Phase Behavior and Thermodynamic and Rheological Properties of

Article pubs.acs.org/IECR

Phase Behavior and Thermodynamic and Rheological Properties of Single- (SDS) and Mixed-Surfactant (SDS + CAPB)-Based Fluids with 3‑Methylbutan-1-ol as the Cosurfactant and Pine Oil as the Organic Phase Atrayee Baruah,* Geetanjali Chauhan, Keka Ojha, and A. K. Pathak Department of Petroleum Engineering, Indian School of Mines, Dhanbad, Jharkhand 826004, India ABSTRACT: The rheological properties of viscoelastic surfactant (VES)-based gels prepared from a single surfactant (sodium lauryl sulfate) and mixed surfactants (cocamidopropyl betaine and sodium lauryl sulfate) are characterized and interpreted in detail with the addition of alkali. The phase diagrams were prepared to identify the gel region. These were pseudoplastic fluids with shear-thinning nature. VES fluids prepared from mixed surfactants consisting of cocamidopropyl betaine and sodium lauryl sulfate presented better rheology as analyzed. The effect of the addition of nanoparticles to this system was also studied in detail for enhancement of the thermal stability. A dynamic rheology test was also conducted to show enhancement of the storage and loss modulus with the addition of alkali and nanoparticles. A miscibility test was conducted to show the miscibility of the prepared gel with oil and water because it is one of the properties of fracturing fluid used to clean the postfractured formation.

1. INTRODUCTION Hydraulic fracturing is one of the stimulation techniques that is used to increase the well productivity of tight or damaged formations in the reservoir by pumping fluid at a relatively high pressure to create fractures and keep them open with solid particles after a fracturing job.1,2 Polymer-free viscoelastic surfactant (VES)-based fracturing fluids have recently gained great importance in the petroleum industry because of their sufficient viscoelasticity to create fractures in the reservoir, and these have good proppant-transporting capacity.3 Surfactantbased fluids are considered clean gels because they break easily by contacting reservoir fluids, which leads to the absence of insoluble residues after fracturing of tight and damaged reservoirs.4−6 These fluids exhibit excellent rheological properties and provide many benefits with high conductivity, low formation damage, and the same fracturing extent at a relatively low concentration unlike polymer-based fluids. VES fluids provide a maximum fracture length and a minimum fracture height compared to polymer-based fluids.7−9 The general advantages of VES fluids include ease of preparation with fewer number of chemicals and equipment required at the well site compared to conventional fluids, no requirement of polymer hydration, cross-linkers, breakers, or other chemical additives, high fracture conductivity and these fluids are able to transport proppants at a relatively lower viscosity, so a reduced friction pressure is achieved during pumping.3,10 VES fluids are composed of low-molecular-weight surfactants that can form long elongated micellar structures that contribute to the viscoelastic behavior in order to increase the fluid viscosity.11 The molecular weight of surfactant molecules is usually less than 1000, while that for the polymer is approximately 2 million.12 These surfactant molecules consist of a hydrophilic head and a long hydrophobic tail.13 The hydrophobic group consists of a hydrocarbon chain with 10−20 carbon atoms. Surfactants are generally classified based on the © XXXX American Chemical Society

charge of the hydrophilic head, which includes anionic (negatively charged), cationic (positively charged), nonionic (uncharged), and zwitterionic (both negatively and positively charged, with zero net charge) surfactants.14,15 The physical nature of the surfactants depends on its tail length, branching of the tail, number of double bonds, and cis/trans configuration.3 The surfactant molecules are like monomers, and the volume ratio of the surfactant tail group to the headgroup is defined as the micelle packing ratio. When the packing ratio is below onethird (headgroup volume dominant), the packing arrangement of the surfactant molecules will produce spherical micelles. If the value is from one-third to one-half (headgroup volume moderately to slightly dominant), the surfactant molecules will arrange into long cylindrical micelles.16 Surfactants with higher packing ratio tend to form larger aggregates of wormlike micelles.17 Microemulsions are isotropic, thermodynamically stable, and low-viscosity solutions of oil and water that are stabilized by surfactant molecules.18,19 The main role of the surfactant is to reduce the interfacial tension between oil and water.20 In the case of ionic surfactants, they alone are unable to reduce the oil/water interfacial tension sufficiently to enable formation of the microemulsion, so cosurfactants are included in the systems that serve to reduce the repulsive interactions between the charged headgroups. This system can be represented in pseudoternary diagrams, which can be easily built and visualized. In order to facilitate their representation, two Special Issue: Energy System Modeling and Optimization Conference 2013 Received: March 7, 2014 Revised: April 28, 2014 Accepted: May 10, 2014

A

dx.doi.org/10.1021/ie500987y | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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out in the presence of distilled water and diesel oil, which is required to clean the formation after fracture.

constituents, namely, surfactant and cosurfactant, are kept in a fixed proportion, forming a “pseudoconstituent”.21 Various surfactant-based fluids have been developed with time. Kalur and Raghavan revealed interesting rheology and phase behavior of the sodium oleate surfactant. This surfactant self-assembles into wormlike micelles in the presence of either an inorganic salt, which screens the intermicellar electrostatic interactions, or a binding salt, which reduces the micellar surface charge.22 A zwitterionic surfactant fluid was utilized by Sullivan and his group in high-permeability formations that provided low friction pressure, stable proppant transport, and high proppant pack conductivity.14 An anionic surfactant fluid was developed by Welton et al. that formed less undesirable emulsions that did not adversely alter the wettability of sandstone formations like the cationic surfactants. This fluid also presented improved fluid loss characteristics.23 Wormlike micelles composed of Tween 80 and Brij are highly responsive to bmimBF4, which is an ionic liquid and was utilized by Guo and Guo.24 Khair and co-workers developed a new anionic surfactant-based fracturing fluid that had easy preparation, good viscosity, low frictional resistance, good stability, and no plastic residue at 30−100 °C. The fluid enabled good suspension and transportation of proppants at relatively lower viscosities than the conventional ones. The developed fluid was sensitive to component concentrations.10 Thampi et al. did a comparative study on the effect of branched alcohols (2-methylbutan-2-ol and 3-methylbutan-1-ol) on the phase behavior and physiochemical properties. Better results were obtained from 3methylbutan-1-ol as the cosurfactant in the preparation of a VES-based gel. The developed gel showed an elastic modulus and viscosity much greater than the threshold value requirements for the fracturing treatment.25 Rao et al. formulated an ionic liquid-in-oil microemulsion that exhibited stability over a wide range of temperatures (from 278 to ≥423 K). These hightemperature-stable microemulsions are suitable for a wide field of applications.26 Wormlike micellar growth with high viscoelastic properties has been reported in an anionic and mixed-surfactant systems consisting of cationic−anionic and ionic−zwitterionic surfactants.27,28 In our previous studies, an oil/water microemulsion gel domain was elucidated for an anionic surfactant (SDS)/ isoamyl alcohol/pine oil/water system at a cosurfactant-tosurfactant (C/S) ratio of 0.5, and rheology of viscoelastic gel samples, its proppant carrying capacity, and break test was carried out.29 In this paper, we have reported a comparative rheology study on the VES-based gels prepared from singlesurfactant (anionic, SDS) and mixed-surfactant (zwitterionic, CAPB, and anionic, SDS) systems. Zwitterionic surfactants have strong interactions or complex formations with anionic surfactants in the presence an aqueous medium, so enhancement of the rheology of VES fluids for a mixed-surfactant system with respect to a single-surfactant system was investigated. Pseudoternary phase diagrams were plotted to identify the gel region of the two systems. The performances of the gel as a function of the type of surfactant used, surfactant concentration, temperature, alkali concentration, and addition of nanoparticles are presented. The fluids prepared had pseudoplastic behavior and exhibited a shear-thinning nature. The fluid had easy formulation of preparation and exhibited good viscosity in the presence of an alkali medium under high shear rate and temperature conditions up to 60 °C. The effect of the addition of nanoparticles on the thermal stability was also determined. The miscibility test of the VES fluid was carried

2. EXPERIMENTAL SECTION 2.1. Materials. Sodium lauryl sulfate [sodium dodecyl sulfate (SDS), CH3(CH2)11OSO3Na], an anionic surfactant of purity greater than 85%, was procured from Loba Chemie Pvt. Ltd., Mumbai, India. Liquid cocamidopropyl betaine (CAPB; [[3-(dodecanoylamino)propyl]dimethylammonio]acetate, C19H38N2O3), a zwitterionic surfactant, consists of both a quaternary ammonium cation and a carboxylate and was obtained from Alpha Chemicals Pvt. Ltd., Navi Mumbai, India. All surfactants were used as received. The cosurfactant 3methylbutan-1-ol (isoamyl alcohol) of greater than 98% purity was purchased from Merk Specialties Pvt. Ltd., Mumbai, India, and was used without any purification. Pine oil was used as the organic phase. Distilled water was used for sample preparation. Sodium hydroxide (NaOH) of greater than 98% purity was supplied by Loba Chemie Pvt. Ltd., Mumbai, India. Silicon dioxide (SiO2) nanoparticle with a size of 15 nm of 99.5% purity was procured from SRL Pvt. Ltd., Mumbai, India. 2.2. Pseudoternary Phase Diagram. The pseudoternary phase diagrams were constructed using a water titration method at a temperature of 22 ± 1 °C. The C/S ratio was fixed at 1:2 by weight in both systems. For each ternary phase diagram, the ratios of oil to the mixture of surfactant and cosurfactant were varied from 1:9 to 9:1 by weight. The mixtures of surfactant, cosurfactant, and oil at their weight ratios were diluted with the dropwise addition of water and were stirred in a magnetic stirrer at a moderate speed. With the addition of 1 mL of water, the mixture system was equilibrated for visual assessment. Phases were identified by visual observation and were classified according to Winsor’s classification (WI, WII, WIII, and WIV). The addition of 1 mL of water was continued until a WII fluid system was obtained, which is basically a two-phase system consisting of a microemulsion and a water-rich region. Finally, a ternary phase diagram was constructed by plotting the weight percentages of C/S, oil, and water. 2.3. Preparation of VES Samples. The VES-based gel systems were prepared, namely, from SDS alone and from a combination of CAPB with SDS. In all of the systems, the water-to-oil (W/O) ratio was fixed at 3:1 by weight. The total C/S ratio in the system was fixed at 1:2 by weight. In the case of a mixed-surfactant system, the proportion of surfactants (S) is in the ratio of 1:2 (CAPB/SDS) by weight. The various VES samples were prepared by mixing distilled water, cosurfactant, and pine oil initially because these are in the liquid phases. The surfactant was added slowly to the stirred liquid mixture in order to form a homogeneous gel and avoid the formation of lumps in the gel. The gels were prepared at a temperature of 22 ± 1 °C. All measurement was done on a weight basis. 2.4. Rheological Measurements. Viscosities of samples were measured using a Parr Physica US 200 rheometer (Anton Parr, Graz, Austria) in a cone-and-plate geometry with the cone of 50 mm diameter and a cone angle of 2°. Viscosity measurements were done with respect to the shear rate and temperature. The test temperature was varied from 30 to 60 °C. The sample required for testing was about 0.5 mL. Frequency sweep measurements were performed using a modular compact rheometer, MCR-302 (Anton Paar, Austria), in order to evaluate the characteristics of a viscoelastic material. Cone-and-plate geometry was used for testing the samples. The cone (CP 50-1/Q1) had a diameter of 50 mm and a cone angle B



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of 1°. About 0.5 mL of the sample is required for testing purposes. 2.5. Miscibility Tests. Miscibility tests of the prepared gels were carried out in the presence of distilled water and diesel oil. These tests were carried out by mixing gel with water or oil in different proportions. The viscosities of the solutions were tested in a Cannon Fenske viscometer by using different orifice diameters as required (25, 50, 150, 200, and 300 mm), which gave the kinematic viscosity in centistokes (cSt). The densities of the fluid were determined to convert the values of the kinematic viscosity (cSt) to absolute viscosities in centipoise (cP). The gel-to-water/oil ratio was fixed at 3:1, 2:1, 1:1, 1:2, and 1:3. The test temperatures were varied from 30 to 60 °C. The tests were performed to determine the miscibility of the gel in water and oil, which could help in the approximation of the breaking characteristics of the gel, thus giving a prediction in recovery of the fracturing fluid after a fracturing job is completed.

3. RESULTS AND DISCUSSION 3.1. Phase Diagram Studies of Single- (SDS) and Mixed-Surfactant (CAPB + SDS) Systems. The phase diagram presentation of the quaternary systems with isoamyl alcohol as the cosurfactant and pine oil as the organic phase is shown in Figure 1a,b at a C/S of 1:2 (0.5). At high concentration of the surfactant, a solid−liquid (SL) biphasic region exists along with a semitransparent solution. At lower surfactant concentration near the water-rich region, a threephase (3E) region exists in the SDS system. In this region, a middle milky emulsion phase along with oil and water phases exists. A two-phase (2E) region exists in all of the systems, which consist of a milky emulsion with excess water. A singleemulsion (1E) region exists and is characterized by a milky liquid. A microemulsion phase (WIV) exists in both systems that is a transparent single isotropic liquid. Near this region, a clear, transparent, and highly viscous fluid mixture region exists that is classified as a gel (VME). A gel is classified as a viscous mixture that does not show a change in the meniscus after tilting to an angle of 90°.25 A viscous, white fluid (WV) region exists near the VME region of the ternary phase diagrams. The VME region is of interest in our present study for the preparation of a VES-based fracturing fluid. The transparent single isotropic microemulsion region (WIV) corresponds to an area of mutual solubility in both systems consisting of single or mixed surfactant/cosurfactant/ pine oil/water, and it occurs in the water-rich domain. Microemulsions in this region form spontaneously at a temperature of 22 ± 1 °C when their components are brought into contact. The main factors determining the range of formation of a microemulsion zone are the physicochemical properties of the oil and aqueous phases, types of surfactants used, existence of a very low surface tension at the oil−water interface, presence of a highly fluid interfacial film of surfactant, and last penetration and association of oil molecules with the interfacial surfactant film.30 The alkanol molecules remain distributed between the aqueous phase and interface. At an optimum level of C/S in both systems, the cosurfactant moves into the cavities between the surfactant molecules, and the microemulsion formed has maximum solubilization. It is found that isoamyl alcohol alone is sparingly soluble in water in the absence of any surfactant, but with the addition of single or mixed surfactant, its solubility in water increases. It is assumed that whenever the concentration of surfactants (single or

Figure 1. Pseudoternary phase diagrams for (a) a SDS/isoamyl alcohol/pine oil/water system and (b) a CAPB + SDS/isoamyl alcohol/pine oil/water system.

mixed) is higher than the critical micellar concentration, isoamyl alcohol is solubilized in the interface and/or at the interior of the micellar aggregates.31 All of the surfactants and alcohol molecules form micelles in the presence of pine oil and an aqueous phase. Thus, a single-phase microemulsion is formed upon the sufficient addition of amphiphiles (surfactant plus alcohol). The growth of micellar formation also depends on the hydrophilicity and geometric size of the surfactant headgroup.32 For the SDS system, the gel region in the ternary diagram starts from 26% C/S. In the case of a CAPB + SDS mixed-surfactant system, the gel region starts from 24% C/S. 3.2. Rheological Properties of a Single-Surfactant (SDS) System. Measurement of the rheological properties is one of the powerful tools to characterize the properties of different surfactant solutions, which in many cases are nonNewtonian. Figure 2 shows variation of the shear stress (τ, Pa) and shear viscosity (η, cP) as a function of the shear rate (γ, s−1) for the three fluids prepared from a single-surfactant (SDS) system of 28, 30, and 32% C/S concentration. The fluid basically interprets a non-Newtonian fluid, and the shape of the C



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Table 1. Values of n and k of a Single-Surfactant (SDS) System value of the flow behavior index, n

value of the consistency index, k

serial no.

% C/S

theoretical

experimental

theoretical

experimental

1 2 3

28 30 32

0.5084 0.4935 0.4795

0.5056 0.4711 0.4667

0.3029 0.3795 0.4688

0.3334 0.3681 0.5227

Figure 3. Variation of the viscosity, η, as a function of the temperature, T, at 100 s−1 shear rate.

shows variation of the viscosity (cP) as a function of the temperature (°C) at a shear rate of 100 s−1. The figure depicts that the viscosity decreases with an increase in the temperature and a decrease in the surfactant concentration. These fluids are composed of rod micelles, and whenever the concentration of the surfactant exceeds a critical value, these micelles entangle and form network wormlike micelles. 32% C/S always presented a higher value of viscosity at any test temperature and shear rate because the growth and entanglement of wormlike micelles are stronger than the other fluids because of increased concentration of the surfactant, due to which it is able to resist higher temperature. Thus, with an increase in the surfactant concentration at a given temperature, the micellar aggregation number (N) increases, and N decreases with an increase in the temperature, a behavior that is usual for ionic surfactants.33 Figure 4 shows the effect of the addition of alkali NaOH on the 32% C/S surfactant-based fluid at 100 s−1 shear rate. The figure depicts that, with the addition of NaOH in the fluid, the viscosity of the fluid increases for any test temperature. The 0.1% NaOH-based 32% C/S VES gel exhibited high viscosity at all temperatures. Because of the electrostatic interactions between the surfactant headgroups, the growth of micelles in the solution is limited, due to which strong threadlike micelle formation is low.34 With the addition of counterions to the solution, electrostatic repulsive forces between the anionic surfactant molecules in a micelle are reduced, thus promoting micelle growth. The addition of alkali greatly screens the headgroup repulsive forces between surfactant molecules. As a result, long, flexible anionic wormlike micelles are formed in the solution, which helps in the entanglement of micelles into a transient network and imparts high viscosity to the sample. Thus, the longer the micelles, the higher the relaxation time

Figure 2. Variation of the (a) shear stress, τ, and (b) shear viscosity, η, as a function of the shear rate, γ, for three samples prepared from a single-surfactant (SDS) system at 50 °C.

flow curves of Figure 2a is basically represented by a power-law equation (Ostwald−de Waele equation): ⎛ dv ⎞ n τ = k⎜ ⎟ ⎝ dy ⎠

(1) −1

where τ is the shear stress (Pa), dv/dy is the shear rate (s ), k is the consistency index in N·s/m2, and n is the flow behavior index, which is dimensionless. Equation 1 was used to find the experimental values of n and k. All three fluids had n values of less than 1 and were almost equivalent to the theoretical values, as tabulated in Table 1. Because the value of n is less than 1, these fluids were pseudoplastic in nature, as defined by a powerlaw equation, where the viscosity of the fluid decreased with an increase in shear. These three fluids consisting of SDS/isoamyl alcohol/pine oil/water indicate a pseudoplastic fluid, as interpreted in Figure 2a, where the graph plots are convex downward and are said to be shear thinning, as shown in Figure 2b, where the viscosity decreases with an increase in the shear rate, which is a typical character of a fluid to have a viscoelastic property. Figure 3 D



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Figure 4. Variation of the viscosity, η, as a function of temperature, T, for a 32% C/S VES fluid with the addition of 0%, 0.05%, and 0.1% NaOH at 100 s−1 shear rate.

and zero-rate viscosity of the solution. So with strongly binding counterions, the resulting surfactant solution resembles a polymer solution with viscoelasticity.35−38 Figure 5 shows variation of the viscosity with increasing shear rate for different temperatures for a 0.1% NaOH-based 32% C/

Figure 6. Variation of the (a) shear stress, τ, and (b) shear viscosity, η, as a function of the shear rate, γ, for samples prepared from a mixedsurfactant (CAPB + SDS) system at 50 °C.

Table 2. Value of n and k of a Mixed-Surfactant (CAPB + SDS) System value of the flow behavior index, n

Figure 5. Variation of viscosity, η, as a function of the shear rate, γ, for a 0.1% NaOH-based 32% C/S VES fluid.

S VES fluid. At all temperatures, the fluid exhibited a shearthinning nature because the viscosity decreased with increasing shear rate and with increasing temperature. The decrease in the viscosity indicates that the network structure of the wormlike micelles is destroyed with shortening of the micelles, which occurs even in the presence of an alkali medium at increased temperature.39 3.3. Rheological Properties of a Mixed-Surfactant (CAPB + SDS) System. The rheological results of a mixedsurfactant system consisting of CAPB and SDS are presented in Figure 6a,b. The fluids prepared from this system also indicated a non-Newtonian behavior. By using eq 1, the experimental values of the flow behavior index, n, and consistency index, k, were determined and summarized in Table 2. The values were almost similar to the theoretical values, having n values of less than 1, thus indicating a pseudoplastic fluid.

value of the consistency index, k

serial no.

% C/S

theoretical

experimental

theoretical

experimental

1 2

28 30

0.3014 0.2335

0.308726 0.225146

2.1555 3.7925

2.302492 3.977085

Figure 6a shows variation of the shear stress (τ) with the shear rate (γ) at 50 °C, where the curves are convex downward, indicating a pseudoplastic fluid. Figure 6b shows variation of the viscosity as a function of the shear rate at 50 °C, indicating that the viscosity decreases with an increase in the shear rate. The decrease in the viscosity is due to a structural breakdown of the existing intermolecular interactions between wormlike micelles in the presence of high shear rate. Figure 7 shows variation of the viscosity as a function of the temperature for 28% and 30% C/S fluids. The higher the concentration of surfactant in the solution, the higher the value of the viscosity for any temperature. In the mixed-surfactant (CAPB + SDS) system, mixed micelles are formed in aqueous solution. The association of the surfactants is basically due to E



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Figure 8. Variation of the viscosity, η, as a function of the temperature, T, for single- and mixed-surfactant systems with the addition of nanoparticles at 100 s−1 shear rate.

Figure 7. Variation of the viscosity, η, as a function of the temperature, T, at 100 s−1 shear rate for a mixed-surfactant (CAPB + SDS) system.

electrostatic attraction of the hydrophilic part between the cationic portion of the zwitterionic surfactant and the anionic portion of the dodecyl sulfate ion in the mixed systems.40 Long micelles are formed by the interaction of zwitterionic (C19) and anionic (C12) surfactants. In addition to neutralization of the micelle charge, in the presence of an alkali medium, the counterions screen the repulsive forces between the charged heads of the anionic surfactants, thus promoting micellar growth. This contributes to the formation of longer-length micelles having longer relaxation time and increased zero-shear viscosity. The zwitterionic surfactant thus acts as a booster of the anionic surfactant, which results in increased aggregation number and packing parameter of the micelles, which allows the formation of spheres to wormlike micelles, contributing to a viscoelastic sample.41 The effect of the addition of alkali to the 30% C/S mixed-surfactant system is also shown, which depicts that, with the addition of alkali, micellar growth is facilitated and a 0.1% NaOH-based 30% C/S VES fluid presented a high value of viscosity. 3.4. Effect of the Addition of Nanoparticles. The effect of the addition of nanoparticles to the mixed surfactant was studied for enhancement of the thermal stability. Nanoparticles used in the study include SiO2. Figure 8 shows the dependence of the viscosity on the temperature of single-surfactant (SDS), mixed-surfactant (CAPB + SDS), and nanoparticle-induced mixed-surfactant systems. The values of the viscosity of the mixed-surfactant system are higher than those of the singlesurfactant system consisting of only SDS. In the presence of a single-surfactant system, SDS has only C12 atoms, due to which smaller micelles are formed with respect to a mixed-surfactant system. This leads to the formation of a VES fluid having low zero-shear viscosity and relaxation time, which indicates the formation of shorter micelles with respect to a mixed-surfactant system even in the presence of an alkali medium. On the other hand, a mixed-surfactant system has mixed micelle formation of longer length because of interactions of the anionic part of SDS and the cationic part of CAPB. Thus, it is possible to obtain a much higher viscosity by using a mixed-surfactant system.42 The relaxation time increases with an increase in the alkyl chain length of the surfactant, which contributes to an increase in the viscosity of the mixed-surfactant system.43 The figure clearly depicts that, for a mixed-surfactant system of 30% C/S

concentration, a higher value of viscosity is obtained because in the solution SDS and CAPB surfactant molecules interact strongly by the electrostatic attractive forces With the addition of 500 ppm of SiO2 nanoparticles in 30% C/S of a mixed-surfactant system, the viscosity in the fluid is enhanced by two mechanisms. First is the entanglement of micelles and second is the formation of micelle−particle junctions, which effectively join two or more micelles. Thus, nanoparticles get incorporated into micellar solutions by micelle−nanoparticle association such that these particles actively participate in the stronger viscoelastic network, which improves the thermal stability of gels.44 The viscosity−temperature relationship can be expressed by an Arrhenius-type equation. η = A exp[Ea /RT ]

(2)

where η is the viscosity, A is a characteristic constant of the material, R is the universal gas constant having a value of 8.314 J K−1 mol−1, T is the absolute temperature in Kelvin, and Ea is the activation energy in J mol−1.45 Figure 9 shows plots of the logarithm of viscosity versus reciprocal temperature. Linear plots (R2 = 0.9815, 0.9594, and 0.9661) were obtained for the three VES samples for a test temperature of 30−60 °C, which is in agreement with an Arrhenius equation. The values of the activation energy were calculated using the slope value (Ea/RT) from eq 2, and the results are tabulated in Table 3. The nanoparticle-induced 30% C/S mixed-surfactant system presented a low value of the activation energy of 13.336 kJ mol−1 compared to the two other fluids. This low value leads to higher thermal stability of this fluid and the presence of a 3D network of micelles involving strong interactions between the macromolecular aggregates than are present in the other fluids.46 3.5. Characterization of the Viscoelastic Properties. This test includes determination of the storage modulus [G′(ω)] and loss modulus [G″(ω)] with variation in the frequency from 1 to 100 s−1. G′(ω) gives a measure of how elastic or solidlike a material is because elastic materials deform instantly as shear is applied, while G″(ω) gives a measure of how viscous or liquidlike a material is. According to the Maxwell model with a single relaxation time (τ), G′(ω) and F



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Figure 10. Variation of the storage (G′) and loss (G″) moduli as a function of the frequency (ω) of a 0.1% NaOH + 32% C/S singlesurfactant (SDS) system.

Figure 9. Plot of ln(η) (cP) versus 1/T (K).

Table 3. Values of the Activation Energy serial no.

fluid sample

activation energy, Ea (kJ mol−1)

1 2 3

0.1% NaOH + 32% C/S (SDS) 0.1% NaOH + 30% C/S (CAPB + SDS) 500 ppm of SiO2 + 0.1% NaOH + 30% C/S (CAPB + SDS)

21.568 14.333 13.336

G″(ω) are related by a complex modulus G*(ω), which is given by47 iωη G*(ω) = G′(ω) + iG″(ω) = (3) 1 + iωτ where ω is the frequency, η is the viscosity, and τ is the relaxation time, which is defined as the characteristic time at which the structured fluid relaxes back to the equilibrium configuration when disturbed by shear oscillation. This time separates into two regions: (i) For ωτ ≪ 1, the system behaves as a viscous fluid with viscosity η. (ii) For ωτ ≫1, the system exhibits elasticity with a storage modulus independent of the frequency. The G′(ω) and G″(ω) curves intersect at a characteristic frequency, ωR, that is dependent on the type and concentration of the surfactants.48 ωR is approximately equal to the reciprocal of relaxation time (τR), which is related to the average length of the micelles. Thus, the relaxation time is defined as21 ωR τR = 1 (4)

Figure 11. Variation of the storage (G′) and loss (G″) moduli as a function of the frequency (ω) of a 0.1% NaOH + 30% C/S mixedsurfactant (CAPB + SDS) system.

The influences of the type of surfactant system used and the effect of the addition of nanoparticles have been explored by oscillatory shear measurements. From Figure 10−12, it can be seen that both storage (G′) and loss (G″) modulus values are almost independent of the frequency (1−100 s−1), which is characteristic of the gel structure and basically occurs because of enhancement of intramicellar interactions in the gel.21 Also at any given frequency, the storage modulus (G′) always presented a higher value than the loss modulus (G″), indicating the viscoelastic nature of the fluids where elasticity is dominant.49,50 A nanoparticle (SiO2)-induced 0.1% NaOHbased 30% C/S mixed-surfactant (CAPB + SDS) system exhibited higher values of G′(ω) and G″(ω) because, in the presence of a nanoparticle, stronger interactions between the macromolecular aggregates occur, which leads to the formation

Figure 12. Variation of the storage (G′) and loss (G″) moduli as a function of the frequency (ω) of a 500 ppm of SiO2 nanoparticle + 0.1% NaOH + 30% C/S mixed-surfactant (CAPB + SDS) system. G



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of a high-density 3D network of wormlike micelles in the fluid. In all three fluids, no crossover of G′(ω) and G″(ω) was observed within the frequency range under investigation (1− 100 s−1). 3.6. Miscibility Test. A miscibility test was carried out for single- and mixed-surfactant-based systems by mixing the fluid in the presence of either diesel oil or water. It was performed to examine the breaking characteristics of the fracturing fluid. The prepared gels were immiscible with diesel oil in all proportions, while they were miscible with water in all proportions. The viscosities of the mixtures of different ratios of gel and water at different temperatures are summarized in Table 4 for the three different fluids.

zero shear, which indicates that, with an increase in the temperature, the viscosity of the mixture decreases. Higher viscosity values were obtained at 2:1 and 3:1 ratios because the quantity of water was less in comparison to that of the gel, so the gel was not broken but presented a low viscosity at an increased temperature of 60 °C. The nanoparticle-induced 30% C/S mixed-surfactant system always presented a higher value of viscosity in all ratios and test temperatures. This is basically due to a high-density 3D network of micelles in the fluid. The results indicate that the formation water can be used a displacing fluid, or if the VES fluid contacts formation water in the reservoir itself, it will break the VES fluid to lower viscosity, which will help in easy recovery of the fracturing fluid after the job is completed.

Table 4. Values of the Viscosity for Different Ratios of Gel and Water Systems

4. CONCLUSIONS In this work, a comparative study of the rheological properties for single- (SDS) and mixed-surfactant (CAPB + SDS) systems was performed. It was found that, for both systems, with an increase in the surfactant concentration, the viscosity of the fluid system increases. The mixed-surfactant system always presented better rheological properties because of the incorporation of a zwitterionic (CAPB) surfactant, which had greater thermal stability. Better rheological properties can be obtained at lower surfactant concentration in a mixed-surfactant (CAPB + SDS) system than those obtained with high surfactant concentration of a single-surfactant (SDS) system. With the addition of nanoparticles in the mixed-surfactant system, the viscosity of the VES fluid was further enhanced. The prepared VES fluids were miscible with water but immiscible with diesel oil. Thus, formation water can be used as a flush fluid for breaking the high-viscosity fluid, which will help in easy recovery of the fluid after a fracturing job is completed. In summary, we have successfully developed a nanoparticle-induced viscoelastic mixed-surfactant-based fluid of 30% C/S that exhibited high viscosity under high shear rate and a temperature of up to 60 °C.

viscosity, cP temperature, °C

1:3

1:2

1:1

2:1

3:1

0.1% NaOH + 32% C/S SDS

30 40 50 60

0.99 0.92 0.71 0.54

2.70 2.11 1.74 1.06

3.98 3.14 2.97 2.31

32.23 26.17 20.36 14.48

98.23 43.50 30.15 16.44

0.1% NaOH + 30% C/S (CAPB + SDS)

30 40 50 60

1.05 0.95 0.76 0.60

3.11 2.64 1.86 1.28

4.24 3.94 3.43 2.54

36.45 31.10 28.07 18.37

129.00 50.61 38.24 22.62

500 ppm + 0.1% NaOH + 30% C/S (CAPB + SDS)

30 40 50 60

1.20 1.01 0.89 0.71

4.17 3.65 3.17 1.96

5.91 4.35 3.95 3.21

38.23 35.45 29.12 19.54

155.23 78.10 37.23 26.26

sample

The results indicate that the three VES fluids presented a low value of viscosity comparable to that of water after mixing it with water at 1:3, 1:2, and 1:1 ratios at all temperatures. This occurs as the wormlike micelles break into nonviscous, more spherical micelles, which can no longer form a network of micelles.51 Figure 13 shows variation of the viscosity with the temperature for these three fluids at 1:3 ratios of gel-to-water at

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-326-2235484. Fax: +91-326-2296632. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Council of Scientific and Industrial Research, India, for financial assistant [CSIR Project 22 (0625)/13/EMR-II] and the Department of Petroleum Engineering, Indian School of Mines, Dhanbad, India. The authors also acknowledge the Division of Petroleum and Natural Gas, CSIR-NEIST, Jorhat, Assam, India for the help in recording some experimental data in their laboratory.

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REFERENCES

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Figure 13. Variation of the absolute viscosity, η, with temperature, T, for a 1:3 ratio of the gel−water mixture. H



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