An experimental investigation on the turbulent drag reduction effect of polyacrylamide solution in the loop pipe

doi:10.21203/rs.3.rs-4878052/v1

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An experimental investigation on the turbulent drag reduction effect of polyacrylamide solution in the loop pipe

https://doi.org/10.21203/rs.3.rs-4878052/v1

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Flexible long-chain polymer molecules with linear structures are widely used in the field of turbulent drag reduction. However, there is no single mechanism that can fully explain all the experimental phenomena of polymer drag reduction. In this paper, we have investigated the relationship between polymer macro-microscopic factors and loop pipe(inner diameter 32mm, wall thickness 3mm, length 19.02m) flow parameters to explain the polymer turbulent drag reduction and degradation mechanisms. Our conclusions are as follows: drag reduction exists in saturated concentration, the higher the Reynolds number corresponds to the larger saturated concentration; there is a maximum drag reduction Reynolds number(Re_max), the higher the concentration corresponds to the larger Re_max; with concentration θ=100ppm (parts per million) and molecular weight increasing, the drag reduction efficiency increases; with θ=100ppm, the solution shows shear thinning behavior, so the polymer molecules are mechanically fractured; in the concentration range θ=2-20ppm, with concentration and polymer particle size in solution increasing, the distribution range becomes wider; the Weissenberg number(Wi) is related to the molecular weight, and the solution shows a better elasticity with the Wi increasing. This paper elucidates the impact of macro-microscopic factors on the elasticity of polymers, thereby enhancing the understanding of the relationship between polymer elasticity and drag reduction efficiency.

Turbulent drag reduction

Polyacrylamide (PAM)

Macro-microscopic

Pipe

Elasticity

The saturation concentration has been found and defined during polymer drag reduction in loop pipe;
A relationship among maximum drag reduction DR_max, Wi, polymer molecular weight and solution concentration has been established;
Turbulent drag reduction and degradation mechanism have been revealed by macro-experimental phenomena and polymer microstructures.

In the high Reynolds number turbulent condition, adding a very small amount of polymer molecules in pipe can obtain a huge energy reduction, in which drag reduction efficiency(DR) can reach more than 80%[1]. As a result, various types of polymer dampeners are widely used in the field of turbulent drag reduction [2–5]. Flexible long-chain polymer molecules with a linear structure are considered to be the most effective drag reducers [6], and polyacrylamide (PAM) is currently common [7]. However, polymers’ turbulent drag reduction behavior and viscoelasticity are not only affected by external macroscopic factors such as Reynolds number(Re) and polymer concentration(θ) but also by internal microscopic factors such as polymer molecular weight, molecular chain structure, and chain flexibility and aggregation [8–11].

Concerning the macroscopic influence of the polymer, it was found that the drag starts to decrease only when the Reynolds number reaches a certain critical value and that there exists a maximum Reynolds number for maximum drag reduction efficiency [12]; polymer concentration has a significant effect on the drag reduction phenomenon, and there exists a critical concentration. Li [13], Andrade [14], and Soares [15] et al measured the drag reduction properties of aqueous solutions of polyacrylamide (PAM) at different concentrations and Reynolds numbers using a rotational rheometer and a pipeline, and they concluded that the Reynolds number affects the degree of stretching of the polymer molecules; Khadom [16], Sandoval [17], Sitaramaiah [18], Varnaseri [19], Wahaibi [20], Hoyt [21], and Jouenne [22] explored the drag reduction phenomena and rheological behavior of PAM solutions in the concentration range of 50 to 2000 ppm (parts per million). They found that the DR ranged from 30–80%, increasing with increasing molecular weight, concentration, and flow rate.

Concerning the microstructural influences of the polymers, DR increases with the molecular weight of the polymer and it can reach a maximum reduction asymptote for polymer drag reduction at lower θ and lower Re, meanwhile, polymers suffer permanent mechanical degradation at a high shear rate [23, 24]. Karami [25], Culter [26], and Ivchenko [27] have found that polymer molecular weight, polymer main chain length and rigidity affect the turbulent reduction efficiency and fracture degradation, with linear flexible polymers being effective in reducing drag and rigid polymers being better able to resist shear degradation. Soares [24], Hunston [28], Buchholz [29], and Brandfellner [30] have found that polymer chain fracture will reduce the polymer molecular weight distribution and DR and that the bond breaks are not random, but vary along the length of the polymer backbone. Vanapall [31] established scaling relationships for the applied wall shear rate induced by turbulence concerning polymer chain fracture, which validated this scaling law at higher Re by Elbing [32]. Cussuol [33] further investigated the effect of polymer depolymerization on DR and found that a solution of 150 ppm PAM recovered 83% of its initial value 21 days after pre-shearing.

Since Toms proposed the theory of additive drag reduction, there have been various mechanisms for polymer drag reduction, mainly shear thinning [1], effective slip [34], turbulence intensity suppression [35, 36], viscous theory [9, 37], and elasticity theory [38]. Recently Housiadas [39] studied the effect of high elasticity and Re on drag reduction and systematically analyzed the elastic and inertial effects in viscoelastic turbulent channel flow, though no theory can fully explain all the experimental phenomena of polymer turbulence drag reduction. As a result, along with the wide application of polymer drag reducers, the critical concentration of polymer drag reducers, maximum drag reduction Reynolds number, polymer molecular weight, polymer turbulence drag reduction mechanism, and its fracture degradation mechanism have triggered a wide range of attention from research scholars. This paper will investigate the relationship between the relationship between polymer macro-microscopic factors and loop pipe(D = 32 mm, δ = 3 mm) flow parameters to explain the polymer turbulent drag reduction and fracture degradation mechanisms.

Materials

Polyacrylamide (PAM) used in our test is produced by Shanghai Dipper Co., LTD., China. The flow time of 1 mol/L NaCl solution and polyacrylamide solution with a concentration of 0.0005 ~ 0.001g/mL is measured using a non-dilute U-viscometer of model 4-0.57mm, and the intrinsic viscosity and molecular weight are calculated based on Eq. (1) and the measured values of Mark-Houwink Eq. (2), and the results are shown in Table 1 below.

$$[\eta ]=\frac{{\sqrt {2\left( {{\eta _{{\text{sp}}}} - \ln {\eta _{\text{r}}}} \right)} }}{\theta }=\frac{{\sqrt {2\left[ {\left( {{t_1}/{t_0} - 1} \right) - \ln \left( {{t_1}/{t_0}} \right)} \right]} }}{{m{w_1}}}$$

$$[\eta ]=K{M^\alpha }$$

Where, η_sp is the value of incremental viscosity; η_r is the value of relative viscosity; θ is the value of the concentration of the test solution, g/dL; t₁ and t₀ is the time for the test solution and 1 mol/L NaCl solution to flow across the viscometer mark, s, respectively; is the mass of the test material, g; w₁ is the mass fraction of the solids content; [η] is the value of the intrinsic viscosity, dL/g; α and K is the empirical constants, α = 0.66, K = 3.73×10^− 4dL/g.

Table 1

The Molecular weights of 5 polyacrylamide samples
Sample number	Time (t)	Relative viscosity	Incremental viscosity	Intrinsic viscosity(dL/g)	Molecular weight (g/mol)
Sample 1	139.8	1.40	0.40	6.72	2805193
Sample 2	124.2	1.25	0.25	4.46	1506913
Sample 3	118.5	1.19	0.19	3.37	986454
Sample 4	113.3	1.14	0.14	2.59	663245
Sample 5	123.3	1.24	0.24	6.98	2969817

Filtered purified water and polyacrylamide (PAM) solution are used in our test. Soares [40] found that there was no increase in shear viscosity after 48h of solution dilution time. Therefore, considering the biodegradation factor and the mechanical degradation of the stirrer, an appropriate amount of solid polyacrylamide is dissolved in 50L of water and mixed and stirred for one hour ahead of time, 24h, until a homogeneous solution has been reached. The test details and conditions are shown in Table 2.

Table 2

Test details and conditions
Test sample	Concentration(ppm)	Molecular weight (g/mol)	Test condition	Purpose of the experiment
PAM	25, 50, 100, 150, 200, 300	2.97×10⁶	Room temperature; 15-50hz	Exploring the concentration effect and the Reynolds number effect
	100	6.63×10⁵; 9.86×10⁵; 1.50×10⁶; 2.80×10⁶	Room temperature; 15-50hz	Exploring the molecular weight effect
	300	6.63×10⁵; 9.86×10⁵; 1.50×10⁶; 2.80×10⁶	Room temperature; 15-50hz, Tested at half-hour intervals	Exploring shear resistance

Experimental setup and measurements

The experimental devices used in the experiment are the loop pipe experimental device, and the model NDJ-5S rotary viscometer and U-viscometer for the viscosity test.

The loop pipe experimental device (Fig. 1) is a single-phase flow cycle device, which consists of a nitrogen purge system, a turbulence cycle test system (including temperature control and pressure difference measurement), an additive quantitative injection system, and a test fluid recovery and sampling system. The test loop pipe length L = 19.02m, the loop pipe inner diameter D = 32mm, the pipe wall thickness δ = 3mm, and the material is cast plate acrylic pipe.

An FM motor is used to control the rotational speed n of the pump by adjusting the frequency f to set the flow rate Q. During the experiment, 50L of the sample to be tested is loaded into the tank, so that the sample to be tested flowed through the pump, the flow meter, the pressure transducers, and finally returned to the tank, and the flow is circulated. The f is increased by 0.5hz from 15hz to 50hz at 10s intervals, and the digital recorder is used to record the data of the flowmeter, thermometer, and pressure transducers at 1s intervals.

The DR is evaluated by measuring the pressure drop ΔP₀, ΔP_a in the loop pipe before and after the addition of the polymer under constant flow conditions, or by measuring the flow rate Q₀, Q_a under constant pressure drop conditions, as shown in Eqs. (3) and (4).

$$DR=(1 - \frac{{\Delta {P_{\text{a}}}}}{{\Delta {P_0}}}) \times 100\%$$

Where, ΔP_a and ΔP₀ are the pressure drop of the additive-polymer and additive-free at the same flow rate, Pa, respectively.

$$DR=(1 - \frac{{{Q_{\text{a}}}}}{{{Q_0}}}) \times 100\%$$

Where Q_a and Q₀ are the flow rates of additive-polymer and additive-free at the same pressure drop, m³/h, respectively.

Repeatable effects

To test the reliability of the device, in standard operation, our test has been repeated in summer and winter for the pure water solution and polyacrylamide solution, respectively. The f is 15hz-50hz, and the results are shown in Fig. 2, and the curves tested for the same kind of samples are overlapped, which indicates that the device is reliable. For the polymer solution, the molecular weight M_v=2.97×10⁶g/mol, θ = 300ppm PAM solution has a flow distribution in the range of 3-12m³/h, which lies below the curve of the pure water solution, showing a drag reduction effect.

Concentration effect

The f is controlled at 15-50hz and the T = 24–28°C in loop pipe. Solutions of polyacrylamide with θ of 25, 50, 100, 150, 200, and 300 ppm are tested and the results are shown in Fig. 3. The polymer molecular interaction diagram is shown in Fig. 5 (a) and the conclusions are as follows: (1) The DR curves of polymers with different Re first increase with increasing θ in the early stage. Before the saturation concentration, the polymer molecules are relatively dispersed in the solution, thus an increase θ will increase the number of effective molecular chains for drag reduction; (2) After reaching the saturation concentration, the DR starts to decrease, according to the concentration effect. Meanwhile, the higher the Re is, the larger the corresponding saturation concentration is. This is because when a polymer concentration is greater than the saturation concentration, the long polymer chains become entangled with each other, requiring a stronger turbulent force to rearrange the polymer molecules to perform drag reduction. Therefore, there is an optimal operating polymer condition, in which the polymer can play its better drag reduction effect.

Reynolds number effect

Our tests are carried out on solutions with θ of 25, 50, 100, 150, 200, and 300 ppm at T = 24–26℃, Re ranged from 15000 ~ 120000 in a turbulent flow. The test results are shown in Fig. 4 and the interaction of the polymer chains is represented in Fig. 5 (b): (1) The maximum drag reduction Reynolds number(Re_max), has been reached for polymers at θ = 25-50ppm in the initial test case, where the polymer long-chain molecules are fully stretched, with a maximum DR of 37%. As the Re increases, the fluid turbulence and the recirculating flow through the pump cause some of the polymer long-chain molecules to be fractured, which results in the DR decreasing. The lower θ is, the more polymer molecules are fractured and the greater the slope of the curve is; (2) The long chains of polymer molecules at θ = 100-300ppm are initially entangled with each other. The higher θ is, the more effective the long chains of polymer molecules are after being stretched, and the higher the slope of the curve is. After being stretched, the polymer molecules will be shared by the polymer molecules through the pump. The viscosity of the solution will decrease, and the drag reduction effect of the long-chain polymer molecules will be lost. The Re_max=78000–80000, and the higher the concentration is, the larger the Re_max is. When Re > Re_max, DR starts to decrease.

Molecular Weight Effect

In the loop pipe, PAM solutions with different molecular weights at θ of 100 and 300 ppm have been tested, within f = 15-50hz and T = 24–28°C. The results are plotted in Fig. 6 and Fig. 7. From Fig. 6, it can be concluded as shown below that at θ = 100ppm, the DR of the polymer increases as the molecular weight of the polymer increases, showing a positive correlation [41]. As shown in Fig. 6 (a), taking the critical flow rate Q_c=7-8m³/h, when the flow rate Q < Q_c, the long-chain polymer molecules can give full play to their roles, and the DR increases; when the flow rate Q > Q_c, the molecular weight of the long-chain polymers is broken by turbulent flow and replaced by polymers with low molecular weights that have limited drag-reducing ability, and thus DR gradually decreases. Converted to Re, as shown in Fig. 6(b), polymer solutions with high molecular weights have higher apparent viscosities, and thus higher DR can be achieved at lower Re.

Comparing with Fig. 6(a) and Fig. 7, the results of PAM solutions with θ of 100 and 300ppm, the conclusions are as follows: (1) Increasing the θ of low molecular weight PAM solution can significantly improve the DR. The initial drag reduction rate of θ = 300 ppm M_v=6.63×10⁵g/mol PAM solution is 8.7% higher than that of θ = 100ppm PAM solution, and the drag reduction rate can reach 27.7% at the flow rate Q = 7m³/h. This is because the increased concentration allows more polymer long-chain molecules to play the role of drag reduction in turbulent flow; (2) Increasing the θ of PAM solutions with high molecular weight causes the long-chain polymers to become entangled with each other, increasing the apparent viscosity and requiring some resistance to separation. Therefore, the higher the molecular weight at the initial test stage is, the greater the reduction in DR, which is 3.7% and 1.3% for M_v=1.50×10⁶g/mol and M_v=9.86×10⁵g/mol PAM solutions at Q = 3.5 m³/h, respectively. Then, along with the increase of turbulence intensity, the long-chain polymer molecules are untangled, and the DR gradually increases, the higher the molecular weight is, the higher the slope of the curve is, and at the flow rate of Q = 12m³/h, the DR of PAM solutions with molecular weights M_v=9.86×10⁵ g/mol and M_v=1.50×10⁶ g/mol is increased by 9.7% and 11.5%, respectively.

Shear resistance behavior

To evaluate the shear resistance of PAM solutions with different molecular weights and different concentrations, in our experiment, we take PAM samples at f of 15hz, 20hz, 30hz, 40hz, and 50hz for the viscosity test, and the results are shown in Fig. 8. Under the same shear situation, the viscosity of PAM solution decreases gradually with the increase of shear rate. The larger the molecular weight of the solution is, the greater the slope of the curve is.

After the completion of the first test of the PAM solution, the test has been repeated at an interval of half an hour and the results are shown in Fig. 9. Our conclusions are as follows: (1) In the first test, Re_max is observed, which the DR declines as the Re exceeds Re_max. Conversely, in the second test, an increase in DR correlates with a continuous enhancement in Re, with the curve ultimately leveling off; (2) When θ = 100ppm, the higher the DR of the polymer solution with high molecular weight, the stronger the shear resistance of the polymer, and the smaller the slope when the curve is reduced; (3) Compared with the first test, the DR is significantly lower in the second test, and the gap between the two test curves decreases as the Re increases, and the larger the molecular weight, the smaller this gap becomes. The difference in DR for PAM solutions with molecular weights M_v=1.50×10⁶g/mol and M_v=9.86×10⁵g/mol is 13.7% and 27.8% at Re = 30,000 and 4.4% and 4.7% at Re = 100,000, respectively. This is due to the first test when subjected to mechanical shear action, the molecular chain is easy to break at the point of rapid fracture. The number of molecular chains increases, and each molecular chain subjected to shear force becomes smaller, the second test then continues to break the chain. For these reasons, high molecular weight polymer solutions have better shear resistance and tend to equilibrate more quickly.

Currently, there are two main explanations for the mechanism: (1) Polymer interaction decomposition, polymer radicals react with dissolved oxygen to form polymer peroxyl radicals, and then Chain scission occurs by a bimolecular reaction between two polymer peroxyl radicals [7]; (2) Polymer chain decomposition, that is, mechanical breakage of the polymer chain. In our experiment, the 30 minutes of standing time as shown in Fig. 9 can not help the polymer long-chain molecules to recover their original drag-reducing ability, suggesting that the polymer molecular chains underwent mechanical breakage the chains. Consistent with the experimental findings of Zhang [42]. Meanwhile, Cussuol [33] found that after pre-shearing the PAM solution, there is a large decrease in the DR after 30 minutes, and even after 21 days only 83% of the initial value of the DR can be recovered, suggesting that irreversible breakage of the polymer chain occurred.

Mechanism discussion

The molecular structure of polymer long chains and the turbulent drag reduction behavior of polymer long chains are demonstrated in Fig. 10. The spatial structure, chain geometry, and flexibility presented by the polymer solution all have a large impact on the drag reduction behavior. Figure 11 shows the particle size distribution of PAM solution at different concentrations, it can be seen that the particle size of PAM in pure water is in the range of 164 nm at concentrations θ = 2ppm and 4ppm. Along with the increase in concentration, the particle size becomes larger and the range of the distribution becomes wider, which suggests that the increase in concentration results in the entanglement of the polymer long-chain molecules with each other. Similarly, the higher the molecular weight of the polymer at high concentration is, the deeper the curling and entanglement of the long-chain molecules are, and the lower the initial drag reduction is, as shown in Fig. 7.

Utilizing the intrinsic viscosity of the polymer, based on the Flory-Fox formula [43], the mean radius of gyration of the polymer can be determined.

$$[\eta ]={\Phi _0}{(\frac{{{h^2}}}{M})^{3/2}}{M^{1/2}}$$

$$R_{g}^{2}=\frac{{{h^2}}}{6}$$

Where $\frac{{{h^2}}}{M}$is a parameter characterizing the flexibility of the polymer chain; $[\eta ]$ is the intrinsic viscosity, mL/g; is the mean square end distance, cm; ${\Phi _0}$ is a universal constant independent of the nature of the polymer, ${\Phi _0}=2.84 \times {10^{23}}{\text{mo}}{{\text{l}}^{ - 1}}$;$R_{g}^{{}}$ is the mean square radius of gyration, cm.

Since the polymer moves with the surrounding solvent and other particles as it flows in solution, the relaxation time of the linear flexible polymer is calculated using the Zimm theory [43, 44] and shown as shown in Eq. (8).

$$\lambda =\frac{{{\mu _S}R_{g}^{3}}}{{{k_B}T}}$$

Where k_B is Boltzmann's constant, 1.38×10^− 23 J·K^− 1; T is the temperature, K; ${\mu _S}$ is the solvent viscosity, Pa.s.

Weissenberg number(Wi) involving relaxation time is defined as shown in Eq. (9).

$$Wi=\lambda \dot {r}=\lambda \frac{{8u}}{D}=\frac{{8u{\mu _S}R_{g}^{3}}}{{D{k_B}T}}$$

Where u is the average velocity, m/s; and D is the pipe diameter, m.

The Wi of PAM solutions of different molecular weights and concentrations are calculated using Eqs. (7) and (9) displayed in Table 3 and Fig. 12, from which the following conclusions have been obtained: (1) At the same concentration, along with the increase of Wi, the maximum drag reduction rate DR_max of different molecular weights increases, and the Wi number increases from 0.005 to 0.113, and corresponding to the increase of DR_max from 13.5–28.2%. Higher Wi implies that the solution has higher elasticity, which inhibits the vortex structure, suggesting that the elasticity of the polymer promotes drag reduction. The higher the elasticity is, the more obvious this facilitating effect is. (2) Comparing the Wi at different concentrations for a given molecular weight, it is found that an increase θ leads to an increase in the Wi corresponding to DR_max, suggesting that an increase θ promotes the elastic action of the polymer. (3) At DR < DR_max, the drag reduction rate increases with increasing Wi; whereas in the later stages of the experiment, the molecular weight of the polymer decreases due to the shear effect of the pump, which results in the curve starting to decrease after reaching DR_max.

Table 3

Maximum drag reduction DR_max and Wi for different molecular weights and concentrations
Molecular weights M_v(g/mol)	Rg (nm)	Concentration θ(ppm)	Maximum drag reduction DR_max(%)	Weissenberg number Wi
663245	34.54	100	13.5	0.005
663245	34.54	300	27.8	0.009
986454	43.03	100	17.0	0.015
986454	43.03	300	29.4	0.027
1506913	54.40	100	18.4	0.032
1506913	54.40	300	31.3	0.061
2805193	76.72	100	28.2	0.113

In our experiment, the drag reduction effects of polyacrylamide in a loop pipe have been investigated. The DR is determined by the pressure drop at the same flow rate, and the main conclusions are as follows:

(1) The saturation concentration of the PAM solution exists, and the higher Re corresponds to the larger saturation concentration; the DR of the polymer is related to the state of the polymer long-chain molecules.

(2) The Re ranges from 15000–120000 in a turbulent flow. In the θ = 25-50ppm, the maximum drag reduction Reynolds number Re_max is reached, and with the increase Re, the DR decreases. In the θ = 100-300ppm, when the Re < Re_max, along with the Re increasing, DR increases; with the Re sequentially increasing, when the Re > Re_max, DR decreases.

(3) The DR increases as the polymer molecular weight increases. At the beginning of the test, increasing θ, the DR increases for low molecular weight PAM solutions, while for high molecular weight PAM solutions, the DR decreases.

(4) The PAM solution’s viscosity decreases gradually with the shear rate increases, and the larger the polymer molecular weight is, the larger the slope of the curve is. Meanwhile, the long-chain polymer molecules inevitably undergo mechanical fracture in the solution, and the larger the molecular weight is, the stronger the shear resistance of the polymer shows.

(5) In the θ = 2-20ppm, as the θ increases, the particle size of the PAM solution increases, along with a wider distribution. The increase θ causes the polymer long-chain molecules to entangle with each other. The Wi number is related to the molecular weight and concentration, and increasing the Wi number can make the solution have better elasticity and inhibit the vortex structure in the flow, thus increasing the DR.

Author contribution Yang Chen designed, analyzed the work and wrote the main text. Minlan He prepared figures, and wrote the manuscript. All authors reviewed the manuscript.

Acknowledgments We would like to acknowledge support from assistance from Ufa State Petroleum Technological University and Southwest Petroleum University.

Funding information This work was supported by the National Natural Science Foundation of China (No.52004241), the Natural Science Foundation of Sichuan Province (No.2022NSFSC1018), the Open Fund Project of SINOPEC Key Laboratory for EOR of Fractured-vuggy Reservoir（34400000-22-ZC0607-0006）and the China Scholarship Council (No.201508090094).

Availability of data and materials The datasets used in the current study are available from the corresponding author upon reasonable request.

Ethical approval Ethical approval is not applicable.

Conflict of interest The authors declared that they have no conflicts of interests in this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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No competing interests reported.

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An experimental investigation on the turbulent drag reduction effect of polyacrylamide solution in the loop pipe

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Abstract

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Highlights

Introduction

Materials and method

Materials

Experimental setup and measurements

Results and discussion

Repeatable effects

Concentration effect

Reynolds number effect

Molecular Weight Effect

Shear resistance behavior

Mechanism discussion

Conclusion

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1