Mechanism Study of the Cross-Linking Reaction of Hydrolyzed

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Mechanism Study of the Cross-Linking Reaction of Hydrolyzed Polyacrylamide/Ac3Cr in Formation Water Lei Zhang,*,†,‡ Chunsheng Pu,*,†,‡ Haibo Sang,†,‡ and Qing Zhao†,‡ Institute of Petroleum Engineering and ‡Research Center of Physical-Chemical Engineering and Technology on the Development of Complex Reservoirs, China University of Petroleum (East China), Qingdao 266580, China

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on September 5, 2015 | http://pubs.acs.org Publication Date (Web): July 15, 2015 | doi: 10.1021/acs.energyfuels.5b00149

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ABSTRACT: The mechanism of the cross-linking reaction between hydrolyzed polyacrylamide (HPAM) and chromium acetate in formation water was systematically studied by viscometry, ultraviolet-visual absorption spectrometry, and core flow experiments. The results show that the process and outcome of the cross-linking reaction between HPAM and chromium acetate is significantly affected by salinity. In formation water, chromium acetate cannot cross-link HPAM when the salinity is too low. With an increase of salinity, the cross-linking reaction occurs, and the degree of the reaction increases to a balance point. When the cross-linking reaction occurs, two different types of the reaction appear under different salinity. The intramolecular crosslinking reaction is the first to happen, whether under high salinity or under low salinity. In this stage, the cross-linking reaction is a first-order reaction and plays a greater role in the whole process of the reaction due to its higher reaction rate and higher reaction degree. Next, the intramolecular cross-linking continues to occur if the formation water is in the low salinity range, but the intermolecular cross-linking reaction occurs if the formation water is in the high salinity range. In this stage, the cross-linking reaction is a multistage reaction. Meanwhile, the experiments quantify a matching relationship between cations in the formation water and the profile control and oil displacement agent. The experimental results in this paper can provide theoretical guidance for the practical application of profile control and oil displacement using HPAM/Ac3Cr.

1. INTRODUCTION The in-depth profile control technology of using a weak gel has the benefit of increasing oil production and decreasing water cut in water flooding oilfields.1−4 On one hand, a weak gel has a certain strength, which can plug the middle- and highpermeability reservoirs to improve the sweep area of water flooding. On the other hand, during the process of subsequent water flooding, a weak gel can migrate into the deep formation, which can improve oil displacement efficiency. So far, a weak gel obtained from chromium acetate (Ac3Cr) cross-linking partially hydrolyzed polyacrylamide (HPAM) is the most widely used.5 Because of the successful application of this technology in oilfields, both domestic and foreign researchers have conducted extensive research on the weak gel system of Cr3+ cross-linking HPAM.6−10 There have been great breakthroughs in the research of cross-linking reaction mechanisms. To date, the microstructure and morphology of the gel is clearly understood. Rafipoor et al.11 suggested that the gel was formed by the polynuclear olation complex ion of chromium cross-linking the carboxyl of the HPAM molecule. Besides, Chen et al.12 thought the fractal structure was composed of nanoscale particles that were tightly packed together based on observations of the microstructure of colloidal dispersion gel of HPAM/Cr3+ by atomic force microscopy. Lin et al.13 determined that the morphology of the linked polymer solution with low polymer concentration was a spherical coil by Leica 360 scanning electron microscopy. Zhao et al.14 found the microstructures of the bulk gel of HPAM/Cr3+ consisted of a three-dimensional network via environmental scanning electron microscopy. The cross-linking reactions between HPAM and high valence metal coagulants can be sorted into two types.15 One is the intramolecular cross-linking reaction that takes place in © 2015 American Chemical Society

different chains within the same HPAM molecules, and the other is the intermolecular cross-linking reaction that takes place among different HPAM molecules. The intermolecular cross-linking reaction has “local” network molecular structures resulting in an increase of the viscosity, such as in the bulk gel. While the intramolecular cross-linking reaction forms “regional” network molecular structures, the viscosity stays the same or even decreases after gelation, observed in the colloidal dispersion gel and the linked polymer solution. For their research on cross-linking reaction steps, Jain et al.16 observed that the cross-linking reaction steps were divided into two stages by analyzing the viscosity change of the HPAM/Cr3+ system. The first step consisted of the polynuclear olation complex ions of chromium slowly coming together with the carboxyl of the HPAM molecule, but not forming a crosslinking bond. The second step occurred when the polynuclear olation complex ions of chromium combined with a carboxyl of one HPAM molecule and coordinated with a carboxyl of another HPAM molecule to generate cross-linking reaction. This result is in accord with the characteristics of the intermolecular cross-linking reaction. For their research of the cross-linking reaction process and kinetics, Vargas-Vasquez and Romero-Zerón6 presented the main factors affecting the reaction kinetics, rheology, gelation time, syneresis, and characterization of polymer gels of HPAM/ Cr3+ in 2008. In 2009, Vargas-Vasquez et al.17,18 used 1H NMR, rheology, and bottle tests to study the HPAM/Cr3+ microgels. The research results were as follows: (1) Changes in the 1H Received: January 21, 2015 Revised: June 25, 2015 Published: June 29, 2015 4701

DOI: 10.1021/acs.energyfuels.5b00149 Energy Fuels 2015, 29, 4701−4710

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Energy & Fuels NMR transverse relaxation (T2) were dominated by Cr3+; (2) 1 H NMR detected changes immediately after HPAM started reacting with Cr3+, but these changes were undetectable by rheology or bottle tests. Moreover, they also used 1H NMR, a bottle test, and UV−vis spectroscopy to analyze the syneresis of the bulk gel of HPAM/Cr3+. They found an empirical correlation between 1H NMR data and gel syneresis. Romero-Zerón et al.19 studied the characterization of crosslinking reaction kinetics and gel strength by using low-field NMR to monitor the gelation process, the liquid/solid transition, and the gel point. The conclusion was that the cross-linking reaction of HPAM/Cr3+ followed a second-order rate law. In addition, Broseta,20 Montanaril,21 Jain,16 Li,22 Cheng,23 et al. established a cross-linking reaction kinetics equation of HPAM/Cr3+ under static conditions. The factors considered in the equation included reservoir temperature, polymer molecular weight, polymer concentration, polymer hydrolysis degree, and the concentration of cross-linking agent. Moreover, Liu et al.24 established a cross-linking reaction kinetics equation of HPAM/Cr3+ under dynamic conditions. However, the results provided by these scholars cannot be compared with each other due to the difference of factors considered and components used in the calculation. Previous studies cannot explain the specific microscopic change procedure to reveal the essence of the cross-linking reaction of HPAM/Cr3+ in formation water. Therefore, it is very important and necessary to further study the mechanism of the cross-linking reaction to improve the success rate of the application of in-depth profile control technology. Influential factors of the cross-linking reaction not only include reservoir temperature and the parameters of polymer and cross-linking agent, but also include the properties and salinity of the formation water. At present, the influence of formation water on the HPAM/Cr3+ system is mainly embodied in macro parameters such as initial viscosity, gel strength, and gel stability,10,20,25−28 but there is only scant research about the influence on the cross-linking reaction procedure and micro change. This paper reveals the micro change and the mechanism of HPAM/Cr3+ in formation water. Although there is variability in the type and concentration of cations in formation water across different oil reservoirs, the most common cations are K+, Na+, Ca2+, and Mg2+. In addition, because the charge type of anions in formation water is the same as the carboxyl of the HPAM molecule, the influence of anions on the cross-linking reaction is much lower than cations. All of the anions in the following experiment are replaced by Cl−. Therefore, it can safely be said that the influence of formation water on the cross-linking reaction process can be reflected in the influence of the most common cations (K+, Na+, Ca2+, Mg2+) on the cross-linking reaction process. In this study, the cross-linking reaction process and mechanism of HPAM/Cr3+ in formation water is revealed by studying the influence of cations on the cross-linking reaction. Meanwhile, our research confirms the degree of influence of different cations on the cross-linking reaction and yields the influence law of cations on gelation as well as the favorable concentration range of cations suitable for gelation. These conclusions can provide an important theoretical basis for the practical application of the weak gel in the deep profile control and oil displacement field.

2. EXPERIMENTAL SECTION 2.1. Reagents and Equipment. The experimental temperature is 25 °C, in accordance with the formation temperature of many of reservoirs in the Yanchang Oilfield, the fourth largest petroleum company in China. The water used in all tests was deionized. HPAM is from Shandong Polymer Biochemicals Co., Ltd. in China. Its molecular weight is 24 million, and its hydrolysis degree is 25%. Anhydrous sodium acetate, chromic chloride hexahydrate, NaCl, KCl, CaCl2, and MgCl2 are all analytically pure and were obtained from Beijing Chemical Reagents Company. The cross-linking agent is a chromium acetate solution consisting of anhydrous sodium acetate and chromic chloride hexahydrate in a proportion of 3:1 (mole ratio), which can be used for up to 3 days after preparation. The concentration of Cr3+ in the chromium acetate solution is 5 mg/mL. The main instruments include a UV2550 ultraviolet−visible spectrophotometer from Shimadzu Corporation and a DV-III Brookfield viscometer from Brookfield Company. The shear rate of measuring viscosity is 7.34 S−1. The physical simulated test equipment is shown in Figure 1.

Figure 1. Physical simulation experiment device. 2.2. Structure of the Chromium Ion in Deionized Water. Prior research shows that the chromium ion goes through the process of complexation, hydrolysis, olation, and further hydrolysis and olation to form a polynuclear olation complex ion when the chromium chloride is dissolved in deionized water.29−32 The structure of the polynuclear olation complex ion of chromium is shown in Figure 2. This type of complex can cross-link the carboxyl of the HPAM molecule to form a gel.

Figure 2. Structure of polynuclear olation complex ion of chromium in deionized water. When mixing the chromium chloride aqueous solution with a sodium acetate aqueous solution according to a 1:3 mol ratio of Cr3+ and CH3COO−, the polynuclear olation complex ion of chromium reopens to go through the process of complexation, hydrolysis, and olation to form new polynuclear olation complex ion of chromium. This is because the polarity of CH3COO− is more than that of OH−. The new polynuclear olation complex ion of chromium is hereafter called a chromium acetate complex in this paper. Its structure is shown in Figure 3. From Figure 3, it can be observed that the coordinate covalent bonds of chromium have been completely occupied by CH3COO− so that the complex ion cannot cross-link the carboxyl of the HPAM molecule to form a gel. 2.3. Principle and Method of Experiments. In the experiments, the concentration of HPAM is 1500 mg/L in the HPAM solution, and the composition of the profile control and oil displacement agent (PCOD agent for short) are 1500 mg/L HPAM and 20 mg/L Cr3+, so the viscosity of the PCOD agent at the initial stage is equal to the 4702


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Concentrations. First, four types of simulated formation water samples with different cation concentrates were prepared by adding NaCl, KCl, CaCl2, and MgCl2 into the deionized water, respectively. The concentrations of each type of cation are 1, 10, 100, 200, 300, 600, 900, 1200, 3000, 6000, 12000, 16000, 20000, 40000, 60000 mg/L. Second, the PCOD agent was prepared with the simulated formation water. The method is comprised of the following steps: (1) 1500 mg/ L HPAM is added into the simulated formation water and fully stirred to form a homogeneous polymer aqueous solution; (2) 20 mg/L Cr3+ is added into the HPAM solution and stirred well. Note that stirring rate must be low and consistent from beginning to end in the experiment. Finally, the viscosity and absorbance of the PCOD agent are measured before and after the cross-linking reaction by viscometer and UV−vis spectrophotometer. (It can be considered that the crosslinking reaction stops when the value of viscosity and absorbance of the PCOD agent no longer change.) The final values are recorded to establish the relationship between viscosity, absorbance difference, and cation concentrations. 2.3.3. Comparison of the Flow Resistance of the PCOD Agent and HPAM Solution When the Viscosity of the PCOD Agent Is Lower than That of the HPAM Solution Using Core Flow Experiments. The flow resistance of the PCOD agent and HPAM solution in a porous medium is compared to reveal the different molecular structure between them by using core flow experiments when the viscosity of the PCOD agent is lower than that of the HPAM solution. In the experiment, to reduce the experimental workload, Na+ is chosen to be the representative cation to prepare the simulated formation water because it is the most common cation in formation water. The experimental temperature is 25 °C. The two pieces of core used in the flow experiment are artificial to maintain the same pore structure. These are bought from Research Institute of Exploration and Development of Daqing Oilfield in China and are made by the cementation of quartz sand and epoxy resin. The injection rate of each kind of fluid is 0.5 cm3/min. The injection volume of the PCOD agent and HPAM solution both are 0.3 PV (PV represents the pore volume). And other parameters of the core flow experiment are shown in Table 1. All solutions are prepared with the simulated formation water. The


Figure 3. Structure of chromium acetate complex in deionized water. viscosity of the HPAM solution. The viscosity of 1500 mg/L HPAM solution prepared with deionized water is 125 mPa·s. 2.3.1. Basic Principle of Experiments. It would be convenient to visually judge whether the cross-linking reaction has occurred by the viscosity change of the PCOD agent in the experiments, but this method may lead to a false conclusion and does not help reveal the nature of the chemical reaction which is caused by the concentration change of each reactant. Therefore, it is necessary to understand the concentration change of the chemicals involved in the cross-linking reaction to reveal the cross-linking reaction mechanism. Mack et al.5 thought the cross-linking reaction of HPAM/Cr3+ was mainly controlled by the concentration of Cr3+ when the number of the carboxyl group was considerably larger than the number of Cr3+ in the HPAM/Cr3+ system. In this study, the concentration of HPAM (25% hydrolysis degree) is 1500 mg/L, and the concentration of Cr3+ is 20 mg/L, so the mole ratio of COO− and Cr3+ is 22:1. Therefore, it is reasonable to speculate that the cross-linking reaction in the experiment is mainly controlled by the Cr3+. Although there are many ways to measure the concentration of Cr3+ in aqueous solution, UV−vis spectrophotometry is the most accurate and rapid method.33 In Tang et al.’s article,34 they studied the ultraviolet spectrogram of Cr3+, which had the maximum absorption peak in a certain band. On the basis of this principle, the absorption curve of the PCOD agent, which is prepared with deionized water and measured by UV−vis spectrophotometer at the initial stage, is shown in Figure 4. From

Table 1. Parameters of Core Flow Experiment square core parameters length/width/ height/cm3

permeability/ 10−3μm2

pore volume/ cm3

30 × 4.5 × 4.5

500

120−122

composition of simulated formation water deionized water + 1200 mg/L Na+

experimental procedure is as follows: (1) The device is connected according to Figure 1; (2) the core is flooded with simulated formation water; (3) the permeability of the core is measured when the pressure is stable; (4) 0.3PV PCOD agent or 0.3PV HPAM solution is injected into the core; (5) the core is flooded with simulated formation water again. The salinity of the formation water requires special consideration because it is necessary to ensure that there is a large viscosity difference between the PCOD agent and HPAM solution. The PCOD agent cannot be injected into the core until its viscosity no longer changes to ensure that the cross-linking reaction is completely finished. The final values are recorded to establish the relationship between injection volume and injection pressure. 2.3.4. Testing the Change of Viscosity and Absorbance of the PCOD Agent with Reaction Time under Different Cross-Linking Degrees. To further research the cross-linking reaction mechanism, the changes in viscosity and absorbance of the PCOD agent with reaction time under different degrees of cross-linking are tested to analyze and understand the cross-linking reaction process and kinetics. These yield the chemical reaction mechanism by characterizing the relationship between the reactant concentration and reaction rate. When the reaction rate is proportional to the first power of the reactant concentration, the reaction is called a first-order reaction. When the reaction rate is proportional to the multiple power of the reactant concentration, the reaction is called a multistage reaction.

Figure 4. Absorption curve of the PCOD agent (1500 mg/L HPAM + 20 mg/L Cr3+) measured by UV−vis spectrophotometer at the initial stage. Figure 4, it can be observed that the maximum peak is observed at 540 nm. Therefore, fixing the wavelength at 540 nm can make the results more comparable in the experiment. The process of the reaction is researched by analyzing how the absorbance value varies with the concentration of Cr3+. In addition, the absorbance difference before and after the cross-linking reaction, rather than absorbance alone, is used to characterize the degree of the cross-linking reaction and calculate kinetic parameters in the following sections to eliminate the effects of the composition changes of reactant or resultant or salinity on absorbance. Therefore, the absorbance difference can represent the reaction degree, which is only related to the concentration change of Cr3+. 2.3.2. Testing the Absorbance and Viscosity of the PCOD Agent before and after the Cross-Linking Reaction under Different Cation 4703


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Energy & Fuels This quantitatively describes the impact of the reactant concentration on the reaction rate. It is feasible to control and adjust the change of viscosity and the cross-linking degree of the PCOD agent by adjusting the reactant concentration after establishing the equation of crosslinking reaction kinetics. In the experiment, the degree of cross-linking of the PCOD agent can be visually reflected by its viscosity, and different cross-linking degrees can be obtained by adjusting the concentration of Na+. Likewise, to reduce the experimental workload, the cross-linking degree can be sorted into three situations. One is in a range where the viscosity of the PCOD agent is lower than that of the HPAM solution under a certain salinity, another is in another range where the viscosity of the PCOD agent is higher than that of the HPAM solution under another certain salinity, and the third is between the two viscosities under a certain salinity. These three situations can represent the crosslinking degree of different types of cross-linking reactions. In the experiment, three groups of formation water samples are prepared with deionized water and three different concentrations of Na+, and then three groups of the PCOD agent are formed by adding 1500 mg/L HPAM and 20 mg/L Cr3+ into three groups of simulated formation water, respectively. Then, the viscosity and absorbance of the PCOD agent are measured at the same time intervals until the cross-linking reaction is completely finished. Finally, the relationship between viscosity, absorbance, and the reaction time is established.

Figure 6. Effect of Na+ and K+ on the viscosity of the PCOD agent under different concentrations.

3. RESULTS AND DISCUSSION 3.1. Cross-Linking Reaction Characteristics under Different Concentrations of Cations. 3.1.1. Change of Viscosity and Absorbance Difference. The relation curves of the gel strength of HPAM/Cr3+ and the concentrations of four types of cations are shown in Figure 5 and Figure 6, which are

Figure 7. Effect of Ca2+ and Mg2+ on the absorbance difference under different concentrations.

Figure 5. Effect of Ca2+ and Mg2+ on the viscosity of the PCOD agent under different concentrations.

established using bottle tests and viscometry. Figure 5 shows the changes in gel strength with increasing concentrations of Ca2+ and Mg2+. Figure 6 shows the changes in gel strength with increasing concentrations of Na+ and K+. The relation curves of absorbance difference of HPAM/Cr3+ before and after the cross-linking reaction and the concentrations of four types of cations are shown in Figure 7 and Figure 8, which are established by UV−vis spectrophotometry. Figure 7 shows the change in the absorbance difference with varying concentrations of Ca2+ and Mg2+. Figure 8 shows the change in the absorbance difference with varying concentrations of Na+ and K+. Finally, the change of pressure drop of the PCOD agent or

Figure 8. Effect of Na+ and K+ on the absorbance difference under different concentrations.

HPAM solution across the core with injection volume is shown in Figure 9, which is established by core flow experiment. From Figure 5 and Figure 6, there is a peak and a trough in the curve, which can be divided into four stages to describe the discipline. (1) When salinity tends to zero, the viscosity of the 4704


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Darcy’s law, which is the classical seepage theory of fluid flow in porous media. Darcy’s law shows that pressure drop has a positive correlation with the viscosity of the fluid. And in the process of subsequent water flooding, the pressure drop of the water displacing the PCOD agent is also higher than that of the water displacing the HPAM. It shows that the physical plugging effect of the PCOD agent in porous media is more significant than that of the HPAM. Combining with the analysis of the above, it can be concluded that the intramolecular cross-linking reaction has occurred. The intramolecular reaction makes the HPAM molecule in the PCOD agent shrink and coil to form a certain scale of spatial structure that is different from the linear structure of HPAM. That spatial structure of the PCOD agent leads to a less hydrodynamic radius, as well as a lower viscosity and a higher migration resistance. By comparing Figure 5 to Figure 7 and Figure 6 to Figure 8, the curve can be described in the following way. (1) The first stage of the curve in Figure 5 and Figure 6 corresponds to the first stage of the curve in Figure 7 and Figure 8, respectively; (2) the second and third stage of the curve in Figure 5 and Figure 6 is corresponding to the second stage of the curve in Figure 7 and Figure 8, respectively; (3) the fourth stage of the curve in Figure 5 and Figure 6 is corresponding to the third stage of the curve in Figure 7 and Figure 8, respectively. From Figure 5 to Figure 8, it can be observed that the salinity has a very significant effect on the cross-linking reaction of HPAM/ Cr3+. First, the cross-linking reaction cannot occur when the salinity tends to zero. Second, with the increase of salinity, although the viscosity of the PCOD agent is less than that of the HPAM solution, the absorbance difference of the PCOD agent begins to increase. This shows that the cross-linking reaction has occurred. And combining with the analysis of Figure 9, this further explains that the cross-linking reaction between HPAM and Cr3+ in this stage mainly consists of intramolecular cross-linking reactions, which are the result of Cr3+ cross-linking the different carboxyls of one HPAM molecule. Third, when the salinity increases to a certain value, the viscosity and the absorbance difference of the PCOD agent largely increase. This shows that the intermolecular reaction between HPAM and Cr3+ has happened, which is the result of Cr3+ cross-linking the carboxyls of different molecules. The intermolecular reaction causes the PCOD agent to form a three-dimensional spatial structure so that the viscosity of the PCOD agent is very high. This type of the gel is the most widely applied and researched in Chinese oilfields.4 With the further increase of salinity, the absorbance difference of the PCOD agent stops changing, which means the degree of the cross-linking reaction is up to its maximum. However, the viscosity of the PCOD agent gradually decreases with the increase of salinity at this stage, which is the result of excess salinity damaging the spatial structure of the PCOD agent. From the description of Figure 5 to Figure 8, we can summarize the influence of salinity on the cross-linking reaction. First, when the amount of salinity tends to zero, a tiny amount of cations cannot promote the dissociation of the chromium acetate complex, so that the chromium ion surrounded by CH3COO− in the solution cannot cross-link the carboxyl of the HPAM molecule. Second, with the increase of cation concentrations, cations compress the double electric layer of polymer to thin the hydration film and reduce the zetapotential. Therefore, the repulsive forces between the electriferous groups decrease, which is advantageous to the cross-linking reaction. On the other hand, cations begin to

Figure 9. Relationship of pressure drop and injection volume (the viscosity of PCOD agent and HPAM solution is 50 mPa·s and 96 mPa· s, respectively. a: water flooding stage; b: chemical flooding stage; c: subsequent water flooding stage).

PCOD agent is equal to the viscosity of the HPAM solution; (2) with the increase of salinity, the viscosity of the PCOD agent is less than that of the HPAM solution; (3) when the salinity increases to a certain value, the viscosity of the PCOD agent increases dramatically and is far greater than that of the HPAM solution; (4) when the salinity further increases, the viscosity of PCOD agent decreases considerably. From Figure 7 and Figure 8, the curve of the absorbance difference can be divided into three stages: (1) When salinity tends to zero, absorbance difference of the PCOD agent is equal to 0; (2) with the increase of salinity, absorbance difference of the PCOD agent increases considerably, which means the change in absorbance value of the PCOD agent before and after cross-linking reaction is continuing to increase; (3) when the salinity increases to a certain value, the absorbance difference of the PCOD agent tends toward stability, which means the absorbance value remains stable. It can be concluded that the degree of the cross-linking reaction will increase to a balance point with the increase of the salinity. Figure 6 shows that the viscosity of the PCOD agent is lower than that of the HPAM solution when the concentration of Na+ is in the range of 300 mg/L to 3000 mg/L. There is a large viscosity difference between the PCOD agent and HPAM solution when the concentration of Na+ is in the range of 600− 1200 mg/L. Therefore, the concentration of Na+ in the core flow experiment is chosen to be 1200 mg/L to better compare and analyze the flow resistance of the PCOD agent and HPAM solution in porous medium. Under 1200 mg/L Na+, the viscosity of the PCOD agent is 50 mPa·s, lower than that of HPAM solution which is 96 mPa.s. From Figure 8, it can be observed that the value of the absorbance difference of the PCOD agent is 1 rather than 0 when the concentration of Na+ is 1200 mg/L. This shows that the cross-linking reaction between HPAM and Cr3+ has occurred. Combining with the above analysis of Figure 6 and Figure 8, it shows a phenomenon that is in line with the characteristics of intramolecular cross-linking reactions. From Figure 9, it can be observed that the pressure drop across the core of the PCOD agent is higher than that of the HPAM solution, but the viscosity of the PCOD agent is lower than that of the HPAM solution. This is the opposite of the conclusion of 4705


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Energy & Fuels participate in the fight against the chromium ion for the ligand, resulting in the breakage of the coordinate covalent bonds of the chromium acetate complex and the release of CH3COO−. Then, the polynuclear olation complex ions of chromium can cross-link the carboxyl of the HPAM molecules, which causes the absorbance difference of the PCOD agent to increase. However, at this stage, the influence of a small quantity of cations on the dissociation of the chromium acetate complex is limited, so only fewer chromium ions can participate in the cross-linking reaction. In addition, HPAM molecules are curly in solution. These eventually cause the intramolecular crosslinking reaction to occur. Third, when the amount of salinity increases to a certain value, the chromium acetate complex is largely dissociated to release a large amount of chromium polynuclear olation complex ions, so that the cross-linking reaction can take place not only inside the same HPAM molecules but also between different HPAM molecules. This is why absorbance difference and viscosity both increase in this stage. And when the salinity enables all of the chromium polynuclear olation complex ions to be dissociated, the viscosity and absorbance difference of the PCOD agent reach a maximum. Finally, with the further increase of the salinity, the absorbance difference of the PCOD agent remains the same, while the viscosity of the PCOD agent decreases. The reason for the former is that all of the chromium polynuclear olation complex ions have been completely released before this stage. The reasons for the latter are chiefly as follows: (1) Too high salinity can severely compress the diffuse electric double layer of HPAM molecules to cause the molecular chain to coil and shrink excessively, and the result is that there is not enough carboxyl to react with Cr3+; (2) too high salinity can cause the complex of chromium to be released too quickly, and the result is that the rate of the cross-linking reaction is too fast to form a gel with stable properties; (3) excess multivalent cations such as Ca2+ and Mg2+ can react with the carboxyl to form an antisoluble deposit, which can cause polymer flocculation. Therefore, the performance of the weak gel is enormously damaged when the salinity is too high. From the analysis of the above, we see that the chromium acetate complex can be dissociated under the action of cations. And the dissociation degree is related to the different cation concentrations. After dissociation, the polynuclear olation complex ions of chromium can cross-link the carboxyl of the HPAM molecules to form a gel with a spatial structure. The gel structure is shown in Figure 10. In Figure 10, R is substitute for hydroxyl or acetate or carboxyl of HPAM molecule, which is decided by the dissociation degree of the chromium acetate complex. 3.1.2. Influence of Different Cations on the Cross-Linking Reaction. From Figure 5 and Figure 7, it can be observed that the cross-linking degree of HPAM/Cr3+ in a solution containing Mg2+ is higher than that of a solution containing Ca2+ at the same concentration. This shows that Mg2+ can better promote the dissociation of the chromium acetate

complex than Ca2+, which implies the Mg2+ can bring the gel to the peak viscosity earlier. The peak viscosity in the system of HPAM/Cr3+ and Mg2+ is higher than that of the system of HPAM/Cr3+ and Ca2+. So the degree of influence of Mg2+ on the gel strength is more than that of Ca2+. Similar to Figure 5 and Figure 7, Figure 6 and Figure 8 show that the cross-linking degree of HPAM/Cr3+ in a solution containing Na+ is higher than that of a solution containing K+ at the same concentration. This shows that Na+ can better promote the dissociation of the chromium acetate complex than K+, which implies that Na+ can bring the gel to the peak viscosity earlier. The peak viscosity in the HPAM/Cr3+ and Na+ system is higher than that of HPAM/Cr3+ and K+ system. So the degree of influence of Na+ on the gel strength is more than that of K+. By comparing the influence of different cations with same charge on the viscosity of the PCOD agent, we conclude that the smaller the ionic radius and relative atomic mass of the ion, the greater the influence on the viscosity of the PCOD agent. Take Ca2+ and Mg2+ as an example. At the same mass concentration, the number of Mg2+ ions in the solution is larger than that of Ca2+ because the relative atomic mass of magnesium ion is smaller than calcium ion. Thus, the total number of charge of Mg2+ is more than that of Ca2+. Moreover, the smaller the ion radius is, the stronger the ability to penetrate. Therefore, the POCD agent is more sensitive to Mg2+. On the whole, divalent cations have a greater influence on the viscosity of the PCOD agent than monovalent cations. The influence order is as follows: Mg2+ > Ca2+ > Na+ > K+. The matching range of the PCOD agent and the concentration of the four types of cation are as follows: Mg2+/ (400−9000) mg/ L, Ca2+/ (1200−18000) mg/L, Na+/ (9000−30000) mg/L, K+/ (16000−55000) mg/L. Too low or too high salinity can prevent Cr3+ from effectively cross-linking HPAM. 3.2. Cross-Linking Reaction Mechanism of HPAM/Cr3+. 3.2.1. Analysis of the Cross-Linking Reaction Process of HPAM/Cr3+. The results of the change of viscosity and absorbance of the PCOD agent with reaction time under three types of cross-linking degree are shown in Figure 11, Figure 12, and Figure 13, respectively. In the experiment, the concentrations of Na+ are chosen to be 1200 mg/L, 8000 mg/

Figure 11. Changes of viscosity and absorbance of the PCOD agent with reaction time under 1200 mg/L Na+.

Figure 10. Structure of gel of HPAM/Cr3+. 4706


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growth phase; (3) steady phase. The three stages of viscosity changes correspond with the three stages of absorbance changes. In the first stage, the rapid growth of absorbance shows that the degree of the cross-linking reaction is increasing rapidly, and the viscosity staying the same or decrease shows that the cross-linking reaction mainly occurs within the HPAM molecule. In the second stage, the slow growth of absorbance shows the degree of the cross-linking reaction is increasing slowly, and the rapid growth of viscosity shows that the crosslinking reaction mainly occurs between HPAM molecules when the salinity of formation water is 8000 mg/L Na+ or 16000 mg/ L Na+. The slow decrease of viscosity shows the cross-linking reaction still mainly occurs within the HPAM molecules when the salinity of formation water is 1200 mg/L Na+. In the third stage, no change in absorbance shows the cross-linking reaction has stopped, so the viscosity also remains stable. After comprehensive analysis, it is concluded that no matter whether the salinity value is high or low, the intramolecular cross-linking of HPAM/Cr3+ occurs first. Then the intermolecular crosslinking occurs under high salinity, or else the intramolecular cross-linking continues to occur under the low salinity. The degree of intramolecular cross-linking in the first stage is higher than that of intermolecular cross-linking or intramolecular cross-linking in the second stage due to a bigger increase of absorbance difference. Moreover, the three figures show that the reaction time decreases and the absorbance difference increases with the increase of the salinity. It can be said that the salinity can directly affect the reaction time, the degree, and the types of the cross-linking reaction. 3.2.2. Cross-Linking Reaction Kinetics of HPAM/Cr3+. Because the number of carboxyl groups is far greater than that of Cr3+ in the system of 1500 mg/L HPAM and 20 mg/L Cr3+, it can be postulated that the cross-linking reaction is mainly controlled by the Cr3+ in terms of the research of crosslinking reaction kinetics. That is, the cross-linking reaction rate is only related to the concentration of Cr3+. When using the absorbance instead of the concentration of Cr3+, the kinetics model of the cross-linking reaction of HPAM/Cr3+ is as follows:



L, and 16000 mg/L, respectively. The reasons for this are that the viscosity of the PCOD agent is at its lowest level when the concentration of Na+ is 1200 mg/L, the viscosity of the PCOD agent is at its highest level when the concentration of Na+ is 16000 mg/L, and the viscosity of the PCOD agent is between the above two when the concentration of Na+ is 8000 mg/L. These results are shown in Figure 6. So the experimental phenomena are more likely to be observed at these three concentrations. By comparison of Figure 11, Figure 12, and Figure 13, it can be observed that each of the three curves of viscosity change of the PCOD agent with reaction time can be divided into three stages, but the change trend is different when the salinity is different. From Figure 11, it can be observed that the three stages of the viscosity curve are as follows: (1) decrease phase; (2) slow decrease phase; (3) steady phase. From Figure 12, the three stages of the viscosity curve are as follows: (1) light decrease phase; (2) rapid growth phase; (3) steady phase. From Figure 13, the three stages of the viscosity curve are as follows: (1) steady phase; (2) rapid growth phase; (3) steady phase. By comparison of Figure 11, Figure 12, and Figure 13, it can be observed that the change trend of absorbance of the PCOD agent with reaction time is the same when the salinity is different. And the change trend of the absorbance can also be divided into three stages: (1) rapid growth phase; (2) slow

dDt = −k(D∞ − Dt )n dt

Dt: the absorbance of HPAM/Cr3+ system at time t; D∞: the absorbance of HPAM/Cr3+ system at the initial time; D0: the absorbance of HPAM/Cr3+ system at the terminal time of the cross-linking; t: cross-linking time, d; n: order of reaction; k: the cross-linking reaction rate constant, 1/d. After integral transform, the mathematical expressions are as follows: n = 1,

ln(D∞ − Dt ) = −kt + ln(D∞ − D0)

n ≠ 1, (D∞ − Dt )1 − n = (1 − n)kt + (D∞ − D0)1 − n

The relation curve of ln(D∞ − Dt) and t, (D∞ − Dt) and t can be obtained by processing the data about the relationships of absorbance and reaction time shown in Figure 11, Figure 12, and Figure 13. The results after processing are shown in Figures 14−19. Figure 14, Figure 16, and Figure 18 respectively show the relationship of ln(D∞ − Dt) and t under three types of salinity. Figure 15, Figure 17, and Figure 19 respectively show the relationship of (D∞ − Dt) and t under three types of salinity. 4707


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Figure 14. Relationship of ln(D∞ − Dt) and t under 1200 mg/L Na+.

Figure 17. Relationship of (D∞ − Dt) and t under 8000 mg/L Na+.

Figure 15. Relationship of (D∞ − Dt) and t under 1200 mg/L Na+. Figure 18. Relationship of ln(D∞ − Dt) and t under 16000 mg/L Na+.

Figure 16. Relationship of ln(D∞ − Dt) and t under 8000 mg/L Na+.

By comparison of Figure 14, Figure 16, and Figure 18, it can be observed that the relationship of ln(D∞ − Dt) and t is approximately linear when the change of absorbance with reaction time is in the first stage shown in Figure 11, Figure 12, and Figure 13. This means that each cross-linking reaction is a first-order reaction in this stage which is intramolecular crosslinking. After linear fitting, the result is n = 1 and k = 0.1751 d−1 for the PCOD agent under 1200 mg/L Na+, n = 1 and k =

Figure 19. Relationship of (D∞ − Dt) and t under 16000 mg/L Na+.

0.2829 d−1 for the PCOD agent under 8000 mg/L Na+, n = 1 and k = 0.391 d−1 for the PCOD agent under 16000 mg/L Na+. By comparing the three sets of data, it is found that the reaction rates of the three are different, and the reaction rate increases with the increase of the salinity. 4708


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optimal matching relationship between the viscosity of the PCOD agent and salinity. (3) The whole process of the cross-linking reaction can be divided into two stages. In the first stage, the intramolecular cross-linking, which comes first between HPAM and Ac3Cr, is a first-order reaction. The reaction rate increases with the increase of salinity. In the second stage, either the intramolecular cross-linking continues to happen under low salinity or the intermolecular cross-linking happens under high salinity until the reaction stops. In this stage, the cross-linking reaction is a multistage reaction. The reaction order and reaction rate increases with the increase of salinity. Comparing with the second stage of the cross-linking reaction, the first stage has a greater effect on the whole process of the cross-linking reaction due to its higher reaction rate and higher absorbance difference.

By comparison of Figure 15, Figure 17, and Figure 19, it can be observed that the relationship of (D∞ − Dt) and t is approximately polynomial when the absorbance change with reaction time is in the second stage shown in Figure 11, Figure 12, and Figure 13. This means that each cross-linking reaction is a multistage reaction in this stage which is intramolecular cross-linking under low salinity or is intermolecular crosslinking under high salinity. After function fitting, the result is n = 1.2 and k = 0.0105 d−1 for the PCOD agent under 1200 mg/ L Na+, n = 1.6, and k = 0.0143 d−1 for the PCOD agent under 8000 mg/L Na+, n = 1.8, and k = 0.0187 d−1 for the PCOD agent under 16000 mg/L Na+. By comparing the three sets of data, it is found that the reaction order and the reaction rate of the three are different. With the increase of the salinity, both the reaction order and the reaction rate increase. The higher the salinity is, the farther and farther away the cross-linking reaction is from the extent of the first-order reaction. By comparing Figure 14 with Figure 15, Figure 16 with Figure 17, Figure 18 with Figure 19, it can be observed that the reaction rate in the second stage of the absorbance change with reaction time is much lower than that in the first stage. The reason for this may be the significant decrease of the reactants concentrations. Besides, the increase of the viscosity of the PCOD agent, which is caused by the intermolecular crosslinking when the salinity in the formation water is high, can also decrease the reaction rate. For a specific oilfield, the parameters of the reservoir such as temperature and salinity are kept constant, so it is feasible to control the cross-linking time by controlling the concentration of Cr3+ and obtain the cross-linking degree and the viscosity of the HPAM/Cr3+ system at a certain time using the cross-linking reaction kinetics equation of HPAM/Cr3+. This is important evidence that can provide guidance in designing and adjusting the construction schemes of profile control and displacement oil such as injection rate, transport distance, injection volume, and so on.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (L.Z.). *E-mail: [email protected] (C.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Major National Science and Technology Projects (20011ZX05009-004) and the National Natural Science Fund (51274229).

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REFERENCES

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4. CONCLUSIONS (1) Cation concentrations have a significant impact on the degree of the cross-linking reaction of HPAM/Ac3Cr. When the cation concentration is too low, the cross-linking reaction of HPAM/Cr3+ cannot occur. With the increase of cation concentration, the cross-linking reaction occurs, and the cross-linking reaction degree, which can be represented by absorbance difference, can increase to a balance point. When the reaction degree is low, the cross-linking reaction mainly occurs within HPAM molecules, which causes the PCOD agent to have lower viscosity and higher migration resistance than the HPAM solution. When the reaction degree is high, the crosslinking reaction occurs not only within HPAM molecules but also between HPAM molecules, which can make the viscosity of the PCOD agent increase drastically. In addition, when the cation concentration is too high, the performance of the PCOD agent will decrease. (2) The effect of bivalent cations on the cross-linking reaction is greater than monovalent cations. For cations with the same charge, the length of the ionic radius is inversely proportional to the impact of the ion on the cross-linking reaction. The influence order of four types of the most common cations is as follows: Mg2+ > Ca2+ > Na+ > K+. It is completely feasible to obtain a PCOD agent with a different viscosity by adjusting the cation concentration. And there is an 4709


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Mechanism Study of the Cross-Linking Reaction of Hydrolyzed

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