Application of Response Surface Methodology for H₂S Removal from Biogas by a Pilot Anoxic Biotrickling Filter

Abstract

In this study, a pilot biotrickling filter (BTF) was installed in a wastewater treatment plant to treat real biogas. The biogas flow rate was between 1 and 5 m³·h⁻¹ with an H₂S inlet load (IL) between 35.1 and 172.4 gS·m⁻³·h⁻¹. The effects of the biogas flow rate, trickling liquid velocity (TLV) and nitrate concentration on the outlet H₂S concentration and elimination capacity (EC) were studied using a full factorial design (3³). Moreover, the results were adjusted using Ottengraf’s model. The most influential factors in the empirical model were the TLV and H₂S IL, whereas the nitrate concentration had less influence. The statistical results showed high predictability and good correlation between models and the experimental results. The R-squared was 95.77% and 99.63% for the ‘C model’ and the ‘EC model’, respectively. The models allowed the maximum H₂S IL (between 66.72 and 119.75 gS·m⁻³·h⁻¹) to be determined for biogas use in a combustion engine (inlet H₂S concentration between 72 and 359 ppm_V). The ‘C model’ was more sensitive to TLV (–0.1579 (gS·m⁻³)/(m·h⁻¹)) in the same way the ‘EC model’ was also more sensitive to TLV (4.3303 (gS·m⁻³)/(m·h⁻¹)). The results were successfully fitted to Ottengraf’s model with a first-order kinetic limitation (R-squared above 0.92).

1. Introduction

Biogas, due to methane high combustion enthalpy, can be considered as an important renewable energy source. Nowadays, international laws such as the Directive of the European Parliament 2009/28/EC (April 23, 2009) recognize biogas as a source of vital energy that can reduce the European Union’s energy dependence. The aim of this directive is to increase consumption of renewable energy by 2020 by at least 20%. The longer-term goal is to achieve net-zero greenhouse emissions by 2050 and it will be necessary to increase investment in clean and energy-efficient technologies by 2.8% of Gross Domestic Product (GDP) (or around € 520–575 billion annually) [1]. Hydrogen sulfide (H₂S) is one of the biggest pollutants in biogas. Therefore, it is necessary to reduce the generation of H₂S in the digester and/or reduce its concentration for most uses of biogas. Apart from its harmful effects on health, the presence of H₂S in biogas is not desirable because it is a corrosive gas. Desulfurization of biogas can be carried out by physical-chemical or biological processes. Physical-chemical processes have been commonly used but biological ones have proven to be a good competitor from economic and environmental points of view [2].

In biological processes the most widely used and studied microorganisms belong to the group of bacterial chemotrophic species, which use reduced sulfur compounds as an energy source and use oxygen (aerobic) or nitrate/nitrite (anoxic) as electron acceptors [3,4]. The biodesulfurization of biogas involves the use of technologies that facilitate appropriate contact between the gas and the liquid. There are several advantages in the use of anoxic biotrickling filters (BTFs) over aerobic ones, and these include reducing the risk of explosion, no dilution of biogas, and a lower limitation in the transfer of matter for nitrate when compared to the necessary oxygen absorption [5,6]. In contrast, the cost and availability of large amounts of nitrate can be limiting for the application of anoxic systems. Although ammonia-rich wastewater could be nitrified and used, Zeng et al. [3] used a biogas digestion slurry after nitrification to feed a BTF to achieve stable operation.

The H₂S inlet load (IL) in BTFs is an important parameter in the design of this type of equipment. The IL and the elimination capacity (EC) describe the performance of the BTFs with respect to the removal efficiency (RE) of the contaminant and allow the design of the system, depending on the biogas flow rate that needs to be treated and the inlet H₂S concentration. Values for a critical EC of between 100 and 130 gS·m⁻³·h⁻¹ and a maximum EC between 140 and 280 gS·m⁻³·h⁻¹ have been reported for both aerobic and anoxic biotrickling filters [5,7].

A model can be applied to relate input variables (pollutant inlet concentration, gas flow, electron acceptor concentration, etc.) and design variables (specific surface area of the support, equipment dimensioning, etc.) with the outputs (concentration of the pollutant at the outlet, production of biological reaction products, consumption of reagents, etc.). Empirical models (black box models) are characterized by a high predictive power, but their parameters lack physical significance [8]. They are based on statistically significant relationships between the input and output variables. Stationary-state models have been used to describe biofilters since the early 1980s [9,10,11]. Anoxic BTFs have been described by empirical [12,13] and dynamic [14,15] models. For instance, Soreanu et al. [13] proposed a second-order empirical model using a central composite design (CCD) and the biogas flow rate and the H₂S concentration as input variables, with the H₂S RE obtained as a response variable. Almenglo et al. [15] developed a model that considered the most relevant phenomena such as advection, absorption, diffusion and biodegration. Dynamic models provide a better understanding of the process, but their complexity means that they are seldom used for BTFs.

The aim of the work described here was to study the effects of gas (F_G) and liquid (F_L) flow rates and nitrate concentration ([N-NO₃^–]) along the packed bed on the outlet H₂S concentration and the EC. Two empirical models were proposed to describe the outlet H₂S concentration and the EC. Moreover, the H₂S concentrations were measured along the bed and fitted using Ottengraf’s model [9].

2. Materials and Methods

2.1. Experimental Set-up

An anoxic BTF at pilot scale (Figure 1) was installed in the wastewater treatment plant (WWTP) ‘Bahía Gaditana’ (San Fernando, Spain) and it was fed with biogas from one of their sludge anaerobic digesters. The internal diameter was 0.5 m and the bed height was 0.85 m. The BTF was packed with open-pore polyurethane foam cubes (800 units, 25 kg·m⁻³, 600 m²·m⁻³) (Filtren TM25450, Recticel Iberica, Spain). The recirculation medium pH was kept at 7.4 and the temperature at 30 °C.

The nitrate feeding was done in batch mode and automatized by oxide reduction potential (ORP) (setpoint of −365 mV) [16]: when nitrate was exhausted a fixed liquid volume (25 L) was purged, then a nitrate solution (500 gNaNO₃·L⁻¹) was added to the recirculation medium and finally treated water from the WWTP was added to get a working volume. The nitrate depletion time (NDT) was the time between nitrate feedings, i.e., the time in which microorganisms consumed the nitrate added. NDT was dependent of IL and maximum nitrate concentration reached in the nitrate feeding cycle. The volume of the nitrate solution added was modified in concordance to maintain an NDT between 3 and 4 h. This volume ranged in a linear manner between 0.14 and 0.7 L for an H₂S IL between 33.3 and 177 gS·m⁻³·h⁻¹. During the nitrate depletion time the H₂S concentrations in the outlet stream and along the bed height (0.2, 0.4, 0.6 and 0.8 m) were measured every 30 min, and samples of the recirculation medium were taken for nitrate, nitrite and sulfate measurement. Further information about the system can be found elsewhere [15,16]. A schematic representation of the experimental set-up is provided in Figure 2.

The H₂S concentration in the biogas stream was measured using a gas chromatograph with a thermal conductivity detector (GC-450, Bruker, Germany) and a specific gas sensor (GAsBadge® Pro, Industrial Scientific, USA) was used for H₂S concentrations below 500 ppm_V. Sulfate, nitrite and nitrate were measured by a turbidimetric method (4-500-SO₄²⁻ E), a colorimetric method (45000-NO₂⁻ B) and by an ultraviolet method (4500-NO₃⁻ B), respectively [17].

2.2. Experimental Design

A response surface model from a full factorial three-level three-factor design (3³) was developed including two replicates at the central point. 3³ design allows us to obtain a second-order polynomial using only three levels [18,19]. The three factors were gas flow rate (F_G), liquid flow rate (F_L) and nitrate concentration. The levels of the factor studied, and the values calculated for H₂S IL (Equation (1)), trickling liquid velocity (TLV) (Equation (2)) and empty bed residence time (EBRT) (Equation (3)) are provided in

Table 1. Levels of the factor tested in the experimental design (3³).

Factor	Levels of Factors
	(–1)	(0)	(+1)
FG (m3·h−1)	1	3	5
FL (m3·h−1)	1	2	3
[N-NO3−] (mg·L−1)	1.4 ± 1.1	35.3 ± 2.4	70.5 ± 10.2
IL1 (gS·m3·h−1)	35.1 ± 1.5	109.1 ± 11.7	172.4 ± 3.4
TLV2 (m·h−1)	5.09	10.18	15.27
EBRT1 (s)	600	200	120

¹ Values calculated for F_G values of 1, 2, and 5 m³·h⁻¹, respectively, ² Values calculated for F_L values of 1, 2 and 3 m³·h⁻¹, respectively.

.

$$IL=\frac{F_G}{V}·{[H_{2}S]}_i$$

(1)

$$TLV=\frac{F_L}{A},$$

(2)

$$EBRT=\frac{V}{F_G},$$

(3)

$$EC=IL·RE,$$

(4)

$$RE=\frac{[H_{2}S{]}_i-[H_{2}S{]}_o}{{[H_{2}S]}_i},$$

(5)

where IL is the inlet load (gS·m⁻³·h⁻¹), V is the bed volume (m³), [H₂S]_i is the inlet H₂S concentration (gS·m⁻³), [H₂S]_o is the outlet H₂S concentration (gS·m⁻³), RE is the removal efficiency, EC is the elimination capacity, TLV is the trickling liquid velocity (m·h⁻¹), EBRT is the empty bed residence time (s) and A is the cross-sectional area of the bed (m²).

The experimental results were fitted with two empirical models. The first model, the concentration model (‘C model’), fitted the outlet H₂S concentration as a response variable. The second model, the elimination capacity model (‘EC model’), fitted the EC as a response variable. In both models the independent variables were TLV, the H₂S IL and the nitrate concentration (factors from Table 1). Instead of F_G, H₂S IL was chosen because the IL included the effect of the inlet H₂S concentration (Equation (1)). In addition, TLV was used rather than F_L because it allows a comparison with other BTFs. In both cases a second-order polynomial model was used to predict the outlet H₂S concentration and the EC values. The data were analyzed using Statgraphics^® Centurion XVIII (v.18.1.10).

2.3. Ottengraf’s Model

Ottengraf’s model [9,20] describes the concentration of pollutants in biofilters for steady-state processes. The analytical solution of the model was obtained in three ideal situations:

• There is no diffusion limitation and the biofilm is fully active, and hence the conversion rate is controlled by a zero-order reaction rate. The solution is described by Equation (6). K₀ is a pseudo zero-order rate (g·m⁻³·s⁻¹) and is proportional to the zero-order reaction rate constant (k₀, Equation (7)).
• There is diffusion limitation and therefore the mass transfer rate to the biofilm is insufficient compared to biological substrate utilization rate. The solution is described by Equation (8).
• There is no diffusion limitation and the biofilm is fully active, and hence the conversion rate is controlled by a first-order reaction rate. The solution is described by Equation (6). K₁ is a pseudo first-order rate constant (s⁻¹) (Equation (10)) and is proportional to the first-order rate constant (k₁, Equation (10)).

$$\frac{\left[H_{2}S\right]}{{[H_{2}S]}_0}=1-\frac{K_0·H}{{[H_{2}S]}_0·U_G},$$

(6)

$$\mathrm{With}, K_0=\delta ·A_S·k_0,$$

(7)

$$\frac{\left[H_{2}S\right]}{{[H_{2}S]}_0}={\left[1-\frac{H}{U_G}\sqrt{\frac{A_S·K_0·D^{\prime }}{2·{[H_{2}S]}_0·m·\delta }}\right]}^2,$$

(8)

$$\frac{\left[H_{2}S\right]}{{[H_{2}S]}_0}=exp\left(-\frac{H·K_1}{m·U_G}\right),$$

(9)

$$\mathrm{With}, K_1=A_S·D^{\prime }/\delta ·\varphi ·\tanh \varphi , \mathrm{and} \varphi =\delta \sqrt{k_1/D^{\prime }}$$

(10)

where, H is the height of the tower (m), [H₂S]₀ is the inlet concentration (g·m⁻³), U_G is the superficial gas velocity (m·s⁻¹), A_S is the specific area (m²·m⁻³), δ is the biofilm thickness (m), m is the distribution coefficient at equilibrium (m = G_G/C_L) and D′ is the effective diffusion coefficient (m²·s⁻¹).

3. Results and Discussion

3.1. Empirical Model

The sulfate and nitrite concentrations were almost constant during the experiments; the sulfate concentration was 8.9 ± 1.6 gS-SO₄·L⁻¹ and nitrite concentration was between 0.1 and 10 mgN-NO₂⁻·L⁻¹. The H₂S RE obtained during the experimentation carried out to obtain the empirical model is shown in Figure 3.

As expected, a high H₂S RE was found at low F_G (lower H₂S IL). Therefore, the best results were for an F_G of 1 m³·h⁻¹, where the H₂S IL was 35.1 ± 1.5 gS·m⁻³·h⁻¹ and the RE between 97.3 and 99.5%. Under these conditions, the effects of the nitrate concentration and TLV were negligible. However, at higher biogas flow rates the decrease in the nitrate concentration led to a lower H₂S RE. In anoxic biofiltration nitrate (or nitrite) is the electron acceptor, so its concentration must be a significant factor on the BTF performance, and this is even more important considering that the use of a nitrate feed controlled by ORP [16] leads to a decrease in the nitrate concentration until depletion.

The RE versus the TLV values for the three F_G (EBRT of 600, 200 and 120 s) are listed in

Table 2. Removal efficiencies at different trickling liquid velocity (TLVs) and empty bed residence time (EBRT).

TLV (m·h−1)	EBRT (s) 1
	600	200	120
5.09	99.39	84.73	79.31
10.18	99.24	93.08	83.06
15.27	99.53	97.65	92.13

¹ The H₂S ILs were 35.1±1.5, 109.1±11.7 and 172.4±3.4 gS·m⁻³·h⁻¹, for 600, 200 and 120 s, respectively.

. When the nitrate concentration was not limiting, the TLV effect on H₂S RE was only notable for an F_G equal to or greater than 3 m³·h⁻¹ (i.e. for H₂S IL of 109.1 ± 11.7 and 172.4 ± 3.4 gS·m⁻³·h⁻¹). Thus, for an F_G of 3 m³·h⁻¹, the H₂S was between 84.7 and 97.6% and for 5 m³·h⁻¹ the range was between 79.3 and 92.1%. The improvement observed could be explained by various effects: a higher wetted area [21], an increase in the hold-up liquid (6.4, 8.5 and 10.6 L for 5.1, 10.2 and 15.3 m·h⁻¹) and a higher area in contact with the flowing liquid, as proposed by Almenglo et al. [15].

Consequently, the influence of the nitrate concentration in the recirculating liquid on the H₂S RE was dependent of two factors: the H₂S IL and the TLV. A higher TLV level supplies a higher nitrate availability in the biofilm. TLV has usually been kept constant in anoxic BTFs between 10 [22] and 15 [23] m·h⁻¹, but for a high H₂S IL it would be interesting to study the effect of this parameter. As in aerobic BTFs, where TLV is a key operational variable, in aerobic BTFs the regulation of TLV improves the oxygen mass transfer along the packed bed [24]. Fernández et al. [6] studied the effect of the TLV (2−20.5 m·h⁻¹) on H₂S RE in an anoxic BTF, for H₂S ILs from 93 to 201 gS·m⁻³·h⁻¹, packed with open pore polyurethane foam (the same support material as used in this study). It was found that there was no discernable influence for TLV values higher than 5 m·h⁻¹ for H₂S IL values below 157 gS·m⁻³·h⁻¹. However, at an H₂S IL of 201 gS·m⁻³·h⁻¹ it was observed that TLV values below 15 m·h⁻¹ produced a significant decrease in the H₂S RE from 92 to 85% at 4.5 m·h⁻¹. On using polypropylene Pall rings [25] the optimal TLV was also 15 m·h⁻¹ at high H₂S IL (>201 gS·m⁻³·h⁻¹) although TLV did not have any effect at low H₂S IL (< 78.4 gS·m⁻³·h⁻¹). Zeng et al. [3] studied the effect of TLV between 2.63 an 9.47 m·h⁻¹ (H₂S IL < 86.92 gS·m⁻³·h⁻¹) and achieved an efficient removal of H₂S for the lowest TLV, probably due to the larger height-diameter (H/D) ratio (10.9) and the higher EBRT (342 s). A high H/D ratio and a low EBRT improve the gas-liquid mass transfer [26] but increase the installation cost due to the higher pressure drop [27] and the higher volume of the packed bed.

The statistical results for the ‘C model’ show the significance and high predictability of the regression model. The R-squared was 95.77%, the residual standard deviation was 0.1784 and the mean absolute error was 0.1224. The Durbin–Watson statistic was 1.00088 (p-value = 0.0001) and this shows a possible autocorrelation in the sample with a significance level of 5.0%. Moreover, the plot of residual versus predicted values (Figure 4a) does not show any patterns and we can assume a good correlation between the model prediction and the experimental results. The second-order polynomial model fitted with calibration data is represented by Equation (11).

$$\begin{array}{l}{C}_{G,H2S}=-0.27436+0.0203426·TLV+0.0203127·IL-0.00935431·\left[N–N{O}_3^{-}\right]\\ -0.00120525·TL{V}^2-0.000824025·TLV·IL+0.000411032\\ ·TLV·\left[N–N{O}_3^{-}\right]+0.00000476214·I{L}^2-0.0000513469·IL\\ ·\left[N–N{O}_3^{-}\right]+0.0000617476·{\left[N–N{O}_3^{-}\right]}^2\end{array}$$

(11)

As can be seen in Figure 4b, the most influential factor on the outlet H₂S concentration was the H₂S IL (p-value 2.26·10⁻⁸). Moreover, the TLV and nitrate concentration had a negative effect on the outlet H₂S concentration with p-values of 5.26·10⁻¹⁴ and 5.34·10⁻⁴, respectively. It is interesting to note that the interaction AB (IL and TLV) was significant (p-value 1.18·10⁻⁵) and therefore the effect of one variable depended on the value of another. This behavior can be seen in Figure 3, where the TLV had an effect on the RE at high H₂S IL but not at low ones.

The response surface for the ‘C model’ is shown in Figure 5. The model can be used to predict the factor limits to achieve a desired H₂S outlet concentration. Depending on the combustion engine company, the inlet H₂S limit is in the range 100–500 mg·Nm⁻³ (72–359 ppm_V at 25 °C) [28]. Therefore, for a nitrate concentration of 35.5 mgN-NO₃⁻·L⁻¹ and TLV of 15.27 m h⁻¹ the maximum H₂S IL would be 66.72 and 119.75 gS·m⁻³·h⁻¹ for outlet H₂S concentrations of 72 and 359 ppm_V, respectively.

The statistical results for the ‘EC model’ show a higher significance and predictability of the regression model when compared with the ‘C model’. The R-squared was 99.63%, the residual standard deviation was 2.545 and the mean absolute error was 1.646. The Durbin–Watson statistic was 1.7041 (p-value = 0.0626), although the p-value was higher than 5% there were no traces of autocorrelation—as verified by checking the residual plot (Figure 6a). The second-order polynomial model fitted with calibration data is represented by Equation (12).

$$\begin{array}{l}EC=11.0413-2.30638·TLV+0.844035·IL+0.172511·\left[N–N{O}_3^{-}\right]\\ +0.090618·TL{V}^2+0.0225828·TLV·IL-0.00947479·TLV\\ ·\left[N–N{O}_3^{-}\right]-0.00231493·I{L}^2+0.00184907·L·\left[N–N{O}_3^{-}\right]\\ -0.00194474·{\left[N–N{O}_3^{-}\right]}^2\end{array}$$

(12)

As can be seen in Figure 6b, the most influential factor on the EC was the H₂S IL (p-value 1.81·10⁻²⁸). Moreover, the TLV and nitrate concentration had a positive effect on the EC with p-values of 2.37·10⁻¹¹ and 1.38·10⁻⁵, respectively. In this case, the interactions AB (IL and TLV) and BC (IL and nitrate concentration) and the quadratic term (BB or IL²) were more significant than the nitrate concentration. Therefore, H₂S IL and TLV had a greater effect on the EC than the nitrate concentration.

The response surface for the ‘EC model’ is shown in Figure 7. As expected, for high H₂S IL (>109.1 ± 11.7 gS·m⁻³·h⁻¹) or high biogas flow rate (F_G > 3 m³·h⁻¹) an increase in EC was observed when the nitrate concentration and TLV were increased.

A sensitivity analysis was performed by calculating the partial derivative in both models [29]. The maximum and minimum values for the variation of estimated variables corresponding to each factor are provided in

Table 3. Sensitivity analysis.

Factor	‘C Model’		‘EC Model’
	Maximum	Minimum	Maximum	Minimum
TLV	0.0078	–0.1579	4.3303	–1.252
IL	0.0177	0.0045	1.1553	0.1657
[N-NO3−]	0.0038	–0.159	0.4363	–0.1801

. For the ‘C model’ the maximum negative effect corresponded to a TLV of –0.1579 (gS·m⁻³)/(m·h⁻¹) and the maximum positive effect was for an H₂S IL of 0.0177 (gS·m⁻³)/(gS·m⁻³·h⁻¹). However for the ‘EC model’ the maximum effects were due to TLV values of –1.252 (gS·m⁻³)/(m·h⁻¹) and 4.3303 (gS·m⁻³)/(m·h⁻¹).

3.2. Ottengraf’s Model

The concentration profiles along the bed height were analyzed using Ottengraf’s model, without nitrate concentration limitations, for H₂S IL values between 33 and 176 gS·m⁻³·h⁻¹ and TLV values between 5.09 and 15.27 m·h⁻¹. The linear adjustments are provided in

Table 4. Adjustments using Ottengraf’s model.

IL (gS·m−3·h−1)	TLV (m·h−1)	Zero-Order Diffusion		Zero-Order Kinetic		First-Order Kinetic
		r2	k (s−1)	r2	k (s−1)	r2	k (s−1)
36	5.09	0.62	0.0018	0.3	0.012	0.95	0.008
35	10.18	0.57	0.0018	0.26	0.012	0.92	0.0087
33	15.27	0.52	0.0018	0.22	0.011	0.93	0.0092
130	5.09	0.95	0.0011	0.94	0.011	0.93	0.0031
108	10.18	0.91	0.0012	0.82	0.01	0.93	0.0036
104	15.27	0.93	0.0014	0.77	0.01	0.96	0.0057
170	5.09	0.97	0.0009	0.96	0.0079	0.96	0.0025
176	10.18	0.88	0.001	0.79	0.0091	0.93	0.0029
167	15.27	0.86	0.0011	0.74	0.0092	0.95	0.0034

according to the following simplifications: controlled by zero-order diffusion, zero-order kinetic and first-order kinetic. The behavior of the concentration profile for 5.09 m·h⁻¹ and 130 and 170 gS·m⁻³·h⁻¹ could be explained using a zero-order simplification for diffusion or kinetic. However, for all other conditions the first-order kinetic simplification can be applied. The kinetic constant was in the range between 0.0025 and 0.0092 s⁻¹.

To our knowledge, Ottengraf’s model has not be applied to biogas desulfurization, although studies on H₂S removal from air have been modeled using Ottengraf’s model [30,31,32,33].

Jin et al. [32] found that the zero-order kinetic limitation described the outlet H₂S concentration (TLV of 0.62 m·h⁻¹ and a maximum H₂S IL around 30 gS·m⁻³·h⁻¹). Oyarzún et al. [30] applied zero-order diffusion equations for an inlet H₂S concentration below Ks (Monod saturation constant) and zero-order kinetic equation and inlet concentration above Ks. The microbial kinetic of the biotrickling filter presented in this work can be described by a Haldane model [15], with an affinity constant for sulfide (Ks) of 8.4 gS·m⁻³ and a gas concentration in equilibrium of 1.28 gS·m⁻³. This concentration is considerably lower than the minimum inlet concentration employed in this work (5.55 gS·m⁻³). Therefore, the study was carried out at an inlet H₂S concentration higher than Ks with a first-order kinetic as obtained by Oyarzún et al. [30].

4. Conclusions

The influence of the nitrate concentration was dependent on TLV and H₂S IL, with its influence increasing for lower TLV and higher H₂S IL. The empirical models obtained by the response surface methodology for the factorial design of three factors at three levels (3³) were able to predict the outlet H₂S concentration and the EC with a R-squared of 95.77% and 99.63% without autocorrelation. The most influential factors on the outlet H₂S concentration and EC were the H₂S IL and TLV, with the nitrate concentration being less significant. For biogas use in a CHP system the maximum H₂S IL should be between 66.72 and 119.75 gS·m⁻³·h⁻¹ (TLV of 15.27 m·h⁻¹ and nitrate concentration of 35.5 mgN-NO₃⁻·L⁻¹). Moreover, Ottengraf’s model was applied successfully considering a first-order kinetic limitation simplification with an R-squared above 0.92.