International Journal of Trend in Scientific Research and Development (IJTSRD) Volume 5 Issue 6, September-October 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470 @ IJTSRD | Unique Paper ID – IJTSRD47619 | Volume – 5 | Issue – 6 | Sep-Oct 2021 Page 1424 Numerical Simulation on Micromixing of Non-Newtonian Fluids in a Stirred-Tank Reactor by Using Parallel Reactions Atibeni, R.; Kamal, M.; Abduelmaged, A.; Ebrahim, A. Department of Chemical Engineering - Faculty of Engineering, Sabratha University, Sabratha, Libya ABSTRACT Micromixing of Non-newtonian fluid in a stirred-tank reactor with Rushton turbine is investigated numerically by using E model. It is characterized by the product selectivity of parallel competitive reactions. Model is implemented and is validated using experimental data in the literature. The simulations show that a higher agitation speed, and a feeding location closer to the discharge area of the impeller favor micromixing and the reaction rate. These results provide useful guidelines for the scale-up of industrial reactors of non-Newtonian fluid with parallel chemical reactions, and the comparison between the experimental and numerical results confirms the accuracy of the simulations. KEY WORDS: Mixing; Non-Newtonian fluids; E model How to cite this paper: Atibeni, R. | Kamal, M. | Abduelmaged, A. | Ebrahim, A. "Numerical Simulation on Micromixing of Non-Newtonian Fluids in a Stirred-Tank Reactor by Using Parallel Reactions" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456- 6470, Volume-5 | Issue-6, October 2021, pp.1424- 1429, URL: www.ijtsrd.com/papers/ijtsrd47619.pdf Copyright © 2021 by author (s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0) 1. INTRODUCTION: Today’s consumer society requires more, better quality and innovative products from a wide variety of industries, such as the production of plastics and synthetic resins, man-made fibers, polymers, paints and varnishes, drugs and pharmaceuticals, agricultural chemicals, food and drinks. All of these industries have one point in common: the raw materials are converted into final products by means of chemical reactions in an environment that involves fluid flow. mixing plays very important role in achieving the desired products and reducing unwanted by-products, which is very important from environmental and economic points of view. If mixing to a certain degree lets more materials react to form the wanted products, and reduces the amount of by-products, as a result there will be less amounts of waste to be treated and disposed to the environment. On the other hand, increasing the mixing speed or the fluid viscosity, increases the power needed to rotate the mixer, which would be more expensive and energy related to pollution will be caused. The use of non-Newtonian fluids is very frequent in many industrial operations, particularly in mixing processes. Such fluids often have complex rheological properties, which can increase operating costs and can create other problems during the mixing process. The viscosity, as one of the most important property of the fluid, has a great significance in processes, in which the rheological properties of the fluid are changing with time. Due to a close relation of the viscosity to torque on the impeller in the mixing vessel[1]. To achieve the desired degree of mixing with high efficiency and less by-products more research has to be carried out and that also will be beneficial for the environment. Much modelling as well as experimental work has been done to understand mixing and especially for micro-mixing [2, 3, 4, 5, 6]. The hydrodynamics of non-Newtonian flows at broad range Reynolds number generated by an axial impeller (A310) in a single-phase using CFD modeling and PIV measurement to validate results. The authors demonstrate that the flow field below the IJTSRD47619 International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47619 | Volume – 5 | Issue – 6 | Sep-Oct 2021 Page 1425 impeller is highly dependent on the rheological behaviour of the fluid [8]. Similar impact assessment studies of hydrodynamic conditions on mixing process [9,10], concerning the stability of Pickering emulsion (oil-water mixture with hydrophilic glass beads) in the baffled tank with Rushton turbine (RT) or pitched blade turbine (PBT). The authors found that the energy dissipated and the size of the high shear zone around the impeller are key information to create the emulsion with the desired droplet sizes. The heat transfer data for agitated Newtonian and non-Newtonian fluids related to Nusselt number depends on impeller diameter in the agitated vessel [11]. The authors, by using experimental data, correlated viscosity with of Reynold, Prandtl number and Nusselt Number, which were evaluated at the impeller tip. But still not enough to understand the mixing process of non-Newtonian. More studies will to be able to give better picture and understanding of mixing. Since mixing is connected to the environment through industry and it is a global concern to protect the environment; this work is concerned with mixing, especially micro-mixing of Non-Newtonian fluid in a stirred tank reactor with Rushton turbine which is investigated numerically by using E model and compared with experimental data in the literature[7]. 2. Engulfment models Mass balance for reaction zone: i i i Vr c EV dt Vc d + > < = ) ( , dt dV c dt Vc d V dt Vc d i i i + = ) ( ) ( i i i i r c c E dt dc + − ≥ ≤ = ) ( For irreversible, second order parallel reactions P B A K→  + 1 (2.1) Q C A K→  + 2 (2.2) A is the limiting reagent. The integral product distribution with respect to Q may be generally defined as. reacted A of mole yielded Q of mole X Q = (2.3) The states of mixing influence the product distributions in different ways for different sequences of adding reagents. 2.1. Addition of A to premixed B and C: V 0 C co C BO V AO C AO Fig.2.1 Addition of A to premixed B and C When mixing is perfect, no molecular-scale concentration gradients (or segregation) exist; the product distribution is determined by chemical kinetics. When segregation is complete, the product distribution does not depend on the kinetics, but on the relative frequency with which A comes in to contact with B and C, i.e., on the ratio of initial concentrations of C and B. Suppose that reaction (2.1) is instantaneous and the B and C is initially equimolar. XQ is written as 0 0 0 0 0 0 ) ( A A C A C Q C V C V AM V C V X + − = (2.4) When partial segregation exists, product distribution may be analyzed in terms of the E model of micromixing. When self-engulfment is negligible, according to E model, the mass balances of substances A, B, and C give C A B A A A A c c k c c k c c E d dc 2 1 ) ( − − − > < = α (2.5) B A B B B c c k c c E d dc 1 ) ( − − > < = α (2.6) C A C C C c c k c c E d dc 2 ) ( − − > < = α (2.7) if the first reaction can be treated as instantaneous A and B cannot coexist at a given point and a new composition variable u may be introduced: B A c c u − = (2.8) It follows that. 2 u u C A + = (2.9) 2 u u CB − = (2.10) Eqs (2.5) and (2.6) then simplify to a single equation 2 ) ( 2 u u c k u u E d du C + − − > < = α (2.11) International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47619 | Volume – 5 | Issue – 6 | Sep-Oct 2021 Page 1426 Whilst Eq (2.7) becomes 2 ) ( 2 u u c k c c E d dc C C C C + − − > = α (2.12) Dimensionless variables for the solution of Eqs (2.11) and (2.12) may be introduced using CA0 as reference concentration: 0 A i i c c C = 0 A c u U = (2.13) av E T α = (2.14) Eqs (2.11) and (2.12) written in dimensionless form become Cc U U D U U dT dU a 2 ) ( + − − > < Φ = (2.15) Cc U U D C C dT dC a C C C 2 ) ( + − − > < Φ = (2.16) av A E c k Da 0 2 = (2.17) υ ε av av E 058 .0 = (2.18) ν ε 3 5 N Npd av = (2.19) av ε ε = Φ (2.20) Where the ф is the specific local energy dissipation rate. Da is the ratio of characteristic times for micromixing by engulfment and chemical reaction. This dimensionless number can also be written in terms of the concentration which the reagent A would have if it had all been added to the reactor and well mixed before reacting. Average Damkohler number Daav can then be used instead of Da: av A E AM a c k Da ) 1 ( 0 2 + = (2.21) 0 0 ) 1 ( AV AM f V a − = (2.22) The initial conditions for the reaction zone and the surroundings are given by Eqs (2.23) and (2.24) respectively. 1 ) 0 ( = U 0 ) 0 ( = CC (2.23) a c c U A B 1 0 0 − = − >= < a c c C A C C 1 0 0 = >= < (2.24) C Q C AM a X ) 1 ( 1 + − = (2.25) The mass balance to update the concentration in the surroundings is therefore. [ ] j a AM C C AM j a C j i j i j i + Φ + > < Φ − + >= < − σ θ θ θ σ / ) exp( ) ( / ) exp( 5 .0 . 1 . 5 . 0 . (2.26) Where j = 0 corresponds to the known concentrations in Eq. (2.24). In the present work, we made some modification to this model to suitable for the calculation of Non-Newtonian fluid. I.e. before they did not consider side reaction when they chose the precipitation reaction as one of the two parallel competing reactions. This is probably because in their case, the limited concentrated sodium hydroxide was fed rapidly into the vessel. The fast injection may reduce the chance of the formation of [Cu2 (OH)2]SO4. It should be pointed out that in the rapid feed case, it is macro- and meso-mixing rather than the micromixing that determines the distribution of product of complex reactions. But in our case, the limited concentrated sodium hydroxide was fed very slowly in to the vessel. That means, slow injection give the chance for the formation of [Cu2(OH)2]SO4, and micromixing is the controlling regime. For that, we added ( ) f − 1 to equation (2.22), where f is the factor of copper ion loss due to side reactions. According to the literature the following assumptions are made for the formation of a flow field generated by a Rushton turbine in a stirred tank. Mean flow is characterized by plug circulation flow along one streamline. The tank can be divided in to 6 characteristic flow regions, that is, region 1: impeller swept volume; region 2: radial flow in turbine discharge; region 3: axial flow along the wall; region 4: radial flow near top or bottom; region 5: axial flow along the shaft and region 6: flow in the center. These regions are shown in fig (2.2). International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47619 | Volume – 5 | Issue – 6 | Sep-Oct 2021 Page 1427 Fig 2.2 Schematic diagram of flow field Table 2.1 ф correlations for each region [12]. Region ф correlations 1 ф1 = 33.8 2 ф2 = 178.6 r* - 55 for 1/3 < r* < 0.46 ф2 = 268.7 exp(- 4.98 r*) for 0.46 < r* < 0.8 3 ф3 = 1.7 exp(- 2.5 z*) for upper loop ф3 = 1.7 exp(- 6.1 z*) for lower loop 4 ф4 = 0.02 + 0.08 r* 5 ф5 = 2.23 – 1.95 z* for upper loop ф5 = 2.45 – 5.21 z* for lower loop 6 ф6 = 0.08 In the present work. r* = r/R for the feed position (2) r* = 0.4075 that means the feed position at region 2 in this case ф2 = 178.6 r* - 55 = 178.6 * 0.4075 – 55 = 17.78 But the feed position (1) at the region 5 in this case ф5 = 2.23 – 1.95 z* z* = z / R = 0.912 for position (1), that means ф5 = 2.23 – 1.95 * 0.912 = 0.45 In this work we use different impeller diameter for that we suppose ф at the feed position (1) is 0.4 and 20 at feed position (2) approximately. 3. Results and discussion The Engulfment model were used to calculate XQ, and the results compared with experiment [7],were pictured in Fig 3.1~3.3. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47619 | Volume – 5 | Issue – 6 | Sep-Oct 2021 Page 1428 50 100 150 200 250 300 0 .00 0 .05 0 .10 0 .15 0 .20 0 .25 0 .30 A tibeni(2016), location L1 Sim ulation, location L1 A tibeni(2016), location L1 Sim ulation, location L1 X Q N (r.p .m ) Fig (3.1) XQ vs. N Exp and Cal for 0% HEC and two feed position 50 100 150 200 250 0.0 0.1 0.2 0.3 0.4 Atibeni(2016),location L1 Simulation, location L1 Atibeni(2016),location L2 Simulation, location L2 XQ N (r.p.m) Fig (3.2) XQ vs. N Exp and Cal for 0.1% HEC and two feed position 100 150 200 250 300 350 400 450 500 0.0 0.1 0.2 0.3 0.4 XQ N (r.p.m) Atibeni(2016),Location L1 Simulation, Location L1 Atibeni(2016),Location L2 Simulation, Location L2 Fig (3.3) XQ vs. N Exp and Cal for 0.5% HEC and two feed position International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47619 | Volume – 5 | Issue – 6 | Sep-Oct 2021 Page 1429 The data obtained when the NaOH solution was added just below the free surface of the liquid and in the impeller discharge flow. Higher selectivity when the feed located at the surface. This can be explained by the widely varying energy dissipation rates throughout a stirred tank reactor with the local energy dissipation rates near the liquid surface much smaller than the impeller discharge. This leads to the segregation between reactants being greater offering a larger chance for the side reaction to occur. Thus, for each speed, XQ decreases in going from position (1) to position (2), i.e. from position of low to high local energy dissipation rates, position (2) in the impeller discharge, This feed position has very good micromixing. Figure (1,2,3) shows that XQ different for different feed position. And the same observation for different HEC concentration. also shows that the comparison between experimental results and E model is good especially the trend of the curve is very well for all HEC concentrations also the relation between the by-product and the speed for different feed position and different viscosity is very well for experimental results and also E model. 4. CONCLUSION The effects of impeller speed, feed position and viscosity on the yields of by-product (XQ) were investigated. The experiments results show that XQ as a measure of the amount of by product was strongly depends on the viscosity of the liquid. XQ increases greatly as the viscosity of HEC increases, and decreases with increasing impeller speed. As we may expect, feeding at the impeller region has a lower XQ than feeding at the liquid surface due to the difference of local energy dissipation. the engulfment model (E- model) was modified to suit the working reactions in this work. The product distributions predicted by modified E-model were in reasonable agreement with the experimental data. The results are of importance to the design and scale-up of industry stirred reactors with fast complex reactions. 5. References [1] M. Dular, T. Bajcar, L. Slemenik-Perse, M. Zumer and B. Sirok, Numerical Simulation And Experimental Study Of Non-Newtonian Mixing Flow With A free Surface, Brazilian Journal of Chemical Engineering, Vol. 23, No. 04, pp. 473 - 486, October - December, 2006 [2] Bourne, J. R. and Yu, S., An experimental study of micromixing using two parallel reactions, Proc 7th Eur Conf Mixing, Belgium, 18–20, September, 1991, 67–75. [3] Baldyga, J., Bourne, J. R. and Hearn, S. J., Interaction between Chemical reactions and mixing on various scales, [J] Chem Engng Sci, 1997, 52: 457–466. [4] Ying Han, Jia-Jun Wang, Xue-Ping Gu, Lian- Fang Feng, Numerical simulation on micromixing of viscous fluids in a stirred-tank reactor, Chemical Engineering Science, 2012, 74, 9-17. [5] Baoqing Liu, Yijun Zheng, Bolin Huang, Luyan Qian, Zhijiang Jin, The influence of feeding location on the micromixing performance of novel large-double-blade impeller, [J] The Taiwan Institute of Chemical Engineers, 2015, 52, 65–71 [6] Yanli Qu, Jingcai Cheng, Zai-Sha Mao and Chao Yang, A perspective review on mixing effect for modeling and simulation of reactive and anti solvent crystallization processes, React. Chem. Eng., 6, pp 183-196, 2021 [7] Rajab. A. Atibeni, Kamal M. Sassi, Mustafa T. Yagub, The Influence of Viscosity on Micromixing Process for Non-Newtonian Fluids, University Bulletin – ISSUE No.- 18- Vol. (2) – May - 2016. [8] del Pozo, D.F.; Liné, A.; Van Geem, K.M.; Le Men, C.; Nopens, I. Hydrodynamic analysis of an axial impeller in a non-Newtonian fluid through particle image velocimetry. AIChE J. 66, 6939, 2020. [9] Abdulrasaq, U.K.; Ayranci, I. The effect of hydrodynamic parameters on the production of Pickering emulsions in a baffled stirred tank. AIChE J. 65, 16691, 2019. [10] Tsabet, È.; Fradette, L. Effect of the properties of oil, particles, and water on the production of Pickering emulsions. Chem. Eng. Res. Des. 97, 9–17, 2015. [11] Sk, A.A.; Kumar, P.; Kumar, S. Effect of impeller diameter on Nusselt number in mechanically agitated vessel. Int. J. Num. Meth. Heat Fluid Flow. 30, 2225–2235, 2020. [12] Shengyao. YU, 1993, “Micromixing and parallel reactions”, for the degree of Doctor of Technical Sciences. Zurich. Diss. ETH No. 10160