Validation of a rapid procedure to determine biofilter performances

Accepted Manuscript Title: Validation of a rapid procedure to determine biofilter performances ´ Dumont Author: Eric PII: DOI: Reference:

S2213-3437(17)30212-9 http://dx.doi.org/doi:10.1016/j.jece.2017.05.022 JECE 1625

To appear in: Received date: Revised date: Accepted date:

27-3-2017 28-4-2017 14-5-2017

´ Please cite this article as: Eric Dumont, Validation of a rapid procedure to determine biofilter performances, Journal of Environmental Chemical Engineeringhttp://dx.doi.org/10.1016/j.jece.2017.05.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Validation of a rapid procedure to determine biofilter performances

Éric DUMONT UMR CNRS 6144 GEPEA, IMT Atlantique, Campus de Nantes, La Chantrerie, 4 rue Alfred Kastler, CS 20722, 44307 Nantes Cedex 3, France Corresponding author: [email protected]

Graphical abstarct

Highlights     

A procedure to determine quickly the ECmax value of a biofilter is proposed A biofilter filled with expanded schist was used for the treatment of H2S The procedure was successfully applied within a 10 % error The coexistence of both zero-order regimes in the biofilter was evidenced The Thiele modulus cannot be used to characterize the biodegradation limiting factor

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Abstract This study introduces a new strategy to determine the maximum Elimination Capacity (ECmax) of a biofilter within a 10 % error from a single experiment of 2 hours. The procedure requires several ports for H2S measurement along the length of the biofilter in order to establish accurately the relative concentration profile versus the residence time of the gas. The ECmax value was directly deduced from the derivative of the curve at the y-intercept assuming that three kinetic regimes occur along the packing material, i.e. zero-order kinetics with reaction limitation in the lower part; zero-order kinetics with diffusion limitation in the upper part; and first-order kinetics at the outlet of the biofilter. The procedure was successfully applied to a laboratory-scale biofilter filled with expanded schist as the packing material for the treatment of H2S. At an Empty Bed Residence Time (EBRT) of 19.3 s, ECmax values were determined for 6 experiments corresponding to loading rates from 25.4 to 57.4 g m3 h-1 (inlet concentration up to 300 mg m-3) and compared with the value previously calculated from the classic technique based on the modified Michaelis-Menten model. The results showed that ECmax values calculated from both the rapid and classic procedures were in agreement. Moreover, the coexistence of both zero-order regimes in a large middle part of the biofilter was also evidenced for each of the six experiments carried out. However, the critical concentration separating both regimes could not be accurately assessed and, consequently, the Thiele modulus could not be used to characterize the limiting factor influencing the biodegradation.

Keywords: Biofiltration; H2S; Model; Thiele modulus; Mass transfer

2

Nomenclature

A: Biofilm surface area per volume of packing material (m2biofilm m-3packing material) C: Pollutant concentration (g m-3) D: Diffusion coefficient (m2 s-1) Da: Damköhler number EBRT: Empty Bed Residence Time (s-1) EC: Elimination Capacity (g m-3 h-1) EC*: Maximum Elimination Capacity in the absence of inhibition (g m-3 h-1); Haldane model H: Biofilter height (m) k: Kinetic constant (g m-3biofilm h-1) K: Saturation constant (g m-3); Monod model K’s: Saturation constant (g m-3); Haldane model KI: Inhibition constant (g m-3); Haldane model Ks: Saturation constant (g m-3); modified Michaelis-Menten model LR: Loading Rate (g m-3 h-1) m: Partition coefficient = (CG/CL) (-) Pe: Péclet number Q: Gas flow rate (m3 s-1) RE: Removal Efficiency (%) U: Gas velocity (m s-1) V: Packed bed volume (m3) x: Length (m) 3

Greek letters G0: Gibbs free energy of reaction (kJ)  Thiele modulus (-)  Dimensionless length coordinate in the biofilm (-)  Biofilm thickness (m) : Biofilter surface area (m2) lump: Lump parameter (g1/2 m−3/2packing material s−1) 1: Constant (g m-3 h-1); (31) 2: Constant (h-1); (32) 3: Constant (h-1); (33)

Subscript

crit: Critical G: Gas phase in: Inlet L: Liquid phase max: Maximum out: Outlet

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1. Introduction Due to the various sources of hydrogen sulfide (H2S) emission and its high toxicity, it is crucial to investigate effective methods for its removal, especially when these sources, such as sewage plants and industry, are located near human settlements. Depending on the pollutant concentration and the loading rate, biofiltration has become a common process for H2S treatment, standing out as an effective, environmentally friendly, economical and low-energy-demanding technology. Hydrogen sulfide is transferred from the gas to an aqueous phase where it is oxidized by aerobic microorganisms at atmospheric pressure and ambient temperature according to the following reactions [1,2]: H2S + 0.5 O2 → S0 + H2O

(G0 = -209.4 kJ/reaction)

(1)

H2S + 2 O2 → 2 H+ + SO42- (G0 = -798.2 kJ/reaction)

(2)

Under oxygen-limiting conditions [Eq. (1)], H2S oxidation leads to a deposit of elemental sulfur (S0) and under excess amounts of oxygen [Eq. (2)], H2S treatment can produce sulfuric acid (H2SO4), which acidifies the environment of the microorganisms. The most energy is released when sulfide is oxidized to sulfate [Eq. (2)]. Studies carried out on both laboratory and full-scale bioreactors indicated that diversified microbial communities exist. Sulfide oxidizing bacteria (SOB) allowing oxidation of sulfide encompass several genera such as Xanthomonas, Thiobacillus [3], Acidithiobacillus, Achromatium, Beggiatoa, Thriothrix, Thioplaca, and Thermotrix [4]. The most common H2S-oxidizing bacteria found are acidophilic, such as Thiobacillus thiooxidans [5]. The metabolism of species such as Thiobacillus, Beggiatoa, Thriothrix, Thermotrix, has been extensively studied for the oxidation of sulfur reduced compounds and characteristics of some of them are reviewed by Syed et al. [6]. Several operating 5

conditions may affect biofilter performances for gas treatment: H2S concentration, temperature, pH, moisture, nutrients, oxygen levels, EBRT (Empty Bed Residence Time), and pressure drops. According to these operating conditions, the performances can be either mass transfer or kinetically controlled. Change in EBRT has a significant influence on the limiting step while change in temperature affects mass transfer and biological reactions in opposite ways. To date, a large body of experimental data on H2S biofiltration has been published, and several mathematical models describing the elimination of pollutants in biofilters have been built for design purposes and process optimization. Despite this knowledge, the determination of the maximum Elimination Capacity (ECmax) of a biofilter, which represents the maximum amount of H2S degraded per unit of biofilter volume, still requires several weeks of work with daily analyses of pollutant concentrations. Moreover, if the operating conditions (temperature, humidity, loading rate) cannot be more or less controlled over time, ECmax determination can be relatively inaccurate at the laboratory scale [7], and practically impossible at the pilot scale or on an industrial biofilter. As a result, the development of a procedure to determine quickly the overall performance of a biofilter is required. In order to reduce the time needed for this assessment, a simple protocol was proposed by Deshusses and Johnson [8], which involved determining two pollutant concentration profiles along the height of a three-segment biofilter under carefully chosen conditions. The main objective of this study was to establish a database for pollutant removal rates in biofilters. The target was to obtain a result in 48 h or less for each tested pollutant. However, this protocol, developed as a standard test method, cannot be applied to assessing the performances of a biofilter operating under varying conditions. Therefore, the first objective of the present work was to develop a new procedure to determine rapidly the maximum elimination capacity of a biofilter irrespective of the operating conditions, i.e. at the laboratory or industrial scale. The aim was to obtain the ECmax value within a 10 % error from a 6

single experiment of 2 hours under steady-state conditions. As this time is very short, the steadystate can be considered as a realistic assumption. H2S was chosen as the pollutant target because it is one of the most common contaminants considered by biofiltration studies [9], but the procedure could also be used to determine the ECmax of a biofilter removing either pollutants other than H2S or a mixture of pollutants. The second objective of this work was to characterize the rate-limiting step in a biofilter, which might differ along the height of the reactor [10]. In fact, the gradual rise of the polluted gas along the packed bed leads to a continuous change in the operating conditions, mainly due to the decrease in the pollutant concentration, and therefore the transition between the biological limiting regime and the mass transfer limiting regime could be determined as a function of the biofilter height. In order to achieve these objectives, data obtained from experimental measurements carried out in a laboratory-scale biofilter treating H2S under steady-state conditions were interpreted using the model of Ottengraf and Van den Oever [11] and the modified Michaelis-Menten model. The model of Ottengraf and Van den Oever [11] was revisited for this purpose. The present paper is organized as follows. In the first part, both models are introduced and critically analyzed. In the second part, the rapid procedure to determine ECmax is described. In the third part, the H2S biofiltration results used to validate the rapid procedure are presented. These data originate from the experiment carried out by Courtois et al. [7]. The description of the laboratory-scale experiment is given and the biofilter performances obtained are summarized. In the last part, the experimental data from Courtois et al. [7] are interpreted using the rapid procedure, and the calculated ECmax values are compared with the ECmax value reported in the previous paper.

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2. Biofiltration modeling The operational parameters for a biofilter are defined hereafter. In these equations, Q is the gas flow rate (m3 h-1), V is the packed bed volume (m3), and CGin and CGout are the inlet and outlet pollutant concentrations, respectively (g m-3).

Loading Rate

LR =

Q C V Gin

(3)

Elimination Capacity

EC =

Q (C − CGout ) V Gin

(4)

Removal Efficiency

RE = 100

Empty Bed Residence Time

EBRT =

Gas velocity

U=

Q Ω

(CGin − CGout ) CGin

V Q

(5)

(6)

(7)

Fig.1 presents a typical curve of biofilter performance. At low loading rates, the system can reach 100 % removal efficiency, whereas at high loading rates, the removal efficiency is less than 100 %, either because the pollutant does not have time to diffuse into the biofilm (the EBRT is typically too short), or because the biofilm cannot fully absorb the pollutant (the pollutant concentration being too high). At more elevated loading rates, the elimination capacity tends towards an asymptotic value corresponding to the maximum elimination capacity (ECmax). At a constant EBRT, the curve corresponding to Fig. 1 is obtained by gradually increasing the H2S concentration at the biofilter inlet until the maximum elimination capacity is reached, which can require several weeks.

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Biofilter modeling started in the early 1980s and some of the most significant models are summarized in Devinny et al. [5], Lim and Lee [12] and Deshusses and Shareefdeen [13]. Most of them are based on the biofilm theory originally developed by Ottengraf and Van den Oever [11]. All models take into account the mechanisms governing biofiltration, i.e. the transfer of the pollutant from the gas to the liquid phase, the diffusion into the biofilm and the biodegradation reaction. Whereas the first models were usually simple in order to obtain an analytical solution (steady-state models), the increased power of computer calculations in the 1990s enabled more realistic transient models to be developed. At the end of the 1990s, models using quantitative structure activity relationships (QSARs) also sought to predict the performances of biofilters. Today, artificial neural networks (ANNs) and fuzzy logic-based models are being considered as modeling alternatives for biofilter design and performance prediction [14]. However, in spite of this progress in modeling, the use of simple and analytical models enabling biofilter performance to be determined easily, i.e. ECmax, is still preferred.

2.1. Model of Ottengraf and Van den Oever [11] Despite the complexity of the phenomena occurring in a biofilter (physical, chemical and biochemical), Ottengraf and Van den Oever [11] proposed a simple model, which is still widely applied or adapted [9,15–20]. It is based on the theoretical model built by Jennings et al. [21] for a submerged biological filter. In this model, the pollutant diffuses from the gas phase into the biofilm fixed in a support where it is degraded. Under the steady-state assumption, the driving force for mass transfer between the gas phase and the biofilm is typically represented as in Fig. 2. For the gas phase, the assumptions are: (i) the gas flow is a plug flow; (ii) the mass transfer resistance in the gas phase is negligible (i.e. equilibrium occurs at the gas-biofilm interface). For 9

the biofilm, the assumptions are: (i) the biofilm thickness is small relative to the support particle (hence, a flat geometry can be assumed for the biofilm); (ii) the biomass concentration is homogeneous in the reactor volume; (iii) in the biofilm, pollutant is transported by diffusion, which is described by an effective diffusion coefficient D; (iv) the kinetics of the pollutant degradation reactions in the biofilm are of zero-order, which assumes a very low value of the Michaelis-Menten constant (K) in the Monod equation. The Monod equation is an empirical mathematical model for the growth of microorganisms that has the same form as the MichaelisMenten equation:

k = k max

CL K + CL

(8)

According to this equation, three different cases can be considered [Fig. 3]: (i) if the pollutant concentration is very low (i.e. CL<>K), zero-order kinetics with reaction limitation occur and k is a constant irrespective of the CL value (= kmax); (iii) between these two cases, zero-order kinetics with diffusion limitation are assumed. In the model of Ottengraf and Van den Oever [11], the biofilter performances are assumed to be either mass transfer or biologically controlled because the H2S concentrations to be treated are high enough to consider a zero-order kinetic regime. However, pragmatically, if the bioreactor is efficient, the pollutant concentration decreases all along the biofilter to tend to around zero at the outlet. In other words, the three cases considered above have to exist in the biofilter with more or less clear borders between each of them [Fig. 4]. If the H2S concentration is relatively high at the biofilter outlet, both zero-order kinetic regimes occur in the biofilter, with the biological

10

limitation regime located at the bottom of the bioreactor and the diffusion limitation regime at the top.

Based on the assumptions proposed by Ottengraf and Van den Oever [11], the differential equation describing the pollutant concentration in the biofilm is:

D

d2 C L −k=0 dx 2

(9)

with the boundary conditions [Fig. 2 ]:

x = 0;

CL =

CG m

(10)

x = δ;

dCL =0 dx

(11)

The solution of the differential equation is: CL 1 ϕ2 (σ2 − 2σ) =1+ C G ⁄m 2 CG ⁄CGin

(12)

with:

ϕ = δ√

mk k = δ√ D CGin D CLin

(13)

where  is the Thiele modulus,  = x/ is the dimensionless length coordinate in the biofilm, and m = (CG/CL) is the gas liquid partition coefficient obtained from Henry’s law. The dimensionless parameter called the Thiele modulus was initially developed to describe the relationship between

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diffusion and reaction rate in porous catalyst pellets [22]. In this case, a large value of the Thiele modulus implies that the internal diffusion limits the overall rate of the reaction occurring in a straight cylindrical pore, whereas for a small value, the surface reaction is rate-limiting. Thus, the value of the Thiele modulus can be used to determine the limiting factor of the reaction. It is also used in determining the effectiveness factor for catalyst pellets [Fig. 5] [23]. Similarly, in the case of biofiltration, the Thiele modulus is the ratio between the reaction rate and the diffusion rate [Eq. (13)]. A large value of the Thiele modulus (due to a large value of k) implies a mass transfer limitation whereas a small value implies that pollutant degradation is biologically limited, in agreement with Fig. 5 [24,25].

The two situations of zero-order kinetics expected to be common in biofilters [Fig. 2] were then considered by Ottengraf and Van den Oever [11]. First case: zero-order kinetics with reaction limitation The biofilm is fully active all along its thickness  and the pollutant concentration has no effect on the biodegradation rate [Fig. 2]. The conversion rate of the pollutant is then controlled by the biological reaction rate. From the gas phase mass balance on the pollutant along the height of the biofilter (H), Ottengraf and Van den Oever [11] calculated the pollutant conversion: CG k δ A H =1− CGin CGin U

(14)

It follows that the pollutant removal efficiency is:

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CGin − CG k δ A H = CGin CGin U

(15)

Combining [Eqs. (3,4,15)], the elimination capacity is: EC = k δ A

(16)

According to Eq. (16), the degradation of the pollutant is only due to the biofilm performances. Therefore, such performances can easily be known from the determination of the overall parameter EC (in g m-3packing material h-1) including the parameters not measurable with accuracy (k,  and A). Moreover, the assumption of zero-order kinetics with reaction limitation implies that the elimination capacity given by Eq. (16) corresponds to ECmax because k = kmax in this case (Fig. 3). Such an assumption is especially realistic at the bottom of the biofilter when the pollutant concentration is high.

Second case: zero-order kinetics with diffusion limitation In this case, the diffusion of the pollutant into the biofilm is low in comparison with the biodegradation rate. As a result, the biofilm is not fully active and the depth of penetration is smaller than the biofilm thickness  [Fig. 2]. The conversion rate of the pollutant is then controlled by the rate of diffusion. As the rate of diffusion depends on the gradient of the pollutant in the biofilm, i.e. by the concentration level at the interface, this situation occurs at lower pollutant concentration in the gas phase. Assuming a pollutant concentration close to zero at  = 1, Ottengraf and Van den Oever [11] calculated the critical value of the Thiele modulus separating the diffusion limitation and the reaction limitation: 13

ϕcrit = δ√

mk = √2 D CG

(17)

Such a value of the Thiele modulus is logically in agreement with the original value describing the transition between diffusion and reaction rate in porous catalyst pellets [Fig. 5]. According to Ottengraf and Van den Oever [11], at gas concentrations CG corresponding to this value, both regimes control the elimination capacity of the biofilter. From the gas phase mass balance on the pollutant along the height of the biofilter, the pollutant conversion for  >  crit is: 2

CG k D H = (1 − A √ ) CGin 2 m CGin U

(18)

Combining Eqs. (3,4,6,18), the elimination capacity is: 2

k D EBRT √ EC = LR [1 − (1 − A √ ) ] 2m LR

(19)

Eq. (19) demonstrates that both regimes control the biofilter performances (through the parameters k and EBRT). For a given ability of the microorganisms to degrade the pollutant (i.e. k constant), the elimination capacity will logically drop with an increase in the superficial gas velocity corresponding to a decrease in the EBRT value. This finding was used to propose a tool to compare the performance of different biofilters whatever their composition (mixture or layers of different packing materials) and whatever the EBRT [9]. For this purpose, Eq. (19) was rewritten in the following form:

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2

EBRT EC = LR [1 − (1 − α𝑙𝑢𝑚𝑝 √ ) ] LR

(20)

with:

k D 2m

α𝑙𝑢𝑚𝑝 = A √

(21)

By varying the EBRT in the biofilter at a constant gas concentration, the corresponding elimination capacity values can be recorded and it is possible to draw the graph (1-EC/LR)1/2 versus (EBRT/LR)1/2. A straight line is obtained whose y-intercept is equal to one and the slope is - lump. For a given pollutant, the lump value depends only on the values of A and k (lump ∼ A k1/2), which enables an overall comparison between the performances obtained for different biofilters. According to both cases considered by the model, the pollutant concentration profile along the height of the biofilter is linear for a biological limitation [Eq. (14)] and quadratic for a diffusional limitation [Eq. (18)].

Remarks about the Thiele modulus and the limiting regime Three remarks can be made: 1. In the model developed by Ottengraf and Van den Oever, the use of the Thiele modulus as a dimensionless parameter enabling to describe the behavior of a biofilter pragmatically has drawbacks. For example, by analogy with a straight cylindrical pore in porous catalyst pellets, the 15

geometrical parameter used in the definition of the Thiele modulus given in (13 is the biofilm thickness (). Therefore, the main disadvantage of the Thiele modulus used in biofiltration is that its calculation depends on two parameters ( and k) that cannot be (i) accurately known or measured, and (ii) considered uniform along the length of the biofilter. Let us look first at the biofilm, whichis considered the most important parameter responsible for the degradation of pollutants in biofilters [26]. The biofilm may be a smooth, relatively uniform layer of cells embedded in a polysaccharide gel that is mostly water [5]. It is a complex microbial ecosystem whose structure in real biofilters remains poorly known. According to the literature data, the biofilm thickness  can vary from tens of micrometers to more than 1 cm, with an average of 1 mm [27]. In the specific case of H2S biofiltration, the biofilm thickness reported in the literature is not higher than some tens of micrometers [28]. Moreover, due to growth, decay and detachment of microorganisms, the biofilm morphology fluctuates in thickness and geometry over time as well as along the biofilter [29]. As a result, and in spite of non-destructive and destructive experimental tools currently available for biofilm analysis [30–32], the experimental determination of the thickness of biofilms attached to packing material remains a challenge. Given that the Thiele modulus is directly dependent on biofilm thickness, it appears that its value can vary from one or two orders of magnitude according to the  value. Moreover, fluctuations in biofilm thickness can occur around the same particle and, consequently, both concentration profiles described in Fig. 2 can be found simultaneously at the same location in the biofilter. In other words, the value of the Thiele modulus can be simultaneously higher and lower than the critical value, indicating that both zero-order limiting regimes coexist. Secondly, regarding the reaction rate constant k, this represents the reaction rate per unit of volume of the biolayer (i.e. in g m-3biofilm h-1). Therefore, as the k value depends on both the thickness and the surface area of the

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biofilm, and taking into account the large inaccuracy in the biofilm thickness determination explained above, it is clear that the value of the Thiele modulus in a biofilter cannot be calculated accurately. Consequently, the calculation of this value is certainly not a good way to predict whether the biofilter regime is controlled biologically or by mass transfer. In fact, most modeling studies only describe the change in biofilter performances (or the change in pollutant concentrations along the biofilter length) theoretically according to the value of the Thiele modulus or an optimal value of the biofilm thickness [33–35]. However, ultimately, only the experimental data would potentially be able to evidence the transition between reaction- and diffusion-limiting steps in biofilters. 2. Some studies have also considered that first-order kinetics occur in the whole biofilter [36–39]. Authors have used a Convection Diffusion Reactor (CDR) model to describe the biodegradation in the biofilter. The CDR model is defined as follows: CG D AH = exp (− ϕ tanh(ϕ)) CGin δ U

(22)

in which  is the Thiele modulus defined for first-order kinetics:

ϕ = δ√

k D

(23)

Although the Thiele modulus given in Eq. (23) differs from that expressed by Eq. (13), its accurate calculation also remains impossible. Nonetheless, good agreement between the model and experimental data has been reported in the case of biofilters treating BTEX mixtures [38], paint solvent mixtures [36] and H2S [37]. In the latter case, the authors assumed a biofilm

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thickness of 40 m and a specific surface area of 3,042 m2/m3 to fit the experimental data satisfactorily. 3. It should be noted that mathematical analyses based on dimensionless numbers other than the Thiele modulus (e.g. Damköhler and Péclet numbers) have also been used to highlight whether the reaction is mass transfer or biologically controlled [24,35,40,41]. The Damköhler number (Da) is used in chemical engineering to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring in a system. The Péclet number is defined as the ratio between the diffusive and convective mass transfer in the reactor (Pe = HU/D). For instance, without actually providing evidence, Goncalves and Govind [41] suggested that biofilters are kinetically controlled when the Péclet number is 2 106 and both mass transfer and kinetically controlled for higher values.

2.2 Modified Michaelis-Menten model for biofilters By assuming plug air flow in the biofilter column, Hirai et al. [42] applied a Michaelis-Mententype equation to determine the performances of peat biofilters treating sulfur compounds. The equation is in the form:

−

dCG 1 CG = ECmax dh U K S + CG

(24)

In this model, there is no distinction between the gas phase and the biofilm phase. Moreover, there is no consideration of the limitation regimes in the biofilter. By integrating Eq. (24) in the conditions of CG = CGin at h = 0 and CG = CGout at h = H, the following equation is obtained:

18

1 KS 1 1 = + EC ECmax Cln ECmax

(25)

with:

Cln =

CGin − CGout C ln ( Gin⁄C ) Gout

(26)

From the linear relationship between 1/EC and 1/Cln, the maximum elimination capacity ECmax and the kinetic constant Ks are calculated from the slope and the y-intercept, respectively [42]. This simple model, currently called the “modified Michaelis-Menten model” in biofiltration, expresses the analogy between the curves given in Fig. 1, showing a typical curve describing the overall biofilter performances, and in Fig. 3 representing the Michaelis-Menten equation. Incidentally, the reciprocal of Eq. (25) has the same mathematical form as the Michaelis-Menten equation [Eq. (8)]:

EC = ECmax

Cln K S + Cln

(27)

It should be pointed out that Eq. (25) to Eq. (27) are only valid if CGout > 0 in Eq. (26). In other words, for an efficient packing material, determining the ECmax value from Eq. (25) requires feeding the biofilter with high H2S concentrations in order to have RE < 100 %. Such a procedure sometimes needs several weeks of work with daily analyses of pollutant concentrations. According to the modified Michaelis-Menten model, a biofilter can be considered a “black box” enabling the experimental data to be modeled on the whole, whatever the complexity of the phenomena occurring in a biofilm. In the present case, the physical meaning of Ks corresponds to the pollutant concentration that must be treated in order to reach ECmax/2. As a result, the packing

19

material with a small Ks value presents a large affinity for the pollutant and the removal rate will tend toward ECmax for small inlet concentrations. For H2S treatment, the model has been satisfactorily used to determine the ECmax/Ks ratio for different packing materials, which can give information about the specific activity of the microorganisms colonizing the packed bed [1, 38– 42]. However, for some pollutants such as H2S, the treatment of a large loading rate due to high concentrations can inhibit the biodegradation [Fig. 1] leading to a bias in the determination of the ECmax value (which is overestimated). In the case of inhibition, it is preferable to use the “Haldane model” including a substrate inhibition term KI: EC ∗ Cln EC = C2 K ′s + Cln + ( ln⁄K ) I

(28)

where K’s is the inhibition constant and EC* is the maximum elimination capacity in the absence of inhibition. The relationship between EC* and ECmax is given by the following equation [48]:

ECmax =

EC ∗ 1 + 2√(K ′s ⁄K I )

(29)

For instance, from the analysis of a set of H2S biodegradation measurements carried out in a laboratory-scale biofilter filled with expanded schist at EBRT = 24 s, Romero Hernandez et al. [47] calculated an ECmax value of 46 g m-3 h-1 using the Michaelis-Menten model [Eq. (27)] and a value of 29 g m-3 h-1 using the Haldane model [Eqs. (28,29)] corresponding to a difference of 58 %.

3. Description of the rapid procedure for determining ECmax

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According to Fig. 3, the kinetic regime in the packing material should be related to the H2S concentration at the biofilter inlet. As determining the ECmax value from the modified MichaelisMenten equation [Eq. (25)] requires feeding the biofilter with high H2S concentrations in order to have RE < 100 % (see Section 2.2,), it can be assumed that the three kinetic regimes may occur in the biofilter at different locations with transitional zones as shown in Fig. 4. Consequently, a zero-order regime with reaction limitation should occur at the bottom of the biofilter up to a given height. At this location, the kinetic regime changes and becomes zero-order with diffusion limitation. In this case, the biofilter performances are lower than, or at best equal to, those at the inlet of the packing material. Depending on the H2S concentration applied at the biofilter inlet, the zero-order regime with diffusion limitation can exist up to the biofilter outlet [Eq. (18)], or be replaced by first-order kinetics in the last few centimeters of the packing material [Eq. (22)]. Therefore, the rapid procedure for determining the ECmax value suggested here involves recording the H2S concentrations at different locations along the biofilter in order to draw the curve of CG/CGin versus H/U. For this purpose, several ports for H2S measurement are required along the length of the biofilter, especially near the inlet where they have to be closely grouped in order to detect the linear part of the CG/CGin vs. H/U curve characterizing the zero-order regime with reaction limitation described by Eq. (14). The ECmax value given by Eq. (16) can then be deduced from the derivative of Eq. (14) at the biofilter inlet, i.e. at H = 0: CG ) ECmax CGin =− | H CGin d( ) U H=0

d(

(30)

21

Basically, taking into account the time needed to carry out all the H2S measurements along the biofilter, the total time of the experiment for determining ECmax is less than 2 hours. Some comments can be made about this rapid procedure. 1. The procedure involving determining the kinetic regime in the packing material through pollutant concentration measurements along the length of the biofilter is not new. More than twenty years ago, the kinetic regime of H2S biodegradation in a biofilter was investigated by Chung et al. [16] and Yang and Allen [49] using the mathematical model described in Section 2.1. Indeed, it is possible to fit the experimental data with the appropriate equation. Depending on the kinetics occurring in the biofilter, Eqs. (14,18,22) can be expressed in the following linear forms: H U

(31)

CG H = α2 CGin U

(32)

CG H ) = α3 CGin U

(33)

Zero-order kinetics with reaction limitation

CGin − CG = α1

Zero-order kinetics with diffusion limitation

1−√

First-order kinetics

𝑙𝑛 (

The authors varied the inlet concentrations experimentally from low to high values and Eqs. (3133) were applied until the most appropriate expression was found. However, the main drawback of this procedure was that the authors assumed that the same kinetic regime occurred throughout the biofilter irrespective of the change in pollutant concentration along the packing material, which is clearly not true. Using this technique for a compost biofilter (EBRT = 16 s), Yang and Allen [49] determined that the kinetics were first-order for H2S inlet concentrations lower than 200 ppm, zero-order with reaction limitation for concentrations higher than 400 ppm, and zero-

22

order with diffusion limitation in the intermediate concentration range. In the same way, Chung et al. [16] proposed the following H2S inlet concentrations as limiting values: 20 ppm and 60 ppm for a Thiobacillus thioparus CH11 bioreactor; 35 ppm and 80 ppm for a Pseudomonas putida CH11 bioreactor (bacteria were immobilized with Ca-alginate on 3.0 mm diameter beads; EBRT = 27 s). Limiting values were thus significantly different between both studies, probably in relation to the packing material used. 2. Assuming that the three kinetic regimes exist along the biofilter (or only both zero-order kinetic regimes in the case of very high H2S concentrations at the biofilter inlet), Eqs. (31-33) could be applied to determine the transition between the kinetic regimes. However, the number of sample ports for H2S measurements should be sizable. Moreover, the CGin value should be reassessed between each change. Nonetheless, Eqs. (31-33) will be useful to confirm whether or not the kinetic regime is reaction-limited at the biofilter inlet. 3. As previously indicated, the treatment of very high H2S concentrations can inhibit the biodegradation [Fig. 1] leading to a bias in the determination of the ECmax value from the modified Michaelis-Menten model. Such a bias is due to a lack of experimental data to establish the complete EC vs. LR curve given in Fig. 1. The use of the rapid procedure described in this paper avoids overestimating the ECmax value. In fact, the inhibition due to high H2S concentration implies that the kinetic regime is inevitably reaction-limited, especially at the biofilter inlet. As a result, Eq. (30) should give the real value of ECmax. It can be highlighted that the decrease in the H2S concentration along the packing material should reduce inhibition effects and potentially increase the biofilter performances. In this case, the CG/CGin vs. H/U curve would be characterized by two linear parts with different slopes.

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4. Data used to validate the rapid procedure The rapid procedure for determining biofilter performances was applied to experimental data published earlier [7]. 4.1 Materials and method The biofiltration experiment is extensively commented on Courtois et al. [7]. The biofilter, constructed with a plastic cylinder (8 cm in diameter), was filled with expanded schist as the packing material to a height of 160 cm (corresponding to a volume of 8 L). In addition to expanded schist, a small layer of UP20 (1 cm thick) was added at the top of the bed. This synthetic material, developed in the laboratory, is used to provide all the nutrients needed for biomass development [44–47]. The physical properties of expanded schist and UP20 (Fig. 6) are, respectively: bulk density, 633 and 940 kg m-3; apparent density, 1120 and 1890 kg m-3; average diameter, 10 and 7 mm; water retention capacity, 6 and 48 %; specific surface area, 600 and 705 m2 m-3. The biofilter was inoculated with activated sludge from a wastewater treatment plant in the city of Nantes (France). No particular treatment or acclimatization was carried out on the activated sludge to prepare it for H2S treatment. To maintain optimal bed humidity, tap water was sprayed onto the top of the biofilter for 5 min each hour, corresponding to 80 mL each time. The polluted gas entered the column in an upward load flow mode. The flow rate (1.5 m3 h-1 corresponding to a superficial air velocity of 0.083 m s-1 i.e. 298 m h-1) was determined in order to work at an EBRT value of 19.3 s. The stream was obtained from a mixture of H2S (97.7 % purity) with air. The H2S stream was controlled by a 5850S Brooks mass flow controller. The biofilter was equipped with 9 sampling ports located at 0 (inlet port), 20, 40, 60, 80, 100, 120, 24

140 and 160 cm (outlet port) of column height to measure H2S concentration [Fig. 4] and to establish the concentration profile along the column. H2S concentrations were measured with an Onyx 5250 device (Cosma, France; accuracy ± 1 %) calibrated with a gas standard. All experiments were carried out at atmospheric pressure and ambient temperature. During the running period, the temperature within the biofilter was continuously monitored but not controlled. Depending on the outdoor temperature, it ranged between 15.5 °C and 27 °C during the whole experiment. The effect of the inlet gas concentration (from 28 to 308 mg m-3 corresponding to LR from 6.2 to 57.4 g m-3 h-1) on the removal efficiency of H2S was evaluated. In the present study, all the experiments for which LR ≥ 25.4 g m-3 h-1 were used to test the rapid procedure. The operating conditions corresponding to these 6 experiments (noted Exp 1-6) are given in Table 1. For all experiments, the pH of the leachate was around 2. As a result, under these acidic conditions, once transferred from the gas phase to the liquid phase, molecular H2S predominated in the biofilter rather than its ionic forms HS-, and S2-.

4.2 Results As can be seen in Fig. 7A, the biofilter was able to reach 100 % RE for LR up to 26 g m-3 h-1. Moreover, for LR values higher than 40 g m-3 h-1, the removal efficiency surprisingly increased. Thus, the RE value was higher for Exp 5 than for Exp 4 despite the increased loading rate applied. For Exp 6, corresponding to the maximum LR value of 57.4 g m-3 h-1, the RE value remained roughly unchanged in comparison with Exp 5 (around 78 %). This was mainly due to the rise in temperature when the measurements at high LR were made (summer 2013). In fact, the 25

temperature rose dramatically from 17 °C to 22 °C during the operating period, which led to an increase in microbial activity and thus a higher elimination capacity of the biofilter. This change in the operating conditions during the experimental period, widely encountered in biofiltration studies, caused an inaccuracy in the determination of the biodegradation kinetics, as illustrated in Fig. 7B. By applying the modified Michaelis-Menten model [Eq. (25)] to fit the whole usable experimental data (i.e. the six operating conditions for which RE < 100 %), the ECmax value was calculated to be 36.4 g m-3 h-1 and the saturation constant Ks value was 10.9 g m-3 [7]. Fig. 7B highlights that Exps 4 and 6 were not well modeled using the modified Michaelis-Menten equation. Basically, the accurate determination of ECmax and Ks parameters using the double inverse representation 1/EC vs. 1/Cln requires a great deal of data [42,45,50–52] involving carrying out experiments over a long time. Therefore, ECmax and Ks values could differ only slightly if the time needed to determine them was significantly shortened.

5. Use of the rapid procedure to determine ECmax. Results and discussion The rapid procedure was applied to each of the six operating conditions for which a removal efficiency lower than 100 % was recorded [Fig. 7]. Fig. 8 presents an example of ECmax determination for LR = 25.4 g m-3 h-1 (Exp 1). According to this figure, the concentration profile was clearly linear at the biofilter inlet and quadratic from the middle to the top of the biofilter. Consequently, the kinetic regime was zero-order with reaction limitation at the inlet and the ECmax value can be deduced from the slope of the linear part according to Eq. (30). Table 1 summarizes the ECmax values determined from Exps 1 to 6. All were calculated from Eq. (30) 26

using experimental H2S measurements corresponding to CGin and values recorded at ports 1 to 3 in Fig. 4 (i.e. the first four experimental points from the bottom of the biofilter were used to fit Eq. (14) and Ks values were then deduced by combining Eqs. (4,6,27):

Ks =

(ECmax EBRT − CGin + CGout ) C ln ( Gin⁄C ) Gout

(34)

In Eq. (34), the EBRT value is 19.3 s and CGin and CGout are the gaseous H2S concentrations recorded at H = 0 m and H = 1.6 m, respectively. ECmax values calculated from the derivative of the curve at H = 0 [Eq. (30)] were compared with the value determined by the classic double inverse representation technique [Eq. (25)] using the six sets of experimental data. According to Fig. 9, ECmax values determined from Exps 1, 2, 3 and 5 were in agreement with the result reported in Courtois et al. [7]. Differences between values were less than ± 5.3 % (Table 1). Consequently, it can be concluded that the rapid procedure can determine the overall biofilter performances satisfactorily. For Exp 4 and Exp 6, differences were 19.1 % and 77.1 %, respectively. For both these experiments, this finding was not surprising and the large difference obtained for Exp 6 agreed with the high removal efficiency recorded for this experiment (around 78 %; [Fig. 7A]. Such a result highlights the advantage of using the rapid procedure to determine biofilter performances. In fact, in addition to avoiding bias in the determination of the biodegradation kinetics in the case of long experiments, the rapid procedure has the considerable advantage of accurately determining the biofilter performances in real time, i.e. following the change in biofilter performances over time. In other words, such a rapid procedure of about 2 hours could be used to determine the performances of any biofilter, even on an industrial scale, provided that the concentration profile along the height of the packing material could be established accurately. In this case, the accuracy of the ECmax determination can be assessed as 27

around ± 10 % depending on the number of data used to fit Eq. (14). In addition, this rapid procedure could be used as a reliable methodology to optimize the major operating parameters. According to Fig. 8, the transition between both zero-order kinetic regimes in the biofilter was clearly evidenced from the H2S concentration profile. The profile was linear for the bottom half of the packing material (i.e. for the first four or five measurements from the bottom of the biofilter) and quadratic for the top half of the packing material. As a result, in this operating condition, the transition between both regimes occurred roughly in the middle of the column. The (H/U)crit value corresponding to the transition can be calculated by equalizing Eq. (14) and Eq. (18). 2

1−

k δ AH k D H = (1 − A √ ) CGin U 2 m CGcrit U

(35)

Then, the critical concentration value (CGcrit) corresponding to the transition between both regimes can be deduced from Eq. (14). The results obtained for all operating conditions are given in Table 1. Considering all experiments, the transition between both zero-order regimes occurred in the packed bed at a height between 0.57 and 0.96 m from the bottom of the biofilter, and the critical concentration varied significantly from 47 to 185 mg m-3, i.e. by a four-fold factor. This result clearly demonstrates that it is pointless to try to assess precisely the transition between regimes. At a given height, the degradation performances are limited by a combination of both limiting steps and the transition occurs over a large part of the biofilter. This interpretation is clearly evidenced in Fig. 10, which gives an analysis of the data reported in Fig. 8 by means of Eqs. (31-33). As a large number of data was used to plot the three curves, the different kinetic regimes appear clearly, which was not the case in the original papers in which a single regime 28

was assumed all along the packing bed [16,49]. The degradation kinetics are clearly “reactionlimited” at the bottom of the biofilter [Fig. 10A] and “diffusion-limited” over a large part of the biofilter [Fig. 10B]. Although the H2S concentration at the biofilter outlet tended to zero, the first-order regime cannot be evidenced in Fig. 10C. Therefore, this proof of the coexistence of both zero-order regimes in the biofilter reinforces the literature data that assume complex relationships between mass transfer and degradation kinetic rates along the height of bioreactors [10]. It should be noted that both zero-order regimes were found to coexist in a large middle part of the biofilter in each of the six experiments (not shown). As a result, in this part, it could be concluded that the value of the Thiele modulus was around its critical value defined by Eq. (17) in agreement with Fig. 5. An attempt was made to solve Eqs. (16-18) in order to assess the three unknown parameters A, , and k. However, since the critical concentration separating both regimes could not be accurately determined, this attempt failed. Consequently, the use of a parameter such as the Thiele modulus is not appropriate for characterizing the limiting factor influencing the biodegradation. At most, it is possible to indicate that the value of the Thiele modulus is small at the biofilter inlet because the kinetic regime is clearly “reaction-limited”. For Exps 1 to 6 corresponding to LR ≥ 30 g m-3 h-1, the coexistence of a zero-order regime controlled by diffusion and a first-order regime in the upper part of the biofilter could be considered. However, it should be emphasized that the Convection Diffusion Reactor (CDR) model, which assumes that the first-order kinetic regime occurs in the whole biofilter [36–39], cannot be applied to describe H2S biodegradation by a biofilter filled with expanded schist. Fig. 8 clearly highlights that Eq. (22) cannot be used for this purpose. The possibility that a first-order kinetic regime occurs in the whole biofilter will be discussed later in the text.

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According to Table 1, the values of the saturation constant Ks determined from the modified Michaelis-Menten model ranged from 9 ± 3 to 18 ± 8 mg m-3 for Exps 1, 2, 3 and 5. These values were of the same order of magnitude as that calculated by Courtois et al. [7], i.e. 10.9 mg m-3. For Exps 4 and 6, Ks values were around four times higher, 63 ± 15 and 70 ± 20 mg m-3, respectively. Such a difference has a significant influence on the modeled curves of the modified MichaelisMenten model characterizing each experiment. Fig. 11 shows the representation of the relative curves corresponding to all experiments. On the y-axis, elimination capacity (EC) values were calculated [Eq. (27)] for gas concentration values arbitrarily ranging between 0 and 800 mg m-3 and from ECmax values and KS values given in Table 1. On the x-axis, representations were shifted to take into account the H2S concentration values at the biofilter inlet. For Exps 1, 2, 3 and 5, elimination capacities at the biofilter inlet were higher than 90 % of the maximum value (ECmax) and the assumption of the biologically limited zero-order regime was thus clearly verified. For Exps 4 and 6, the curves were more flattened in relation to the high Ks values. Elimination capacities at the biofilter inlet were around 70-80 % of the maximum value, making it possible to have reservations about the assumption of a biologically limited zero-order regime. However, such reservations can be excluded because the inlet concentrations were higher for Exps 4 and 6 than for Exps 1, 2 and 3. Consequently, the kinetic regime was necessarily “reaction-limited” at the biofilter inlet. Nonetheless, it is interesting to consider the modeling of the concentration profiles for Exps 4 and 6. According to Fig. 12, the concentration profiles corresponding to Exp 6 could clearly be modeled using a linear part [Eq. (14)] and a quadratic part [Eq. (18)], as for Exps 1, 2, 3 and 5 [Fig. 8] and the ECmax value was deduced from the derivative of the curve at the y-intercept. However, it was also possible to model the profile

30

satisfactorily in its entirety using either an exponential function [Eq. (22)] or a quadratic function. The ability of a quadratic function to model the profile can be reasonably explained by the coexistence of both zero-order regimes in the biofilter as explained above. However, the ability of an exponential function to model the concentration profile well is due to the mathematical expression of the exponential function rather than the real existence of a first-order kinetic regime at the biofilter inlet. In fact, mathematically, the exponential function can be characterized by a power series: ∞

exp(x) = ∑ n=0

xn x x2 x3 =1+ + + +⋯ n! 1 2 6

(36)

As observed in Fig. 12, the modeling using a quadratic function is quite close to that using the exponential form and consequently the exponential function was satisfactorily approximated using a polynomial of degree 2. The same observation can be made for Exp 4 (not shown). Such a mathematical consideration could explain some data in the literature reporting that a first-order kinetic regime occurs in the whole biofilter even at high pollutant concentrations [36–39]. According to Fig. 12, the whole biofilter can be modeled assuming zero-order kinetics with diffusion limitation. Consequently, since the kinetic regime is diffusion-limited at the biofilter inlet, the biofilter performances could be determined from the tangent line to the curve described by Eq. (18) at H = 0, i.e. by the derivative at the y-intercept: CG ) 2kD CGin = −A√ | H m CGin d( ) U H=0

d(

(37)

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In such a case, Eq. (37) should be approximately equal to Eq. (30). According to Fig. 12, the value of Eq. (37) is -221.2 h-1 whereas that of Eq. (30) is -209.3 h-1, i.e. a difference of 5.7 % (for Exp 4, the difference is 6.1 %; not shown). However, even if the difference can be considered negligible, determining ECmax from Eq. (30) is preferable from a physical point of view.

6. Conclusion The procedure to determine rapidly the overall degradation performances of a biofilter (ECmax) was successfully applied to a laboratory-scale biofilter filled with expanded schist as the packing material for the treatment of H2S. The results obtained were in agreement with the ECmax value previously calculated from the classic technique based on the modified Michaelis-Menten model. Fundamentally, the procedure showed that a zero-order regime with reaction limitation occurs at the biofilter inlet for the operating conditions applied (EBRT = 19.3 s; LR ≥ 25.4 g m3 h-1 and H2S concentration ≥ 136 mg m-3). The accuracy of ECmax determination is around ± 10 % depending on the number of data used. Moreover, the coexistence of both zero-order regimes in a large middle part of the biofilter was evidenced for each of the six experiments carried out. However, the critical concentration separating both regimes could not be accurately assessed and, consequently, the Thiele modulus could not be used to characterize the limiting factor influencing the biodegradation.

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In addition, to avoid bias in the determination of the biodegradation kinetics in the case of long experiments, even in the case of inhibition, the rapid procedure has the considerable advantage of accurately determining the overall biofilter performances in real time, i.e. following the change in biofilter performances over time. In other words, such a rapid procedure of about 2 hours could be used to determine the performances of any biofilter, even at an industrial scale, provided that the concentration profile along the height of the packing material could be established with accuracy. This procedure will be useful to determine the performances of biofilters used to treat gas highly loaded in H2S and optimize the major operating parameters. Moreover, it should also be suitable for biofilters treating a mixture of sulfur reduced pollutants. Future experiments should be carried out to validate the procedure for pollutants with Henry’s coefficient values significantly different from that of H2S.

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Fig. 1 Typical curve describing biofilter performances. Fig. 2 Pollutant concentration profile in the biofilm (a: reaction limitation; b: diffusion limitation).

Fig. 3 Michaelis-Menten representation and kinetic expressions considered by the Ottengraf and Van den Oever model according to the pollutant concentration value in the biofilm.

Fig. 4 Example of kinetic regimes that can occur in a biofilter and expressions of the corresponding elimination capacity (EC) according to the Ottengraf and Van den Oever model [11]. Fig. 5 Effectiveness factor as a function of the Thiele modulus developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets. The shape of the curve depends on the order of the reaction [23]. Fig. 6 Photographs of packing materials: (left) expanded schist; (right) synthetic nutritional material UP20. Fig. 7 Biofilter performances. (A) Removal efficiency versus loading rate (EC values in g m-3 h-1). (B) Elimination capacity as a function of H2S concentration (circles: experimental points; black line: modified MichaelisMenten model fitting the experimental points; LR values in g m-3 h-1).

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Fig. 8 H2S elimination profile according to the residence time in the biofilter H/U and the packing material height (Exp 1; LR = 25.4 g m-3 h-1; EBRT = 19.3 s; CGin = 136 mg m-3).

Fig. 9 Comparison between the six ECmax values determined by the rapid procedure (bar) and the ECmax value calculated by Courtois et al. [7] according to Eq. (30).

Fig. 10 Tests for determining the kinetic regime in the biofilter according to Eqs. (31-32). (Exp 1; LR = 25.4 g m-3 h-1; EBRT = 19.3 s; CGin = 136 mg m-3). Fig. 11 Modeled elimination capacity values (EC) calculated using the modified MichaelisMenten equation Eq. (27). For comparison, plots are shifted to take into account the inlet concentration value of each experiment.

Fig. 12 H2S elimination profile according to the residence time in the biofilter H/U and the packing material height (Exp 6; LR = 57.4 g m-3 h-1; EBRT = 19.3 s; CGin = 308 mg m-3).

38

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Table 1. Experimental results obtained from the rapid procedure for 6 experiments (ECmax is the difference between the ECmax value determined using the rapid procedure and the ECmax value calculated by Courtois et al. [7]).

LR (g m-3 h1 ) H (m) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

H/U (h) 0.0000 0.0007 0.0013 0.0020 0.0027 0.0034 0.0040 0.0047 0.0054

Exp 1

Exp 2

Exp 3

Exp 4

Exp 5

Exp 6

25.4

27.7

30.0

37.8

40.7

57.4

CG (mg m-3)

H/U (s) 0.0 2.4 4.8 7.2 9.7 12.1 14.5 16.9 19.3

136.3 117.8 91.5 63.1 45.9 26.3 12.7 6.3 0.6

148.4 120.0 98.9 70.9 52.3 37.3 24.3 7.5 1.5

160.5 141.9 117.2 87.4 63.5 45.2 31.9 19.0 11.6

203.0 162.6 144.8 119.6 104.3 88.9 76.1 62.1 53.9

218.4 199.7 168.0 140.0 120.4 99.9 80.3 61.0 44.8

308.0 261.3 222.1 179.2 162.4 134.4 112.0 84.9 68.1

ECmax (g m-3 h-1)

34.9 ± 2.7

38.3 ± 2.3

34.6 ± 3.3

43.4 ± 3.6

37.8 ± 2.2

64.5± 5.7

 ECmax (%)

-4.1

5.3

-4.9

19.1

3.8

77.1

Ks (mg m-3)

9±3

13 ± 3

14 ± 7

63 ± 15

18 ± 8

070 ± 020

(H/U)crit (h)

0.0026

0.0020

0.0032

0.0018

0.0023

0.0019

(H/U)crit (s)

9.2

7.3

11.6

6.4

8.3

6.9

Hcrit (m)

0.76

0.61

0.96

0.53

0.69

0.57

CGcrit (mg m-3)

047

70

49

126

131

185

39