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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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