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1Mechanistic Description of Convective Gas−Liquid Mass Transfer in
2Biotrickling Filters Using CFD Modeling
3Patricio A. Moreno-Casas,
†
Felipe Scott,
†
JoséDelpiano,
†
JoséA. Abell,
†
Francisco Caicedo,
‡
4Raúl Muñoz,
§
and Alberto Vergara-Ferná
ndez*
,†
5
†
Green Technology Research Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago 7620001,
6Chile
7
‡
Facultad de Ingeniería, Universidad Mariana, San Juan de Pasto 520002, Colombia
8
§
Institute of Sustainable Processes, Universidad de Valladolid, Valladolid 47005, Spain
9*
SSupporting Information
10 ABSTRACT: The gas−liquid mass transfer coefficient is a key parameter
11 to the design and operation of biotrickling filters that governs the
12 transport rate of contaminants and oxygen from the gas phase to the
13 liquid phase, where pollutant biodegradation occurs. Mass transfer
14 coefficients are typically estimated via experimental procedures to
15 produce empirical correlations, which are only valid for the bioreactor
16 configuration and range of operational conditions under investigation. In
17 this work, a new method for the estimation of the gas−liquid mass
18 transfer coefficient in biotrickling filters is presented. This novel
19 methodology couples a realistic description of the packing media
20 (polyurethane foam without a biofilm) obtained using microtomography
21 with computational fluid dynamics. The two-dimensional analysis
22 reported in this study allowed capturing the mechanisms of the complex
23 processes involved in the creeping porous air and water flow in the
24 presence of capillary effects in biotrickling filters. Model predictions matched the experimental mass transfer coefficients
25 (±30%) under a wide range of operational conditions.
1. INTRODUCTION
26 Biotechnologies represent a cost-competitive and environ-
27 mentally friendly alternative to conventional physical/chemical
28 technologies for the treatment of malodorous, volatile organic
29 compounds (VOCs), greenhouse gases, and biogas.
1
Of them,
30 biotrickling filtration has become increasingly popular in the
31 past decade based on its low gas residence time of operation
32 (15−40 s
1,2
) and the potential to control key environmental
33 parameters for microbial growth such as temperature, pH, and
34 the concentrations of nutrients and toxic inhibitory metabo-
35 lites.
3,4
Biotrickling filters (BTFs) are packed-bed units where
36 the packing material promotes an effective gas−liquid contact,
37 while supporting biofilm growth because of a continuous
38 supply of liquid medium.
1
Hence, the design of this technology
39 relies on the accurate description of both microbial biofilm
40 kinetics and gas−liquid−solid interactions.
4
However, while
41 the kinetics of pollutant biodegradation in biofilms have been
42 consistently studied, the hydrodynamics of gas and liquid
43 circulation determining pollutant mass transfer in the packing
44 material of BTF are still poorly understood.
5,6
In fact, gas−
45 liquid mass transfer in this bioreactor configuration is typically
46 characterized using empirical methodologies for the determi-
47 nation of the global volumetric mass transfer coefficient (KLa)
48 based on simplified mathematical models.
7−9
The experimental
49
estimation of the volumetric mass transfer coefficient in BTF,
50
as reviewed by Estrada et al.,
9
San Valero et al.,
4
Dumont,
10
51
and Dupnock and Deshusses,
11
is performed using VOC
52
concentration measurements in the gas and liquid phases and
53
CO2absorption in caustic water as the main experimental
54
techniques. Unfortunately, the aforementioned approaches do
55
not provide insights regarding the liquid and gas distribution
56
and channeling inside the packed column (wetted area,
57
velocity and pressure profiles, preferential flows). Therefore,
58
new and more powerful techniques are required to describe all
59
complex phenomena determining the gas−liquid pollutant
60mass transport in BTF.
61
In this context, the recent advances in computational fluids
62
dynamics (CFD) along with the increase in computational
63
power over the past decades has enabled the use of this
64
powerful modeling tool for the design of off-gas treatment
65
biotechnologies, which represents a new application in this
66
field.
12
In order to study the complex geometry of a porous
67matrix, three-dimensional (3D) digital imaging such as
Received: May 2, 2019
Revised: November 16, 2019
Accepted: December 2, 2019
Published: December 2, 2019
Article
pubs.acs.org/est
© XXXX American Chemical Society ADOI: 10.1021/acs.est.9b02662
Environ. Sci. Technol. XXXX, XXX, XXX−XXX
*Unknown *|ACSJCA |JCA11.2.5208/W Library-x64 |research.3f (R4.2.i1:4953 |2.1) 2018/04/01 14:00:00 |PROD-WS-121 |rq_118395 |12/09/2019 04:33:23 |8|JCA-DEFAULT
68 computational tomography or microtomography (depending
69 on the resolution needed) can be used to assess the flow
70 dynamics and compute the parameters of interest. For
71 instance, the combination of 3D imaging and CFD techniques
72 can be employed to obtain pressures and velocities at the pore
73 scale. The coupling of CFD and computational micro-
74 tomography has been used in recent years to analyze the
75 flow through porous media,
13,14
thus allowing for the
76 characterization of the flow at the microscale. To the best of
77 our knowledge, these techniques have never been applied in
78 biofiltration systems for air treatment. A recent work by Prades
79 and co-workers applied the CFD approach by using a
80 commercial code, where biological reactions were coupled to
81 flow equations in order to simulate the liquid velocities and
82 oxygen consumption in a flat plate (rather than a porous
83 support) biofilm bioreactor.
12
The latter CFD simulation
84 represented an important step forward toward the description
85 of gas−liquid flow in porous media BTF.
86 The present work explores the potential of CFD for the
87 description of the gas−liquid mass transport in an abiotic BTF
88 (not inoculated with microorganisms) using O2as a model gas
89 and a detailed description of the polyurethane foam (PUF)
90 support system obtained using 3D microtomography. The
91 predictions of this CFD modeling approach were compared
92 with the volumetric mass transfer coefficients empirically
93 determined in a 6 L BTF operated under multiple operational
94 conditions typically encountered under industrial scale.
2. MATERIALS AND METHODS
95 2.1. Mathematical Model. The effect of capillarity should
96 be considered when assessing the flow of liquid and gas (two-
97 phase flow) in a porous material with sufficiently small pores
98 because liquid meniscus attached to the porous material can
99 impact the flow of both phases. This can be achieved by adding
100 a term to the fluid linear momentum or Navier−Stokes (NS)
101 equations and by applying the Volume of Fluids (VOF
102 technique.
15
The NS equations (eq 1) can be coupled to the
103 continuity equation (eq 2) for each fluid (liquid and gas) to
104 obtain the pressure and velocity fields, while the liquid−gas
105 interphase can be tracked by using the transport equation for
106 the volume fraction of the two phases (eq 3). Both fluids were
107 considered to be Newtonian, incompressible, isothermal, and
108 immiscible.
16
ρ
ρμ
∂
∂+·∇ =−∇+ +∇ +
i
k
j
j
jy
{
z
z
z
U
tUU p g U F
2
s
109 (1)
∇
·=U0
110 (2)
αααα
∂
∂+∇· +∇· − =
tUU() ((1 ))
0
c
111 (3)
112 where, ρis the fluid density (kg m−3), Uis the velocity vector
113 (u,v,w) for the x,y, and zdirections (m s−1), respectively, gis
114 the acceleration of gravity (m s−2), prepresents the pressure
115 vector in space (Pa), μdenotes the dynamic viscosity of the
116
fluid (kg·m−1·s−1), the operator
∇
=
∂
∂
∂
∂
∂
∂
()
,,
xyz
, and FSis
117 the surface tension force (N·m−1). The variable αis the VOF
118 indication function, which can be defined as the quantity of
119 liquid per unit volume at each computational cell (i.e., if α=1,
120 the cell contains only liquid, if α= 0, the cell contains only gas,
121 else there will be a mixture of both phases). Finally, the last
122 term in eq 3 is a mathematical expression required to avoid
123excessive numerical diffusion, where UCrepresents the
124convenient velocity field to compress the gas−liquid
125interphase. The above equations were solved in OpenFOAM,
126where solutions to eqs 1 and 2were obtained by applying the
127well-known predictor−corrector technique pressure-implicit
128with splitting of operators algorithm,
17
while the mathematical
129tracking of the interphase was achieved by solving eq 3
130discretized in the interFoam solver.
18
1312.1.1. Determination of the Volumetric Mass Transfer
132Coefficient (KLa). The volumetric mass transfer coefficient, KLa
133(s−1or h−1), is the product of the mass transfer coefficient, KL
134(m s−1), and the specific surface area, a(m2m−3), where the
135mass transfer occurs. The specific surface area is the ratio of
136the surface S(m2) of contact between the two phases, or
137interfacial area, and the volume V(m3) of the bioreactor.
19
138Several theories are typically used to determine KL:film
139theory, penetration theory, surface renewal theory, and
140boundary layer theory.
20−23
However, only the boundary
141layer theory takes into account the hydrodynamic character-
142ization of the system and provides a more realistic
143interpretation of the mass transfer phenomena occurring at
144the boundary layer.
24
145The concentration distribution of a species A, CA, within the
146air boundary layer is a function of its location, CA=CA(x,y)
147and its thickness, δm, and it also depends on the distance from
148the plate leading edge.
24
In this regard, the momentum
149diffusivity and the mass diffusivity play a key role in the overall
150mass transfer phenomena, which can be accounted for with the
151Schmidt number, Sc. Whenever the momentum diffusivity is
152larger than the mass diffusivity, Sc is larger than 1
25
and δ/δm=
153Sc1/3. Moreover, an expression for an average Sherwood
154number, Shav, can be developed by connecting the average
155plate Reynolds number, Rel=ρV∞l/μ,(V∞, is the air free
156stream velocity, right above the end of the boundary layer) and
157an average Schmidt number, Scav, along a flat plate of length l
24
==
S
hKl
DRe Sc0.664( ) ( )
av
L
AB
l
1/2 1/
3
158
(4)
159where KLis the average mass transfer coefficient along the
160plate length, l, and DAB is the diffusion coefficient between
161fluids A and B (air and water, 2 ×10−9m2s−1
26
). Considering
162that Sc =ν/DAB, an expression for the computation of the mass
163transfer coefficient can be obtained.
ν=
−
∞
−
KlV D0.664( ) ( ) ( ) ( )
L
1/2 1/2 1/6
AB
2/
3
164
(5)
165where νis the kinematic viscosity of the gas phase (1.51 ×10−5
166m2s−1for air). In the present study, the flat plate stands for the
167liquid−gas interphase, which is not flat. However, it will be
168assumed to be nearly flat for computational purposes. The
169estimation of the specific area per unit volume of reactor is
170deferred to Section 3.2. All constants applied in this study
171assume a temperature of 22 °C in order to be able to compare
172numerical and experimental results.
1732.2. PUF Packing 3D Microtomography. In order to
174solve the NS equations, a detailed and realistic description of
175the boundary conditions at the fluid−solid interface is needed,
176which requires a highly resolved 3D image of the porous
177media. Nowadays, it is possible to construct such image by
178using X-ray computed microtomography (μCT). In the
179present study, a SKYSCAN 1272 high resolution X-ray
180microtomography scanner from Bruker was used with a
181maximum resolution of 0.35 μm. Because of the high
Environmental Science & Technology Article
DOI: 10.1021/acs.est.9b02662
Environ. Sci. Technol. XXXX, XXX, XXX−XXX
B
182 resolution needed to obtain images of the PUF support, a small
183 sample of the PUF support of the cylindrical reactor was
184 scanned in the μCT. The height, width, and depth of the
f1 185 sample were 1.58, 1.58, and 0.76 cm, respectively (Figure 1A).
186 The 3D image was saved in stl (stereolithography) format and
187 later used in OpenFOAM.
188 A two-dimensional (2D) slice of the original 3D digitalized
189 image was used in the present study because of the high
190 computational cost required to numerically solve the flow (see
191 Figure 1). The 2D image used in the simulations was 1.58 cm
192 ×1.58 cm. From the 2D image, a fine grid was generated in
193 OpenFOAM in order to discretize the porous voids within the
194 PUF, where the liquid (water) and gas (air) were allowed to
195 flow. A sample of the 2D mesh is shown in Figure 1, where the
196
void spaces indicate the presence of the foam, and the
197
discretized surfaces show the areas where the water and air will
198
flow in the x−yplane (where yis vertical). In order to find a
199
sound grid resolution (number of cells) to simulate all the
200
cases of interest in the present work, a grid independence
201
analysis was carried out (see Figure S1 in the Supporting
202Information).
203
Because the computational domain is much smaller than the
204
complete BTF, the digitalized PUF was assumed to be far away
205
from the BTF inlet and outlet and far away from the column
206
inner walls. In this way, the velocity conditions of the
207
digitalized PUF at the top and bottom were maintained from
208
the experimental setup, while on the sides, cyclic/periodic
209 f2
effects were used to mimic BTF operation (see Figure 2). The
210
results from each simulation were considered to be
211
representative of the average behavior of the BTF, while wall
212
effects (air and water flow interaction with the reactor inner
213
walls) were assumed to be negligible. The velocity boundary
214
conditions, for the 2D grid, were left and right boundaries had
215
a periodic condition; upper and lower boundaries were defined
216
by the inlet and outlet water and air velocities according to
217
each case of study. Wherever there is PUF support, the
218
condition was defined as nonslip or zero velocity condition.
219
The initial conditions for velocity and pressure, for the air and
220
water flows, were defined in accordance with each numerical
221
trial, which in turn was connected to a particular experimental
222 t1
condition (see Table 1). The time step for all simulations was
223
fixed at 0.001 s, and data were also saved every 0.001 s. The air
224
and water flow in the BTF occurred in the ydirection (vertical
225
direction). Thus, water entered the biofilter from the top and
226
moved downward, while the air entered from the bottom of
227
the biofilter and moved upward. A zero-pressure gradient
228
condition was imposed in the support, whereas for the right
229
and left borders, the boundary condition was set to cyclic/
230
periodic. For the inlet and outlet boundaries, the pressure was
231
computed according to the velocity at each boundary cell by
232
applying a total pressure set to p0= 0, while as the velocity U
233changed, the pressure was adjusted as p=p0+ 0.5|U|2.
Figure 1. (A) Digitalized PUF image using μCT. (B) PUF image
showing the computational domain (slice right at the PUF center).
(C) Computational domain used for simulations. (D) Mesh zoom.
White areas indicate the presence of PUF. Only PUF void areas were
discretized.
Figure 2. Schematization of the boundary conditions for the 2D microscale computational domain. BC stands for boundary conditions.
Environmental Science & Technology Article
DOI: 10.1021/acs.est.9b02662
Environ. Sci. Technol. XXXX, XXX, XXX−XXX
C
234 2.3. Experimental Determination of the Volumetric
235 Mass Transfer Coefficient in the BTF. The KLavalues for
236 O2were empirically determined in a 6 L polyvinyl chloride
237 absorption column (0.08 m diameter ×1mheight)
238 interconnected to a 1.5 L glass stirred tank reactor (magneti-
239 cally stirred at 300 rpm). The absorption column was packed
240 with a 4 L PUF cylinder, while the liquid level in the stirred
241 tank was maintained at 1 L. The concentration of dissolved
242 oxygen (DOC) was measured in the stirred tank reactor using
243 a polarographic DOC probe coupled to an O2transmitter 4100
244 (Mettler Toledo GmbH, Urdolf, Germany), which according
245 to the manufacturer exhibited a response time of 90 s to
246 achieve 98% of the equilibrium concentration in a step change
247 from an air-saturated solution to an oxygen-free aqueous
248 solution at 25 °C. Distilled water was used as a model liquid
249 medium in the BTF to avoid any interference of the salt
250 concentrations. (A) A Watson Marlow 520 peristaltic pump
251 was used to recycle the liquid medium from the stirred tank to
252 the top of the absorption column, which was equipped with a
253 cylindrical spray tubing (0.3 cm tip diameter ×10.5 cm length)
254 located 4.5 cm above the PUF packed bed. Figures 2 and S2
255 (Supporting Information) (B) illustrate a schematic of the
256 experimental BTF and water irrigation system, respectively.
257 The volumetric gas−liquid mass transfer coefficients for O2
258 were determined using the gassing-out method at empty bed
259 gas residence times (EBRTs) of 17, 36, 60, and 240 s and
260 liquid velocities of 2, 4, 11, and 17 m h−1at each EBRT. The
261 gassing-out method was selected because of its simplicity, the
262 absence of dangerous chemicals, and our previous expertise
263 using it.
9
Prior to the determination of the KLa,the DOC in
264 the recirculating liquid medium was depleted with helium
265 supplied from the bottom of the BTF counter-currently with
266 the trickling liquid medium (at the corresponding liquid
267 velocity and EBRT). Then, the helium stream was replaced
268 with air at the target operational conditions and the DOC
269 monitored to saturation. The empirical determinations of the
270 KLawere conducted in duplicate at 22 ±1°C (controlled
271 using a thermostatic water bath) using O2mass balances in the
272 BTF and stirred tank reactor (6), and the experimental data
273 obtained in the test above are described.
8
The abiotic BTF was
274modeled as 10 interconnected continuous stirred tank reactors
275(CSTRs) as follows
=−+−
i
k
j
j
jy
{
z
z
z
C
tKa C
HCQ
VCC
d
d() ( )
G
L,out
1
LO L,out
1L
c
L,in L, out
1
2
276(6)
=−
+−={}
−
i
k
j
j
jy
{
z
z
z
tKa C
HC
Q
VCC j
dC
d()
( ) 2, ..., 9
j
j
jj
L,out
LO
G
L,out
L
c
L,out
1
L,out
2
277
(7)
=−
+−
i
k
j
j
jy
{
z
z
z
C
tKa C
HC
Q
VCC
d
d()
()
L,out
10
LO
G
L,out
10
L
c
L,out
9
L,out
10
2
278
(8)
=−
C
t
Q
VCC
d
d()
L,in L
T
L,out
10
L,in
279
(9)
280where CL,in and CL,outjstand for the dissolved O2concentration
281(g m−3) at the inlet and outlet of each CSTR representing the
282absorption column (the first CSTR is at the top of the abiotic
283BTF); His Henry’s law constant for O2(dimensionless), QL,
284the recirculating liquid velocity (m3h−1), VC, the packed bed
285volume (m3), and VT, the volume of the stirred tank (m3). In
286the estimation of KLavalues in CSTRs, it is necessary to
287account for the response time of the electrode when the
288response time of the probe is in the same order of magnitude
289as 1/KLa.
27
This requirement arises because the delay in the
290electrode response produces a delayed DOC concentration
291measurement and thus an underestimation of the KLavalue.
28
292However, in our system the concentration of DOC in the
293CSTR changes in small increments as oxygen-rich water
294flowing out of the abiotic BTF enters the CSTR, where the
295electrode is positioned. Moreover, the dynamic of flow
296circulation in the abiotic BTF and in the CSTR already
297introduced delays that are accounted for in the model.
Table 1. Experimental KLa, and Estimated KL,a, and KLaUsing CFD Simulations for the Experimental Conditions Tested
operational
condition water velocity
(m h−1)EBRT
(s) estimated a
(m−1)estimated KL
(m h−1)experimental
KLa(h−1)
a
error in CL,in predictions
(g m−3)
b
case 1 2 240 233.59 0.476 112.58 ±3.16 0.09
case 2 4 240 190.53 0.700 144.04 ±6.46 0.07
case 3 11 240 180.35 0.693 125.16 ±2.93 0.12
case 4 17 240 227.42 0.699 156.60 ±7.26 0.24
cse 5 2 60 223.82 0.567 122.29 ±3.84 0.09
case 6 4 60 215.07 0.675 112.13 ±4.88 0.21
case 7 11 60 205.19 0.748 167.86 ±4.23 0.11
case 8 17 60 193.27 0.688 167.21 ±7.91 0.23
case 9 2 36 234.54 0.579 173.39 ±6.82 0.08
case 10 4 36 141.97 0.832 183.68 ±5.59 0.08
case 11 11 36 218.09 0.742 232.89 ±12.37 0.18
case 12 17 36 209.07 0.905 259.24 ±15.66 0.21
case 13 2 17 190.72 0.696 189.28 ±7.78 0.09
case 14 4 17 150.05 1.009 212.50 ±6.73 0.07
case 15 11 17 210.37 1.062 249.60 ±16.15 0.20
case 16 17 17 208.76 1.154 380.87 ±29.72 0.19
a
Estimated KLavalue from the experimental information and its 95% confidence interval.
b
Average error calculated as the mean value of the
absolute value differences between measured and predicted (CL,in in eq 9) DOC concentrations.
Environmental Science & Technology Article
DOI: 10.1021/acs.est.9b02662
Environ. Sci. Technol. XXXX, XXX, XXX−XXX
D
298 The KLavalues for the 16 experiments shown in Table 1
299 were estimated by nonlinear fitting to the experimental data (in
300 triplicate) to the model described by equations (6) using
301 MATLAB’s nlinfit function with default options. The 95%
302 confidence intervals for the estimated KLavalues were
303 calculated using MATLAB’s nlparci function. The comparison
304 between model predictions and DOC concentration exper-
305 imental data is provided in Supporting Information.
3. RESULTS AND DISCUSSION
306 3.1. Experimental Mass Transfer Coefficients in a BTF
307 with PUF as Packing Material. The experimental results
308 obtained for KLaof oxygen dissolving into a trickling aqueous
309 solution under the 16 operational conditions tested are shown
310 in Table 1. Higher values of KLawere obtained at higher
311 trickling medium velocities and lower EBRTs (i.e., higher air
312 velocities). From a fluid mechanics perspective, the water
313 moving downward due to gravity interacts with the air moving
314 upward, causing shear at the water−air interface. Hence, two
315 mass transfer mechanisms may occur simultaneously: (i)
316 diffusion of O2into water due to differences in O2
317 concentration between the two phases, and (ii) diffusion of
318 O2into water due to turbulence (momentum exchange) or
319 shear between the moving fluids at the interface. The
320 magnitude of the shearing interaction between the two fluids
321 at the interface depends on the local Reynolds number of the
322 fluid film in each section of the wetted-column.
24,29
Hence,
323 two boundary layers are formed: a concentration boundary
324 layer and a velocity or momentum boundary layer.
24,25
325 Table 1 showsthattheempiricalKLadecreased by
326 approximately 50% when the EBRT increased by a factor of
327 14, regardless of the trickling liquid velocity. On the other
328 hand, the increase in KLawhen the trickling liquid velocity
329 increased from 2 to 17 m h−1depended on the EBRT, with
330 increases of 200, 300, 240, and 230% at EBRTs of 17, 36, 60,
331 and 240 s, respectively. A similar behavior was reported by
332 Lebrero et al.
8
and Estrada et al.
30
for toluene and methane
333 KLain BTF. Estrada et al.
31
reported KLavalues for oxygen in
334 the range 30−300 h−1in an abiotic BTF with PUF as the
335 support, using liquid velocities between 0.5 and 5.0 m h−1and
336 EBRTs between 12 and 250 s.
337 3.2. Simulation of a 2D PUF Slide of the BTF Using
338 CFD and Comparison of Predicted and Experimental O2
339 Mass Transfer Coefficients. A2DCFDnumerical
340 simulation with a detailed description of the porous media
341 was used in order to elucidate the physical mechanisms of O2
342 gas−liquid mass transfer in a BTF at laboratory scale. 2D
343 simulations were chosen over the 3D approach because of their
344 model simplicity and the significant reduction in computa-
345 tional costs. Before all, operational conditions were simulated
346 and a sensitivity analysis for mesh independence was carried
347 out (see Figure S1 in the Supporting Information). The
348 analysis of the computational results was based on steady-state
349 conditions, which were reached with real time simulations of
350 10 s. In addition, it should be stressed that one of the main
351 objectives of these simulations was to obtain a quantitative
352 measure of the specific surface area, where O2is dissolved into
353 water, that is, the gas−liquid interphase. Once the resulting
354 distribution of the two phases was identified, the water−air
355 interphase area (WAIA) was computed (see Figure S3 in the
356 Supporting Information).
f3 357 The results obtained under steady state are shown in Figure
f3 358 3. The simulation results are displayed in terms of the
359distribution of water, air, and air velocity vectors. The air
360velocity vector arrows graphically show the locations where
361preferential flow occurs as a result of the distribution of water
362patches. Preferential flow spots are likely to occur when two
363large patches of water separated by a small distance where air
364flows through are formed by the flow.
365The numerical simulations conducted also showed that the
366volumetric mass transfer coefficient was greatly affected by the
367variations in EBRT and water velocity. As shown in Figure S4
368(Supporting Information), the variations in KLawere more
369significant at low EBRTs, that is, changes in water feeding
370velocity greatly impacted the mass transport of oxygen into
371water at lower EBRT (higher air velocities). While at the
372highest EBRT analyzed (EBRT 240 (s)), the variations in
373water velocity exhibited a lower impact on KLa. This can be
374explained by the increase of shear stresses near the water−air
375interphase, causing an increase in the O2mass transfer rate, a
376phenomenon that can be described using the boundary layer
377theory. This was represented in the numerical computations as
378an increase in the relative velocity difference between the
379water−air interphase and the free stream velocity of the air,
380V∞.
381The BTF water velocities directly impacted the diffusion of
382oxygen from the air into the trickling aqueous solution at the
383microscale level. The air free stream velocity (V∞) gradually
384increased when increasing the trickling water velocity (see
385Figure S5 in the Supporting Information) at EBRTs of 60, 36,
386and 17. According to eq 7,KLincreases as the square root of
387V∞, and therefore, more oxygen is dissolved into water because
388of the increase of air flow momentum near the air−water
389interface. In addition, when the air flow was too low (EBRT
390240), this variable did not affect the mass transport process.
391On the contrary, at low EBRT, the variations in water
Figure 3. Water and air fraction results for the 2D PUF simulations.
Dark gray color indicates the presence of water and light gray
indicates the presence of air. White areas indicate the presence of
PUF. Each row shows results for four different EBRT, from top to
bottom: 240, 60, 36, and 17 s. Each column shows results for four
different water velocities, from left to right: 2, 4, 11, and 17 m h−1.
Arrows indicate velocity vectors (m s−1), with velocity values
indicated in the color bar. Cases are numerated from 1 to 16 in
accordance with Table 1.
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Environ. Sci. Technol. XXXX, XXX, XXX−XXX
E
392 velocities determined the distribution of water blobs, hence
393 modifying the flow conditions of the air flow near each blob
394 and therefore changing V∞.
395 The WAIA, the boundary layer, and the velocities of air
396 moving along the water−air interphase can be estimated using
f4 397 postprocessing (see Figure 4). Data from the cells conforming
398 such interface can be extracted from the simulation and the
399 location, length, and area of the water−air interphase. From
400 each cell conforming the air−water interface, a computational
401 algorithm was used to estimate the air velocity of each cell
402 above and perpendicular to the interface computational cells.
403 When the air velocity remained constant, the boundary layer
404 thickness position was identified (red dots in Figure 4), and
405 the air free-stream velocity information was recorded and used
406 to compute the average V∞. At this point, all information for
407 the computation of KLwas available (i.e., interface length, free-
408 stream velocity, fluid kinematic viscosity, and the air−water
409 diffusion coefficient). Then, the average KLfor each segment of
410 the air−water interface was computed. The diffusion
411 coefficient of O2into water (2 ×10−9m2s−1
26
)at22°C
412 was used. In addition, the total WAIA for that case was divided
413 by the computational domain volume (4.93 ×10−8m3)in
414 order to obtain a(m2m−3), which allowed the estimation of
415 KLa. The KLavalues estimated using CFD simulations for
416 operational conditions 1−16 are shown in Table 1. The WAIA
417 estimated from the simulations range from 142 to 235 m2m−3.
418 The WAIA did not strongly correlate with the improvement of
419 KLabut it does correlate with V∞(see Figures S5 and S6 in the
420 Supporting Information). This suggests that under the
421 operational conditions tested in this study, the enhancement
422 in the air flow momentum near the WAIA played a key role in
423 increasing the oxygen mass transfer in the BTF.
424 The simulation results agree (within ±30%) with the
f5 425 experimental values of KLabelow 300 h−1(Figure 5). Dorado
426 et al.
32
determined the mass transfer coefficient for four
427packing materials, including PUF, and compared the results
428obtained with several literature correlations. None of the
429existing correlations provided an accurate description of the
430gas−liquid mass transfer coefficient for PUF. Among the
431correlations evaluated by Dorado et al.,
32
the equation
432reported by Van Krevelen & Hoftijzer
33
and the correlation
433proposed by Kim and Deshussees
7
predicted mass transfer
434coefficients nearly 1 order of magnitude lower than the
435experimental results. An attempt of fitting our experimental
436results using the constants and equations reported by Kim and
437Deshussees
7
and Van Krevelen and Hoftijzer,
33
produced on
438average values representing only 23.5 and 18.9% of the
439experimental values, respectively. At this point, it must be
440stressed that other correlations for the estimation of KLain
441packed columns are typically not suitable in PUF-packed BTF
442because relevant parameters, such as the packing equivalent
443diameter, are not available.
444The differences between the experimental and predicted KLa
445shown in Figure 5 may be due to the fact that this is a 2D
446microsimulation of a limited sample of PUF (0.0158 m ×
4470.0158 m). In addition, neither 3D nor wall effects (the latter
448entailing a local velocity reduction and channeling because of
449the presence of the column BTF inner wall) were considered
450in this simulation. At this point, it should be also stressed that
451the boundary layer theory used to compute the average KL
452values was capable of capturing the dynamics of the system.
453Other theories such as the film theory, penetration theory, and
454surface renewal theory provided KLavalues one or more orders
455of magnitude lower than their experimental counterparts, likely
456due to the fact that the latter techniques did not include the
457dynamic effects of the moving fluids (data not shown). The
458results here obtained highlighted the potential of the CFD
459modeling approach used to describe the volumetric mass
460transfer coefficients for different air and water flow conditions,
461despite all simplifications made in the simulations and the
462small computational domain used to mimic the operation of a
4633D BTF column. A significant contribution of the present
464study to the field of gas treatment arises from the detailed
465description of the distribution of water patches formed because
466of the influence of surface tension in the PUF structure. The
467air flow in the BTF was not sufficient to overcome the water
468surface tension, even at the highest air velocities applied in the
Figure 4. Graphical computation of the interfacial area, boundary
layer thickness, and air free stream velocity under the steady state.
Water−air interface is shown as black dots (one dot represents one
computational cell). White patches indicate the presence of water.
Red dots represent the boundary layer interface where the air free-
stream velocity, V∞, is reached. Blue arrows indicate air velocity
vectors.
Figure 5. Comparison between simulated (Sim) and experimental
(Exp) results of KLa. Diagonal broken lines limit the match between
experimental and simulation results. White circles show the actual
simulated vs experimental results for the 16 operational conditions
tested. Error bars represent the 95% confidence interval for the KLa
values estimated from the experiments in Table 1.
Environmental Science & Technology Article
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Environ. Sci. Technol. XXXX, XXX, XXX−XXX
F
469 experimental and computational runs. However, the combina-
470 tion of water moving downward and air flowing upward was
471 capable of breaking the water “bubbles”down and help gravity
472 to break the water patches into smaller ones. In this context,
473 the presence of a large number of small patches of water
474 creates a much larger air−water interphase than a large water
475 patch containing the same amount of water. Similarly, a larger
476 air−water interphase mediates a larger specific surface area for
477 O2to dissolve into water, and therefore a higher KLa.
478 Although more experimental validation and CFD model
479 refinement are required to attain a realistic description of the
480 system, the CFD modeling platform here developed allows
481 obtaining key operational data at any point of the BTF. For
482 instance, the determinations of the actual gas velocities inside
483 the BTF column are very difficult to obtain experimentally
484 without perturbing the natural flow patterns but could be easily
485 recorded via CFD simulations. Similarly, the influence of key
486 operational parameters on the interfacial area and free-stream
487 velocities can be easily determined using this novel modeling
488 approach.
489 ■ASSOCIATED CONTENT
490 *
SSupporting Information
491 The Supporting Information is available free of charge at
492 https://pubs.acs.org/doi/10.1021/acs.est.9b02662.
493 Grid independence analysis for the selection of the grid
494 discretization, schematic of the experimental apparatus
495 used for the determination of the mass transfer
496 coefficient, calculation example of the WAIA, analysis
497 of the modeled KLabehavior as a function of the
498 experimental variables, and model fitting versus exper-
499 imental data of the DOC concentration in the 16
500 experiments for the determination KLa(PDF)
501 ■AUTHOR INFORMATION
502 Corresponding Author
503 *E-mail: aovergara@miuandes.cl. Phone: + 562 2618 1441.
504 ORCID
505 Raúl Muñoz: 0000-0003-1207-6275
506 Alberto Vergara-Ferná
ndez: 0000-0002-6075-9137
507 Notes
508 The authors declare no competing financial interest.
509 ■ACKNOWLEDGMENTS
510 The present work has been sponsored by the CONICYT
511 Chile (National Commission for Scientific and Technological
512 Research) project Fondecyt 1190521. The financial support
513 from the Regional Government of Castilla y León is also
514 gratefully acknowledged (UIC71 and CLU-2017-09). J.D.
515 thankfully acknowledges funding from projects Fondecyt
516 1180685, CONICYT Basal FB0008, and from Fondo de
517 Ayuda a la Investigacion (FAI), Universidad de los Andes,
518 INV-IN-2017-05.
519 ■NOTATION LIST
520 CL,in dissolved O2concentration measured by the electrode,
gm
−3
521 CL,outjdissolved O2concentration of the jth CSTR in the BTF
model, g m−3
522 DAB diffusion coefficient of oxygen in water, m2s−1
523 gacceleration of gravity, m s−2
524HHenry’s law constant for O2
525KLavolumetric mass transfer coefficient, h−1
526QLrecirculating liquid flow, m3h−1
527ppressure vector in space, Pa
528RelReynolds number
529Sc Schmidt number
530Sh Sherwood number
531Uvelocity vector, m s−1
532VCpacked bed volume, m3
533VTstirred tank reactor volume, m3
534δmboundary layer thickness, m
535ρfluid density, kg m−3
536μdynamic viscosity of a fluid, kg·m−1·s−1
537νkinematic viscosity of the gas phase, m2s−1
538
539
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