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Intensification of mass transfer in a pulsed bubble column
Accepted Manuscript Title: Intensification of mass transfer in a pulsed bubble column Author: P. Budzy´nski A. Gwiazda M. Dziubi´nski PII: DOI: Reference:
S0255-2701(16)30597-9 http://dx.doi.org/doi:10.1016/j.cep.2016.12.004 CEP 6908
To appear in:
Chemical Engineering and Processing
Received date: Accepted date:
10-11-2016 11-12-2016
Please cite this article as: P.Budzy´nski, A.Gwiazda, M.Dziubi´nski, Intensification of mass transfer in a pulsed bubble column, Chemical Engineering and Processing http://dx.doi.org/10.1016/j.cep.2016.12.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Intensification of mass transfer in a pulsed bubble column P. Budzyński, A. Gwiazda, M. Dziubiński 1)Faculty of Process and Environmental Engineering,
Lodz University of Technology, 90-924 Lodz, Wolczanska 213, Poland
Graphical abstract
Highlights
Application of pulsation to the bubble column intensifies its operation A wide range of data concerning hydrodynamics of pulsed-bubble columns is presented Mass transfer coefficient in pulsed bubble column increased be order of magnitude Model equation for mass transfer coefficient in pulse-bubble column is presented Bjerknes force is introduced in model consideration.
Notation a
– specific surface of mass transfer [m2/m3]
c0
– initial concentration of oxygen in water [mg/dm3]
c
– current concentration of oxygen in water [mg/dm3]
C
*
– equilibrium concentration of oxygen in water [mg/dm3]
D
– equivalent diameter for a column with square cross-section [m]
d0
– nozzle diameter [mm]
dbDs – diameter of sphere of given volume [m] dp
– diameter of pulsation exciter disk [m] 1
dbP – equivalent diameter of gas bubble [m] f
– frequency of exciter disk pulsations [Hz]
fw* – the first basic frequency of pulsations (resonance) which corresponds to the frequency of the first specific pulsations of the system [Hz] f1*
– the second frequency of specific (resonance) pulsations [Hz]
f2*
– the third frequency of specific (resonance) pulsations [Hz]
Hc – total column height [m] Hk – final liquid height in the column [m] Hm – height of liquid-gas mixture in the column [m] Hp – initial liquid height in the column [m] kL
– mass transfer coefficient in the liquid [m/s]
kLa – volumetric mass transfer coefficient [s-1] kx
– coefficient defined by equation (23) [-]
kp
– coefficient defined by equation (24) [-]
kλ
– coefficient defined by equation (28) [-]
M
– pulsating mass [kg]
m
– slope factor defined by equation (13)
P
– power input [W]
uG – superficial gas velocity [mm/s] uGC – critical gas velocity defined by equation (1) [m/s] uGi – velocity of gas flowing from injector to the liquid [m/s] QG – volumetric gas flow rate [dm3/h] Sp
– exciter disk surface [m2]
SD – liquid surface area (cross-sectional area of the column) [m2] T
– water temperature [°C]
t
– time [s]
VbDs – gas bubble volume defined by equation (32) [m3] VL
– volume of liquid phase inside liquid-gas mixture [m3]
VR – volume of liquid-gas mixture [m3] 2
Xp
– amplitude of disk vibrations [mm]
Yi
– free liquid surface deflections [cm]
Z
– energy efficiency ratio [1/J]
Greek letters: εG
– measured gas hold-up in two phase mixture [%]
εGcalc.– calculated gas hold-up in two phase mixture [%] λ
– wave length of standing wave [m]
σw
– surface tension of water [N/m]
μw
– viscosity of water [Pas]
ρN
– density of nitrogen [kg/m3]
ρA
– density of air [kg/m3]
ρw
– density of water [kg/m3]
ω
– angular frequency = 2πf [rad/s]
Γ
– coefficient of pulsation intensity [-]
Subscripts G
– gas
L
– liquid
0
– without pulsation
(*) – resonance pulsation min – minimum max – maximum
1. Introduction Recently, many papers on the intensification of technological processes and unit operations in the field of chemical engineering have been published. Main aims of these studies [1-5] include improvement of the efficiency of technological processes and quality of products, reduction of equipment dimensions and energy demand, improvement of heat and mass transfer conditions and reduction of pollutant emissions to the environment. One of the fields of these studies is the intensification of mass transfer in bubble columns. 3
Bubble columns are the basic type of contactors used in mass transfer unit operations for liquidgas and solid-liquid-gas systems. A number of equipment design concepts are applied in industrial bubble columns [6,7] to account for substantial changes of physical properties along the apparatus. These devices have a capacity ranging from a few litres (dm3) up to several hundred cubic meters (m3). To achieve satisfactory process parameters, a number of design concepts can be used in the bubble column. The solutions can be divided into two basic groups. One group includes constructions in which horizontal or vertical baffles are installed in the reaction chamber of a bubble column. This type of solution is used to change flow direction of a twophase mixture. In addition, the baffles induce vortices at their edges which increase gas hold-up in the liquid phase and improve mass transfer due to surface renewal. An example of this solution is an air-lift column with vertical baffles and internal circulation [8]. Another example is a column with horizontal baffles (perforated or shelf baffles) [9]. Unfortunately, these devices can work effectively only in a narrow range of process parameters which significantly reduces flexibility of the process control and applications of such columns. The other group consists of solutions in which stirrers or vibration exciters are installed inside the reaction chamber of a bubble column. The use of stirrers can improve mass transfer coefficients in a fairly wide range and, as a result, the intensification of renewal of mass transfer surface during the process. However, this solution has some drawbacks that must be taken into account. The first disadvantage is that, although stirrers enhance circulation in the column, they also cause unfavourable changes in the hydrodynamics of liquid-gas mixture flow. As a result of centrifugal and axial forces acting on the mixture, back-mixing and phase separation may occur which significantly decrease the volumetric mass transfer coefficients. Furthermore, dead zones may be formed in the contactor and high shear rates can occur on the stirrer edges which cause that they are not applicable for certain purposes, e.g. submerged fermentation. Another widely applied method for the intensification of mass transfer in bubble columns is the use of pulsations in a gas-liquid mixture. This solution consists in introducing pulsations directly inside the bubble column [10-18] or subjecting the entire column to pulsations (shaker type reactors) [18]. In both cases, additional horizontal baffles may be employed within the column to induce increasing phase disturbance [9]. In the case of pulsations introduced into the continuous phase in the 4
bubble column, e.g. by a vibration exciter operating at an appropriate frequency and amplitude, bubble breakup occurs. Another favourable phenomenon is a significant reduction or even elimination of bubble rise caused by the Bjerknes forces, which is an additional force opposite to buoyancy occur in a pulsed bubble column. This force decreases the bubble velocity and hence enhances the contact time. As a result, it is possible to adjust process parameters in such a way that gas bubbles fill the entire column volume, including dead zones, and plug flow of bubbles as well as lack of back-mixing inside the bubble column occur which significantly increases the gas hold-up and contributes to mass transfer intensification. An additional advantage is a possibility to affect process conditions by controlling the frequency and amplitude of pulsations. In the pulsed bubble columns this can be accomplished without interfering with the gas-liquid mixture which is particularly important in the processes during which significant changes of liquid viscosity occur, e.g. submerged fermentation. The main disadvantage of pulsed bubble columns is that the best results of mass transfer intensification are obtained at resonant frequencies which cause formation of standing pressure waves in the column. An improper use of the resonant frequency may however cause severe damage to the system. In this study an attempt was made to determine the effect of pulsations with resonant frequencies on gas hold-up and volumetric mass transfer coefficient in the pulsed bubble column with slenderness ratio 3 < Hp/D < 14.5.
2. Experimental The experimental set-up is shown schematically in Fig. 1. Experiments were carried out in a pulsed bubble column (I-1) made of glass, with square cross section. Column side length was D = 0.135 m, whereas its height was Hc = 2.25 m. The glass column was mounted on a steel stand (I-2) and connected to it by a set of springs (I-3). At the bottom of the column a circular vibration exciter disk (II-1) made of steel with diameter dp = 0.105 m and thickness of 10 mm was installed. The disk was tightly sealed to the elastic membrane and connected to an eccentric drive (II-2) installed on the motor shaft (II-3). Pulsation frequency (f) of the exciter disk was set by controlling the speed of motor (II-3) using inverter (II-4). The frequency could be changed from 1 Hz to 70 Hz and pulsation amplitude Xp could range from 0.25 mm up to 2 mm by setting eccentric drive (II- 2). 5
Fig.1
Air was supplied through valve ZG, rotameter (III-1) and next to column (I-1) through grate injector (III-2). The injector was equipped with 20 outlets, each with diameter d0 = 0.8 mm. The position, number and diameters of the outlets were specially chosen so that the gas flow expanded uniformly over the entire cross-sectional area of the column and was free for a maximum air flow velocity through the injector outlets, uG0i. This is important because gas bubbles of almost equal diameters are generated and flow through the column – a phenomenon which does not occur in the case of jet flow. It is also possible to predict the diameters with a satisfactory accuracy using the Davidson and Schuler equation[19]. A criterion adopted for the calculation of critical gas velocity uGC separating free flow and jet flow of bubbles was the equation proposed by Wallis [20] which referred to gas flow from the injector nozzle (with radius r0). The equation based on the study of Kutateladze and Styrikovich [21] has the following form:
u
GC
1
G 1 4
g L G
2 1.25 g L G r 2 0
(1)
Upon a simple transformation we obtain the equation for critical gas velocity uGC during outflow from the injector: 1
uGC
1 2 g L G 4 1.25 1 g L G r 2 0 G 2
(2)
The largest volumetric air flow rate supplied to the column was 600 dm3/h which corresponded to gas velocity uG1= 16.57 m/s inside a single injector outlet (nozzle radius do=0.8 mm). Critical velocity calculated from equation (2) was uGC=39.85 m/s. It can be assumed that the whole experiment was performed at free flow of air bubbles in water. For continuous assessment of oxygen concentration in the liquid the experimental set-up was equipped with external circulation loop (IV) (cf. Fig. 1). Liquid was collected by peristaltic pump (IV-1) from the lower part of the column, below the vibration exciter disk. Then, it was forced through temperature control (V-1.2) and measuring cell, where probe (VI-1) measured dissolved oxygen concentration (ci) and liquid temperature (Ti). An oxygen probe Oxi 3310 Setz Incl. Cellox 325-3 (WTW, Germany) was used to measure oxygen concentration in the liquid. Water was pumped 6
through a circulation system at a constant volumetric flow rate Qw = 0.0117 dm3/s. The experimental medium was tap water of density ρw = 1000 kg/m3, interfacial tension σw= 726.710-4 N/m and viscosity μw= 110-3 Pas. A dispersed phase was technical nitrogen from a gas tank and air with densities ρN=1.25 kg/m3 and ρA=1.2 kg/m3, respectively. The experiments were carried out at temperature T = 18-20°C. To clearly describe the measurement procedure the subsequent operations are shown schematically in Fig. 2 and 3. Figure 2 shows the amount of liquid or liquid-gas mixture in the column in the subsequent phases A, B, C, and D. Figure 3 illustrates changes in oxygen concentration ci as a function of time t. Zones A, B, C, and D marked in both drawings are of the same time limits. The measurements were carried out using the following procedure. In the first step, pulsation amplitude, Xp, was determined. Next, column (I-1) was filled with water to the desired height Hp. For an accurate determination of liquid height a set of holes in the column side wall (Zi) was used (cf. Fig. 2A). Then, through valve (ZG), rotameter (III-1) and injector (III-2) nitrogen was introduced into the liquid at a predetermined volumetric flow rate Qp, (cf. Fig. 2B). Volumetric gas flow rates QGi of 200, 400 and 600 dm3/h were used in the measurements. These values correspond to superficial gas velocities equal to uGi = 3.1, 6.2 and 9.3 mm/s, respectively. When oxygen concentration in water reached a certain low level (the end of oxygen saturation process was set for oxygen concentration ci < 0.1 mg/dm3), hydraulic seal Zi was opened to let overflowing water Vov into the measuring vessel. At the same time, the position of three-way gas valve ZG was changed and in place of nitrogen air was supplied to the column. Volumetric air flow rate Qp was equal to nitrogen flow rate Fig.2
QN, (cf. Fig. 2C). After determining oxygen concentration (cf. Fig. 3, zone B), the vibration exciter was turned off and heights Hk, Hov were measured (cf. Fig. 2, zone D). Then, instead of nitrogen, air was introduced (cf. Fig. 2, zone C) and changes in oxygen concentration as a function of time were measured from point
Fig.3
C to point D. 2.1. Gas hold-up Gas hold-up was measured by the overflow method, according to the procedure described above. The value of gas hold-up was calculated according to formula (3):
7
G
H p Hk Hp
H ov Hp
(3)
In the case of pulsed bubble columns the overflow method has been chosen to measure gas holdup because such measurements are far more accurate than reading the average height of a pulsating liquid-gas mixture. This is especially justified when the first basic pulsation frequencies fw* are applied in columns with low slenderness ratio Hp/D < 6. In such cases the observed free liquid surface deflections (Yi) were greater than the column diameter D. When applying the first resonant pulsation frequency, the values of free liquid surface deflections (Yi) were inversely proportional to slenderness of the pulsed bubble column (cf. Fig. 4). Average values of these deflections are presented in Fig. 4 as a function of column slenderness ratio Hp/D for the first basic frequency of pulsations f = fw*.
Fig.4
Analysis of Fig. 4 also shows that while applying the first resonant frequency the size of free liquid surface deflections (Yi) decreases when gas is introduced into the column. This is true for all slenderness ratios Hp/D examined.
2.2. Volumetric oxygen transfer coefficient Volumetric oxygen transfer coefficient was determined by the
classical dynamic method,
Ellenberger and Krishna [14]. The measurements were based on dynamic changes in dissolved oxygen concentration during saturation of water with oxygen from the air (cf. Fig. 3, from point C to point D). Assuming simplifications, similarly as in the works of many authors, e.g. Kantarci et al. [6], Gaddis [7], Waghmare et al. [10], Ellenberger and Krishna [14], it can be stated that:
d cVL kL c* c aVR dt
(4)
where a is a specific mass transfer surface [m2/m3], defined as
a
F VR
(5)
where: ΔF – interfacial surface area [m2] Gas hold-up G and liquid hold-up L in the liquid-gas mixture are described by equations (6) and (7), respectively:
G
VG VR
(6)
8
L
VL VR
(7)
where: VG, VL - gas and liquid volume in the liquid-gas mixture, respectively [m3]. Thus, after substituting transformed equation (7) into equation (4), it will take the form:
d cVL V k L c* c a L dt L
(8)
After transformation, formula (9) is obtained:
VL
dc V k L a c* c L dt L
(9)
Then, after dividing both sides of equation (9) by VL:
dc k L a * c c dt L
(10)
Providing that L = 1 - G, equation (10) assumes the form:
1 G dc k La c* c dt
(11)
Integration of equation (11) using initial conditions of t = 0 and c = 0 leads to:
ln
c* c mt c*
(12)
By presenting experimental data in a semi-logarithmic scale, we determine slope factor (m) and on this basis the volumetric mass transfer coefficient, using the following formulas:
kLa 1 G
(13a)
k L a m 1 G
(13b)
m and
2.3. Basic frequencies (resonant frequencies) To describe dynamic behaviour of liquid in the column, a dynamic model of the first order was applied. This model is analogous to the model of Bretsznajder and Pasiuk [18]. For the first-order dynamic model we consider response of the ideal mass system suspended on a spring. For this model, the first basic frequency of pulsations fw* and subsequent resonant frequencies of pulsations f1*, f2*,…, can be described by the equation:
f i * Bi
1 M
(14a)
where: Bi - constant, used for establishing amplitude XM.
9
It should be noted that for such conditions standing pressure waves occur along the column height. The ratio of subsequent resonant frequencies fi* for constant pulsation amplitude XM is 1 : 3 : 5... or 1/(2n-1) where n = 1, 2, 3, .... In accordance with the accepted nomenclature, the first resonant frequency (for n = 1) is called the basic frequency of the system. In the present study it is determined as fw* and f1* for n = 2, f2* for n = 3 and so on, as in the previous works of Budzyński and Dziubiński [11-13]
The wavelength of the i-th resonant standing wave λi is defined as follows:
i
4 H mi 2 n 1
(14b)
For the first specific frequencies i = 1 and next for the first resonant frequency i = 2, for the second resonant frequency i = 3 and so on. The propagation velocity of pressure wave wmi is defined as follows: wmi f i * i
(14c)
2.4. Power input Total power input (Pc) is defined as the sum of power input from gas injection per unit mass (PG) and power input from pulsations applied (PM) also per unit mass. Pc is defined like in [13] and described by equation (14):
Pc PG PM
(15)
where: PG - power input from gas injection per unit mass defined by formula (16):
PG g uG / M
(16)
where: uG - superficial gas velocity, M - pulsating mass. Power input from applied pulsations per unit mass, PM, is defined by equation (17): 1 2 X M i*3 / M 2 The value of angular frequency ω*i is defined as: PM
2 f *
*
i
i
(17)
(18)
where: fi* - i-th resonant frequency of pulsation, XM - amplitude of total pulsating mass in the column [m]. 10
Amplitude XM is defined by equation (19), similarly as in [23,24]: XM X p
Sp SD
(19)
where: Xp - amplitude of vibration excitement, Sp - exciter disk surface [m], SD - liquid surface area [m2].
3. RESULTS 3.1. The effect of power added to the system on gas hold-up and volumetric mass transfer coefficient Selected results of measurements of gas hold-up εG and volumetric mass transfer coefficient kLa, presented as a function of pulsation frequency, are shown in Fig. 5 (lines connecting experimental Fig.5
points in the figure are intended only to represent trends in the changes of measurement data). From the analysis of Fig. 5 it follows clearly that with an increasing pulsation frequency there is a periodic increase of gas hold-up εG and volumetric mass transfer coefficient in water kLa. The maximum values of these parameters appear when the same resonant frequencies are used. The ratio of empirically established values of resonant frequencies was 1: 3: 5 ... which was in accordance with the values predicted by the first-order model (mass M suspended on a vibrating spring). These results are analogous to those obtained by Baird [27] Bretsznajder and Pasiuk [18] Ellenbergerg [17] or Budzyński and Dziubiński [11-13]. The impact of column slenderness ratio Hp/D on changes in gas hold-up εG and the dependence of volumetric oxygen transfer coefficient kLa on power input per unit mass of the mixture Pc/M was analysed. Selected results of the measurements are given in Figures 6a, b to 11a, b. These graphs show results of measurements for pulsation amplitude Xp = 1 mm. For the remaining amplitudes the results for both gas hold-up and volumetric mass transfer coefficient are analogous. An increase of pulsation amplitude caused an increase of gas hold-up and mass transfer coefficient. A decrease of
Fig. 6a, 6b
the amplitude caused a decline of both coefficients.
Fig. 7a, 7b Fig. 8a, 8b
11
The analysis of changes in gas hold-up and volumetric mass transfer coefficient as a function of power input per unit mass leads to a conclusion that in the tested range of pulsation frequencies and
Fig. 9a, 9b Fig. 10a, 10b Fig. 11a, 11b
amplitudes it is not possible to establish a simple proportion between superficial gas velocity, gas hold-up and the volumetric mass transfer coefficient like in the classic bubble columns [6,7]. Both gas hold-up and volumetric mass transfer coefficient depend not only on total power input Pc but also on pulsation intensity and standing pressure wave along the column height. The presence of the standing wave during the application of resonant frequency causes significant changes in the flow hydrodynamics of gas bubbles. Along the column height, a decrease or even suppression of bubble rise velocity was observed. These changes in hydrodynamics occurred in the arrows of standing pressure waves (cf. Fig. 12, zones a, b, c, d). The results are analogous to these obtained by Budzyński and Dziubiński [13] and Ellenberger et al. [16].
Fig. 12
Gas hold-up increased several times when resonant frequency was used. This phenomenon is a result of the Bjerknes force acting on gas bubbles which is in opposite direction to the buoyancy forces (cf. [11-17, 23, 24]). The use of resonant frequencies caused a significant increase in the volumetric mass transfer coefficient. However, it cannot be stated that these two values, i.e. gas holdup and volumetric mass transfer coefficient, were directly proportional to each other. Such proportionality can be found instead in relation to superficial gas velocity uGo. With increasing gas velocity both gas hold-up G and volumetric mass transfer coefficients kLa were growing proportionally. With a decrease of column slenderness the gas hold-up increased which was not accompanied by a proportional increase in the volumetric mass transfer coefficient of oxygen. On the other hand, with the increase of slenderness, the measured gas hold-up decreased while increasing the value of volumetric mass transfer coefficient of oxygen. These differences can be attributed to the fact that an increase in deflections of free surface area Yi which take place in low columns (low slenderness), shortens the free flow path of bubbles (Hmi). Furthermore, the time of gas bubble flow (t) through a layer of liquid-gas mixture also decreased (cf. Fig. 2). Shortening of the time of bubble flow (time for liquid-gas contact) clearly reduces the volumetric mass transfer coefficient kLa.
3.2. The effect of free liquid surface deflections on gas hold-up measurement
12
The analysis of a series of images (cf. Fig. 4) led to a conclusion that the greatest free liquid surface deflections Yi occurred when the first resonant frequency of pulsations fw* was used. Changes in free liquid surface deflections Yi during pulsations at the first basic frequency fw* as a function of slenderness ratio of the column Hp/D are shown in Fig. 13. Figure 14 illustrates changes in the value of free liquid surface deflections Yi during pulsations with the first basic frequency fw* as a function of power input per unit mass Pc. Figure 13 shows that the greatest values of Yi factor occurred in an aerated column. With an increasing velocity of gas introduced to the column the deflections decreased. Analysis of the impact of power input per unit mass shows that an increase in the power input Pc
Fig. 13 Fig. 14
causes an increase of free liquid surface deflections (cf. Fig. 14). It should be noted that the increase in power input is mainly caused by an increase of power input from applied pulsations PM. The increase of this power is caused by an increased frequency of pulsations (cf. equation (16), amplitude XM is constant). The free surface deflections are caused by the fact that the arrow of standing pressure wave is situated on the free surface of the mixture (liquid). The largest deflections were observed during pulsations at the first resonant frequency. These conditions are similar to the longest wavelength
H = 4Hp (cf. equation (14a,b)). The suppression of free surface deflections being a result of increased gas flow rate (increase of superficial gas velocity) is due to an increased gas hold-up. The increase of gas hold-up is caused by a growing number of gas bubbles retained in the liquid-gas mixture. The increasing number of gas bubbles is known to cause standing wave energy dissipation [28]. Additionally, one should take into account that the largest number of bubbles were accumulating in the arrows of standing waves. One such arrow occurs at the liquid free surface. Consequently, bubbles were concentrating close to the surface and “airbags” were forming which suppressed deflections of free surfaces [22].
3.3. The effect of slenderness ratio on gas hold-up Figure 15 shows changes of gas hold-up G when the first basic frequency of pulsations fw* as a function of column slenderness ratio Hp/D was used. The total power input per unit of pulsating mass Pc is shown in Fig. 16.
Fig. 15
13
Analysing the impact of column slenderness ratio Hp/D and the size of free surface deflections on gas hold-up it should be noted that we are dealing with two working areas of pulsed bubble columns. In the first area for columns of slenderness ratio Hp/D < 6 (cf. Fig. 3, points a, b, c, d) a significant effect of the free surface oscillation on gas hold-up can be observed. In the second area for column slenderness ratio Hp/D > 8 the impact of free surface deflections can be considered negligible. Moreover, gas hold-up depends directly on the gas flow rate like in the classic bubble columns (cf. Fig. 4, images e, f, g, h). For example, for gas velocity uG = 9.3 mm/s and slenderness ratio of 8 < Hp/D < 13.5 gas hold-up G is virtually constant and equal approximately to 2% up to 4%. For the column slenderness ranging from approximately 8 to 3, the value of gas hold-up increases from approximately 4% to approximately 13% (see Fig. 15).
Fig. 16
An increase of gas hold-up is caused not only by free liquid surface deflections Yi but also by power input per unit mass (cf. Fig. 16). It is clear that at a constant amplitude of pulsations Xp and increasing frequency of vibrations fw* for a column of constant diameter D with a decrease of the column height its slenderness ratio Hp/D decreases and power input per unit mass introduced to the pulsating liquid increases.
4. A METHOD PROPOSED FOR THE CALCULATION OF OPERATING PARAMETERS OF PULSED BUBBLE COLUMNS 4.1. Calculations of gas hold-up Gas hold-up can be calculated in the work of Budzyński and Dziubiński [13], using the formula:
G calc . G 0 k max k min
(20)
where:
a u 0 G
0.4
G0
(21)
where: uG- - superficial gas velocity [m/s]. Constant a0 depends on the number of nozzles in the injector, and changes its value from 0.15 to 0.2 according to Kantarci et al. [6]. Coefficient kmin is defined as: 0.1
k min k x k p
(22)
kx - coefficient accounting for an increase of gas hold-up caused by pulsations in the two-phase mixture is defined as:
14
D k x 2i 1 H p
0.5
(23)
i - takes values for the first basic frequency i = 1, and i = 2,3 ... for successive resonant frequencies of pulsations, respectively. On the other hand, kp is the power input for gas injection PG to the total power Pc = PM +PG (defined by equations (15) and (16)) and added to the system defined as:
kp
PG PM PG (24)
Another factor kmax appearing in equation (20) is a term concerning an increase of gas hold-up. This increase results from the reduction of flow velocity of gas bubbles due to the introduction of pulsations with resonant frequency to the liquid-gas mixture. In the case of a standing wave the bubble rise velocity will be reduced due to the Bjerknes force [10-16, 22-26]. This force is opposite to the buoyancy force and is proportional to the pulsation intensity factor Γ. The kmax factor is defined as follows: k max 1 2 i 1
0. 8
(25)
where: Γ- pulsation intensity factor defined by equation (26): X M *i
2
2g
(26)
A comparison of gas hold-up calculated from equation (20) with the values obtained experimentally during pulsations with resonant frequencies is given in Fig. 17. Analysis of this figure shows that the values of gas hold-up obtained experimentally are comparable to the values calculated using the proposed model (equation (20)) which is true for the vast majority of experimental data. A maximum deviation of the experimental data from the proposed model is ± 7.5%. The model is valid for slenderness ratio Hp/D > 5. Figure 17 also shows a full range of results together with three points for Hp = 0.42 (Hp/D = 3.11) which differ significantly from the values predicted by this model. The three points differ from the model with an error exceeding ± 30%. It is assumed that such behaviour
Fig. 17
15
is caused by a significant effect of liquid surface pulsation on the experimentally determined values of gas hold-up (cf. photographs in Fig. 4a and Fig. 4b).
4.2. Calculation of volumetric oxygen mass transfer coefficient in liquid Based on results of the measurements and a few reports in the literature, the following correlation is proposed to calculate the volumetric mass transfer coefficient kLa in pulsed bubble columns: k L a calc. 0.58
G1.5 0.6 d bP
k 0.5
(27)
where: kλ - factor correcting changes in the bubble flow hydrodynamics along the column height resulting from resonant standing waves. This factor is defined as: D
(28)
k
where: λ - length of the i-th resonant standing wave defined by the formula:
i
4 Hp 2i 1
(29)
It is proposed to calculate the equivalent bubble diameter dbP from the following equation:
d bP d bDS k 0p.11
(30)
where:
dbDs 6VbDS
1
(31)
3
The kp factor was defined earlier by correlation (24). Bubble volume VbDs is proposed to be calculated using the equation given by Davidson and Schuler [19]. For free gas flow regime and for gas flowing into the liquid with characteristics similar to those of water, VbDs has the following form:
VbDs 1.378 QG / i0
6/5
g
3
5
(32)
where: i0 – number of nozzles in a grate diffuser. Figure 18 illustrates a comparison of volumetric mass transfer coefficients determined experimentally and calculated using equation (27).
Fig. 18
16
Figure 18 shows that volumetric mass transfer coefficients determined experimentally are slightly different from these calculated using model equation (27) for all the experimental data obtained. The maximum error of description of the experimental data by the proposed model (27) is equal to ± 10%. Based on the experimental and literature data, the following equations are proposed to calculate volumetric mass transfer coefficient kLa in the bubble column without pulsations:
for 3 < Hp/D < 8
for 8 < Hp/D < 14.5
H p 0.82 k L a0 calc. 0.12 uG D
0.25
H p 0.82 k L a0 calc. 0.58 uG D
(33a) 0.18
(33b)
Figure 19 shows a comparison of volumetric mass transfer coefficients determined experimentally and calculated from equations (33a) and (33b). Fig. 19
Figure 19 shows that the values of volumetric mass transfer coefficient determined experimentally are slightly different from the values determined by equations (33a) and (33b). Such results were obtained for all experimental data. The maximum error of the description of experimental data with the use of the proposed model is ± 10%. It should be emphasized that kLa values obtained for a bubble column without pulsations were an order of magnitude smaller than the experimental values obtained in a pulsed bubble column (see Fig. 18 and 19). This demonstrates a significant intensification of mass transfer caused by pulsations introduced to the liquid-gas mixture in a pulsed bubble column.
5. EFFICIENCY OF PULSED BUBBLE COLUMNS An efficiency coefficient Z is proposed in this study (cf. equation (33)) to assess operating parameters of the pulsed bubble columns. This coefficient is the ratio of mass transfer coefficient kLa to power input per unit mass Pc/M.
Z
kLa Pc / M
(33)
The values of Z coefficient for maximum aeration efficiencies obtained during pulsations at resonant Fig. 20
frequencies are presented in Fig. 20. 17
When analysing results presented in Fig. 20 it becomes clear that for the entire range of investigated resonant frequencies of pulsation fi*, column slenderness Hp/D and superficial gas velocities uG the efficiency coefficient Z reaches the highest values when pulsations with basic resonant frequencies fw* are used. With the rise of column slenderness during pulsations at resonant frequencies the efficiency ratio increases up to Z = 4.5, while the slenderness ratio reaches Hp/D = 13.5. The value of Z coefficient during pulsations at higher basic frequencies (f1* and f2*) remains virtually constant on the level of Z < 1 for the whole range of the tested slenderness ratios Hp/D. A graphical interpretation of equations (27), (33a) and (33b) is shown in Fig. 21.
Fig. 21
Diagram in Fig. 21 was prepared under the assumption that the following parameters are known: height of the liquid in the column Hp, column diameter (or equivalent diameter) D, nozzle diameter d0, number of nozzles in a grate injector, total volumetric gas flow rate QG, exciter disk surface Sp, the amplitude of disk vibrations XP and physicochemical properties of phases. In order to determine lines visible in the diagram, the following steps were used. The first basic frequency of pulsations (resonant frequency) fw*, was calculated from equation (14). Column slenderness was calculated as a ratio of the liquid height in the column Hp to column diameter D (cf. point A in Fig. 21). Assuming that the amplitude of disk vibrations XP was constant, power input from gas injection per unit mass PG was calculated using equation (16), while equation (17) was used to calculate power input from the applied pulsation PM. The calculated values of PG and PM made it possible to determine the position of point C. The intersection of lines passing through points A and C is designated by point B (cf. Fig. 21). By changing the height of liquid in the column Hp in the operating range of 3 < Hp/D < 14.5 and making similar calculations, the following function was established Hp/D = f(1 + PM/PG) for uG = const. (uG = 3.1 mm/s, uG = 6.2 mm/s and uG = 9.3 mm/s). The next step was to calculate gas hold-up εGcalc. from equation (20) and volumetric mass transfer coefficient kLacalc. from equation (27). The volumetric mass transfer coefficient without pulsation kLa0calc. was calculated from equation (33a). Formula (33a) was used for columns with slenderness ratio Hp/D < 8 and formula (33b) for columns with Hp/D > 8. The values of kLacalc./kLa0calc. ratio were put on the y-axis, (cf. point E in Fig. 21). Based on the position of points C and E, point F was obtained. Performing calculations for subsequent column heights Hp in the entire expected range of operation, i.e. 3 < Hp/D < 14.5, and making subsequent calculations as above, 18
function kLacalc./kLa0calc. = f(1 + PM/PG) was plotted for uG = const. (uG = 3.1 mm/s, uG = 6.2 mm/s and uG = 9.3 mm/s). The proposed diagram enables easy determination of working conditions of the pulsed bubble column. For example, for a column of Hp/D = 5 (point A) and superficial gas velocity equal to 3.1 mm/s, a horizontal line is plotted on the right y-axis from point A to point B where it intersects the dotted line denoting the column operation line at superficial gas velocity equal to 3.1 mm/s. Then, from point B a line perpendicular to the x-axis is plotted. Intersection of this line with the x-axis marks the position of point C. Point C is used to specify power increment 1+(PM/PG) in order to obtain the first basic frequency of pulsations fw* (at which standing pressure wave occurs along the column height). A perpendicular line from point C to the line of volumetric growth of mass transfer coefficient (the growth caused by applying pulsations into the liquid) allows us to establish the position of point F (see Fig. 21). By plotting a straight line from point F to the y-axis the position of point E is determined. Point E indicates the maximum possible value of an increase in the volumetric mass transfer coefficient due to pulsations introduced into the liquid-gas mixture. The values of this increase are compared to the values kLa0 without pulsations at superficial gas velocity uG equal to 3.1 mm/s.
6. Conclusions In the study an extensive investigation program of the hydrodynamics of gas bubble flow and mass transfer in pulsed bubble columns with slenderness ratio 3.0 < Hp/D < 14.5 was presented. The effect of pulsations of the exciter disk over pulsation frequencies varying from 1 to 70 Hz and amplitudes from 0.25 mm to 2 mm on gas hold-up εG, volumetric oxygen mass transfer coefficient kLa and free liquid surface deflections Yi was determined. Based on the research performed the following conclusions were drawn. 1. The application of pulsations in a bubble column caused a significant, even several-fold increase of gas hold-up and mass transfer coefficient as compared to the classic bubble column. 2. When using resonant frequencies in the column, a clear effect of the standing pressure wave on gas bubbles flowing through the pulsating liquid was observed. The flowing gas bubbles under the
19
influence of the Bjerknes forces gathered in the liquid at the column height where arrows of the standing wave occurred (cf. Fig. 5 and photographs in Fig. 12). 3. At resonant frequencies in the columns with slenderness ratio Hp/D > 8 the volumetric oxygen mass transfer coefficients were practically proportional to gas hold-up in water. With decreasing slenderness of the columns, for Hp/D < 8 a change in the nature of bubble flow through the liquid layer was observed. At the free surface (in the wave arrow) a layer of bubbles was formed, and at Hp/D equal to approximately 3.0 the bubble layer was transformed into foam which filled almost the entire column. 4. Equation (21) proposed to calculate gas hold-up in the pulsed bubble column was verified experimentally with an accuracy of ±7.5%. Equation (27) was developed to calculate volumetric oxygen mass transfer coefficient kLa at pulsations with resonant frequencies, while equations (33a) and (33b) were proposed to identify the values of kLa in an analogous bubble column without liquid pulsation. Equations (27), (33a) and (33b) were confirmed experimentally with an accuracy of ±10%. 5. In order to determine the energy efficiency of oxygen transfer to water in the pulsed bubble column, the Z coefficient was proposed. The coefficient for basic resonant frequencies fw* reached values several times greater than in the case when subsequent resonant frequencies f1* and f2* …. were applied in the entire range of superficial gas flow rates. The highest efficiency coefficients Z were obtained when pulsed bubble columns with the highest slenderness ratio and pulsation frequencies equal to basic resonant frequencies fw* were used. 6. On the basis of the proposed model relationships describing flow hydrodynamics and mass transfer in the pulsed bubble column a diagram was developed to determine the optimum operating conditions of such columns (Fig. 21), and as a result the conditions for maximum intensification of the mass transfer process.
References
20
[1] A.-K. Kunzea, P. Lutze, M. Kopatschek, J.F. Maćkowiak, J. Maćkowiak, M. Grünewald, A. Górak, Mass transfer measurements in absorption and desorption: Determination of mass transfer parameters, Chem. Eng. Research and Design. (2015) 440-452. [2] N.M. Nikacevic, A.E.M. Huesman, P.M.J. Van den Hof, A.I. Stankiewicz, Opportunities and challenges for process control in process intensification, Chem. Eng. Process. (2012) 1-15. [3] E. Drioli, A.I. Stankiewicz, F. Macedonio, Membrane engineering in process intensification – An overview, Journal of Membrane Science (2011) 380, 1-8. [4] J.A. Moulijn, A. Stankiewicz, J. Grievink, A. Górak, Process intensification and process systems engineering: a friendly symbiosis, Comput. Chem. Eng. (2008) 3-11. [5] T. van Gerven, A. Stankiewicz, Structure, energy, synergy, time-the fundamentals of process intensification, Ind. Eng. Chem. Res. (2009) 48, 2465-2474. [6] N. Kantarci, F. Borak, K.O. Ulgen, Bubble column reactors, Process Biochem. (2005) 40, 22632283. [7] E.S. Gaddis Mass transfer in gas-liquid contactors, Chemical Engineering and Processing (1999), 38, 503-510. [8] J.C. Merchuk, Bioreactors, Air-lift Reactors, Ben-Gurion University of the Negev Beer-Sheva, Israel (2010) 320-349. [9] M.S.N. Oliveira, X. Ni, Gas hold-up and bubble diameters in a gassed oscillatory baffled column, Chemical Engineering Science (2001) 56, 6143-6148. [10] Y.G. Waghmare, R.G. Rice, F.C. Knopf, Mass transfer in a viscous bubble column with forced oscillations, Ind. Eng. Chem. Res. (2008) 47, 5386-5394. [11] P. Budzyński, The effect of viscosity of liquid continuous phase on gas hold up in a pulsating bubble reactor, Chem. Process. Eng. (2007) 28, 995-1005. [12] P. Budzyński, Flow hydrodynamics of gas bubbles in a pulsed-bubble column. Scientific Bulletin of the Technical University of Lodz (2011) 1-183, 1107, ISSN 0137-4834. [13] P. Budzyński, M. Dziubiński, Intensification of bubble column performance by introducing pulsation of liquid, Chem. Eng. Process. (2014) 78, 44-57. [14] J. Ellenberger, R. Krishna, Improving mass transfer in gas-liquid dispersion by vibration excitant, Chem. Eng. Sci. (2002) (57) 4809-4815. 21
[15] J. Ellenberger, R. Krishna, Influence of low-frequency vibrations on bubble and drop sizes formed at a single orifice, Chem. Eng. Process. (2003) 42,15-21. [16] J. Ellenberger, J.M. van Baten, R. Krishna, Exploiting the Bjerknes force in bubble column reactors, Chem. Eng. Sci. (2005) 60, 5962-5970. [17] R. Krishna, J. Ellenberger, M.I. Urseanu and F.J Keil, Utilisation of bubble resonance phenomena to improve gas-liquid contact, Naturwissenschaften (2000) 87, 455-459. [18] S. Bretsznajder, W. Pasiuk, Absorption in a pulsed column – Part II: Phenomena on liquid surface induced by pulsation, Przemysł Chemiczny (1964) 43 (2) 74-79 (in Polish). [19] J.F. Davidson, B.O.G. Schuler, Bubble formation at an orifice in an inviscid liquid, Trans. Instn. Chem. Eng. (1960) 38, 335. [20] G.B. Wallis, One dimensional two-phase flow. Mc-Graw-Hill Company, New York (1969). [21] S.S. Kutateladze, M.A. Styrikovich, Hydraulics of Gas-Liquid Systems. Wright Field trans FTS-9814/v, Moscow (1958). [22] R.H. Buchanan, G. Jameson, D. Oedjoe, Cyclic migration of bubbles in vertically vibrating columns, Ind. Eng. Chem. Fundam. (1962) 1 (2) 82-86. [23] F.C. Knopf, J. Mia, R.G. Rice, Pulsing to improve bubble column performance: I low gas rates, AIChE J. (2006) 52 (3) 1103-1115. [24] F.C. Knopf, J. Mia, R.G. Rice, Pulsing to improve bubble column performance: II jetting gas rates, AIChE J. (2006) 52 (3) 1116-1126. [25] G.J. Jameson, J.F. Davidson, The motion of bubble in a vertically oscillating liquid: theory for an in viscid liquid and experimental results, Chem. Eng. Sci. (1966) 21, 29-33. [26] G.J. Jameson, The motion of bubble in a vertically oscillating viscous liquid, Chem. Eng. Sci. (1966) 21, 35-48. [27] M.H.L. Baird, Sonic resonance of bubble dispersions, Chem. Eng. Sci. (1963) 18, 685-687. [28] A. Prosperetti, Bubble phenomena in sound fields: Part two, Ultrasonics (1984) 22, 115-124. [29] Y.G. Waghmare, F.C. Knopf, R.G. Rice, The Bjerknes effect: explaining pulsed-flow behavior in bubble columns, AIChE J. (2007) 53 (7) 1678-1686.
22
List of figures Fig. 1. Schematic of the experimental set-up.
Fig. 2. Schematic of measurement procedure.
Fig. 3. Example of oxygen concentration changes in water as a function of time, for Xp = 1 mm, uG = 9.3 mm/s, Hp= 1.02 m, f = 18 Hz.
Fig. 4. Selected images of free liquid surface deflections for the first resonant frequency f*w at Xp = 1 mm, where: a) H0 = 0.42 m, uG = 0; b) H0 = 0.42 m, uG = 6.2 mm/s; c) H0 = 0.82 m, uG = 0; d) H0 = 0.82 m, uG = 6.2 mm/s; e) H0 = 1.42 m, uG = 0; f) H0 = 1.42 m, uG = 6.2 mm/s; g) H0 = 1.82 m, uG = 0; h) H0 = 1.82 m, uG = 6.2 mm/s.
Fig. 5. Some results of the measurement of gas hold-up εG and volumetric mass transfer coefficient of oxygen, kLa, presented as a function of pulsation frequency f.
Fig. 6. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 3.11.
Fig. 7. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 4.6.
Fig. 8. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 6.07.
23
Fig. 9. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 7.55.
Fig. 10. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 9.03.
Fig. 11. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 13.58.
Fig. 12. The effect of standing pressure wave on the distribution, size and concentration of gas bubbles along the column height for H0 = 0.82 m, Xp = 1mm, uG = 6.2 mm/s, where: a) f = 0; b) f = f*w (10 Hz); c) f = f*1 (35 Hz); d) f = f*2 (55 Hz).
Fig. 13. Average values of free liquid surface deflection Yi as a function of slenderness ratio of the column Hp/D for pulsations equal to the first basic pulsation frequencies f = fw*.
Fig. 14. Average values of free liquid surface deflections Yi as a function of total power Pc per unit mass M for pulsations equal to the first basic pulsation frequencies f = fw*.
Fig. 15. Values of gas hold-up as a function of the column slenderness ratio Hp/D for pulsations equal to the first basic frequency of pulsations f= fw*.
Fig. 16. Values of gas hold-up as a function of total power input per unit of pulsating mass Pc, for pulsations equal to the first resonant frequency of pulsation f= fw*.
Fig. 17. Comparison of gas hold-up values obtained experimentally and calculated from equation (20) for pulsations at resonant frequencies.
24
Fig. 18. Comparison of volumetric mass transfer coefficients obtained experimentally and calculated from equation (27) for pulsations with resonant frequencies.
Fig. 19. Comparison of volumetric mass transfer coefficients obtained experimentally and calculated from equations (33a) and (33b) for a bubble column without pulsations.
Fig. 20. Changes of Z coefficient as a function of column slenderness ratio Hp/D.
Fig. 21. Diagram used to determine the operating point of the pulsed bubble column.
25
Figure 1
26
Figure 2
Figure 3
27
Figure 4
Figure 5
28
Figure 6
Figure 7
Figure 8
29
Figure 9
Figure 10
Figure 11
30
Figure 12
Figure 13
31
Figure 14
Figure 15
32
Figure 16
Figure 17
33
Figure 18
Figure 19
34
Figure 20
Figure 21
35
S0255-2701(16)30597-9 http://dx.doi.org/doi:10.1016/j.cep.2016.12.004 CEP 6908
To appear in:
Chemical Engineering and Processing
Received date: Accepted date:
10-11-2016 11-12-2016
Please cite this article as: P.Budzy´nski, A.Gwiazda, M.Dziubi´nski, Intensification of mass transfer in a pulsed bubble column, Chemical Engineering and Processing http://dx.doi.org/10.1016/j.cep.2016.12.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Intensification of mass transfer in a pulsed bubble column P. Budzyński, A. Gwiazda, M. Dziubiński 1)Faculty of Process and Environmental Engineering,
Lodz University of Technology, 90-924 Lodz, Wolczanska 213, Poland
Graphical abstract
Highlights
Application of pulsation to the bubble column intensifies its operation A wide range of data concerning hydrodynamics of pulsed-bubble columns is presented Mass transfer coefficient in pulsed bubble column increased be order of magnitude Model equation for mass transfer coefficient in pulse-bubble column is presented Bjerknes force is introduced in model consideration.
Notation a
– specific surface of mass transfer [m2/m3]
c0
– initial concentration of oxygen in water [mg/dm3]
c
– current concentration of oxygen in water [mg/dm3]
C
*
– equilibrium concentration of oxygen in water [mg/dm3]
D
– equivalent diameter for a column with square cross-section [m]
d0
– nozzle diameter [mm]
dbDs – diameter of sphere of given volume [m] dp
– diameter of pulsation exciter disk [m] 1
dbP – equivalent diameter of gas bubble [m] f
– frequency of exciter disk pulsations [Hz]
fw* – the first basic frequency of pulsations (resonance) which corresponds to the frequency of the first specific pulsations of the system [Hz] f1*
– the second frequency of specific (resonance) pulsations [Hz]
f2*
– the third frequency of specific (resonance) pulsations [Hz]
Hc – total column height [m] Hk – final liquid height in the column [m] Hm – height of liquid-gas mixture in the column [m] Hp – initial liquid height in the column [m] kL
– mass transfer coefficient in the liquid [m/s]
kLa – volumetric mass transfer coefficient [s-1] kx
– coefficient defined by equation (23) [-]
kp
– coefficient defined by equation (24) [-]
kλ
– coefficient defined by equation (28) [-]
M
– pulsating mass [kg]
m
– slope factor defined by equation (13)
P
– power input [W]
uG – superficial gas velocity [mm/s] uGC – critical gas velocity defined by equation (1) [m/s] uGi – velocity of gas flowing from injector to the liquid [m/s] QG – volumetric gas flow rate [dm3/h] Sp
– exciter disk surface [m2]
SD – liquid surface area (cross-sectional area of the column) [m2] T
– water temperature [°C]
t
– time [s]
VbDs – gas bubble volume defined by equation (32) [m3] VL
– volume of liquid phase inside liquid-gas mixture [m3]
VR – volume of liquid-gas mixture [m3] 2
Xp
– amplitude of disk vibrations [mm]
Yi
– free liquid surface deflections [cm]
Z
– energy efficiency ratio [1/J]
Greek letters: εG
– measured gas hold-up in two phase mixture [%]
εGcalc.– calculated gas hold-up in two phase mixture [%] λ
– wave length of standing wave [m]
σw
– surface tension of water [N/m]
μw
– viscosity of water [Pas]
ρN
– density of nitrogen [kg/m3]
ρA
– density of air [kg/m3]
ρw
– density of water [kg/m3]
ω
– angular frequency = 2πf [rad/s]
Γ
– coefficient of pulsation intensity [-]
Subscripts G
– gas
L
– liquid
0
– without pulsation
(*) – resonance pulsation min – minimum max – maximum
1. Introduction Recently, many papers on the intensification of technological processes and unit operations in the field of chemical engineering have been published. Main aims of these studies [1-5] include improvement of the efficiency of technological processes and quality of products, reduction of equipment dimensions and energy demand, improvement of heat and mass transfer conditions and reduction of pollutant emissions to the environment. One of the fields of these studies is the intensification of mass transfer in bubble columns. 3
Bubble columns are the basic type of contactors used in mass transfer unit operations for liquidgas and solid-liquid-gas systems. A number of equipment design concepts are applied in industrial bubble columns [6,7] to account for substantial changes of physical properties along the apparatus. These devices have a capacity ranging from a few litres (dm3) up to several hundred cubic meters (m3). To achieve satisfactory process parameters, a number of design concepts can be used in the bubble column. The solutions can be divided into two basic groups. One group includes constructions in which horizontal or vertical baffles are installed in the reaction chamber of a bubble column. This type of solution is used to change flow direction of a twophase mixture. In addition, the baffles induce vortices at their edges which increase gas hold-up in the liquid phase and improve mass transfer due to surface renewal. An example of this solution is an air-lift column with vertical baffles and internal circulation [8]. Another example is a column with horizontal baffles (perforated or shelf baffles) [9]. Unfortunately, these devices can work effectively only in a narrow range of process parameters which significantly reduces flexibility of the process control and applications of such columns. The other group consists of solutions in which stirrers or vibration exciters are installed inside the reaction chamber of a bubble column. The use of stirrers can improve mass transfer coefficients in a fairly wide range and, as a result, the intensification of renewal of mass transfer surface during the process. However, this solution has some drawbacks that must be taken into account. The first disadvantage is that, although stirrers enhance circulation in the column, they also cause unfavourable changes in the hydrodynamics of liquid-gas mixture flow. As a result of centrifugal and axial forces acting on the mixture, back-mixing and phase separation may occur which significantly decrease the volumetric mass transfer coefficients. Furthermore, dead zones may be formed in the contactor and high shear rates can occur on the stirrer edges which cause that they are not applicable for certain purposes, e.g. submerged fermentation. Another widely applied method for the intensification of mass transfer in bubble columns is the use of pulsations in a gas-liquid mixture. This solution consists in introducing pulsations directly inside the bubble column [10-18] or subjecting the entire column to pulsations (shaker type reactors) [18]. In both cases, additional horizontal baffles may be employed within the column to induce increasing phase disturbance [9]. In the case of pulsations introduced into the continuous phase in the 4
bubble column, e.g. by a vibration exciter operating at an appropriate frequency and amplitude, bubble breakup occurs. Another favourable phenomenon is a significant reduction or even elimination of bubble rise caused by the Bjerknes forces, which is an additional force opposite to buoyancy occur in a pulsed bubble column. This force decreases the bubble velocity and hence enhances the contact time. As a result, it is possible to adjust process parameters in such a way that gas bubbles fill the entire column volume, including dead zones, and plug flow of bubbles as well as lack of back-mixing inside the bubble column occur which significantly increases the gas hold-up and contributes to mass transfer intensification. An additional advantage is a possibility to affect process conditions by controlling the frequency and amplitude of pulsations. In the pulsed bubble columns this can be accomplished without interfering with the gas-liquid mixture which is particularly important in the processes during which significant changes of liquid viscosity occur, e.g. submerged fermentation. The main disadvantage of pulsed bubble columns is that the best results of mass transfer intensification are obtained at resonant frequencies which cause formation of standing pressure waves in the column. An improper use of the resonant frequency may however cause severe damage to the system. In this study an attempt was made to determine the effect of pulsations with resonant frequencies on gas hold-up and volumetric mass transfer coefficient in the pulsed bubble column with slenderness ratio 3 < Hp/D < 14.5.
2. Experimental The experimental set-up is shown schematically in Fig. 1. Experiments were carried out in a pulsed bubble column (I-1) made of glass, with square cross section. Column side length was D = 0.135 m, whereas its height was Hc = 2.25 m. The glass column was mounted on a steel stand (I-2) and connected to it by a set of springs (I-3). At the bottom of the column a circular vibration exciter disk (II-1) made of steel with diameter dp = 0.105 m and thickness of 10 mm was installed. The disk was tightly sealed to the elastic membrane and connected to an eccentric drive (II-2) installed on the motor shaft (II-3). Pulsation frequency (f) of the exciter disk was set by controlling the speed of motor (II-3) using inverter (II-4). The frequency could be changed from 1 Hz to 70 Hz and pulsation amplitude Xp could range from 0.25 mm up to 2 mm by setting eccentric drive (II- 2). 5
Fig.1
Air was supplied through valve ZG, rotameter (III-1) and next to column (I-1) through grate injector (III-2). The injector was equipped with 20 outlets, each with diameter d0 = 0.8 mm. The position, number and diameters of the outlets were specially chosen so that the gas flow expanded uniformly over the entire cross-sectional area of the column and was free for a maximum air flow velocity through the injector outlets, uG0i. This is important because gas bubbles of almost equal diameters are generated and flow through the column – a phenomenon which does not occur in the case of jet flow. It is also possible to predict the diameters with a satisfactory accuracy using the Davidson and Schuler equation[19]. A criterion adopted for the calculation of critical gas velocity uGC separating free flow and jet flow of bubbles was the equation proposed by Wallis [20] which referred to gas flow from the injector nozzle (with radius r0). The equation based on the study of Kutateladze and Styrikovich [21] has the following form:
u
GC
1
G 1 4
g L G
2 1.25 g L G r 2 0
(1)
Upon a simple transformation we obtain the equation for critical gas velocity uGC during outflow from the injector: 1
uGC
1 2 g L G 4 1.25 1 g L G r 2 0 G 2
(2)
The largest volumetric air flow rate supplied to the column was 600 dm3/h which corresponded to gas velocity uG1= 16.57 m/s inside a single injector outlet (nozzle radius do=0.8 mm). Critical velocity calculated from equation (2) was uGC=39.85 m/s. It can be assumed that the whole experiment was performed at free flow of air bubbles in water. For continuous assessment of oxygen concentration in the liquid the experimental set-up was equipped with external circulation loop (IV) (cf. Fig. 1). Liquid was collected by peristaltic pump (IV-1) from the lower part of the column, below the vibration exciter disk. Then, it was forced through temperature control (V-1.2) and measuring cell, where probe (VI-1) measured dissolved oxygen concentration (ci) and liquid temperature (Ti). An oxygen probe Oxi 3310 Setz Incl. Cellox 325-3 (WTW, Germany) was used to measure oxygen concentration in the liquid. Water was pumped 6
through a circulation system at a constant volumetric flow rate Qw = 0.0117 dm3/s. The experimental medium was tap water of density ρw = 1000 kg/m3, interfacial tension σw= 726.710-4 N/m and viscosity μw= 110-3 Pas. A dispersed phase was technical nitrogen from a gas tank and air with densities ρN=1.25 kg/m3 and ρA=1.2 kg/m3, respectively. The experiments were carried out at temperature T = 18-20°C. To clearly describe the measurement procedure the subsequent operations are shown schematically in Fig. 2 and 3. Figure 2 shows the amount of liquid or liquid-gas mixture in the column in the subsequent phases A, B, C, and D. Figure 3 illustrates changes in oxygen concentration ci as a function of time t. Zones A, B, C, and D marked in both drawings are of the same time limits. The measurements were carried out using the following procedure. In the first step, pulsation amplitude, Xp, was determined. Next, column (I-1) was filled with water to the desired height Hp. For an accurate determination of liquid height a set of holes in the column side wall (Zi) was used (cf. Fig. 2A). Then, through valve (ZG), rotameter (III-1) and injector (III-2) nitrogen was introduced into the liquid at a predetermined volumetric flow rate Qp, (cf. Fig. 2B). Volumetric gas flow rates QGi of 200, 400 and 600 dm3/h were used in the measurements. These values correspond to superficial gas velocities equal to uGi = 3.1, 6.2 and 9.3 mm/s, respectively. When oxygen concentration in water reached a certain low level (the end of oxygen saturation process was set for oxygen concentration ci < 0.1 mg/dm3), hydraulic seal Zi was opened to let overflowing water Vov into the measuring vessel. At the same time, the position of three-way gas valve ZG was changed and in place of nitrogen air was supplied to the column. Volumetric air flow rate Qp was equal to nitrogen flow rate Fig.2
QN, (cf. Fig. 2C). After determining oxygen concentration (cf. Fig. 3, zone B), the vibration exciter was turned off and heights Hk, Hov were measured (cf. Fig. 2, zone D). Then, instead of nitrogen, air was introduced (cf. Fig. 2, zone C) and changes in oxygen concentration as a function of time were measured from point
Fig.3
C to point D. 2.1. Gas hold-up Gas hold-up was measured by the overflow method, according to the procedure described above. The value of gas hold-up was calculated according to formula (3):
7
G
H p Hk Hp
H ov Hp
(3)
In the case of pulsed bubble columns the overflow method has been chosen to measure gas holdup because such measurements are far more accurate than reading the average height of a pulsating liquid-gas mixture. This is especially justified when the first basic pulsation frequencies fw* are applied in columns with low slenderness ratio Hp/D < 6. In such cases the observed free liquid surface deflections (Yi) were greater than the column diameter D. When applying the first resonant pulsation frequency, the values of free liquid surface deflections (Yi) were inversely proportional to slenderness of the pulsed bubble column (cf. Fig. 4). Average values of these deflections are presented in Fig. 4 as a function of column slenderness ratio Hp/D for the first basic frequency of pulsations f = fw*.
Fig.4
Analysis of Fig. 4 also shows that while applying the first resonant frequency the size of free liquid surface deflections (Yi) decreases when gas is introduced into the column. This is true for all slenderness ratios Hp/D examined.
2.2. Volumetric oxygen transfer coefficient Volumetric oxygen transfer coefficient was determined by the
classical dynamic method,
Ellenberger and Krishna [14]. The measurements were based on dynamic changes in dissolved oxygen concentration during saturation of water with oxygen from the air (cf. Fig. 3, from point C to point D). Assuming simplifications, similarly as in the works of many authors, e.g. Kantarci et al. [6], Gaddis [7], Waghmare et al. [10], Ellenberger and Krishna [14], it can be stated that:
d cVL kL c* c aVR dt
(4)
where a is a specific mass transfer surface [m2/m3], defined as
a
F VR
(5)
where: ΔF – interfacial surface area [m2] Gas hold-up G and liquid hold-up L in the liquid-gas mixture are described by equations (6) and (7), respectively:
G
VG VR
(6)
8
L
VL VR
(7)
where: VG, VL - gas and liquid volume in the liquid-gas mixture, respectively [m3]. Thus, after substituting transformed equation (7) into equation (4), it will take the form:
d cVL V k L c* c a L dt L
(8)
After transformation, formula (9) is obtained:
VL
dc V k L a c* c L dt L
(9)
Then, after dividing both sides of equation (9) by VL:
dc k L a * c c dt L
(10)
Providing that L = 1 - G, equation (10) assumes the form:
1 G dc k La c* c dt
(11)
Integration of equation (11) using initial conditions of t = 0 and c = 0 leads to:
ln
c* c mt c*
(12)
By presenting experimental data in a semi-logarithmic scale, we determine slope factor (m) and on this basis the volumetric mass transfer coefficient, using the following formulas:
kLa 1 G
(13a)
k L a m 1 G
(13b)
m and
2.3. Basic frequencies (resonant frequencies) To describe dynamic behaviour of liquid in the column, a dynamic model of the first order was applied. This model is analogous to the model of Bretsznajder and Pasiuk [18]. For the first-order dynamic model we consider response of the ideal mass system suspended on a spring. For this model, the first basic frequency of pulsations fw* and subsequent resonant frequencies of pulsations f1*, f2*,…, can be described by the equation:
f i * Bi
1 M
(14a)
where: Bi - constant, used for establishing amplitude XM.
9
It should be noted that for such conditions standing pressure waves occur along the column height. The ratio of subsequent resonant frequencies fi* for constant pulsation amplitude XM is 1 : 3 : 5... or 1/(2n-1) where n = 1, 2, 3, .... In accordance with the accepted nomenclature, the first resonant frequency (for n = 1) is called the basic frequency of the system. In the present study it is determined as fw* and f1* for n = 2, f2* for n = 3 and so on, as in the previous works of Budzyński and Dziubiński [11-13]
The wavelength of the i-th resonant standing wave λi is defined as follows:
i
4 H mi 2 n 1
(14b)
For the first specific frequencies i = 1 and next for the first resonant frequency i = 2, for the second resonant frequency i = 3 and so on. The propagation velocity of pressure wave wmi is defined as follows: wmi f i * i
(14c)
2.4. Power input Total power input (Pc) is defined as the sum of power input from gas injection per unit mass (PG) and power input from pulsations applied (PM) also per unit mass. Pc is defined like in [13] and described by equation (14):
Pc PG PM
(15)
where: PG - power input from gas injection per unit mass defined by formula (16):
PG g uG / M
(16)
where: uG - superficial gas velocity, M - pulsating mass. Power input from applied pulsations per unit mass, PM, is defined by equation (17): 1 2 X M i*3 / M 2 The value of angular frequency ω*i is defined as: PM
2 f *
*
i
i
(17)
(18)
where: fi* - i-th resonant frequency of pulsation, XM - amplitude of total pulsating mass in the column [m]. 10
Amplitude XM is defined by equation (19), similarly as in [23,24]: XM X p
Sp SD
(19)
where: Xp - amplitude of vibration excitement, Sp - exciter disk surface [m], SD - liquid surface area [m2].
3. RESULTS 3.1. The effect of power added to the system on gas hold-up and volumetric mass transfer coefficient Selected results of measurements of gas hold-up εG and volumetric mass transfer coefficient kLa, presented as a function of pulsation frequency, are shown in Fig. 5 (lines connecting experimental Fig.5
points in the figure are intended only to represent trends in the changes of measurement data). From the analysis of Fig. 5 it follows clearly that with an increasing pulsation frequency there is a periodic increase of gas hold-up εG and volumetric mass transfer coefficient in water kLa. The maximum values of these parameters appear when the same resonant frequencies are used. The ratio of empirically established values of resonant frequencies was 1: 3: 5 ... which was in accordance with the values predicted by the first-order model (mass M suspended on a vibrating spring). These results are analogous to those obtained by Baird [27] Bretsznajder and Pasiuk [18] Ellenbergerg [17] or Budzyński and Dziubiński [11-13]. The impact of column slenderness ratio Hp/D on changes in gas hold-up εG and the dependence of volumetric oxygen transfer coefficient kLa on power input per unit mass of the mixture Pc/M was analysed. Selected results of the measurements are given in Figures 6a, b to 11a, b. These graphs show results of measurements for pulsation amplitude Xp = 1 mm. For the remaining amplitudes the results for both gas hold-up and volumetric mass transfer coefficient are analogous. An increase of pulsation amplitude caused an increase of gas hold-up and mass transfer coefficient. A decrease of
Fig. 6a, 6b
the amplitude caused a decline of both coefficients.
Fig. 7a, 7b Fig. 8a, 8b
11
The analysis of changes in gas hold-up and volumetric mass transfer coefficient as a function of power input per unit mass leads to a conclusion that in the tested range of pulsation frequencies and
Fig. 9a, 9b Fig. 10a, 10b Fig. 11a, 11b
amplitudes it is not possible to establish a simple proportion between superficial gas velocity, gas hold-up and the volumetric mass transfer coefficient like in the classic bubble columns [6,7]. Both gas hold-up and volumetric mass transfer coefficient depend not only on total power input Pc but also on pulsation intensity and standing pressure wave along the column height. The presence of the standing wave during the application of resonant frequency causes significant changes in the flow hydrodynamics of gas bubbles. Along the column height, a decrease or even suppression of bubble rise velocity was observed. These changes in hydrodynamics occurred in the arrows of standing pressure waves (cf. Fig. 12, zones a, b, c, d). The results are analogous to these obtained by Budzyński and Dziubiński [13] and Ellenberger et al. [16].
Fig. 12
Gas hold-up increased several times when resonant frequency was used. This phenomenon is a result of the Bjerknes force acting on gas bubbles which is in opposite direction to the buoyancy forces (cf. [11-17, 23, 24]). The use of resonant frequencies caused a significant increase in the volumetric mass transfer coefficient. However, it cannot be stated that these two values, i.e. gas holdup and volumetric mass transfer coefficient, were directly proportional to each other. Such proportionality can be found instead in relation to superficial gas velocity uGo. With increasing gas velocity both gas hold-up G and volumetric mass transfer coefficients kLa were growing proportionally. With a decrease of column slenderness the gas hold-up increased which was not accompanied by a proportional increase in the volumetric mass transfer coefficient of oxygen. On the other hand, with the increase of slenderness, the measured gas hold-up decreased while increasing the value of volumetric mass transfer coefficient of oxygen. These differences can be attributed to the fact that an increase in deflections of free surface area Yi which take place in low columns (low slenderness), shortens the free flow path of bubbles (Hmi). Furthermore, the time of gas bubble flow (t) through a layer of liquid-gas mixture also decreased (cf. Fig. 2). Shortening of the time of bubble flow (time for liquid-gas contact) clearly reduces the volumetric mass transfer coefficient kLa.
3.2. The effect of free liquid surface deflections on gas hold-up measurement
12
The analysis of a series of images (cf. Fig. 4) led to a conclusion that the greatest free liquid surface deflections Yi occurred when the first resonant frequency of pulsations fw* was used. Changes in free liquid surface deflections Yi during pulsations at the first basic frequency fw* as a function of slenderness ratio of the column Hp/D are shown in Fig. 13. Figure 14 illustrates changes in the value of free liquid surface deflections Yi during pulsations with the first basic frequency fw* as a function of power input per unit mass Pc. Figure 13 shows that the greatest values of Yi factor occurred in an aerated column. With an increasing velocity of gas introduced to the column the deflections decreased. Analysis of the impact of power input per unit mass shows that an increase in the power input Pc
Fig. 13 Fig. 14
causes an increase of free liquid surface deflections (cf. Fig. 14). It should be noted that the increase in power input is mainly caused by an increase of power input from applied pulsations PM. The increase of this power is caused by an increased frequency of pulsations (cf. equation (16), amplitude XM is constant). The free surface deflections are caused by the fact that the arrow of standing pressure wave is situated on the free surface of the mixture (liquid). The largest deflections were observed during pulsations at the first resonant frequency. These conditions are similar to the longest wavelength
H = 4Hp (cf. equation (14a,b)). The suppression of free surface deflections being a result of increased gas flow rate (increase of superficial gas velocity) is due to an increased gas hold-up. The increase of gas hold-up is caused by a growing number of gas bubbles retained in the liquid-gas mixture. The increasing number of gas bubbles is known to cause standing wave energy dissipation [28]. Additionally, one should take into account that the largest number of bubbles were accumulating in the arrows of standing waves. One such arrow occurs at the liquid free surface. Consequently, bubbles were concentrating close to the surface and “airbags” were forming which suppressed deflections of free surfaces [22].
3.3. The effect of slenderness ratio on gas hold-up Figure 15 shows changes of gas hold-up G when the first basic frequency of pulsations fw* as a function of column slenderness ratio Hp/D was used. The total power input per unit of pulsating mass Pc is shown in Fig. 16.
Fig. 15
13
Analysing the impact of column slenderness ratio Hp/D and the size of free surface deflections on gas hold-up it should be noted that we are dealing with two working areas of pulsed bubble columns. In the first area for columns of slenderness ratio Hp/D < 6 (cf. Fig. 3, points a, b, c, d) a significant effect of the free surface oscillation on gas hold-up can be observed. In the second area for column slenderness ratio Hp/D > 8 the impact of free surface deflections can be considered negligible. Moreover, gas hold-up depends directly on the gas flow rate like in the classic bubble columns (cf. Fig. 4, images e, f, g, h). For example, for gas velocity uG = 9.3 mm/s and slenderness ratio of 8 < Hp/D < 13.5 gas hold-up G is virtually constant and equal approximately to 2% up to 4%. For the column slenderness ranging from approximately 8 to 3, the value of gas hold-up increases from approximately 4% to approximately 13% (see Fig. 15).
Fig. 16
An increase of gas hold-up is caused not only by free liquid surface deflections Yi but also by power input per unit mass (cf. Fig. 16). It is clear that at a constant amplitude of pulsations Xp and increasing frequency of vibrations fw* for a column of constant diameter D with a decrease of the column height its slenderness ratio Hp/D decreases and power input per unit mass introduced to the pulsating liquid increases.
4. A METHOD PROPOSED FOR THE CALCULATION OF OPERATING PARAMETERS OF PULSED BUBBLE COLUMNS 4.1. Calculations of gas hold-up Gas hold-up can be calculated in the work of Budzyński and Dziubiński [13], using the formula:
G calc . G 0 k max k min
(20)
where:
a u 0 G
0.4
G0
(21)
where: uG- - superficial gas velocity [m/s]. Constant a0 depends on the number of nozzles in the injector, and changes its value from 0.15 to 0.2 according to Kantarci et al. [6]. Coefficient kmin is defined as: 0.1
k min k x k p
(22)
kx - coefficient accounting for an increase of gas hold-up caused by pulsations in the two-phase mixture is defined as:
14
D k x 2i 1 H p
0.5
(23)
i - takes values for the first basic frequency i = 1, and i = 2,3 ... for successive resonant frequencies of pulsations, respectively. On the other hand, kp is the power input for gas injection PG to the total power Pc = PM +PG (defined by equations (15) and (16)) and added to the system defined as:
kp
PG PM PG (24)
Another factor kmax appearing in equation (20) is a term concerning an increase of gas hold-up. This increase results from the reduction of flow velocity of gas bubbles due to the introduction of pulsations with resonant frequency to the liquid-gas mixture. In the case of a standing wave the bubble rise velocity will be reduced due to the Bjerknes force [10-16, 22-26]. This force is opposite to the buoyancy force and is proportional to the pulsation intensity factor Γ. The kmax factor is defined as follows: k max 1 2 i 1
0. 8
(25)
where: Γ- pulsation intensity factor defined by equation (26): X M *i
2
2g
(26)
A comparison of gas hold-up calculated from equation (20) with the values obtained experimentally during pulsations with resonant frequencies is given in Fig. 17. Analysis of this figure shows that the values of gas hold-up obtained experimentally are comparable to the values calculated using the proposed model (equation (20)) which is true for the vast majority of experimental data. A maximum deviation of the experimental data from the proposed model is ± 7.5%. The model is valid for slenderness ratio Hp/D > 5. Figure 17 also shows a full range of results together with three points for Hp = 0.42 (Hp/D = 3.11) which differ significantly from the values predicted by this model. The three points differ from the model with an error exceeding ± 30%. It is assumed that such behaviour
Fig. 17
15
is caused by a significant effect of liquid surface pulsation on the experimentally determined values of gas hold-up (cf. photographs in Fig. 4a and Fig. 4b).
4.2. Calculation of volumetric oxygen mass transfer coefficient in liquid Based on results of the measurements and a few reports in the literature, the following correlation is proposed to calculate the volumetric mass transfer coefficient kLa in pulsed bubble columns: k L a calc. 0.58
G1.5 0.6 d bP
k 0.5
(27)
where: kλ - factor correcting changes in the bubble flow hydrodynamics along the column height resulting from resonant standing waves. This factor is defined as: D
(28)
k
where: λ - length of the i-th resonant standing wave defined by the formula:
i
4 Hp 2i 1
(29)
It is proposed to calculate the equivalent bubble diameter dbP from the following equation:
d bP d bDS k 0p.11
(30)
where:
dbDs 6VbDS
1
(31)
3
The kp factor was defined earlier by correlation (24). Bubble volume VbDs is proposed to be calculated using the equation given by Davidson and Schuler [19]. For free gas flow regime and for gas flowing into the liquid with characteristics similar to those of water, VbDs has the following form:
VbDs 1.378 QG / i0
6/5
g
3
5
(32)
where: i0 – number of nozzles in a grate diffuser. Figure 18 illustrates a comparison of volumetric mass transfer coefficients determined experimentally and calculated using equation (27).
Fig. 18
16
Figure 18 shows that volumetric mass transfer coefficients determined experimentally are slightly different from these calculated using model equation (27) for all the experimental data obtained. The maximum error of description of the experimental data by the proposed model (27) is equal to ± 10%. Based on the experimental and literature data, the following equations are proposed to calculate volumetric mass transfer coefficient kLa in the bubble column without pulsations:
for 3 < Hp/D < 8
for 8 < Hp/D < 14.5
H p 0.82 k L a0 calc. 0.12 uG D
0.25
H p 0.82 k L a0 calc. 0.58 uG D
(33a) 0.18
(33b)
Figure 19 shows a comparison of volumetric mass transfer coefficients determined experimentally and calculated from equations (33a) and (33b). Fig. 19
Figure 19 shows that the values of volumetric mass transfer coefficient determined experimentally are slightly different from the values determined by equations (33a) and (33b). Such results were obtained for all experimental data. The maximum error of the description of experimental data with the use of the proposed model is ± 10%. It should be emphasized that kLa values obtained for a bubble column without pulsations were an order of magnitude smaller than the experimental values obtained in a pulsed bubble column (see Fig. 18 and 19). This demonstrates a significant intensification of mass transfer caused by pulsations introduced to the liquid-gas mixture in a pulsed bubble column.
5. EFFICIENCY OF PULSED BUBBLE COLUMNS An efficiency coefficient Z is proposed in this study (cf. equation (33)) to assess operating parameters of the pulsed bubble columns. This coefficient is the ratio of mass transfer coefficient kLa to power input per unit mass Pc/M.
Z
kLa Pc / M
(33)
The values of Z coefficient for maximum aeration efficiencies obtained during pulsations at resonant Fig. 20
frequencies are presented in Fig. 20. 17
When analysing results presented in Fig. 20 it becomes clear that for the entire range of investigated resonant frequencies of pulsation fi*, column slenderness Hp/D and superficial gas velocities uG the efficiency coefficient Z reaches the highest values when pulsations with basic resonant frequencies fw* are used. With the rise of column slenderness during pulsations at resonant frequencies the efficiency ratio increases up to Z = 4.5, while the slenderness ratio reaches Hp/D = 13.5. The value of Z coefficient during pulsations at higher basic frequencies (f1* and f2*) remains virtually constant on the level of Z < 1 for the whole range of the tested slenderness ratios Hp/D. A graphical interpretation of equations (27), (33a) and (33b) is shown in Fig. 21.
Fig. 21
Diagram in Fig. 21 was prepared under the assumption that the following parameters are known: height of the liquid in the column Hp, column diameter (or equivalent diameter) D, nozzle diameter d0, number of nozzles in a grate injector, total volumetric gas flow rate QG, exciter disk surface Sp, the amplitude of disk vibrations XP and physicochemical properties of phases. In order to determine lines visible in the diagram, the following steps were used. The first basic frequency of pulsations (resonant frequency) fw*, was calculated from equation (14). Column slenderness was calculated as a ratio of the liquid height in the column Hp to column diameter D (cf. point A in Fig. 21). Assuming that the amplitude of disk vibrations XP was constant, power input from gas injection per unit mass PG was calculated using equation (16), while equation (17) was used to calculate power input from the applied pulsation PM. The calculated values of PG and PM made it possible to determine the position of point C. The intersection of lines passing through points A and C is designated by point B (cf. Fig. 21). By changing the height of liquid in the column Hp in the operating range of 3 < Hp/D < 14.5 and making similar calculations, the following function was established Hp/D = f(1 + PM/PG) for uG = const. (uG = 3.1 mm/s, uG = 6.2 mm/s and uG = 9.3 mm/s). The next step was to calculate gas hold-up εGcalc. from equation (20) and volumetric mass transfer coefficient kLacalc. from equation (27). The volumetric mass transfer coefficient without pulsation kLa0calc. was calculated from equation (33a). Formula (33a) was used for columns with slenderness ratio Hp/D < 8 and formula (33b) for columns with Hp/D > 8. The values of kLacalc./kLa0calc. ratio were put on the y-axis, (cf. point E in Fig. 21). Based on the position of points C and E, point F was obtained. Performing calculations for subsequent column heights Hp in the entire expected range of operation, i.e. 3 < Hp/D < 14.5, and making subsequent calculations as above, 18
function kLacalc./kLa0calc. = f(1 + PM/PG) was plotted for uG = const. (uG = 3.1 mm/s, uG = 6.2 mm/s and uG = 9.3 mm/s). The proposed diagram enables easy determination of working conditions of the pulsed bubble column. For example, for a column of Hp/D = 5 (point A) and superficial gas velocity equal to 3.1 mm/s, a horizontal line is plotted on the right y-axis from point A to point B where it intersects the dotted line denoting the column operation line at superficial gas velocity equal to 3.1 mm/s. Then, from point B a line perpendicular to the x-axis is plotted. Intersection of this line with the x-axis marks the position of point C. Point C is used to specify power increment 1+(PM/PG) in order to obtain the first basic frequency of pulsations fw* (at which standing pressure wave occurs along the column height). A perpendicular line from point C to the line of volumetric growth of mass transfer coefficient (the growth caused by applying pulsations into the liquid) allows us to establish the position of point F (see Fig. 21). By plotting a straight line from point F to the y-axis the position of point E is determined. Point E indicates the maximum possible value of an increase in the volumetric mass transfer coefficient due to pulsations introduced into the liquid-gas mixture. The values of this increase are compared to the values kLa0 without pulsations at superficial gas velocity uG equal to 3.1 mm/s.
6. Conclusions In the study an extensive investigation program of the hydrodynamics of gas bubble flow and mass transfer in pulsed bubble columns with slenderness ratio 3.0 < Hp/D < 14.5 was presented. The effect of pulsations of the exciter disk over pulsation frequencies varying from 1 to 70 Hz and amplitudes from 0.25 mm to 2 mm on gas hold-up εG, volumetric oxygen mass transfer coefficient kLa and free liquid surface deflections Yi was determined. Based on the research performed the following conclusions were drawn. 1. The application of pulsations in a bubble column caused a significant, even several-fold increase of gas hold-up and mass transfer coefficient as compared to the classic bubble column. 2. When using resonant frequencies in the column, a clear effect of the standing pressure wave on gas bubbles flowing through the pulsating liquid was observed. The flowing gas bubbles under the
19
influence of the Bjerknes forces gathered in the liquid at the column height where arrows of the standing wave occurred (cf. Fig. 5 and photographs in Fig. 12). 3. At resonant frequencies in the columns with slenderness ratio Hp/D > 8 the volumetric oxygen mass transfer coefficients were practically proportional to gas hold-up in water. With decreasing slenderness of the columns, for Hp/D < 8 a change in the nature of bubble flow through the liquid layer was observed. At the free surface (in the wave arrow) a layer of bubbles was formed, and at Hp/D equal to approximately 3.0 the bubble layer was transformed into foam which filled almost the entire column. 4. Equation (21) proposed to calculate gas hold-up in the pulsed bubble column was verified experimentally with an accuracy of ±7.5%. Equation (27) was developed to calculate volumetric oxygen mass transfer coefficient kLa at pulsations with resonant frequencies, while equations (33a) and (33b) were proposed to identify the values of kLa in an analogous bubble column without liquid pulsation. Equations (27), (33a) and (33b) were confirmed experimentally with an accuracy of ±10%. 5. In order to determine the energy efficiency of oxygen transfer to water in the pulsed bubble column, the Z coefficient was proposed. The coefficient for basic resonant frequencies fw* reached values several times greater than in the case when subsequent resonant frequencies f1* and f2* …. were applied in the entire range of superficial gas flow rates. The highest efficiency coefficients Z were obtained when pulsed bubble columns with the highest slenderness ratio and pulsation frequencies equal to basic resonant frequencies fw* were used. 6. On the basis of the proposed model relationships describing flow hydrodynamics and mass transfer in the pulsed bubble column a diagram was developed to determine the optimum operating conditions of such columns (Fig. 21), and as a result the conditions for maximum intensification of the mass transfer process.
References
20
[1] A.-K. Kunzea, P. Lutze, M. Kopatschek, J.F. Maćkowiak, J. Maćkowiak, M. Grünewald, A. Górak, Mass transfer measurements in absorption and desorption: Determination of mass transfer parameters, Chem. Eng. Research and Design. (2015) 440-452. [2] N.M. Nikacevic, A.E.M. Huesman, P.M.J. Van den Hof, A.I. Stankiewicz, Opportunities and challenges for process control in process intensification, Chem. Eng. Process. (2012) 1-15. [3] E. Drioli, A.I. Stankiewicz, F. Macedonio, Membrane engineering in process intensification – An overview, Journal of Membrane Science (2011) 380, 1-8. [4] J.A. Moulijn, A. Stankiewicz, J. Grievink, A. Górak, Process intensification and process systems engineering: a friendly symbiosis, Comput. Chem. Eng. (2008) 3-11. [5] T. van Gerven, A. Stankiewicz, Structure, energy, synergy, time-the fundamentals of process intensification, Ind. Eng. Chem. Res. (2009) 48, 2465-2474. [6] N. Kantarci, F. Borak, K.O. Ulgen, Bubble column reactors, Process Biochem. (2005) 40, 22632283. [7] E.S. Gaddis Mass transfer in gas-liquid contactors, Chemical Engineering and Processing (1999), 38, 503-510. [8] J.C. Merchuk, Bioreactors, Air-lift Reactors, Ben-Gurion University of the Negev Beer-Sheva, Israel (2010) 320-349. [9] M.S.N. Oliveira, X. Ni, Gas hold-up and bubble diameters in a gassed oscillatory baffled column, Chemical Engineering Science (2001) 56, 6143-6148. [10] Y.G. Waghmare, R.G. Rice, F.C. Knopf, Mass transfer in a viscous bubble column with forced oscillations, Ind. Eng. Chem. Res. (2008) 47, 5386-5394. [11] P. Budzyński, The effect of viscosity of liquid continuous phase on gas hold up in a pulsating bubble reactor, Chem. Process. Eng. (2007) 28, 995-1005. [12] P. Budzyński, Flow hydrodynamics of gas bubbles in a pulsed-bubble column. Scientific Bulletin of the Technical University of Lodz (2011) 1-183, 1107, ISSN 0137-4834. [13] P. Budzyński, M. Dziubiński, Intensification of bubble column performance by introducing pulsation of liquid, Chem. Eng. Process. (2014) 78, 44-57. [14] J. Ellenberger, R. Krishna, Improving mass transfer in gas-liquid dispersion by vibration excitant, Chem. Eng. Sci. (2002) (57) 4809-4815. 21
[15] J. Ellenberger, R. Krishna, Influence of low-frequency vibrations on bubble and drop sizes formed at a single orifice, Chem. Eng. Process. (2003) 42,15-21. [16] J. Ellenberger, J.M. van Baten, R. Krishna, Exploiting the Bjerknes force in bubble column reactors, Chem. Eng. Sci. (2005) 60, 5962-5970. [17] R. Krishna, J. Ellenberger, M.I. Urseanu and F.J Keil, Utilisation of bubble resonance phenomena to improve gas-liquid contact, Naturwissenschaften (2000) 87, 455-459. [18] S. Bretsznajder, W. Pasiuk, Absorption in a pulsed column – Part II: Phenomena on liquid surface induced by pulsation, Przemysł Chemiczny (1964) 43 (2) 74-79 (in Polish). [19] J.F. Davidson, B.O.G. Schuler, Bubble formation at an orifice in an inviscid liquid, Trans. Instn. Chem. Eng. (1960) 38, 335. [20] G.B. Wallis, One dimensional two-phase flow. Mc-Graw-Hill Company, New York (1969). [21] S.S. Kutateladze, M.A. Styrikovich, Hydraulics of Gas-Liquid Systems. Wright Field trans FTS-9814/v, Moscow (1958). [22] R.H. Buchanan, G. Jameson, D. Oedjoe, Cyclic migration of bubbles in vertically vibrating columns, Ind. Eng. Chem. Fundam. (1962) 1 (2) 82-86. [23] F.C. Knopf, J. Mia, R.G. Rice, Pulsing to improve bubble column performance: I low gas rates, AIChE J. (2006) 52 (3) 1103-1115. [24] F.C. Knopf, J. Mia, R.G. Rice, Pulsing to improve bubble column performance: II jetting gas rates, AIChE J. (2006) 52 (3) 1116-1126. [25] G.J. Jameson, J.F. Davidson, The motion of bubble in a vertically oscillating liquid: theory for an in viscid liquid and experimental results, Chem. Eng. Sci. (1966) 21, 29-33. [26] G.J. Jameson, The motion of bubble in a vertically oscillating viscous liquid, Chem. Eng. Sci. (1966) 21, 35-48. [27] M.H.L. Baird, Sonic resonance of bubble dispersions, Chem. Eng. Sci. (1963) 18, 685-687. [28] A. Prosperetti, Bubble phenomena in sound fields: Part two, Ultrasonics (1984) 22, 115-124. [29] Y.G. Waghmare, F.C. Knopf, R.G. Rice, The Bjerknes effect: explaining pulsed-flow behavior in bubble columns, AIChE J. (2007) 53 (7) 1678-1686.
22
List of figures Fig. 1. Schematic of the experimental set-up.
Fig. 2. Schematic of measurement procedure.
Fig. 3. Example of oxygen concentration changes in water as a function of time, for Xp = 1 mm, uG = 9.3 mm/s, Hp= 1.02 m, f = 18 Hz.
Fig. 4. Selected images of free liquid surface deflections for the first resonant frequency f*w at Xp = 1 mm, where: a) H0 = 0.42 m, uG = 0; b) H0 = 0.42 m, uG = 6.2 mm/s; c) H0 = 0.82 m, uG = 0; d) H0 = 0.82 m, uG = 6.2 mm/s; e) H0 = 1.42 m, uG = 0; f) H0 = 1.42 m, uG = 6.2 mm/s; g) H0 = 1.82 m, uG = 0; h) H0 = 1.82 m, uG = 6.2 mm/s.
Fig. 5. Some results of the measurement of gas hold-up εG and volumetric mass transfer coefficient of oxygen, kLa, presented as a function of pulsation frequency f.
Fig. 6. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 3.11.
Fig. 7. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 4.6.
Fig. 8. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 6.07.
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Fig. 9. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 7.55.
Fig. 10. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 9.03.
Fig. 11. Changes in gas hold-up (a) and volumetric mass transfer coefficient (b) as a function of power added to the system per unit of water mass, Hp/D = 13.58.
Fig. 12. The effect of standing pressure wave on the distribution, size and concentration of gas bubbles along the column height for H0 = 0.82 m, Xp = 1mm, uG = 6.2 mm/s, where: a) f = 0; b) f = f*w (10 Hz); c) f = f*1 (35 Hz); d) f = f*2 (55 Hz).
Fig. 13. Average values of free liquid surface deflection Yi as a function of slenderness ratio of the column Hp/D for pulsations equal to the first basic pulsation frequencies f = fw*.
Fig. 14. Average values of free liquid surface deflections Yi as a function of total power Pc per unit mass M for pulsations equal to the first basic pulsation frequencies f = fw*.
Fig. 15. Values of gas hold-up as a function of the column slenderness ratio Hp/D for pulsations equal to the first basic frequency of pulsations f= fw*.
Fig. 16. Values of gas hold-up as a function of total power input per unit of pulsating mass Pc, for pulsations equal to the first resonant frequency of pulsation f= fw*.
Fig. 17. Comparison of gas hold-up values obtained experimentally and calculated from equation (20) for pulsations at resonant frequencies.
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Fig. 18. Comparison of volumetric mass transfer coefficients obtained experimentally and calculated from equation (27) for pulsations with resonant frequencies.
Fig. 19. Comparison of volumetric mass transfer coefficients obtained experimentally and calculated from equations (33a) and (33b) for a bubble column without pulsations.
Fig. 20. Changes of Z coefficient as a function of column slenderness ratio Hp/D.
Fig. 21. Diagram used to determine the operating point of the pulsed bubble column.
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Figure 1
26
Figure 2
Figure 3
27
Figure 4
Figure 5
28
Figure 6
Figure 7
Figure 8
29
Figure 9
Figure 10
Figure 11
30
Figure 12
Figure 13
31
Figure 14
Figure 15
32
Figure 16
Figure 17
33
Figure 18
Figure 19
34
Figure 20
Figure 21
35