V can be expressed as

9

where V contains the solute electrostatic potential on the cavity surface, and matrix A (in CPCM) is defined as⁴³

10

11

with r⃗_i and r⃗_j being the coordinates of tesserae i and j, respectively, ε the dielectric constant of the solvent, and S_i the area of tessera i.

The electrostatic component of the free energy of a solute in solution (G_es) can be written as⁴⁴

12

where ΔG_es is expressed as⁴⁴

13

and V_i indicates the value of the electrostatic potential due to the solute on the ith tessera.

Calculating the total energy of the molecule in vacuum (E°), the electrostatic energy of the molecule (ΔG_es), and the non-electrostatic contribution (ΔG_CD), the solvation free energy (ΔG_sol) can be approximated as^45,46

14

where the non-electrostatic term includes the short-range Van der Waals solute–solvent interactions and the energy needed to build the cavity (cavitation term). In order to simulate the scCO₂ solvent with CPCM, a dielectric constant representative of scCO₂ at 100 bar and 50 °C was used. In this paper, we used an experimental dielectric constant of 1.215.⁴⁷

To study the solvation of several silicones, a CPCM model was used to calculate solvation free energies using the BP86 level of density functional theory (due to its lower computational cost as shown in previous studies⁴⁸) utilizing the ORCA^49,50 quantum mechanics software.

Laboratory Rolling Ball Measurements

The rolling ball allows the measurement of fluid viscosity under reservoir conditions. This apparatus consists of a metallic ball, which falls within a tube containing the fluid at the required pressure and temperature (Figure 2). The ball is initially held magnetically in the upper section of the tube and later dropped, electronically measuring the time required to reach the sensor at the bottom end of the apparatus. The viscosity measurements presented in this paper were carried out at an apparatus tilt (θ) of 70° with a ball diameter of 0.64 cm, and the apparatus was calibrated with hexane. Viscosity tests were carried out at 180 bar and 55 °C to emulate reservoir conditions and later at different temperatures to better understand its effect on the polymer-nanofluid solution’s rheology.

Figure 2.

Rolling ball apparatus setting.

As the tube’s length and ball diameter remain constant, the viscosity of the fluid can be calculated as

15

where μ is the fluid viscosity, K is a constant unique to the set of tests, t is the time that takes the ball to roll from the top to the bottom of the apparatus, δ_b is the density of the ball, and δ_f is the density of the fluid. By comparing the rolling balls’ measurement of the tested fluid with the measurements of a known fluid with similar viscosity (i.e., hexane), the tested fluid’s viscosity can be calculated using the following equation:

16

where μ_t is the tested fluid’s viscosity, μ_h is the viscosity of hexane, t_t is the rolling time with the tested fluid, t_h is the rolling time with hexane, and δ_h is the density of hexane.

Different polymer–scCO₂ mixtures were tested in a Ruska rolling ball viscometer. The AK 12,500 and AK 60,000 silicone fluids were used to study linear PDMS, while Silres KX (having a proprietary molecular structure) was used to study silicone resin (Table 1). PDMS samples were chosen with similar and lower MWs than previous studies regarding silicone nanofluids²¹ as they are expected to have higher solubilities in CO₂ than the high-MW silicones such as the ones used by Bae and Irani⁹ and therefore require less co-solvent. While using lower-MW silicones would require higher polymer concentrations to obtain the same viscosities, the overall additive concentration is lower due to the reduced need for a co-solvent. Both linear PDMS and silicone resins were provided by Wacker Silicones. Coated nanoparticles from PlasmaChem were added to the silicones to generate nanofluids (Table 2). The nanoparticle’s hydrophobic coating was chosen to assist dispersion. The AK 12,500 silicone was mixed with a 10% w/w nanoparticle concentration, while the AK 60,000 PDMS was mixed with 5, 10, and 30% w/w nanoparticle concentrations to understand the effect of the polymer’s MW and nanoparticles on the scCO₂ viscosity. Nanoparticles were first dispersed in linear PDMS overnight using a heated ultrasonic bath. Afterward, they were prepared in an 80% m/m toluene—20% m/m polymer–nanoparticle mixture to facilitate the dissolution of the mixture in CO₂. Toluene was chosen as a co-solvent based on Bae and Irani’s experiments, who benchmarked PDMS as a CO₂ thickener.⁹ In order to mix the additive in carbon dioxide, the samples were left in the rolling ball apparatus for up to 3 days, heated at 80–90 °C, and with occasional rocking in order to stabilize the mixture and obtain consistent viscosity measurements.

Table 1. Silicone Polymers.

silicone (type)	viscosity (Cp)	Mw	substituent type	degree of cross-linking	main functionality	SiO2 content
Silres AK 60,000	60,000	∼63,500	methyl
Silres AK 12,500	12,500	∼39,500	methyl
Silres KX	6–12 (50% wt. xylene)	8000–15,000	methyl	71%	ethoxy/silanol	88%

Table 2. Nanoparticle Properties.

NP type	size (nm)	coating	type of coating
silica	14	PDMS	chemically attached

Results and Discussion

The design of scCO₂ thickeners was carried out in two steps. First, the relative solubilities of several silicone-based components were estimated using the CPCM solvation model to determine scCO₂-philicity. Afterward, the viscosity of the CO₂ solution with the chosen candidate was measured in a rolling ball apparatus and contrasted with that of PDMS of different MWs and increasing addition of nanoparticles.

Prediction of Solubility Using the CPCM Solvation Model

To understand the solubility of silicone polymers and resins in scCO₂, ΔG_solv of several silicones were calculated using CPCM solvation models in order to determine their CO₂-philicity.

Common functional silicones were modeled having six functional repeating units and two trimethyl siloxane end groups (Table 3). PDMS molecules were analyzed with different amounts of repeating units in order to contrast solubilities as a function of MW. MQ resin and silsesquioxiane were included in order to determine how different types of structures affect solubility.

Table 3. Structure and Size of Linear Silicone Polymers.

Overall, the CPCM solvation model showed good agreement with the expected solubility behavior from the literature^12,13,42 and revealed itself to be a suitable method to test and design solutes for scCO₂. The utilization of a computational calculation significantly reduced the screening time and cost by reducing the need of purchasing or synthesizing and testing the polymers.

In the case of functional silicones in Table 3, only ΔG_solv could be calculated for many compounds due to unavailable data (vapor pressure/dielectric constant). As solubility is dependent on the difference between ΔG_solv and ΔG₁^○, functional groups’ effect on solubility could be analyzed using the vapor pressure of monomers and eq 4. Solvation free energies for linear and functional PDMS are shown in Figure 3.

Figure 3.

Solvation free energy of linear silicones. (●) represent functional silicones as numbered in Table 3, and ( ) represent linear PDMS of different MWs.

As expected, linear silicones with functional groups containing oxygen or nitrogen had lower solvation free energy than the equivalent MW PDMS. Simulations show that the addition of oxygen or nitrogen enhances the electrostatic interactions with the medium, while methyl or other alkyl groups augmented ΔG_solv. The methoxy functional group had the highest rate of oxygen to carbon atoms and therefore was expected to have a relatively low ΔG_solv and higher solubility in scCO₂. Amino groups also appear to improve interactions with the solvent. Nonetheless, while we found that polar groups enhanced solvation, it should be noted that polar groups in the extremities of the molecules generate strong intermolecular interactions, such as hydrogen bonding, with adjacent molecules leading to poor solubility. This could explain why poly(vinyl acetate) is soluble in CO₂, while poly(acrylic acid) is not.⁵¹ Amino groups do reduce ΔG_solv and are useful for carbon capture, but their hydrogen bond interaction would reduce their ability to disperse, lowering their solubility in CO₂.

While vapor pressure data for poly dimethoxy siloxane (compound 4) are not available in the literature, it is possible to infer that the vapor pressure is lower than that of PDMS comparing the vapor pressure data of tetramethoxysilane (PubChem CID: 12682)⁵² and tetramethylsilane (PubChem CID: 6396).⁵³ Using eq 4, we see that the solubility enhancement is not significant as the exponential term is offset by the lower vapor pressure of the methoxy-functional silicone. In order to further analyze alkoxy-silicones, additional calculations for poly(MTES-co-TEOS) (compound 9, Table 4) were performed as the polymer’s dielectric constant data are available from the literature.

Table 4. Structure of poly(MTES-co-TEOS).

Poly(MTES-co-TEOS) has a dielectric constant of 3.5,⁵⁴ and for linear silicones (compound 1, n = 10), we used a dielectric constant of 2.2.⁵⁵ ΔG₁^○ can be calculated with the available data, and solubility enhancement can be estimated using eq 6. As shown in Table 5, while ΔG_solv of alkoxy-silicones is lower than that of PDMS, it is offset by the lower ΔG₁. Therefore, alkoxy functional silicones do not exhibit enhanced solubility in scCO₂. Nonetheless, their impact on solubility is moderate; therefore, having a reduced number of alkoxy groups (as happens in many silicone resins since they are used to cure them) would not significantly impact the silicone resin’s solubility.

Table 5. Solubility Increment of Alkoxy-Silicone over PDMS.

	density (g/cm3)	Mw (g/mol)	Ms (mol/cm3)	ΔGsolv (J/mol)	ΔG1 (J/mol)	Spoly(MTES-co-TEOS)/SPDMS
poly (MTES-co-TEOS)	1.0656	877	0.0012	814	–186	0.94
PDMS (n = 10)	0.9755	904	0.0011	884	331

The studied resins and silsesquioxanes are shown in Table 6. They have the potential to be significantly better CO₂ thickeners than linear PDMS as their structure has a greater effect on solution viscosity. Additionally, partially cross-linked silicone rubbers are expected to be CO₂-philic as they have a similar, or even lower, solubility parameter (δ = 7.3–7.5 cal^1/2/cm^3/2) than linear PDMS (δ = 7.5 cal^1/2/cm^3/2).⁵⁷ These Hildebrand solubility parameters are in the range of those of scCO₂, which vary from 3.7 to 8 cal^1/2/cm^3/2 at pressures over 10 MPa.⁵⁸

Table 6. Structure and Size of Resins and Silsesquioxanes.

In this study, we compared the MQ silicone resin (compound 10), methyl terminated silsesquioxane (compound 11), silica gel (compound 12), and octaphenyl-silsesquioxane (compound 13) in order to understand the effect of different structures and substituent group types in solubility (Table 6).

MQ resin and linear PDMS have comparable ΔG_solv as they have the same amount of methyl groups per silicon and oxygen atoms. In contrast, silsesquioxane has a lower ΔG_solv showing that these three-dimensional structures are more CO₂-philic than linear silicones (Figure 4), in agreement with Doherty et al.¹² findings. Silsesquioxanes have a lower ΔG_solv due to the higher silicone oxide to methyl ratio, while having non-polar groups in the extremities of the molecule. As expected, silica (compound 12) has even lower solvation free energy due to the hydroxyl group, which adds to the polarity of the molecule enhancing the electrostatic interaction with the medium. Unfortunately, as discussed for amine functional groups, the hydrogen bonding of the hydroxyl group would account for higher intermolecular interactions, diminishing their solubility.

Figure 4.

Solvation free energy of resins and silsesquioxanes. (●) represent compounds as numbered in Table 6, and ( ) represent linear PDMS of different MWs.

Solubility enhancement of methyl and phenyl silsesquioxanes was estimated using eq 6. For PDMS (compound 1, n = 5 and n = 11), silsesquioxane (compound 11), and octaphenyl-silsesquioxane (compound 13), we used dielectric constants of 2.2,⁵⁵ 2.6,⁵⁹ and 2.8,⁶⁰ respectively. While the exponential term of the solubility comparison of silsesquioxane and PDMS in eq 6 is slightly lower than 1, the higher density,^55,61 and therefore higher molarity of silsesquioxane, determines that they are 20% more soluble than linear PDMS of a similar MW (Table 7). In contrast, phenyl groups are found to reduce silsesquioxane’s solubility in scCO₂.

Table 7. Solubility Increment of Silsesquioxanes over PDMS.

	density (g/cm3)	MW (g/mol)	Ms (mol/l)	ΔGsolv (j/mol)	ΔG1 (j/mol)	Ssilsesquioxane/SPDMS
silsesquioxane	1.2761	537	2.4	427	–194	1.20
PDMS (n = 5)	0.9755	533	1.8	695	283
octaphenyl-silsesquioxane	1.361	1034	1.3	959	–531	0.88
PDMS (n = 11)	0.9755	978	1.0	979	408

It is observed that polar groups (e.g., Si–O) are beneficial for reducing ΔG_solv; nonetheless, having polar groups on the external part of the molecule could be detrimental to their solubility as they increase intermolecular interactions. By increasing polar groups within the internal part of the molecule while having non-polar groups (e.g., methyl) in the outer layer of the molecule, reducing intermolecular interactions, solubility is enhanced. Due to this, silsesquioxanes are predicted to be more soluble than linear PDMS, the leading CO₂ thickening polymer so far,⁴² and functional silicones. Methyl silicone resins also have good rheological properties, commercial availability, non-reactivity, and a moderate cost.

Viscosity Measurements Using the Rolling Ball

Solubility in scCO₂ and viscosity enhancement are the two fundamental properties looked for in CO₂ thickeners. Computational methods can be used to understand solvation and solubility in order to do a fast additive screening. Unfortunately, state-of-the-art computational (molecular dynamics) viscosity calculations for these types of systems are not as reliable. Therefore, solution viscosities of the narrowed-down candidates were measured directly in the laboratory through rolling ball experiments, which provide not only direct viscosity measurements but also indirect qualitative information of solubility and quickness of the solute–solvent mixture through the time taken to stabilize measurements. Unfortunately, we were not capable of conducting direct visual observation of the mixtures due to the lack of availability of the appropriate equipment. Further research utilizing windowed cells should be carried out in future work to verify the occurrence and long-term stability of a single phase in order to corroborate the findings presented in this paper.

As previously stated by the solubility screening, silicones with branched/cage-like structures with methyl substituent groups appear to be the most promising candidates. We continued by measuring CO₂ with methyl silicone resin mixture viscosity and compared it to PDMS-based nanofluids. In order to compare thickening capability, we prepared nanofluids with two linear silicones of different MWs and increasing concentrations of hydrophobic silica nanoparticles (Table 8). Viscosity measurements of commercial silicone resin and PDMS (with and without nanoparticles) dispersed in scCO₂ were tested in a rolling ball apparatus at 180 bar and 55 C and calculated using eq 16.

Table 8. Thickened CO₂ Viscosity Measured at 55 °C and 180 bar.

additive	type	silicone (mg)	NP (mg)	concentration (m/m %) in CO2	viscosity (cp)
1	pure CO2				0.0662
2	AK 12,500	720	80	5.60	0.3
3	AK 12,500	560	240	5.60	unstable
4	AK 60,000	800	0	5.60	0.27
5	AK 60,000	760	40	5.60	0.38
6	AK 60,000	720	80	5.60	0.54
7	AK 60,000	560	240	5.60	unstable
8	AK 60,000 (without toluene)	950	50	6.90	0.5
9	KX resin	1000	0	6.90	0.25
10	KX resin	900	100	6.90	0.24
11	NPs (with toluene)	0	650	4.50	unstable

Within the MW range of these experiments, the viscosity of the CO₂-based nanofluid increased with the linear polymer’s MW as well as with nanoparticle concentration. In the case of resins, nanoparticle addition had an opposite effect on viscosity. This could be due to the reduction in the overall resin concentration. Nanoparticles alone, without the addition of polymers, did not significantly increase the mixturés viscosity and were unstable. It appears that while nanoparticles do not have a direct effect on the solution’s viscosity, they enhance the thickening capacity of PDMS by aiding the creation of networks capable of further increasing viscosity. Due to the structure of resins, nanoparticles appear not to aid the formation of networks and have no significant effect on viscosity.

All readings from linear silicones with and without nanoparticles (additives 2–8, Table 8) required hours or even days of rocking at high temperatures (80–90 °C for mixing, which was further lowered to reach experimental conditions) to stabilize, even with large concentrations of co-solvent. Increasing MW and nanoparticle concentration also affected the difficulty of stabilizing measurements as compound 6 took the longest to stabilize. Since PDMS additives required such long times to stabilize, even though some eventually showed steady readings, their long-term stability should be further studied. Also, the nanofluid additive formed clumps in the apparatus when the gas was released and the pressure dropped, leading to doubts on their stability at lower pressures (e.g., within production wells or their vicinity). Larger concentrations of nanoparticles lead to higher formation of clumps in the apparatus. This may be due to the fact that higher concentrations of nanoparticles increase the probability of aggregation.⁶³ On the other hand, for methyl-silicone resins [additives 9 and 10 (Table 8), which are analogues of compound 11 (Table 6)], viscosity measurements stabilized very fast (within seconds) without the need of rocking or increasing the system temperature and showed no signs of clumping as the gas was vented from the apparatus. As silicone resins stabilized significantly faster than linear PDMS, even with a lower co-solvent concentration, it qualitatively implies that they mix more rapidly and are significantly more soluble in scCO₂ than the linear PDMS. This is aligned with the findings of the QM simulations, where the higher degree of Si–O bonds reduced the solvation free energy of silicone resins, while the outer methyl/methyl-siloxy groups aid the intermolecular repulsion, improving their solubility. It is also notable that the silicone resin showed a similar viscosity increment to linear silicones (AK 60,000) while having over 5 times lower MW. In addition, the viscosity effect of PDMS and nanoparticles (additive 5) decreased with temperature, reaching 0.27 cp at 68 °C and 0.23 cp at 90 °C. On the other hand, the viscosity of resin-thickened CO₂ was very stable with temperature, decreasing only down to 0.23 cp at 135 °C from 0.25 cp at 55 °C (Figure 5).

Figure 5.

Viscosity of thickened CO₂ with nanofluids and resins at different temperatures. (●) represent silicone resin (additive 9 as numbered in Table 8), and ( ) represent PDMS with 5% NP (additive 5 as numbered in Table 8).

Therefore, resins attained the targeted range of viscosities analyzed in previous studies,³² which would ensure miscible conditions (with a moderate pressure drop) and optimize volumetric sweep efficiency. Higher CO₂ viscosities, than targeted, would lead to a significant pressure drop in the reservoir which could endanger microscopic sweep efficiency as the system falls below minimum miscibility pressure. The good rheological properties, even at high temperatures, and the enhanced solubility of silicone resins confirm that they are better CO₂ thickeners than PDMS (even when nanoparticles are added to the linear silicones)

While using resins, it is advisable to consider their size in comparison to the reservoir’s rock pore throat diameter. The relatively low MW of the Silres KX resin would ensure compatibility with most reservoir rocks and achieve appropriate viscosity increments for low- to medium-permeability reservoirs. Nonetheless, larger-MW silicone resins may be used in higher-permeability reservoirs, where more viscous CO₂ may be required, as they have larger pore throat diameters.

Resins can also have a significant impact in shale reservoirs (shale EOR and dry-fracking) where the viscous fluid is meant to travel through fractures and small pore throat diameters are not a limitation. Therefore, higher-MW silicone resin polymers can be utilized since the size of the resin would not be an issue. In the case of unconventional EOR, the thickened gas could enhance conformance through the fractured network, while only neat CO₂ (no polymer) would enter the matrix.

While bibliography suggests the use of a co-solvent to increase the solubility of PDMS,⁹ we observed that the used PDMS and nanoparticles were sufficiently soluble in scCO₂ (additive 8, table 8). This may be due to the use of a lower-MW silicone than previously used in other papers. However, like with all linear PDMS additives, it required rocking for long periods at high temperatures to stabilize.

We found that at high nanoparticle concentrations, nanoparticles in both toluene and PDMS were unstable. While the fluid viscosity was apparently increased, the readings were not even and therefore unreliable. It was later confirmed that the nanoparticles coalesced and agglomerated, forming a gel-like fluid that obstructed the viscometer’s inner tube. It was also observed that this phenomenon increased as a function of time. While this could be attributed to the nanoparticle concentration and type, it is suggested to study nanoparticle behavior for each specific case taking all conditions (e.g., lower pressure and temperature at producer wells) into consideration.

Conclusions

In this paper, a novel approach for CO₂-philic thickener design was developed. Solubility comparison from QM calculations using an implicit solvent model of several PDMSs, functional linear silicones, and silsesquioxanes was used to screen candidates and further understand solubility mechanisms. Subsequently, the viscosities of CO₂ solutions with linear silicones and resins with the addition of nanoparticles were measured using a rolling ball apparatus. Effective thickeners were developed in a more efficient manner, achieving a target viscosity of 0.25–0.5 cp, which is believed to be optimal for many CO₂ EOR implementations.

The QM solvation model was shown to be a suitable method for fast screening of soluble compound candidates by determining relative solubility in scCO₂ prior to laboratory testing, significantly reducing the time of polymer design. Computational methods allow for flexibility in the molecular design and do not require the synthesis of every candidate. Candidates’ solubilities can be further understood and compared using available polymer/monomer data. Whenever reliable vapor pressures were not available, we introduced a method for estimating polymer solubility in CO₂ by calculating ΔG_solv and the solvation free energy of the candidate in its liquid (ΔG₁^○).

Different silicone-based polymers (with addition of toluene) may serve as useful CO₂ additives and help disperse PDMS-coated silica nanoparticles. Nanoparticles appear to enhance PDMS capacity to thicken CO₂, although the same results were not observed when added to silicone resins.

Methyl silicone resins were found to be efficient CO₂ thickeners as they are more soluble and have better rheological properties than linear PDMS. They have a higher impact on solution viscosity than linear PDMS, achieving target viscosities at a lower MW and at a wide range of temperatures. Not only they are better thickeners but also silicone resins have a low cost and are commercially available, making them an economically viable solution.

This opens the door for future research with different types and MWs of silicone resins. As unconventional resources are not limited by small pore-throat diameters in the fractures, significantly higher-MW resins could also be used to control CO₂ viscosity in shale EOR or dry-fracking operations. While promising, further research in windowed vessels should be carried out to further validate the solubility and stability of resins and PDMS nanofluids in scCO₂. Further core flood experiments would also be required in order to understand rock–fluid interactions such as polymer adsorption and apparent viscosity in different porous mediums.

The authors declare no competing financial interest.