In accordance to Copyright requirements, this is a Pre-Print Version of this paper published in: “Polymers for Advanced Technologies” To cite the paper please visit: http://onlinelibrary.wiley.com/doi/10.1002/pat.3254/full And Please Cite as: M. Baghban Salehi, E. Vasheghani Farahani, M. Vafaie Sefti, A. Mousavi Moghadam, and H. Naderi. "Rheological and transport properties of sulfonated polyacrylamide hydrogels for water shutoff in porous media." Polymers for Advanced Technologies. 25(4): 396-405 (2014). DOI: 10.1002/pat.3254
Rheological and Transport Properties of Sulfonated Polyacrylamide Hydrogels for Water Shutoff in Porous Media Mahsa Baghban Salehia, Ebrahim Vasheghani-Farahani*a, Mohsen Vafaie Seftia, Asefe Mousavi Moghadama, Hasan Naderib 1 2
Chemical Engineering Department, Tarbiat Modares University, 14115-143 Tehran, Iran. Center for Exploration and Production Studies and Research Division, Research Institute of Petroleum Industry (RIPI), 18745-4163, Tehran, Iran.
*
Corresponding author: Prof. E. Vasheghani-Farahani Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran Email address: evf@ modares.ac.ir Other authors email:
[email protected] (M. Baghban Salehi),
[email protected] (A. Mousavi Moghadam).
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Abstract In this research an optimal hydrogel, based on sulfonated polyacrylamide, was synthesized by statistical design of experiments using central composite method. This new hydrogel composed of sulfonated polyacrylamide (AN125VLM) and chromium triacetate as copolymer and crosslinker, respectively. The bottle and rheological tests were conducted to investigate the gelation time, thermal stability, gel strength and also ultimate elastic modulus, complex modulus and yield stress. It was found that copolymer concentration had the main effect in both rheological and transport properties of hydrogels. The sample prepared at optimum condition, i.e., copolymer concentration of 26,340 ppm and crosslinker/copolymer ratio of 0.12, had an ultimate elastic modulus of 29.9 kPa, yield stress of 800 Pa and complex modulus of 32 kPa. A coreflooding test through fracture was carried out to examine the optimum gel performance in a porous media. A value of 483 for the residual resistance factor ratio of water to oil confirmed the high ability of the hydrogel in reducing the relative permeability of water to oil in fractured media. Keywords: Hydrogel, Bottle test, Rheological test, Creep test, Coreflooding 1. Introduction As the oil-producing wells mature, water production in these wells becomes a more serious problem. Remediation techniques for controlling water production, referred to conformance control, are selected on the basis of the water source and the method of entry into the wellbore [1]. Water shutoff methods can be classified into two different types: mechanical and chemical. The mechanical methods are limited to the application of specific completion tools as dual systems to avoid water conning or the use of hydro-cyclones to separate water while it is being produced [2]. On the other hand, the chemical methods, extensively used in the last decade [3, 4], consist primarily of chemical products pumping into the producer or injector wells. Polymer gels for improved oil recovery (IOR), which is typically composed of two main components; a polymer or copolymer, and a crosslinker (dissolvable in water), are injected into the target zones [5]. Most of these systems, based on polymer/crosslinker solutions, are turned from low viscosity liquids (gelant) into strong or weak gels depending on their formulations and surrounding media after a given time. These gels, which are the basis of most water shutoff treatments, can partially or completely block the channels through which water is being produced. The most common polymers used for gel treatment of hydrocarbon reservoirs are polyacrylamides (HPAMs) with varying degrees of hydrolysis and molecular weight (MW). Chromium acetate/partially hydrolyzed polyacrylamide [6, 7] or polyethyleneimine/copolymer of acrylamide and t-butyl acrylate [8] are two well-known examples of these hydrogels. The former is an ionic crosslinked gel and the latter is a covalent gel. Selection of a polymer gel system for a given well treatment strongly depends on the reservoir’s conditions, such as temperature, salinity and hardness, as well as on the pH of the water used for preparation of the gelant. Other parameters in this case include salinity of the formation water, permeability of the target zone, and the lithology of the formation [9-12]. Gelation time and gel strength are the main factors to select the suitable gel system. Among the different techniques for measuring the consistency of gelling systems (such as bottle test and rheological tests), rheology is considered as the most complete technique of characterization of polymer systems [13]. Recently, two methods have been introduced for the rheological tests of polymer gels: a) The gel polymer in liquid state is subjected to shear flow. In this method, the measured viscosity increases with increasing of the extent of reaction until the stress reaches the limits of the instrument or until the materials break; b) Small amplitude
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oscillatory shear gives the components of the complex modulus, storage modulus and loss modulus during the crosslinking process, which shows the viscoelastic behavior of the gel system [14-16]. Because of the disproportionate permeability reduction (DPR) property of polymer gels in water shutoff operations in petroleum field, the yield stress as a rheological property of the gel systems must be investigated to assure gel placement into the fractures of the reservoirs [17-19]. To synthesize a polymer gel with desirable water shutoff performance, the statistical design of the experiments by response surface methodology (RSM) [20] using central composite design (CCD) was applied. Hydrogels were prepared for the first time using a low MW copolymer of sulfonated polyacrylamide and chromium triacetate as a crosslinker. The experiments were carried out in two general steps: First the bottle test method was accomplished for the all planed experiments to indicate the gelation time, gel strength and thermal stability, visually. Then the rheological tests were carried out by the dynamic rheometer on the gelant solutions and the resulting gels. The ultimate elastic modulus and complex modulus were determined through conducting the rheological tests on the gelant solutions. Then the rheological tests were applied on the selected samples of hydrogels to study the steady shear test and yield stress. Second, the optimum gel, out of the experiments of the first step, was applied on the coreflooding test to determine the water and oil relative permeability and the residual resistance factor in porous media. The presented optimal hydrogel would have the desirable properties such as the gelation time, gel strength and thermal stability as well as yield stress and the gel ability to reduce the relative permeability of water to oil in porous media. 2. Experimental Methodology To determine the optimum conditions for preparation of hydrogels with desirable properties for water shutoff, the experiments were carried out in two steps (Fig. 1).
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1st step: Out of porous media
Design of Experiments (Central Composite Design)
Rheological Test
Bottle Test
Gelant Experiments
Equilibrium Elastic Modulus Complex Modulus
Gel Experiments
Steady Shear Test Yield Stress
Gelation Time Gel Strength Thermal Stability
Optimum Gel Sample
Water Relative Permeability Oil Relative Permeability Residual Resistance Factor
Coreflooding Test
2nd step: In porous media
Final Gel Performance
Figure 1. A schematic diagram of experimental steps.
2.1. Materials The hydrogels were prepared by a copolymer of 2-acrylamido-2-methyl-propanesulfonic-acid sodium salt (AMPS) and acrylamide (AcA) (Fig. 2) with an average molecular weight of 2105 Dalton and sulfonation degree of 25%, provided by SNF Co. (France) In powder form, it is also called sulfonated polyacrylamide (PAMPS) under the trade name of AN125VLM. It was used in gel preparation with the aim of increasing the gelation time and the injection ability of the gelant solution in porous media. Chromium triacetate, as an ionic crosslinker was purchased in powder form from Carlo Erba Co. (Italy). CH2 O
CH
m
CH2 O
C
CH
n
C NH
NH2 CH3
C
CH3
CH2 O
S
O
O Na
Figure 2. Sulfonated polyacrylamide structure.
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2.2. Hydrogels Perpetration In this work, the hydrogels of sulfonated polyacrylamide using chromium triacetate as crosslinker were prepared at room temperature according to the following steps. First, a stock solution of copolymer with 4.5% (w/v) concentration was prepared by mixing the copolymer powder and distilled water for 24 hour. The mixture was then held, without stirring, for 2 days to obtain a homogeneous solution. Shortly before the experiment, the copolymer solutions were diluted by distilled water to the designed concentrations, and the mixture were stirred for 5 min. Chromium triacetate was also mixed with distilled water at room temperature (according to the experimental design composition) using a magnetic stirrer (Stuart CB162, UK) for 5 min to prepare crosslinker solution. Finally, the copolymer and crosslinker solutions were mixed for 10 min to obtain the gelant solution. Since, most of the south Iranian reservoirs have a high temperature (around 90oC), this temperature was selected for the experiments. It is worth nothing that each designed sample was divided into two parts, one used for the bottle test and the other for the rheological experiments. 2.3. Design of Experiments In the first step, the bottle and rheological experiments were carried out according to the designed plan, given in Table 1, using central composite design with two factors in five levels. A wide range of copolymer concentration (5,000-30,000 ppm) and crosslinker/copolymer ratio (0.05-0.5) was applied to determine their effect on gelation time. The experimental plan for gel preparation is also presented in Table 2. Table 1. The level of variables in CCD. Low axial Low Center Variable 1.41 factorial (-1) (0) A: Copolymer Concentration (ppm) 5,000 8,660 17,500 B: Crosslinker/Copolymer Ratio 0.05 0.12 0.28
High factorial (+1) 26,340 0.43
High axial 1.41
30,000 0.5
Table 2. The experimental plan for gel preparation. A B Sample No. Coded Actual (ppm) Coded Actual -1 8660 -1 0.12 1 +1 26340 -1 0.12 2 -1 8660 +1 0.43 3 +1 26340 +1 0.43 4 -1.41 5000 0 0.28 5 +1.41 30000 0 0.28 6 0 17500 -1.41 0.05 7 0 17500 +1.41 0.50 8 0 17500 0 0.28 9 0 17500 0 0.28 10 0 17500 0 0.28 11 0 17500 0 0.28 12
The coded value of each factor, calculated by Eq. (1), was used to present the final equation for the response prediction in terms of dimensionless coded values.
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Xi
(X i (XH
X)
(1)
XL ) / 2
where, X i is the value of the ith factor, X is the mean value, and X H and X L are the maximum and minimum values of the design, respectively. So the central point of this experimental design with two variables would be (0,0), star points of (±α, 0) and (±α, 0), and factorial points of (±1, ±1). Generally, in the CCD method, the response surface is presented as quadratic equation (Eq. 2) [21]: k
k
i 1
i j
y β 0 βx i β ii x i2
k
β x x ε ij
i
(2)
j
1 i j
Where, 's are quadratic coefficients/model parameters, xixj is the multiply of binary variables (interactions), xi2 is nonlinear term, y is response (observation) and is the statistical random error term [22]. Four center points (samples 9-12) were also designed and assumed to measure the probable random errors during the experiments. 2.4. Bottle Test Bottle test method provides a semi-quantitative measurement of gelation time and gel strength. In this method, the gel strength during its formation is expressed as an alphabetic code of A through I, which was defined by Sydansk [23]. For this purpose, the gelant solutions, were prepared according to the CCD plan (Table 2) at 90oC. Then they were transferred into high thermal resistance glass tubes. The glass tubes were inverted at various time intervals and the corresponding gel property was recorded under the influence of gravity. The samples were kept for 8 weeks in oven (90oC) to study the thermal stability of the gels. 2.5. Rheological Characterization The dynamic rheological measurements of both gelant and gel samples were performed using a Paar-Physica universal spectrometer, model MCR501 (Austria) with plate-plate geometry. As the mentioned rheometer has the thermal controller, the experiments were conducted at 90oC. The gelant rheological measurements were made in a dynamic rheometer fixed with smooth plate-plate surfaces of 50 mm diameter and 3 mm gap. Each sample was measured in the rheometer for 60 minutes at 90oC, constant strain of 1% (fitted with the desired linear viscoelastic range of gelant) and frequency of 1 Hz. The elastic, G , and viscous, G , responses of the gelant show the rheology properties; where, G represents the storage modulus or the stress energy temporarily stored during the fluid force of the test and G represents the stress energy used to initiate flow, and transformed into the shear heat. Increase in the elastic modulus of the gelant with time shows the reaction between copolymer chains and crosslinker. By time passing and completion of gelation, the elastic modulus would be constant and independent of time, which is presented as ultimate elastic modulus, Gu . Also complex modulus, G * , which quantifies the total consistency of the system, represents the fluid resistance to external perturbation [24]: G*
G
2
G
2
0.5
(3)
In order to determine the suitable composition of the copolymer and crosslinker/copolymer ratio for gel preparation, not only the gelant properties but also the rheological properties and the gel placement in porous media must be studied. Also, by calculating the yield stress of the gel, the lack of flowing due to pressure drop in the reservoir can be ensured. In this research, the yield 6
stress was measured by using the MCR501 rheometer fixed with rough plate-plate surfaces of 25 mm diameter and 1 mm gap without the influence of wall slip. 2.6. Coreflooding Test To investigate the optimum gel performance in fractured reservoirs, an out-crop of the reservoir rock was tested by coreflooding test to determine the initial oil and water permeability without fracture. The schematic of the coreflooding set up is shown in Fig. 3.
Figure 3. Schematic of the coreflooding set up.
Figure 4. A view of fractured core with spacers.
The following experimental procedure was carried out for coreflooding through the fractured core: 1. To create the fractured core, an out-crop of low permeability reservoir rock with 3.6 cm of diameter and 7.2 cm of height (to ensure of deficiency of the gelant penetration into matrix) was cut in the middle by cutting device (Fig. 4). It was vacuumed off by pump (ILMVAC GmbH Co.) to ensure the removal of excess air before the injection. 2. The fractured core was saturated by formation water (the formulation was based on the average formation water of Iranian reservoirs). The absolute permeability of the sample was calculated using Darcy equation. Porosity was also measured dividing the volume of the injected water to the total vacancy volume. 3. Crude oil (prepared from one of the Iranian reservoirs) was injected into core in different rates at 90oC. The oil relative permeability of the rock before gel (kro)1 at the saturation of connate water (Scw) was calculated by the registered pressure gradients. Thus oil relative permeability was determined by the slope of the pressure gradient versus the rate using Darcy equation.
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4. Formation water was injected in several rates at 90oC and the pressure gradients were noted. As described in step 3, the water relative permeability before gel (krw)1 was measured at the saturation of residual oil (Sor). 5. 60 ml of the gelant with the optimum composition based on of the rheological properties was prepared and injected into the core. 6. In order to form the gel, the experimental system was kept intact for 2 days at 90oC (based on the results of bottle test). 7. To calculate the water relative permeability (krw)2 and the oil relative permeability (kro)2 after gel, the formation water and oil were injected into the core in different rates of injection, respectively. Then, by calculating the residual resistance factor [25], the ability of the gel in reducing water permeability was determined in contrast with oil permeability: RRFoil
k k ro
1
ro
2
;
RRFwater
k k rw
1
rw
2
(4)
3. Results and Discussion 3.1. Gelation time The final results of bottle test are shown in Table 3. Table 3. The results of bottle test for the designed gel. 9 10 11 12 Sample No. 1 2 3 4 5 6 7 8 Time (hr) Central Points A A A A A A A A A A A A 1 A A A A A A A A A A A A 2 A B A B A B A A A A A A 3 A D A B A D C A A A A A 4 A E A D A E D A A A A A 5 A E A E A E E A A A A A 7 A F A E A F F A A A A A 9 A F A F A F F A A A A A 15 B F A F A G G B B B B B 24 C G A F A G G B D E E E 35 D H A F A H G D E E E E 48 E H A G A I G E G F G G 72 E H A G A I G F G G G G 100 E I A H A I G G G G G G 150 E I B H A I G G G G G G 300 F I E H C I G G S G S S 360 (15 days) G I G H E I G H S S S S 480 (20 days) H I S I G I S I S S S S 720 (30 days) S I S I S I S I S S S S 960 (40 days) S I S I S I S I S S S S 1390 (58 days) *S stands for “Syneresis”
To determine the effect of copolymer concentration and crosslinker/copolymer ratio on the gelation time, an alphabetic code of G was considered as a suitable code for this purpose. The central composite design resulted to a quadratic polynomial model in terms of coded values which correlates the gelation time with two variables as follow: Gelation time (h) 93.25 263.4 A 39.13 B 18.5 AB 181.5 A 2 5.6 B 2 (5)
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where, A is copolymer concentration, B is crosslinker/copolymer ratio and AB is the interaction of two factors on the gelation time as a response. The coefficient of each factor and its sign indicate the importance and type of the parameter effect on the response. As can be seen, the copolymer concentration with the greatest coefficient was identified as the main effect on reducing the gelation time. Figure 5 shows the experimental data versus the predicted response values. It is worth to mention that yi , y and ˆy , show the experimental data, the average of the experimental data and the values predicted by the model, respectively. The overlap of actual data and the predicted response is due to two reasons: the R-square value is 0.995, and the F-value of this curve compared with other curves (linear, third order and more) is larger. The results of the analysis of variance for fitted quadratic curve (Table 4) show the high accuracy of the presented mode (P≤0.0001).
Figure 5. Predicted values vs. actual values of the gelation time. Table 4. The ANOVA results of the developed model for gelation time. Sum of square DOF Mean square F-value Gelation time(hr)
Model Residual
ˆyi
y yi
2
ˆy i
2
P-value
7.86E 005
5
1.57E+005
260.86
< 0.0001
3614.42
6
602.4
-
-
The interactive effect of two factors on gelation time can be observed in Fig. 6-a. As shown, at constant values of crosslinker/copolymer ratio, the gelation time decreases by increase of the copolymer concentration. It is also indicated that at constant concentration of copolymer, the variation of crosslinker/copolymer ratio has negligible effect on the gelation time. Therefore, the concentration of copolymer was the controlling factor of the gelation time. As illustrated in figure 6, at copolymer concentration lower than 17,500 ppm, the gelation time becomes too long. So it would not be suitable in field operation. As can be seen in Fig. 6-b, the maximum value of response was in the minimum value of copolymer concentration while it was not sensitive to factor B. Fig. 6 and Table 4 show that samples 3 and 9 did not retain water in their structure and shrinkage (syneresis), sample 5 was a weak network, and gelation time of sample 1 was long. Therefore,
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these hydrogels are not appropriate for field operation. According to the gel structure, there is a two-phase heterogeneity in its structure (dense phase and dilute phase), which is due to the network processing [26, 27]. In contrast to the dilute phase, the dense phase with higher mechanical strength is highly crosslinked. Increasing of copolymer or crosslinker concentration may affect both phases. However, increasing of the copolymer concentration at constant concentration of crosslinker may lead to increase in physical entanglements of the copolymer chains. The rheological experiments would be necessary to determine the suitable components of the gel for strengthening of the gel network.
a b Figure 6. Effect of copolymer concentration and crosslinker/copolymer ratio on gelation time (a: Contour plot, b: Response surface plot).
3.2. Rheological Gelant Experiments The results of ultimate elastic modulus measurement of the gelant samples were inserted into the DX7 software to correlate the ultimate elastic modulus to copolymer concentration and crosslinker/copolymer ratio by a quadratic polynomial model as: Gu (Pa) 4702 7736 A 3357 B 4872 AB 4355 A2 3381 B2
(6)
The predicted values of Gu based on Eq. (6) of rheology experiments versus actual values are illustrated in Fig. 7. The value of R-square=0.975 shows the high accuracy of mathematical model to predict Gu . The interaction between the two factors mentioned above has the most effect after copolymer concentration on the ultimate elastic modulus as response. As can be figured out of Table 5, the results of the analysis of variance of model and residual, the p-value of 0.0027 indicates the goodness of fit to experimental data.
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Figure 7. Predicted values vs. actual values of the ultimate elastic modulus. Table 5. The ANOVA results of the developed model for the ultimate elastic modulus. Sum of square DOF Mean square F-value P-value Ultimate Elastic Modulus (Pa)
Model Residual
ˆ yi ˆ yi
y yi
2
7.73E+008
5
1.55E+008
31.11
