Unwanted water production together with oil and gas production is a striking problem in oil and gas industries, and many approaches have been examined to overcome this major problem. Preformed particle gels (PPGs) showed dramatically good properties for this purpose in mature oil and gas reservoirs. In this study, we carefully synthesized an efficient series of PPGs with using a design of experiments (DOE) software. Acrylamide (AAm)/Acrylic acid (AA) mole ratio, N,N’-methylenebisacrylamide (MBA) mole percentage and swelling time were considered as key parameters to examine PPG swelling behavior. Our results presented a detailed empirical correlation, which could significantly predict the swelling capacity of PPGs in CaCl 2 salt solution (200 , 000 ppm).
Today, the remained oil in the most of oil reservoirs is a heavy oil. Because of increasing demand for energy sources, enhanced oil recovery (EOR) from oil reservoirs has been vastly considered in the worldwide. There are several approaches to upgrade the heavy oil from reservoirs such as gas injection, water flooding, thermal, and chemical methods. In many EOR approaches, it is tried to reduce oil viscosity and literally squeeze oil through the pores of the oil matrix.
Producing unwanted water together with oil is a big trouble for the most of producers in many EOR processes. Because unwanted water production increases the corrosion level, environmental worries, burden on fluid-handling facilities and eventually workover costs, it is contrary to the economically oil production. When the amount of unwanted water production exceeds the economic limitations of water oil ratio (WOR), the production is winded up and the well is closed. Hence, a major objective of many oil producers is to control unwanted water production.
There are different ways to control unwanted water production from oil and gas reservoirs; solutions that are relatively inexpensive to more complex. Gel treatment is one of the successful methods to control unwanted water production from fractured oil reservoirs [
Based on the currently available evidences, the most important parameters that affect the PPG performance are its synthesis approach [
Despite all experimental and field investigations carried out on the use of PPG samples to control unwanted water production [
Design of experiments (DOE) software is a benefit tool to elucidate and optimize the vital parameters affecting the desired experiments with minimum possible tests. There are many design methods in DOE. Response surface methodology (RSM), introduced by Box and Wilson [
In this study, we first synthesized 17 PPG samples by free radical approach based on CCD suggested runs. Then, we swelled PPGs in CaCl2 salt water and examined their swelling behavior. After that, we presented an empirical correlation that it can predict the swelling percentage of PPG samples. In the end, we evaluated the accuracy of our proposed correlation.
Acrylamide (AAm, Sigma-Aldrich, >99%) and acrylic acid (AA, Sigma-Aldrich, > 99%) were two monomers used in this study. N,N’-methylenebisacrylamide (MBA, Sigma-Aldrich, >99%) and sodium persulfate (Na2S2O8, Sigma-Aldrich, >98%) were used as a crosslinking agent and an initiator, respectively. Distillated water was used as solvent in the synthesis experiments. CaCl2 (CaCl2, Merck Company, 99%) salt solution with the concentration of 200,000 ppm was used in swelling experiments.
To synthesis PPG samples and study their swelling behaviors, we considered the mole ratio of AAm/AA, mole percentage of MBA and swelling time as the dominant factors.
Process Variables | Designation | Units | −1 Level | +1 Level |
---|---|---|---|---|
Acrylamide/Acrylic Acid | AAm/AA | … | 2.40 | 9.65 |
N,N’ methylenebisacrylamide | MBA | Mole % | 4 | 20 |
Time | Time | min | 3.00 | 180.00 |
Therefore, in this work the values of 2.41, 4.82, and 9.65 for AAm/AA mole ratio and the values of 4, 16, 18 and 20 for MBA mole percentage were considered to cover the entire acceptable range of key parameters.
To achieve our aim, synthesizing an efficient set of PPG samples with an optimum swelling percentage, CCD suggested 17 experiments that three of them were replicated as the central points.
To perform the 17 designed experiments, we first prepared crosslinking solutions. To do so, a certain amount of MBA, based on the suggested mole percentage by CCD, was fully dissolved in 1.0 mL of distillated water in a waterless volumetric flask 5.0 mL (borosilicate glass 3.3). Then, initiator solution was provided by carefully adding 0.1 grams of K2S2O8 to 1.0 mL of distillated water in a dry volumetric flask (5.0 mL, borosilicate glass 3.3). After that, 0.5 grams of AAm was quite solved in 1.0 mL of distillated water in a 10.0 mL falcontube for each experiment. 0.2 mL of the crosslinking solution was then meticulously added to the falcontube by using a microliter pipette (100 - 1000 µL, WATSON NEXTY Japan). In the end, 0.1 mL of the initiator solution (by using the microliter pipette) was quickly augmented to the falcontube to begin the synthesis reaction. Immediately after that, the falcontube was completely closed and quickly put in the oil bath that it was heated to exactly 80˚C. The falcontubes were kept in the oil bath just for three hours.
To investigate the swelling percentage of PPG samples, we first prepared CaCl2 salt solution with the concentration of exactly 200,000 ppm. Then for each synthesized PPG sample, we carefully weighed 2.0 grams of PPG and swelled it in 20 mL of the prepared CaCl2 salt solution. In a certain swelling time, which specified by CCD, swollen PPG sample was removed from the salt solution, its extra water was quickly taken with the use of a Whatman filter paper (40:8 µm), and carefully weighed by a digital balance (BP 210 S, German). All the tests were carried out at room temperature. The swelling percentage of PPG samples was then calculated by Equation (1).
Swelling percentage = m t − m o m o × 100 (1)
where, mt and mo are the wet and dry weight of PPG samples, respectively.
Run | AAm/AA (mole ratio) | MBA (mole %) | Time (min) |
---|---|---|---|
1 | 4.82 | 14 | 90 |
2 | 9.65 | 20 | 3 |
3 | 4.82 | 20 | 90 |
4 | 9.65 | 4 | 180 |
5 | 4.82 | 4 | 90 |
6 | 2.41 | 20 | 3 |
7 | 9.65 | 4 | 3 |
8 | 4.82 | 14 | 180 |
9 | 2.41 | 4 | 180 |
10 | 4.82 | 14 | 3 |
11 | 2.41 | 14 | 90 |
12 | 2.41 | 4 | 3 |
13 | 4.82 | 14 | 90 |
14 | 9.65 | 20 | 180 |
15 | 4.82 | 14 | 90 |
16 | 2.41 | 20 | 180 |
17 | 9.65 | 16 | 90 |
In this study, we synthesized 17 PPG samples as previously described to examine the swelling behavior of hydrogels. To check the desirability of the synthesized PPG structure and its morphology, Fourier transform infrared spectroscopy (FT-IR, Shimadzu FTIR-8300) and scanning electron microscopy (SEM, VEGA3 TESCAN, at 20 kV) were fulfilled. As an example, FT-IR of PPG sample 5 was shown in
After reviewing the correctness of the performed synthesis experiments, we investigated the swelling behavior of PPG samples in CaCl2 salt solution. To do
so, the swelling experiments were carried out as previously described; the results were given to the software. CCD used these data to offer a mathematical model, which can predict the swelling percentage of PPG samples.
Based on the fit summary analysis, CCD suggested a quadratic model for the response.
Run | AAm/AA (mole ratio) | MBA (mole %) | Time (min) | Swelling (%) |
---|---|---|---|---|
1 | 4.82 | 14 | 90 | 240.73 |
2 | 9.65 | 20 | 3 | 49.39 |
3 | 4.82 | 20 | 90 | 228.91 |
4 | 9.65 | 4 | 180 | 420.77 |
5 | 4.82 | 4 | 90 | 267.21 |
6 | 2.41 | 20 | 3 | 27.45 |
7 | 9.65 | 4 | 3 | 65.78 |
8 | 4.82 | 14 | 180 | 374.68 |
9 | 2.41 | 4 | 180 | 157.54 |
10 | 4.82 | 14 | 3 | 67.18 |
11 | 2.41 | 14 | 90 | 69.10 |
12 | 2.41 | 4 | 3 | 31.88 |
13 | 4.82 | 14 | 90 | 248.88 |
14 | 9.65 | 20 | 180 | 252.09 |
15 | 4.82 | 14 | 90 | 258.05 |
16 | 2.41 | 20 | 180 | 95.91 |
17 | 9.65 | 16 | 90 | 199.68 |
Source | Sum of Squares | df | Mean Square | F-Value | p-value |
---|---|---|---|---|---|
Model | 11.8076 | 5 | 2.36152 | 154.4337 | <0.0001 |
A-AAm/AA | 1.919111 | 1 | 1.919111 | 125.502 | <0.0001 |
B-MBA | 0.262023 | 1 | 0.262023 | 17.1352 | 0.0016 |
C-Time | 6.48566 | 1 | 6.48566 | 424.1356 | <0.0001 |
A2 | 1.869314 | 1 | 1.869314 | 122.2455 | <0.0001 |
C2 | 0.448605 | 1 | 0.448605 | 29.33693 | 0.0002 |
Residual | 0.168206 | 11 | 0.015291 |
Since the vital properties of the model are in the statistically confident level of 95%, the proposed model is significant; these properties are the P-value less than 0.0001 and the F-value equal to 154.43. On the basis of ANOVA results, A, B, C, A2 and C2 terms are dominant factors, which have P-value less than 0.0500.
To adjust the response surface and the process parameters, CCD suggested a natural log transformation model. The value of R square was almost one (
Std. Dev. | 0.123659 | R-Squared | 0.985954 |
---|---|---|---|
Mean | 4.89977 | Adj R-Squared | 0.97957 |
C.V. % | 2.523766 | Pred R-Squared | 0.96118 |
PRESS | 0.464902 | Adeq Precision | 38.38345 |
ln ( Swelling % ) = + 5.78 + 0.44 × A − 0.16 × B + 0.81 × C − 0.9 × A 2 − 0.39 × C 2 (2)
where A, B, and C are the previously defined parameters as key factors.
The diagnostic tab showed the validation of the model by the normal (
Which process parameter can more affect response surface? To find the answer, CCD changed one factor over its entire range while other factors were kept constant. The perturbation plot is a useful approach to compare the effect of vital factors on the response surface. It checks the deviation of each parameter from a reference point defined by CCD. The lower parameter deviation, the more effective parameter.
The contour plot shown in
maximum swelling percentage at the low mole percentage of MBA and the average mole ratio of AAm/AA.
To optimize the swelling percentage of PPG samples in CaCl2 salt water, in the numerical optimization tab, we considered the variation range of each key parameter in the same as its previously defined range (
To check the accuracy of the proposed optimization solutions, we performed the synthesis experiments based on the suggested values by CCD (
Generally, we used CCD method to carry out synthesis experiments. The accuracy of the network structure of synthesized hydrogels was confirmed by FT-IR and SEM results. Swelling experiments revealed that the average amount of AAm/AA mole ratio, low amount of MBA mole percentage and high amount of swelling time could create optimal conditions to have a maximum swelling capacity. In the end, CCD proposed an empirical correlation, which could well predict the swelling behavior of PPG samples. Confirmatory experiments indicated that there were good agreements between actual and predicted results. Although there were some errors in suggested solutions for optimizing swelling conditions, they were negligible.
Solutions | AAm/AA (mole ratio) | MBA (mole %) | Time (min) | Desirability |
---|---|---|---|---|
1 | 6.94 | 4 | 180 | 1 |
2 | 6.94 | 4.5 | 180 | 1 |
3 | 6.94 | 5 | 180 | 1 |
4 | 6.5 | 4 | 180 | 1 |
5 | 7.3 | 4 | 180 | 1 |
6 | 7 | 4 | 180 | 1 |
Run | AAm/AA (mole ratio) | MBA (mole %) | Time (min) | Predicted swelling (S %) | Obtained swelling (S %) |
---|---|---|---|---|---|
1 | 6.94 | 4 | 180 | 609.98 | 607.54 |
2 | 6.94 | 4.5 | 180 | 603.92 | 600.76 |
3 | 6.94 | 5 | 180 | 597.92 | 598.32 |
4 | 6.5 | 4 | 180 | 603.10 | 601.65 |
5 | 7.3 | 4 | 180 | 603.61 | 601.98 |
6 | 7 | 4 | 180 | 609.67 | 606.96 |
The present study awards a significant empirical correlation to predict swelling behaviors of PPGs in CaCl2 salt solution. The accuracy of the presented correlation was verified by several synthesis experiments. Although the synthesis mechanism of hydrogels remains to be determined, the suggested correlation can be used as a diagnostic test for many of polymer researchers. Since PPG treatment is one of the best cost-effective approaches for oil and gas producers to control unwanted water production, our study provides the framework for future studies to assess PPG performance in CaCl2 salt solution.
The authors are grateful to the Shiraz University and Enhanced Gas Condensate Recovery Research Group for supporting this research.
The authors declare no conflicts of interest regarding the publication of this paper.
Heidari, S., Doust, J.S. and Esmaeilzadeh, F. (2018) Synthesis of Poly(AAm-co-AA) and Investigation of its Swelling Behavior: Using Response Surface Methodology (RSM). Modeling and Numerical Simulation of Material Science, 8, 65-78. https://doi.org/10.4236/mnsms.2018.84004