Modeling of a Two-Bed Reactor for Low-Temperature Removal of Nitrogen Oxides in Nitric Acid Production

Abstract

In this study, the modeling of the low-temperature catalytic abatement of NO_X and N₂O from tail gases in a weak nitric acid plant utilizing a single-pressure 0.716 MPa system was performed. A one-reactor concept assumes that in the first bed, NO_X is reduced by ammonia on a commercial vanadia–alumina catalyst, and in the second bed, N₂O is decomposed on a proprietary nickel–cobalt catalyst. The kinetics of N₂O decomposition on a Cs/Ni_0.1Co_2.9O₄ catalyst was experimentally studied in an isothermal flow reactor. The reaction rate constants were determined by varying the residence time and temperature; these data formed the basis for modeling kinetics and heat and mass transport in an adiabatic reactor in which the low-temperature mitigation of nitrogen oxides occurred. Taking into account the given spatial limitations inside the reactor and the allowable temperatures, the layer heights were evaluated to ensure a residual NO_X and N₂O content of less than 50 ppm. Catalyst loading using layers in a commercial reactor was estimated for the tail-gas flow rates of 46,040–58,670 m³/h. Simulations showed that the optimum inlet temperature was 260 °C; in this case, the NO_X and N₂O conversion targets were achieved in the range of 46,040–58,670 m³/h while adhering to catalyst bed height and outlet temperature limitations.

1. Introduction

Capturing greenhouse gases is one of the greatest technological challenges. Of these GHGs, nitrous oxide (N₂O) has 310 times more global warming potential than CO₂. Human activities such as agriculture, fuel combustion, wastewater management, and industrial processes are increasing the amount of N₂O in the atmosphere. Globally, about 40% of total N₂O emissions come from anthropogenic sources. Stimulated by the need for fertilizers, the production of nitric acid results in N₂O emissions that can be reduced through technological upgrades and the use of abatement equipment. In nitric acid production, N₂O emissions are estimated at 300,000–400,000 t/year [1]. The emission of N₂O exclusively depends on the ammonia combustion process. Once formed, N₂O passes unreacted through the plant and is not affected by the operating conditions. In weak nitric acid production, all known approaches to N₂O reduction can be classified into several groups, according to their ranking in terms of the technological process. The most widely used are the primary, secondary, and tertiary systems for N₂O abatement. The primary methods consist of the optimization of the composition of a platinoid gauze pack and operating conditions of an ammonia burner, aimed at the formation of free volumes for the homogeneous decomposition of nitrous oxide at high temperatures. This results in the suppression of the N₂O formation during the oxidation of NH₃ and the interaction of the reaction products with the “leaked” ammonia. The secondary methods assume the decomposition of nitrous oxide on the catalyst installed in the hot zone immediately downstream of the gauze packs. Yara, BASF, J. Matthey, and Heraeus have proposed high-temperature ceramic-supported catalysts based on precious metals or metal oxides [2]. Tertiary abatement measures ensure the removal of N₂O in the tail gas (the stream leaving the absorber) via direct catalytic decomposition (de-N₂O process) (

Table 1. Methods of tail-gas purification.

The Purification Method	Temperature, °C	Catalyst	Process	Reactor	Technology Developed by
Non-selective catalytic reduction (reducing agents: H2, hydrocarbons)	720–770	Pd-containing	de-NOx de-N2O	NSCR	GIAP
Selective catalytic reduction (reducing agents: NH3)	250–520	MnO2, CuO, Fe2O3, Zeolite, V/Al	de-NOx	SCR	BASF BIC RAS
EnviNOx®	350–520	Zeolite	de-NOx de-N2O	EnviNOx	Uhde

). They have great advantages, as they do not affect the other elements of the nitric acid production process and can be applied in several variants [3]. In European countries, the N₂O emissions per ton of the produced nitric acid vary considerably, as evidenced by the current guidelines for estimating national N₂O emissions as specified by the internationally recognized IPCC (Intergovernmental Panel on Climate Change) [1]. The N₂O emission factor for HNO₃ production can range from <2 to 19 kg N₂O per ton of 100% HNO₃.

Combining two consecutive catalytic beds to remove NO_X and N₂O at close temperatures is in line with the current technological trends and can be accomplished in a single reactor [4]. The layer-by-layer loading of various catalysts is a well-known technique, and it is also used in waste-gas purification processes. For example, it is used in Uhde’s EnviNO_x® variants of integrated nitrogen oxides (NO_x and N₂O) abatement technology [3]. Several years ago, ThyssenKrupp Industrial Solutions commercialized technologies EnviNO_x® for tail-gas purification in a two-bed reactor at medium temperatures [3]. In one version, the catalytic decomposition of N₂O occurs on an iron–zeolite catalyst at 425–520 °C in the first bed; NO_X is catalytically reduced by ammonia to N₂ on a similar catalyst in the second bed. In another version, which is suitable for lower tail-gas temperatures of 300–500 °C, ammonia is injected together with these gases; SCR NO_X with ammonia occurs in the first bed, and N₂O reduction occurs in the second bed after the addition of natural gas or propane.

In Russia, industrial weak nitric acid plants with a capacity of 345 t/day operating at a single pressure of 0.716 MPa (UKL plant) are equipped with reactors for the low-temperature selective catalytic reduction of nitrogen oxides by ammonia from tail gases. The design of the SCR reactor allows for the setup of not only a bed of SCR catalyst, the height of which is ~0.5 m, but also a bed of de-N₂O catalyst up to 0.7 m high. Thus, tail-gas purification can be carried out in a single reactor, by using catalytic beds providing both SCR of NO_x with ammonia and de-N₂O in the temperature range of 250–300 °C [5,6]; the catalyst arrangement options in the adiabatic reactor can vary. However, if the de-N₂O catalyst is placed in the first bed, ammonia must be injected before the second bed, where the de-NO_x catalyst is located. This will require precise ammonia control to eliminate the extra N₂O formation during SCR. Therefore, based on the actual temperature modes for SCR and de-N₂O catalysts, the most rational seems to be the option in which the first bed contains an SCR catalyst (NH₃ is introduced together with tail gases), and the second bed contains an N₂O decomposition catalyst. This option can be readily tailored to the existing industrial reactors. Currently used at UKL plants, the abatement of NO_x by SCR provides NO_x level < 50 ppm, which meets environmental standards. This process is carried out on the aluminum–vanadium catalysts AVK-10 and AOK-78-55 with V₂O₅ content of 12–12.5%, and MnO₂ of 1–1.5% can be added as well. An improved technology made it possible to reduce the content of vanadium pentoxide to 5–7% [7] from 12–15% [8] while maintaining high activity and selectivity for molecular nitrogen. Usually, V/Al SCR catalysts operate in the temperature range of 220–280 °C without loss of selectivity for N₂. As the gases after SCR contain 0.15% N₂O, 2.5% O₂, and 3% H₂O [5,6], it is essential to use a de-N₂O catalyst, which can work in a close temperature range and in the reaction medium after the SCR catalyst.

The decomposition of N₂O is an irreversible exothermic reaction. It proceeds via two mechanisms: the Langmuir–Hinshelwood (L–H) mechanism characterized by the low activation energy of the stage of surface oxygen diffusion and recombination (stage 1), and the Eley–Rideal (E–R) mechanism characterized by the high activation energy of surface diffusion, which requires large amounts of energy for oxygen diffusion (stage 3) [9,10,11]:

N₂O + S → N₂↑ + S…Osurf

(1)

2 S…Osurf ↔ 2S + O₂↑ (L-H),

(2)

2 S … Osurf + N₂O → 2 S + O₂↑ + N₂ ↑ (E-R),

(3)

where S is the active site of the surface, and S…O surf is the oxygen adsorbed on the active site of the surface. For various oxide systems, stages (2) and (3) were found to be relatively slow compared with stage (1). In other words, O₂ desorption can be considered the rate-determining stage of the catalytic decomposition of N₂O regardless of the mechanism of O₂ formation. Thus, the kinetics of de-N₂O depends on temperature, pressure, and the competitive adsorption of inhibitors (O₂ and H₂O) on active sites.

A variety of catalytic systems for the low-temperature decomposition of N₂O includes [12,13] platinum-group metals (Ru, Rh, Pd, Ir, and Pt), oxides of rare-earth elements, and oxides of transition d-elements (in particular, Cu, Ni, Co, and Fe) [14,15,16,17,18]. Many catalytic systems containing noble metals and elements of the rare-earth subgroup are deactivated in the presence of inhibitors and have a high cost, which makes it difficult to use them as catalysts for exhaust-gas purification. To date, the spinel-like structure of Co₃O₄ oxide, as well as the binary substituted oxides based on it, have proved to be the most promising candidates for de-N₂O due to the redox ability of cobalt, a high concentration of oxygen vacancies, and a weak Co-O bond [19,20]. The substitution of Co atoms in certain positions of the spinel oxide matrix has a significant effect on the binding energy of the active center with oxygen. Magnesium and nickel substituted by Co₂O₃ spinels demonstrated the highest activity in the reaction of N₂O decomposition. The incorporation of Ni²⁺ or Mg²⁺ into the Co₃O₄ structure promotes better desorption of O₂ and lowers the temperature of de-N₂O [21,22,23,24,25,26]. Both cations can displace cobalt not only in the tetrahedral environment but also to some extent in the octahedral one [27]. This leads to structural distortions with an increase in the bond lengths in octahedra and a decrease in tetrahedra. The effect is more pronounced for nickel-substituted Co₃O₄ spinels and to a lesser extent for magnesium-substituted ones. The modification of Co₃O₄ spinels with alkali metal cations makes them more active and resistant to inhibitors [28,29]. The beneficial effect of different alkali promoters on the Co₃O₄ activity in nitrous oxide decomposition increases in the following order: Li ≪ Na < Rb ≅ K < Cs [28,29]. This is consistent with a decrease in the electronegativity values from Li to Cs [30]. Most studies on the effect of the nature of the alkaline modifier and its precursors were mainly conducted for pure Co₃O₄ spinels.

The catalysts based on Ni(Mg)-substituted cobalt spinels modified with alkali metals Cs/Ni(Mg)_xCo_3−xO₄ [9,31,32] are promising for low-temperature N₂O decomposition as second-bed catalysts in the abatement of NO_x and N₂O from tail gases [5,31].

The main novelty of this paper lies in presenting a single-reactor concept with the low-temperature catalytic control of NO_x and N₂O from the tail gases emitted at weak nitric acid plants. In the first bed, NO_x is reduced by ammonia, and in the second bed, N₂O is decomposed on a proprietary catalyst. More than half of the industrial plants producing nitric acid in Russia utilize a low-temperature V–Al catalyst to remove NO_X emissions using SCR. Under such conditions, a low-temperature N₂O decomposition catalyst is required. A new Cs/Ni_0.1Co_2.9O₄ catalyst for the decomposition of nitrous oxide at low temperatures is also another new aspect of this paper.

The main objective of this study is to determine the conditions for the combined low-temperature catalytic purification of NO_x and N₂O from the tail gases of weak nitric acid plants, providing NO_x and N₂O removal rates of at least 98%, i.e., to no more than 50 ppm, in a single two-bed reactor. It is assumed that a commercially available vanadium–aluminum catalyst [6,7,8] is used for the SCR of NO_X, and a new Cs/Ni_0.1Co_2.9O₄ catalyst is used for the low-temperature decomposition of N₂O [9,33]. The following restrictions should be taken into account:

-

The catalyst bed height should not exceed the maximum allowable space according to the UKL plant’s catalytic purification reactor design: 0.5 m for SCR and 0.7 m for de-N₂O;

-

The maximum temperature in the SCR catalyst bed should not exceed 280 °C because the selectivity of vanadium–aluminum catalysts decreases at a higher temperature.

2. Results and Discussion

2.1. Kinetic Modeling

The experimental data obtained in the isothermal flow reactor and plotted in Figure 1 (symbols) demonstrate that the proper choice of residence time and reaction temperature makes it possible to achieve a high nitrous oxide conversion efficiency, in the range of 95–99% even at moderate temperatures. The highest degree of N₂O conversion was obtained at 250–280 °C. The stable operation of the catalyst was maintained for at least 2 h.

The evaluated values of the pre-exponential factor (k₀) and the activation energy (E_a) of the de-N₂O reaction rate constant (k) were found to be 7.23·10⁸ s⁻¹ and 77.15 kJ/mol, respectively (

Table 2. Kinetic constants for de-N₂O reaction.

Kinetic Parameters		Confidence (+/−)
k0, s−1	Ea, J/mol	k0, s−1	Ea, J/mol
7.23·108	77,150	0.37·108	3360

). The results of modeling based on the estimated parameters are plotted in Figure 3 (lines).

2.2. Process Modeling

The calculations showed that an increase in the flow rate of gas entering the reactor reduced the residence time (τ) in the catalyst bed, which led to a decrease in the conversion of nitrogen oxides (X). To increase τ, it is necessary to increase the height of the catalyst bed, but in this case, the H_max limitation could not be met.

At $T_g^{in}$ = 230–240 °C, the height of the second bed significantly exceeded 0.7 m for all the Q values from the considered range. An increase in $T_g^{in}$ led to an increase in the reaction rate, which made it possible to achieve the required conversion at a lower H. Since SCR and de-N₂O reactions are exothermic, the temperature increased along the height of each layer. The maximum adiabatic temperature rise (ΔT_ad) in the first layer at the required conversion of the initial amount of NO_x was approximately 20 degrees and in the second layer at the required conversion of N₂O—4.04 degrees. The temperature at the outlet of the first bed was equal to $T_g^{in}+\mathsf{\Delta }\mathrm{T}a{d}_1$, and at $T_g^{in}$ = 270 °C, it became higher than the permissible value of 280 °C.

The conversion and temperature profiles along the bed heights at the maximum gas flow rate of Q = 58,670 m³/h and $T_g^{in}$ = 250 °C are presented in Figure 2. The temperature of 270 °C at the outlet of the first bed was within the temperature limit T_max. However, under these conditions, the height of the first bed was 0.52 m, and the height of the second bed was 0.79 m; thus, the heights of both these layers exceeded the permissible values.

At the fixed $T_g^{in}$ = 250 °C, if Q decreased (i.e., the residence time τ increased), the bed height required to achieve a given conversion rate decreased (Figure 3, solid lines). With Q ≤ 52,000 m³/h, the height of each bed was within the specified limits, and T_max did not exceed 280 °C.

Figure 4 shows the NO_x and N₂O conversion and temperature profiles along the beds at $T_g^{in}$ = 270 °C and Q = 58,670 m³/h. A higher inlet temperature contributed to a much lower bed height for any Q, which allowed the specified limits to be reached. However, the outlet temperature in the first bed considerably exceeded the limit of 280 °C for all Q values (Figure 3, dash-dotted lines), which is unacceptable for an SCR catalyst. Therefore, the implementation of the process at $T_g^{in}$ = 270 °C was not possible.

At $T_g^{in}$ = 260°C, the bed heights also became lower, but the maximum temperatures did not exceed the specified limits. For all the Q values from the considered range, the limits for the allowable height of the first and second catalyst bed were determined (Figure 5, dashed lines).

The simulation results at $T_g^{in}$ = 260 °C and the maximum gas flow rate Q = 58,670 m³/h are shown in Figure 5. The temperature at the SCR bed outlet was 279.9 °C. The calculated bed height was 0.5 m for the SCR catalyst and 0.67 m for the de-N₂O catalyst, which satisfied all the given limitations.

Thus, the mathematical modeling of catalytic NO_x and N₂O abatement from tail gas demonstrated that when the temperature of the tail gas was $T_g^{in}$ = 250 °C, the process provided an acceptable residual content of NO_x and N₂O if the flow rate of the tail gas was Q ≤ 52,000 m³/h, and at $T_g^{in}$ = 260 °C, for all the Q values from the considered range. The restrictions of the bed heights in the adiabatic reactor and the maximum temperature restrictions in the SCR bed were met for both options. The hydraulic resistance of the beds and the weight of catalysts are given in

Table 3. The bed heights, the total pressure drop along the beds, and catalyst loading.

${\mathit{T}}_{\mathit{g}}^{\mathit{i}\mathit{n}},°\mathbf{C}$	Bed	Q, m3/h (STP)	H, m	ΔP *, kPa	G, tons
250	SCR	46,040	0.42	3.01	4.29
	de-N2O		0.63	6.87	6.43
	SCR	47,038	0.43	3.20	4.39
	DeN2O		0.64	7.25	6.53
260	SCR	46,040	0.40	2.92	4.08
	de-N2O		0.53	5.89	5.41
	SCR	47,038	0.41	3.11	4.18
	de-N2O		0.54	6.23	5.51
	SCR	55,035	0.47	4.78	4.80
	de-N2O		0.63	9.68	6.43
	SCR	56,400	0.48	5.11	4.90
	de-N2O		0.64	10.27	6.53
	SCR	57,600	0.49	5.43	5.00
	de-N2O		0.66	11.02	6.74
	SCR	58,670	0.50	5.73	5.10
	de-N2O		0.67	11.57	6.84

* Calculated at 1 atm.

.

For a rough comparison of the simulation results with the literature data, we used the data given in [34] when calculating the N₂O decomposition reactor at 450 °C on a cobalt-containing catalyst (Co-Mg-Al, K-promoted) in the form of 3 × 3 mm extrudates. To achieve the target conversion rate of 90% (100 ppm N₂O residual) at a flow rate of 30,000 m³/h (STP), 11.5 m³ (ca. 15 tons) of catalyst was required, with a pressure drop of 20 kPa over the catalyst bed. As can be seen from Table 6, a smaller catalyst volume (up to 8 m³) and a pressure drop (up to 12 kPa) were required to destroy 1500 ppm N₂O to a residual 50 ppm; hence, the catalyst weight and hydraulic resistance of the bed were less than those for a similar reactor.

When the process was run at $T_g^{in}$ = 250 °C and Q = 46,040–47,038 m³/h, the pressure drop did not exceed 9.9–10.5 kPa, and the total catalyst weight was 10.7–10.9 tons (Table 3). At $T_g^{in}$ = 260 °C and Q = 46,040–58,670 m³/h, ΔP was in the range of 8.8–17.3 kPa, and G was 9.5–11.9 ton (Table 6). It should be emphasized that with a flow rate of ~46,000–47,000 m³/h, the process operation at 260 °C can slightly save the catalyst load and pressure drop compared with the variant at $T_g^{in}$ = 250 °C. In a wider range of flow rates, an inlet temperature of 260 °C can be regarded as the optimal value to ensure high abatement performance, no catalyst overheating, low-pressure drop, and catalyst loading.

The combination of a NO_x SCR catalyst and a N₂O decomposition catalyst in one reactor is very attractive. This approach does not require considerable engineering and reconstruction work for the existing plants equipped with low-temperature SCR de-NO_x technology. There are about 100 industrial nitric acid plants in Russia, more than half of which use low-temperature V–Al catalysts to remove NO_x using SCR from the tail gas and are the main source of nitrous oxide emissions. Under such conditions, traditional high-temperature catalysts for the decomposition of N₂O (iron-containing zeolites) would require additional gas heating, which is not economically feasible. The use of a combined tail-gas cleaning system with a low-temperature N₂O decomposition catalyst makes it possible to reduce the energy costs for tail-gas heating and avoid CO₂ emissions, which is inevitable during high-temperature nonselective N₂O reduction with hydrocarbons. To protect the environment from the harmful effects of N₂O emissions, the development of a combined NO_x + N₂O abatement system is useful and relevant.

3. Experimental

Through the co-precipitation of the aqueous solutions of Co(NO₃)₂·6H₂O (REAHIM, Moscow, Russia) and Ni(NO₃)₂·6H₂O (REAHIM, Moscow, Russia) salts, a substituted cobalt spinel Ni_xCo_3-xO₄ with a molar degree of substitution x = 0.1 was obtained. Precipitation was performed at room temperature, and pH = 8–8.5; (NH₄)₂CO₃ (REAHIM, Moscow, Russia) was used as a precipitant. The precipitate was filtered off, washed to pH = 7, and dried for 10 h at a temperature of 120 °C. The dry precipitate was modified via impregnation with 2 wt% cesium (CsNO₃ solution) (REAHIM, Moscow, Russia). Ethylene glycol and citric acid were added to the impregnating solution containing cesium nitrate (the Pechini method). After calcination for 2 h at 450 °C, a 2% Cs/Ni_0.1Co_2.9O₄ (Cs/Ni-Co) sample was obtained. All chemicals were 99.9% pure (purissimum).

The phase composition of the sample was determined using X-ray phase analysis (XRD) on a Bruker D8 diffractometer (Karlsruhe, Germany) using CuK_α radiation (λ = 1.5418 Å).

The sample was scanned point by point with an interval of 0.05° in the 2θ range from 10 to 70°. Figure 6 shows that the X-ray pattern of the sample corresponds to the spinel phase. The structural parameters were calculated using the FullProff program (a = b = c = 8.088 Å). The size of the coherent scattering region (CSR~260 Å) was determined using the Selyakov–Scherer formula. The specific surface area of the sample (S_sp = 32 m²/g) was measured through argon sorption at 77K, followed by thermal desorption, at four points of the sorption equilibrium with a SORBI-M 4.1 instrument (ZAO META, Novosibirsk, Russia) using the SORBI-M Version 4.2 software. Helium was used as a carrier gas. Specific surface area values were calculated using the BET method. High-pressure mercury porosimetry with an AutoPore IV 9500 V1.09 instrument (Micromeritics, Norcross, GA, USA) was used for studying the porous structure of the catalyst (the median pore diameter of the sample was 0.03 μm).

In kinetic experiments, the activity was determined on a laboratory setup (Figure 7) with an isothermal flow reactor in the flow rates range of 5.4–1.8 l/h (residence time 0.27–0.8 s); the catalyst was tested as a 0.25–0.50 mm fraction with the following reaction mixture at the inlet: 1500 ppm N₂O, 2.5% O₂, ~3% H₂O, and He balance. The kinetic experiments were carried out at atmospheric pressure (an increase of 0.01 atm was allowed). The N₂O concentration at the reactor inlet and outlet was determined online at 120 °C using an FT-801 FT-IR spectrometer (Simex, Novosibirsk, Russia).

4. Mathematical Model

4.1. Description of the Reaction System and Governing Equations of the Model

Mathematical modeling is an effective tool for predicting the conditions that ensure the highest catalyst performance in the low-temperature purification of tail gases from nitrogen oxides in adiabatic reactors. This will contribute to the optimization of operating expenses during the practical implementation of the proposed single-reactor concept at UKL plants.

When formulating the mathematical model, it should be taken into account that the adiabatic fixed-bed reactor under consideration has a thermally insulated wall to minimize heat losses, and the catalytic beds feature a large diameter-to-height ratio. Therefore, radial heat and mass transfers have no significant influence and can be neglected in the model, but it is important to consider the conductive heat transfer and diffusive mass transfer in the axial direction.

To provide the necessary residence time at a bed height of 0.5–0.7 m, the linear gas velocity in the reactor should not exceed 1.0–1.5 m/s. At such linear velocities, the interphase heat and mass transfers between the catalyst and the gas can affect the performance of the catalyst [35,36,37]. Thus, to simulate the NO_x and N₂O abatement process in an adiabatic two-bed reactor, we used a stationary two-phase mathematical model for each catalytic bed that took into account the following factors:

-

Convective heat and mass transfers in the gas phase;

-

Axial diffusion in the gas phase;

-

Axial heat transfer due to thermal conductivity in the solid phase;

-

Interphase heat and mass transfers;

-

Chemical reactions (SCR of NO_x with ammonia in the first bed, N₂O decomposition in the second bed);

-

Heat release as a result of exothermic reactions in the solid phase.

4.2. Governing Equations of the Model

The mass and energy balance equations and the boundary conditions for each bed of the adiabatic reactor are given in

Table 4. The stationary non-isothermal mathematical model of the catalytic process in adiabatic reactor.

Balance Equation	Boundary Conditions
Mass balance
Gas phase
$-u_0\frac{\partial y_{gi}}{\partial z}+\frac{\partial }{\partial z}\left(\frac{P}{T_g}\cdot \frac{T_0}{P_0}\cdot D_i^e\frac{\partial y_{gi}}{\partial z}\right)+S_{sp}\cdot {\beta }_i\cdot \frac{P}{T_g}\cdot \frac{T_0}{P_0}\cdot \left(y_{ci}-y_{gi}\right)=0,\hspace{0.33em}i=1,N\hspace{1em}(4)$ Solid phase $-S_{sp}\cdot {\beta }_i\cdot \frac{P}{T_g}\cdot \frac{T_0}{P_0}\cdot \left(y_{ci}-y_{gi}\right)+{\nu }_i\cdot V_m\cdot W=0,\hspace{0.33em}i=1,N\hspace{1em}(5)$	$\begin{array}{l}z=0:\frac{P}{T_g}\cdot \frac{T_0}{P_0}\cdot D_i^e\frac{\partial y_{gi}}{\partial z}=u_0\left(y_{gi}^{in}-y_{gi}\right);\hspace{1em}(8)\\ z=H:\frac{\partial y_{gi}}{\partial z}=0.\hspace{1em}(9)\end{array}$
Energy balance
Gas phase
$c_p\left(T_{ref}\right)\frac{u_0}{V_m}\frac{\partial T_g}{\partial z}=S_{sp}\cdot \alpha \cdot \left(T_c-T_g\right)\hspace{1em}(6)$	$\begin{array}{l}z=0:T_g=T_g^{in},\hspace{0.33em}\frac{\partial T_c}{\partial z}=0;\hspace{1em}(10)\\ z=H:\frac{\partial T_c}{\partial z}=0.\hspace{1em}(11)\end{array}$
Solid phase
$-\frac{\partial }{\partial z}\left({\lambda }^e\frac{\partial T_c}{\partial z}\right)=S_{sp}\cdot \alpha \cdot \left(T_c-T_g\right)+\left(-\Delta H\right)\cdot W\hspace{1em}(7)$

. In the first bed, the reaction of SCR NO_x with ammonia proceeds at a rate of W_SCR and enthalpy (−ΔH_SCR), while in the second bed, the reaction of de-N₂O proceeds at a rate of W_N2O and enthalpy (−ΔH_N2O). At the inlet to the first bed, the inlet values of species concentrations $y_{gi}^{in}$ and temperature $T_g^{in}$ are set. At the inlet to the second bed, the species concentrations after the first bed are taken as inlet values $y_{gi}^{in}$, and the temperature at the outlet from the first bed is taken as $T_g^{in}$.

For calculating model parameters, we used the correlations given in

Table 5. Correlations for calculating model parameters.

Parameter	Equation		Refs.
Heat and mass transfers in the gas and solid phases
Effective axial dispersion coefficient of the k-th substance in the gas phase	$\begin{array}{l}\frac{1}{{\mathrm{Pe}}_z}=\frac{0.28}{\mathrm{Re}\cdot \mathrm{Sc}}+0.25\left(1+\frac{1}{1+750\cdot {\mathrm{Re}}^{-2}}\right)+\\ 0.03\frac{E^2}{\left(1+E\right)}\cdot \frac{1}{{\left(\mathrm{Re}\cdot \mathrm{Sc}\right)}^{-1}+0.5E^{1/2}},\hspace{0.33em}E=4.2{\mathrm{Re}}^{-0.5}\end{array}$	(12)	[38,39]
Effective axial thermal conductivity coefficient in the solid phase	${\lambda }^e={\lambda }_g\cdot \left(7+B{\mathrm{Re}}_m\mathrm{Pr}\right)$	(13)	[38,40,41]
Internal mass transfer
Knudsen diffusion coefficient	$D_K=97r_p\sqrt{\frac{T_{ref}}{M}}$	(14)	[42]
Effective diffusion coefficient for the de-N2O catalyst Effectiveness factor for the de-N2O catalystObserved reaction rate of de-N2O	$D_c^e=P_e{\left(\frac{1}{D_m}+\frac{1}{D_K}\right)}^{-1}$	(15)	[42]
	$\eta =\left(\frac{3}{\psi }\right)\cdot \left[\left(\frac{1}{th\left(\psi \right)}\right)-\frac{1}{\psi }\right],\hspace{0.33em}\psi =\frac{d_p}{2}\cdot \sqrt{\frac{k}{D_c^e}}$	(16)
	$W=\eta \cdot k\cdot C_{N_{2}O}$	(17)
External heat and mass transfers
Sherwood number	$\mathrm{Sh}=0.395{\mathrm{Re}}_m^{0.64}\cdot {\mathrm{Sc}}^{1/3}$	(18)	[38]
Nusselt number	$\mathrm{Nu}=0.395{\mathrm{Re}}_m^{0.64}\cdot {\mathrm{Pr}}^{1/3}$	(19)	[38]
Pressure drop and catalyst loading
Pressure drop along the bed	$\Delta P=H\cdot \left[150\frac{{\left(1-\epsilon \right)}^2}{{\epsilon }^3}\cdot \frac{\mu \cdot u}{d_p{}^2}+1.75\frac{\left(1-\epsilon \right)}{{\epsilon }^3}\cdot \frac{\rho \cdot u^2}{d_p}\right]$	(20)	[38,43]
Catalyst loading	$G=V\cdot \gamma$	(21)

.

Table 6. Catalyst dimensions, stoichiometric equations, enthalpies, and kinetic equations.

Bed	Catalyst	Reaction	Kinetic Equation
SCR	V/Al, Cylinders, 5 × 15 mm	${\mathrm{NH}}_3+\mathrm{NO}+0.25{\mathrm{O}}_2\to {\mathrm{N}}_2+1.5{\mathrm{H}}_2\mathrm{O},$ (−ΔHSCR) = 407 kJ/mol	$W_{SCR}=k\cdot C_{N{O}_x}$
de-N2O	Cs/Ni0.1Co2.9O4, Cylinders, 3 × 5.2 mm	${\mathrm{N}}_2\mathrm{O}\to {\mathrm{N}}_2+0.5{\mathrm{O}}_2,$ (−ΔHN2O) = 81 kJ/mol	$W_{N_{2}O}=k\cdot C_{N_{2}O}$

shows the catalyst dimensions, stoichiometric equations, enthalpies, and kinetic equations for SCR NO_x via ammonia and de-N₂O reactions. In [31], it was shown that the reaction rate of SCR NO_x using ammonia on a V₂O₅/Al₂O₃ catalyst can be determined using a first-order kinetic equation with respect to NO_x. The kinetic constants (k₀ = 252.1 s⁻¹ and E_a = 13,390 J/mol) correspond to the observed reaction rate of the SCR of nitrogen oxides with ammonia on catalyst granules in the form of cylinders 5 × 15 mm [44]. In [31,45,46], it was shown that the reaction rate of the nitrous oxide decomposition on oxide Ni/Co-containing catalysts can be determined using a first-order equation with respect to N₂O. The effectiveness factor and the observed reaction rate of N₂O decomposition for the catalyst granules with a diameter of 3.4 mm were calculated during the simulation using Equations (13) and (14) (Table 5).

To estimate the kinetic parameters, we used the Levenberg–Marquardt optimization method [46,47] implemented in the COMSOL Multiphysics package. To determine the kinetic constants at different temperatures, the experimental data were approximated using an isothermal plug-flow model.

Thermophysical and thermodynamic parameters, coefficients of axial heat and mass transfers, as well as interphase heat and mass exchange values (Table 5), were calculated at the reference temperature. For solving the system of partial differential equations with appropriate boundary conditions (1)–(8), we used the COMSOL Multiphysics package, which is a common tool for modeling catalytic reactors [48,49,50,51].

4.3. Input Data for the Calculations

The mathematical modeling of the process was performed by varying the inlet parameters in the ranges that are common in industrial UKL plants:

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Inlet temperature ($T_g^{in}$): 230–270 °C;

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Gas flow rate (Q): 46,040–58,670 m³/h (STP), which corresponds to the linear velocity of 1.128–1.437 m/s.

Fixed values:

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Reactor diameter: 3.8 m;

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Gas composition at the inlet to the first bed (vol.%): NO_x—0.15, NH3—0.165, N₂O—0.15, oxygen—5, water—2, and nitrogen—by balance;

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Working pressure: 0.716 MPa.

As a result of modeling, catalyst loading using layers was determined to provide the target degree of NO_x and N₂O removal from the tail gas, as mentioned below; the calculations were performed taking into account the following restrictions:

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The catalyst bed height (H) should not exceed the maximum allowable space according to the UKL plant’s catalytic purification reactor design: 0.5 m for SCR, 0.7 m for de-N₂O [5,6];

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The maximum temperature in the SCR catalyst bed (Tmax) should not exceed 280 °C because the selectivity of aluminum–vanadium catalysts decreases at a higher temperature;

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The emissions of NO_x and N₂O at the reactor outlet should be less than 50 ppm, which, at the preset inlet concentrations of nitrogen oxides, corresponds to a conversion rate of not less than 98%.

The total pressure drop in the reactor was also calculated based on the obtained bed heights.

5. Conclusions

Our experimental studies of N₂O decomposition on a Cs/Ni_0.1Co_2.9O₄ catalyst in an isothermal flow reactor within a temperature range of 160–250 °C proved that a N₂O conversion rate of up to 95–99% could be obtained at a residence time of 0.6–0.8 s. The reaction rate constants k₀ = 7.23·10⁸ s⁻¹ and E_a = 77.15 kJ/mol were determined and further used for modeling the process. Mathematical modeling allowed us to estimate the parameters of a commercial two-bed reactor for NO_x and N₂O low-temperature mitigation in a nitric acid plant to ensure that a residual content of each would be less than 50 ppm, under temperature and spatial constraints. The effect of inlet temperature and tail-gas flow rate on the degrees of conversion and catalyst bed heights was simulated. At the optimal inlet temperature of ~260 °C, the process can be performed in the widest range of tail-gas flow rates varying from 46,040 to 58,670 m³/h.