A water-soluble hyperbranched copolymer based on a dendritic structure for low-to-moderate permeability reservoirs

Abstract

In this study, a modified dendritic functional monomer (named DA) consisting of 1,3-propanediamine as the initiated core was prepared and utilized to react with acrylamide (AM), acrylate (AA) and 2-acrylamido-2-methyl propane sulfonic acid (AMPS) to synthesize a water-soluble hyperbranched copolymer (noted HPDA) for low-to-moderate permeability reservoirs through a redox free radical polymerization strategy. The copolymer was characterized by a series of experiments, including IR, ¹H NMR, DLS and AFM. It was observed expectedly that the HPDA solution displayed a distinct topological structure in solution, resulting in a smaller mean diameter in comparison to the linear polymer. Furthermore, the rheology performances and anti-shearing properties of HPDA were investigated, which demonstrated that the introduced dendritic structure could endow the polymer with great viscosity retention and excellent elasticity in a relatively high frequency region. Based on the sand packed tube displacement experiment, a favorable matching relationship could be found between the size of the sheared HPDA and the pore throat as the permeability ranged from 500 to 100 mD. Moreover, compared with the linear polymer, AM/AA/AMPS, the sheared HPDA solution of 2000 mg L⁻¹ could significantly increase the efficiency of oil recovery to 21.9% and 17.5% by controlling the displacing phase mobility and constructing an appreciable resistance factor and residual resistance factor in the 500 and 260 mD porous media.

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Introduction

With the gradual emergence of high water cuts, the stable production of oil fields becomes extremely difficult in high permeability reservoirs.^1–5 The low-to-moderate permeability reservoir is of considerable academic and technological interest due to its abundant reserves.⁶ According to the domestic SY/T6169-1995 standard, the air permeability of a moderate permeability reservoir ranges from 50 × 10⁻³ μm² to 500 × 10⁻³ μm². And reservoirs with a permeability of less than 50 × 10⁻³ μm² are known as low and ultra-low permeability reservoirs. These kinds of reservoirs tend to present a number of unique characteristics, such as a small pore throat, high specific surface area, and strong heterogeneity.^7,8 In view of this, prior researchers have studied hydraulic fracturing technology to optimize the pore structure and seepage channel around the well for enhanced oil recovery (EOR) in the early period of development. For example, Gringarten et al.⁹ reported that analytical solution, which was employed to study the unsteady behaviour of single-phase fluid from a well containing a single horizontal fracture, indicated the existence of four different flow periods. Bian et al.¹⁰ recorded that the daily oil production enhanced 1.25 times after hydraulic fracturing, and the long-term stimulation effect was substantial. In a more indoor-oriented work, Arp et al.¹¹ pointed out that it was possible to increase production through controlling fracture height during the hydraulic operations. However, following the later long-term water flooding, the pore structure and the physical parameters of the fractured reservoirs will be changed constantly which could cause formation of high permeability channels.¹² In other words, enhancing recovery efficiency remains a considerable challenge for low-to-moderate permeability reservoirs after fracturing and it is urgent to find an available method.

Inspired by the EOR method of high permeability formation, plenty of researchers have focused on introducing the chemical flooding technique, particularly polymer flooding, into the mid-to-low permeability reservoir.^13,14 At the moment, this notion would create an evident issue of whether there exists an appropriate matching relationship between the polymers and pore throat. On the basis of the bridge principle,¹⁵ when the hydrodynamic radius (R_h) of the polymer molecules is 0.46 times bigger than the pore throat radius, a relatively stable blockage would be formed in the pore throat. Currently, commercial polymers utilized as thickening agents in practice are partially hydrolysed polyacrylamide (HPAM) and biological polymers. Their average molecular diameter is about 4–16 μm, much larger than the pore throat of low-to-moderate permeability reservoirs with a size in the order of 10⁻² to 10 microns.¹⁶ Therefore, the molecular diameter of conventional linear polymers is not compatible with the reservoir pore throat radius. Besides, poor shear resistance limits the popular application of such widely used polymers. Polymer molecular chains will be cut off when the polymer solution passes through the pump, pipeline, perforation, and porous medium at high speed, so the viscosity of the polymer solution will be reduced greatly.^17–19 Moreover, the shearing force of the mid-to-low permeability reservoir is more intense due to its diminutive pore throat. Obviously, the previous analyses suggest that polymers for low-to-moderate permeability reservoirs should meet the following three demands: (1) suitable hydrodynamic radius for favourable injection properties, (2) anti-shear degradation, and (3) most necessarily, capacity of EOR, that is to say, the power of establishing a high resistance factor (RF) and residual resistance factor (RRF). Given the unique aqueous and low molecular weight characteristics, a dendritic skeleton whose structure is similar to that of a three-dimensional (3D) sphere and branches²⁰ may be promising for chemical EOR applications of low-to-moderate permeability reservoirs. A highly branched structure makes its hydrodynamic radius lower than that of a linear polymer with a similar molecular weight, which could permit comfortable injection for low-to-medium permeability reservoirs, and makes its integral structural system be unaffected by shearing.

In recent decades, among dendritic macromolecules, polyamidoamine (PAMAM) has been attracting increasing attention in many countries, and is made up of methyl acrylate and amino groups through a Michael addition reaction.^21–24 Serving as its terminal group, amidogen, which could be easily modified, has been used extensively in several practices, like biological medicine,^25,26 surfactants,²⁷ catalysis,²⁸ nanomaterials,²⁹ and so forth. Considerable research demonstrated that PAMAM displayed nice solubility and could achieve ten generations,³⁰ whereas a poor molecular weight together with a lower thickening efficiency limit popular application in EOR of such polymers.

Consequently, the primary objective of this study is to synthesize a water-soluble hyperbranched copolymer for the low-to-moderate permeability reservoir containing the ideal properties of a dendritic structure and flexible molecular polymers. We have preferentially sought to introduce an unsaturated double bond into PAMAM to synthesize a modified dendrite functional monomer (DA) using 1,3-propanediamine as the initiated core (Scheme 1a). The hyperbranched copolymer (HPDA, Scheme 1b) was obtained by the copolymerization of acrylamide (AM), acrylic acid (AA), 2-acrylamido-2-methyl propane sulfonic acid (AMPS) and the surfmer DA. The morphology of HPDA was characterized by IR, ¹H NMR, DLS, SLS and AFM. A series of experiments was carried out to further investigate its feasibility for EOR in low-to-moderate permeability reservoir, such as rheological performance, anti-shear degradation, injection property and mobility control ability.

Scheme 1 (a) The synthesis route of DA, and (b) the structure of HPDA.

Experimental

Reagents and materials

1,3-Propanediamine (PDA) was purchased from Chengdu Aike chemical technology Co., (Chengdu/China). Methyl acrylate (MA), acrylic acid (AA), maleic anhydride (MAH), and ethanol (C₂H₅OH) purchased from Chengdu KeLong Chemical Reagent Co., Ltd (China) were of analytical grade and used without further purification. Acrylamide (AM, KeLong) and 2-acrylamide-2-methyl propane sulfonic acid (AMPS, KeLong) were used after purification. Other supplementary materials were purchased and used directly without further purification. Water was doubly distilled and deionized by passing through an ion exchange column.

Synthesis of DA

A certain amount of PDA was placed in a flask with a magnetic stirrer and dissolved in C₂H₅OH until the solution mixed to a homogeneous system. Then excess MA was dripped slowly by a constant pressure funnel under constant stirring and at a temperature of 25 °C. After reacting for 24 h, the product was distilled under reduced pressure at 50 °C and a light yellow jelly (GA0.5) was obtained. Similarly, GA0.5 and methyl alcohol blended in an appropriate feed composition were added to a round bottom flask. And then, PDA was dripped slowly into the flask. The reaction time was 24 h at 25 °C, and the product was named GA1.0, which was purified by vacuum distillation at 72 °C. GA1.5 and GA2.0 were prepared in consistence with the above approach by gradually repeating the Michael addition and amidation reaction. The IR and ¹H NMR spectra of the dendritic macromolecules (GA0.5–2.0) are listed in the ESI (Fig. S3 and S4 in the ESI†). The modified dendrite functional monomer (DA) was synthesized by the following method: MAH was dissolved in N,N-dimethylformamide (DMF) and GA2.0 dissolved by DMF was added slowly. The reaction was carried out at 70 °C for 6 h, and DA was obtained through precipitation with trichloromethane and vacuum filtration. The synthesis route is shown in Scheme 1a, the optimal synthetic conditions are presented in Table 1, and the conditions for optimizing are provided in the ESI.†

Table 1 Optimal synthetic conditions of DA

Item	n(PDA) : n(MA)	n(GA0.5) : n(PDA)	n(GA1.0) : n(MA)	n(GA1.5) : n(PDA)	n(GA2.0) : n(MAH)	Solvent (C2H5OH) (wt%)
Content	1 : 8	1 : 24	1 : 35	1 : 48	1 : 13	30

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Preparation of the hyperbranched polymer HPDA

The hyperbranched polymer HPDA was prepared via aqueous solution copolymerization, and its structure is shown in Scheme 1b. Monomers were dissolved in degassed and distilled water with a certain mass ratio, adjusting the pH of the solution to 7. After keeping the solution in a water bath heater at 45 °C, the indicated loading of the initiator (n(NaHSO₃) : n((NH₄)₂S₂O₈) = 1 : 1) solutions was added slowly. Copolymerization was carried out under N₂ atmosphere for 6–8 hours. Ultimately, the product was precipitated with acetone and dried in a vacuum oven at 40 °C for 7 h to yield the corresponding polymer. The AM/AA/AMPS copolymer was synthesized using the same method. The copolymerization conditions are presented in Table 2 and the optimal copolymerization conditions are given in the ESI.†

Table 2 Copolymerization conditions of HPDA

Item	Concentration	AM	AA	DA	AMPS	Initiator
Content (wt%)	25	69.3	29.7	0.4	1	0.2

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Characterization

Infrared (IR) spectra of the monomer DA and polymer HPDA were measured with KBr pellets using a Perkin Elmer RX-1 spectrophotometer (Beijing Rayleigh Analytical Instrument, China). ¹H NMR was recorded on a Bruker 400 MHz nuclear magnetic resonance spectrometer (Bruker Daltonics, U.S.A.) with D₂O solvent. The hydrodynamic diameter (R_h) and distribution of the samples were obtained using a BI-200SM wide angle dynamic laser light scattering (DLS) instrument. Moreover, static laser scattering (SLS) was employed to analyse the weight average molecular weight (M_w) and root mean square radius (R_g) of the polymers at 532 nm. The scanning angle ranged from 30° to 120° with a polymer concentration of 30–100 mg L⁻¹. The morphologies of the polymer were observed by atomic force microscopy (AFM; Nanoscope IIIa). For comparison, unsheared as well as sheared polymers through Mixing Speed Governor (WT-VSA2000B) at 3500 rpm for 20 s were also used in DLS, SLS and AFM tests.

Rheology test

HPDA and poly(AM/AA/AMPS) solutions of 2000 mg L⁻¹ were prepared utilizing distilled water as the solvent at room temperature. The apparent viscosity was measured using a HAAKE MARS RS600 Rheometer (Haake Technik Co., Germany) in the range of shear rates 0.001 to 100 s⁻¹, at 65 °C. Simultaneously, HAAKE MARS RS600 was employed to determine the elastic modulus (G′) and viscous modulus (G′′) of both polymers in order to obtain their viscoelasticity properties.

Shearing resistance test

The shearing resistance of the polymer solution including mechanical shearing and porous media shearing was evaluated using the viscosity retention rate as the target which was calculated from the current viscosity divided by the initial viscosity. To investigate the effect of the mechanical shear force on the polymer apparent viscosity, we measured the apparent viscosity of the samples with diverse concentrations before and after being sheared by Mixing Speed Governor (WT-VSA2000B) at 3500 rpm for 20 seconds. Then we changed the shear time varying from 10 to 60 s, and tested the apparent viscosity of the HPDA and AM/AA/AMPS solutions of 2000 mg L⁻¹ to obtain the effect of mechanical shear time on the polymer solutions. Eventually, the influence of shear strength on the apparent viscosity was studied by setting the shear strength at 3500, 7000, 11 500, 14 500 and 17 000 rpm, in order. Furthermore, the blast-hole model was engaged to simulate the porous media shearing, and Fig. 1 shows its flowchart. Primarily, 40–60 mesh gravel particles were pressed in a 25 cm long blast-hole model with an inner diameter of 1 cm, following by the compaction of 100–120 mesh quartz sand near the exit of the model. Then the model was saturated with brine to measure the porosity by the weight method which should be about 37%. During the experiment, the apparent viscosity was recorded after the polymer solution with various concentrations passing though the blast-hole model under a 40.4 mL min⁻¹ flow rate. Besides, the apparent viscosity of the 2000 mg L⁻¹ polymer solution sheared via the blast-hole model at the different flow rate of 20.2–101 mL min⁻¹ was tested in order to study the effect of shear rate of a porous medium on the polymer solution. All apparent viscosity tests were carried out at 7.34 s⁻¹ and 65 °C using a Brookfield DV-III Programmable Rheometer (Brookfield Co., America).

Fig. 1 Schematic diagram of the porous media shear.

Sand packed tube displacement experiment

The sand packed tube displacement experiments were carried out at approximately 65 °C as described in ref. 31. The tubes (30 cm in length and 2.5 cm in inner diameter) were packed with 100–120 mesh quartz sand that was washed with an 18% hydrochloric acid solution and then with a massive amount of water until the pH reached 7. The crude oil with a viscosity of 4.6 mPa s at 65 °C and brine with a TDS of 8766.28 mg L⁻¹ were used in the experiments whose ionic composition is shown in Table 3. The flooding rates both of the polymer flooding and subsequent water flooding were set as 1.0 mL min⁻¹ and kept unchanged. The injection of HPDA in low-to-moderate permeability reservoirs was characterized by a pressure drop. Its mobility control ability can be achieved through analysing the resistance factor (RF) and residual resistance factor (RRF) which were calculated using the following equations:³²where K_W and K_P are the aqueous and polymer phase permeability, respectively (mD), μ_W and μ_P are the aqueous and polymer viscosity, respectively (mPa s), and K_Wb and K_Wa are the aqueous phase permeability before and after polymer flooding, respectively, where K_Wb = K_W (mD).

Table 3 Ionic composition of the brine

Ions	Na^+, K^+	Ca^2+	Mg^2+	HCO3^−	SO4^2−	Cl^−
Content (mg L^−1)	3167.42	99.98	98.92	200.01	100.01	5099.94

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The EOR of the polymer solutions was calculated via the following equation:³³

EOR = E_T − E_W (3)

where EOR is the enhanced oil recovery using a polymer solution (%), E_T is the oil recovery of the whole displacement process (%), and E_W is the oil recovery of water flooding (%).

Results and discussion

Characterization of DA and HPDA

IR. The chemical structures of DA and HPDA were confirmed by IR spectroscopy as shown in Fig. 2a. In the spectrum curve of DA, the peaks at 3253 cm⁻¹ and 3065 cm⁻¹ were the stretching vibration and bending vibration of N–H, respectively. The characteristic absorptions of methylene groups in the skeleton were observed at 2965 cm⁻¹. The 1664 cm⁻¹ peak was assigned to the stretching vibration of C=O. The peak at 1247 cm⁻¹ was the result of the stretching vibration of C–O, while the 1446 cm⁻¹ peak was attributed to the bending vibration of O–H. The characteristic absorption peak at 1552 cm⁻¹ and 968 cm⁻¹ indicated the presence of C=C. Similarly, it could be seen from HPDA curve that the absorption peak of C–H of methyl and methylene presented at 2929 cm⁻¹ and 2869 cm⁻¹, respectively. And the stretching vibration of C=O displayed at 1673 cm⁻¹ gave a stronger absorption as it existed in both structures of DA and AM. The broad peak ranging from 3096 cm⁻¹ to 3426 cm⁻¹ was the overlap of N–H in the skeleton and –CONH₂ in the polymeric main chain. The peaks at 1446 cm⁻¹ and 1397 cm⁻¹ corresponded to the structure of –COOH. Compared with the spectrum curve of DA, we could find the appearance of new characteristic absorption peaks of S=O at 1173 cm⁻¹ and 1041 cm⁻¹ and the disappearance of the absorption peak of C=C. As expected, the IR spectrum confirm the presence of AM, AA, AMPS and DA.

Fig. 2 (a) IR and (b) ¹H NMR spectra of DA and HPDA.

¹H NMR. Fig. 2b shows the ¹H NMR spectra of the dendritic skeleton monomer and the water-soluble hyperbranched copolymer. In the ¹H NMR spectrum of DA, the chemical shift at 1.68–3.59 ppm was related to the protons of –CH₂–. At 6.26 ppm, the proton peak of –CH=C– was monitored. The signals observed at 7.60 and 7.86 ppm were attributed to the proton peak of –NH– bonded with the carbonyl C=O. The ¹H NMR spectrum of HPDA exhibited the following chemical shifts: the proton peaks of –CH₂– and –CH– in the polymeric main chain were 1.51 and 2.06 ppm, respectively. The proton signal of –NH– (7.38 ppm) was associated with the dendritic skeleton monomer in the polymer. Furthermore, the chemical shift at 8.50 ppm was due to the –CH–NH₂ group existing in the monomer AM. The signal at 4.02 ppm was assigned to the proton of –CH₂–SO₃Na which shows the existence of the AMPS functional monomer in the hyperbranched copolymer HPDA. Hence, the structure of HPDA was in accordance with the initial design based on the ¹H NMR data.

Molecular weight and diameter distribution. For low-to-moderate permeability reservoirs, the molecular dimension of the polymer employed in EOR applications should be matched with the pore throat radius. In this study, the diameter distribution of the synthesized polymers is displayed in Fig. 3, and the basic structural parameters are listed in Table 4. One observes that the experimental radius of the unsheared HPDA solution is 191 nm, which is less than the poly(AM/AA/AMPS) diameter of 252 nm with a similar M_w value. The significant difference in R_h between the linear polymer and the hyperbranched polymer indicated that the dendritic skeleton monomer could radically copolymerize with other water-soluble monomers to form a hyperbranched spherical structure. As seen in the figure, almost no change was discovered in the broad diameter distribution of sheared HPDA, yet the poly(AM/AA/AMPS) broad distribution showed a significant left-shift. And it was found that the diameter distribution intensity of the sheared HPDA solution somewhat exhibited an obvious reduction in comparison to that of the unsheared one at a particle size of above 560 nm, resulting in the diameter of the sheared HPDA dropping to 153 nm, which is higher than that of the poly(AM/AA/AMPS) solutions (129 nm). The phenomena were due to the fact that the shearing action could destroy part of the branched chain of the hyperbranched polymer HPDA, but the overall structure would not be affected.^34,35 In this case, after being sheared, the poly(AM/AA/AMPS) solution possessed a smaller molecular dimension than that of the HPDA solution, which should be conducive to the injection into the medium-to-low permeability reservoir. However, its poor viscosity might go against the capacity of building mobility control. Cao et al.¹⁵ exhibited that the polymer would not plug formation when the ratio of the pore throat radius to R_g of the polymer exceeds 5. And the bridging principle also indicated that a stable jam would be generated in the pore throat when the R_h of the polymer molecules is greater than 0.46 times the pore throat radius.¹⁵ Based on the preceding description, the experimental R_h and R_g value of HPDA of 191 nm and 66 nm separately revealed that the applicable minimum diameter of the pore throat for the hyperbranched polymer is 0.33 μm.

Fig. 3 Diameter distribution for HPDA and poly(AM/AA/AMPS) of 2000 mg L⁻¹ in deionized water.

Table 4 Structural parameters of poly(AM/AA/AMPS) and HPDA

Sample	10^7 Mw (g mol^−1)	Rg (nm)	Rh^a (nm)	Solubility in water^b
a Polymer concentration: 2000 mg L^−1.b ++, easily soluble; +, soluble.
Poly(AM/AA/AMPS)-unsheared	1.55	207	252	++
Poly(AM/AA/AMPS)-sheared	1.41	142	129	—
HPDA-unsheared	1.72	66	191	+
HPDA-sheared	1.68	53	153	—

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Morphology of HPDA. To investigate the morphology of HPDA, AFM was utilized on an unsheared and sheared hyperbranched polymer solution at a concentration of 2000 mg L⁻¹. For the sake of contrastive analysis, poly(AM/AA/AMPS) solutions with identical content were studied as well. From Fig. 4a, it is obvious that the morphology of the linear polymer was irregular and presented to a certain extent a network structure under the conditions of scan size = 10.00 μm and data scale = 60 nm. Furthermore, some bulges could be observed in this situation. That was due to the disordered aggregation of macromolecular chains, which conforms to the consequences reported by Pu et al.³⁵ Nevertheless, the dendritic skeleton structure was imported into coiled hydrophilic chains resulting in the formation of a tree topology microstructure for the hyperbranched polymer HPDA (Fig. 4c). A much smoother surface could be discovered in the microstructure of HPDA in comparison to poly(AM/AA/AMPS), implying that the stretched long polyacrylamide chains as flexible chain were around the dendritic backbone. Most significantly, the regular microstructure with a uniform cavity and reticular shape could be observed when the conditions changed to scan size = 3.00 μm and data scale = 40 nm (Fig. 4e). This unique characteristic was considered to originate from the fact that the polyacrylamide branched chains of HPDA orderly arrange to form a 3D structure.

Fig. 4 AFM images of (a) poly(AM/AA/AMPS)-unsheared, scan size = 10.00 μm, data scale = 60 nm; (b) poly(AM/AA/AMPS)-sheared, scan size = 3.00 μm, data scale = 100 nm; (c) HPDA-unsheared, scan size = 10.00 μm, data scale = 100 nm; (d) HPDA-sheared, scan size = 10.00 μm, data scale = 80 nm; (e) HPDA-unsheared, scan size = 3 μm, data scale = 40 nm; (f) HPDA-sheared, scan size = 3.00 μm, data scale = 40 nm.

Fig. 4b reveals that the network structure of the linear polymer solution was dismantled and formed microparticles after being sheared. A few filaments were sought out between sectional microparticles, but the mutual effect was quite feeble. This poor shearing resistance could support the fact that the poly(AM/AA/AMPS) solution exhibited such a low viscosity through porous media that it could not establish mobility control effectively.^19,36 In contrast, as shown in Fig. 4d, shearing force made the fractional branching chain of the HPDA solution break, whereas its integral structure was invariant in principle which was consistent with the results obtained in the DLS studies. On further changing the conditions to scan size = 3.00 μm and data scale = 40 nm (Fig. 4f), a more dense reticular shape could be obtained in comparison to the polymer without shearing. This distinctive observation was deemed to be stemmed from the space steric effect between the original branching molecules which prevents the molecule interaction. Having been mechanically sheared, the breakage of a sectional side chain caused a negative effect on steric hindrance and a positive effect on molecular interactions leading to the density of a mesh structure.³⁷ Thus, the successfully incorporated dendritic region generates an obvious increase of the shearing resistance of the hyperbranched polymer.

All characterization tests suggested that the hyperbranched polymer, based on a modified dendritic skeleton monomer, comprising of hydrophilic long chains as exterior flexible units, was successfully synthesized. Simultaneously, DLS and AFM studies revealed that the HPDA solution displayed a much smaller molecular dimension and preferable shearing resistance compared to the linear polymer solution.

Rheology performances

After hydraulic fracturing, the injected fluid for EOR would flow along the crevice, and a significant portion of the low-to-moderate permeability reservoir was bypassed. As a result, the unrecovered oil was left as microscopic droplets of residual oil.¹² The polymer with a good rheology performance has a pulling effect to those small oil blocks in the dead angles of formation.³⁸ Compared with a Newtonian fluid with the same viscosity, the viscoelastic polymer solution has a greater sweep volume.³⁹ Thus, the rheological performance for the polymer solution is a fundamental necessity for improving the displacement efficiency.

The variation of the apparent viscosity was curved based on the shearing rate (Fig. 5a). It was obvious that the apparent viscosity of the HPDA solution is lower than that of poly(AM/AA/AMPS) under a low shear rate. This could be explained by its smaller hydrodynamic radius in comparison to that of the poly(AM/AA/AMPS) solution. With the increase of shear rate, the apparent viscosity of the linear polymer decreased sharply, however the HPDA solution first showed a slight shear thickening under a shear rate of less than 0.008 s⁻¹, which was conducive to the viscosity retention of the polymer in formation. And then it presented a shearing thinning behaviour which suggests a favourable injection performance for HPDA in mid-to-low permeability reservoirs. At a relatively high shear rate, the HPDA solution showed a higher apparent viscosity that was considered to be derived from the excellent anti-shearing of the dendritic structure of HPDA and poor shear degradation of the linear structure of poly(AM/AA/AMPS).

Fig. 5 (a) The shear thinning behavior and (b) the viscoelastic behavior of the polymer solutions.

Fig. 5b displays the viscoelastic behaviours of the HPDA and poly(AM/AA/AMPS) solutions of 2000 mg L⁻¹. It was clear that both the elastic modulus (G′) and viscous modulus (G′′) of the HPDA solution were higher than that of poly(AM/AA/AMPS), manifesting that a better viscoelasticity could be achieved for the hyperbranched polymer. For HPDA, at a low frequency where the value of G′ was below that of G′′, the viscous modulus played a dominating role. Above the frequency at which the curves of G′ and G′′ cross each other, the copolymer solutions gave priority to the elastic characteristics. The frequency at the node in the elasticity domination state for poly(AM/AA/AMPS) was larger than that of HPDA. We could attribute this phenomenon to the fact that the irregular network of poly(AM/AA/AMPS) governed by linear chain entanglement was damaged fatally by stress. Although the dendritic mesh structure of the HPDA solution showed deformation under the effect of stress, which would cause the stress relaxation character, the obstinate intermolecular interaction could help the solution structure remain relatively complete.³⁷

Anti-shearing properties

In the injection and displacement process, the polymer solutions used as mobility control agents would be severely degraded by exposure to shear action from the pump, pipeline, wellbore, bullet hole and porous media, so the viscosity of the polymer solution will be greatly reduced.^17,18 Hill et al.⁴⁰ reported the effect of shear force on a partially hydrolysed polyacrylamide and a biopolysaccharide utilizing core shear and Mixer-Constant Speed. It was found that degradation occurred at high shear rates near the wellbore area. Furthermore, the viscosity of both polymers could be reduced by shear degradation, and its incidence depended on the shear rate and shear time. In this article, Mixing Speed Governor (WT-VSA2000B) was employed to simulate the mechanical shear degradation of the pipeline and wellbore, and the blast-hole model was engaged to simulate the shear of porous media.

The effect of the mechanical shear rate and shear time on the apparent viscosity of the polymer solutions was investigated, and the results are shown in Fig. 6. For the unsheared polymer solutions, the apparent viscosity of HPDA displayed a rising trend with increasing concentration, but it was relatively lower than that of poly(AM/AA/AMPS) due to the hyperbranched structure. However, this construction was capable of promoting excellent shear resistance which led to a better viscosity retention for HPDA. When the copolymer solution was sheared at 3500 rpm for 20 s, it was found that the maximum retention rate of HPDA was 87.0% while that of poly(AM/AA/AMPS) was 70.5% (Fig. 6a). As shown in Fig. 6b, with increasing the shear time from 0 s to 60 s, the entangled chains of the linear polymer of 2000 mg L⁻¹ gradually began to disentangle, resulting in the reduction of viscosity. In contrast, the changes in apparent viscosity of the HPDA solution with an identical concentration were extremely small, and there was even a recovery phase at a shear time ranging from 20 s to 30 s. Eventually, a steady retention rate (84.6%) was obtained under the concentration of 2000 mg L⁻¹, which was larger than that of the poly(AM/AA/AMPS) solution (60.0%). The unusual thickening property was attributed to the presence of the steric effect between the branched chains of HPDA. At the primary phase of shear action, the steric effect among the peripheral flexible chain led to a limit in the extension of the polymer chain.⁴¹ With further increases in shear time, a sharp decline was observed in the steric effect, which caused the easy stretch of the polymer chain and the slight rebound of apparent viscosity.³⁷ From Fig. 6c, it is clear that both the HPDA and poly(AM/AA/AMPS) solutions showed a shear thinning behaviour with increasing shear rate. Nevertheless, a higher viscosity retention rate was obtained for the HPDA solution which resulted from the morphologic discrepancy between the two polymers.

Fig. 6 Effect of (a) the shear force, (b) the shear time, and (c) the shear strength on the apparent viscosity of the HPDA and poly(AM/AA/AMPS) solution.

The apparent viscosity of the polymer samples related to the polymer concentration and shear rate of the pore media are curved as shown in Fig. 7. Under a fixed injection velocity of 40.4 mL min⁻¹ for the blast-hole model, the change in trend of the apparent viscosity related to the polymer concentration for HPDA was consistent with that for poly(AM/AA/AMPS) (Fig. 7a). The greatest viscosity retention rate of the HPDA solution was 99.2% at 1500 mg L⁻¹, and larger than 83.5% under mechanical shearing, which was derived from the fact that the orientation force from the pore throat caused the molecular deformation rather than the interruption of the chain.⁴² Meanwhile for the linear poly(AM/AA/AMPS) at 2000 mg L⁻¹ this was only 59.32%, and lower than 67.0% under mechanical shearing. As shown in Fig. 7b, a slight divergence of the apparent viscosity and retention rate could be observed between HPDA and poly(AM/AA/AMPS) at a relatively low injection velocity. When increasing the flow rate to 101 mL min⁻¹, the balanced viscosity retention rate of the 2000 mg L⁻¹ HPDA solution could reach 83.4%, while that of poly(AM/AA/AMPS) was 45.4% and still presented a declining trend. All the results of the above experiments suggested that the HPDA solution possessed an outstanding shear resistance power.

Fig. 7 Effect of (a) shear force and (b) shear rate of porous medium on the apparent viscosity of the HPDA and poly(AM/AA/AMPS) solution.

Feasibility of HPDA in low-to-moderate permeability reservoirs

It is well known that the polymer solution before injection formation would suffer mechanical shear in the stage of preparation, the pipeline and wellbore. Therefore, when the polymer solution was injected into the porous medium, its structure has been damaged partly.⁴² To investigate the feasibility of the hyperbranched polymer in low-to-moderate permeability reservoirs, 2000 mg L⁻¹ polymer solutions prepared with brine and sheared at 3500 rpm for 20 s were employed to study the injection performance, mobility control ability and EOR ability.

Injection and mobility control ability. The flow characteristic curves of HPDA and poly(AM/AA/AMPS) under various permeabilities are presented in Fig. 8. As seen in the figure, the hyperbranched polymer displays excellent injection performance at the permeability of 500–100 mD, but it is inferior to that of poly(AM/AA/AMPS). Because the injection pressure gradually increased during the injection of the polymer solution, the stable injection pressure of HPDA was 809.1, 1269.3 and 5180.6 × 10⁻³ MPa at about 500, 300 and 100 mD formation, respectively, which is much higher than that of poly(AM/AA/AMPS). The finding just confirmed the outcome of the DLS study that the diameter of poly(AM/AA/AMPS) (129 nm) was lower than that of HPDA (153 nm) after being sheared. On the other hand, the undulate pressure could be observed at the stable stage of the HPDA profile (Fig. 8a–c). We mainly attributed this to an elastic response of the hyperbranched polymer.⁴² The polymer could adsorb, accumulate and bridge the pore–throat channels to reduce water permeability.³⁴ While the displacement entered the deep-seated reservoirs and the injection pressure reached a certain threshold, the bridge layers would make a breakthrough under the tensile force of the porous media due to the good deformation properties of the polymer branched chain, which accelerated the deep oil displacement immensely. Fig. 8d reveals that the displacement pressure both of HPDA and poly(AM/AA/AMPS) sharply increased with the cumulative injection volume increasing under a lower permeability of 60 mD. Additionally, the injection pressure did not achieve a balanced value unexpectedly at the cumulative injection volume of 14 PV, suggesting that a poor matching relationship existed between the size of the polymer and the pore throat as the permeability was below 100 mD. Oddly, the theoretical injection permeability for the sheared HPDA solution of 2000 mg L⁻¹ of 153 nm diameter was 53 mD, which was calculated by the Carman–Kozeny equation.⁴³ The disagreement between the experimental injection permeability and the calculated value could be explained by the diameter distribution (Fig. 3). A relatively high frequency peak at 500–1000 nm could be discovered in the diameter distribution curve of the sheared HPDA solution that would yield a stable congestion for porous media. It should be noted that the extension and tangles between the polymer fork chains would also reduce the suitability.

Fig. 8 Flow characteristic curves of the HPDA and poly(AM/AA/AMPS) solution at a permeability of about (a) 500 × 10⁻³ μm, (b) 300 × 10⁻³ μm, (c) 100 × 10⁻³ μm and (d) 60 × 10⁻³ μm.

The RF and the RRF constructed by polymer flooding are recorded in Table 5. It was obvious that HPDA exhibited eminent mobility control ability in a moderate permeability reservoir that was favourable for enhancing the oil recovery. For instance, for the 300 mD reservoir, the HPDA solution could achieve a much higher RF (51.6) and RRF (16.6) in comparison to those of the poly(AM/AA/AMPS) solution (23.2 and 6.6) under the same conditions. And the value was less than that in the lower permeability reservoir (65.4 and 25.2). These results could be explained by the pattern of the HPDA and poly(AM/AA/AMPS) solutions to build a residual resistance factor. The linear polymer reinforces the solution viscosity through molecular chain entanglement, implying that its chains were vulnerable to the violent shear and tensile action from low-to-moderate permeability porous media. So it could spontaneously cause severe destruction of the morphology structure.⁴⁴ In view of this, R_h would decrease sharply and the mobility control ability would greatly reduce under stratigraphic conditions. From Fig. 8a–c, the injection pressure of poly(AM/AA/AMPS) improved rapidly and attained an equilibrium value at a polymer injection volume of only 5–11 PV, indicating that the time for the decayed poly(AM/AA/AMPS) solution to achieve adsorption and retention equilibrium was fairly short in the porous medium. Moreover, during the subsequent water flooding, the polymer was swept handily, because its RRF was constructed resting in physical adsorption.⁴⁵ Thus, the water flooding pressure showed a sharp decreasing trend to a low level. In contrast, the hyperbranched polymer exhibited excellent elasticity to distort under the stretching force of porous media (Fig. 5b) in the presence of unmatched pore throats. As a result, its injection pressure increased slowly and obtained a relatively high stable value at about 8–11 PV injection volume. Since surface adsorption and mechanical trapping were employed to construct percolating resistance point by point in this period, the HPDA solution could sequentially count on the captured molecule to drop the water phase permeability remarkably.

Table 5 RF and RRF of HPDA and poly(AM/AA/AMPS)

Polymer	Permeability (mD)	Water saturation pressure (10^−3 MPa)	Polymer solution pressure (10^−3 MPa)	Water flooding pressure (10^−3 MPa)	RF	RRF
HPDA	487.2	50.2	809.1	274.2	48.4	16.4
AM/AA/AMPS	484.0	50.5	251.3	43.7	14.9	2.6
HPDA	331.4	73.8	1269.3	481.8	51.6	19.6
AM/AA/AMPS	306.1	79.9	616.6	174.8	23.2	6.6
HPDA	102.9	237.6	5180.6	1999.1	65.4	25.2
AM/AA/AMPS	116.5	210.0	2216.0	591.6	31.7	8.5

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EOR ability. The capability of enhancing oil recovery for the HPDA and poly(AM/AA/AMPS) solutions was investigated in diverse permeability sand packs, illustrated in Table 6. As the permeability was 500 mD approximately, following a water cut to 98% for water flooding, 0.3 PV polymer flooding and subsequent water flooding could further increase the (HPDA) oil recovery to 21.9%, in comparison with the 13.5% oil recovery of the linear polymer (Fig. 9). Simultaneously, sample no. 3 could reach a relatively high value of 17.5%, larger than that of sample no. 4 (12.4%). These results suggested that the hyperbranched polymer displays a more outstanding EOR ability than that of the linear polymer under the same conditions, which should contribute to its favourable shearing resistance, rheology performances and mobility control properties.

Table 6 EOR of HPDA and poly(AM/AA/AMPS)

Sample	Polymer	Permeability (mD)	ET (%)	EW (%)	EOR (%)
1#	HPDA	485.3	46.5	24.6	21.9
2#	AM/AA/AMPS	488.9	39.4	25.9	13.5
3#	HPDA	274.4	34.9	17.4	17.5
4#	AM/AA/AMPS	258.0	29.5	17.1	12.4

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Fig. 9 EOR ability for HPDA and poly(AM/AA/AMPS).

Conclusions

A novel hyperbranched polymer (HPDA) was synthesized by aqueous free radical polymerization for low-to-moderate permeability reservoirs. IR, ¹H NMR, DLS and AFM actually confirmed its chemical structure and morphology. Furthermore, rheology, shearing resistance and sand packed tube displacement experiments were carried out to evaluate the feasibility of HPDA in low-to-moderate permeability reservoirs. Consequently, the incorporated DA monomer containing a dendritic structure could shrink the hydrodynamic radius and reinforce the anti-shearing properties. There was a compatible matching relationship between the size of HPDA and the pore throat at the permeability of 100–500 mD. And the higher EOR values of 21.9% and 17.5% by constructing the RF and RRF in a porous medium could be obtained in comparison to linear poly(AM/AA/AMPS) under a similar permeability. To broaden its application for a high temperature and high mineralization low permeability reservoir, further investigation of the hyperbranched polymer with various branching degrees, introducing functional pendants into the flexibility chains of the polymer periphery, is in progress.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 51404208), the second Youth Backbone Teachers Project of Southwest Petroleum University, the Open Fund (Grant No. PLN1433) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University), the National Undergraduate Training Programs for Innovation and Entrepreneurship (Grant No. 201510615008) and the Undergraduate Extracurricular Open Experiment of Southwest Petroleum University (Grant No. KSZ15070).

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Footnote

† Electronic supplementary information (ESI) available: Optimum synthesis conditions of monomer DA; IR and ¹H NMR spectrogram analysis of GA0.5–GA2.0; optimum copolymerization conditions; and three additional figures. See DOI: 10.1039/c6ra06397g

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