Influence of Hydrolyzed Polyacrylamide (HPAM) Molecular Weight on

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Influence of HPAM molecular weight on the cross-linking reaction of HPAM/Cr3+ and transportation of HPAM/Cr3+ in micro-fractures Lei Zhang, Liming Zheng, Jingyang Pu, Chunsheng Pu, and Shuxia Cui Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02230 • Publication Date (Web): 26 Oct 2016 Downloaded from http://pubs.acs.org on November 1, 2016

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Influence of HPAM molecular weight on the cross-linking reaction of HPAM/Cr3+ and transportation of HPAM/Cr3+ in micro-fractures Lei Zhang,*,†,‡ Liming Zheng, †,‡ Jingyang Pu,§ Chunsheng Pu,*,†,‡ and Shuxia Cui †,‡ †

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 §

Department of Geosciences and Geological and Petroleum Engineering, Missouri University of

Science and Technology, Rolla 65409, Missouri, United States Abstract: The influence of the molecular weight (Mw) of hydrolyzed polyacrylamide (HPAM) on the cross-linking reaction of HPAM/Cr3+ and the transportation of HPAM/Cr3+ in micro-fractures is systematically studied using viscometry, ultraviolet-visible absorption spectrophotometry, and displacement experiment with a visual micro-fractured model. The results show that a high Mw of HPAM is advantageous to the intramolecular cross-linking reaction of the HPAM/Cr3+ system but disadvantageous to the transportation of the HPAM/Cr3+ system in micro-fractures. At the intramolecular cross-linking stage, the injection pressure of the HPAM/Cr3+ system in micro-fractures is almost equal to that of the HPAM solution, which undergoes no change with the degree of the cross-linking reaction. The higher the HPAM Mw, the earlier the intramolecular cross-linking ends, thus, the intermolecular cross-linking reaction of HPAM/Cr3+ occurs earlier, which leads to an earlier increase in the injection pressure of the HPAM/Cr3+ system. Moreover, there is a matching relationship between the fracture aperture and the HPAM/Cr3+ system to minimize the chromatographic separation when the HPAM/Cr3+ system transports in the micro-fracture. For the conformance control of a fractured tight oil reservoir, we conclude that an HPAM/Cr3+ system with a low Mw of HPAM can more easily enter the deep reservoir to expand the swept volume on a larger scale. However, the system with a high Mw of HPAM can form a gel with a higher viscosity to produce a higher plugging strength. Key words: HPAM molecular weight; cross-linking reaction of HPAM/Cr3+; transportation; micro-fracture; injection pressure 1. INTRODUCTION In China, there are many fractured tight reservoirs, such as the Yanchang oilfield and the Changqing oilfield, which presently play an important role in the oil industry. The development of natural micro-fractures is the key characteristic of this type of reservoir. Moreover, most of the oil wells in the reservoir are stimulated by hydraulic fracturing to make the oil flow at an acceptable rate. In the process of water-injection development, crude oil production has declined rapidly, and the water cut has risen rapidly due to the existence of fracture channeling-paths. These characteristics of the development of the reservoir result in poor economic benefits.1-4 Therefore, seeking the correct technology for water control is of great significance. To increase oil production and decrease water cut of a heterogeneous reservoir, the conformance control technology of using polymer gels has been proved to be an efficient method.5-8 Among the polymer gels, the hydrolyzed polyacrylamide (HPAM) and chromium acetate (Cr3+) system is the most common due to good adaptability and low price,9-14 which has achieved good results in conventional sandstone reservoirs, but has obtained poor results in fractured tight reservoirs.15-20 One of the most common failure phenomena in the fractured tight reservoir is the failure of the injection of the gelling

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solution into the fractures. Therefore, it is necessary to study the process of the cross-linking reaction of HPAM/Cr3+ and the rule of transportation of HPAM/Cr3+ into the fractures, which can reveal the rule of the change in viscosity and injection pressure of HPAM/Cr3+ into the fractures to develop a suitable HPAM/Cr3+ system, which can expand the swept volume on a large scale. As is well-known, HPAM is the main skeleton of the polymer gel, which can greatly influence the properties of the gel. Among the evaluation indicators of the polymer for conformance control, molecular weight (Mw) is one of the most important, because it has an important influence on the process of the change in the cross-linking reaction of the HPAM/Cr3+ system. The relationship of the change of viscosity of the HPAM/Cr3+ system with the cross-linking time can directly influence the rule of transportation of the HPAM/Cr3+ system in the reservoir. Thus it is a significantly meaningful to study the mechanism of influence of HPAM Mw on the cross-linking reaction of HPAM/Cr3+ and the transportation of the HPAM/Cr3+ system in the fractures. For their research on the influence of the HPAM Mw on the cross-linking reaction of the HPAM/Cr3+ system, Broseta et al.21, 22 had studied the reaction characteristics of two polyacrylamide/chromium (III) formulations. In their paper, the low-molecular weight polyacrylamide was 0.21 million g/mol, which was far out of the currently used range of 3 million to 30 million g/mol in oilfields in China. In 2004, Sydansk et al.23 developed a polymer gel by combining both high and low Mw polymers to improve the performance of water shutoff treatments in a fractured production well. In 2013, Reddy et al.24 found an increase in HPAM Mw can allow for a reduction in the HPAM concentration, which can achieve a significant reduction in the polymer concentrations while retaining the gel performance. In 2014, Ren et al.25 suggested that the polymer Mw can affect the gelation time, the gel strength, and its stability, but they only described the experimental phenomenon. The other existing research results mainly show the influence of HPAM Mw on the gel strength.26-34 The previous studies are mainly focused on the influence of HPAM Mw on the macroscopic performances of the polymer gel.35-38 However, the influence of the HPAM Mw on the process of the change in the cross-linking reaction of HPAM/Cr3+ has not yet been studied. In our previous studies,39 the whole process of the cross-linking reaction of HPAM/Cr3+ was divided into two types. One is the intramolecular crosslinking reaction that takes place by Cr3+ cross-linking the different carboxyls within the same HPAM molecules, and the other is the intermolecular crosslinking reaction that takes place by Cr3+ cross-linking the different carboxyls of different HPAM molecules.40 Therefore, one of the main objectives of this paper is to ascertain the mechanism of the influence of the HPAM Mw on the intramolecular and intermolecular cross-linking reaction of HPAM/Cr3+ under different conditions. For their research on the transportation of the HPAM/Cr3+ system in the reservoir, He et al.41 found the three-dimensional network structure of the polymer gel was seriously weakened when the polymer gel propagated in porous media. Hajilary et al.34 had developed a novel method to study the radial flow of the polymer gel in porous media. Yu et al.42 found that the time of dynamic gelation in porous media was much longer than that of static gelation in porous media and ampoule bottles. However, the flow characteristics of the HPAM/Cr3+ system in a fracture channeling-path are different from those in porous medium channeling-path; thus, the research results of the transportation of the HPAM/Cr3+ system in the conventional reservoir cannot be applied to a fractured tight reservoir. However, there are only a few studies on transportation of the HPAM/Cr3+ system in natural micro-fractures, and almost all of those are focused on the loss of the gelling solution from the fracture face into the adjoining matrix.43-46 Thus, it is necessary to study the influence of the HPAM Mw on the transportation of the HPAM/Cr3+ system in micro-fractures to improve the application effect of HPAM/Cr3+ system in a


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fractured tight reservoir. In this paper, the study starts by measuring the changes of the macro-parameters (viscosity, cross-linking time, reaction rate, and reaction degree). These can reveal the process of the change of the cross-linking reaction of HPAM/Cr3+ with different HPAM Mw. Next, the HPAM/Cr3+ systems with different HPAM Mw and with different degree of reaction are injected into the micro-fractures. The experimental results can reveal the transportation mechanism of the HPAM/Cr3+ system in micro-fractures and provide an important theoretical basis for determining a matching relationship between the HPAM/Cr3+ system and the size of the fractures. 2. EXPERIMENT SECTION 2.1. Reagents and Equipment. HPAM with three different Mw were obtained from Beijing Hengju Chemical Co., Ltd. in China. Their Mw are 3 million, 12 million, and 22 million g/mol. Their degrees of hydrolysis are all 25%. Corresponding values between the viscosity of HPAM solution and the mass concentration (Cm) of HPAM are shown in Fig. 1. Chromium acetate solution is obtained from Shandong Shida Oilfield Technical Services Co., Ltd. in China. The concentration of Cr3+ in the chromium acetate solution is 5 mg/mL. Simulated formation water is prepared with 10000 mg/L NaCl and deionized water, which is used for preparing the HPAM solution and the HPAM/Cr3+ system in the experiment. The pH of all of the solutions is fixed at 7. Other instruments include a UV2550 ultraviolet-visible spectrophotometer (Shimadzu Corporation, Japan) and a DV-III Brookfield viscometer (Brookfield Company, America). Before viscosity measurement of the samples, the viscometer is calibrated by using a few standard sample fluids. And the details of calibrations of the viscometer are given in S1. Thus, the viscosity of each of the samples is measured at a shear rate of 20 s-1 at room temperature.

Viscosity of HPAM solution (mPa.s)

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800

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Fig. 1. Corresponding values of the viscosity of HPAM solution versus HPAM Cm. In the experiment, the visual fractured model shown in Fig. 2 is used to simulate the micro-fractures in the fractured reservoir, which is made by using epoxy resin adhesive cementing the two pieces of single frosted glass along the sides. The fracture apertures are controlled by evenly paving a small amount of different particle sizes of quartz sands on the fracture surface. Then, two holes are drilled at both ends of the fractured model, which can simulate the inlet and outlet. The fractured model has the features of controllable fracture aperture, pressure resistance, and visualization. The volume of the fracture is equal to that of saturated water, which can be used to calculate the value of fracture aperture.


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The sizes of quartz sands and the parameters of the models used in the experiment are shown in Tab. 1. The physical simulation experiment device for displacement is shown in Fig. 3.

Fig. 2. The visual micro-fractured model. Tab. 1. The size of four different fractured models No.

fracture

fracture

length (cm)

width (cm)

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50

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4

the size of quartz sand mesh

particle size

number

(µm)

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0

35

1000

13

50

500

25

65

300

48

90

0 means that there is no quartz sand between the two pieces of single frosted glass.

Fig. 3. A diagram of the physical simulation experiment for displacement. 2.2. Cross-linking reaction 2.2.1. The basic principle of the experiments As we know that SEM or AFM is a very important technical means to study the microstructure of polymer gel. And it has perfectly revealed the microstructure changes between HPAM and the intermolecular cross-linking HPAM/Cr3+ system. But the microstructures of HPAM and the intramolecular cross-linking HPAM/Cr3+ system may not have obvious difference by SEM or AFM study. Details for the microstructures of HPAM and the HPAM/Cr3+ system are given in S2. On the other hand, the workload is large by SEM or AFM study when the experiments are tested at many different points in time. Therefore, the most accurate and rapid method — UV−vis spectrophotometry


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is used to reveal the change of the reaction of HPAM/Cr3+ with time. In our previous studies, we had measured the change in the absorbance of the HPAM/Cr3+ system with reaction time to reveal the mechanism of the cross-linking reaction of HPAM/Cr3+ by ultraviolet-visible absorption spectrophotometry. We set the wavelength of UV-VIS spectrophotometer at 540 nm and speculated that the crosslinking reaction was mainly controlled by the Cr3+ concentration when the mole number of — COO- was considerably larger than that of Cr3+. The change of absorbance instead of the change of the concentration of Cr3+ is used to establish the reaction kinetics equation.39 Based on these principles, in the experiment, the changes in the viscosities and absorbances of the three different HPAM/Cr3+ systems in the whole process of the cross-linking reaction are measured by viscometry and ultraviolet-visible absorption spectrophotometry to reveal the influence of the HPAM Mw on the cross-linking reaction of HPAM/Cr3+. The reaction kinetics equations are established by the relationship between the change in absorbance of the HPAM/Cr3+ system and the cross-linking time, which is as follows:

݀‫ܦ‬௧ = −݇(‫ܦ‬ஶ − ‫ܦ‬௧ )௡ ݀‫ݐ‬ After an integral transform, the mathematical expressions are as follows:

n = 1， ln(‫ܦ‬ஶ − ‫ܦ‬௧ ) = −kt + ln(‫ܦ‬ஶ − ‫ܦ‬଴ ) n ≠ 1， (‫ܦ‬ஶ − ‫ܦ‬௧ )ଵି௡ = (1 − ݊)݇‫ ݐ‬+ (‫ܦ‬ஶ − ‫ܦ‬଴ )ଵି௡ 2.2.2 Testing absorbances and viscosities under the same Cm Each of the three types of HPAM/Cr3+ systems consists of 3000 mg/L HPAM and 50 mg/L Cr3+. The three different Mw of the HPAM correspond to the three types of HPAM/Cr3+ systems. In the experiment, the mole ratio of —COO- to Cr3+ is 17.6:1; therefore, it can be postulated that the cross-linking reaction is mainly controlled by the Cr3+. The absorbances and viscosities of the three different HPAM/Cr3+ systems (the three systems) are measured using a UV-VIS spectrophotometer and viscometer, respectively, under the dynamic conditions. The dynamic condition is that the cross-linking reactions are tested by the bottle test at a shear rate of 20 s-1. The experimental data are recorded at regular intervals until the crosslinking reactions are completely finished. 2.2.3 Testing absorbances and viscosities under the same initial viscosities The initial viscosities of the three systems are all fixed at 70 mPa.s at a shear rate of 20 s-1. The three cross-linking reactions are also tested under the dynamic conditions, which is described in Section 2.2.2. The composition of the HPAM/Cr3+ system with an HPAM Mw of 3 million is 5600 mg/L HPAM and 50 mg/L Cr3+. After gelation, the gel viscosity is 6000 mPa.s. The composition of the HPAM/Cr3+ system with an HPAM Mw of 12 million is 3000 mg/L HPAM and 50 mg/L Cr3+. After gelation, the gel viscosity is 5100 mPa.s. The composition of the HPAM/Cr3+ system with an HPAM Mw of 22 million is 2000 mg/L HPAM and 50 mg/L Cr3+. After gelation, the gel viscosity is 4600 mPa.s. In the experiment, the mole ratios of —COO- and Cr3+ in the three systems are 33:1, 17.6:1, and 12:1. Thus, it can also be postulated that the cross-linking reactions of the three are mainly controlled by the Cr3+. The absorbances and viscosities of the three systems are measured using a UV-VIS spectrophotometer and viscometer, respectively, at regular intervals until the cross-linking reactions are completely finished. Then, the relationship between viscosities, absorbances and the reaction time is established. 2.3 Transportation of HPAM/Cr3+ in micro-fractures. 2.3.1 Testing chromatographic separation Five types of HPAM/Cr3+ systems are chosen as the subjects according to the descriptions in Section


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2.2.2 and 2.2.3, which are as follows: (1) the system of 3000 mg/L HPAM with 22 million Mw and 50 mg/L Cr3+, (2) the system of 3000 mg/L HPAM with Mw of 3 million and 50 mg/L Cr3+, (3) the system of 3000 mg/L HPAM with Mw of 12 million and 50 mg/L Cr3+, (4) the system of 2000 mg/L HPAM with Mw of 22 million and 50 mg/L Cr3+, (5) the system of 5600 mg/L HPAM with Mw of 3 million and 50 mg/L Cr3+. The detailed scheme of the displacement experiment is shown in Tab. 1. The ahead fluid, the main slug, and the subsequent fluid are immediately injected into the micro-fractures in sequence from the inlet by the physical simulation experiment device after preparation. When the fluid is discharged from the outlet, the concentration of Cr3+ in the discharged fluid is measured using a UV-VIS spectrophotometer. To eliminate the difference caused by different Mw of HPAM on the absorbance, 500 mg/L ClO2 solution is added to the HPAM/Cr3+ system to fully degrade the high-molecular HPAM. The volume ratio of the ClO2 solution and the HPAM/Cr3+ system is 1: 10. Then, the concentration of Cr3+ in the HPAM/Cr3+ system after degradation is measured using a UV-VIS spectrophotometer. Before the experiment, absorbance values of a series of HPAM/Cr3+ systems with different concentrations of Cr3+ after degradation are measured using a UV-VIS spectrophotometer. The calibration curve of the absorbance values of Cr3+ with different concentration is obtained and presented in Fig. 4. Tab. 2. The detailed scheme of the displacement experiment of different HPAM/Cr3+ systems Parameters of parallel fracture Injection parameters of chemical agents model the total No. fracture HPAM ahead subseque number pore main slug aperture Mw fluid nt fluid of volume (1PV) (µm) (g/mol) (1PV) (1PV) 3 fracture (cm ) 1 35 10 6.125 3000 mg/L 3000 3000 2 50 10 8.75 HPAM and mg/L mg/L 50 mg/L 3 65 5 5.688 HPAM HPAM 22 Cr3+ 4 90 5 7.875 million 2000 mg/L 5 35 10 6.125 2000 2000 HPAM and 6 50 10 8.75 mg/L mg/L 50 mg/L HPAM HPAM 7 65 5 5.688 Cr3+ 3000 mg/L 8 35 10 6.125 3000 3000 12 HPAM and 9 50 10 8.75 mg/L mg/L million 50 mg/L HPAM HPAM 10 65 5 5.688 Cr3+ 3000 mg/L 11 35 10 6.125 3000 3000 HPAM and 12 50 10 8.75 mg/L mg/L 50 mg/L HPAM HPAM 13 65 5 5.688 3 Cr3+ million 5600 mg/L 14 35 10 6.125 5600 5600 HPAM and 15 50 10 8.75 mg/L mg/L 50 mg/L HPAM HPAM 16 65 5 5.688 Cr3+ As known from the calculation, the pore volume of the fractured model is small. For example, 0.1 pore volume (PV) of the fractured model with an aperture of 35 µm is only 0.06125 cm3. This leads to failure in the concentration measurement because the experiment operations cannot be implemented. Therefore, several fractured models are combined in parallel to increase the pore volume of the fracture in the experiment. The schematic diagram of parallel mode of the three fractured models is shown in Fig. 3. This can make the quantity of 0.1 PV increase several fold, which ensures that the concentration


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measurement can be successfully performed. Every time the volume of fluid discharged from the outlet reaches 0.1 PV, the concentration of Cr3+ in the 0.1 PV of fluid is measured. When the absorbance value is measured, the concentration of Cr3+ contained in the discharged fluid can be obtained using the calibration curve shown in Fig. 4.

y=0.0081x+0.3786 R2=0.9879

0.8

Absorbance

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0.6

0.4

0.2 0

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Cr3+ concentration (mg/L)

Fig. 4. Calibration curve of concentration and absorbance of Cr3+ in the HPAM/Cr3+ system after degradation. 2.3.2 Testing pressure difference across the micro-fracture of the HPAM/Cr3+ system According to the experimental results in Section 2.3.1, a suitable fracture aperture is chosen to ensure that the degree of chromatographic separation is the smallest when the HPAM/Cr3+ system transports in the micro-fracture. The five HPAM/Cr3+ systems are the same as described in Section 2.3.1. The HPAM/Cr3+ solution is then injected into the single fractured model under a different cross-linking time at an injection rate of 0.2 cm3/min. Because the outlet is connected to the atmosphere, the injection pressure is equal to the pressure difference of HPAM/Cr3+ system across the micro-fracture from the inlet to the outlet. When the injection pressure is stable, the numerical values are recorded to establish the injection pressure curve of HPAM/Cr3+ in the micro-fractures at different cross-linking time. 3. RESULTS and DISCUSSION. 3.1 Influence of HPAM Mw on the cross-linking reaction under the same Cm The characteristics of the cross-linking reaction of the three systems are shown in Fig. 5 and Fig. 6. Fig. 5 shows the changes in viscosities of the three systems with reaction time. Fig. 6 shows the changes in absorbances of the three systems with reaction time. From Fig. 5, it can be observed that each of the curves of the viscosities can be divided into the following two stages: (1) During the first stage, the viscosities stay the same or slightly decrease; (2) During the second stage, the viscosities increase greatly. However, the corresponding times of the changes in viscosity of the three systems are different. The durations of the first and second stages of the HPAM/Cr3+ system with a low Mw of HPAM are both longer than those of the HPAM/Cr3+ system with a high Mw of HPAM. We conclude that the lower the molecular weight, the longer the cross-linking reaction time there is when the Cm are the same. From Fig. 6, it can be observed that the trends in the change in the absorbances of the three systems are the same. This suggests that the process of the cross-linking reaction of the three systems are the same. However, the degree of the cross-linking reactions of the three systems is different due to


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the different increases in absorbance. Combining the analysis of Fig. 5 and Fig. 6, in the first stage, a large increase in the absorbances of the three systems shows the cross-linking reactions have occurred, and the reaction rates are high. In our previous studies, we found that the pressure drop across the core of the HPAM/Cr3+ system is higher than that of the HPAM solution while the viscosity of the HPAM/Cr3+ system is slightly lower than that of the HPAM solution in the first stage.39 We thought the reaction in this stage is the intramolecular crosslinking reaction, which makes the HPAM molecule in HPAM/Cr3+ system shrink and coil to form a certain scale of spatial structure and leads to a less hydrodynamic radius, a lower viscosity and a higher flow resistance. In the second stage, a slight increase in the absorbances and a large increase in the viscosities of the three systems show the crosslinking reactions continue to occur, and the reaction rates slow down. We thought the reaction in this stage is the intermolecular cross-linking reaction, which causes the HPAM/Cr3+ system to form a three-dimensional spatial structure and leads to a higher viscosity. By comparing the results, it is found that the increase in the absorbances in the first stage are higher than those in the second stage, which shows that the degree of the crosslinking reaction in the first stage is higher than that in the second stage.

100000

3 million Mw 12 million Mw 22 million Mw

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intramolecular crosslinking

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Fig. 5. The changes of viscosities of the three with reaction time under the same Cm. 3 million Mw

14


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Reaction time (h)

Fig. 6. The changes in absorbance of the three systems with reaction time under the same Cm. The results of processing the data about the relationships of absorbances and reaction time of the three systems in Fig. 6 are shown in Fig. 7 and Fig. 8 according to the reaction kinetic equations. Fig. 7


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and Fig. 8, respectively, show the reaction kinetic curve of the three systems in the intramolecular and intermolecular cross-linking stages. As shown in Fig. 7, it can be observed that the reactions of the three systems in the intramolecular cross-linking stage can be regarded as a first-order reaction. However, in this stage, the reaction rates are different. The reaction rates of the HPAM/Cr3+ systems with HPAM Mw of 3 million, 12 million, and 22 million are 0.0403 h-1, 0.0499 h-1, and 0.059 h-1, respectively. These show that the reaction rate of intramolecular cross-linking increases with an increase in the HPAM Mw. On the one hand, the degree of shrinking and coiling of HPAM is greater due to the flexible long chain of HPAM when the HPAM Mw is higher, which can lead to having a larger proportion of the different carboxyls of one HPAM molecule close to each other. On the other hand, the viscosity of HPAM/Cr3+ system increases with the increase of HPAM Mw; therefore, the resistance force of Cr3+ escaping from carboxyls in the solution with higher Mw of HPAM is greater. These two points are favorable for the intramolecular cross-linking reaction. From Fig. 8, it can be observed that the reactions of the three systems in the intermolecular cross-linking stage can be regarded as a multistage reaction. In this stage, the reaction orders and reaction rates of the three systems are all different. The reaction orders of the HPAM/Cr3+ system with 3 million, 12 million, and 22 million Mw of HPAM are 1.65, 1.85, and 1.93, respectively. The reaction rates of the HPAM/Cr3+ system with HPAM Mw of 3 million, 12 million, and 22 million are 0.0068 h-1, 0.01 h-1, and 0.013 h-1, respectively. Moreover, the reaction orders and the reaction rates both increase with an increase in the HPAM Mw. On the one hand, the entanglement between the HPAM molecules increases with an increase in the HPAM Mw; therefore, the contact between the HPAM molecules is closer. On the other hand, the high viscosity can prevent Cr3+ from escaping from the carboxyls. These two points are favorable for the occurrence of the intermolecular cross-linking reaction. In addition, the absorbance differences of HPAM/Cr3+ system with HPAM Mw of 3 million, 12 million, and 22 million are 4.48, 4.69, and 4.83, respectively. This shows that the degree of the cross-linking reaction increases with an increase in the HPAM Mw. We conclude that when the Cm are the same, the higher the HPAM Mw is, the faster the reaction rate of intramolecular and intermolecular cross-linking and the more thorough the cross-linking reaction of HPAM/Cr3+.


2

linear fitting: ln(D∞-Dt)=-0.0403t+1.5419 linear fitting: ln(D∞-Dt)=-0.0499t+1.5827

1

linear fitting: ln(D∞-Dt)=-0.059t+1.6028

0

ln(D∞-Dt)

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-1 -2 -3 -4 0

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Reaction time (h)

Fig. 7. The reaction kinetics of intramolecular cross-linking of the three systems under the same Cm.


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5

function fitting:(D∞-Dt)-0.65=-0.65×0.0068×t+4.48-0.65 function fitting:(D∞-Dt)-0.85=-0.85×0.01×t+4.69-0.85

4

function fitting:(D∞-Dt)-0.93=-0.93×0.013×t+4.83-0.93

3

D∞-Dt

2

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0 0

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Reaction time (h)

Fig. 8. The reaction kinetics of intermolecular cross-linking of the three systems under the same Cm. 3.2 Influence of HPAM Mw on the cross-linking reaction under the same initial viscosity. Under the same initial viscosity, the characteristics of the cross-linking reaction of the three systems are shown in Fig. 9 and Fig. 10. Fig. 9 shows the changes in viscosities of the three systems with reaction time. Fig. 10 shows the changes in absorbances of the three systems with reaction time. From Fig. 9, it can be observed that the duration of the HPAM/Cr3+ system with low Mw of HPAM in the intramolecular cross-linking stage is longer than that with a high Mw of HPAM. From Fig. 10, it can be observed that the increase of absorbance difference of the HPAM/Cr3+ system with a high Mw of HPAM is greater than that with a low Mw of HPAM in the intramolecular cross-linking stage, while it is less than that with low Mw of HPAM in the intermolecular cross-linking stage. The whole increase in the absorbance difference of the HPAM/Cr3+ system with high Mw of HPAM is less than that with a low Mw of HPAM in the whole process of the cross-linking reaction. These trends in change are different from those with the same HPAM Cm by comparing Fig. 10 with Fig. 6. Combining the analysis of Fig. 9 and Fig. 10, it means that the degree of the cross-linking reaction of a HPAM/Cr3+ system with a low Mw of HPAM is higher than that with a high Mw of HPAM. The reason for this is that HPAM Cm is relatively high when HPAM Mw is low with the same initial viscosity, which leads to a high degree of the cross-linking reaction. 3 million Mw 12 million Mw 6000

4000 3000

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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90 80 70 60

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Fig. 9. The changes of viscosities of the three systems with reaction time with the same initial viscosity.


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3 million Mw 14


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Absorbance

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Fig. 10. The changes of absorbances of the three with reaction time under the same initial viscosity. Similar to those of with the same HPAM Cm, the reaction kinetics curves of the three systems under the same initial viscosity are established. Fig. 11 and Fig. 12, respectively, show the reaction kinetic curves of the three systems in the intramolecular and intermolecular cross-linking stage with the same initial viscosity. From Fig. 11, it can be observed that in the intramolecular cross-linking stage, the reaction rates of HPAM/Cr3+ system with HPAM Mw of 3 million, 12 million, and 22 million are 0.045 h-1, 0.049 h-1, and 0.053 h-1, respectively. Although the HPAM Cm is relatively low in the HPAM/Cr3+ system with a high Mw of HPAM, the reaction rate of the HPAM/Cr3+ system with a high Mw of HPAM is high. This means that a high Mw is beneficial for the occurrence of the intramolecular cross-linking reaction. When the HPAM Mw is high, the HPAM molecule is easy to shrink and coil in the solution, which is beneficial for entrapping Cr3+. From Fig. 12, it can be observed that in the intermolecular cross-linking stage, the reaction rates of HPAM/Cr3+ system with HPAM Mw of 3 million, 12 million, and 22 million are 0.011 h-1, 0.0098 h-1, and 0.0086 h-1, respectively. The reaction rate of the HPAM/Cr3+ system with a high Mw and low Cm of HPAM is lower that with a low Mw and high Cm of HPAM. This means that Cm has an important influence on the intermolecular crosslinking reaction. 3 million Mw 12 million Mw 22 million Mw 2

linear fitting: ln(D∞-Dt)=-0.045t+1.595 linear fitting: ln(D∞-Dt)=-0.049t+1.569 linear fitting: ln(D∞-Dt)=-0.053t+1.545

0

ln(D∞-Dt)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-2

-4 0

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Fig. 11. The reaction kinetics of intramolecular cross-linking of the three systems under the same initial viscosity.


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3 million Mw 12 million Mw 22 million Mw 5

function fitting:(D∞-Dt)-0.98=-0.98×0.011×t+4.9-0.98 function fitting:(D∞-Dt)-0.84=-0.89×0.0098×t+4.68-0.84 function fitting:(D∞-Dt)-0.72=-0.72×0.0086×t+4.58-0.72

4

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D∞-Dt

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Fig. 12. The reaction kinetics of intermolecular cross-linking of the three systems under the same initial viscosity. 3.3 Influence of HPAM Mw on chromatographic separation. The essence of chromatographic separation is that the different components of a mixture have different migration rates in the stationary phase. In this paper, the chromatographic separation of HPAM/Cr3+ can be reflected by Cr3+ concentration profiles in the discharged fluid. According to the injection scheme in Tab. 2, on the condition that there is no chromatographic separation, Cr3+ cannot be detected in the produced fluid until 1 PV of fluid is discharged from the outlet. However, in the actual performance of the displacement experiment, Cr3+ can be detected early in the discharged fluid. The experimental result of the chromatographic separation of transportation of the five HPAM/Cr3+ systems in different micro-fractures is shown in Fig. 13. It can be observed from Fig. 13 that the HPAM Mw and fracture aperture have a great influence on the Cr3+ concentration profiles. In the binary mixture of the HPAM/Cr3+ system, the average hydrodynamic radius of HPAM is several hundred nanometers, while the radius of the complex compound of Cr3+ is less than 1 nanometer. Comparing this to the size of the fracture aperture, Cr3+ is free to move in micro-fractures, but HPAM cannot. Therefore, the main reason for chromatographic separation is that the action of fracture surface on HPAM can lead to a different transportation rate between the HPAM and Cr3+. Fig. 13a, b, and c are the results of chromatographic separation of transportation of the three systems with the same Cm but different HPAM Mw in different micro-fractures. From Fig. 13a, it can be observed that the concentration distribution curve of Cr3+ moves to the right until to a certain position with the increase in fracture aperture and then remains the same. It shows that the degree of chromatographic separation is gradually reduced until a stable state is reached with increasing fracture aperture. For example, when the fracture aperture increases from 35 µm to 50 µm and then 65 µm, the volume of discharged fluid increases from 0.5 PV to 0.6 PV and then 0.9 PV when Cr3+ can be detected. When the HPAM/Cr3+ system transports in a micro-fracture, the stress state of HPAM is affected by the fracture surface. The process of transportation in a micro-fracture is shown in Fig. 14. From Fig. 14, it can be observed that the average flow rate of Cr3+ is higher than that of HPAM under the influence of the fracture surface. With the increase of the fracture aperture, the interaction of HPAM and fracture surface decreases due to the decrease in the specific surface of the fracture. The average flow rate of


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HPAM grows closer to that of Cr3+ and the degree of chromatographic separation decreases. When the fracture aperture increases to a certain value, the action of the fracture surface on the HPAM can be ignored and the degree of chromatographic separation remains constant. As shown in Fig. 13a, when the fracture aperture increases to 65 µm and 90 µm, the concentration distribution curves of Cr3+ are almost the same. In this case, the chromatographic separation is only caused by diffusion due to the concentration difference of Cr3+ between the ahead fluid, the main slug, and the subsequent fluid. Comparing to Fig. 13a, b, and c, it can be observed that the degree of chromatographic separation decreases with the decrease in the HPAM Mw. For example, in the micro-fracture with an aperture of 50 µm, the chromatographic separation is serious when the HPAM Mw is 22 million, while the chromatographic separation can be ignored when HPAM Mw is 3 million. As is well-known, when the HPAM Mw is low, the small hydrodynamic radius of HPAM and low viscosity of HPAM/Cr3+ system can lead to a small viscous force of fracture surface on HPAM and a thin boundary layer thickness. This can weaken the acting force of the fracture surface on HPAM. Therefore, the difference in flow rate of HPAM and Cr3+ in a micro-fracture is small when the HPAM Mw is low. Chromatographic separation can lead to the change of concentration distribution of each component in the mixture, which causes poor gelatinization of HPAM and Cr3+. It is adverse for conformance control and water shutoff of a heterogeneous reservoir with high water-cut. The degree of chromatographic separation thus needs to be minimized to improve the application effect of the HPAM/Cr3+ system. From Fig. 13a, b, and c, we can conclude the following: when the HPAM Cm is 3000 mg/L, the HPAM/Cr3+ system with a HPAM Mw of 22 million is appropriate for the micro-fracture with an aperture of more than 65 µm, the HPAM/Cr3+ system with a HPAM Mw of 12 million is appropriate for the micro-fracture with an aperture of more than 50 µm, and the HPAM/Cr3+ system with HPAM Mw of 3 million is appropriate for the micro-fracture with an aperture of more than 35 µm. Fig. 13c, d, and e show the results of chromatographic separation of transportation of the three HPAM/Cr3+ systems with the same viscosity but different HPAM Mw in different micro-fractures. From Fig. 13 c, d, e, it can be observed that the degree of chromatographic separation of the three systems is different in the same micro-fracture with the same viscosity. In this case, the degree of chromatographic separation of the HPAM/Cr3+ system decreases with the decrease in the HPAM Mw. In the same micro-fracture, the degree of the forces of the fracture surface acting on fluids is the same when the viscosities of the fluids are the same, such as the same degree of the effect of tensile stress, adsorption, retention, etc. However, HPAM with a high Mw has a lower number of molecules, on which the same degree of the acting forces has a greater impact. Therefore, the difference in flow rate of the HPAM with a higher Mw and Cr3+ is more obvious. Similarly, when the fracture aperture increases to a certain value, chromatographic separation is only caused by the concentration difference of Cr3+ in the different injection slug. After this, the degree of chromatographic separation no longer changes. From Fig. 13c, d, and e, we can conclude that: when the viscosity of the HPAM/Cr3+ system is 70 mPa.s, the HPAM/Cr3+ system with HPAM Mw of 22 million is appropriate for the micro-fracture with an aperture of more than 65 µm, and the HPAM/Cr3+ systems with HPAM Mw of 12 million or 3 million are appropriate for the micro-fracture with an aperture of more than 50 µm. In addition, comparing Fig. 13a with Fig. 13d and; Fig. 13b with Fig. 13e, it can be observed that the degree of chromatographic separation increases with the increase in HPAM concentration. The increase in concentration increases the number of molecules and the viscosity of the system. The total force of the fracture surface acting on HPAM increases. Therefore, the difference in the flow rates of the HPAM


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and Cr3+ increases with the increase in HPAM concentration.

fracture aperture of 35 µm fracture aperture of 50 µm fracture aperture of 65 µm fracture aperture of 90 µm

(a)

fracture aperture of 35 µm fracture aperture of 50 µm fracture aperture of 65 µm

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0.8

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Fig. 13. Cr3+ concentration profiles in the discharged fluid. (a: transportation of 3000 mg/L HPAM with Mw of 22 million and 50 mg/L Cr3+ in the four types of micro-fractures; b: transportation of 3000 mg/L HPAM with Mw of 3 million and 50 mg/L Cr3+ in the three types of micro-fractures; c: transportation of 3000 mg/L HPAM with Mw of 12 million and 50 mg/L Cr3+ in the three types of micro-fractures; d: transportation of 2000 mg/L HPAM with Mw of 22 million and 50 mg/L Cr3+ in the three types of micro-fractures; e: transportation of 5600 mg/L HPAM with Mw of 3 million and 50 mg/L Cr3+ in the types kinds of micro-fractures.)


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Fig. 14. Transportation of HPAM/Cr3+ in a micro-fracture under the action of the fracture surface. 3.4 Flow resistance of HPAM/Cr3+ system in micro-fracture. According to the results in Section 3.3, the micro-fracture with an aperture of 65 µm is chosen to be used for testing the flow resistance of HPAM/Cr3+ in a micro-fracture, which can minimize the influence of chromatographic separation on the cross-linking reaction of HPAM/Cr3+. The results of the flow resistance of HPAM/Cr3+ systems in the micro-fracture under different degrees of the cross-linking reaction are shown in Fig. 15a and b from which it can be observed that there is a stable range of pressure difference in each curve. Based on the above analysis and conclusion in Section 3.1 and 3.2, it is known that the stable range of pressure difference corresponds to the stage of the intramolecular cross-linking reaction. This shows that the injection pressure is not changing with the degree of cross-linking reaction in this stage. The injection pressure of HPAM/Cr3+ system is equal to that of the HPAM solution in the micro-fracture. This conclusion is different from what we have known about the intramolecular cross-linking of polymers (e.g., LPS, CDG, etc.)47 using for improving the injection pressure and flow diversion in porous media. By means of the intramolecular cross-linking reaction, the linear structure of the HPAM molecule is transformed into a two-dimensional structure but not a three-dimensional structure. Although the size of the fracture aperture is small, an HPAM molecule with this two-dimensional structure can freely extend along the length and width direction of micro-fracture. The viscosities of the HPAM/Cr3+ system are almost equal before and after intramolecular cross-linking; therefore, the flow resistance of the HPAM/Cr3+ system at the intramolecular cross-linking stage in micro-fracture has nearly no change. However, when transporting in porous media, due to the small size of the pore and throat, it only extends along the injection direction through its deformation. And the elasticity modulus of cross-linked HPAM is higher than that of the HPAM with the linear structure, which leads to the deformation of cross-linked HPAM being more difficult.47, 48 Therefore, the flow resistance of cross-linked HPAM in porous media is higher than that of HPAM. (a)

(b)



600

Pressure difference (KPa)

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Pressure difference (KPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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400

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Cross-linking reaction time (h)

Fig. 15. Pressure difference across the micro-fracture of the HPAM/Cr3+ system under different degrees of the cross-linking reaction (a: the Cm of the three HPAM/Cr3+ systems are the same; b: the initial


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viscosity of the three HPAM/Cr3+ systems are the same). In addition, the time when the injection pressure increases is different for the different HPAM/Cr3+ systems in the micro-fracture. It increases with the increase in the HPAM Mw, no matter whether under the same Cm or the same initial viscosity. According to the conclusions in Sections 3.1 and 3.2, we have known that the higher the HPAM Mw, the faster the intramolecular cross-linking reaction rate and the earlier the intramolecular crosslinking stage ends. After the intramolecular cross-linking reaction, the intermolecular cross-linking reaction occurs between HPAM and Cr3+, which leads to the formation of the HPAM hydrogel with a three-dimensional space structure. In this case, not only limited by the small space of the micro-fracture, but also being hindered by a large increase in viscosity, the flow resistance of the HPAM/Cr3+ system increases markedly in the micro-fracture. The end results is that the earlier the intermolecular cross-linking reaction begins, the earlier the injection pressure increases. From the analysis of the above, we can draw the following conclusions. For an HPAM/Cr3+ system with high Mw HPAM, the cross-linking reaction more fully forms a gel with higher viscosity, which can produce a higher plugging strength in the micro-fracture. For an HPAM/Cr3+ system with low Mw HPAM, the duration of intramolecular cross-linking reaction is longer, which is beneficial for maintaining a low injection pressure for a longer period and it can transport more easily into the deep reservoir. This is very important for expanding the swept volume of the fractured heterogeneous reservoir on a larger scale to EOR. 4 CONCLUSIONS. (1) Under the same Cm, the reaction rate and the reaction degree of HPAM/Cr3+ system with high Mw HPAM are both higher than that with low Mw HPAM in the stages of intramolecular and intermolecular cross-linking. (2) With the same initial viscosity, the reaction rate of the HPAM/Cr3+ system with high Mw HPAM is higher than that with low Mw HPAM in the intramolecular cross-linking stage, while they are lower than that with low Mw HPAM in the intermolecular cross-linking stage. Thus, a high Mw is beneficial for the intramolecular cross-linking reaction, and a high Cm is beneficial for the intermolecular cross-linking reaction. (3) Chromatographic separation of transportation of the HPAM/Cr3+ system in a micro-fracture is greatly affected by the fracture aperture, HPAM Mw, and HPAM concentration. Its degree increases with the decrease in fracture aperture, the increase in HPAM Mw and the HPAM concentration. There is a matching relationship between the HPAM/Cr3+ system and fracture aperture. When HPAM Cm is 3000 mg/L, the system with an HPAM Mw of 22 million is suitable for the micro-fracture with an aperture of more than 65 µm, the system with an HPAM Mw of 12 million is suitable for the micro-fracture with an aperture of more than 50 µm, and the system with an HPAM Mw of 3 million is suitable for the micro-fracture with an aperture of more than 35 µm. When the viscosity of HPAM/Cr3+ system is 70 mPa.s, the system with an HPAM Mw of 22 million is suitable for the micro-fracture with an aperture of more than 65 µm, and the systems with HPAM Mw of 12 million or 3 million are both suitable for the micro-fracture with an aperture of more than 50 µm. (4) At the intramolecular cross-linking stage, the injection pressure of the HPAM/Cr3+ system in the micro-fracture is almost equal to that of the HPAM solution. The pressure exhibits no change with the degree of the crosslinking reaction. The duration of the intramolecular crosslinking of an HPAM/Cr3+ system with low Mw HPAM is longer, but the system with high Mw HPAM can form a gel with a higher viscosity.


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ASSOCIATED CONTENT Supporting Information S1, Calibrations of the viscometer. S2, AFM and SEM images of HPAM and the HPAM/Cr3+ system. AUTHOR INFORMATION Corresponding author: *E-mail addresses: [email protected] (Zhang, L.); [email protected] (Pu, C.). Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This study was supported by the Fundamental Research Funds for the Central Universities (16CX02020A) and the national natural science funds (51274229; 51104173). NOMENCLATURE HPAM = hydrolyzed polyacrylamide Cr3+ = chromium acetate Mw = molecular weight Cm = mass concentration Dt = the absorbance of HPAM/Cr3+ system at time t D∞ = the absorbance of HPAM/Cr3+ system at the terminal time of the cross-linking D0 = the absorbance of HPAM/Cr3+ system at the initial time t = crosslinking time, h n = order of reaction k = the crosslinking reaction rate constant, 1/h the three systems = the three different HPAM/Cr3+ systems PV = pore volume LPS = linked polymer solution CDG = colloidal dispersion gel REFERENCES (1) Hao, M.; Liu, X.; Hu, Y.; Yang, Z.; Hou, J. Acta Petrolei Sinica 2007, 28(5), 93-98. (2) Wu, Z.; Hu, W.; Song, X.; Ran, Q.; Gan, J. Acta Petrolei Sinica 2009, 30(5), 728-734. (3) Wang, Y.; Song, X.; Tian, C.; Shi, C.; Li, J.; Hui, G.; Hou, J.; Gao, C.; Wang, X.; Liu, P. Petrol. Explor. Dev. 2015, 42(2), 222-228. (4) Fan, T.; Song, X.; Wu, S.; Li, Q.; Wang, B.; Li, X.; Li, H.; Liu, H. Petrol. Explor. Dev. 2015, 42(4), 496-500. (5) Ghaithan, A. A. Arab. J. Sci. Eng. 2012, 37, 1131-1141. (6) Lu, X.; Wang, S.; Wang, R.; Wang, H.; Zhang, S. Petrol. Explor. Dev. 2011, 38, 576-582 (in Chinese). (7) Vossoughi, S. J. Pet. Sci. Eng. 2000, 26, 199-209. (8) Dai, C.; You, Q.; Zhao, F. Pet. Sci. Technol. 2010, 28, 1307-1315. (9) Mack, J. C.; Smith, J. E. Proceedings of SPE International Symposium on Improved on Recovery, Tulsa, Oklahoma, April 17-20, 1994; SPE Paper 27780. (10) Vargas-Vasquez, S. M.; Romero-Zerón, L. B. Pet. Sci. Technol. 2008, 26, 481-498. (11) Natarajan, D.; McCool, C. S.; Green, D. W.; Willhite, G. P. Proceedings of SPE International


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