Gelation Kinetics of Hydrogels Based on Acrylamide–AMPS–NVP Terpolymer, Bentonite, and Polyethylenimine for Conformance Control of Oil Reservoirs

Relatively smaller volumes of gelling systems had been used to address conformance problems located near the wellbore in oil reservoirs with harsh temperature and salinity conditions. These gelling systems were formulated with high concentrations of low-molecular-weight acrylamide-based polymers crosslinked with polyethylenimine (PEI). However, for in-depth conformance control, in which large gelant volumes and long gelation times were required, lower-base polymer loadings were necessary to ensure the economic feasibility of the treatment. In this study, a gelling system with high-molecular weight 2-acrylamido-2-methylpropane sulfonic acid (AMPS), N-vinyl-2-pyrrolidone (NVP), acrylamide terpolymer, and PEI, with the addition of bentonite as a filler, was formulated. The influence of the gelant formulation and reservoir conditions on the gelation kinetics and final gel strength of the system was investigated through bottle tests and rheological tests. The addition of clay in the formulation increased the gelation time, thermal stability, and syneresis resistance, and slightly improved the final gel strength. Furthermore, samples prepared with polymer and PEI concentrations below 1 wt %, natural bentonite, and PEI with molecular weight of 70,000 kg/kmol and pH of 11: (i) presented good injectivity and propagation parameters (pseudoplastic behavior and viscosity ~25 mPa·s); (ii) showed suitable gelation times for near wellbore (~5 h) or far wellbore (~21 h) treatments; and (iii) formed strong composite hydrogels (equilibrium complex modulus ~10–20 Pa and Sydansk code G to H) with low syneresis and good long-term stability (~3 to 6 months) under harsh conditions. Therefore, the use of high-molecular-weight base polymer and low-cost clay as active filler seems promising to improve the cost-effectiveness of gelling systems for in-depth conformance treatments under harsh conditions of temperature and salinity/hardness.


Introduction
Conformance control is a permeability-reducing treatment that can be applied to decrease or eliminate an oil recovery conformance problem in the wellbore or within the reservoir located near to or far from the wellbore (distances > 15 m). The problems include: (i) excessive and competing water or gas production emanating from a casing leak or flow behind the pipe; (ii) poor sweep efficiency and/or excessive co-production of the oil recovery drive fluid in a matrix-rock reservoir resulting from substantial permeability variation or anomalies (e.g., fractures); and (iii) water or gas from an Mg 2+ ), making them more favorable for high salinity/hardness applications than acrylate-acrylamide copolymers [19][20][21][22]. Also, the addition of lamellar clays to gelling formulations had been used to reduce the final cost of systems (filler), to increase the thermal resistance and mechanical strength (elastic modulus), as well as to reduce the syneresis and sensitivity to salinity of the (nano)composite hydrogels formed [23][24][25][26][27].
Therefore, the objective of this study was to investigate the effect of different parameters on the viscosity, gelation kinetics, and final gel strength of acrylamide-AMPS-NVP terpolymer, bentonite, and PEI systems through visual consistency testing (bottle tests) and dynamic shear tests. These parameters included (i) the gelant components, such as polymer concentration, crosslinker concentration, crosslinker properties (molecular weight and initial pH value), clay type (polycationic, sodium or organically modified), and clay concentration; as well as (ii) the reservoir conditions, such as temperature and salinity (total dissolved salt and salt type). Figure 1 shows the 13 C-NMR spectrum of the AMPS-NVP-AM terpolymer. The assignment of the peaks of the sample (Table 1) is in agreement with chemical shifts reported in the literature for acrylamide-based copolymers [15,[28][29][30][31][32][33][34].     The chemical shifts and peak areas (A) of the carbonyl carbons were used to determine the acrylamide (AM), AMPS, and NVP moieties of the polymer samples (Equations (1)-(3), respectively). Table 2 shows the AM, AMPS, and NVP moieties determined by 13 C-NMR, and the weight average molecular weight (M w ) and polydispersion (PD) assessed by gel permeation chromatography (GPC) of the polymer. Table 2. Chemical composition, molecular weight, and polydispersion of the polymer sample.

Evaluation of the Injectivity and Propagation of the Gelling Systems
The initial consistency and the viscosity profiles of the gelants prepared in injection water were used to evaluate the injectivity and propagation capacity of the systems within reservoir rocks. According to the Sydansk visual code [11,35], all gelants prepared in oilfield brines presented liquid-like behavior at 25 • C and were classified with code ≤ B. Even though important, these preliminary static visual measurements (bottle tests) did not appropriately reflect how the gelling systems behaved in various shear regimes during conformance treatment, such as (i) during preparation in the surface facilities and injection through the tubing from the surface to the formation (usually coil tubing with reduced cross section), where shear rates above 1,000 s −1 could be found (i.e., mixing devices and pumps); and (ii) during propagation in the perforations and formation, where shear rates lower than 20 s −1 were generally found [36]. Therefore, it is important to understand how the viscosity of the gelling systems is affected by different shear rates, and how the viscosity of the gelant varies at a constant shear rate typically found in oil reservoirs, in order to evaluate, respectively, the injectivity and the propagation capacity of the formulations.
According to the experimental results, all gelants behaved as pseudoplastic non-Newtonian fluids under the conditions analyzed ( Figure 2).
At rest, the gelling systems offered resistance to flow, mainly due to hydrogen bonding, entanglement of the polymer and crosslinker chains, and intra and intermolecular electrostatic repulsions promoted by the ionized sulfonate groups (-SO 3 − ), which led to the unfolding of the base polymer chains and improved the dispersion of the negatively charged clay particles. As the shear rate increased, there was a reduction of the apparent viscosity of the systems due to the disentanglement and alignment of the polymer and crosslinker chains and clay tactoids in the flow direction. Such behavior was reversible and the gelling systems recovered their original viscosity when the applied shear was reduced or ceased. At higher shear rates, when the disentanglement and alignment of the polymer and PEI chains and clay tactoids in the flow direction were maximum, the gelling systems tended asymptotically to a constant and defined apparent viscosity value. This moderate pseudoplastic behavior is extremely desirable to ensure good injectivity of gelants in conformance-improvement treatments. Near the wellbore, where high shear rates were found, the lower viscosity of pseudoplastic fluids reduced the fluid flow resistance, and thus decreased the power required for their injection into the reservoir. Away from the wellbore, where small average Gels 2019, 5, 7 5 of 23 shear rates were found, a moderate increase in the fluid viscosity assisted the oil displacement in the reservoir without creating an additional flow resistance.
Gels 2018, 4, x 5 of 23 disentanglement and alignment of the polymer and crosslinker chains and clay tactoids in the flow direction. Such behavior was reversible and the gelling systems recovered their original viscosity when the applied shear was reduced or ceased. At higher shear rates, when the disentanglement and alignment of the polymer and PEI chains and clay tactoids in the flow direction were maximum, the gelling systems tended asymptotically to a constant and defined apparent viscosity value. This moderate pseudoplastic behavior is extremely desirable to ensure good injectivity of gelants in conformance-improvement treatments. Near the wellbore, where high shear rates were found, the lower viscosity of pseudoplastic fluids reduced the fluid flow resistance, and thus decreased the power required for their injection into the reservoir. Away from the wellbore, where small average shear rates were found, a moderate increase in the fluid viscosity assisted the oil displacement in the reservoir without creating an additional flow resistance.
As expected, the shear viscosity of the gelants decreased at neutral pH values, and increased with rising polymer concentration, crosslinker concentration, molecular weight, and/or clay concentration due to (i) the increase in the polymer and PEI entanglements; (ii) the inter-and intramolecular electrostatic repulsion between the anionic sulfonate charged groups (-SO3 − ) that uncoiled the polymer chains, and the negative surface of the clay particles, which improved the particle dispersion; (iii) the adsorption of the polymer and the crosslinker on the clay particles by means of hydrogen bonds between the protons of the amide groups (-CONH2) of PEI and acrylamide, as well as the carbonyl oxygen of the NVP, and the silanol (-Si-OH) and aluminol (-Al-OH) groups of the clay platelets; and (iv) the clay/clay tactoid interactions [37][38][39].
In addition, all formulations except F4, prepared with PEI 750,000 kg/kmol, and F7, presented apparent viscosity between 10 and 30 mPa·s at a constant shear rate of 7.3 s −1 ( Figure 2); these values recommended to ensure good propagation of the gelling systems in porous media [4,6,40,41]. Therefore, the polymer concentration and molecular weight of the crosslinker were the parameters that most strongly affected the viscosity of the gelants. Gels 2018, 4, x disentanglement and alignment of the polymer and cross direction. Such behavior was reversible and the gelling when the applied shear was reduced or ceased. At higher alignment of the polymer and PEI chains and clay tactoid gelling systems tended asymptotically to a constant and d  This moderate pseudoplastic behavior is extremely de in conformance-improvement treatments. Near the wellbo lower viscosity of pseudoplastic fluids reduced the fluid power required for their injection into the reservoir. Awa shear rates were found, a moderate increase in the fluid vi reservoir without creating an additional flow resistance.
As expected, the shear viscosity of the gelants decre with rising polymer concentration, crosslinker concen concentration due to (i) the increase in the polymer an intramolecular electrostatic repulsion between the anion uncoiled the polymer chains, and the negative surface o particle dispersion; (iii) the adsorption of the polymer an means of hydrogen bonds between the protons of th acrylamide, as well as the carbonyl oxygen of the NVP, an OH) groups of the clay platelets; and (iv) the clay/clay tact In addition, all formulations except F4, prepared wit apparent viscosity between 10 and 30 mPa·s at a constant recommended to ensure good propagation of the gelli Therefore, the polymer concentration and molecular weig that most strongly affected the viscosity of the gelants.

F1,
Gels 2018, 4, x disentanglement and alignment of the polyme direction. Such behavior was reversible and t when the applied shear was reduced or ceased alignment of the polymer and PEI chains and gelling systems tended asymptotically to a con This moderate pseudoplastic behavior is e in conformance-improvement treatments. Nea lower viscosity of pseudoplastic fluids reduc power required for their injection into the rese shear rates were found, a moderate increase in reservoir without creating an additional flow r As expected, the shear viscosity of the g with rising polymer concentration, crosslin concentration due to (i) the increase in the intramolecular electrostatic repulsion betwee uncoiled the polymer chains, and the negativ particle dispersion; (iii) the adsorption of the means of hydrogen bonds between the pr acrylamide, as well as the carbonyl oxygen of t OH) groups of the clay platelets; and (iv) the c In addition, all formulations except F4, p apparent viscosity between 10 and 30 mPa·s at recommended to ensure good propagation Therefore, the polymer concentration and mo that most strongly affected the viscosity of the F2, Gels 2018, 4, x disentanglement and alignment of direction. Such behavior was reve when the applied shear was reduce alignment of the polymer and PEI c gelling systems tended asymptotic This moderate pseudoplastic b in conformance-improvement treat lower viscosity of pseudoplastic f power required for their injection i shear rates were found, a moderate reservoir without creating an addit As expected, the shear viscos with rising polymer concentratio concentration due to (i) the incre intramolecular electrostatic repuls uncoiled the polymer chains, and particle dispersion; (iii) the adsorp means of hydrogen bonds betwe acrylamide, as well as the carbonyl OH) groups of the clay platelets; an In addition, all formulations e apparent viscosity between 10 and recommended to ensure good pr Therefore, the polymer concentrati that most strongly affected the visc F3, and Gels 2018, 4, x disentanglement an direction. Such beh when the applied sh alignment of the pol gelling systems tend This moderate p in conformance-imp lower viscosity of p power required for shear rates were fou reservoir without cr As expected, th with rising polym concentration due t intramolecular elect uncoiled the polym particle dispersion; means of hydrogen acrylamide, as well OH) groups of the c In addition, all apparent viscosity b recommended to e Therefore, the polym that most strongly a F4 with polyethylenimine (PEI) pH 7; Gels 2018, 4, x disentanglement and alignment of the polymer and crosslinker cha direction. Such behavior was reversible and the gelling systems re when the applied shear was reduced or ceased. At higher shear rates alignment of the polymer and PEI chains and clay tactoids in the flo gelling systems tended asymptotically to a constant and defined app  This moderate pseudoplastic behavior is extremely desirable to e in conformance-improvement treatments. Near the wellbore, where lower viscosity of pseudoplastic fluids reduced the fluid flow res power required for their injection into the reservoir. Away from the shear rates were found, a moderate increase in the fluid viscosity ass reservoir without creating an additional flow resistance.
As expected, the shear viscosity of the gelants decreased at ne with rising polymer concentration, crosslinker concentration, m concentration due to (i) the increase in the polymer and PEI en intramolecular electrostatic repulsion between the anionic sulfona uncoiled the polymer chains, and the negative surface of the clay particle dispersion; (iii) the adsorption of the polymer and the cro means of hydrogen bonds between the protons of the amide acrylamide, as well as the carbonyl oxygen of the NVP, and the silan OH) groups of the clay platelets; and (iv) the clay/clay tactoid intera In addition, all formulations except F4, prepared with PEI 750 apparent viscosity between 10 and 30 mPa·s at a constant shear rate recommended to ensure good propagation of the gelling system Therefore, the polymer concentration and molecular weight of the that most strongly affected the viscosity of the gelants. F4, disentanglement and alignment of the polymer and cros direction. Such behavior was reversible and the gelling when the applied shear was reduced or ceased. At higher alignment of the polymer and PEI chains and clay tactoid gelling systems tended asymptotically to a constant and d  This moderate pseudoplastic behavior is extremely d in conformance-improvement treatments. Near the wellb lower viscosity of pseudoplastic fluids reduced the flui power required for their injection into the reservoir. Aw shear rates were found, a moderate increase in the fluid v reservoir without creating an additional flow resistance.
As expected, the shear viscosity of the gelants decr with rising polymer concentration, crosslinker conce concentration due to (i) the increase in the polymer a intramolecular electrostatic repulsion between the anio uncoiled the polymer chains, and the negative surface particle dispersion; (iii) the adsorption of the polymer a means of hydrogen bonds between the protons of t acrylamide, as well as the carbonyl oxygen of the NVP, a OH) groups of the clay platelets; and (iv) the clay/clay tac In addition, all formulations except F4, prepared wi apparent viscosity between 10 and 30 mPa·s at a constant recommended to ensure good propagation of the gell Therefore, the polymer concentration and molecular wei that most strongly affected the viscosity of the gelants. direction. Such behavior was reversible and when the applied shear was reduced or ceased alignment of the polymer and PEI chains and gelling systems tended asymptotically to a con This moderate pseudoplastic behavior is e in conformance-improvement treatments. Nea lower viscosity of pseudoplastic fluids reduc power required for their injection into the res shear rates were found, a moderate increase in reservoir without creating an additional flow As expected, the shear viscosity of the g with rising polymer concentration, crosslin concentration due to (i) the increase in the intramolecular electrostatic repulsion betwee uncoiled the polymer chains, and the negati particle dispersion; (iii) the adsorption of the means of hydrogen bonds between the pr acrylamide, as well as the carbonyl oxygen of OH) groups of the clay platelets; and (iv) the c In addition, all formulations except F4, p apparent viscosity between 10 and 30 mPa·s a recommended to ensure good propagation Therefore, the polymer concentration and mo that most strongly affected the viscosity of the F6, and alignment of the polymer and gelling systems tended asympt This moderate pseudoplas in conformance-improvement t lower viscosity of pseudoplas power required for their inject shear rates were found, a mode reservoir without creating an a As expected, the shear vi with rising polymer concent concentration due to (i) the i intramolecular electrostatic re uncoiled the polymer chains, particle dispersion; (iii) the ad means of hydrogen bonds b acrylamide, as well as the carb OH) groups of the clay platelet In addition, all formulatio apparent viscosity between 10 recommended to ensure good Therefore, the polymer concen that most strongly affected the F4 with PEI 750,000 kg/kmol and alignment of the polymer and PEI chains and clay tactoids in the flow direction we gelling systems tended asymptotically to a constant and defined apparent viscosity   This moderate pseudoplastic behavior is extremely desirable to ensure good inje in conformance-improvement treatments. Near the wellbore, where high shear rate lower viscosity of pseudoplastic fluids reduced the fluid flow resistance, and th power required for their injection into the reservoir. Away from the wellbore, whe shear rates were found, a moderate increase in the fluid viscosity assisted the oil dis reservoir without creating an additional flow resistance.
As expected, the shear viscosity of the gelants decreased at neutral pH value with rising polymer concentration, crosslinker concentration, molecular weig concentration due to (i) the increase in the polymer and PEI entanglements; (i intramolecular electrostatic repulsion between the anionic sulfonate charged gro uncoiled the polymer chains, and the negative surface of the clay particles, whi particle dispersion; (iii) the adsorption of the polymer and the crosslinker on the means of hydrogen bonds between the protons of the amide groups (-CON acrylamide, as well as the carbonyl oxygen of the NVP, and the silanol (-Si-OH) an OH) groups of the clay platelets; and (iv) the clay/clay tactoid interactions [37][38][39].
In addition, all formulations except F4, prepared with PEI 750,000 kg/kmol, a apparent viscosity between 10 and 30 mPa·s at a constant shear rate of 7.3 s −1 (Figur recommended to ensure good propagation of the gelling systems in porous m Therefore, the polymer concentration and molecular weight of the crosslinker wer that most strongly affected the viscosity of the gelants. As expected, the shear viscosity of the gelants decreased at neutral pH values, and increased with rising polymer concentration, crosslinker concentration, molecular weight, and/or clay concentration due to (i) the increase in the polymer and PEI entanglements; (ii) the inter-and intramolecular electrostatic repulsion between the anionic sulfonate charged groups (-SO 3 − ) that uncoiled the polymer chains, and the negative surface of the clay particles, which improved the particle dispersion; (iii) the adsorption of the polymer and the crosslinker on the clay particles by means of hydrogen bonds between the protons of the amide groups (-CONH 2 ) of PEI and acrylamide, as well as the carbonyl oxygen of the NVP, and the silanol (-Si-OH) and aluminol (-Al-OH) groups of the clay platelets; and (iv) the clay/clay tactoid interactions [37][38][39].
In addition, all formulations except F4, prepared with PEI 750,000 kg/kmol, and F7, presented apparent viscosity between 10 and 30 mPa·s at a constant shear rate of 7.3 s −1 ( Figure 2); these values recommended to ensure good propagation of the gelling systems in porous media [4,6,40,41]. Therefore, the polymer concentration and molecular weight of the crosslinker were the parameters that most strongly affected the viscosity of the gelants.

Influence of the Gelant Components and Reservoir Conditions on the Gelation Time and Gel Strength
The influence of the gelant components and reservoir conditions on the gelation kinetics and final gel strength of acrylamide-AMPS-NVP terpolymer, bentonite, and PEI systems was assessed by varying individually each parameter, while keeping the others constant.

Polymer Concentration
Gelants with higher polymer concentration presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength) ( Figure 3). As the polymer concentration increased in the gelling system, so did the intermolecular entanglements, hydrogen bonds between the polymer chains and clay particles, and intra and intermolecular electrostatic repulsions between sulfonate groups of AMPS (-SO 3 − ) and newly charged carboxylate groups (-COO − ) formed by the thermal hydrolysis of the acrylamide at temperatures above 80 • C, which uncoiled the polymer chains and improved the dispersion of the negatively charged particles within the gelant. As a result, more crosslinking sites of the polymer chains (acrylamide groups) became accessible to react with PEI, reducing the gelation time and increasing the final gel strength.
more crosslinking sites of the polymer chains (acrylamide groups) became accessible to react with PEI, reducing the gelation time and increasing the final gel strength.
As previously discussed, even though the system prepared with a polymer concentration of 1.0 wt % (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = H and G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth conformance treatments due to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43].  more crosslinking sites of the polymer chains (a PEI, reducing the gelation time and increasing th As previously discussed, even though the sy wt % (F7) showed gelation time around 5 h and H and G*e ~ 18 Pa), this formulation was conside due to the high viscosity at low shear rates (~5 polymer concentration from 1.0 wt % (F7) to 0.6 mPa·s, increased the gelation time to 13 h, and c deformable type (with Sydansk code = F and G*e system. Therefore, greater polymer loadings were r However, higher polymer concentrations result propagation of the systems) and shorter g improvement treatments, in which low viscosit opposing effects must be properly balanced [42,4  , 0.6 wt % (F4); and , 1.0 w more crosslinking sites of the polymer chains (acrylam PEI, reducing the gelation time and increasing the final As previously discussed, even though the system p wt % (F7) showed gelation time around 5 h and formed H and G*e ~ 18 Pa), this formulation was considered uns due to the high viscosity at low shear rates (~50 mPa polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F mPa·s, increased the gelation time to 13 h, and changed deformable type (with Sydansk code = F and G*e ~ 9 Pa), system. Therefore, greater polymer loadings were required However, higher polymer concentrations resulted in h propagation of the systems) and shorter gelation improvement treatments, in which low viscosities and opposing effects must be properly balanced [42,43]. ns and improved the dispersion of the negatively charged particles within the gelant. As a result, e crosslinking sites of the polymer chains (acrylamide groups) became accessible to react with reducing the gelation time and increasing the final gel strength.
As previously discussed, even though the system prepared with a polymer concentration of 1.0 (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = d G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth conformance treatments to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base mer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 ·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly rmable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling m. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. ever, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and agation of the systems) and shorter gelation times. Thus, for in-depth conformanceovement treatments, in which low viscosities and longer gelation times were required, these sing effects must be properly balanced [42,43]. mproved the dispersion of the negatively charged particles within the gelant. As a result, inking sites of the polymer chains (acrylamide groups) became accessible to react with g the gelation time and increasing the final gel strength. viously discussed, even though the system prepared with a polymer concentration of 1.0 owed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = 18 Pa), this formulation was considered unsuitable for in-depth conformance treatments high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base centration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 ased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling re, greater polymer loadings were required to formulate stronger composite hydrogels. igher polymer concentrations resulted in higher viscosities (limiting the injectivity and of the systems) and shorter gelation times. Thus, for in-depth conformancent treatments, in which low viscosities and longer gelation times were required, these fects must be properly balanced [42,43].  s and improved the dispersion of the negatively charged particles within the gelant. As a result, crosslinking sites of the polymer chains (acrylamide groups) became accessible to react with reducing the gelation time and increasing the final gel strength. As previously discussed, even though the system prepared with a polymer concentration of 1.0 (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = d G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth conformance treatments to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base mer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly mable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling m. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. ever, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and agation of the systems) and shorter gelation times. Thus, for in-depth conformanceovement treatments, in which low viscosities and longer gelation times were required, these sing effects must be properly balanced [42,43]. oved the dispersion of the negatively charged particles within the gelant. As a result, ng sites of the polymer chains (acrylamide groups) became accessible to react with e gelation time and increasing the final gel strength. sly discussed, even though the system prepared with a polymer concentration of 1.0 ed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = a), this formulation was considered unsuitable for in-depth conformance treatments viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base tration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling greater polymer loadings were required to formulate stronger composite hydrogels. r polymer concentrations resulted in higher viscosities (limiting the injectivity and the systems) and shorter gelation times. Thus, for in-depth conformanceeatments, in which low viscosities and longer gelation times were required, these must be properly balanced [42,43].
Complex modulus (─) and gel strength (--) versus time for samples prepared in field water with 0.8 wt % of clay, 0.5 wt % of PEI, and different polymer concentrations.
As previously discussed, even though the system prepared with a polymer concentration of 1.0 wt % (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = H and G* e~1 8 Pa), this formulation was considered unsuitable for in-depth conformance treatments due to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly deformable type (with Sydansk code = F and G* e~9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformance-improvement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43].

Crosslinker Concentration
Gelants with higher PEI concentration presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength) ( Figure 4). As the crosslinker concentration increased in the gelling system, a greater number of crosslinking sites became available to react with Gelants with higher PEI concentration presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength) ( Figure 4). As the crosslinker concentration increased in the gelling system, a greater number of crosslinking sites became available to react with the acrylamide groups of the polymer chains, reducing the gelation time and increasing the final gel strength.
With formulation F4 as reference, when the crosslinker concentration increased twofold to 1.0 wt % (F6), the viscosity of the gelant increased to 29 mPa·s and the gelation time decreased to 9 h. However, the system formed a deformable non-flowing gel after 48 h (with Sydansk code = G and G*e ~ 14 Pa). Nevertheless, the growth rate of the equilibrium complex modulus (G*e) promoted by the increase of the crosslinker concentration was less pronounced than the rate provided by the increase in the polymer concentration, and the final strength of the composite hydrogels was mainly determined by the concentration of polymer in the formulation rather than the concentration of PEI [16,44].
Furthermore, when PEI was not added, as in formulation F2, or the concentration of the crosslinker was too low (<0.1 wt %), the gelation did not take place and the system presented liquidlike behavior (Sydansk code = A and G*e ~ 0.1 Pa). However, this does not mean that the higher the crosslinker concentration, the better the gel performance will be.
Adding crosslinker in excess may lead to over-crosslinking of the polymer chains, and consequently can cause syneresis of the hydrogels, reducing the blocking effectiveness of the gel treatment [42,45,46].
In this study, gelling systems with crosslinker concentration above 1.0 wt % presented syneresis after 30 days. Therefore, to achieve long-term stability, it is very important to use suitable crosslinker concentrations in the formulation of gelling systems [43,47].

Crosslinker Molecular Weight
Gelants prepared with PEI with higher molecular weight presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength). As the molecular weight of the crosslinker increased, more crosslinking sites became available to react with the acrylamide groups, reducing the gelation time and increasing the final gel strength. deformable type (with Sydansk code = F and G*e ~ system. Therefore, greater polymer loadings were re However, higher polymer concentrations resulte propagation of the systems) and shorter ge improvement treatments, in which low viscositi opposing effects must be properly balanced [42,4  , 0.6 wt % (F4); and , 1.0 w deformable type (with Sydansk code = F and G*e ~ 9 Pa), system. Therefore, greater polymer loadings were required However, higher polymer concentrations resulted in hi propagation of the systems) and shorter gelation improvement treatments, in which low viscosities and opposing effects must be properly balanced [42,43]. ·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly rmable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling m. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. ever, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and agation of the systems) and shorter gelation times. Thus, for in-depth conformanceovement treatments, in which low viscosities and longer gelation times were required, these sing effects must be properly balanced [42,43]. ased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling re, greater polymer loadings were required to formulate stronger composite hydrogels. igher polymer concentrations resulted in higher viscosities (limiting the injectivity and of the systems) and shorter gelation times. Thus, for in-depth conformancent treatments, in which low viscosities and longer gelation times were required, these fects must be properly balanced [42,43]. , 0.5 wt % (F4); and s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly mable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling m. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. ever, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and agation of the systems) and shorter gelation times. Thus, for in-depth conformanceovement treatments, in which low viscosities and longer gelation times were required, these sing effects must be properly balanced [42,43]. the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling greater polymer loadings were required to formulate stronger composite hydrogels. r polymer concentrations resulted in higher viscosities (limiting the injectivity and the systems) and shorter gelation times. Thus, for in-depth conformanceeatments, in which low viscosities and longer gelation times were required, these must be properly balanced [42,43].
Complex modulus (─) and gel strength (--) versus time for samples prepared in field water with 0.8 wt % of clay, 0.5 wt % of PEI, and different polymer concentrations.
Nevertheless, the growth rate of the equilibrium complex modulus (G* e ) promoted by the increase of the crosslinker concentration was less pronounced than the rate provided by the increase in the polymer concentration, and the final strength of the composite hydrogels was mainly determined by the concentration of polymer in the formulation rather than the concentration of PEI [16,44].
Furthermore, when PEI was not added, as in formulation F2, or the concentration of the crosslinker was too low (<0.1 wt %), the gelation did not take place and the system presented liquid-like behavior (Sydansk code = A and G* e~0 .1 Pa). However, this does not mean that the higher the crosslinker concentration, the better the gel performance will be.
Adding crosslinker in excess may lead to over-crosslinking of the polymer chains, and consequently can cause syneresis of the hydrogels, reducing the blocking effectiveness of the gel treatment [42,45,46].
In this study, gelling systems with crosslinker concentration above 1.0 wt % presented syneresis after 30 days. Therefore, to achieve long-term stability, it is very important to use suitable crosslinker concentrations in the formulation of gelling systems [43,47].

Crosslinker Molecular Weight
Gelants prepared with PEI with higher molecular weight presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength). As the molecular weight of the crosslinker increased, more crosslinking sites became available to react with the acrylamide groups, reducing the gelation time and increasing the final gel strength.
With formulation F4 prepared with PEI with 70,000 kg/kmol as reference, when the molecular weight of the crosslinker increased tenfold to 750,000 kg/kmol, the viscosity increased to 37 mPa·s and the gelation time decreased to 9 h. However, the system formed a strong gel after 48 h (with Sydansk Gels 2019, 5, 7 8 of 23 code = G and G* e~1 1 Pa). On the other hand, when the molecular weight of the crosslinker was 10,000 kg/kmol, the viscosity decreased to 21 mPa·s, the gelation time increased to 16 h, and formed a highly deformable gel after 48 h (with Sydansk code = F and G* e~5 Pa).
The growth rate of the equilibrium complex modulus (G* e ) promoted by the increase in the molecular weight of the crosslinker was less pronounced than the rate caused by the increase in the crosslinker concentration. Furthermore, the addition of the crosslinker with a higher molecular weight caused syneresis of the hydrogels after 30 days at lower concentrations (above 0.5 wt %). Therefore, the crosslinker molecular weight can be used to fine tune the gelation kinetics and final gel strength of gelant formulations.

Crosslinker Initial pH Value (Gelant pH Value)
During the preparation of the systems, we observed that the initial pH of the crosslinker controlled the pH value of the formulation. For instance, samples prepared with PEI having a pH value of 11 presented pH values around 11. Therefore, the discussion that follows applies to both effects-the initial pH value of PEI and the initial pH value of the gelling system.
The initial pH value of PEI or of the gelant changed the gelation kinetics and the final gel strength significantly. Gelants prepared with PEI with initial acid or alkaline pH values presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength) than formulations prepared with PEI having the initial pH of 7.
With formulation F4 prepared with PEI with the initial pH value of 11 as reference, when the pH value was around 7, the viscosity was slightly reduced to 21 mPa·s, the gelation time increased to~21 h, and the final gel strength was substantially reduced to G* e~1 Pa (with Sydansk code = C). In contrast, when the initial pH value of PEI was around 2, the viscosity increased to 23.5 mPa·s, the gelation time decreased to~12 h, and the final gel strength declined to G* e~5 Pa (with Sydansk code = E). In contrast, when the initial pH value of PEI was around 2, the viscosity increased to 23.5 mPa·s, the gelation time decreased to~12 h, and the final gel strength declined to G* e~5 Pa (with Sydansk code = E). When the initial pH value of PEI was around 9, the viscosity increased to 22 mPa·s, the gelation time decreased to~15 h, and the final gel strength declined to G* e~6 Pa (with Sydansk code = F).
In acid or alkaline conditions, the hydrolysis rate of the amide groups of the terpolymer was greater than that at the pH value of 7 [42]. Hence, the intra and intermolecular electrostatic repulsion between the newly charged carboxylate groups (-COO − ) and the existing sulfonate groups (-SO 3 − ) uncoiled the polymer chains. As a result, the acrylamide groups became more accessible to the crosslinker molecules, reducing the gelation time and increasing the final gel strength. Furthermore, the formation of stable three-dimensional structure (chemical hydrogel) by means of transamidation reactions (covalent bonding between the crosslinker and acrylamide-based polymer chains) depended on the initial nucleophilic attack of the amine nitrogen of the PEI on the carbonyl carbon of the amide groups of the polyacrylamide [8,9].
Nevertheless, according to Man [48], around 73%, 50%, 33%, 25%, and 4% of the unshared electron pairs of the nitrogen of the primary, secondary, and tertiary amino groups of the PEI were protonated at pH values of 2, 4, 5, 8, and 10, respectively. Thus, the nucleophilicity of PEI with acid-neutral pH values significantly decreased, making it less effective in crosslinking the acrylamide-based terpolymer, which led to embrittlement of the hydrogels (gel breakage). These results were in accordance with other findings reported in the literature [8,49].
Moreover, the protonation of PEI under acid or neutral pH values created positive charges along the polymer backbones. The intra-and intermolecular electrostatic repulsions among the charged groups promoted the extension of the crosslinker chains, favoring the adsorption of the PEI chains onto the negatively charged clay surfaces (even though the clay edges were positively charged), and the agglomeration of clay particles through the neutralization of the charged sites. On the other hand, under alkaline conditions there were insufficient positive charges on the polymer backbone of PEI to keep the molecules extended through inter-and intrachain electrostatic repulsions, and both the edges and faces of the clay platelets carried negative charges. The lack of positive charges and the more compact conformation of the polymer chains reduced the adsorption of PEI onto the negatively charged clay particles, disfavoring the flocculation of the clay. Thus, more amino groups of the crosslinker were effectively available to react with the acrylamide-based copolymer chains, increasing the final gel strength [50].
In this study, we observed that PEI with a pH value of at least 9 was required to produce stable and homogeneous composite hydrogels. The deprotonated form of the PEI (with more primary and secondary unshared electron pairs of nitrogen available) was more reactive with the amide groups of the polymer.
Therefore, when designing a conformance-improvement treatment, it is important to take into account factors that can lead to changes in the pH value of the crosslinker or the gelant (e.g., gelant mixing with reservoir fluids, reaction/adsorption of the gelant components with the formation, and presence of sour gases such as CO 2 and H 2 S).

Clay Concentration
Gelants prepared with a higher clay concentration presented longer gelation times and slightly greater storage modulus, and thus complex modulus (final gel strength). In the absence of clay, the polymer chains were randomly crosslinked by PEI, forming conventional hydrogel structures. However, when clay was added to the gelant formulation, the nonionic functional groups of the polymer chains (acrylamide and NVP) adsorbed onto the bentonite particles through strong hydrogen bonds between the amide protons of the acrylamide and the carbonyl oxygen of the NVP and the silanol (-Si-OH) and aluminol (-Al-OH) groups of the clay platelets, reducing the number of crosslinking sites effectively available to react with PEI, thereby delaying the gelation reactions [39].
Moreover, the adsorption of the polymer chains onto the clay particles reinforced the hydrogel network, mainly through the formation of clay networks and the diffusion of polymer chains through clay tactoids (restricting their mobility). Within the composite hydrogel structure, the clay particles acted as active fillers, contributing to slightly increase the elastic modulus of the gel [23,[51][52][53].
With formulation F4 as reference, when the clay concentration increased twofold to 1.6 wt % (F5), the viscosity of the gelant increased to 26 mPa·s, the gelation time was delayed to 15 h, and the final gel strength slightly increased to G* e~1 0 Pa (Sydansk code F). On the other hand, when no clay was added to the formulation (F3), the viscosity of the gelant decreased to 19 mPa·s, the gelation time decreased to 11 h, and the final gel strength decreased to G* e~6 .5 Pa (Sydansk code F).
Furthermore, the final strength (complex modulus) of the composite hydrogels remained unchanged during the thermal aging process for a longer period than the conventional hydrogels (with no clay), indicating a greater thermal stability of these hybrid clay/polymer structures (~6 months).
In the presence of high salinity/hardness brines (e.g., formation water), the composite hydrogels exhibited less syneresis than the conventional hydrogels. The higher resistance to volume shrinkage was attributed to the interaction of the clay tactoids with polymer segments throughout the gel network.
Although the addition of clay to the gelant formulation increased the gelation time, the thermal stability and the syneresis resistance of the composite hydrogel, when added above a certain concentration (1.6 wt %) the proper dispersion of the clay particles between polymer chains did not take place [23,54].

Clay Type
In the X-ray diffraction spectra ( Figure 5), the sodium bentonite, polycationic bentonite, and organically modified bentonite had strong peaks at 2θ of around 6.8 • , 5.9 • , and 4.8 • , respectively, which corresponded to basal spacing of approximately 13, 15, and 18 Å. According to the results shown in Figure 5, it is possible to suggest the morphology of the formed hydrogels. The sodium bentonite formed nanocomposite hydrogels with exfoliated structure in distilled water, with bentonite platelets dispersed in the polymer matrix at nanoscale ( Figure 6). This resulted in stronger interactions between the polymer chains and clay layers, resulting in greater final gel strength. However, it reduced the gelation time, probably because the individual clay platelets acted as additional crosslinking sites for the polymer chains ( Figure 6). shown in Figure 5, it is possible to suggest the morphology of the formed hydrogels. The sodium bentonite formed nanocomposite hydrogels with exfoliated structure in distilled water, with bentonite platelets dispersed in the polymer matrix at nanoscale ( Figure 6). This resulted in stronger interactions between the polymer chains and clay layers, resulting in greater final gel strength. However, it reduced the gelation time, probably because the individual clay platelets acted as additional crosslinking sites for the polymer chains ( Figure 6).   shown in Figure 5, it is possible to suggest the morphology of the formed hydrogels. The sodium bentonite formed nanocomposite hydrogels with exfoliated structure in distilled water, with bentonite platelets dispersed in the polymer matrix at nanoscale ( Figure 6). This resulted in stronger interactions between the polymer chains and clay layers, resulting in greater final gel strength. However, it reduced the gelation time, probably because the individual clay platelets acted as additional crosslinking sites for the polymer chains ( Figure 6).   Gelants with higher polymer co modulus, and thus complex modul increased in the gelling system, so d the polymer chains and clay particle sulfonate groups of AMPS (-SO3 − ) a thermal hydrolysis of the acrylami chains and improved the dispersion more crosslinking sites of the polym PEI, reducing the gelation time and As previously discussed, even t wt % (F7) showed gelation time arou H and G*e ~ 18 Pa), this formulation due to the high viscosity at low sh polymer concentration from 1.0 wt % mPa·s, increased the gelation time to deformable type (with Sydansk code system. Therefore, greater polymer load However, higher polymer concentra propagation of the systems) and improvement treatments, in which opposing effects must be properly b Gelants with higher polymer concentra modulus, and thus complex modulus (fina increased in the gelling system, so did the the polymer chains and clay particles, and sulfonate groups of AMPS (-SO3 − ) and new thermal hydrolysis of the acrylamide at t chains and improved the dispersion of the n more crosslinking sites of the polymer cha PEI, reducing the gelation time and increas As previously discussed, even though wt % (F7) showed gelation time around 5 h H and G*e ~ 18 Pa), this formulation was co due to the high viscosity at low shear rat polymer concentration from 1.0 wt % (F7) t mPa·s, increased the gelation time to 13 h, a deformable type (with Sydansk code = F an system. Therefore, greater polymer loadings w However, higher polymer concentrations r propagation of the systems) and short improvement treatments, in which low vi opposing effects must be properly balanced

Influence of the Gelant Components and Reservoir Conditions on the Gelation Time and Gel Streng
The influence of the gelant components and reservoir conditions on the gelation kinetics final gel strength of acrylamide-AMPS-NVP terpolymer, bentonite, and PEI systems was asse by varying individually each parameter, while keeping the others constant.

Polymer Concentration
Gelants with higher polymer concentration presented shorter gelation times and greater sto modulus, and thus complex modulus (final gel strength) ( Figure 3). As the polymer concentr increased in the gelling system, so did the intermolecular entanglements, hydrogen bonds bet the polymer chains and clay particles, and intra and intermolecular electrostatic repulsions bet sulfonate groups of AMPS (-SO3 − ) and newly charged carboxylate groups (-COO − ) formed b thermal hydrolysis of the acrylamide at temperatures above 80 °C, which uncoiled the pol chains and improved the dispersion of the negatively charged particles within the gelant. As a r more crosslinking sites of the polymer chains (acrylamide groups) became accessible to react PEI, reducing the gelation time and increasing the final gel strength.
As previously discussed, even though the system prepared with a polymer concentration wt % (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk co H and G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth conformance treatm due to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a h deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the ge system.
Therefore, greater polymer loadings were required to formulate stronger composite hydro However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity propagation of the systems) and shorter gelation times. Thus, for in-depth conform improvement treatments, in which low viscosities and longer gelation times were required, opposing effects must be properly balanced [42,43].

Influence of the Gelant Components and Reservoir Conditions on the Gelation Time and Gel Strength
The influence of the gelant components and reservoir conditions on the gelation kinetics and final gel strength of acrylamide-AMPS-NVP terpolymer, bentonite, and PEI systems was assessed by varying individually each parameter, while keeping the others constant.

Polymer Concentration
Gelants with higher polymer concentration presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength) ( Figure 3). As the polymer concentration increased in the gelling system, so did the intermolecular entanglements, hydrogen bonds between the polymer chains and clay particles, and intra and intermolecular electrostatic repulsions between sulfonate groups of AMPS (-SO3 − ) and newly charged carboxylate groups (-COO − ) formed by the thermal hydrolysis of the acrylamide at temperatures above 80 °C, which uncoiled the polymer chains and improved the dispersion of the negatively charged particles within the gelant. As a result, more crosslinking sites of the polymer chains (acrylamide groups) became accessible to react with PEI, reducing the gelation time and increasing the final gel strength.
As previously discussed, even though the system prepared with a polymer concentration of 1.0 wt % (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sydansk code = H and G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth conformance treatments due to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reduction of the base polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of the gelant to 24 mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to a highly deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system.
Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43].

Influence of the Gelant Components and Reservoir Conditions on the Gelation
The influence of the gelant components and reservoir conditions on t final gel strength of acrylamide-AMPS-NVP terpolymer, bentonite, and P by varying individually each parameter, while keeping the others constant.

Polymer Concentration
Gelants with higher polymer concentration presented shorter gelation t modulus, and thus complex modulus (final gel strength) ( Figure 3). As th increased in the gelling system, so did the intermolecular entanglements, h the polymer chains and clay particles, and intra and intermolecular electros sulfonate groups of AMPS (-SO3 − ) and newly charged carboxylate groups thermal hydrolysis of the acrylamide at temperatures above 80 °C, whic chains and improved the dispersion of the negatively charged particles with more crosslinking sites of the polymer chains (acrylamide groups) became PEI, reducing the gelation time and increasing the final gel strength.
As previously discussed, even though the system prepared with a poly wt % (F7) showed gelation time around 5 h and formed a strong gel after 48 H and G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth due to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, th polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the vis mPa·s, increased the gelation time to 13 h, and changed the quality of the g deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the bloc system.
Therefore, greater polymer loadings were required to formulate strong However, higher polymer concentrations resulted in higher viscosities (lim propagation of the systems) and shorter gelation times. Thus, for improvement treatments, in which low viscosities and longer gelation tim opposing effects must be properly balanced [42,43].

Influence of the Gelant Components and Reservoir Conditions on the Gelation Time and G
The influence of the gelant components and reservoir conditions on the gelation final gel strength of acrylamide-AMPS-NVP terpolymer, bentonite, and PEI systems by varying individually each parameter, while keeping the others constant.

Polymer Concentration
Gelants with higher polymer concentration presented shorter gelation times and g modulus, and thus complex modulus (final gel strength) ( Figure 3). As the polymer increased in the gelling system, so did the intermolecular entanglements, hydrogen bo the polymer chains and clay particles, and intra and intermolecular electrostatic repuls sulfonate groups of AMPS (-SO3 − ) and newly charged carboxylate groups (-COO − ) f thermal hydrolysis of the acrylamide at temperatures above 80 °C, which uncoiled chains and improved the dispersion of the negatively charged particles within the gelan more crosslinking sites of the polymer chains (acrylamide groups) became accessible PEI, reducing the gelation time and increasing the final gel strength.
As previously discussed, even though the system prepared with a polymer concen wt % (F7) showed gelation time around 5 h and formed a strong gel after 48 h (with Sy H and G*e ~ 18 Pa), this formulation was considered unsuitable for in-depth conforman due to the high viscosity at low shear rates (~50 mPa·s). Nevertheless, the reductio polymer concentration from 1.0 wt % (F7) to 0.6 wt % (F4) decreased the viscosity of th mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a st deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability system. Therefore, greater polymer loadings were required to formulate stronger compos However, higher polymer concentrations resulted in higher viscosities (limiting the i propagation of the systems) and shorter gelation times. Thus, for in-depth improvement treatments, in which low viscosities and longer gelation times were re opposing effects must be properly balanced [42,43].  shown in Figure 5, it is possible to suggest the morphology of the form bentonite formed nanocomposite hydrogels with exfoliated structur bentonite platelets dispersed in the polymer matrix at nanoscale (Figure interactions between the polymer chains and clay layers, resulting in However, it reduced the gelation time, probably because the individ additional crosslinking sites for the polymer chains ( Figure 6).  bentonite formed nanocomposite hydrogels with exfoliated struc bentonite platelets dispersed in the polymer matrix at nanoscale (Figu interactions between the polymer chains and clay layers, resulting However, it reduced the gelation time, probably because the indi additional crosslinking sites for the polymer chains ( Figure 6).  , organically modified bentonite composite (distilled water); bentonite formed nanocomposite hydrogels with exfoliated structure in distilled water, with bentonite platelets dispersed in the polymer matrix at nanoscale (Figure 6). This resulted in stronger interactions between the polymer chains and clay layers, resulting in greater final gel strength. However, it reduced the gelation time, probably because the individual clay platelets acted as additional crosslinking sites for the polymer chains ( Figure 6).  bentonite formed nanocomposite hydrogels with exfoliated structure in distilled water, with bentonite platelets dispersed in the polymer matrix at nanoscale (Figure 6). This resulted in stronger interactions between the polymer chains and clay layers, resulting in greater final gel strength. However, it reduced the gelation time, probably because the individual clay platelets acted as additional crosslinking sites for the polymer chains ( Figure 6).  , organically modified bentonite composite (distilled water); , polycationic bentonite composite (distilled water); and , sodium bentonite nanocomposite (distilled water).
, polycationic bentonite composite (distilled water); and bentonite formed nanocomposite hydrogels with exfoliated structu bentonite platelets dispersed in the polymer matrix at nanoscale (Figure interactions between the polymer chains and clay layers, resulting i However, it reduced the gelation time, probably because the indivi additional crosslinking sites for the polymer chains ( Figure 6).  bentonite formed nanocomposite hydrogels with exfoliated structure in distil bentonite platelets dispersed in the polymer matrix at nanoscale (Figure 6). This res interactions between the polymer chains and clay layers, resulting in greater fi However, it reduced the gelation time, probably because the individual clay p additional crosslinking sites for the polymer chains ( Figure 6).  , organically modif composite (distilled water); , polycationic bentonite composite (distilled water); sodium bentonite nanocomposite (distilled water).
On the other hand, the sodium bentonite formed partially intercalated structures in field brine (with divalent ions)-in which the polymer chains were inserted into the interlayer space of the clay particles, and were weakly bound to the hydrated interlayer cations and to the silicate layers by van der Waals forces and hydrogen bonds, respectively ( Figure 5)-shifting the 2θ peak to lower angles (5.45 • ), corresponding to basal spacing of approximately 16 Å.
The polycationic bentonite and organically modified bentonite probably formed microcomposite structures both in distilled water and field water. The XRD spectra of these composite hydrogels looked essentially the same as those obtained for the clay powders, which indicated that the polymer chains did not penetrate between the clay layers (there was no shifting of the X-ray d-spacing), interacting only with the external surfaces of the tactoids or aggregates of tactoids ( Figure 5) [52,[55][56][57][58][59][60][61][62][63][64].
These morphologies reduced the interactions between polymer chains and clay particles when compared to fully exfoliated nanostructures. As a result, these composite hydrogels presented longer gelation times and weaker gel strengths when compared to the sodium bentonite nanocomposite hydrogel prepared in distilled water.
The (nano)composite hydrogel prepared in distilled water with sodium bentonite, polycationic bentonite, and organically modified bentonite presented viscosities around 420, 310, and 205 mPa·s; gelation times <1 h; and final gel strengths (G* e ) around 67, 52, and 38 Pa (with Sydansk code = H), respectively. Nevertheless, in field water with high salinity/hardness, the superior performance of the sodium bentonite over the other two clays was not observed. The gelling systems prepared with pure commercial clays Cloisite Na + and Cloisite 30B presented rheological behavior, gelation time, and final gel strength similar to the one formulated with low-cost natural polycationic bentonite (viscosity~24 mPa·s, gelation time~13 h, G* e~9 Pa, and Sydansk code = F).

Temperature
During conformance treatment, gelling systems were exposed to several temperature gradients. First, during preparation in the topside facilities, the gelants were exposed to variations in the ambient temperature. Soon after being injected into the reservoir, the gelants cooled down the formation surrounding the wellbore, leading to temperatures much lower than the reservoir temperature. In the absence of convective flow, the temperature to which the gelant was exposed rose slowly due to the low thermal conductivities of the reservoir rocks and fluids. After an appropriate reservoir shut-in time, the gelants finally reached the reservoir temperature. Figure 7 shows the gelation kinetics of gelling systems at different temperatures. Gelants prepared at higher temperatures presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength).
At room temperature (25 • C), all studied gelant systems prepared in desulfated seawater did not gel for six days. This behavior was highly desirable for formulations applied in conformance treatments because if these systems were mixed in the topside facilities, and could not be promptly injected into the formation due to any operational problem, the gelants would not gel in the mixing tank, and would still be available to be pumped into the target zone for approximately one week.
For reservoir temperatures above 65 • C, since the gelation reactions were endothermic, the greater the temperature was, the faster was the gelation kinetics (crosslinking reaction between the polymer and the crosslinker) and the stronger was the final gel strength.
Higher temperatures led to an increase in the molecular mobility of polymer chains, so more crosslinks could be formed. Furthermore, higher temperatures can cause thermal hydrolysis of acrylamide groups (increasing the acrylate moieties in the polymer backbone), accelerating the crosslinking reactions due to the greater accessibility of the acrylamide groups by PEI resulting from the electrostatic repulsions between the newly charged carboxylate groups and the sulfonate groups [42,43,65,66]. With formulation F4 crosslinked at 85 °C as reference, when the temperature increased to 105 °C, the gelation time decreased to 7 h, but a strong gel was formed after 48 h (with Sydansk code = G and G*e of 16 Pa).
Therefore, to slow down the gelation kinetics of these gelling systems for in-depth conformance treatment of hot reservoirs, it is necessary to use gelants with lower crosslinker and greater clay concentrations, add chemical retardants to the formulation, or pre-flush the treated zone to cool it before the gelling system is injected [15].

Salinity (Total Dissolved Solids-TDS)
During conformance treatment, the gelling systems were exposed to several salinity gradients. First, in the topside facilities gelants were prepared by mixing the polymer and crosslinker with injection water. In offshore applications, desulfated seawater was generally used for this purpose. Fresh water or any other production brine available may also be used in gelant formulations, especially in onshore applications. After being injected into the reservoir, the gelling systems came progressively into contact with reservoir fluids, and their original water could be partially or totally replaced by the formation water.
For conformance treatments within the well or in the formation near the wellbore (at distances <15 m), the gel setting may occur with the injection water salinity. For in-depth conformance treatments, the gel setting within the reservoir generally occurs in a brine with intermediate salinity between that of the injection water and the connate water, represented in this study by the field water composition. Gel setting may also occur under high connate water salinity if the gelant reaches an aquifer during the treatment.
The gelation time and the final gel strength were strongly dependent on the total salt content (ionic strength) of the water in which the gelants were prepared (e.g., injection water) and the hydrogels were formed (e.g., field water) [16,19,52]. Figure 8 shows the gelation kinetics of gelling systems with different salinities. Gelants prepared with less saline brines presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength).
The salts interacted directly with the clay particles and the macromolecules binding to the hydrophilic charged groups of the filler and polymer (e.g., sulfonate and formed carboxylate groups). system. Therefore, greater polymer loadings w However, higher polymer concentrations propagation of the systems) and shor improvement treatments, in which low v opposing effects must be properly balance system. Therefore, greater polymer loadings were re However, higher polymer concentrations resulte propagation of the systems) and shorter ge improvement treatments, in which low viscositi opposing effects must be properly balanced [42,4  rmable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling m. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. ever, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and agation of the systems) and shorter gelation times. Thus, for in-depth conformanceovement treatments, in which low viscosities and longer gelation times were required, these sing effects must be properly balanced [42,43]. type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling re, greater polymer loadings were required to formulate stronger composite hydrogels. igher polymer concentrations resulted in higher viscosities (limiting the injectivity and of the systems) and shorter gelation times. Thus, for in-depth conformancent treatments, in which low viscosities and longer gelation times were required, these fects must be properly balanced [42,43]. , 85 • C; and ore, greater polymer loadings were required to formulate stronger composite hydrogels. igher polymer concentrations resulted in higher viscosities (limiting the injectivity and of the systems) and shorter gelation times. Thus, for in-depth conformancent treatments, in which low viscosities and longer gelation times were required, these fects must be properly balanced [42,43]. Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling polymer loadings were required to formulate stronger composite hydrogels. mer concentrations resulted in higher viscosities (limiting the injectivity and systems) and shorter gelation times. Thus, for in-depth conformancets, in which low viscosities and longer gelation times were required, these be properly balanced [42,43].
With formulation F4 crosslinked at 85 • C as reference, when the temperature increased to 105 • C, the gelation time decreased to 7 h, but a strong gel was formed after 48 h (with Sydansk code = G and G* e of 16 Pa).
Therefore, to slow down the gelation kinetics of these gelling systems for in-depth conformance treatment of hot reservoirs, it is necessary to use gelants with lower crosslinker and greater clay concentrations, add chemical retardants to the formulation, or pre-flush the treated zone to cool it before the gelling system is injected [15].

Salinity (Total Dissolved Solids-TDS)
During conformance treatment, the gelling systems were exposed to several salinity gradients. First, in the topside facilities gelants were prepared by mixing the polymer and crosslinker with injection water. In offshore applications, desulfated seawater was generally used for this purpose. Fresh water or any other production brine available may also be used in gelant formulations, especially in onshore applications. After being injected into the reservoir, the gelling systems came progressively into contact with reservoir fluids, and their original water could be partially or totally replaced by the formation water.
For conformance treatments within the well or in the formation near the wellbore (at distances <15 m), the gel setting may occur with the injection water salinity. For in-depth conformance treatments, the gel setting within the reservoir generally occurs in a brine with intermediate salinity between that of the injection water and the connate water, represented in this study by the field water composition. Gel setting may also occur under high connate water salinity if the gelant reaches an aquifer during the treatment.
The gelation time and the final gel strength were strongly dependent on the total salt content (ionic strength) of the water in which the gelants were prepared (e.g., injection water) and the hydrogels were formed (e.g., field water) [16,19,52]. Figure 8 shows the gelation kinetics of gelling systems with different salinities. Gelants prepared with less saline brines presented shorter gelation times and greater storage modulus, and thus complex modulus (final gel strength). As a result, these negatively charged groups were shielded by the metal ions, especially by divalent cations. This screening effect caused the polymer chains to shrink in a random coil configuration (smaller hydrodynamic volume), and the clay tactoids to aggregate. Thereby, the clay/polymer interactions were weakened, and potential crosslinking sites of the polymer chain were not as accessible to react with PEI, resulting in longer gelation time and weaker composite hydrogels [16,42]. With formulation F4 crosslinked with field water (56,012 mg/L TDS) as reference, when the salinity increased to 123,582 mg/L (connate water), the gelation time increased to 18 h and the gel strength after 48 h declined to G*e ~ 4 Pa (with Sydansk code = E).
Therefore, for the permeability-reducing treatment of conformance problems in which high salinity/hardness connate water is present (such as when 2D water is coning up from an aquifer underlying the oil reservoir through a vertical fracture or other reservoir irregularity of a vertical wellbore), higher polymer loadings and/or pre-flushing the treated zone with fresh water might be necessary. Furthermore, in cases in which wide fractures or large vugs are present, the mechanical strength and plugging characteristics of the gel can be increased by adding particulate matter (e.g., sand, fibers, nutshells, clay, etc.) [1].

Salt Type
In order to better understand the influence of the charge and the size (radius) of the cations on the gelation kinetics of the acrylamide-based systems, four cations of chloride salts (with the same anion) were evaluated-sodium (Na + ), potassium (K + ), calcium (Ca 2+ ), and magnesium (Mg 2+ ), as shown in Figure 9.
As previously discussed, for the negatively charged sites of the polymer (formed carboxylate and sulfonate groups) and clay particles, the mono-and divalent cations had an electrostatic shielding effect, which reduced the electrostatic repulsion between the anionic groups of the polymer chain and clay tactoids.
Furthermore, the mono-and divalent cations interacted with the uncharged groups (acrylamide and NVP) of the polymer chain, and with the deprotonated PEI due to attractive forces between cations and polymer dipoles. The most likely binding sites were the amide carbonyl oxygen of the deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformance improvement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. , 56,012 mg/L (field water); and system. Therefore, greater polymer loadings were required to formulate stronger composite However, higher polymer concentrations resulted in higher viscosities (limiting the inje propagation of the systems) and shorter gelation times. Thus, for in-depth co improvement treatments, in which low viscosities and longer gelation times were requ opposing effects must be properly balanced [42,43]. deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. The salts interacted directly with the clay particles and the macromolecules binding to the hydrophilic charged groups of the filler and polymer (e.g., sulfonate and formed carboxylate groups). As a result, these negatively charged groups were shielded by the metal ions, especially by divalent cations. This screening effect caused the polymer chains to shrink in a random coil configuration (smaller hydrodynamic volume), and the clay tactoids to aggregate. Thereby, the clay/polymer interactions were weakened, and potential crosslinking sites of the polymer chain were not as accessible to react with PEI, resulting in longer gelation time and weaker composite hydrogels [16,42].
With formulation F4 crosslinked with field water (56,012 mg/L TDS) as reference, when the salinity increased to 123,582 mg/L (connate water), the gelation time increased to 18 h and the gel strength after 48 h declined to G* e~4 Pa (with Sydansk code = E).
Therefore, for the permeability-reducing treatment of conformance problems in which high salinity/hardness connate water is present (such as when 2D water is coning up from an aquifer underlying the oil reservoir through a vertical fracture or other reservoir irregularity of a vertical wellbore), higher polymer loadings and/or pre-flushing the treated zone with fresh water might be necessary. Furthermore, in cases in which wide fractures or large vugs are present, the mechanical strength and plugging characteristics of the gel can be increased by adding particulate matter (e.g., sand, fibers, nutshells, clay, etc.) [1].

Salt Type
In order to better understand the influence of the charge and the size (radius) of the cations on the gelation kinetics of the acrylamide-based systems, four cations of chloride salts (with the same anion) were evaluated-sodium (Na + ), potassium (K + ), calcium (Ca 2+ ), and magnesium (Mg 2+ ), as shown in Figure 9.
As previously discussed, for the negatively charged sites of the polymer (formed carboxylate and sulfonate groups) and clay particles, the mono-and divalent cations had an electrostatic shielding effect, which reduced the electrostatic repulsion between the anionic groups of the polymer chain and clay tactoids. approximately 43,41,19,and 11 Pa. The valence, hydration shell strength and size of the cations affected the interaction with hydrophilic sites of the polymer, PEI, and clay particles, as well as with surrounding water molecules, which influenced the viscosity, gelation time, final gel strength, and clay dispersion in the acrylamide-based systems studied. These results were in accordance with other findings reported in the literature [43,68,69]. Cations with greater charge densities (ionic charge/ion size)-higher valences and smaller radii -delayed the gelation and decreased the viscosity, the clay dispersion, and the final gel strength of acrylamide-based systems more intensely. Furthermore, cations with stronger hydration shells and same valence exerted a weaker influence on the viscosity, clay coagulation, and gelation kinetics of the gelling systems.
The cation valence (ion charge) was the main parameter that influenced the viscosity, gelation kinetics, and clay dispersion within the hydrogel. Divalent cations (Ca 2+ and Mg 2+ ), with higher ionic charges (higher valences), had a more pronounced effect on the gelation delay, as well as on the reduction of the viscosity, clay dispersion, and final gel strength, than monovalent cations (Na + and K + ).
Moreover, for cations with the same valence and weaker hydration shells, the ion size appeared to be the parameter responsible for the variation in viscosity and gelation kinetics of the gelling systems. For instance, in aqueous solutions, monovalent ions (Na + and K + ), with loose hydration layers constantly breaking-reforming, bound directly to hydrophilic sites of the polymer, PEI, and clay particles, with minor interference of the hydration shell. As a result, the dehydrated sodium cations (Na + ), with smaller radius (ionic radius of 0.95 Å ), and thus with greater charge densities, delayed gelation and reduced the viscosity and the final gel strength more significantly than the dehydrated potassium cations (K + ) (ionic radius of 1.33 Å ) [43,[70][71][72]. polycationic bentonite composite (brine); g, organically modified bentonite in natura; h, organic modified bentonite composite (distilled water); and i, organically modified bentonite compo (brine).   deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of the gelling system. Therefore, greater polymer loadings were required to formulate stronger composite hydrogels. However, higher polymer concentrations resulted in higher viscosities (limiting the injectivity and propagation of the systems) and shorter gelation times. Thus, for in-depth conformanceimprovement treatments, in which low viscosities and longer gelation times were required, these opposing effects must be properly balanced [42,43]. , NaCl; mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking abi system. Therefore, greater polymer loadings were required to formulate stronger comp However, higher polymer concentrations resulted in higher viscosities (limiting th propagation of the systems) and shorter gelation times. Thus, for in-dept improvement treatments, in which low viscosities and longer gelation times were opposing effects must be properly balanced [42,43]. mPa·s, increased the gelation time to 13 h, and changed the quality of the gel from a stiff to deformable type (with Sydansk code = F and G*e ~ 9 Pa), decreasing the blocking ability of th system. Therefore, greater polymer loadings were required to formulate stronger composite h However, higher polymer concentrations resulted in higher viscosities (limiting the inject propagation of the systems) and shorter gelation times. Thus, for in-depth conf improvement treatments, in which low viscosities and longer gelation times were requir opposing effects must be properly balanced [42,43]. , MgCl 2 ; and mPa·s, increased the gelation time to 13 h, and cha deformable type (with Sydansk code = F and G*e ~ system. Therefore, greater polymer loadings were req However, higher polymer concentrations resulted propagation of the systems) and shorter gel improvement treatments, in which low viscositie opposing effects must be properly balanced [42,43  , 0.6 wt % (F4); and , 1.0 wt mPa·s, increased the gelation time to 13 h, and changed t deformable type (with Sydansk code = F and G*e ~ 9 Pa), d system. Therefore, greater polymer loadings were required However, higher polymer concentrations resulted in hig propagation of the systems) and shorter gelation improvement treatments, in which low viscosities and opposing effects must be properly balanced [42,43]. Furthermore, the mono-and divalent cations interacted with the uncharged groups (acrylamide and NVP) of the polymer chain, and with the deprotonated PEI due to attractive forces between cations and polymer dipoles. The most likely binding sites were the amide carbonyl oxygen of the polymer chain and the amine nitrogen of PEI, which carried a partially negative charge because of the resonant states of dipoles [67,68].
The valence, hydration shell strength and size of the cations affected the interaction with hydrophilic sites of the polymer, PEI, and clay particles, as well as with surrounding water molecules, which influenced the viscosity, gelation time, final gel strength, and clay dispersion in the acrylamide-based systems studied. These results were in accordance with other findings reported in the literature [43,68,69].
Cations with greater charge densities (ionic charge/ion size)-higher valences and smaller radii -delayed the gelation and decreased the viscosity, the clay dispersion, and the final gel strength of acrylamide-based systems more intensely. Furthermore, cations with stronger hydration shells and same valence exerted a weaker influence on the viscosity, clay coagulation, and gelation kinetics of the gelling systems.
The cation valence (ion charge) was the main parameter that influenced the viscosity, gelation kinetics, and clay dispersion within the hydrogel. Divalent cations (Ca 2+ and Mg 2+ ), with higher ionic charges (higher valences), had a more pronounced effect on the gelation delay, as well as on the reduction of the viscosity, clay dispersion, and final gel strength, than monovalent cations (Na + and K + ).
Moreover, for cations with the same valence and weaker hydration shells, the ion size appeared to be the parameter responsible for the variation in viscosity and gelation kinetics of the gelling systems. For instance, in aqueous solutions, monovalent ions (Na + and K + ), with loose hydration layers constantly breaking-reforming, bound directly to hydrophilic sites of the polymer, PEI, and clay particles, with minor interference of the hydration shell. As a result, the dehydrated sodium cations (Na + ), with smaller radius (ionic radius of 0.95 Å), and thus with greater charge densities, delayed gelation and reduced the viscosity and the final gel strength more significantly than the dehydrated potassium cations (K + ) (ionic radius of 1.33 Å) [43,[70][71][72].
Also, the monovalent cations of the solution (Na + and K + ) partially exchanged with the interlamellar ions of the polycationic bentonite, improving the particle dispersion within the hydrogel (Figure 10a,b) due to partial exfoliation of the clay platelets, contributing to reduce the gelation time, and also increased the viscosity of the gelant and the final strength of the composite hydrogels. Also, the monovalent cations of the solution (Na + and K + ) partially exchanged with the interlamellar ions of the polycationic bentonite, improving the particle dispersion within the hydrogel (Figure 10a,b) due to partial exfoliation of the clay platelets, contributing to reduce the gelation time, and also increased the viscosity of the gelant and the final strength of the composite hydrogels. In contrast, with divalent cations, more strongly solvated by water molecules than the monovalent cations, the viscosity, gelation kinetics, and clay dispersion within the hydrogel were influenced by the hydration shell strength of the ions.
Calcium ions (Ca 2+ ), which have relatively loose hydration layers that can be easily dehydrated by the electrostatic attraction between cation and negative groups of polymer chains and/or clay particles, were weakly influenced by the hydration shell during cation-polymer-clay interactions. On the other hand, magnesium ions (Mg 2+ ), which have stable (difficult to dehydrate) hydration shells, interacted more weakly and indirectly with the polymer chains and clay particles than Ca 2+ ions because the dense and strongly adhered hydration layer prevented the Mg 2+ cations from approaching the polymer chains and clay tactoids. As a result, the hydrated calcium cations (Ca 2+ ), with smaller radius (hydrated radius of 4.1 Å ), and thus with greater charge densities, delayed gelation and reduced the viscosity and the final gel strength more significantly than the hydrated magnesium cations (Mg 2+ ) (hydrated radius of 4.3 Å ) [43,70,71,73].
Furthermore, the Ca 2+ ions acted as coagulants, bonding to the negatively charged clay particles, increasing their settling behavior, and thus the heterogeneity of the formed composite hydrogel (Figure 10d). In contrast, the Mg 2+ ions, due to their greater hydration shells, did not bind to the clay particles, acting instead as ionic crosslinkers in the medium, complexing with sulfonate (-SO3 − ) and carboxylate (-COO − ) groups of the polymer chains [74], and increasing the viscosity, strength, and instability (syneresis) of the hydrogel (Figure 10c).
Besides varying with the charge density and the hydration shell strength of the cations, the magnitude of the salt-type influence on the increase of the gelation time, as well as on the reduction of the viscosity, final gel strength, and clay dispersion within the acrylamide-based hydrogels followed the Hofmeister series-Ca 2+ > Mg 2+ > Na + > K + . Table 3 presents an overview of the qualitative influence of the different parameters studied on the gelation time and final gel strength of AMPS-NVP-acrylamide-PEI-clay based systems. In contrast, with divalent cations, more strongly solvated by water molecules than the monovalent cations, the viscosity, gelation kinetics, and clay dispersion within the hydrogel were influenced by the hydration shell strength of the ions.

Overview of the Influence of the Different Parameters Studied on the Gelation Time and Gel Strength
Calcium ions (Ca 2+ ), which have relatively loose hydration layers that can be easily dehydrated by the electrostatic attraction between cation and negative groups of polymer chains and/or clay particles, were weakly influenced by the hydration shell during cation-polymer-clay interactions. On the other hand, magnesium ions (Mg 2+ ), which have stable (difficult to dehydrate) hydration shells, interacted more weakly and indirectly with the polymer chains and clay particles than Ca 2+ ions because the dense and strongly adhered hydration layer prevented the Mg 2+ cations from approaching the polymer chains and clay tactoids. As a result, the hydrated calcium cations (Ca 2+ ), with smaller radius (hydrated radius of 4.1 Å), and thus with greater charge densities, delayed gelation and reduced the viscosity and the final gel strength more significantly than the hydrated magnesium cations (Mg 2+ ) (hydrated radius of 4.3 Å) [43,70,71,73].
Furthermore, the Ca 2+ ions acted as coagulants, bonding to the negatively charged clay particles, increasing their settling behavior, and thus the heterogeneity of the formed composite hydrogel (Figure 10d). In contrast, the Mg 2+ ions, due to their greater hydration shells, did not bind to the clay particles, acting instead as ionic crosslinkers in the medium, complexing with sulfonate (-SO 3 − ) and carboxylate (-COO − ) groups of the polymer chains [74], and increasing the viscosity, strength, and instability (syneresis) of the hydrogel (Figure 10c). Besides varying with the charge density and the hydration shell strength of the cations, the magnitude of the salt-type influence on the increase of the gelation time, as well as on the reduction of the viscosity, final gel strength, and clay dispersion within the acrylamide-based hydrogels followed the Hofmeister series-Ca 2+ > Mg 2+ > Na + > K + . Table 3 presents an overview of the qualitative influence of the different parameters studied on the gelation time and final gel strength of AMPS-NVP-acrylamide-PEI-clay based systems.

Conclusions
The injectivity, propagation, gelation time, and final gel strength of AMPS-NVP acrylamide terpolymer/PEI/bentonite were strongly influenced by the gelant formulation and field conditions (temperature and salinity/hardness). The greater the polymer, the crosslinker concentration, the PEI molecular weight or the PEI initial pH value in the gelant, or the reservoir temperature, the shorter was the gelation time and the greater was the storage modulus, and thus the complex modulus (final gel strength) of the system. On the other hand, the greater the salinity and/or hardness of the medium, the longer was the gelation time and the weaker was the final gel strength.
The polymer concentration, salinity/hardness, and temperature were the parameters that most strongly affected the gelation time, and hence how deep the gelant can penetrate into the formation, as well as how long the reservoir shut-in time should be during conformance treatment. Moreover, the final gel strength was mainly controlled by the polymer concentration, divalent ion concentration, and crosslinker concentration and molecular weight. Nevertheless, the higher the crosslinker concentration or molecular weight, the higher was the composite hydrogel syneresis.
The addition of clay to the gelant formulation increased the gelation time, thermal stability, and syneresis resistance of the composite hydrogel, and slightly increased the final gel strength.
Of the samples evaluated, formulation F4 prepared with polymer and PEI concentrations below 1 wt %, low-cost polycationic natural bentonite, and PEI with M w of 70,000 kg/kmol and initial pH value around 11: (i) presented suitable rheological behavior to ensure good injectivity and propagation in porous media (moderate pseudoplastic fluid and viscosity~24 mPa·s at 7.3 s −1 ); (ii) showed sufficient gelation time for the treatment of targeted zones located far from the wellbore (e.g.,~7 h); and (iii) formed strong composite hydrogels under subsurface conditions (G* e~1 6 Pa and Sydansk scale G, after 48 h at 105 • C), presenting good blocking ability characteristics, low syneresis, and good long-term stability (~3 to 6 months).
Therefore, the use of high-molecular-weight base polymers (>1,000,000 kg/kmol) and the addition of inexpensive natural bentonites as active fillers in the formulations of OCP systems are promising for in-depth conformance treatments under harsh conditions (high temperature, high salinity, and high hardness).

Materials
The gelling systems were prepared using a commercial sample of acrylamide, 2-acrylamido-2-methylpropane sulfonic acid, and N-vinyl-2-pyrrolidone terpolymer (PAM-AMPS-NVP), supplied by SNF Inc. (Riceboro, GA, USA). Three samples of bentonites were tested as fillers-a Brazilian natural polycationic bentonite (with calcium and magnesium exchangeable cations), supplied by Bentonit União do Nordeste Ltda (São Paulo, Brazil); a sodium bentonite (Cloisite Na + ); and an organically modified bentonite (Closite 30B), both supplied by Southern Clay Products (Gonzales, TX, USA). Three samples of branched polyethylenimine (PEI) with pH value around 11, and weight average molecular weights (M w ) of 10,000, 70,000, and 750,000 kg/kmol, supplied by Polysciences Inc. (Warrington, PA, USA), were used as crosslinkers. The pH value of PEI was adjusted to 2, 7, or 9 by adding a few drops of 1.0 M HCl solution when necessary. Oilfield brines with representative composition of the salinity/hardness found in the gelant during preparation (injection water), gel setting within the reservoir (field water), or contact with an aquifer (connate water), as shown in Table 4, were prepared with NaCl, KCl, CaCl 2 , and MgCl 2 ·6H 2 O, supplied by Vetec Química Fina Ltda (Duque de Caxias, Brazil).

Characterization of the Samples
The chemical composition of the polymer sample was determined by 13 C-NMR spectroscopy with a Varian Mercury VX 300 MHz spectrometer (International Equipment Trading Ltd., Mundelein, IL, USA), at a frequency of 75.4 MHz, acquiring about 48,000 transients at 40 • C. The spectrum was calibrated using sodium 3-(trimethylsilyl)-2,2 ,3,3 -tetradeuteropropionate (TSP) methyl as an internal reference (zero ppm). The polymer solution was prepared in heavy water (D 2 O).
The weight average molecular weight (M w ) and the polydispersion (PD) of the acrylamide-based sample were assessed by gel permeation chromatography (GPC, Malvern Panalytical, Malvern, UK) with a Max VE 2001, GPC Solvent/Sample Module, Viscotek chromatograph equipped with differential refractometer, viscometer, ultraviolet, and light scattering detectors, and three columns in series with an exclusion limit of 2 × 10 7 .
The microstructure of the clays and the acrylamide-based composite hydrogels prepared in distilled water and field brine were analyzed by X-ray diffraction with a Rigaku Ultima IV diffractometer (Rigaku, Tokyo, Japan), with Cu-filtered Kα radiation, at 40 kV and 20 mA. The samples were scanned in 2θ ranges from 1 • to 20 • with a step size of 0.05 • .

Gelling System Preparation
Polymer solutions and clay dispersions were prepared by slowly mixing the polymer and clay in distilled water or oilfield brines (Table 4) under moderate magnetic stirring (330 rpm) for 72 h at room temperature (25 • C). Then the clay dispersions were added to the polymer solutions, and the mixtures were stirred further for 1 h. Finally, the crosslinking agent (PEI) was added, and the systems were stirred for another 15 min before conducting bottle tests and rheological tests.
Initially, all gelling systems (Table 5) were prepared using Brazilian natural polycationic bentonite as filler and PEI with M w of 70,000 kg/kmol and pH value around 11 as crosslinker in order to evaluate individually the influence of the polymer concentration, clay concentration, and PEI concentration on the viscosity of the systems prepared with injection water at 25 • C, and on the gelation kinetics and final gel strength of the systems prepared in field water (56,012 mg/L TDS) at 85 • C. Then, additional gelling systems were prepared based on the standard composition F4 (Table 5), varying exclusively (i) the clay type (sodium bentonite or organically modified bentonite); (ii) the molecular weight of the crosslinker (10,000 kg/kmol or 750,000 kg/kmol); (iii) the pH value of the crosslinker (2, 7, or 9); (iv) the temperature during the gelation process (65 • C or 105 • C); (v) the salinity during the gelation process (0 mg/L, 33,489 mg/L, or 123,582 mg/L TDS); and (vi) the salt type of the brine during the gelation process (1 wt % NaCl, 1 wt % KCl, 1 wt % CaCl 2 , or 1 wt % MgCl 2 ), while keeping the other parameters unaltered.
These additional formulations were evaluated to better understand the impact of the clay type, PEI molecular weight, and pH value on the viscosity, gelation kinetics, and final gel strength, and to assess the impact of the reservoir conditions (temperature, salinity, and salt type) on the gelation process of the systems. Only the most important results of these additional formulations are presented in Section 3, while the individual parameter altered in relation to the standard F4 composition is mentioned in the text and/or in the caption of the figures.

Evaluation of the Injectivity, Propagation, Gelation Kinetics, and Gel Strength
Four important parameters for conformance-improvement treatments of oil reservoirs were assessed by bottle tests and rheological tests-the injectivity and propagation of the gelling systems and the gelation time and final strength (equilibrium consistency) of the hydrogels. The measured quantities in this study were reproducible with an error of less than 10%. All measurements were repeated three times and the average values of the measured quantities were reported.

Bottle Test
Bottle tests were performed by adding 20 mL of gelant in glass bottles with cap (60 mL). Then, the bottles were sealed and placed in an air circulation chamber with controlled temperature set to 65, 85, or 105 • C. For up to 48 h, at varying time intervals, the bottles containing the gelling formulations were vertically inverted and gel strength codes were assigned to the samples according to the behavior (flowability) observed.
The gel strength scale A to J proposed by Sydansk [11], visually presented by Tessarolli et al. [35], was used in this study-A for no visually detectable gel formed; B for highly flowing gel; C for flowing gel; D for moderately flowing gel; E for slightly flowing gel; F for highly deformable non-flowing gel; G for moderately deformable non-flowing gel; H for slightly deformable non-flowing gel; I for rigid gel; and J for rigid ringing gel.
The gelation point of each formulation (transition from liquid to solid) was considered to occur when the gel strength code changed from B to C [75][76][77].

Rheological Tests
Steady and oscillatory shear tests were performed with a Haake MARS 60 rheometer using cone-plate (C60) and coaxial cylinder (CC25) geometries, respectively (Table 6). Monitor the evolution of the storage modulus (G'), loss modulus (G"), and complex modulus (G*) as a function of time without any mechanical disturbance or destruction of the elastic structure of the hydrogel. The gelation time of each sample was determined when G* started to increase rapidly (inflection point). The storage modulus (G') represents the portion of the stress energy that is temporarily stored during the test, but can be recovered afterwards. The loss modulus (G") represents the portion of the stress energy that is used to initiate the flow and is irreversibly transformed into shear heat. The complex modulus (G*) is a rheological parameter that quantifies the total resistance (consistency) of a gelling system against the maximum applied strain. The G* value is related to the storage modulus (G') and loss modulus (G") according to Equation (4). Funding: This study received no external funding.