Synthesis and laboratory testing of a novel calcium-phosphonate reverse micelle nanofluid for oilfield mineral scale control

Abstract

Mineral scale blockage is a severe challenge to the oil and gas industry. Scale inhibitors are routinely injected (squeezed) into downhole formation to control the scale threat. Other than the conventional aqueous scale inhibitor products, non-aqueous inhibitor packages are more suitable for certain low water cut and water sensitive production wells. In this study, a novel reverse micelle based inhibitor nanomaterial fluid (nanofluid) was prepared to serve as a non-aqueous scale inhibitor delivery vehicle. The nanofluid was prepared by mixing component micelle solutions at room temperature to form scale inhibitor nanomaterials. The physicochemical properties of the prepared inhibitor nanomaterials, morphology, skeletal structure and thermal decomposition, were evaluated by electron microscopy, infrared spectra and thermal gravitational analyses, respectively. The transportability of the inhibitor nanofluid was investigated via column flow-through tests. Results show that the nanofluid is transportable in a calcite medium. Furthermore, preflush solutions can impact the nanomaterial transport behavior and an organic preflush is observed to enhance the nanofluid transport compared with aqueous solution preflush. The potential field application of this reverse micelle inhibitor nanomaterial product was assessed via laboratory squeeze simulation studies. The results suggest that this non-aqueous inhibitor nanofluid exhibits an enhanced performance compared with the conventional acidic pill solution in terms of extending the squeeze lifetime. This is the first report of the synthesis of reverse micelle based scale inhibitor nanofluid and the investigation of the transport and return behavior of this product for the purpose of oilfield scale control.

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Introduction

Inorganic mineral scales (hereafter referred to as scales) are minerals typically formed on a surface due to local saturation with respect to inorganic salts.¹ The major categories of scales encountered in oilfield operations include carbonate (e.g., calcium carbonate) and sulfate (e.g., barium sulfate) scales. Together with hydrate blockage and asphaltene deposition, scale deposition and blockage are the most severe production chemistry and flow assurance related challenges for oil and gas productions, particularly for offshore deepwater operations.² A range of oilfield operational problems can be triggered due to scale deposition and blockage, including pipeline throughput reduction, operational risk increase, corrosion attack, heat transfer impedance and increase in operational costs.³ It was reported that almost 20% of all regional downtime for a major oil company in early 2000 was attributed to scale damage.⁴ In order to control scale damage to oil production facilities, various scale control strategies have been implemented to prevent or delay scale formation. The most common method is to apply scale inhibitor chemicals (inhibitors) to the production facilities of concern via either continuous chemical injection or bull heading through production wells (scale squeeze treatment). Scale inhibitors are a group of chemicals capable of reducing scale formation and precipitation rates by preventing the scale mineral crystal nucleation and crystal growth.^1,2 Generally speaking, there are two major types of scale inhibitors, polymers and non-polymers like aminophosphonates (phosphonates).⁵ If the scale management strategy involves delivering the inhibitors deep into the formation to prevent scale damage inside formation or across well perforations, scale squeeze treatment is the only available option to achieve chemical delivery into formation pore space. Scale squeeze is a well-established procedure for both onshore and offshore scale control.^1,5,6 Normally, a volume of preflush solution is injected prior to the injection of a volume of concentrated scale inhibitor solution (also called “pill solution”) through an oil-producing well into reservoir formation. The pill solution is typically an aqueous solution of inhibitor. The pH of the phosphonate pill solution is normally very acidic due to the presence of strong acid in the product (acidic pill). Subsequently, the injected inhibitor is pushed deeper into the reservoir by another volume of fluid (also called overflush fluid). Upon completion of reservoir overflushing, the oil-producing well will be shut-in for a period of time to allow the delivered inhibitors to affix to the surface of formation materials. Following the shut-in period, the well will be put back on production and the reservoir fluids (hydrocarbons and formation water) will flow over the surfaces of reservoir materials into the well. Alongside the reservoir fluids production, the injected scale inhibitor will be gradually released into the produced water and flows into the production well to inhibit scale deposition (also called inhibitor return). Typically, the inhibitor pill solution is an aqueous solution of either phosphonate based inhibitor or polymeric inhibitor. However, in the past two decades, there is a growing body of evidences suggesting that aqueous scale squeeze treatment might not always be the most suitable option, particularly to low water cut and water sensitive fields.^1–11 Water cut is the ratio of the volume of water produced to the volume of total liquids produced from a well. Certain field conditions favor application of a non-aqueous based treatment due to the concerns of formation damage, hydrate blockage and gas lifting requirement.^1,2 In general, the benefits of a non-aqueous treatment include minimizing water related formation damage (e.g., well productivity impairment, clay mobilization or swelling and pore throat constriction), reduced process upset, expedited well clean up time and possibly extended squeeze lifetime.^7,8 The squeeze lifetime is the duration of a squeeze treatment protection time before inhibitor return concentration drops below the minimum required concentration.¹ Additionally, there is a growing demand of carrying out squeeze treatment prior to initial water breakthrough (preemptive squeezing) for deepwater subsea satellite development. It is not technically feasible or financially viable to conduct preemptive squeeze into dry or low water cut subsea wells.⁹ The scale inhibitors in non-aqueous packages are usually based on conventional phosphonate and polymeric scale inhibitor species.⁹ The active scale inhibitors in the non-aqueous packages are allowed to partition into the aqueous phase on contact with the aqueous produced water following the squeeze treatment.^3,10 Once the non-aqueous inhibitor molecules partition into the aqueous phase, these molecules are expected to demonstrate inhibition efficiency and retention properties similar to those of the generic water-based products.¹⁰ It is desirable to prepare a non-aqueous inhibitor package which can be delivered deep into the formation without causing formation damage; once these non-aqueous inhibitor materials are delivered into the target formation zone, they can be transferred from non-aqueous phase through a combined hydrolysis and partition process into aqueous phase after squeeze treatment to control scale deposition as the water cut increases.

As summarized by Kelland,² a variety of non-aqueous scale inhibitor compositions are available including: oil soluble inhibitors, totally water-free materials in organic solvent blends; invert emulsion, microemulsion or nanoemulsions and encapsulated products. Microemulsions are thermodynamically stable microdispersions and formed by mixing oil and water and typically surfactants, with little or no energy input owing to their thermodynamic stability. In other words, microemulsions can form spontaneously in the presence of surfactants.¹¹ Generally there are two types of microemulsions: oil-in-water (micelle) and water-in-oil (reverse micelle). The required condition for microemulsion to form is a low interfacial tension between the oil and water so that dispersion forces can overcompensate the remaining interface free energy.¹² The presence of surfactant is mainly to reduce interfacial tension. However, as pointed by Collins et al.,¹¹ it is often necessary to add a second cosurfactant (e.g., nonionic surfactants) together with the primary ionic surfactant. The added cosurfactant will also serve to reduce the microemulsion system viscosity and to increase the entropy of the dispersion. A number of microemulsion scale inhibitor products have been synthesized.^2,5–11,13 For instance, Miles et al.¹³ reported the formulations of a range of water-in-oil microemulsion based inhibitor deliver systems by use of complexing agents. Investigation of these materials focused on physicochemical properties, phase behavior, coreflood tests and inhibitor desorption. Additionally, modeling studies have been undertaken to compare non-aqueous and aqueous scale inhibitor squeeze treatments. These modeling studies focus on understanding the impacting factors on squeeze treatment lifetime and wellbore friction and also the impact of surfactant preflush.^4,14 Ideally, the inhibitor-containing microemulsions are expected to be deployed deep into the formation while maintaining their stability during pill injection and subsequent overflush stages. These delivered inhibitor microemulsions should be tuned to break post squeeze treatment at a combination of reservoir conditions (pH, temperature, salinity, etc.) to release water-soluble inhibitors into aqueous production brine to control scale.^2,11

Despite a large number of microemulsion based inhibitor products being reported, the transport and retention mechanisms of these non-aqueous inhibitor products are less well understood.⁹ In this study, calcium-phosphonate nanomaterial was prepared in a water-in-oil microemulsion (reverse micelle) medium. This novel reverse micelle based nanomaterial fluid (nanofluid) was prepared by mixing a calcium-containing microemulsion solution with another microemulsion solution containing a common phosphonate inhibitor at room temperature. The prepared inhibitor reverse micelle nanofluid (RMNF) was characterized to understand its physicochemical properties. Furthermore, laboratory transport experiments were conducted via column flow-through tests in calcite medium to investigate the transportability of RMNF. The impact of aqueous overflush vs. non-aqueous overflush on nanomaterial transport was studied. Finally, a squeeze simulation test was carried out to evaluate the potential application of RMNF for oilfield scale control. To the best of our knowledge, it is the first time the synthesis of a reverse micelle based inhibitor nanofluid is reported. Furthermore, this paper reports the first systematic investigation of the transport behavior of a microemulsion based scale inhibitor nanomaterial system in formation medium environment.

Experimental section

Chemicals

Commercial grade diethylenetriamine pentakis(methylenephosphonic acid) (DTPMP) with 50% activity was used as the scale inhibitor. Chemicals employed in this study such as sodium chloride, calcium chloride, hydrochloric acid, sodium hydroxide and ethanol were reagent grade and purchased from Fisher Scientific. Organic solvent isooctane, anionic surfactant bis(2-ethylhexyl) sulfosuccinate sodium salt (AOT, 95%), nonionic surfactant nonaethylene glycol monododecyl ether (C₁₂(EO)₉), 2-(N-morpholino)ethanesulfonic acid (MES) buffer and tritiated water were purchased from Sigma-Aldrich. Deionized water (DI water) was prepared by reverse osmosis and ion exchange water purification process.

Synthesis of calcium–DTPMP reverse micelle nanofluid

In a typical synthesis reaction, approximately 10 g of AOT solution and 4 g of C₁₂(EO)₉ solution were added into 100 mL isooctane solution in a 150 mL glass beaker, followed by constant stirring for 15 min to prepare the surfactant mixture solution. Then, in a 100 mL glass baker 5 mL of an aqueous solution containing 0.16 M CaCl₂ and 0.02 M MES was added dropwise to 50 mL of the prepared surfactant mixture solution, while constantly stirred at room temperature (21 °C). A clear translucent solution containing CaCl₂ RM can be obtained. Similarly, in another 100 mL glass beaker 5 mL of an aqueous solution of 0.04 M DTPMP with sodium chloride (pH = 9.0, neutralized by 2.0 M NaOH) was added dropwise to 50 mL of the prepared surfactant mixture solution, while constantly stirred at room temperature. A clear translucent solution containing Na–DTPMP RM was obtained. Ca–DTPMP RMNF was prepared by mixing the previously obtained CaCl₂ RM solution with Na–DTPMP RM solution in a 200 mL glass beaker with stirring at room temperature and a translucent solution was obtained. Upon completion of the solution mixing, the resultant Ca–DTPMP RMNF was filtered through a 1 μm filter (Merck Millipore Corp.) to remove any undissolved particles. The resultant solution is Ca–DTPMP RMNF with a pH value of ca. 5.8. The nanofluid was centrifuged at 6500 rpm for 10 min and little deposit was found at the bottom of the solution.

Characterization of the Ca–DTPMP reverse micelle nanofluid

Transition electron microscopy (TEM) analysis was performed on a JEOL 2000 FX electron microscope at 130 kV. Samples for TEM analysis were prepared by dripping RMNF onto a copper grid coated with amorphous carbon-holey film. RM solid was acquired by adding ethanol into the prepared nanofluid in 1 : 1 v/v ratio and subsequently centrifuging the mixture at 6500 rpm for 15 min. A large amount of white precipitates can be found at the bottom of the solution. The acquired nanomaterial solid was then extracted, washed by DI water and dried in an oven at 100 °C overnight to remove the interstitial water and characterized by Fourier Transform Infrared (FT-IR) and thermogravimetric analysis (TGA) analyses. The stoichiometric ratios of calcium to DTPMP in the solid sample were determined by dissolving the pre-washed RM precipitates in 1 M HCl and measuring the aqueous phase calcium and phosphorus concentrations. FT-IR spectrum was investigated on a Nicolet FT-IR spectrometer with KBr pellet technique with the spectrometer range of 4000 to 400 cm⁻¹. TGA was carried out using a thermal analysis instrument SDT 2960. Samples were heated at a rate of 10 °C min⁻¹ from 25 to 1100 °C in an atmosphere of flowing argon (100 mL min⁻¹).

Reverse micelle nanofluid column breakthrough experiments

The experimental setup and procedure of the column breakthrough experiments were conducted in a manner similar to those in our previous studies.^15–17 Briefly, calcite (Iceland spar, Creel Chihuahua, Mexico) with a grain size of 106–180 μm was chosen as the formation medium material and washed by 1 mM acetic acid to remove fine particles and impurities, followed by DI water rinsing. Subsequently, calcite was packed in to an Omnifit column with 1.02 cm ID and 8 cm length (Bio-Chem Fluidics, Boonton, NJ). The pore volume (PV) and dispersion coefficient of the packed column was measured via a non-reactive tracer (tritiated water, ³H₂O) column breakthrough test. PV is defined as the void space volume of the core and PV can be calculated as the total volume subtracted by the core material volume. Following the tracer test, inhibitor RMNF transport experiments were conducted by injecting several PV of the nanofluid through the column packed with calcite. The effect of preflush fluid was investigated by flushing the column with either isooctane solution or 2 M NaCl prior to pumping the RMNF. The flow rate in both transport tests was approximately 60 mL h⁻¹, corresponding to a linear pore velocity of ca. 2.9 cm min⁻¹.

Reverse micelle nanofluid laboratory squeeze simulation tests

The laboratory squeeze simulation test of the Ca–DTPMP RMNF in calcite medium was similar to the procedure of the previous studies using totally contained squeeze simulation apparatus.^{15,16,18–20} Briefly, a column (1.02 cm ID and 8 cm length) packed with calcite material (approximately 10 g) was pre-flushed with a solution containing 1 M NaCl and 0.01 M NaHCO₃ for about 10 PV. Subsequently, half of a PV of the prepared Ca–DTPMP RMNF was injected into the column, followed by another half a PV overflush by 1 M NaCl solution. Upon completion of the overflush treatment, the column was shut-in for 24 h to allow the partitioning of the delivered DTPMP inhibitor from RM droplets to attach to the surfaces of calcite. Subsequently, the column was eluted with a synthetic brine solution (0.025 M CaCl₂, 0.015 M NaHCO₃ and 1 M NaCl, sparged with 100% CO₂) from an opposite direction under 75 psi back pressure. The prepared synthetic brine was in equilibrium with respect to calcite, to simulate the flow back (return) of reservoir fluids in the field following a squeeze treatment. The column experiments were conducted at 70 °C with a flow rate of 60 mL h⁻¹ or a linear pore velocity of 2.8 cm min⁻¹. The effluent solution was collected and analyzed for DTPMP concentration to establish the DTPMP flow back curve (return curve).

Analytical methods

Calcium and DTPMP concentrations were analyzed by inductively coupled plasma-optical emission spectrometer (ICP-OES) (Optima 4300 Dv, Perkin-Elmer). The wavelengths for calcium and phosphorus measurements are 317.933 and 213.617 nm, respectively. A solution containing 5 mg L⁻¹ yttrium (371.029 nm) was utilized as internal standard solution. Each sample measurement was repeated for five times and the mean value of these measurements was reported. The standard deviation for every sample measurement was less than 0.5%. Measurement of low concentrations of DTPMP was realized by digesting DTPMP to form phosphate and then producing the phosphomolybdenum blue complex and measuring spectrophotometrically at 890 nm.²¹ Spectrophotometric method is able to measure phosphonate from as low as 0.1 to 2.5 mg L⁻¹ as phosphate, which corresponds to 0.12 to 3 mg L⁻¹ as DTPMP.

Results and discussion

Synthesis and characterization of the inhibitor reverse micelle nanofluid

Microemulsion is formed by spontaneous mixing of water, oil and surfactant(s). As elaborated previously, surfactants are added to the RM system mainly to reduce interfacial tension. A key property of a reverse micelle system is the solubilization of water or aqueous solution.²² Studies show that by incorporating nonionic surfactant, the solubilization for this ionic and nonionic surfactant mixture in nonpolar system will greatly increase and addition of electrolyte will decrease the system water solubilization.^23,24 Anionic AOT is one of the most widely investigated surfactants in terms of RM solubilization due to AOT's versatile capacity in forming RM in hydrocarbon oils at various concentrations.²⁵ AOT/isooctane RM system has also been extensively studied.²⁶ In this study, nonionic surfactant C₁₂(EO)₉ was mixed with AOT in isooctane system to prepare the surfactant mixture solution for RM synthesis. RM solution containing CaCl₂ is prepared by mixing a volume of aqueous solution of CaCl₂ with the surfactant mixture solution. In light of the fact that a clear translucent solution can be obtained upon mixing, it can be deduced that solubilization capacity of the surfactant mixture was not exceeded by mixing with CaCl₂ aqueous solution. In a similar manner, RM solution containing sodium DTPMP was acquired. DTPMP is a commonly used oilfield phosphonate inhibitor.¹ Eventually, Ca–DTPMP RMNF was obtained by mixing of these two RM solutions at room temperature, as depicted in the schematic diagram in Fig. 1. MES buffer was added into the RM system to control the pH of the water domain to ca. 5.8 pH. The resultant Ca–DTPMP RMNF (ca. 110 mL) contains approximately 10 mL of water domain and 100 mL of organic domain. TEM microimage (Fig. 2) shows that the morphology of the obtained Ca–DTPMP RM nanomaterials is in an approximately spherical shape with an average diameter of 250 nm. It should be noted that although some researchers restrict the term nanomaterials to materials with a diameter less than 100 nm, others refer to the nanomaterials as those with a dimension less than 1000 nm.²⁷ The stability of the prepared RM solution can be examined by centrifuging the RM solution at 6500 rpm for 10 min. By the end of the centrifugation, little precipitate was found at the bottom of the solution, indicative of a satisfactory stability of the nanofluid at ambient temperature. The stability of the nanofluid was also tested at 70 °C, which is a representative temperature for oil-producing reservoir. After being statically placed in a water bath at 70 °C for 4 h, the RM solution was still stable with little precipitate at the bottom. As reported by Fathi et al.,²⁸ particle size can be an useful indication of the micellar system stability, which is considerably influenced by the addition of salt. Normally, a stable RM particle should have a particle size in the range of tens of nanometers and the addition of salt can increase the particle size to the range of hundreds of nanometers. Based on the measured particle size of ca. 250 nm by TEM in this study, one might argue that the obtained RM system might not be as stable as the salt-free micellar system and might agglomerate over time. However, as pointed by Graeve et al.,²⁹ the presence of protective action of the surfactant can prevent RM agglomeration. In this study, both AOT and C₁₂(EO)₉ surfactants were added to enhance the stability of the inhibitor micellar structure. This explains the observed stability of RM at both room temperature and at 70 °C and even after centrifuging treatment at 6500 rpm for 10 min.

Fig. 1 Schematic diagram of synthesis procedure of Ca–DTPMP nanofluid in isooctane in the presence of AOT and C₁₂(EO)₉ surfactants.

Fig. 2 TEM microimage of the prepared reverse micelle nanomaterials.

Ethanol is added to Ca–DTPMP RMNF to break the micellar structure, in that introducing excess alcohol can induce destabilization of reverse micelles.³⁰ By adding ethanol and subsequently centrifuging the mixture solution at 6500 rpm for 10 min, a large amount of white precipitates can be observed at the bottom of the solution, signifying the destructive function of ethanol to the RM system. The resultant white precipitates were collected and washed to prepare for elemental ratio analysis, FT-IR and TGA characterization. The elemental ratio analysis of the acquired white Ca–DTPMP complex suggests that the calcium to DTPMP ratio is 2.8. Thus, the developed Ca–DTPMP solid in RM is in the form of Ca_2.8H_4.4DTPMP. The skeletal structure of the prepared RM solids was investigated by FT-IR. The FT-IR spectrum (Fig. 3) shows that the RM solids have multiple bands visible at 986, 1059, 1430 and 3400 cm⁻¹. The bands at 986 and 1059 cm⁻¹ correspond to phosphonate P–OH vibrations³¹ and P–O–Ca stretching vibration.³² The band at 1430 cm⁻¹ is attributed to the C–H bending in the –CH₂– groups.³² The broad band at 3400 cm⁻¹ is assigned to the adsorbed surface water molecules.³³ The existence of P–OH and P–O–Ca bonds, as confirmed by FT-IR spectrum, suggests of the presence of available coordination sites for phosphoryl oxygen atoms and also complexation of calcium with phosphoryl oxygen atoms. This is in agreement with the aforementioned formula of Ca_2.8H_4.4DTPMP. Based on a previous study,³⁴ the acid–base and calcium complex solution chemistry of DTPMP has been determined and a simple polymer type model has been proposed to calculate the DTPMP–base and calcium complex stability constants. Considering the RMNF synthesis conditions in this study, the Ca–DTPMP complex composition is calculated by this model as: 4.9% of the Ca–DTPMP complexes contained one Ca²⁺ ion, e.g. Ca₁H₄DTPMP⁴⁻; 40.6% two Ca²⁺, e.g. Ca₂H₄DTPMP²⁻; 47.3% three Ca²⁺, e.g. Ca₃H₃DTPMP¹⁻; and 7.1% four Ca²⁺ e.g. Ca₄H₂DTPMP_aq.^0±. Thus, according to this modeling result, the calculated weighted average complex composition is Ca to DTPMP of 2.6, which correlates well with the experimentally measured Ca to DTPMP ratio of the complex of 2.8 in the RM. TGA characterization was conducted by recording the solid weight loss from 35 to 900 °C with a total weight loss of approximately 17% by the end of the test (Fig. 4). The overall TGA weight loss profile can be divided into three sections: 30 to 100 °C; 200 to 700 °C and above 900 °C. The evaporation of adsorbed water occurred during the temperature range of 30 to 100 °C. The weight loss over the range of 200 °C to 700 °C corresponds to the removal of lattice water and decomposition of organic fraction of the phosphonates.^31,32,35

Fig. 3 FT-IR spectrum of the solid Ca–DTPMP reverse micelle precipitates.

Fig. 4 TGA profile of the solid Ca–DTPMP reverse micelle precipitates.

Transport of reverse micelle nanofluid in calcite medium

Transportability of the prepared nano/sub-micron sized scale inhibitor materials is a critical factor governing the potential application of these materials for oilfield scale control.^15,20 These inhibitor nanomaterials serve as a delivery vehicle to place the inhibitors deep into formation. Ideally, the prepared inhibitor nanomaterials should be able to transport deep into the “toe” of the oil-producing formation so as to expand the surface area of the formation protected against mineral scale deposition. In this study, a series of column flow-through experiments in the packed bed columns have been conducted to examine the transportability of the prepared RMNF in calcite medium. Calcite was chosen as the representative formation medium material in that calcite is the most active ingredient among various types of formation minerals to react with phosphonate inhibitors.^36,37 Similar to our previous studies, the transport of RM nanomaterials can be delineated by advection and diffusion mechanism as well as particle filtration and attachment mechanism.^15,17 Of particular interest in this study is the impact of preflush fluid on RM nanomaterial transport. In an oilfield squeeze treatment, the preflush solution is designed to displace production fluids inside well tubing and wellbore back into formation, acting as a buffer or spacer between these fluids and the main pill solution. Additionally, preflush treatment can clean up formation surfaces to enhance inhibitor retention and to reduce well clean up time.^6,38

From the perspective of advection and diffusion, the transport of RM nanomaterial in RMNF is dictated by advection and diffusion. Mathematically, such process can be described by one dimensional advection dispersive equation with addition of a term describing first order deposition:^39–41

where R represents the retardation factor owing to RM nanomaterial reversible adsorption to the formation medium; C (mg L⁻¹) denotes the effluent RM nanomaterial concentration at a given time; t (min) is the time; D (cm² min⁻¹) accounts for the hydrodynamic dispersion coefficient; x (cm) represents the distance of the RM nanomaterial transport inside the calcite column; and v (cm min⁻¹) is the linear pore velocity calculated as v = Q/πr²ε, where Q is the flow rate (mL h⁻¹); ε is the calcite medium porosity (0.43 in this study), and r (cm) is the cross sectional radius of the column bed (0.51 cm in this study). Linear pore velocity, also called seepage velocity, is the average travel velocity for the nanomaterial to move through the axial direction of the calcite column. J_d (min⁻¹) is the first order deposition rate coefficient of the nanomaterial to calcite medium surfaces. The first term of eqn (1) accounts for the RM nanomaterial concentration change with time at a given location; the second term accounts for concentration change associated with diffusion or mixing; the third term gives change in concentration arising from advection and the last term is the RM nanomaterial mass removal modeled as a first order deposition process.⁴¹

First, a tritiated water tracer test was conducted to measure the packed column PV and D value (details in the ESI†). Once the D value in calcite medium is available, the mathematical solution to eqn (1) can be obtained considering a clean bed filtration model:^41,42

Table 1 summarizes the conditions of the transport experiments of RM nanomaterial in calcite medium at the pore velocity of ca. 2.9 cm min⁻¹ at 70 °C. Both isooctane and 2 M NaCl solutions were employed in this study as the preflush fluids prior to the injection of RMNF into calcite. As a comparison, Table 1 also includes the experimental condition of a prior transport study involving an aqueous based Ca–DTPMP nanofluid (hereafter referred to as NF-II) in calcite medium at a similar pore velocity of 3.07 cm min⁻¹ at 70 °C with 1 M NaCl as preflush solution.¹⁷ This Ca–DTPMP NF-II was prepared by dispersing Ca–DTPMP precipitates in an aqueous solution containing SDBS surfactant. A breakthrough curve of the RM in calcite medium can be established as the change in the normalized effluent RM concentration as a function of the number of PV (Fig. 5 and 6). The RM concentration can be calculated based on the measured phosphonate concentration in the effluent solution. According to Fig. 5, evidently RMNF show a lower and delayed breakthrough by the end of 4 PV, compared with NF-II. Such difference in breakthrough can be quantified by calculating the R and J_d values of each study (Table 2). R values are calculated to be 1.08 and 2.44, respectively and J_d values of 0.019 and 0.42 min⁻¹, respectively. Retardation factor R accounts for the retardation effect arising from sorption of the particulate materials to the formation medium (calcite). Thus, a higher R value in the RM transport experiment indicates of a stronger sorption of RM to calcite medium surfaces. It can be envisaged that both Ca–DTPMP reverse micelles and Ca–DTPMP NF-II are surrounded by a layer of anionic surfactants of AOT and SDBS, respectively. One possible explanation is that, compared with AOT, the sulfonate groups of SDBS molecules subject the NF-II to a stronger negative surface charge, leading to a stronger repulsive force against the calcite medium, which are also negatively charged. Additionally, the spatial orientation of SDBS molecules might provide a more prominent steric hindrance against calcite surfaces, compared with AOT. The considerable difference between the calculated J_d values suggests of a more pronounced removal of RM nanomaterials by calcite medium surfaces. Since both experiments were conducted at a similar pore velocity and at the same temperature in calcite medium, the difference in J_d value should be attributed to the difference in the interaction of the inhibitor materials with calcite surfaces. The NF-II is dispersed in an aqueous suspension while RM is in an isooctane organic system. While contacting with calcite medium surface, the water domain of the RM might gradually dissolve the surface layer of calcite lattice leading to migration of dissolved Ca²⁺ and HCO₃⁻ species into the RM system. The introduction of foreign species increases the RM system ionic strength, resulting in destabilization of the RM system^25,43 and further removal by the calcite surfaces. Because of the sorption and removal effects from calcite medium surfaces, the breakthrough level of RM after 4 PV was only 34% compared with 89% for the NF-II (Table 2 and Fig. 5).

Table 1 Testing conditions for column transport experiments

Experiment	Form of inhibitor added	Preflush fluid	Flow rate, Q (mL h^−1)	Pore velocity (cm min^−1)^a	Formation medium	Formation porosity	Experimental temperature (°C)	Dispersion coefficient, D (cm^2 min^−1)
a The glass column inner diameter in Test-1 (ref. 17) was 0.66 cm compared with 1.02 cm in this study (Test 2 & 3).
Test-1 (Zhang et al.^17)	Aqueous nanofluid	1 M NaCl	28.4	3.07	Calcite	0.45	70	0.09
Test-2 (this study)	Reverse micelle nanofluid	2 M NaCl	63.4	2.99	Calcite	0.43	70	0.068
Test-3 (this study)	Reverse micelle nanofluid	Isooctane	60.0	2.85	Calcite	0.43	70	0.065

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Fig. 5 Breakthrough profiles of Ca–DTPMP nanomaterials (NF-II) from a previous study¹⁷ and Ca–DTPMP reverse micelle nanofluid in this study. Both transport experiments were conducted at a similar pore velocity of ca. 3 cm min⁻¹ and employed NaCl as the preflush fluid. The diamond and triangle markers represent experimentally measured breakthrough levels; while the dashed lines denote the calculated breakthrough levels based on eqn (2).

Fig. 6 Breakthrough profiles of inhibitor reverse micelle with preflush solution as isooctane or 2 M NaCl at a similar pore velocity of ca. 2.9 cm min⁻¹. The square and triangle markers represent experimentally measured breakthrough levels; while the dashed lines denote the calculated breakthrough levels based on eqn (2).

Table 2 Transport experimental results from the standpoint of advection and diffusion

Experiment	Preflush fluid	Flow rate, Q (mL h^−1)	Pore velocity (cm min^−1)	Observed C/C0 (%)	Calculated C/C0 (%)	Removal coefficient, Jd (min^−1)	Retardation factor, R
Test-1 (Zhang et al.^17)	1 M NaCl	28.4	3.07	89	96	0.019	1.08
Test-2 (this study)	2 M NaCl	63.4	2.99	34	32	0.42	2.44
Test-3 (this study)	Isooctane	60.0	2.85	52	48	0.26	2.34

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In this study, the impact of preflush solution on RMNF transport in calcite medium was studied by preflushing the calcite column with an aqueous solution (2 M NaCl) or an organic solution (isooctane) prior to the RM transport experiment. The preflush fluid for an oilfield squeeze operation is normally an aqueous saline solution compatible with formation materials. In this study, the aqueous preflush fluid contains 2 M NaCl (corresponding to 120 000 mg L⁻¹ NaCl), which can be encountered in a field scale squeeze operation. It shows that by switching from NaCl solution to isooctane preflush fluid, the RM breakthrough level increases from 34 to 52% by the end of 4 PV and the breakthrough curve seems to have a tendency to further increase post 4 PV (Fig. 6). Table 2 summarizes the calculated R and J_d values, as well as the calculated breakthrough levels based on eqn (2). It can be concluded that, by comparing these two RM transport studies at the same pore velocity, the calculated R values are relatively close (2.34 vs. 2.44) while the calculated J_d values are quite different (0.26 vs. 0.42). Based on the aforementioned discussion, retardation factor is a reflection of the sorption behavior of the RM nanomaterials to calcite medium surface. Since the same RM nanomaterials were employed in these two transport studies in calcite medium, a similar R value in both studies is expected. The J_d value signifies the deposition kinetics of the RM to calcite surfaces. As discussed previously,^40,44 J_d value is determined by the height of the energy barrier from the viewpoint of DLVO theory. In other words, compared with the isooctane, preflushing the calcite column with 2 M NaCl reduces the energy barrier between the RM and calcite surfaces, resulting in an enhanced deposition of RM. Preflushing the calcite medium with isooctane will displace the aqueous brine solution previously stored in the pore space out of the calcite column and also coat the calcite particle surfaces with a layer of isooctane. On the other hand, preflushing calcite with 2 M NaCl will saturate the column pore space with saline brine. The 2 M NaCl brine introduced will get in contact with RMNF, leading to a reduction in the micellar system stability. The destabilized RM will have a higher tendency to deposit onto the surface of calcite during transport study. This argument can be supported by the laboratory study of the electrolyte concentration impact on solubilization behavior of the mixed micellar systems.⁴³ By investigating the RM systems formed by mixing AOT with a group of nonionic surfactants in a number of organic solvents (including isooctane), a maximum NaCl concentration (C_max-NaCl) can be identified in each RM system. If the NaCl concentration introduced to the micellar system exceeds C_max-NaCl, the RM will becomes unstable, characterized by a dramatic increase in solution turbidity.⁴³ Similar observation was confirmed by the study of AOT with other common nonionic surfactants in different oils.²⁵ Thus, it can be argued that in this study, compared with isooctane preflush, preflushing column with 2 M NaCl solution subjects the RM system to exceed its C_max-NaCl, leading to RM system destabilization.

From a particle filtration and attachment standpoint, the transport of RM nanomaterials is a course of RM nanomaterials being continuously removed by formation medium via collection and attachment of RM to calcite surfaces. The deposition of RM to calcite medium surface includes two consecutive steps: collection of RM by calcite medium surfaces (particle collection) and subsequent attachment of the RM to calcite surface (particle attachment).⁴⁵ A collection efficiency (η₀) and an attachment efficiency (α) were introduced to describe the particle collection and attachment processes, respectively. The collection efficiency (η₀) considers the particle collection due to Brownian diffusion, interception and sedimentation. Thus, the η₀ term can be expressed as the sum of these three mechanisms:^39,45

η₀ = η_D + η_I + η_G (3)

where η_D, η_I and η_G are the single collector efficiency components arising from Brownian diffusion, interception and sedimentation, respectively. The detailed calculations of these components follow the effort of Tufenkji and Elimelech⁴⁶ (details in the ESI†). Table 3 lists the calculated collection efficiency values for the three transport tests of interest. It shows that RM collection efficiency due to Brownian diffusion (η_D) noticeably exceeds the other two terms (η_I and η_G) and thus dominates the overall calculated η₀ values. Such observations are in agreement with the results of the transport of various types of sub-micron sized particles in different porous media.^47–49 Typically, the Brownian diffusion will be dictating the collection of particles to the medium surface within the particle size range of 1 μm.⁴⁵ The attachment efficiency (α) is given bywhere d_c is the diameter of the calcite medium particles (143 μm in this study). α value is a function of the calculated η₀ value as well as the breakthrough level. The higher the α value, the higher the tendency for RM nanomaterials to attach to calcite medium surfaces.

Table 3 Transport experimental results from the standpoint of filtration and attachment

Experiment	Preflush fluid	Pore velocity (cm min^−1)	Observed C/C0 (%)	ηD (×10^−4)	ηI (×10^−4)	ηG (×10^−4)	η0 (×10^−4) (=ηD + ηI + ηG)	α (×10^−2)
Test-1 (Zhang et al.^17)	1 M NaCl	3.07	89	80.7	6.7	5.5	92.9	3.1
Test-2 (this study)	2 M NaCl	2.99	34	96.9	6.0	4.1	107.0	21.0
Test-3 (this study)	Isooctane	2.85	52	100.5	6.1	4.3	110.9	12.3

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As shown in Table 3, with η₀ value being similar (0.00929 vs. 0.0107), the α value calculated from the transport of RM (Test-2) is about 7 times higher than that from NF-II transport (Test-1), which can be elucidated by the decline in breakthrough level from 89 to 34%. On the other hand, the impact of preflush fluid on RM transport can be elaborated by investigating the calculated α value from Test-2 and Test-3. Table 3 shows that at a similar pore velocity of 2.9 cm min⁻¹, with a comparable η₀ value (ca. 0.01), preflushing the calcite column with 2 M NaCl (Test-2) leads to an increase of α value from 12.3 to 21.0, compared with the scenario of isooctane preflushing (Test-3). This increase in α value with NaCl preflush can be attributable to the fact that introducing 2 M NaCl solution into the packed column can destabilize the RM system upon contact, which agrees with the aforementioned discussions of the calculated J_d values. As discussed previously,^39,45,50,51 particles can be either irreversibly captured in the collectors' primary minimum of the interaction energy profile or weakly attached to the secondary energy minimum of the collectors (calcite medium), depending on the physicochemical conditions and particle surface affinity of the transport phenomenon. If the particles are weakly affixed to the secondary energy minimum, non-DLVO forces like hydrodynamic dragging force can exert an impact on the particle attachment to the collector surfaces, thus impacting the α value. In this study, the α values were calculated to be different with variation in preflush solution. This suggests that the attachment of RM to the calcite medium surfaces is expected to be weak at secondary energy minimum and sensitive to non-DLVO forces. By virtue of the observed destabilization effect of aqueous saline brine onto RM, it can be argued that a carefully selected non-aqueous preflush fluid is more suitable for this type of non-aqueous inhibitor squeeze treatment design to enhance the inhibitor RM travel distance deep into the formation.

Laboratory squeeze simulation of inhibitor reverse micelle nanofluid

Since a typical field scale squeeze treatment comprises of different stages of preflush, pill injection, overflush, shut-in and return production, laboratory squeeze simulation test is purposely designed to simulate the field squeeze treatment to evaluate the performance of a squeeze design with successive steps of preflush, pill injection, overflush, shut-in and inhibitor return in a laboratory setup. In this study, the long-term inhibitor return is simulated via eluting the column with a synthetic brine which is in equilibrium with calcite. This is similar to what occurs in a reservoir as formation brine flows back over the pill. It is essential that the DTPMP inhibitor contained inside the RM system can be effectively partitioned and released into the aqueous brine, upon contact with the production brine after the shut-in period. In order to understand the return performance of the inhibitor RM, a squeeze simulation was carried out by injecting one half PV of inhibitor RM followed by overflushing by another half PV of 1 M NaCl, which is a common overflush fluid. After shutting in the column for 24 h, the column was eluted with a synthetic brine from the reverse direction with effluent phosphonate concentration being monitored. For comparison, a previous study testing an acidic DTPMP pill and another aqueous based Ca–DTPMP nanofluid (hereafter referred to as NF-III)²⁰ were included and compared with the RM return in this study. The NF-III was prepared by chemical precipitation of Ca–DTPMP with the assistance of phosphino-polycarboxylic acid. According to the conditions of these squeeze simulation studies (Table 4), all three experiments were conducted by use of a synthetic brine of the same composition with the same pore flow velocity of 2.8 cm min⁻¹ at 70 °C in calcite medium. As summarized in Table 5, all three tests achieved an inhibitor return of higher than ca. 80%, i.e., 80% of the injected DTPMP either in the form of acidic pill or nanomaterials was eluted out of the column by the end of the return test. A DTPMP inhibitor return profile can be established by plotting the effluent DTPMP concentration as a function of PV of synthetic brine eluted (returned). According to the plotted return profiles (Fig. 7), all three studies show of a similar pattern of DTPMP return: a DTPMP return concentration was as high as almost 1000 mg L⁻¹ within the first few PV; following the initial several PV, DTPMP return concentration quickly drop to dozens of mg L⁻¹ within the first 100 PV; after ∼300 PV the return concentration gradually reached the level of a few mg L⁻¹; 600 PV and beyond, the return concentrations fell into the regime of sub mg L⁻¹ and extended for several more hundreds of PV, until the end of the squeeze test. The squeeze test was ended when DTPMP return concentration drop below the detection limit, which is typically around 0.12 mg L⁻¹ based on the HACH method. The total return volumes for these three tests (acidic pill, NF-III and RM) are 870, 1440 and 1316 PV, respectively (Table 5). Normally, a higher return PV in a squeeze simulation test is preferred since it translates to a longer field squeeze lifetime suggesting an extended period of protection time against scale deposition. Hence, it can be argued that the prepared inhibitor RM exhibited a desirable return performance comparable to the Ca–DTPMP NF-III and exceeded the conventional acidic pill treatment in terms of extending the inhibitor squeeze lifetime. The observation from this study on RM return can be compared with other squeeze tests evaluating various types of non-aqueous inhibitor products. Guan et al. reported the synthesis of ethylene glycol based oil-soluble inhibitor products containing penta-phosphonate.⁷ It is found that both aqueous and non-aqueous systems show a similar level of performance in terms of inhibitor long-tail return post flush period. Chen et al. developed a non-aqueous low density inhibitor package using a polymer containing acrylate and amine for downhole treatment.⁸ This study showed that the aqueous treatment resulted in an extended squeeze lifetime compared with the non-aqueous counterpart. However, this difference can be partially impacted by the addition of squeeze life enhancer and a larger pill solution volume in the water based squeeze. Miles et al. prepared a water-in-oil formulation containing a range of scale inhibitors.¹³ Squeeze tests performed under a field condition showed that non-aqueous products exceeded those obtained from a comparable water based formulation.

Table 4 Summary of the physiochemical conditions of each squeeze simulation test

Experiment	Form of inhibitor added	Formation medium	Squeeze fluid compositions	Squeeze fluid pH	Squeeze temperature (°C)	Flow rate (mL h^−1)	Pore velocity (cm min^−1)	PV (mL)
Squeeze Test-1 (Shen et al.^20)	Acidic pill	Calcite	0.025 M CaCl2, 0.015 M NaHCO3, 1 M NaCl and bubbled with 100% CO2	5.54	70	90	2.8	8
Squeeze Test-2 (Shen et al.^20)	Aqueous nanofluid	Calcite		5.54	70	90	2.8	8
Squeeze Test-3 (this study)	Reverse micelle nanofluid	Calcite		5.54	70	60	2.8	3

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Table 5 Summary of the experimental results of each squeeze simulation test

Experiment	Form of inhibitor added	Formation medium	DTPMP injected^a (mg)	Percent of inhibitor returned^b (%)	Total volume returned^c (PV)	Initial pIP	Final pIP	NSL (bbl. kg^−1)
a “DTPMP Injected” corresponds to the mass of DTPMP injected prior to the squeeze simulation test.b “Percent of Inhibitor Returned” is the ratio of the mass of inhibitor returned by the end of the test to the mass of inhibitor injected at the beginning of the test.c “Total Volume Returned” represents the total volume of synthetic brine flushed during the squeeze simulation test.
Squeeze Test-1 (Shen et al.^20)	Acidic pill	Calcite	32	87	870	50.4	53.9	1370
Squeeze Test-2 (Shen et al.^20)	Aqueous nanofluid	Calcite	32	79	1440	50.2	54.1	2270
Squeeze Test-3 (this study)	Reverse micelle nanofluid	Calcite	8.6	91	1316	50.8	53.7	2900

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Fig. 7 DTPMP return profiles from three laboratory squeeze simulation studies involving an acidic pill from a previous study;²⁰ an aqueous inhibitor nanofluid (NF-III) from a previous study;²⁰ and the reverse micelle based nanofluid in this study.

Furthermore as discussed previously,^18,19 phosphonate inhibitors are retained in calcite-bearing formation by forming metal-phosphonate salts. Thus, the release of phosphonate from Ca-phosphonate solid complexes during inhibitor return is proposed to be controlled by the dissolution of Ca-phosphonate precipitates into the production brine. Therefore, the course of Ca–DTPMP RM return of DTPMP can be viewed as a continuous dissolution of Ca–DTPMP solid complex into the synthetic brine. In light of a proposed solution-speciation model,³⁴ the DTPMP return profiles can be delineated by calculating the negative logarithm of ion activity product (pIP) of the Ca–DTPMP complex throughout the duration of squeeze simulation tests. The pIP calculation is based on the formula of Ca₃H₄DTPMP and is in the form of:

pIAP = −log₁₀[(Ca²⁺)³{H⁺}⁴(DTPMP¹⁰⁻)] (5)

where parentheses accounts for molar concentration and braces for activity. The free calcium ion (Ca²⁺) and DTPMP¹⁰⁻ species concentrations were calculated from the total DTPMP concentrations in aqueous phase via a speciation model.³⁴ Fig. 8 plots the calculated pIP of these three squeeze simulation studies as a function of the return brine PV. For all three tests, the initial pIP at the onset of the brine return (ca. 1 PV) was between 50 and 51. With the progress of the synthetic brine flushing, the pIP gradually reached approximately 53 between 300 and 500 PV and further increased to ca. 54 between 700 and 800 PV for all three tests. pIP values post 800 PV for all three tests maintained relatively stable at the level of 54 till the end of the squeeze simulation tests, as summarized in Table 5. The reported pIP for the amorphous phase Ca–DTPMP complex is about 50 and the crystalline Ca–DTPMP of 54 (ref. 21). Evidently, the formed Ca–DTPMP complexes in these three squeeze simulation tests gradually developed from initially an amorphous phase into a crystalline phase which has a much lower solubility in the synthetic brine. It can be argued that the slow dissolution of crystalline Ca–DTPMP solid into the synthetic brine is responsible for the low DTPMP return concentration post 700 PV in the RM return study.

Fig. 8 Calculated pIP values for three laboratory squeeze simulation studies. The small inserted figure at the lower right corner is a part (up to 100 PV) of a zoom of the main figure.

Note that the aforementioned inhibitor return volumes (i.e., 870, 1440 and 1316 PV) are also impacted by the loading of DTPMP inhibitor to the column prior to the synthetic brine flushing. The potential application of the prepared inhibitor RMNF in oilfield scale control can be better illustrated by calculating the material's normalized squeeze lifetime (NSL), which is the ratio of effective return volumes and the mass of inhibitors injected.⁵² As for the RM return in this study, the total return volume (ca. 3.9 L) is the product of the number of PV returned (1316 PV) with the column PV (3 mL). Considering the mass of inhibitor injected (8.6 mg), the NSL for RM in this study can be obtained by:

In a similar manner, the NSL values for the acidic pill return and NF-III return can be calculated as 1370 and 2270 bbl. kg⁻¹, respectively. The significance of the calculated NSL value can be revealed by assuming 1000 kg of active inhibitor is deployed in a squeeze treatment, these NSL values would correspond to 2.9 × 10⁶, 2.3 × 10⁶ and 1.4 × 10⁶ barrels of production brine protected, respectively for RMNF, NF-III and conventional pill. The total protection time will depend upon the specific daily water production volumes. The calculated NSL values further confirm that the return of the RMNF and NF-III are comparable and both are superior to the acidic pill in terms of extending inhibitor squeeze lifetime. For low water cut or water sensitive wells, application of such inhibitor reverse micelle nanofluid in a squeeze operation is expected to achieve the objective of scale control while minimizing the potential formation damage.

Conclusions

In this study, the prepared reverse micelle nanofluid contains Ca–DTPMP complex, which is stabilized by the presence of AOT and a nonionic surfactant. The nanofluid is stable at both room temperature and 70 °C. This product is determined to be transportable in calcite medium. Transportability of this product can be impacted by the selection of preflush solution. It is found that isooctane preflush can enhance the breakthrough level compared with preflushing with NaCl aqueous solution. It is suggested that upon contacting with NaCl solution, the micellar structure can be destabilized, leading to a more pronounced deposition onto calcite surfaces. Laboratory squeeze simulation tests confirmed that the inhibitor nanofluid can return phosphonate inhibitor into aqueous brine, during which process the amorphous phase Ca–DTPMP complex gradually develops into a crystalline phase. It is evident that this inhibitor nanofluid shows an enhanced squeeze lifetime compared with the conventional pill solution, suggesting of a potential for future oilfield scale control application and adding a reliable method to squeeze the wells early while the water production rate is low.

Acknowledgements

The authors would like to acknowledge the financial support by Brine Chemistry Consortium including Baker Hughes, BWA, CARBO, Cenovus, Chevron, ConocoPhillips, Dow, EOG Resources, GE, Hess, Halliburton, Italmatch, Kemira, Kinder Morgan, Lubrizol, Marathon Oil, NALCO Champion, Occidental, Petrobras, RSI, Saudi Aramco, Schlumberger, Shell, SNF, Statoil and Total. This work was supported by the NSF Nanosystems Engineering Research Center for Nanotechnology-Enabled Water Treatment (ERC-1449500).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra01228k

‡ Present address: Baker Hughes Inc., Houston, Texas, USA.

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