Hydrodynamic modeling of the jet bubbling reactor


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1 Hydrodynamic modeling of the jet bubbling reactor CORNEL MUNTEA*, IOAN CĂLDARE**, IOAN GIURCA*, DORIN CRISTIAN NĂSTAC*** * Building Services Engineering Department, Technical University of ClujNapoca ** Mechanic Engineering Department, Technical University of ClujNapoca *** Building Services Engineering Department, Transilvania University of Braşov Boulevard December 21, no , , ClujNapoca Romania Abstract: This paper presents a hydrodynamic model for a very diluted pollution absorber, the jet bubbling reactor (JBR). Also it propose a mathematical model for the principal reactor features using the mass transfer local coefficients, k G and k L, in accordance with the double film theory. KeyWords: jet bubbling reactor, hydrodynamic modeling, reaction solution, sulfur dioxide, flue gases, flue gas desulphurization. 1 Introduction The retention of sulfur dioxide from flue gases is mainly by washing them with a solution of reactant. The absorption of gases in solutions is a physicalchemical process in which two phenomena occur: mass transfer, which is a physical process, followed by chemical reaction. Because chemical reactions are dependent on the physical and chemical properties of reactants, just mass transfer is influenced by the type and characteristics of reactors used. The present paper aims to analyze a reactor used less flue gas desulphurization, the jet bubbling reactor. This, in the principle, is made up of a lot of vertical pipes, immersed in the reaction solution (fig. 1). The reactor is continuously fed with the reaction solution of a given concentration is, also, continuously removed from the reactor at a rate corresponding to the solution containing the reaction product. Through vertical pipes, the flue gas are blown in the reaction solution, and this, because Archimedes Force of liquid, bubbled through the liquid upward vertical assigning gas bubbles are circular, outside pipes bubbling. 2 Model presentation In the analysis that follows we will focus on a single vertical pipe with diameter (d) (wall thickness is neglected) and depth of immersion (h) (fig. 2). Fig. 1 Jet Bubbling Reactor CT 121 Fig. 2 Hydrodynamic model scheme ISBN:
2 We consider the following working hypotheses:  stationary working regime  gases that go with a certain velocity in the liquid layer, immediately receive upward vertical velocity, around the pipe submerged, the upward flow area of the gas bubbles is constant and being limited by the outer circumference of the pipe the diameter is d and also an outer circumference with diameter x, which is going to determine it  bubbles are characterized by: V b  unit volume of a bubble V b, N b  number of bubbles per unit volume of reactor N b, bubble surface area relative to volume bubble av (for sferic bubble a v = 6/d b ), bubble diameter d b, ascending velocity of bubbles w b  consider the reaction solution is a move up and down (z axis) without there is a radial component of movement  given that the gas to be cleaned is very dilute d and the depth of immersion, h, is relatively low, we consider that the volume of a bubble V b, emains constant. Also, on this hypothesis w b and a v can be considered as constant. We consider the chemical reaction of the type: A + b B products 3 The process rate definition To calculate the process rate of mass transfer with chemical reaction, the best theori is twofilm theory (Lewis and Whitman). mass transfer. This implied in each of the two films of a concentration gradient. Thus, as shown in figure 3, gas film, the concentration or the partial pressure decrease from the value y A, respective p A, to value y Ai, respective p Ai, and liquid film, from the value x Ai, respective c Ai, to value x A respective c A. Resistance at the interface separating the two phases can be neglected, so here are created conditions for equilibrium between y Ai and x Ai concentrations or p Ai and c Ai, therefore these concentrations can be correlated to the equilibrium curve y Ai = f(x Ai ) or p Ai = f(c Ai ) (fig. 4). Fig. 4 Echilibrium curve y Ai = f(x Ai ) The flow N A transferred from gas phase to liquid phase is equal to the process rate v p. N A = v p = k y (y A  Y Ai ) = k x (x Ai  x A ) (1) Respective: N A = v p = k G (p A  p Ai ) = k L (c Ai  c A ) (2) Fig. 3 Concentration gradients in the gaslichid interface According to this, mass transfer from the gas phase in the liquid phase, at the interface, in both phases form a film, which is the main resistance to Where mass transfer occurs at low concentrations of A (cases we are interested) it can be considered that these coefficients are equal along the process. To find their values need to be correlated with the similarity theory using dimensional analysis for the reactor examined. It is impossible to determine the values of the mass transfer coefficients at the interface. Therefore, overall mass transfer coefficients are used; they refer to the size of the gasliquid equilibrium curve, which are generally known. If rewrite process rate relationships are obtained: v p = K y (y A  Y A *) = Kx (x A *  x A ) (3) ISBN:
3 respective: v p = K G (p A  p A *) = K L (c A *  c A ) (4) In our study, solubility follow Henry's law, so, between overall and individual coefficients may be determined following equations: 1/K y = 1/k y + H/k x (5) 1/K x = 1/k x + H/k y (6) respective: 1/K G = 1/k G + H/k L (7) 1/K L = 1/k L + 1/Hk G (8) Where H is Henry's constant. Where mass transfer accompanied by chemical reaction occurs, if its rate is high, the process will be accelerated, so that the relations above will encompass and the chemical accelerating factor, Φ. This parameter is well known in the theory of chemical reactors. By specifying the above mentioned, the following correlation between overall and individual mass transfer coefficients: Respective: 1/K L = 1/Φk L + 1/Hk G (10) 4 Balance sheets of the jet bubbling reactor  Balance equation of the gas entering the reactor tube: D Vg = w g (11) Wg and d are chosen; neglecting the thickness of pipe  Balance equation for bubbles upward: D Vg = wb (x 2  d 2 )/ε g (12) If x is determined on a laboratory model under certain conditions, and by means of a pulsed jet also determine w b, from (12), volumetric fraction of gas, ε g can be calculated, being able to compare with data from specialized literature.  The molar balance equation of the reactor A, gas phase of reactor element: 1/K G = 1/k G + H/Φk L (9) = v p a v V b N b S x (13) residual gas flow decreased in reactor element dz retained residual gas flow  From equation (13) with the simplifying assumptions, it result: V p = K G.p (y A  ) (16) By entering (16) to (14), we obtain: p = v p a v (14)  Process rate will be: = K G. a v (y A  ) (17) When separating the variables and integrating, we obtain: v p = K G (p A  H.c A ) = K G. p (y A  ) (15)  It is assumed that the liquid phase is completely homogeneous, so c A = c Ai With this specification, we obtain: = (18) So, the depth of the immersion is given by: ISBN:
4 h = (19) Commonly, when designing a reactor, c A1 and c A2 are given, and volume flow of fluid is calculated.  Molar balance equation of A, in liquid phase the entire volume of between exterior and sparger pipe circumference to diameter x: + a v V b N b S x dz = + v RA V x (1  ε g ) (20) The reaction rate depends on several factors, such as: the level of reaction, reactant concentrations, temperature.  If the relation (20) is inserted process rate (16), taking into account the vertical variation of concentration y A, is obtained: (  )  v RA h (1  ε g ) = (  c A2 ) (21) is denoted by  the apparent velocity of the liquid in the reactor w L = (22) In this way we can find the necessary flow of solution in the reactor.  Molar balance equation for B in the liquid phase, written for the whole volume of the reaction: D VL (c B2  c B1 ) = b [D MG (y A1  y A2 )  D VL (c A1  c A2 )] (23) the flux of substance B flow substance that reacts with A flow of substance B extracted through the circulation solution From this relationship, we can calculate the concentration of reactant B at the exit of the reactor, c B1. 6 Conclusion This paper propose a hydrodynamic model to study the jet bubbling rector in order to establish ways of designing. To establish design relationships will be determined at the laboratory scale, the following types of relationships:  the relationships for local mass transfer coefficients, k G and k L ;  relationships for ascending velocity of bubbles, w b ;  relationships for volumetric fraction of gas, ε g ;  relationships for bubble surface area relative to volume bubble, a v. Notations a v  bubble surface area relative to volume bubble [m 2 /m 3 ] b  the stoichiometric equivalent of reaction dimensionless number c A, c Ai  the concentration of A in the liquid mass, that is at the interface of the liquid film [kmol/m 3 ] ISBN:
5 c B1, c B2  the concentration of the reaction B substance to exit from the reactor respectively reactor inlet [kmol/m 3 ] d  pipe diameter [m] D VG  gas volume flow entering the pipe reactor [m 3 /s] D VL  volume flow of fluid through which circulates gases bubbled [m 3 /s] H  Henry's constant [Nm/kmol] k G  local mass transfer coefficient on the gas [kmol/ns] k L  local mass transfer coefficient on the liquid k x, k y  local mass transfer coefficients in the liquid or gas [kmol/m 2 s] K G  overall mass transfer coefficient in the gas phase [kmol/ns] K L  overall mass transfer coefficient in liquid phase K x, K y  overall mass transfer coefficients in the liquid or gas [kmol/m 2 s] N b  umber of bubbles per unit volume of reactor [1/m 3 ] P  the total pressure of the gas [N/m 2 ] p A  partial pressure of A in the gas volume [N/m 2 ] p Ai  partial pressure of A at the interface [N/m 2 ] R  universal gas constant [J/kmol. K] S x  the flow area of the ascending gas bubbles [m 2 ] T  gas temperature [K] v p  the process rate [kmol/m 2 s] v R,A  reaction rate of A [kmol/m 3 s] V b  unit volume of a bubble [m 3 ] V x  the considered reaction volume [m 3 ] w b  ascending velocity of bubbles w g  gas velocity w L  the apparent velocity of the liquid in the reactor x  that surrounds the circumference diameter bubbles in ascending movement [m] x A, x Ai  the molar fraction of A in the liquid volume [kmol/kmol liquid] y A, y Ai  the molar fraction of A in the gas volume [kmol/kmol gas] c A *, x A *, p A *, y A *  values of equilibrium gas phase  liquid phase of component A ε g  volumetric fraction of gas Φ  the chemical accelerating factor [2] Muntea, C., Contribuţii teoretice şi experimentale privind instalaţiile de desulfurare a gazelor de ardere, Teză de doctorat, Universitatea Tehnică din ClujNapoca, ClujNapoca, 1998, pp [3] Muntea, C., Căldare, I., Giurca, I., Flue Gas Desulphuriation Using Jet Bubbling Reactor. Proceedings of the 2nd International Conference on Energy and Environment Technologies and Equipment (EEETE '13), June 13, 2013, Braşov, Romania. [4] Muntea, C., Transferul de masă întrun reactor gazlichid. Conferinţa Naţională de Termotehnică cu participare internaţională, vol 1, mai 1998, Piteşti. [5] PasiukBronikowska, W., Ziajda, J., Kinetics of Aqueous SO 2 oxidation. In Presence of CalciumWorld Congres III of Chemical Engineering, Tokio 1986, vol. IV. [6] J. Zhao, S. Su, N. Ai, X. Zhu, Modelling Advances in Environment. Technologies, Agriculture, Food and Animal Science ISBN: References: [1] Borgwardt, R.H., Bruce K.R., Effect of Specific Surface Aria on the Reactivity of CaO with SO 2. X1. AIchE Journal, Vol. 32, nr. 2, Feb ISBN:
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