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Mass transfer estimation for bubble column scale up
Chemical Engineering Science 205 (2019) 350–357
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Mass transfer estimation for bubble column scale up S.S. Deshpande a,⇑, K. Kar a, J. Pressler a, I. Tebeka b, B. Martins c, D. Rosenfeld b, J. Biggs c a
The Dow Chemical Company, Core R&D, Midland, MI 48674, USA The Dow Chemical Company, Hydrocarbons R&D, Freeport, TX 77541, USA c The Dow Chemical Company, Hydrocarbons R&D, Sao Paulo 04794, Brazil b
h i g h l i g h t s aU s g b , in estimating the gas-liquid mass transfer coefficient during bubble column scaling up. The existing correlations are found to adequately describe our experimental results, suggesting such correlations are scale insensitive. Using a dimensionless mass transfer efficiency, we show that b = 1 is appropriate and present a method to calculate a once the type of sparger (coarse or fine bubble distributor) is chosen. Explored the suitability of power-law type correlation, kL a ¼
a r t i c l e
i n f o
Article history: Received 4 January 2019 Received in revised form 30 March 2019 Accepted 5 May 2019 Available online 7 May 2019
a b s t r a c t The productivity of a bubble column reactor (BCR) critically depends upon gas-liquid mass transfer coefficient, kL a. The prediction of kL a as function of design and operating conditions is central to BCR scale up. A large number of researchers have successfully characterized kL a experimentally in terms of superficial gas velocity, U sg using the power law relation kL a ¼ aU bsg , with a; b as fit parameters. We probe the applicability of such correlations to the design of a scaled up BCR,which differs from laboratory BCR in two important aspects: (i) the scale of operation, which can be O 102 103 times larger, and (ii) the type of sparger used. To this end, experiments were performed with air and water in a pilot scale (DC ¼ 1:6 m diameter) BCR using a coarse bubble sparger. We found that the existing correlations do, indeed, describe kL a over a wide range of BCR sizes, suggesting that these correlations are fairly scale insensitive. However, the correlations provide no means to capture the role of sparger explicitly. We cast our experimental kL a values in terms of a mass transfer efficiency and independently recover the power law relation with b ¼ 1. We suggest that the role of sparger design can be incorporated in the definition of a through the well-documented sparger efficiency factors. The a and b estimates thus obtained are in good agreement with the literature. Ó 2019 Published by Elsevier Ltd.
1. Introduction Bubble column reactors (BCRs) are multiphase mass-transfer devices intended to bring about rapid dissolution of a sparged gas into a liquid phase. The aim is typically to replenish the dissolved gas which is consumed during a liquid phase reaction. The liquid phase could be stationary, or flowing in a cocurrent or countercurrent manner relative to the sparged air. In the current work, we are interested in bubble columns where the liquid phase is stationary. Although bubble columns typically provide lower rates of gas dissolution than agitated aerated tanks and inline gas-liquid contactors (Paul et al., 2004), the absence of moving parts, ease ⇑ Corresponding author. E-mail addresses: (S.S. Deshpande).
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https://doi.org/10.1016/j.ces.2019.05.011 0009-2509/Ó 2019 Published by Elsevier Ltd.
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of maintenance and low operation cost makes them attractive in industrial aerobic fermentation, and other applications where gas-liquid mass transfer is essential (see Shah et al., 1982; Shah, 1979; Önsan and Avci, 2016). Rate of mass transfer from the sparged gas to the liquid phase determines the productivity of the reactor. Mathematically, in a well mixed BCR, this rate can be described by the mass conservation equation
dðV l C Þ ¼ kL aV l ðC C Þ; dt
ð1Þ
where C is the dissolved gas concentration (O2 in the present work), C is its saturation concentration, V l is the liquid volume, and kL a is a kinetic parameter, called the gas-liquid mass transfer coefficient. Physically, once a gas-liquid interface is formed, it is assumed that an infinitesimally thin film on the liquid side of the interface reaches the saturation concentration C almost instantaneously
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Nomenclature C C Cm DC H H kL a K _ O2 ;g m
dissolved oxygen concentration, [kg-O2/m3-water] dissolved oxygen concentration at saturation, [kg-O2/ m3-water] dissolved oxygen concentration, as measured by the probe, [kg-O2/m3-water] bubble column diameter, [m] liquid height above sparger, [m] Henry’s law constant for oxygen in water (3:9 109 Pa Morrison and Billett, 1952), [Pa] gas-liquid mass transfer coefficient, [s1] efficiency change per unit change in liquid height above sparger, [m1] rate of mass supply of oxygen via sparging, [kg-O2/m3air/s]
(Paul et al., 2004). This is a reasonable assumption here since there are no competing reactions within the film that would deplete the dissolved gas. The concentration of the dissolved species within the bulk of the liquid phase then increases due to diffusion from this saturated film, and the area available for diffusion. The former factor is described in terms of a resistance, 1=kL (see Refs. (Bird et al., 1960; Frossling, 1938) for theories for kL ), and the latter in terms of interfacial area per unit liquid volume, a. Experimentally, neither ‘kL ’ nor ‘a’ can be obtained reliably (Paul et al., 2004); only the product kL a ¼ kL a can be characterized as a lumped parameter. The estimation of kL a has been a topic of research for several decades. For a historical perspectives and current state of understanding of the BCR hydrodynamics and mass transfer, we refer the reader to excellent reviews by Shah et al. (1982), Shah (1979), Shaikh and Al-Dahhan (2013), recent work of Besagni et al. (2017), Besagni et al. (2018), and Rollbusch et al. (2015). Here we only very briefly summarize the learning directly relevant to the topic at hand, namely kL a estimation for BCR scale up. While BCR design (Shah, 1979), fluid properties (Nedeltchev et al., 2014), temperature and pressure (Rollbusch et al., 2015), and presence of contaminants (Vasconcelos et al., 2003) all have some degree of influence on kL a, an overwhelming number of researchers agree that kL a scales very reliably with the superficial gas velocity U sg alone (Shah et al., 1982; Shah, 1979; Besagni et al., 2017; Besagni et al., 2018; Rollbusch et al., 2015; Önsan and Avci, 2016). Eq. (2) is commonly used to describe this scaling law
kL a ¼ aU bsg :
ð2Þ
A review of the literature shows that the b exponent is fairly close to unity regardless of operating conditions. Over a very wide range of conditions where a superficial velocity can be meaningfully defined (i.e. gas is well distributed), b varies only in a narrow window of 0.8–1.15 (Besagni et al., 2018) and even this variation can be broken down by column size. For narrow columns (DC < 0:2 m), where increasing U sg inevitably leads to slug formation, where small air bubbles coalesce to form slugs which are nearly as wide as the column diameter itself. These slugs do not break down into smaller bubbles as they travel upward, and as a result the gas-liquid mass transfer rate suffers. For narrow bubble columns (D < 0:15 m (Wilkinson et al., 1992)), b < 1 is commonly reported (Besagni et al., 2018). On the other hand, in the case of wider columns (DC > 0:2 m (Wilkinson et al., 1992)), bubble coalescence does not lead to the formation of slugs. In fact, the coalesced bubbles undergo subsequent break up and as a result increase in superficial gas velocity brings about proportional increase in kL a. In such situations experiments produce b 1
_ O2 ;l m Ml Q_ g R T U sg Vl
gS ql qO2 ;g u
rate of mass dissolution of oxygen in water, [kg-O2/m3water/s] molar mass of water (0.018 kg/mol), [kg/mol] volumetric gas flow rate, [m3/s] ideal gas constant (8.314 J/mol-K), [J/mol-K] temperature (293 K), [K] superficial gas velocity, [m/s] liquid volume in the BCR V l ¼ p=4D2C H, [m3 ] mass transfer efficiency, [-] mass density of water (1000 kg/m3), [kg/m3] mass density of oxygen in sparged air (0.28 kg-O2/m3air), [kg-O2/m3-air] ratio of actual (C) and saturation (C ) DO concentrations, [-]
(Chern and Yang, 2003; Jackson and Shen, 1978). There is, however, considerable variation in values of a. A part of this variation can be attributed to the fact that a parameter is inherently correlated with b. It can be shown that, given the kL a versus U sg data, a small perturbation on b can produce a substantial variation in a if only a small range of U sg is traversed experimentally. This can be seen from the work of Jackson and Shen (1978), where the superficial gas velocity was limited to only 5 mm/s (1/10th of experiments reported in Shah et al. (1982) and here). Jackson & Shen obtained b ¼ 1:15 (50% greater than Shah et al. (1982)) and a corresponding a ¼ 1:8 which is nearly 400% greater than Shah et al. (1982). Yet, both these predictions apply quite well to our experimental data as long as they are used within the respective U sg ranges (see Fig. 5). A more systematic source of variation is related to differences in the sparger employed (e.g. a ¼ 1:17 for fine diffuser, but 0:47 for coarse (Shah et al., 1982), everything else remaining constant). Such uncertainty in the model parameters is particularly undesirable when extrapolating Eq. (2) to scale up. We note that scale up primarily involves specification of the vessel (i.e. its dimensions, batch volume), specification of the sparger (fine or coarse bubble diffusers), and definition of the operating window (e.g. maximum liquid volume, minimum air flow rate, etc.). The choices must be made such that the scaled up process is reliable, commercially meaningful, and relatively straightforward to maintain over long periods. This, very often, means that the commercial reactor is not simply a geometrically scaled up version of a laboratory reactor. As an example, while it is useful to run a laboratory scale fermentation process with a fine bubble diffuser due to the high mass transfer rates it provides, such a sparger would be difficult to implement at commercial scales due to (i) the high blower cost associated with pressure drop it presents, and (ii) potentially frequent maintenance to prevent fine pore clogging. As a result, a commercial BCR design must resort to a coarse bubble diffuser, which has very different mass transfer characteristics compared to the fine bubble diffusers (Sharaf et al., 2016; Xylem, 2018). Inaccurate estimation of kL a could now lead to undesirable consequences such as lower productivity than demonstrated at lab-scale (e.g. fermenters Mounsef et al., 2015) or higher than expected operating costs (e.g. aeration ponds Joint Task Force of the Water Pollution Control Federation and ASCE, 1988), resulting in a need for complete reassessment and redesign. It is needless to say that a scalable and accurate mass transfer model is an essential component for scaling up bubble column based process. Wilkinson et al. (1992) established three guiding criteria for laboratory scale experiments such that the findings from those
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experiments could be translated to commercial scale bubble columns. These criteria, briefly summarized, are as follows: 1. Bubble column diameter, DC > 0:2 m. This ensures that the bubble column does not operate in the ‘slug flow’ regime under any condition. This is important because an industrial scale BCR will certainly not operate in the slug flow regime. 2. Aspect ratio (AR), defined as ratio of liquid height (H) to BCR diameter (DC ), is greater than 5. This condition is aimed at ensuring that the ‘end effects’ are of insignificant importance. Besagni et al. (2017) questioned this criterion and, with their experiments in DC ¼ 0:24 m experiments, found that critical AR depends on sparger design, operating mode, and liquid phase properties. We further note that DC may not be a relevant lengthscale for normalizing the liquid height when the hydrodynamics are independent of the column diameter (DC > 0:2 m by Wilkinson’s first criterion). As a result, AR may not be a meaningful scale up metric for wide enough bubble columns. 3. Sparger orifice diameter should be greater than 1–2 mm. Such coarse bubble spargers operate robustly in heterogeneous flow regime, characterized by a wide bubble size distribution. As a result, the hydrodynamics and mass transfer are fairly insensitive to details of sparger design. While Wilkinson’s criteria are certainly of great value in establishing minimum requirements for a lab-scale reactor in which to develop a bubble column process, these criteria cannot always be met in practice. For instance, a laboratory scale BCR with DC > 0:2 m and AR> 5 (i.e. > 30 liter working volume) may not be available, or may be too large for lab-scale development work. As another example, in a lab-scale column with height < 0:5 m, the end effects may be too severe for a coarse bubble sparger, forcing the process scientist to use a fine bubble diffuser, violating Wilkinson’s third criterion. In these cases, available correlations of the form given by Eq. (2) must be used to perform scale up calculations. With respect to Eq. (2), we seek to answer the following questions: i. If kL a does indeed scale primarily with U sg , are a and b scale insensitive? What influences their values? ii. How can we extend the kL a relation obtained in a lab-scale BCR with fine bubble to a pilot/commercial scale BCR employing a coarse bubble sparger? To address these questions, we have performed experiments in a large, DC ¼ 1:6 m, diameter bubble column using air and water as working fluids. The scalability of available correlations is examined in Section 3.1. We then invoke a dimensionless mass transfer efficiency (Section 3.2) and propose the use of well-documented efficiency factors (Joint Task Force of the Water Pollution Control Federation and ASCE, 1988; Xylem, 2018) to capture the effect of sparger on kL a.
2. Experimental setup The experimental setup employed here is schematically shown in Fig. 1. The BCR is a 6 m3 , cylindrical steel tank with diameter DC ¼ 1:6 m and height L ¼ 3 m. While we satisfy Wilkinson et al.’s (1992) first criterion of DC > 0:2 m, we do not satisfy the aspect ratio criterion. Nevertheless, as will be clear from discussion in Section 3, the liquid height is always large enough that end effects are unimportant. The tank is aerated using a multi-ring sparger which carries about 50 holes, each approximately 3 mm in diameter. Based on this orifice diameter (i.e. > 1 2 mm, see (Wilkinson et al., 1992; Besagni et al., 2017; Xylem, 2018)), the
sparger is classified as a coarse bubble distributor. It is important to point out that the sparger geometry plays a crucial role in the two-phase hydrodynamics. Specifically, a fine bubble diffuser (e.g. a porous plate) operating at low enough gas flow rates produces a ‘homogeneous’ flow regime which is characterized by nearly mono-sized bubbles. Increasing the flow rate, however, causes the flow to transition into a heterogeneous regime with a wide bubble size distribution (Sharaf et al., 2016). Such regime transitions and associated changes in kL a make it challenging to scale up BCRs with fine bubble diffusers. The coarse bubble distributors, on the other hand, always operate robustly in the heterogeneous flow regime (Sharaf et al., 2016). The resulting hydrodynamics and mass transfer rates are, naturally, insensitivity to exact details of sparger design. Such a robustness (or lack of sensitivity to fine details) is precisely what is needed when scaling up a bubble column reactor. This makes a coarse bubble distributor a natural choice for scaling up BCRs (Wilkinson et al., 1992). Other factors which influence hydrodynamics are fluid viscosity (Besagni et al., 2017), presence of surfactants (Vasconcelos et al., 2003), and presence of solids (Mena et al., 2005). In the present work, we focus on a simpler system consisting of air (q ¼ 1:2 kg/m3) and water (q ¼ 998 kg/m3, ll ¼ 103 Pa s) as the working fluids. With no surfactants added to the water, the air-water surface tension coefficient is r ¼ 0:07 N/m. An experiment starts with filling the tank with water to a predetermined height H above the sparger. Dissolved oxygen (DO), if any, in the water is stripped by sparging nitrogen through the coarse bubble distributor. The DO level in the water is monitored using a YSI ProODOÒ probe. Once the DO level falls below 3% of saturation value (i.e. C < 0:03C ), nitrogen flow is stopped. The sparger is then connected to compressed air. A solenoid valve feeds the BCR with predetermined volumetric flow rate of air, Q_ g , reported at NTP conditions (20 °C, 1 atm). Dissolved oxygen concentration, C ðtÞ is then measured with the DO probe. Once C ðtÞJ0:95C , air sparging is stopped. The dissolved oxygen is then stripped by sparging nitrogen, in preparation for the next experiment. The mass transfer coefficient is obtained from these C ðt Þ curves collected over a range of Q_ g and H. 3. Experimental results Before proceeding to the analysis of the experimental data, we must reiterate the role of air distribution and hydrodynamics on the mass transfer rate. The hydrodynamics are closely related to how uniformly the sparger delivers the air over the BCR crosssection (Rooney and Huibregtse, 1980). For instance, if the sparger delivers air through only a few orifices, that could lead to the formation of maldistribution of air in the tank. Such maldistribution presents itself in the form of a circulating flow on the scale of DC , and periodic sloshing of the liquid in the tank. In the present work, we did not observe such sloshing, which suggests that maldistribution (if any) was insignificant. Additionally, visualization of the bubbles emanating from the liquid surface, shown in Fig. 2, indicates a uniform air distribution in the BCR. Such uniform distribution allows us to define an area averaged superficial gas velocity,
U sg ¼
4Q_ g
pD2C
:
ð3Þ
The current experiments span 0 < U sg < 0:06 m/s. Fig. 3 shows the influence of changing U sg on the rate at which water can be saturated with oxygen. Here the liquid height is fixed at H ¼ 1:2 m. As expected, greater the U sg , faster is the approach to C . These curves are used to determine kL a for each U sg value. Since the probe itself is not infinitely fast, the measured DO concentra-
S.S. Deshpande et al. / Chemical Engineering Science 205 (2019) 350–357
353
Fig. 1. Schematic diagram of experimental setup.
Fig. 2. View from top of the BCR. Air bubbles are distributed fairly uniformly over the BCR cross section.
Fig. 3. Typical C m ðt Þ profiles at different U sg ; H = 1.2 m.
tion C m ðt Þ is somewhat different from the actual DO concentration, C ðtÞ. The response lag, therefore, needs to be taken into account when estimating kL a. For the YSI ProODOÒ probe, which we found
to behave in a linear manner (Garcia-Ochoa and Gomez, 2009), the response delay is sP ¼ 9 s. Correcting for this lag, kL a is obtained by fitting Eq. (4) to C m ðt Þ
354
C m ðt Þ ¼ C þ
S.S. Deshpande et al. / Chemical Engineering Science 205 (2019) 350–357
C C0 sP kL aet=sP ekL at : 1 sP kL a
ð4Þ
Note, Eq. (4) reduces to the solution of Eq. (1) when sP ¼ 0. The thus obtained kL a values are plotted in Fig. 4 as function of U sg for five different liquid heights. Consistent with literature (Vandu and Krishna, 2004; Shah et al., 1982), kL a varies only with the superficial gas velocity and is unaffected by the liquid height (or volume) in the BCR. This is consistent with the work of Yoshida and Akita (1965). A linear fit (R2 > 0:98) to the entire data yields
kL a ¼ 0:74U sg ;
ð5Þ
i.e. b ¼ 1 and a ¼ 0:74 m1. 3.1. Comparison with selected correlations To address the question of scalability of Eq. (2), our experimental data is compared with correlations listed in Table 1, which span a wide range of BCR scales (0:1KDC K7 m), sparger types, and U sg . Those predictions are overlaid on experimental data and our linear fit in Fig. 5, leading to a good agreement. This suggests that it is adequate to use U sg as the scale up parameter and ða; bÞ parameters are largely scale insensitive. Note that these correlations and our experiments span a very wide range of aspect ratios: 0:5KH=DC K50. The good agreement in kL a estimates even for bubble columns with small aspect ratios suggests that Wilkinson et al.’s (1992)H=DC > 5 criterion may not apply rigorously. In other words, the end effects are likely not related to the column diameter, but to sparger design (Besagni et al., 2017). Furthermore, the good agreement is limited to the correlations obtained from using coarse bubble spargers, where the flow invariably falls under heterogeneous bubble regime with uniform bubble distribution over the column cross-section. When a fine bubble sparger is used (Shah et al., 1982) or when a single coarse nozzle is used to aerate the BCR (Hikita et al., 1981), the corresponding mass transfer correlations fail to predict our kL a data. Clearly, the sparger plays an important role in the hydrodynamic regime and mass transfer rates observed in a bubble column. As mentioned previously, it is of value to be able to translate experimental results obtained with a fine bubble diffuser at lab scale ( O 103 m3) to a commercial scale ( Oð10Þ m3) process where a coarse bubble distributor must be used due to its robustness of operation (Wilkinson et al., 1992) and ease of maintenance. 3.2. Mass transfer efficiency We found that the role of sparger in mass transfer phenomenon was quite extensively documented in the context of aeration ponds
(Joint Task Force of the Water Pollution Control Federation and ASCE, 1988; Rooney and Huibregtse, 1980; Eckenfelder, 1952; Xylem, 2018) – a device identical to bubble columns in concept, but very different in its scale. We borrow from that literature, the definition of mass transfer efficiency,
gS ¼
mO2 ;l mO2 ;g
ð6Þ
which represents the ratio of mass of O2 dissolved in water to mass of O2 via sparging. The mass of dissolved oxygen is a function of time and can be written as
mO2 ;l ðt Þ ¼ C 1 ekL at H p=4D2C
ð7Þ
while the mass of oxygen supplied over time is
mO2 ;g ðt Þ ¼ qO2 ;g U sg
p=4D2C t:
ð8Þ
Here, qO2 ;g ¼ 0:28 kg-O2 /m3-air is the mass density of oxygen in sparged air. The efficiency is, then, given by
gS ¼
C H 1 ekL at : qO2 ;g U sg t
ð9Þ
As is clear from Eq. (9), gS ðtÞ ! 0 as t ! 1. This is expected because, at long enough times, C ðt Þ ! C and the subsequently sparged air contributes to no net oxygen dissolution. It is, therefore, meaningful to restrict the calculation of gS to a time period ^t over which C ^t < uC (i.e. unsaturated). This time period is given by
^t ¼ lnð1 uÞ : kL a
ð10Þ
Substituting t ¼ ^t in Eq. (9),
gS ¼
kL aH U sg
C
qO2 ;g
!
u : lnð1 uÞ
ð11Þ
The u ! 1 case represents the situation where gas-liquid mass transfer does not limit the overall reaction rate and consequently the DO concentration reaches saturation after long enough time. The situation of greater interest to BCR scale up is the one where oxygen transfer rate is the limiting factor (e.g. high-productivity bioreactors). In that case, u ! 0 and the mass transfer efficiency is given by
gS ¼
! kL a C H: U sg qO2 ;g
ð12Þ
The thus calculated gS values are plotted in Fig. 6a for all the experiments. Clearly, for a given liquid height gS is quite insensitive to U sg , varying by only about 20% for a 500% increase in U sg .
Fig. 4. Experimental kL a values as function of U sg for different liquid heights, H.
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S.S. Deshpande et al. / Chemical Engineering Science 205 (2019) 350–357 Table 1 Representative kL a correlations spanning wide range of experimental conditions. Source
Conditions
Deckwer et al. (1974) Shah et al. (1982) Hikita et al. (1981) Chern and Yang (2003) Jackson and Shen (1978) Shah et al. (1982)
Multi-hole sparger; Do ¼ 1 mm; 0:004 < U sg < 0:010 m/s Multi-hole sparger; Do ¼ 1 mm; 0:002 < U sg < 0:080 m/s Single tube sparger; Do ¼ 10 mm; U sg > 0:04 m/s Proprietary coarse bubble diffuser; 0:001 < U sg < 0:004 m/s Various coarse bubble diffusers; Do > 4 mm; U sg < 0:005 m/s Fine diffuser Do ¼ 0:15 mm; 0:003 < U sg < 0:080 m/s
DC (m)
HC (m)
a
b
0.2 0.2 0.1, 0.19 0.9 0.07–7 0.15
>1 2–7 2.2 0.6–1.8 10–20 2.5–4.4
0.49 0.47 0.61 0.8 1.8 1.17
0.88 0.82 0.76 1.006 1.15 0.82
Fig. 5. Comparison of all experimentally obtained kL a values with correlations from Table 1.
Therefore, it seems reasonable to neglect this minor variation, and
represent an average value for each liquid height as gS iH . The average efficiency is found to vary linearly with H, as shown in Fig. 6b (errorbars represent spread in gS for the particular liquid height). Thus, we write
hgS i gS ¼ KH;
ð13Þ 1
with K 0:026 m . Such a linear dependence of mass transfer efficiency gS on the liquid height H above the sparger is consistent with experiments on wide aeration vessels (Rooney and Huibregtse, 1980; Chern and Yang, 2003; Jackson and Shen, 1978; Pöpel and Wagner, 1994). The rate a which we found the efficiency to increase with height, K ¼ 2:6% m1, compares very favorably with literature on coarse bubble distributors (Xylem (2018) up to 2.5% m1), the data reported by American Society of Civil Engineers Joint Task
Force of the Water Pollution Control Federation and ASCE, 1988 (2–3% m1), theory of Popel & Wagner Pöpel and Wagner, 1994 (up to 3.3% m1). In fact, the variation of sparger efficiency factor, K, is well documented for different types of spargers (2–4% m1 for coarse bubble diffusers and up to 10% m1 for fine/porous diffusers). It is worth pointing out that our kL a data is described well by the kL a power-law model (see Section 3.1) as well as the mass transfer efficiency model, suggesting the two descriptions are interchangeable. In fact, we now show that Eq. (2) can be obtained from Eq. (12). Eliminating gS using Eq. (13) and noticing that C and qO2;g are related by Henry’s law as
C
qO2 ;g
¼
RT ql ; HðT Þ Ml
Fig. 6. Oxygen transfer efficiency.
ð14Þ
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we now obtain the kL a – U sg relation,
H Ml U sg ; kL a ¼ K RT ql
5. Future work
with b ¼ 1 and
a¼ K
HðT Þ M l RT
ql
ð15Þ
:
ð16Þ
As expected from results of Section 3.1, a shows no dependence on the dimensions of the bubble column. Eq. (16) can be evaluated using HðT ¼ 293 KÞ ¼ 3:9 109 Pa Morrison and Billett, 1952 and K ¼ 0:026 (see Eq. (13) and Fig. 6b) leading to a ¼ 0:75 m1. This is in excellent agreement with the slope of linear kL a versus U sg fit obtained in Fig. 4. While our experiments do not probe the role of sparger type, we refer to the work reported in Shah et al. Shah et al., 1982, where a ¼ 1:17 for fine and a ¼ 0:47 for coarse diffusers has been reported. The 2-3-fold increase in a is consistent with a 2-3-fold increase in K associated with these two sparger geometries Xylem, 2018; Joint Task Force of the Water Pollution Control Federation and ASCE, 1988. Another point to note is that by Eq. (15), kL a is not influenced by the degree of air enrichment (i.e. by changes in partial pressure of oxygen in the air). This is consistent with the work of Zedníková et al. (2018) where identical kL a values were obtained for experiments done with air and with pure oxygen. 4. Conclusion Several prior studies have shown that the mass transfer coefficient in a BCR can be described adequately in terms of superficial gas velocity using correlation of the form
kL a ¼ aU bsg : Our investigation of its applicability to BCR scale up led to the following findings: i. The scaling with U sg alone and values of a; b parameters are, indeed, quite scale insensitive. Prior correlations with similar sparger geometries as in current work successfully describe our kL a results. Nevertheless, the correlation does not offer a way to account for changes in sparger geometry, which are known to significantly influence kL a. ii. Borrowing the notion of mass transfer efficiency from literature on aeration ponds, we explicitly derived the power law relation for kL a with b ¼ 1 and a ¼ ðKHM l Þ= RT ql . Both these parameters are scale independent, as expected. Furthermore, numerical estimation of a is in excellent agreement with experimental data. iii. Embedded in the definition of a is the efficiency factor (K) which depends upon sparger type. Reliable K value estimates for a given type of sparger are already documented in the literature and can be obtained through American Society of Civil Engineers (Joint Task Force of the Water Pollution Control Federation and ASCE, 1988) and technical data sheets provided sparger manufacturers (Xylem, 2018). For the sake of completeness, we merely state here the ranges to be 0:016KKK0:028 m1 for coarse bubble diffusers, and 0:07KKK0:1 m1 for fine bubble diffusers. Having these ranges is particularly useful for scale up, where a fine bubble diffuser is indispensable at lab-scale, but recourse to a coarse bubble sparger is necessary at larger scales for ease of maintenance and operation cost.
The current work did not attempt to characterize the role of fluid viscosity and electrolytes in the liquid phase. It would be of interest to examine whether similar simplification of a and b parameters is warranted even for more complex fluids. Acknowledgements We would like to thank Scott Bury and Chris Stowers for numerous fruitful discussions on bioreactor technology and bubble column design. References Besagni, G., Inzoli, F., De Guido, G., Pellegrini, L.A., 2017. The dual effect of viscosity on bubble column hydrodynamics. Chem. Eng. Sci. 158, 509–538. Besagni, G., Gallazzini, L., Inzoli, F., 2017. On the scale-up criteria for bubble columns, Petroleum. Besagni, G., Inzoli, F., Ziegenhein, T., 2018. Two-phase bubble columns: a comprehensive review. Chem. Eng. 2 (2), 13. Bird, R.B., Stewart, W.E., Lightfoot, E.N., 1960. Transport Phenomena. John Wiley & Sons. Chern, J.-M., Yang, S.-P., 2003. Oxygen transfer rate in a coarse-bubble diffused aeration system. Indust. Eng. Chem. Res. 42 (25), 6653–6660. Deckwer, W.-D., Burckhart, R., Zoll, G., 1974. Mixing and mass transfer in tall bubble columns. Chem. Eng. Sci. 29 (11), 2177–2188. Eckenfelder, W.W., 1952. Aeration efficiency and design: I. Measurement of oxygen transfer efficiency. Sewage Indust. Wastes, 1221–1228. Frossling, N., 1938. Uber die verdunstung fallernder tropfen. Gerlands Beitr. Geophys. 52, 170–216. Garcia-Ochoa, F., Gomez, E., 2009. Bioreactor scale-up and oxygen transfer rate in microbial processes: an overview. Biotechnol. Adv. 27 (2), 153–176. Hikita, H., Asai, S., Tanigawa, K., Segawa, K., Kitao, M., 1981. The volumetric liquidphase mass transfer coefficient in bubble columns. Chem. Eng. J. 22 (1), 61–69. Jackson, M.L., Shen, C.-C., 1978. Aeration and mixing in deep tank fermentation systems. AIChE J. 24 (1), 63–71. Joint Task Force of the Water Pollution Control Federation and ASCE, Aeration- A Wastewater Treatment Process, ASCE Publications, 1988. Mena, P., Ruzicka, M., Rocha, F., Teixeira, J., Drahoš, J., 2005. Effect of solids on homogeneous–heterogeneous flow regime transition in bubble columns. Chem. Eng. Sci. 60 (22), 6013–6026. Morrison, T., Billett, F., 1952. 730. the salting-out of non-electrolytes. Part II. The effect of variation in non-electrolyte. J. Chem. Soc. (Resumed), 3819–3822. Mounsef, J.R., Salameh, D., Louka, N., Brandam, C., Lteif, R., 2015. The effect of aeration conditions, characterized by the volumetric mass transfer coefficient kla, on the fermentation kinetics of bacillus thuringiensis kurstaki. J. Biotechnol. 210, 100–106. Nedeltchev, S., Nigam, K.D., Schumpe, A., 2014. Prediction of mass transfer coefficients in a slurry bubble column based on the geometrical characteristics of bubbles. Chem. Eng. Sci. 106, 119–125. Önsan, Z.I., Avci, A.K., 2016. Multiphase Catalytic Reactors: Theory, Design, Manufacturing, and Applications. John Wiley & Sons. Paul, E.L., Atiemo-Obeng, V.A., Kresta, S.M., 2004. Handbook of Industrial Mixing: Science and Practice. John Wiley & Sons. Pöpel, H.J., Wagner, M., 1994. Modelling of oxygen transfer in deep diffusedaeration tanks and comparison with full-scale plant data. Water Sci. Technol. 30 (4), 71–80. Rollbusch, P., Bothe, M., Becker, M., Ludwig, M., Gruenewald, M., Schlueter, M., Franke, R., 2015. Bubble columns operated under industrially relevant conditions–current understanding of design parameters. Chem. Eng. Sci. 126, 660–678. Rooney, T.C., Huibregtse, G.L., 1980. Increased oxygen transfer efficiency with coarse bubble diffusers. J. (Water Pollut. Control Federation), 2315–2326. Shah, Y.T., 1979. Gas Liquid Solid Reactor Design, vol. 327. McGraw-Hill International Book Company. Shah, Y., Kelkar, B., Godbole, S., Deckwer, W.-D., 1982. Design parameters estimations for bubble column reactors. AIChE J. 28 (3), 353–379. Shaikh, A., Al-Dahhan, M., 2013. Scale-up of bubble column reactors: a review of current state-of-the-art. Indust. Eng. Chem. Res. 52 (24), 8091–8108. Sharaf, S., Zednikova, M., Ruzicka, M., Azzopardi, B., 2016. Global and local hydrodynamics of bubble columns – effect of gas distributor. Chem. Eng. J. Vandu, C., Krishna, R., 2004. Influence of scale on the volumetric mass transfer coefficients in bubble columns. Chem. Eng. Process. 43 (4), 575–579. Vasconcelos, J., Rodrigues, J., Orvalho, S., Alves, S., Mendes, R., Reis, A., 2003. Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors. Chem. Eng. Sci. 58 (8), 1431–1440.
S.S. Deshpande et al. / Chemical Engineering Science 205 (2019) 350–357 Vasconcelos, J., Rodrigues, J., Orvalho, S., Alves, S., Mendes, R., Reis, A., 2003. Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors. Chem. Eng. Sci. 58 (8), 1431–1440. Wilkinson, P., Speck, A., van Dierendonck, L., 1992. Design parameters estimation for scale-up of high-pressure bubble columns. AIChE J. 38 (4).
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Mass transfer estimation for bubble column scale up S.S. Deshpande a,⇑, K. Kar a, J. Pressler a, I. Tebeka b, B. Martins c, D. Rosenfeld b, J. Biggs c a
The Dow Chemical Company, Core R&D, Midland, MI 48674, USA The Dow Chemical Company, Hydrocarbons R&D, Freeport, TX 77541, USA c The Dow Chemical Company, Hydrocarbons R&D, Sao Paulo 04794, Brazil b
h i g h l i g h t s aU s g b , in estimating the gas-liquid mass transfer coefficient during bubble column scaling up. The existing correlations are found to adequately describe our experimental results, suggesting such correlations are scale insensitive. Using a dimensionless mass transfer efficiency, we show that b = 1 is appropriate and present a method to calculate a once the type of sparger (coarse or fine bubble distributor) is chosen. Explored the suitability of power-law type correlation, kL a ¼
a r t i c l e
i n f o
Article history: Received 4 January 2019 Received in revised form 30 March 2019 Accepted 5 May 2019 Available online 7 May 2019
a b s t r a c t The productivity of a bubble column reactor (BCR) critically depends upon gas-liquid mass transfer coefficient, kL a. The prediction of kL a as function of design and operating conditions is central to BCR scale up. A large number of researchers have successfully characterized kL a experimentally in terms of superficial gas velocity, U sg using the power law relation kL a ¼ aU bsg , with a; b as fit parameters. We probe the applicability of such correlations to the design of a scaled up BCR,which differs from laboratory BCR in two important aspects: (i) the scale of operation, which can be O 102 103 times larger, and (ii) the type of sparger used. To this end, experiments were performed with air and water in a pilot scale (DC ¼ 1:6 m diameter) BCR using a coarse bubble sparger. We found that the existing correlations do, indeed, describe kL a over a wide range of BCR sizes, suggesting that these correlations are fairly scale insensitive. However, the correlations provide no means to capture the role of sparger explicitly. We cast our experimental kL a values in terms of a mass transfer efficiency and independently recover the power law relation with b ¼ 1. We suggest that the role of sparger design can be incorporated in the definition of a through the well-documented sparger efficiency factors. The a and b estimates thus obtained are in good agreement with the literature. Ó 2019 Published by Elsevier Ltd.
1. Introduction Bubble column reactors (BCRs) are multiphase mass-transfer devices intended to bring about rapid dissolution of a sparged gas into a liquid phase. The aim is typically to replenish the dissolved gas which is consumed during a liquid phase reaction. The liquid phase could be stationary, or flowing in a cocurrent or countercurrent manner relative to the sparged air. In the current work, we are interested in bubble columns where the liquid phase is stationary. Although bubble columns typically provide lower rates of gas dissolution than agitated aerated tanks and inline gas-liquid contactors (Paul et al., 2004), the absence of moving parts, ease ⇑ Corresponding author. E-mail addresses: (S.S. Deshpande).
[email protected],
https://doi.org/10.1016/j.ces.2019.05.011 0009-2509/Ó 2019 Published by Elsevier Ltd.
[email protected]
of maintenance and low operation cost makes them attractive in industrial aerobic fermentation, and other applications where gas-liquid mass transfer is essential (see Shah et al., 1982; Shah, 1979; Önsan and Avci, 2016). Rate of mass transfer from the sparged gas to the liquid phase determines the productivity of the reactor. Mathematically, in a well mixed BCR, this rate can be described by the mass conservation equation
dðV l C Þ ¼ kL aV l ðC C Þ; dt
ð1Þ
where C is the dissolved gas concentration (O2 in the present work), C is its saturation concentration, V l is the liquid volume, and kL a is a kinetic parameter, called the gas-liquid mass transfer coefficient. Physically, once a gas-liquid interface is formed, it is assumed that an infinitesimally thin film on the liquid side of the interface reaches the saturation concentration C almost instantaneously
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351
Nomenclature C C Cm DC H H kL a K _ O2 ;g m
dissolved oxygen concentration, [kg-O2/m3-water] dissolved oxygen concentration at saturation, [kg-O2/ m3-water] dissolved oxygen concentration, as measured by the probe, [kg-O2/m3-water] bubble column diameter, [m] liquid height above sparger, [m] Henry’s law constant for oxygen in water (3:9 109 Pa Morrison and Billett, 1952), [Pa] gas-liquid mass transfer coefficient, [s1] efficiency change per unit change in liquid height above sparger, [m1] rate of mass supply of oxygen via sparging, [kg-O2/m3air/s]
(Paul et al., 2004). This is a reasonable assumption here since there are no competing reactions within the film that would deplete the dissolved gas. The concentration of the dissolved species within the bulk of the liquid phase then increases due to diffusion from this saturated film, and the area available for diffusion. The former factor is described in terms of a resistance, 1=kL (see Refs. (Bird et al., 1960; Frossling, 1938) for theories for kL ), and the latter in terms of interfacial area per unit liquid volume, a. Experimentally, neither ‘kL ’ nor ‘a’ can be obtained reliably (Paul et al., 2004); only the product kL a ¼ kL a can be characterized as a lumped parameter. The estimation of kL a has been a topic of research for several decades. For a historical perspectives and current state of understanding of the BCR hydrodynamics and mass transfer, we refer the reader to excellent reviews by Shah et al. (1982), Shah (1979), Shaikh and Al-Dahhan (2013), recent work of Besagni et al. (2017), Besagni et al. (2018), and Rollbusch et al. (2015). Here we only very briefly summarize the learning directly relevant to the topic at hand, namely kL a estimation for BCR scale up. While BCR design (Shah, 1979), fluid properties (Nedeltchev et al., 2014), temperature and pressure (Rollbusch et al., 2015), and presence of contaminants (Vasconcelos et al., 2003) all have some degree of influence on kL a, an overwhelming number of researchers agree that kL a scales very reliably with the superficial gas velocity U sg alone (Shah et al., 1982; Shah, 1979; Besagni et al., 2017; Besagni et al., 2018; Rollbusch et al., 2015; Önsan and Avci, 2016). Eq. (2) is commonly used to describe this scaling law
kL a ¼ aU bsg :
ð2Þ
A review of the literature shows that the b exponent is fairly close to unity regardless of operating conditions. Over a very wide range of conditions where a superficial velocity can be meaningfully defined (i.e. gas is well distributed), b varies only in a narrow window of 0.8–1.15 (Besagni et al., 2018) and even this variation can be broken down by column size. For narrow columns (DC < 0:2 m), where increasing U sg inevitably leads to slug formation, where small air bubbles coalesce to form slugs which are nearly as wide as the column diameter itself. These slugs do not break down into smaller bubbles as they travel upward, and as a result the gas-liquid mass transfer rate suffers. For narrow bubble columns (D < 0:15 m (Wilkinson et al., 1992)), b < 1 is commonly reported (Besagni et al., 2018). On the other hand, in the case of wider columns (DC > 0:2 m (Wilkinson et al., 1992)), bubble coalescence does not lead to the formation of slugs. In fact, the coalesced bubbles undergo subsequent break up and as a result increase in superficial gas velocity brings about proportional increase in kL a. In such situations experiments produce b 1
_ O2 ;l m Ml Q_ g R T U sg Vl
gS ql qO2 ;g u
rate of mass dissolution of oxygen in water, [kg-O2/m3water/s] molar mass of water (0.018 kg/mol), [kg/mol] volumetric gas flow rate, [m3/s] ideal gas constant (8.314 J/mol-K), [J/mol-K] temperature (293 K), [K] superficial gas velocity, [m/s] liquid volume in the BCR V l ¼ p=4D2C H, [m3 ] mass transfer efficiency, [-] mass density of water (1000 kg/m3), [kg/m3] mass density of oxygen in sparged air (0.28 kg-O2/m3air), [kg-O2/m3-air] ratio of actual (C) and saturation (C ) DO concentrations, [-]
(Chern and Yang, 2003; Jackson and Shen, 1978). There is, however, considerable variation in values of a. A part of this variation can be attributed to the fact that a parameter is inherently correlated with b. It can be shown that, given the kL a versus U sg data, a small perturbation on b can produce a substantial variation in a if only a small range of U sg is traversed experimentally. This can be seen from the work of Jackson and Shen (1978), where the superficial gas velocity was limited to only 5 mm/s (1/10th of experiments reported in Shah et al. (1982) and here). Jackson & Shen obtained b ¼ 1:15 (50% greater than Shah et al. (1982)) and a corresponding a ¼ 1:8 which is nearly 400% greater than Shah et al. (1982). Yet, both these predictions apply quite well to our experimental data as long as they are used within the respective U sg ranges (see Fig. 5). A more systematic source of variation is related to differences in the sparger employed (e.g. a ¼ 1:17 for fine diffuser, but 0:47 for coarse (Shah et al., 1982), everything else remaining constant). Such uncertainty in the model parameters is particularly undesirable when extrapolating Eq. (2) to scale up. We note that scale up primarily involves specification of the vessel (i.e. its dimensions, batch volume), specification of the sparger (fine or coarse bubble diffusers), and definition of the operating window (e.g. maximum liquid volume, minimum air flow rate, etc.). The choices must be made such that the scaled up process is reliable, commercially meaningful, and relatively straightforward to maintain over long periods. This, very often, means that the commercial reactor is not simply a geometrically scaled up version of a laboratory reactor. As an example, while it is useful to run a laboratory scale fermentation process with a fine bubble diffuser due to the high mass transfer rates it provides, such a sparger would be difficult to implement at commercial scales due to (i) the high blower cost associated with pressure drop it presents, and (ii) potentially frequent maintenance to prevent fine pore clogging. As a result, a commercial BCR design must resort to a coarse bubble diffuser, which has very different mass transfer characteristics compared to the fine bubble diffusers (Sharaf et al., 2016; Xylem, 2018). Inaccurate estimation of kL a could now lead to undesirable consequences such as lower productivity than demonstrated at lab-scale (e.g. fermenters Mounsef et al., 2015) or higher than expected operating costs (e.g. aeration ponds Joint Task Force of the Water Pollution Control Federation and ASCE, 1988), resulting in a need for complete reassessment and redesign. It is needless to say that a scalable and accurate mass transfer model is an essential component for scaling up bubble column based process. Wilkinson et al. (1992) established three guiding criteria for laboratory scale experiments such that the findings from those
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experiments could be translated to commercial scale bubble columns. These criteria, briefly summarized, are as follows: 1. Bubble column diameter, DC > 0:2 m. This ensures that the bubble column does not operate in the ‘slug flow’ regime under any condition. This is important because an industrial scale BCR will certainly not operate in the slug flow regime. 2. Aspect ratio (AR), defined as ratio of liquid height (H) to BCR diameter (DC ), is greater than 5. This condition is aimed at ensuring that the ‘end effects’ are of insignificant importance. Besagni et al. (2017) questioned this criterion and, with their experiments in DC ¼ 0:24 m experiments, found that critical AR depends on sparger design, operating mode, and liquid phase properties. We further note that DC may not be a relevant lengthscale for normalizing the liquid height when the hydrodynamics are independent of the column diameter (DC > 0:2 m by Wilkinson’s first criterion). As a result, AR may not be a meaningful scale up metric for wide enough bubble columns. 3. Sparger orifice diameter should be greater than 1–2 mm. Such coarse bubble spargers operate robustly in heterogeneous flow regime, characterized by a wide bubble size distribution. As a result, the hydrodynamics and mass transfer are fairly insensitive to details of sparger design. While Wilkinson’s criteria are certainly of great value in establishing minimum requirements for a lab-scale reactor in which to develop a bubble column process, these criteria cannot always be met in practice. For instance, a laboratory scale BCR with DC > 0:2 m and AR> 5 (i.e. > 30 liter working volume) may not be available, or may be too large for lab-scale development work. As another example, in a lab-scale column with height < 0:5 m, the end effects may be too severe for a coarse bubble sparger, forcing the process scientist to use a fine bubble diffuser, violating Wilkinson’s third criterion. In these cases, available correlations of the form given by Eq. (2) must be used to perform scale up calculations. With respect to Eq. (2), we seek to answer the following questions: i. If kL a does indeed scale primarily with U sg , are a and b scale insensitive? What influences their values? ii. How can we extend the kL a relation obtained in a lab-scale BCR with fine bubble to a pilot/commercial scale BCR employing a coarse bubble sparger? To address these questions, we have performed experiments in a large, DC ¼ 1:6 m, diameter bubble column using air and water as working fluids. The scalability of available correlations is examined in Section 3.1. We then invoke a dimensionless mass transfer efficiency (Section 3.2) and propose the use of well-documented efficiency factors (Joint Task Force of the Water Pollution Control Federation and ASCE, 1988; Xylem, 2018) to capture the effect of sparger on kL a.
2. Experimental setup The experimental setup employed here is schematically shown in Fig. 1. The BCR is a 6 m3 , cylindrical steel tank with diameter DC ¼ 1:6 m and height L ¼ 3 m. While we satisfy Wilkinson et al.’s (1992) first criterion of DC > 0:2 m, we do not satisfy the aspect ratio criterion. Nevertheless, as will be clear from discussion in Section 3, the liquid height is always large enough that end effects are unimportant. The tank is aerated using a multi-ring sparger which carries about 50 holes, each approximately 3 mm in diameter. Based on this orifice diameter (i.e. > 1 2 mm, see (Wilkinson et al., 1992; Besagni et al., 2017; Xylem, 2018)), the
sparger is classified as a coarse bubble distributor. It is important to point out that the sparger geometry plays a crucial role in the two-phase hydrodynamics. Specifically, a fine bubble diffuser (e.g. a porous plate) operating at low enough gas flow rates produces a ‘homogeneous’ flow regime which is characterized by nearly mono-sized bubbles. Increasing the flow rate, however, causes the flow to transition into a heterogeneous regime with a wide bubble size distribution (Sharaf et al., 2016). Such regime transitions and associated changes in kL a make it challenging to scale up BCRs with fine bubble diffusers. The coarse bubble distributors, on the other hand, always operate robustly in the heterogeneous flow regime (Sharaf et al., 2016). The resulting hydrodynamics and mass transfer rates are, naturally, insensitivity to exact details of sparger design. Such a robustness (or lack of sensitivity to fine details) is precisely what is needed when scaling up a bubble column reactor. This makes a coarse bubble distributor a natural choice for scaling up BCRs (Wilkinson et al., 1992). Other factors which influence hydrodynamics are fluid viscosity (Besagni et al., 2017), presence of surfactants (Vasconcelos et al., 2003), and presence of solids (Mena et al., 2005). In the present work, we focus on a simpler system consisting of air (q ¼ 1:2 kg/m3) and water (q ¼ 998 kg/m3, ll ¼ 103 Pa s) as the working fluids. With no surfactants added to the water, the air-water surface tension coefficient is r ¼ 0:07 N/m. An experiment starts with filling the tank with water to a predetermined height H above the sparger. Dissolved oxygen (DO), if any, in the water is stripped by sparging nitrogen through the coarse bubble distributor. The DO level in the water is monitored using a YSI ProODOÒ probe. Once the DO level falls below 3% of saturation value (i.e. C < 0:03C ), nitrogen flow is stopped. The sparger is then connected to compressed air. A solenoid valve feeds the BCR with predetermined volumetric flow rate of air, Q_ g , reported at NTP conditions (20 °C, 1 atm). Dissolved oxygen concentration, C ðtÞ is then measured with the DO probe. Once C ðtÞJ0:95C , air sparging is stopped. The dissolved oxygen is then stripped by sparging nitrogen, in preparation for the next experiment. The mass transfer coefficient is obtained from these C ðt Þ curves collected over a range of Q_ g and H. 3. Experimental results Before proceeding to the analysis of the experimental data, we must reiterate the role of air distribution and hydrodynamics on the mass transfer rate. The hydrodynamics are closely related to how uniformly the sparger delivers the air over the BCR crosssection (Rooney and Huibregtse, 1980). For instance, if the sparger delivers air through only a few orifices, that could lead to the formation of maldistribution of air in the tank. Such maldistribution presents itself in the form of a circulating flow on the scale of DC , and periodic sloshing of the liquid in the tank. In the present work, we did not observe such sloshing, which suggests that maldistribution (if any) was insignificant. Additionally, visualization of the bubbles emanating from the liquid surface, shown in Fig. 2, indicates a uniform air distribution in the BCR. Such uniform distribution allows us to define an area averaged superficial gas velocity,
U sg ¼
4Q_ g
pD2C
:
ð3Þ
The current experiments span 0 < U sg < 0:06 m/s. Fig. 3 shows the influence of changing U sg on the rate at which water can be saturated with oxygen. Here the liquid height is fixed at H ¼ 1:2 m. As expected, greater the U sg , faster is the approach to C . These curves are used to determine kL a for each U sg value. Since the probe itself is not infinitely fast, the measured DO concentra-
S.S. Deshpande et al. / Chemical Engineering Science 205 (2019) 350–357
353
Fig. 1. Schematic diagram of experimental setup.
Fig. 2. View from top of the BCR. Air bubbles are distributed fairly uniformly over the BCR cross section.
Fig. 3. Typical C m ðt Þ profiles at different U sg ; H = 1.2 m.
tion C m ðt Þ is somewhat different from the actual DO concentration, C ðtÞ. The response lag, therefore, needs to be taken into account when estimating kL a. For the YSI ProODOÒ probe, which we found
to behave in a linear manner (Garcia-Ochoa and Gomez, 2009), the response delay is sP ¼ 9 s. Correcting for this lag, kL a is obtained by fitting Eq. (4) to C m ðt Þ
354
C m ðt Þ ¼ C þ
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C C0 sP kL aet=sP ekL at : 1 sP kL a
ð4Þ
Note, Eq. (4) reduces to the solution of Eq. (1) when sP ¼ 0. The thus obtained kL a values are plotted in Fig. 4 as function of U sg for five different liquid heights. Consistent with literature (Vandu and Krishna, 2004; Shah et al., 1982), kL a varies only with the superficial gas velocity and is unaffected by the liquid height (or volume) in the BCR. This is consistent with the work of Yoshida and Akita (1965). A linear fit (R2 > 0:98) to the entire data yields
kL a ¼ 0:74U sg ;
ð5Þ
i.e. b ¼ 1 and a ¼ 0:74 m1. 3.1. Comparison with selected correlations To address the question of scalability of Eq. (2), our experimental data is compared with correlations listed in Table 1, which span a wide range of BCR scales (0:1KDC K7 m), sparger types, and U sg . Those predictions are overlaid on experimental data and our linear fit in Fig. 5, leading to a good agreement. This suggests that it is adequate to use U sg as the scale up parameter and ða; bÞ parameters are largely scale insensitive. Note that these correlations and our experiments span a very wide range of aspect ratios: 0:5KH=DC K50. The good agreement in kL a estimates even for bubble columns with small aspect ratios suggests that Wilkinson et al.’s (1992)H=DC > 5 criterion may not apply rigorously. In other words, the end effects are likely not related to the column diameter, but to sparger design (Besagni et al., 2017). Furthermore, the good agreement is limited to the correlations obtained from using coarse bubble spargers, where the flow invariably falls under heterogeneous bubble regime with uniform bubble distribution over the column cross-section. When a fine bubble sparger is used (Shah et al., 1982) or when a single coarse nozzle is used to aerate the BCR (Hikita et al., 1981), the corresponding mass transfer correlations fail to predict our kL a data. Clearly, the sparger plays an important role in the hydrodynamic regime and mass transfer rates observed in a bubble column. As mentioned previously, it is of value to be able to translate experimental results obtained with a fine bubble diffuser at lab scale ( O 103 m3) to a commercial scale ( Oð10Þ m3) process where a coarse bubble distributor must be used due to its robustness of operation (Wilkinson et al., 1992) and ease of maintenance. 3.2. Mass transfer efficiency We found that the role of sparger in mass transfer phenomenon was quite extensively documented in the context of aeration ponds
(Joint Task Force of the Water Pollution Control Federation and ASCE, 1988; Rooney and Huibregtse, 1980; Eckenfelder, 1952; Xylem, 2018) – a device identical to bubble columns in concept, but very different in its scale. We borrow from that literature, the definition of mass transfer efficiency,
gS ¼
mO2 ;l mO2 ;g
ð6Þ
which represents the ratio of mass of O2 dissolved in water to mass of O2 via sparging. The mass of dissolved oxygen is a function of time and can be written as
mO2 ;l ðt Þ ¼ C 1 ekL at H p=4D2C
ð7Þ
while the mass of oxygen supplied over time is
mO2 ;g ðt Þ ¼ qO2 ;g U sg
p=4D2C t:
ð8Þ
Here, qO2 ;g ¼ 0:28 kg-O2 /m3-air is the mass density of oxygen in sparged air. The efficiency is, then, given by
gS ¼
C H 1 ekL at : qO2 ;g U sg t
ð9Þ
As is clear from Eq. (9), gS ðtÞ ! 0 as t ! 1. This is expected because, at long enough times, C ðt Þ ! C and the subsequently sparged air contributes to no net oxygen dissolution. It is, therefore, meaningful to restrict the calculation of gS to a time period ^t over which C ^t < uC (i.e. unsaturated). This time period is given by
^t ¼ lnð1 uÞ : kL a
ð10Þ
Substituting t ¼ ^t in Eq. (9),
gS ¼
kL aH U sg
C
qO2 ;g
!
u : lnð1 uÞ
ð11Þ
The u ! 1 case represents the situation where gas-liquid mass transfer does not limit the overall reaction rate and consequently the DO concentration reaches saturation after long enough time. The situation of greater interest to BCR scale up is the one where oxygen transfer rate is the limiting factor (e.g. high-productivity bioreactors). In that case, u ! 0 and the mass transfer efficiency is given by
gS ¼
! kL a C H: U sg qO2 ;g
ð12Þ
The thus calculated gS values are plotted in Fig. 6a for all the experiments. Clearly, for a given liquid height gS is quite insensitive to U sg , varying by only about 20% for a 500% increase in U sg .
Fig. 4. Experimental kL a values as function of U sg for different liquid heights, H.
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S.S. Deshpande et al. / Chemical Engineering Science 205 (2019) 350–357 Table 1 Representative kL a correlations spanning wide range of experimental conditions. Source
Conditions
Deckwer et al. (1974) Shah et al. (1982) Hikita et al. (1981) Chern and Yang (2003) Jackson and Shen (1978) Shah et al. (1982)
Multi-hole sparger; Do ¼ 1 mm; 0:004 < U sg < 0:010 m/s Multi-hole sparger; Do ¼ 1 mm; 0:002 < U sg < 0:080 m/s Single tube sparger; Do ¼ 10 mm; U sg > 0:04 m/s Proprietary coarse bubble diffuser; 0:001 < U sg < 0:004 m/s Various coarse bubble diffusers; Do > 4 mm; U sg < 0:005 m/s Fine diffuser Do ¼ 0:15 mm; 0:003 < U sg < 0:080 m/s
DC (m)
HC (m)
a
b
0.2 0.2 0.1, 0.19 0.9 0.07–7 0.15
>1 2–7 2.2 0.6–1.8 10–20 2.5–4.4
0.49 0.47 0.61 0.8 1.8 1.17
0.88 0.82 0.76 1.006 1.15 0.82
Fig. 5. Comparison of all experimentally obtained kL a values with correlations from Table 1.
Therefore, it seems reasonable to neglect this minor variation, and
represent an average value for each liquid height as gS iH . The average efficiency is found to vary linearly with H, as shown in Fig. 6b (errorbars represent spread in gS for the particular liquid height). Thus, we write
hgS i gS ¼ KH;
ð13Þ 1
with K 0:026 m . Such a linear dependence of mass transfer efficiency gS on the liquid height H above the sparger is consistent with experiments on wide aeration vessels (Rooney and Huibregtse, 1980; Chern and Yang, 2003; Jackson and Shen, 1978; Pöpel and Wagner, 1994). The rate a which we found the efficiency to increase with height, K ¼ 2:6% m1, compares very favorably with literature on coarse bubble distributors (Xylem (2018) up to 2.5% m1), the data reported by American Society of Civil Engineers Joint Task
Force of the Water Pollution Control Federation and ASCE, 1988 (2–3% m1), theory of Popel & Wagner Pöpel and Wagner, 1994 (up to 3.3% m1). In fact, the variation of sparger efficiency factor, K, is well documented for different types of spargers (2–4% m1 for coarse bubble diffusers and up to 10% m1 for fine/porous diffusers). It is worth pointing out that our kL a data is described well by the kL a power-law model (see Section 3.1) as well as the mass transfer efficiency model, suggesting the two descriptions are interchangeable. In fact, we now show that Eq. (2) can be obtained from Eq. (12). Eliminating gS using Eq. (13) and noticing that C and qO2;g are related by Henry’s law as
C
qO2 ;g
¼
RT ql ; HðT Þ Ml
Fig. 6. Oxygen transfer efficiency.
ð14Þ
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we now obtain the kL a – U sg relation,
H Ml U sg ; kL a ¼ K RT ql
5. Future work
with b ¼ 1 and
a¼ K
HðT Þ M l RT
ql
ð15Þ
:
ð16Þ
As expected from results of Section 3.1, a shows no dependence on the dimensions of the bubble column. Eq. (16) can be evaluated using HðT ¼ 293 KÞ ¼ 3:9 109 Pa Morrison and Billett, 1952 and K ¼ 0:026 (see Eq. (13) and Fig. 6b) leading to a ¼ 0:75 m1. This is in excellent agreement with the slope of linear kL a versus U sg fit obtained in Fig. 4. While our experiments do not probe the role of sparger type, we refer to the work reported in Shah et al. Shah et al., 1982, where a ¼ 1:17 for fine and a ¼ 0:47 for coarse diffusers has been reported. The 2-3-fold increase in a is consistent with a 2-3-fold increase in K associated with these two sparger geometries Xylem, 2018; Joint Task Force of the Water Pollution Control Federation and ASCE, 1988. Another point to note is that by Eq. (15), kL a is not influenced by the degree of air enrichment (i.e. by changes in partial pressure of oxygen in the air). This is consistent with the work of Zedníková et al. (2018) where identical kL a values were obtained for experiments done with air and with pure oxygen. 4. Conclusion Several prior studies have shown that the mass transfer coefficient in a BCR can be described adequately in terms of superficial gas velocity using correlation of the form
kL a ¼ aU bsg : Our investigation of its applicability to BCR scale up led to the following findings: i. The scaling with U sg alone and values of a; b parameters are, indeed, quite scale insensitive. Prior correlations with similar sparger geometries as in current work successfully describe our kL a results. Nevertheless, the correlation does not offer a way to account for changes in sparger geometry, which are known to significantly influence kL a. ii. Borrowing the notion of mass transfer efficiency from literature on aeration ponds, we explicitly derived the power law relation for kL a with b ¼ 1 and a ¼ ðKHM l Þ= RT ql . Both these parameters are scale independent, as expected. Furthermore, numerical estimation of a is in excellent agreement with experimental data. iii. Embedded in the definition of a is the efficiency factor (K) which depends upon sparger type. Reliable K value estimates for a given type of sparger are already documented in the literature and can be obtained through American Society of Civil Engineers (Joint Task Force of the Water Pollution Control Federation and ASCE, 1988) and technical data sheets provided sparger manufacturers (Xylem, 2018). For the sake of completeness, we merely state here the ranges to be 0:016KKK0:028 m1 for coarse bubble diffusers, and 0:07KKK0:1 m1 for fine bubble diffusers. Having these ranges is particularly useful for scale up, where a fine bubble diffuser is indispensable at lab-scale, but recourse to a coarse bubble sparger is necessary at larger scales for ease of maintenance and operation cost.
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