Effects of Fracture and Matrix on Propagation Behavior and Water

Aug 14, 2015 - the water shut-off performance are clearly understood.13 ..... volume. (cm3). K*matrix. (mD). 1. 1.05. 8.02. 2.52. 4.97. 0.95. 100. 2. ...
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Effects of Fracture and Matrix on Propagation Behavior and Water Shut-off Performance of a Polymer Gel Yingrui Bai,† Falin Wei,† Chunming Xiong,† Junjian Li,*,‡ Ruyi Jiang,§ Hanbing Xu,† and Yong Shu† †

Research Institute of Petroleum Exploration & Development, PetroChina, Beijing, 100083, P. R. China China University of Petroleum (Beijing), Beijing, 102249, P. R. China § Department of Science and Technology Management, China National Petroleum Corporation, Beijing 100007, P. R. China ‡

ABSTRACT: The influence of reservoir parameters on water shut-off treatment in hydraulic or natural fractured reservoirs remains unclear. In the present study, effects of fracture width and matrix permeability on propagation behavior and water shutoff performance of a polymer gel have been investigated. Results show that the fracture width can greatly affect the injection pressure of the gelant, but the effect of the matrix permeability is relatively slight. During the gelant propagation in fracture, because of the concentration and pressure differences, the gelant loses itself from fracture into matrix to form a gelant filter cake on the fracture face. The smaller the fracture width is, the greater the gelant loses; moreover, a higher gelant loss degree occurs in relatively high permeable matrix. After the cross-linking reaction between polymer and chromium, the gelant filter cake becomes into a gel filter cake. The cementing strength of the gel filter cake and the strength of the gel inside fractures greatly affect the shut-off performance of the gel for fractures. Therefore, an appropriate loss degree of the gelant which improves the thickness and the rigidness of the gel filter cake can enhance the water shut-off performance. Moreover, due to that both the narrow fracture and the high permeable matrix contribute to the gelant loss, the polymer gel presents favorable water shut-off performance in cores with a small fracture width or high permeable matrix.

1. INTRODUCTION Fractured reservoirs which contain hydraulic fractures or natural fractures occupy an important position in oilfields. In the process of oil production, water or other injected fluids are easy to break through into oil wells along fractures and make the watered out well become common.1,2 The excessive water production not only burdens the subsequent water disposal but also shortens the development life of an oilfield because of the decreased economic value.3,4 Therefore, much work should be done to control the useless water production in fractured reservoirs. Many kinds of water shut-off agents have been used in field tests. Among these agents, the cross-linked polymer gel is relatively low-cost and has shown its effectiveness for water shut-off treatment in heterogeneous reservoirs.5 However, the effectiveness and the longevity of the gel in fractured reservoirs still need to be improved. Zhu et al.6 once reported that, because of the relatively high pressure gradient which was exerted on the gel along with the severe washout effect of oil or formation brine in fractures, the shut-off effectiveness of the partially hydrolyzed polyacrylamide (HPAM)/chromium gel was worse in fractured reservoirs than that of this gel in heterogeneous reservoirs. To improve the washout resistance of the cross-linked gel, many kinds of gel systems have been studied. Moradi-Araghi et al.7 studied a stable phenolformaldehyde gel which survived over 9 months at 149 °C in seawater containing 1700 mg/L hardness. Al-Muntasheri8 and Jia9 also reported a polyacrylamide and t-butyl acrylate (PAtBA)/polyethylenimine (PEI) gel system with a favorable washout resistance in fractures. Nowadays, most of the scholars drew their attention on the development of new kinds of water shut-off agents or on the © 2015 American Chemical Society

improvement of the properties of existing agents. Goudarzi et al.10 synthesized a kind of preformed particle gel (PPG) and proved its water control performance using a transparent and open fracture model in laboratory. Al-Ghaza et al.11 developed a chemical packer made from fiber and epoxy resin to efficiently control water production in gas wells. There is no doubt that new kinds of water shut-off agents have contributed to the improvement of the water shut-off efficiency in recent years; however, the complex synthetic process and the high cost were always harmful to the wide application of the new agents.12 In contrast, the polymer gel is still a kind of promising agent for water shut-off in fractured reservoirs if the mechanism of the gel-rock interaction and the effect of reservoir parameters on the water shut-off performance are clearly understood.13 As is well-known, the permeability of a fracture to water or oil is much higher than that of the adjoining matrix.14 Therefore, the propagation and residence behaviors of water shut-off agent in fracture are different from those in porous media. Seright has systematically studied the shut-off performance of a polymer/Cr(III) gel in fractures with different fracture parameters.1,2,15,16 He also designed a procedure which contained 11 steps to size the gelant treatment in fractures. However, in Seright’s experiments, before injecting the gelant into fracture, the gelant was aged for a period of time (longer than the gelation time of the gelant) to form a mobile gel which was called “preformed gel”.17 This is generally not in conformity with the operation practice in some oilfields of China. Zhao et al.18 explored the influence of fracture width on Received: March 19, 2015 Revised: August 14, 2015 Published: August 14, 2015 5534

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Energy & Fuels Table 1. Compositional Analysis of Formation Brine ions

K+ + Na+

Ca2+

Mg2+

CO32−

HCO3−

SO42−

Cl−

concentration (mg/L) total salinity (mg/L)

3023.5

131.3

21.5

39.8 7508.8

379.6

34.1

3879.0

rocks using a coring machine, and processing end faces of each core to keep them parallel; (2) placing homogeneous cores in an oven at 60 °C for 24 h to make them dried; (3) putting cores into a core holder in turn, vacuumizing them using a vacuum pump, and then injecting the formation brine with an injection rate of 0.2 mL/min to measure the water permeability of each core; (4) completely drying cores again; (5) dissecting each homogeneous core into halves along its longitudinal direction; (6) placing a rectangular rigid plastic slice which has a given thickness, a width of 12 mm, and a length of 100 mm into halves of cores, and clamping cores to prevent them moving; (7) cementing halves of cores using a epoxy adhesive at two edges which were unclosed due to the relatively small width of the plastic slice compared with the diameter of the core; (8) removing the plastic slice from cores, and then cores with different sizes of synthetic fractures were prepared. After the preparation of fractured cores, the real width and height of the fracture were measured using a vernier caliper, and the measured water permeability of each homogeneous core equaled its matrix permeability. 2.3. Gelant and Gel Preparation. A gelant which consists of 0.30 wt % HPAM and 0.50 wt % SD107 was applied in experiments. First, the HPAM feedstock solution (0.60 wt %) was prepared using HPAM powder and formation brine, and it was aged at 25 °C for 24 h to ensure the uniform dissolution. The gelant was prepared with the mixture of a predetermined volume of the HPAM feedstock solution, SD107, and formation brine at room temperature (about 25 °C). The apparent viscosity of the fresh gelant was 302.3 mPa·s which was measured at 65 °C using a Brookfield DV-III viscometer with a shear rate of 7.34 1/s. To explore the gelation behavior of this gel system, a series of prepared gelants were sealed in bottles and placed into an oven with a temperature of 65 °C. At regular intervals, a bottle was taken out to measure the apparent viscosity of each gelant at 65 °C using a Brookfield DV-III viscometer. According to the experimental data, the apparent viscosity of this gelant began to sharply rise after 10 h (the initial gelation time), and it indicates the beginning of the cross-linking reaction between HPAM and Cr(III).21 Thirty hours later, the gelant completely gelled into a nonflowing gel with an apparent viscosity of 9,745 mPa·s which was measured with a shear rate of 7.34 1/s. Therefore, the initial gelation time of 10 h and the final gelation time of 30 h were adopted to evaluate this gelant or gel system in the following experiments. 2.4. Propagation Behavior Test. Fractured cores with different fracture widths and matrix permeabilities were used to investigate the propagation behavior of the gelant in fractures. According to the experimental requirements, both the dimensions of fracture widths and the values of matrix permeabilities can be divided into three grades. A series of fractured cores with fracture widths of about 1, 2, and 5 mm, or with matrix permeabilities of around 100, 50, and 10 mD were prepared, respectively. Petrophysical properties of fractured cores are shown in Table 2. During the propagation tests, cores were successively placed into a core holder, vacuumized using a vacuum pump, and saturated by formation brine. Then the fresh gelant (ungelled) was injected into cores with an injection rate of 0.20 mL/min. The injection volume and the total injection pressure were automatically collected using a set of professional software. To eliminate the influence of the tubes leading into and out of the fracture on the pressure drop, pretests were conducted to measure the pressure drop of the gelant when the gelant flowed through a same length and inside diameter plastic tube with an injection flow rate of 0.20 mL/min (named as Pinvalid). In the process of gelant propagation tests, the total pressure drop Ptotal was recorded, and the effective pressure drop Peffective which was generated only in the fracture equaled the difference between the Ptotal and the Pinvalid. In the

the water shut-off performance of HPAM gels using fractured cores, and data presented that the critical injection pressure was inversely related to the fracture width, but the effect of the adjacent matrix was not in the consideration. During the gelant injection, despite the huge difference between the permeability of fracture and that of its adjoining matrix, a part of the gelant can diffuse from fracture into matrix.19 Seright held that the leak-off or loss of the gelant was harmful to the gel formation in fracture, and a main objective for the application of the “preformed gel” in his experiments was to eliminate the gelant loss.17 On the contrary, Ganguly et al.20 proved that a proper loss degree of gelant from fracture into matrix contributed to the water shut-off performance. Except for Seright and Ganguly, few scholars have been investigated the loss behavior of the water shut-off agent during its injection in fracture. In this study, laboratory experiments were conducted using a kind of common HPAM/Cr(III) gel and prepared fractured cores. Two main objectives of this work are (1) to explore the propagation behavior of a HPAM/Cr(III) gelant in fractures with different fracture widths; (2) to investigate the water shutoff performance of the gel for fractures. Another subobjective is to study the gelant loss behavior and its effect on the water shut-off performance in fractured cores with different fracture widths and matrix permeabilities.

2. EXPERIMENTAL SECTION 2.1. Chemicals and Fluids. The commercial water-soluble partially hydrolyzed polyacrylamide (HPAM, Hengju Chemical Group Corporation, China) was used as the polymer with an average molecular weight of 12 000 kDa, a degree of hydrolysis of about 25%, and a purity of over 98 wt %. Chromium(III) acetate (SD107, Shandong Shida Oilfield Technical Services Co., Ltd., China) was used as the cross-linker with the effective concentration of about 40 g/L. Formation brine was made in laboratory, and its compositional analysis is shown in Table 1. Sodium chloride, calcium chloride, calcium chloride, magnesium chloride, sodium bicarbonate, and sodium sulfate (Sinopharm Chemical Reagent Co., Ltd., China) were analytical reagents and used to prepare the formation brine. 2.2. Fractured Core Preparation. Cores with fractures were used in experiments and the schematic of the fractured core is shown in Figure 1. The preparation procedure of fractured cores was briefly described as follows: (1) coring homogeneous cylindrical cores with a diameter of 25 mm and a length of 80 mm from candidate outcrop

Figure 1. Schematic of fractured core sample. 5535

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out from the core holder and dissected into halves along its transverse direction. Because of the gelant loss from fracture into matrix, methylene blue also seeped into matrix to dye sands near the fracture. After that, microscopic images (magnified 75 and 150 times) which contained part of fracture and dyed matrix were obtained using an Anyty microscope (3R-MSUSB401). Meanwhile, the average and maximum loss depths of the gelant were measured using an Anyty processing software. The total loss ratio of the gelant and the matrix damage rate were quantitatively evaluated using a modified core holder with two sampling taps symmetrically distributed in the middle position of the core holder. The function of two sampling taps is to sample the liquid which flows out of the core matrix and to inject brine directly into the matrix; therefore, the fracture direction of each core must be perpendicular to two sampling taps. Moreover, two end faces of each core except for the fracture was sealed using epoxy to prevent the fluid from flowing out of end faces of the matrix. During the evaluation of the gelant loss, five fracture volumes of the dyed gelant were injected in cores with different fracture widths or matrix permeabilities with an injection rate of 0.20 mL/min, just like what have done in previous experiments. The fluid produced from the sampling taps was precisely collected using a pipet, and the total loss ratio of the gelant was the ratio of the cumulative loss volume to the total injection volume of the gelant. To evaluate the matrix damage after gelant loss and gel formation, homogeneous cylindrical cores with a diameter of 25 mm and a length of 80 mm were used. The original permeabilities of cores were about 100, 50, and 10 mD, respectively, which were same with those of fractured cores. The gelant loss volume per unit area in each fractured core was calculated on the basis of the average loss depth of the gelant, the total area of fracture face, and the average porosity of the matrix. The gelant volume that required to be injected into the homogeneous core equaled the product of the gelant loss volume per unit area and the core face area. Then the gelant was injected into homogeneous cores with an injection rate of 0.20 mL/min using a syringe pump. After gel formation, the residual permeability of each core was measured using the subsequent brine flowing along the opposite direction of the gelant injection direction. The permeability damage was calculated using eq 1.

Table 2. Petrophysical Properties of Synthetic Fractured Cores core code

fracture width (mm)

length (cm)

diameter (cm)

total pore volume (cm3)

fracture volume (cm3)

K*matrix (mD)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.05 1.98 4.96 2.01 2.04 1.02 2.02 4.97 1.99 2.01 1.00 1.98 5.01 1.99 2.03

8.02 7.99 8.03 8.01 7.97 7.98 8.03 8.02 7.99 8.02 7.97 7.98 8.00 8.01 8.02

2.52 2.51 2.53 2.49 2.51 2.48 2.49 2.49 2.48 2.50 2.52 2.51 2.48 2.49 2.52

4.97 6.73 9.41 5.40 4.11 5.09 6.80 9.35 5.37 4.19 4.88 6.78 9.49 5.48 4.05

0.95 1.91 4.56 1.88 1.92 0.88 1.88 4.38 1.91 1.86 0.96 1.81 4.80 1.91 1.87

100 100 100 50 10 100 100 100 50 10 100 100 100 50 10

a

Note: K*matrix means that the permeability of the core matrix was measured using the corresponding homogeneous core, as shown in section 2.2.

subsequent data processing, only the effective pressure drop Peffective was adopted. The real-time effective pressure gradient was the ratio of the real-time effective injection pressure to the length of the core. The real-time pore volume (PV) or fracture volume (FV) of the gelant injected was the ratio of the real-time injection volume to pore or fracture volume of the core. The gelant consisted of 0.30 wt % HPAM and 0.50 wt % SD107. 2.5. Gelation Loss and Matrix Damage Test. To visually study the loss degree of gelant from fracture into matrix, the methyleneblue was used to dye the fresh gelant with a concentration of 5 mg/L. Before the experiments, absorbance values of a series of dyed gelants which contained different concentrations of methyleneblue were measured using an ultraviolet spectrophotometer (UV 1901, Shanghai Lengguang Technology Co., Ltd.) with the wavelength of 665 nm. The fitting straight line of these absorbance values was obtained and presented in Figure 2. Five fracture volumes of the dyed gelant were

Kdamage =

K 0 − K1 × 100% K0

(1)

where Kdamage is the core permeability damage ratio; K0 is the original core permeability in mD; K1 is the residual core permeability in mD. 2.6. Water Shut-off Performance Test. In tests for the evaluation of the gel shut-off performance in cores with different fracture widths and matrix permeabilities, the initial formation brine was first injected in each core with an injection rate of 0.2 mL/min until the total injection pressure changed slightly. Then the fresh gelant was injected with an injected volume of 5.0 FV, and the core was sealed in the core holder and placed in an oven with a temperature of 65 °C. To ensure the gel formation, the placement time of each core was the final gelation time (30 h) of the gelant. Next, the subsequent formation brine injection was carried out; meanwhile, the real-time total injection pressure and the injection volume were automatically collected. Over 10.0 FV formation brine was injected into each core until the final total injection pressure leveled off. In the subsequent data processing, the stable effective pressure drop of the formation brine was calculated by means of subtracting the invalid pressure drop from the total pressure drop, just like what has been done in gelant propagation tests. The water residual resistance factor (Frr) was adopted to assess the shut-off performance of the gel system. It is defined as the permeability reduction of the core caused by the gel treatment, and it equals the ratio of the water permeability of core before the gel treatment to the water permeability of core after the gel treatment at a same brine injection rate.22 According to eq 2, the water residual resistance factor can be calculated by dividing the stable effective injection pressure

Figure 2. Absorbance evolution of methylene blue solution with different concentrations. injected into cores with different fracture widths or matrix permeabilities. At regular intervals, the fluid produced from the outlet was collected, and its absorbance value was measured; the methylene blue concentration contained in the produced fluid was obtained using the fitting straight line shown in Figure 2, and the normalized methyleneblue concentration was the ratio of the methylene blue concentration of the produced fluid to the initial methylene blue concentration (5 mg/L). After the gelant injection, cores were taken 5536

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Energy & Fuels before the gel treatment by the stable effective injection pressure after the gel treatment.23

Frr =

K0 ΔP1 = K1 ΔP0

despite the different fracture widths of three cores, the change trends of three pressure gradient curves were similar. The pressure gradient rapidly increased at the beginning of the gelant injection and leveled off when the injected volume (PV or FV) reached a certain point. With the increase of the fracture width from 1.05 to 4.96 mm, due to the decrease of the gelant flow resistance, the increasing rate of the pressure gradient slowed down, and the stable pressure gradients were 29.64, 22.31, and 17.08 kPa/m, respectively. Moreover, when the injection pressure gradient leveled off, with the fracture width increasing from 1.05 mm to 1.98 and 4.96 mm, the injected pore volume of the gelant in cores 1−3 gradually increased from 0.40 PV to 0.51 and 0.70 PV; however, the injected fracture volumes of the gelant gradually decreased and they were 2.23, 1.76, and 1.44 FV, respectively. When the core size was certain, the increase of the fracture width led to a sharp increase of the total pore volume of the core. Therefore, with the increase of the fracture width from 1.05 to 4.96 mm, despite the decrease of the injected fracture volumes of the gelant before the injection pressure leveled-off, the total injected pore volume of the gelant showed a growing trend. The decrease of the injected fracture volume of the gelant indicates the different propagation behaviors of the gelant in fractures with different fracture widths.24 When the fracture width is small, the contact area between a unit volume of gelant and the fracture face is relatively large; it contributes to the gelant loss from fracture into matrix, and the injected fracture volume of gelant correspondingly increased.25 The relatively high injection pressure may also intensify the above phenomenon. With the growth of the fracture width, due to the decrease of the flow resistance of the gelant, the loss degree of the gelant is correspondingly weakened, and the injected fracture volume of the gelant when the injection pressure levels off becomes relatively small. The effect of the fracture width on the gelant loss in fractures was described in detail in section 3.1.3. 3.1.2. Effect of Matrix Permeability on Gelant Injection. Experiments were also performed to explore the effect of the matrix permeability on the injection pressure of gelant. The fracture widths of three cores (cores code 2, 4, and 5 in Table 2) used in experiments were 1.98, 2.01, and 2.04 mm, respectively, and the matrix permeabilities were about 100, 50, and 10 mD, respectively. The fracture width difference among three cores was so slight that it was neglected in our experiments. Figures 5 and 6 illustrate the injection pressure gradients responding as a function of the injected pore volume and fracture volume of the gelant in cores 2, 4, and 5. The pressure gradient evolution was similar to that in Figures 3 and 4. The pressure gradient rapidly increased at the beginning stage of the gelant injection and leveled off when the injected pore or fracture volume reached a certain point. The final stable values of injection pressure gradients were close (21−22 kPa/m) despite of the matrix permeability difference among three cores. In addition, although fracture volumes of three cores were nearly the same (1.91, 1.88, and 1.92 cm3, respectively), there was a difference among the injected pore or fracture volumes of gelant in three cores when pressure gradients leveled off. As shown in Figures 5 and 6, with the reduction of the matrix permeability from 100 to 10 mD, the injected pore volume of the gelant decreased from 0.51 to 0.44 PV and the injected fracture volume was reduced from 1.76 to 1.18 FV as the pressure gradient reached a stable value, i.e., when the fracture

(2)

where K0 is the water permeability of core in milidarcy (mD) before gel treatment; K1 is the water permeability of core in millidarcy (mD) after gel treatment; P0 is the stable effective injection pressure in kilopascal (kPa) before gel treatment; P1 is the stable effective injection pressure in kilopascal (kPa) after gel treatment.

3. RESULTS AND DISCUSSION 3.1. Propagation Behavior of Gelant in Fractures. During the gelant injection process, the real-time injection pressure gradient and the injected volume of the gelant which includes the injected fracture volume and the total pore volume (fracture volume pluses matrix pore volume) are usually applied to evaluate the propagation behavior of the gelant in cores.18 Moreover, the injection pressure gradient was adopted to study the effects of fracture width and matrix permeability on the gelant injection. The “fracture width” and the “matrix permeability” were abbreviated to “FW” and “MP”, respectively. 3.1.1. Effect of Fracture Width on Gelant Injection. Three cores (core codes 1−3) with different fracture widths (1.05, 1.98, and 4.96 mm, respectively) and a same matrix permeability of 100 mD were used to investigate the effect of the fracture width on the injection pressure gradient of the gelant. Pressure data responded as a function of the pore volume and fracture volume of gelant injected were collected and plotted in Figures 3 and 4. Both two figures show that,

Figure 3. Pressure gradient responds as a function of pore volume of gelant injected in cores with different fracture widths.

Figure 4. Pressure gradient responds as a function of fracture volume of gelant injected in cores with different fracture widths. 5537

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Figure 7. Normalized methylene blue concentration versus injected fracture volume of gelant in cores with different fracture widths. Figure 5. Pressure gradient responds as a function of pore volume of gelant injected in cores with different matrix permeabilities.

before the normalized concentration curve leveled off; with the increase of the fracture width from 1.02 mm to 2.02 and 4.97 mm, both the required injected volumes of the gelant were reduced to about 2.0 FV. The result indicates that the resident volume of the methylene blue in cores increased with the reduction of the fracture width. Figure 8 shows the microscopic images of the gelant loss in three cores with fracture widths of 1.02, 2.02, and 4.97 mm, respectively; the matrix permeabilities of three cores were about 100 mD. It can be found that the closer the matrix gets to the fracture face, the darker the matrix is dyed, and it manifests the methylene blue loss or migration process from fracture to matrix. By comparing the dyed degrees of three cores, we conclude that the smaller the fracture width is, the deeper the gelant loses into the matrix. To further investigate the loss degree of the gelant in fractures with different fracture widths, the average and maximum loss depths in three microscopic images were measured, and data were shown in Figure 9. It indicates that, with the increase of the fracture width from 1.02 mm to 2.02 and 4.97 mm, the average loss depth of the gelant was reduced from 2.12 mm to 1.38 and 1.04 mm, and the maximum loss depth also decreased from 3.67 mm to 2.11 and 1.53 mm. Tests 1−3 in Table 3 simulated the matrix damage when the fracture widths were 1.02, 2.02, and 4.97 mm, respectively. The gelant volumes that needed to be injected into homogeneous cores were calculated, and the matrix permeability damage ratios were shown in Table 3. Data show that the matrix permeability damage was only 8.2% even if the largest loss volume of the gelant was injected in the test 1. It indicates that the effect of the gelant loss on the matrix permeability was less and the small loss volume of the gelant under the current experimental condition accounts for this phenomenon. The total loss ratios of the gelant were also evaluated using three cores with a same matrix permeability of 100 mD and different fracture widths of 1.03, 2.02, and 5.01 mm, respectively; meanwhile, the average loss depths of the methylene blue in three cores were also measured and shown in Figure 10. It illustrates that the total loss ratio of gelant was as high as 0.27 when the fracture width was 1.03 mm, but it was rapidly reduced to 0.04 when the fracture width was 5.01 mm. The average loss depth of the gelant was a little bigger than that in cores 6−8, but their change trends were similar. The result was also consistent with that obtained in cores 6−8: the smaller the fracture width is, the greater the gelant loses. The main reason is that when the gelant propagates in a fracture, it will

Figure 6. Pressure gradient responds as a function of fracture volume of gelant injected in cores with different matrix permeabilities.

widths of cores are similar, to achieve a stable injection pressure, a relatively small volume of the gelant is required to be injected into a fractured core with relatively low matrix permeability. It is because that the degree of the gelant diffusion or penetration from fracture into matrix decreased with the reduction of the matrix permeability, and it results in a reduction of the cumulative lost volume of the gelant.20 The effect of the matrix permeability on the loss degree of the gelant was discussed in the section 3.1.4. 3.1.3. Effect of Fracture Width on Gelant Loss. According to the above discussion, with the decrease of the fracture width, both the gelant diffusion and the injection pressure increase, and it results in relatively large volume of the gelant loss from fracture into matrix. To study the loss degree of the gelant in cores with different fracture widths, experiments were conducted using a gelant dyed by methylene blue and cores (cores code 6−8) with fracture widths of 1.02, 2.02, and 4.97 mm, respectively. The experimental procedure has been described in section 2.5. The normalized concentration of methylene blue versus the injected fracture volume of the gelant in cores with different fracture widths was plotted in Figure 7. It indicates that the normalized concentration of methylene blue in the produced fluid showed a change trend which first increased and then leveled off with the increase of the injected fracture volume of the dyed gelant. However, a difference also emerged among three curves: when the fracture width was relatively small (1.02 mm), about 3.0 FV dyed gelant was required to be injected 5538

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Figure 8. Microscopic images of gelant loss from fracture into matrix (magnified 75 times). (a) Fracture width is 1.02 mm; (b) fracture width is 2.02 mm; (c) fracture width is 4.97 mm.

decrease of the fracture width; it compelled the gelant to penetrate into the matrix and resulted in the increase of the gelant or methylene blue diffusion. Therefore, the concentration of the methylene blue measured in the produced gelant was correspondingly lowered. Ganguly20,25 studied the loss behavior of the Cr(III)-PHPA gelant in fractured porous cores, and he concluded that a high pressure contributed to the gelant loss from fracture into matrix, and it was consistent with the result of the present study. 3.1.4. Effect of Matrix Permeability on Gelant Loss. To investigate the effect of the matrix permeability on the gelant loss, tests were performed using three cores (cores code 6, 9, and 10) with similar fracture widths (about 2.0 mm) and different matrix permeabilities of 100, 50, and 10 mD, respectively. The normalized concentration of methylene blue in the produced fluid was measured and presented in Figure 11.

Figure 9. Average and maximum loss depths of gelant from fracture into matrix in cores with different fracture widths.

Table 3. Permeability Damage Ratio of Matrix in Homogeneous Cores test code

1

2

3

4

5

core permeability (mD) permeability damage ratio (%)

100 8.2

100 6.2

100 4.8

50 9.9

10 14.7

Figure 11. Normalized concentration of methylene blue versus fracture volume of gelant injected in cores with different matrix permeabilities.

It shows that the normalized concentration of methylene blue rapidly increased when the injected fracture volume of the gelant was less than 2.0 FV and then it leveled off to a steady state. Moreover, when the injected fracture volumes of the gelant in three cores were the same, the normalized methylene blue concentration decreased with the matrix permeability increasing, and it indicates that more methylene blue resided in the core with high matrix permeability. The main reason is that the higher the matrix permeability is, the smaller the flow resistance of the dyed gelant shows. Mou et al.26 also observed a similar loss phenomenon of a cross-linked acidic gelant in naturally fractured carbonate cores, he attributed the increase of the gelant loss to the increasing porosity of the matrix after the acidulation, and his result was similar to ours.

Figure 10. Average loss depth and total loss ratio of gelant from fracture into matrix in core with different fracture widths.

diffuse or penetrate into the adjacent matrix to form a “gelant filter cake” because of the concentration and pressure differences between the gelant in fracture and brine in matrix. The increasing loss degree of the gelant in a small fracture may be a reasonable reason for the above phenomenon. A possible reason for the gelant diffusion increase is the relatively large contact area between a unit volume of gelant and the fracture face in a small fracture. The injection pressure may be also an indirectly influencing factor on the gelant loss. Figures 3 and 4 show that the injection pressure gradient rapidly rose with the 5539

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Figure 12. Microscopic images of gelant loss from fracture into matrix (magnified 75 times). (a) matrix permeability is 100 mD; (b) matrix permeability is 50 mD; (c) matrix permeability is 10 mD.

Figure 12 presents the microscopic images of the gelant loss in cores with different matrix permeabilities of 100, 50, and 10 mD, respectively. By comparing the matrix dyed degrees of three cores, we found that the dyed degree of the matrix became weaker with the reduction of the matrix permeability. Figure 13 illustrates the average and maximum loss depths of

Figure 14. Average loss depth and total loss ratio of gelant from fracture into matrix in cores with different matrix permeabilities.

show that the average loss depths of gelant in three cores were also a little bigger than those in cores 6, 9, and 10. The result was consistent with the illustration of Figure 13, and it can be ascribed to the lower flow resistance of the gelant when it penetrated from fracture into matrix with a higher permeability. 3.2. Water Shut-off Performance of Gel in Fractures. To evaluate the water shut-off performance of the HPAM/ Cr(III) gel in cores with different fracture widths and matrix permeabilities, five fracture volumes of the gelant were injected in fractured cores, and then cores were sealed until the gel formed. After that, subsequent formation brine was injected, and the residual resistance factor (Frr) of brine was calculated to assess the water shut-off performance. 3.2.1. Effect of Fracture Width on Water Shut-off Performance. Figure 15 illustrates the residual resistance factor (Frr) of brine versus the fracture volume of brine injected in

Figure 13. Average and maximum loss depths of gelant from fracture into matrix in cores with different matrix permeabilities.

the gelant from fracture to matrix when the matrix permeabilities were 100, 50, and 10 mD, respectively. When the matrix permeability was 100 mD, the average and maximum loss depths were 1.38 and 2.11 mm, respectively; with the matrix permeability decreased to 50 mD, the average and maximum loss depths decreased to 1.07 and 1.60 mm; with a further reduction of the matrix permeability to 10 mD, the average and maximum loss depths were obviously lowered to only 0.51 and 0.81 mm, respectively. Tests 2, 4, and 5 in Table 3 simulated the matrix damage when the matrix permeabilities were 100, 50, and 10 mD, respectively, and the permeability damage ratios were shown in Table 3. It shows that the matrix damage was aggravated with the increase of the matrix permeability even if the gelant loss volume showed a decreasing trend, and it indicates that the matrix with a lower permeability was more easily to be damaged. To further evaluate the effect of matrix permeability on the loss ratio of the gelant, three cores with same fracture width of 2 mm and different matrix permeabilities of 100, 50, and 10 mD, respectively, were applied based on the test procedure shown in section 2.5. Data in Figure 14 show that the total loss ratios of gelants were 0.105, 0.071, and 0.035, respectively. It indicates that the gelant loss ratio decreased with the reduction of the matrix permeability. The average loss depths of gelants in three cores were also measured and plotted in Figure 14. Data

Figure 15. Residual resistance factor of brine versus fracture volume of brine injected in cores with different fracture widths. 5540

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Energy & Fuels cores (cores code 11−13) with different fracture widths (1.00, 1.98, and 5.01 mm). The change trends of three curves are similar. At the beginning of the subsequent brine injection after gel formation, both the injection pressure and the Frr rapidly increased. With the growth of the brine injection pressure to a certain value which was named the peak pressure or rupture pressure, the gel was ruptured, and the Frr reached the highest value. After that, the injection pressure significantly decreased and finally leveled off after several fracture volumes of brine were injected. Figure 15 also indicates that, with the increase of the fracture width, three maximum Frr values which were corresponding to three peak pressure values were similar, but the leveled-off Frr values showed a decreasing trend after 10.0 FV of brine were injected. The peak pressure gradients in three tests were shown in Figure 16. It presents that, when the fracture width was 1.00

Figure 17. Gel filter cake on the fracture face after subsequent formation brine injection (magnified 500 times). (a) fracture width is 1.00 mm; (b) fracture width is 5.01 mm.

of the fracture width, and it was consistent with the discussion above. To explore the rupture type of the gel in fractures with different widths, injected fracture volumes of brine which were corresponding to peak pressure gradients in three tests were calculated, as shown in Figure 16. It presents that, with the fracture width increasing from 1.00 mm to 1.98 and 5.01 mm, the injected fracture volumes of brine were enhanced from 0.89 FV to 0.73 and 0.55 FV when the pressure reached its peak value. However, the produced volume of the gel was not so much due to that part of injected brine had penetrated into matrix before the gel was extruded out of the fracture. With the increase of the fracture width, the difference between the input and output decreased but still existed. This phenomenon hints that brine broke through from the internal structure of the cross-linked gel when the fracture width increased. 3.2.2. Effect of Matrix Permeability on Water Shut-off Performance. As discussed above, in the process of the gelant injection, the matrix permeability has a great effect on the loss degree of the gelant. In addition, it also affects the degree of brine leak-off in the process of subsequent brine injection. To investigate the effect of the matrix permeability on the water shut-off performance of the gel in fractures, three tests were conducted using cores (cores code 12, 14, and 15) with a similar fracture width and different matrix permeabilities of 100, 50, and 10 mD, respectively. The experimental procedure was consistent with what has been described in section 2.6. Figure 18 illustrates the residual resistance factor (Frr) evolution versus the injected fracture volume of brine in cores 12, 14, and 15. At the primary stage of the brine injection, the injection pressure was rapidly built because the pressure was

Figure 16. Fracture volume with peak injection pressure of brine injected in cores with different fracture widths.

mm, the peak pressure gradient was 672.36 kPa/m, and it was more than two times higher than that when the fracture width was 5.01 mm (237.99 kPa/m), i.e., the peak pressure was significantly reduced with the increase of the fracture width. As mentioned in the section 3.1, part of the gelant lost into matrix to form a gelant filter cake on the fracture face. After a period of cross-linking reaction between HPAM and chromium, a rigid gel filter cake formed in situ; meanwhile, a strong gel also generated inside the fracture. The shut-off performance of the gel for fractures depends on the gel strength and the cementing strength of the gel filter cake between gel and fracture face.27 If the gel strength is higher than the cementing strength, brine usually breaks through along the fracture face, but the network structure of the gel may be ruptured under a high brine injection pressure if the gel strength is not strong enough.28 In our experiments, the resident phenomenon of the gel was also observed. Figure 17 presents the existence of the gel filter cake on fracture face after subsequent formation brine injection. It can be observed that, when the fracture width was 1.00 mm, a thick gel filter cake dyed by methyleneblue still existed on the fracture face; however, the gel filter cake was scarce when the fracture width was 5.01 mm. It manifests relatively strong cementing strength between the gel and fracture face when the fracture was relatively narrow. The main reason is that the gelant loss ratio is relatively high in a narrow fracture, and then the gel filter cake formed on the fracture face is more rigid and uneasy to be washed out by formation brine. Seright29 also noted that the pressure gradient required for gel extrusion in fractures was inversely proportional to the square

Figure 18. Residual resistance factor of brine versus fracture volume of brine injected in cores with different matrix permeabilities. 5541

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increase of the matrix permeability, the matrix porosity rose and the loss degree of the gelant was correspondingly enhanced. After the gel formation, a thick gel filter cake on the fracture face could build a strong barrier effect on the penetration of the injected brine;30 therefore, subsequent brine could not easily rupture the gel along the fracture face to reduce the shut-off performance of the gel.

not high enough to extrude the gel forward, and it resulted in a sharp increase of the Frr. With the continuous injection of brine, the Frr did not reach its peak value until the injection pressure reached the peak or rupture pressure; after that, the gel was ruptured and extruded out of the fracture by the brine. With a further brine injection, because of the brine washout effect, Frr gradually decreased and finally stabilized. Figure 18 also indicates that, with the decrease of the matrix permeability from 100 to 10 mD, the steady Frr value was reduced from 37.23 to 16.85 after the injection of 10.0 FV brine, and it means that the shut-off performance of the gel for fracture was weakened with the decrease of the matrix permeability. The peak pressure gradients of three tests were shown in Figure 19. When the matrix permeability was reduced from 100

4. CONCLUSIONS The study demonstrates that both the fracture width and the matrix permeability have great effects on the propagation behavior and the water shut-off performance of the polymer/ chromium(III) acetate gel system in fractures. (1) The fracture width can greatly affect the gelant injection pressure. With the reduction of the fracture width, the injection pressure of gelant obviously decreased. In contrast, the matrix permeability has a relatively slight effect on the gelant injection pressure. (2) During the gelant injection in fractured core, part of the gelant penetrates into matrix to form a gelant filter cake on the fracture face. Both the narrow fracture and the high permeable matrix can enhance the loss degree of the gelant, and that results in the different injected volume of gelant when the injection pressure levels off. (3) During the fracture treatment using a gel system, the gel strength of the gel inside the fracture and the cementing strength of the gel filter cake greatly affect the water shutoff performance. (4) An appropriate loss degree of the gelant has a positive influence on the gel filter cake formation. Therefore, the polymer gel presents favorable water shut-off performance in cores with small fracture width or high matrix permeability. During the gel treatment in fractured reservoirs, especially when fractures have various fracture widths, it should be considered that the fracture width and the matrix permeability have great effects on the injection pressure and the loss degree of gelant, and the injection pressure needs to be designed and the loss degree of gelant should be predicted based on laboratory experiments. Further, both the injection pressure and the gelant loss degree are closely related to the gel composition; therefore, proper gel composition (such as proper gel concentration or polymer molecular weight) is essential for the success of gel treatment.

Figure 19. Fracture volume with peak injection pressure of brine injected in cores with different matrix permeabilities.

to 50 and 10 mD, the peak pressure gradient decreased from 378.36 to 257.14 and 245.58 kPa/m. Data indicate that with the reduction of the matrix permeability, the water shut-off performance of the gel for fractures was weakened. Figure 19 also presents that with the decrease of the matrix permeability, the injected fracture volumes of brine which were corresponding to the peak pressures gradually decreased (0.73, 0.61, and 0.53 FV), and it reflects a low degree of brine penetration from fracture into matrix. Figure 20 exhibits the existence of the gel filter cake on the fracture face after subsequent formation brine injection.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the PetroChina Innovation Foundation (Grant No. 2014D-5006-0203) and the National Natural Science Foundation of China (Grant No. 51404280 and 51274237).

Figure 20. Gel filter cake on the fracture face after subsequent formation brine injection (magnified 500 times). (a) Matrix permeability is 100 mD; (b) matrix permeability is 10 mD.

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Compared with the gel filter cake in Figure 20b, the gel filter cake in Figure 20a was obviously thicker, and it is attributed to the increase of the cementing strength between the gel filter cake and fracture face when the matrix permeability was high. When the fracture size of a fractured core was fixed, with the

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