Chapter 3 Rheological Studies of Polymer Gel Systems

Rheological Studies of Polymer Gel Systems

CHAPTER 3 RHEOLOGICAL STUDIES OF POLYMER GEL SYSTEMS 3.1. INTRODUCTION The rheological behavior of polymer gel solution is the fundamental parameter for its application in the oilfields (Chauveteau et al., 1997; Yadav and Mahto, 2011; 2012). For pumping the polymer gel solutions through the tubing into the formation the study of the rheological behavior is essential for certain duration depending upon the depth of the well to ascertain flow ability of gel solution before the formation of stiff or rigid gel (Chang et al., 1985; 1988; Yadav and Mahto, 2013). The time for the stiff or rigid gel formation can be controlled from minutes to week by varying the formulation parameters (Al-Muntasheri, 2007; Mortimer et al., 2001). The temperature, polymer concentration, crosslinker concentration, ph and salinity are the important parameters which affect on the rheological behavior of the polymer gel system (Grattoni et al., 2001; Park and Song, 2010). Different equations have been used to describe the flow behavior of polymer gel system. The rheological behavior of polymer gel system is non-newtonian, in which there is a nonlinear relationship between shear stress and shear rate (Kelessidis and Maglione, 2006; Mahammad et al., 2007; Koohi et al., 2010). These polymer gel systems do not display simple behavior and require more complex model for their characterization (Kavanagh and Ross-Murphy, 1998; Mortensen et al., 1994; Song et al., 2006; Tsitsilianis et al., 2010; Maghzi et al., 2013). In this work, the rheological behavior of partially hydrolyzed polyacrylamide (PHPA)- hexamine-hydroquinone and partially hydrolyzed polyacrylamide-hexamine-pyrocatechol gel solutions were studied. The rheological models for these systems were also determined and validate with the experimental results. 34

3.2. EXPERIMENTAL SECTION 3.2.1. Materials The materials used for this work are partially hydrolyzed polyacrylamide (degree of hydrolysis is 29.59%), hexamine, pyrocatechol, hydroquinone, sodium chloride, hydrochloric acid and sodium hydroxide. Partially hydrolyzed polyacrylamide, in the form of white crystalline powder (procured from Oil and Natural Gas Corporation Limited, Mumbai, India) was used as the water soluble polymer for carrying out the experimental work. The organic cross-linkers hexamine and pyrocatechol were obtained in solid form from renowned manufacturers (hexamine: Otto Kemi Mumbai, India and pyrocatechol: Central Drug house (P) Ltd. New Delhi, India). Hydroquinone is procured from Ranbaxy Fine Chemicals Ltd., New Delhi, India. Sodium chloride is used to maintain the salinity of polymer gelant, purchased from Nice Chemical Pvt. Ltd. Cochin, India. Hydrochloric acid and sodium hydroxide are used for the adjustment of ph. (Hydrochloric acid: Central Drug house Ltd. New Delhi, India and sodium hydroxide: S. D. Fine Chem Ltd. Mumbai, India). 3.2.2. Equipment All rheological measurements were performed in a stress controlled Physica Rheolab MC1 (Figure 3.1). It is a rotational rheometer based on the Searle principle. It features a DC motor drive and optical encoder which provides excellent speed regulation, dynamic range and transient response. These features provide superior performance in comparison with rheometers using gear driven (indirect) or stepper motor drives. It enables precise measurements of fluid viscosity over the widest range of conditions available today. This machine is not equipped with a high pressure cell and measurement at high temperature is not allowed. Hence, gel had to be cured in hot air oven. The cured samples were transferred to the rheometer and tests were conducted at 30 C. 35

Chapter 3 Figure 3.1. Physica Rheometer MC1 3.2.3. Experimental procedure Initially stock solution of partially hydrolyzed polyacrylamide in brine solution (1.0 wt. %) was prepared and kept for aging at ambient temperature for 24 hrs. Further fresh solutions of both polymer gels (PHPA-HMTA-Hydroquinone and PHPA-HMTA-Pyrocatechol) were prepared in brine ahead of mixing the polymer and crosslinkers to form gelant. The appropriate solution of partially hydrolyzed polyacrylamide, crosslinkers (hexaminehydroquinone and hexamine-pyrocatechol) and brine were thoroughly mixed at room temperature by magnetic stirrer. The ph of the gelant solution was measured by Century CP-901 digital ph meter. The ph of the gelant was maintained using 1N sodium hydroxide and 1N hydrochloric acid. Finally, the solution was transferred into small glass bottles and kept at the desired temperature in the hot air oven. At regular intervals of time rheological behavior at different shear rates was measured using rhometer. 36

3.3. RESULTS AND DISCUSSION 3.3.1. Effect of various parameters on the partially hydrolyzed polyacrylamide (PHPA) hexamine (HMTA) - Hydroquinone gel solution 3.3.1.1. Ageing effect on the rheological behavior of PHPA-HMTA-Hydroquinone gel solution The gel point is defined as the time needed to reach the inflection point on the viscosity vs. time curve (Figure 3.2). This method has been widely used by several authors (Mortimer et al., 2001; Jia et al., 2010; 2011). Before the gel formation, the viscosity of the gelling solution is relatively low; therefore, it can be measured accurately. After the gel formation, it will be hard to get an accurate viscosity value. The strength of the cross-linking polymer solution is hard to measure and also hard to define, when the gel has reached a certain high strength (Koohi et al., 2010). 11 10 9 8 7 PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.% Temp.- 100 C Shear rate (s -1 ):- 1.81 2.58 124 1200 Viscosity (Pa.s) 6 5 4 3 2 1 0-1 -1 0 1 2 3 4 5 6 7 8 Heating time (hrs.) Fig 3.2. Effect of time on evolution of rheological behavior of PHPA-HMTA- Hydroquinone gel solution at 100 C and ph 8.5 (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) 37

Fig 3.2 shown illustrates the viscosity evolution as a function of heating time at 100 C for gelling solutions containing PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.3 wt.% prepared in brine. The readings were taken at different shear rates. The apparent viscosity increases with the increase in time intervals at any particular shear rate. The gelation behavior will determine the injection period and how deep in to the formation the gel solution can be placed. 3.3.1.2. Effect of temperature on the rheological behavior of PHPA-HMTA- Hydroquinone gel solution Fig 3.3 shown illustrates the viscosity evolution as a function of time for gelling solutions containing PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.3 wt.% prepared in brine. The readings were taken at different shear rates. The apparent viscosity increases with the increase in temperature at any particular shear rate. The gels formed at higher temperature are more viscous hence has greater ability to shut-off water in reservoirs and enhance oil production. Before gel formation, the viscosity of the gelling solution is relatively low; therefore it can be measured easily and accurately but after gel formation it is hard to obtain accurate readings (Jia et al., 2011). Thus, the mechanical strength of cross-linked partially hydrolyzed polyacrylamide gel increases with the increase in temperature. The elastic modulus increased gradually upon the addition of the cross-linkers until it reached a constant level indicating that the gel formation reaction is over. When the measurements were taken it was observed in each case that initially the reading remains constant for some time known as the induction time and then it starts increasing indicating the onset of gelation. Addition of cross-linker to the solution increased until it reached a maximum where increasing the cross-linker concentration results in syneresis. Higher concentrations of cross-linker prevented gel formation. Therefore, there are concentration limits that crosslinker should not exceed in order for the gel to form and this 38

is known as critical crosslinker concentration. Initially the viscosity was found to decrease due to temperature as is known for any solution which in this case may be due to the breaking up of the molecular chains as a result of cross-linking reaction. As the time progresses polymer undergoes hydrolysis and the gelant starts thickening which results in an increase in viscosity. Also it was observed that the values of gelant viscosity increases with temperature at constant shear rate, which reflects that the viscosity of crosslinked polymer gel solution increase with temperature with the passage of time. This increased viscosity leads to gel formation which in turn behaves as flow diverting agent or blocking agent for controlling excessive water production in the oil fields. 10 9 8 7 PHPA 1.0 wt.%, HMTA 0.4wt.% and Hydroquinone 0.4 wt.% At 5 hrs. Shear rate (s -1 ):- 1.81 2.58 124 1200 Viscosity (Pa.s) 6 5 4 3 2 1 0 30 40 50 60 70 80 90 100 110 120 130 Temperature ( C) Fig 3.3. Effect of temperature on evolution of rheological behavior of PHPA-HMTA- Hydroquinone gel solution at ph 8.5 (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) 39

3.3.1.3. Effect of polymer concentration on the rheological behavior of PHPA-HMTA- Hydroquinone gel solution Due to cross-linking a lattice like structure is formed which consists of two domains: dilute domain (free draining space) and dense domain (non-draining space). The dense domains are centered on the cross-linked regions where the polymers are bound together and extend outward by the entanglement of the free polymer onto the cross-linked regions. They are much less permeable than the dilute domains (Grattoni et al., 2001). Viscosity (Pa.s) 10 8 6 4 2 HMTA 0.4 wt.% and Hydroquinone 0.4 wt.% at 5 hrs. Shear rate (s -1 ): 1.81 2.58 124 1200 0 0.8 0.9 1.0 1.1 1.2 PHPA concentration (wt.%) Fig 3.4. Effect of Polymer concentration on evolution of rheological behavior of PHPA-HMTA-Hydroquinone gel solution at ph 8.5 and 100 C (HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) Even at the lowest polymer concentration, all the cross-linker reacts with polymer to form gel hence an increase in polymer concentration will mainly increase the number of free polymer coils which increases the viscosity of the gelant (Koohi et al., 2010). In order to check the effect of polymer concentration, five solutions were prepared in brine of 1.0 wt% salinity with PHPA concentrations of 0.8, 0.9, 1.0, 1.1 and 1.2 wt% with the same 40

concentration of HMTA (0.4 wt.%) hydroquinone (0.3 wt.%). Fig 3.4 depicts the change in viscosity with increase in polymer concentration. The gels at higher concentration were very stiff in nature and formed in lesser time interval. This analysis was done with the help of bottle testing after certain time intervals. 3.3.1.4. Effect of crosslinkers concentration on the rheological behavior of PHPA- HMTA- Hydroquinone gel solution A comparative study of the variation of apparent viscosity of different polymer gelants having the same concentration of both the cross-linkers with a constant polymer concentration of 1.0 wt % at room temperature is shown in the flow curve of Fig 3.5 The graph showed that the value of viscosity increases with an increase in concentration of the cross-linkers at constant polymer concentration. Viscosity (Pa.s) 7 6 5 4 3 2 PHPA 1.0 wt.% at 5 hrs. Shear rate (s -1 ): 1.81 2.58 124 1200 1 0 0.3/0.3 0.4/0.3 0.4/0.4 0.5/0.4 HMTA/Hydroquinone concentration (wt.%) Fig 3.5. Effect of Crosslinkers concentration on evolution of rheological behavior of PHPA-HMTA-Hydroquinone gel solution at ph 8.5, time intervals 5 hrs and 100 C (PHPA 1.0 wt.%) 41

The constant concentration of PHPA 1.0 wt.% to study the variation in gel strength at room temperature. Thus, greater concentration of the cross- linker results in the increase of gel strength of the polymer gel (Koohi et al., 2010). Fig 3.5 depicts the increasing trend of viscosity with an increase in concentration of HMTA and hydroquinone during gelation. As shown in Fig 3.5 the readings were taken at a shear rate of 1.81, 2.58, 124 and 1200 sec -1 after 5 hrs of gelation at a temperature of 100 C. This shows that the mechanical strength of the gel formed increases with an increase in concentration of cross-linkers. The lower the cross-linkers concentration, the worse the degrees of cross-linking. The solubility of the polymer gel increases with low cross-linking density; therefore the degree of water swelling of the gel gets reduced. Hence the gels of weak strength are formed. The shear stress increases with an increase in concentration of cross-linkers since greater crosslinking takes place on the polymer chain. 3.3.1.5. Effect of salinity on the rheological behavior of PHPA-HMTA- Hydroquinone gel solution Gelants were prepared in brines containing various salts concentrations. In this study, NaCl was used to examine the effect of sodium ions on the gelation time of this system. It was observed that at a given shear rate, the apparent viscosity diminished as NaCl concentration increased. Different samples were prepared with a constant polymer content, PHPA 1.0 wt.%, HMTA 0.4 wt.% and hydroquinone 0.3 wt.% in brine of salinity varying from 1.0 wt.% to 4.0 wt.%. Then, the viscosity of these solutions was measured at 30 C at different shear rates as shown in Figure 3.6. The excess monovalent cations present in gel system screen the negative charges on the polymer molecule structure so that the positive crosslinker ions could not easily access the negative sites to react with them thus the crosslinking density decreases with reduction in elastic modulus of the gel (Cai and Huang, 2001). The elasticity of the gelants decreased with increase in salinity. 42

Viscosity (Pa.s) 8 7 6 5 4 3 2 PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.% at 5 hrs. Shear rate (s -1 ): 1.81 2.58 124 1200 1 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Salinity (wt.%) Fig 3.6. Effect of salinity on evolution of rheological behavior of PHPA-HMTA- Hydroquinone gel solution at ph 8.5, time intervals 5 hrs and 100 C (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) 3.3.1.6. Effect of ph on the rheological behavior of PHPA-HMTA- Hydroquinone gel solution Different polymer gel systems have different range of ph over which they can maintain their stability. The ph range over which the experiments were carried out was from 7.0 to 9.0. Figure 3.7 shows the ph ranges between 7.0 to 9.0 have no significance effect on the gelation time. From the experiments carried out in the laboratory it was found that HMTA/hydroquinonel cross-linked partially hydrolyzed polyacrylamide is stable up to ph 9.0. Above ph 9.0 proper gelation did not take place and syneresis also occurred due to excess crosslinking. The results indicate that a suitable solution ph range for partially hydrolyzed polyacrylamide, hexamine and hydroquinone crosslinking is between 7.0 to 9.0. 43

Viscosity (Pa.s) 8 7 6 5 4 3 2 PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.% at 5 hrs. Shear rate (s -1 ): 1.81 2.58 124 1200 1 0 7.0 7.5 8.0 8.5 9.0 ph Fig 3.7. Effect of ph on rheological behavior of PHPA-HMTA-Hydroquinone gel solution at 8.5 ph, time intervals 5 hrs and 100 C (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) 44

3.3.1.7. Determination of rheological models for PHPA-HMTA-Hydroquinone gel solution (Yadav and Mahto, 2013) The developed polymer gel behaves like a non-newtonian fluid hence viscoplastic flow models may be applied in this system. Here, four inelastic-viscoplastic flow models including a yield stress parameter were employed to make a quantitative evaluation of the steady shear flow behavior of polymer gel solution, and then the applicability of these models was also examined in detail. A general viscoplastic flow model having a yield stress term may be expressed by the following form: τ = τ + kγ Where τ is the shear stress, τ is the yield stress, γ is the shear rate, k is the consistency index, n 1 and n 2 are material parameters related to the material s flow behavior, and consequently, each flow model is determined according to the conditions of n 1 and n 2. Table 3.1 summarizes the viscoplastic flow models adopted in this study and their flow characteristics. Here τ is the yield stress of each model and k is the consistency index related to a high-shear limiting viscosity, γ as the shear rate is increase towards infinity. n is the flow behavior index, a material parameter that determines the shear-thinning nature of a material. In order that the models summarized in Table 1 could predict a shear thinning behavior, both n and n must be positive value and n should be larger than n or equivalent to n. In order to determine the polymer gel solution parameters of each model, a linear regression analysis was used for the Bingham model, while a nonlinear regression analysis method was used for the Herschel-Bulkley, Mizrahi-Berk, and Robertson Stiff models. The calculated values of the polymer gel solution parameters from the viscoplastic flow models along with those of the determination coefficients and its comparison with the experimental values are reported in Tables 3.2-3.7 and Figures 3.8-3.12. 45

All the polymer gel solutions exhibit a marked shear thinning behavior regardless of their ph. As expected, both the yield stress and consistency index values are not same for flow models. The value of flow behavior indices provides a reference for the assessment of a shear thinning nature, and it was observed that developed gelant is shear thinning in nature. The Bingham Plastic, Herschel-Bulkley, Mizrahi-Berk, and Robertson stiff models give an excellent ability to describe the flow behavior of polymer gel solution. All of these four models have the values of determination coefficients near to one and show a clear tendency that the yield stress values are remains not change with change of ph of the polymer gel solution. The similar values of the determination coefficients are obtained for different flow models. The Bingham plastic, Herschel Bulkley, Mizrahi Berk and Robertson Stiff models are all in good agreement with the experimentally measured data over a whole range of shear rates tested. But, Robertson stiff model has better agreement with the experimental values of shear stress and shear rate data of the developed polymer gel system than the other model tested. Table 3.1: Viscoplastic flow models used in this study and their characteristics Flow Model Equation n 1 n 2 γ Shear-thinning condition Bingham Plastic τ = τ + kγ 1 1 k - Herschel Bulkley τ = τ + kγ 1 n 0 0 < n 1 k, if n = 1 Mizrahi Berk τ / = τ / + kγ 0.5 n 0 0 < n 0.5 k 2, if n=0.5 Robertson Stiff τ = k (γ + C) 1 n k, if n = 1 0 < n 1 46

Table 3.2: Experimental values of shear rate and shear stress at different reaction time intervals (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.% at 100 C and ph 8.5) Shear rate Shear stress (Pa) at different reaction time intervals (sec -1 ) 0 (hrs.) 1 (hrs.) 3 (hrs.) 5 (hrs.) 7 (hrs.) 2.58 4.68 6.58 9.06 9.32 14.57 3.54 4.68 6.67 9.13 9.42 15.05 4.85 4.72 6.82 9.36 9.76 15.95 6.72 4.85 6.95 9.61 9.94 16.76 9.29 5.07 7.08 9.82 10.26 17.07 12.9 5.38 7.28 9.91 10.78 17.89 17.8 5.56 7.46 10.04 10.88 18.45 24.6 5.64 7.64 10.3 11.28 18.91 34 5.88 7.82 10.69 11.88 19.36 47 6.39 8.29 10.97 12 20.02 65 6.76 8.86 11.59 12.65 20.78 89.9 7.31 9.27 12.28 13.1 21.34 124 7.48 9.49 12.96 13.9 22.87 172 7.78 9.83 14.1 15.2 24.01 238 8.3 10.26 15.4 17 26.45 329 9.01 10.96 16.7 18.8 28.98 454 9.93 11.91 18.9 20.8 31.56 628 10.72 12.82 20.7 23.5 34.97 868 11.74 13.4 23.14 26.7 39.09 1200 12.98 14.78 25.5 30.1 42.78 47

Table 3.3: Calculated flow model parameters for polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 0 hr at ph 8.5 and 30 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 5.6962 0.0071-0.8954 9.8365 Herschel Bulkley 3.2370 0.2521 0.5143 0.8225 19.1647 Mizrahi Berk 3.6220 0.0590 0.4830 0.8679 14.3459 Robertson Stiff 285.9270 0.1370 0.6390 0.9103 3.9327 Table 3.4: Calculated flow model parameters for polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 1 hr at ph 8.5 and 100 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 7.6985 0.007-0.8850-7.4363 Herschel Bulkley 5.2365 0.2471 0.5164 0.8131 13.5293 Mizrahi Berk 5.4320 0.0610 0.4560 0.9009 11.1643 Robertson Stiff 340.7370 0.2910 0.5470 0.9089 3.2784 Table 3.5: Calculated flow model parameters for polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 3 hr at ph 8.5 and 100 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 10.336 0.0146-0.9474 20.8984 Herschel Bulkley 7.4906 0.1655 0.6682 0.9236 12.4199 Mizrahi Berk 7.7620 0.0430 0.5650 0.9462 9.4818 Robertson Stiff 260.9650 0.2550 0.6440 0.9597 4.7023 48

Table 3.6: Calculated flow model parameters for polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 5 hr at ph 8.5 and 100 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 10.961 0.018-0.9588 10.6412 Herschel Bulkley 7.3286 0.2059 0.6694 0.9173 15.6317 Mizrahi Berk 7.7490 0.0550 0.5540 0.9482 11.2955 Robertson Stiff 278.8160 0.1700 0.7210 0.9666 3.9480 Table 3.7: Calculated flow model parameters for polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 7 hr at ph 8.5 and 100 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 18.188 0.0238-0.9334 3.3605 Herschel Bulkley 10.8371 0.7099 0.5335 0.8448 18.3684 Mizrahi Berk 11.8190 0.1060 0.4790 0.9013 14.1993 Robertson Stiff 296.4710 0.4050 0.6500 0.9455 4.0842 49

100 Experimental values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model Shear stress (Pa) 10 1 1 10 100 1000 10000 Shear rate (sec -1 ) Figure 3.8: Rheogram of polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 0 hr at 8.5 ph and Temperature 30 C 100 Experimental values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model Shear stress (Pa) 10 1 1 10 100 1000 10000 Shear rate (sec -1 ) Figure 3.9: Rheogram of polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 1 hr at 8.5 ph and Temperature 100 C 50

100 Experimental values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model Shear stress (Pa) 10 1 1 10 100 1000 10000 Shear rate (sec -1 ) Figure 3.10: Rheogram of polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 3 hr at 8.5 ph and Temperature 100 C 100 Experimental values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model Shear stress (Pa) 10 1 1 10 100 1000 10000 Shear rate (sec -1 ) Figure 3.11: Rheogram of polymer gel solution (PHPA 1.0 wt.%, HMTA 0.4 wt.% and Hydroquinone 0.4 wt.%) after 5 hr at 8.5 ph and Temperature 100 C 51

3.3.2. Effect of various parameters on the partially hydrolyzed polyacrylamide (PHPA) hexamine (HMTA) - Pyrocatechol gel solution 3.3.2.1. Ageing effect on the rheological behavior of PHPA-HMTA-Pyrocatechol gel solution Fig 3.13 shown illustrates the viscosity evolution as a function of heating time at 90 C for gelling solutions containing PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.% prepared in brine. The readings were taken at different shear rates. The apparent viscosity increases with the increase in time intervals at any particular shear rate. The gelation behavior will determine the injection period and how deep in to the formation the gel solution can be placed. 5 4 PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) Shear rate (sec -1 ) : 2.58 12.9 Viscosity (Pa.s) 3 2 1 0 0 2 4 6 8 10 Heating time (hrs.) Figure 3.13. Change in viscosity with time intervals at constant shear rate, 7.0 ph and 90 C (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) The gel point is defined as the time needed to reach the inflection point on the viscosity vs. time curve (Figure 3.13). This method has been widely used by several authors (Mortimer 53

et al., 2001; Jia et al., 2010; 2011; Yadav and Mahto, 2013). Before the gel formation, the viscosity of the gelling solution is relatively low; therefore, it can be measured accurately. After the gel formation, it will be hard to get an accurate viscosity value. The strength of the cross-linking polymer solution is hard to measure and also hard to define, when the gel has reached a certain high strength. 3.3.2.2. Effect of temperature on the rheological behavior of PHPA-HMTA- Pyrocatechol gel solution Fig 3.14 shown illustrates the viscosity evolution as a function of time for gelling solutions containing PHPA 1.0 wt.% with HMTA 0.5 wt.% and Pyrocatechol 0.5 wt.% prepared in brine. The readings were taken at different shear rates. The apparent viscosity increases with the increase in temperature at any particular shear rate. The gels formed at higher temperature are more viscous hence has greater ability to shut-off water in reservoirs and enhance oil production. Before gel formation, the viscosity of the gelling solution is relatively low; therefore it can be measured easily and accurately but after gel formation it is hard to obtain accurate readings (Jia et al., 2011). Thus, the mechanical strength of cross-linked partially hydrolyzed polyacrylamide gel increases with the increase in temperature. The elastic modulus increased gradually upon the addition of the cross-linkers until it reached a constant level indicating that the gel formation reaction is over. When the measurements were taken it was observed in each case that initially the reading remains constant for some time known as the induction time and then it starts increasing indicating the onset of gelation. Addition of cross-linker to the solution increased until it reached a maximum where increasing the cross-linker concentration results in syneresis. Higher concentrations of cross-linker prevented gel formation. Therefore, there are concentration limits that crosslinker should not exceed in order for the gel to form and this is known as critical crosslinker concentration. 54

Initially the viscosity was found to decrease due to temperature as is known for any solution which in this case may be due to the breaking up of the molecular chains as a result of cross-linking reaction. As the time progresses polymer undergoes hydrolysis and the gelant starts thickening which results in an increase in viscosity. Also it was observed that the values of gelant viscosity increases with temperature at constant shear rate, which reflects that the viscosity of crosslinked polymer gel solution increase with temperature with the passage of time. This increased viscosity leads to gel formation which in turn behaves as flow diverting agent or blocking agent for controlling excessive water production in the oil fields. Viscosity (Pa.s) 1.0 0.8 0.6 0.4 PHPA 1.0 wt.%, HMTA 0.5 wt.% & Pyrocatechol 0.5 wt.% ph 8.0 at Time inervals 3 hrs. Shear rate (sec -1 ) 104 576 0.2 0.0 20 40 60 80 100 120 Temperature ( C ) Fig 3.14. Effect of temperature on evolution of rheological behavior of PHPA-HMTA- Pyrocatechol gel solution at ph 8.0 (PHPA 1.0 wt.%, HMTA 0.5 wt.% and Pyrocatechol 0.5 wt.%) 55

3.3.2.3. Effect of polymer concentration on the rheological behavior of PHPA-HMTA- Pyrocatechol gel solution Due to cross-linking a lattice like structure is formed which consists of two domains: dilute domain (free draining space) and dense domain (non-draining space). The dense domains are centered on the cross-linked regions where the polymers are bound together and extend outward by the entanglement of the free polymer onto the cross-linked regions. They are much less permeable than the dilute domains (Grattoni et al., 2001). Even at the lowest polymer concentration, all the cross-linker reacts with polymer to form gel hence an increase in polymer concentration will mainly increase the number of free polymer coils which increases the viscosity of the gelant. 1.2 1.1 1.0 0.9 HMTA 0.5wt.% & Pyrocatechol 0.4wt.% after 3 hrs Shear rates (sec -1 ) : 124 628 1200 0.8 Viscosity (Pa.s) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.8 0.9 1.0 1.1 1.2 PHPA Concentration (wt.%) Fig 3.15. Effect of Polymer concentration on evolution of rheological behavior of PHPA-HMTA- Pyrocatechol gel solution at ph 8.5 (HMTA 0.5 wt.% and Pyrocatechol 0.4 wt.%) In order to check the effect of polymer concentration, five solutions were prepared in brine of 1.0 wt% salinity with PHPA concentrations of 0.8, 0.9, 1.0, 1.1 and 1.2 wt% with the 56

same concentration of HMTA (0.5 wt.%) Pyrocatechol (0.4 wt.%). Fig 3.15 depicts the change in viscosity with increase in polymer concentration. The gels at higher concentration were very stiff in nature and formed in lesser time interval. This analysis was done with the help of bottle testing after certain time intervals. 3.3.2.4. Effect of crosslinkers concentration on the rheological behavior of PHPA- HMTA-Pyrocatechol gel solution A comparative study of the variation of apparent viscosity of different polymer gelants having the same concentration of both the cross-linkers with a constant polymer concentration of 1 wt % at room temperature is shown in the flow curve of Fig 3.16. The graph shows that the value of viscosity increases with an increase in concentration of the cross-linkers at constant polymer concentration. The constant concentration of PHPA 1.0 wt.% to study the variation in gel strength at room temperature. Thus, greater concentration of the cross- linker results in the increase of gel strength of the polymer gel. Fig 3.16 depicts the increasing trend of viscosity with an increase in concentration of HMTA and pyrocatechol during gelation. As shown in Fig 3.16 the readings were taken at a shear rate of 124, 628 and 1200 sec -1 after 3 hrs of gelation at a temperature of 100 C. This shows that the mechanical strength of the gel formed increases with an increase in concentration of cross-linkers. The lower the cross-linkers concentration, the worse the degrees of cross-linking. The solubility of the polymer gel increases with low cross-linking density; therefore the degree of water swelling of the gel gets reduced. Hence the gels of weak strength are formed. The shear stress increases with an increase in concentration of cross-linkers since greater cross-linking takes place on the polymer chain. 57

1.0 0.9 0.8 0.7 PHPA 1.0 wt.% after 3 hrs. Shear rates (sec -1 ) : 124 628 1200 Viscosity (Pa.s) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.3/0.3 0.4/0.3 0.4/0.4 0.5/0.4 HMTA/Pyrocatechol crosslinker concentration (wt.%) Fig 3.16. Effect of Crosslinkers concentration on evolution of rheological behavior of PHPA-HMTA-Pyrocatechol gel solution at ph 7.5 (PHPA 1.0 wt.%) 3.3.2.5. Effect of salinity on the rheological behavior of PHPA-HMTA-Pyrocatechol gel solution Gelants were prepared in brines containing various salts concentrations. In this study, NaCl was used to examine the effect of sodium ions on the gelation time of this system. It was observed that at a given shear rate, the apparent viscosity diminished as NaCl concentration increased. Different samples were prepared with a constant polymer content, PHPA 1.0 wt.%, HMTA 0.5 wt.% and Pyrocatechol 0.4 wt.% in brine of salinity varying from 1.0 wt.% to 4.0 wt.%. Then, the viscosity of these solutions was measured at 30 C at different shear rates as shown in Figure 3.17. The excess monovalent cations present in gel system screen the negative charges on the polymer molecule structure so that the positive cross-linker ions could not easily access the negative sites to react with them thus the cross-linking density decreases with reduction in 58

elastic modulus of the gel (Cai and Huang, 2001). The elasticity of the gelants decreased with increase in salinity. 1.0 Viscosity (Pa.s) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 PHPA 1.0 wt.%, HMTA 0.5 wt.% and Pyrocatechol 0.4 wt.% after 3 hrs. Shear rate (sec -1 ) : 124 628 1200 0.2 0.1 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Salinity concentration (NaCl) (wt.%) Fig 3.17. Effect of salinity on evolution of rheological behavior of PHPA-HMTA- Pyrocatechol gel solution at ph 7.5 (PHPA 1.0 wt.%, HMTA 0.5 wt.% and Pyrocatechol 0.4 wt.%) 3.3.2.6. Effect of ph on the rheological behavior of PHPA-HMTA-Pyrocatechol gel solution Different polymer gel systems have different range of ph over which they can maintain their stability. The ph range over which the experiments were carried out was from 7.0 to 9.0. Figure 3.18 shows the ph ranges between 7.0 to 9.0 have no significance effect on the gelation time. From the experiments carried out in the laboratory it was found that HMTA/pyrocatechol cross-linked partially hydrolyzed polyacrylamide is stable up to ph 9.0. Above ph 9.0 proper gelation did not take place and syneresis also occurred due to 59

excess crosslinking. The results indicate that a suitable solution ph range for partially hydrolyzed polyacrylamide, hexamine and pyrocatechol crosslinking is between 7.0 to 9.0. 1.0 0.9 0.8 0.7 PHPA 1.0 wt.%, HMTA 0.5 wt.% and Pyrocatechol 0.4 wt.% after 3 hrs. Shear rate (sec -1 ) : 124 628 1200 Viscosity (Pa.s) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 7.0 7.5 8.0 8.5 9.0 ph Fig 3.18. Effect of ph on evolution of rheological behavior of PHPA-HMTA- Pyrocatechol gel solution at 90 C (PHPA 1.0 wt.%, HMTA 0.5 wt.% and Pyrocatechol 0.4 wt.%) 60

3.3.2.7. Determination of rheological models for PHPA-HMTA-Pyrocatechol gel solution (Yadav and Mahto, 2013) In order to determine the polymer gel solution parameters of each model, a linear regression analysis was used for the Bingham model, while a nonlinear regression analysis method was used for the Herschel-Bulkley, Mizrahi-Berk, and Robertson Stiff models. The calculated values of the polymer gel solution parameters from the viscoplastic flow models along with those of the determination coefficients and its comparison with the experimental values are reported in Tables 3.8-3.12 and Figures 3.19-3.22. All the polymer gel solutions exhibit a marked shear thinning behavior regardless of their ph. As expected, both the yield stress and consistency index values are not same for flow models. The value of flow behavior indices provides a reference for the assessment of a shear thinning nature, and it was observed that developed gelant is shear thinning in nature. The Bingham Plastic, Herschel-Bulkley, Mizrahi-Berk, and Robertson stiff models give an excellent ability to describe the flow behavior of polymer gel solution. All of these four models have the values of determination coefficients near to one and show a clear tendency that the yield stress values are remains not change with change of ph of the polymer gel solution. The similar values of the determination coefficients are obtained for different flow models. The Bingham plastic, Herschel Bulkley, Mizrahi Berk and Robertson Stiff models are all in good agreement with the experimentally measured data over a whole range of shear rates tested. But Robertson stiff model has better agreement with the experimental values of shear stress and shear rate data of the developed polymer gel system than the other model tested. 61

Table 3.8. Experimental values of shear rate and shear stress at different time intervals (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) Shear rate (sec -1 ) Shear stress (Pa) at different reaction time intervals 0 hr 3 hrs 6 hrs 9 hrs 2.58 3.49 5.93 6.25 10.41 3.54 3.65 6.12 5.24 11.76 4.85 3.8 6.3 5.75 12.04 6.72 3.89 6.53 6.41 12.87 9.29 3.98 6.73 7.19 13.34 12.9 4.25 6.86 7.04 13.96 17.8 4.44 7.03 7.48 14.56 24.6 4.61 7.23 7.49 14.89 34 4.78 7.53 8.1 15.37 47 5.27 7.93 8.6 15.78 65 5.86 8.43 8.9 16.59 89.9 6.25 9.13 9.43 17.07 124 6.47 9.83 10.3 18.18 172 6.81 10.3 11.5 19.13 238 7.24 11.83 13.1 21.14 329 7.94 13.4 14.9 24.17 454 8.89 15.6 17.4 26.96 628 9.8 17.62 19.9 30.08 868 10.1 20.13 22.8 33.67 1200 11.45 22.4 26.6 37.45 62

Table 3.9: Calculated flow model parameters for polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) at 0 hr, ph 7.5 and 30 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 4.6845 0.0068-0.8671-8.1174 Herschel Bulkley 2.130 0.2704 0.5018 0.7942 25.4002 Mizrahi Berk 2.4372 0.0994 0.4136 0.8510 18.7692 Robertson Stiff 205.3200 0.1360 0.6310 0.8788 6.6037 Table 3.10: Calculated flow model parameters for polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 3 hrs at 7.5 ph and 90 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 7.1737 0.0146-0.9563 13.0932 Herschel Bulkley 4.5052 0.1399 0.6937 0.9285 17.8821 Mizrahi Berk 4.8104 0.0561 0.5399 0.9512 12.7169 Robertson Stiff 218.5710 0.1110 0.7470 0.9631 5.1421 Table 3.11: Calculated flow model parameters for polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 6 hrs at ph 7.5 and 90 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 7.2198 0.0181-0.9544 68.5897 Herschel Bulkley 2.5593 0.3632 0.5882 0.8785 39.1473 Mizrahi Berk 3.4865 0.1097 0.4828 0.9313 23.7666 Robertson Stiff 155.2680 0.1310 0.7510 0.9554 9.4640 63

Table 3.12: Calculated flow model parameters for polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 9 hrs at ph 7.5 and 90 C Flow Models Parameters τ or C k (Pa.s n-1 ) n R 2 Avg. % Error Bingham Plastic 14.118 0.0224-0.9398 6.5448 Herschel Bulkley 7.0577 0.7382 0.5172 0.8368 23.7736 Mizrahi Berk 8.1910 0.1232 0.4640 0.8939 17.4067 Robertson Stiff 232.5390 0.3300 0.6640 0.9489 5.3534 100 Shear Stress (Pa) 10 Experimental values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model 1 1 10 100 1000 10000 Shear rate (s -1 ) Figure 3.19. Rheogram of polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 0 hr at 7.5 ph and Temperature 30 C 64

Shear Stress (Pa) 100 10 Experimental value Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model 1 1 10 100 1000 10000 Shear Rate (s -1 ) Figure 3.20. Rheogram of polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 3 hrs at 7.5 ph and Temperature 90 C 100 10 Shear stress (Pa) 1 Experimental values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model 0 1 10 100 1000 10000 Shear rate (sec -1 ) Figure 3.21. Rheogram of polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 6 hrs at 7.5 ph and Temperature 90 C 65

100 Shear stress (Pa) 10 Experimental Values Bingham Plastic Model Herschel Bulkley Model Mizrahi Berk Model Robertson Stiff Model 1 1 10 100 1000 10000 Shear rate (sec -1 ) Figure 3.22. Rheogram of polymer gel solution (PHPA 0.9 wt.%, HMTA 0.4 wt.% and Pyrocatechol 0.4 wt.%) after 9 hrs at 7.5 ph and Temperature 90 C 66

3.4. CONCLUSIONS The following conclusions may be drawn from present study: 1. The viscosity of partially hydrolyzed polyacrylamide-hexamine-hydroquinone and partially hydrolyzed polyacrylamide-hexamine-pyrocatechol gel solutions increases with increase in ageing time, temperature, polymer concentration and crosslinker concentration. But, increase in salinity concentration viscosity is decreases. 2. The partially hydrolyzed polyacrylamide-hexamine-hydroquinone and partially hydrolyzed polyacrylamide-hexamine-pyrocatechol gel solutions shows the negligible effect on ph. 3. The partially hydrolyzed polyacrylamide-hexamine-hydroquinone and partially hydrolyzed polyacrylamide-hexamine-pyrocatechol gel solutions behave like a non- Newtonian shear thinning fluid. 4. The nonlinear rheological models like Herschel Bulkley, Mizrahi Berk and Robertson stiff models are found to be more suitable compare to the linear rheological model like Bingham Plastic flow model for partially hydrolyzed polyacrylamide-hexaminehydroquinone and partially hydrolyzed polyacrylamide-hexamine-pyrocatechol gel systems. 5. Out of three nonlinear rheological models (Herschel Bulkley, Mizrahi Berk and Robertson stiff), Robertson stiff model has better agreement with the experimental values of shear stress and shear rate data of the partially hydrolyzed polyacrylamidehexamine-hydroquinone and partially hydrolyzed polyacrylamide-hexaminepyrocatechol gel systems. 67