Introduction

Selective catalytic reduction (SCR) technology involves the reduction of oxides of nitrogen (NOx) into nitrogen and water by reaction with ammonia (NH3) on a surface of a catalyst (Mohan et al. 2020). It is widely used in the abatement of NOx from compression ignition engines running on diesel and biodiesel blends (Praveena and Martin 2018). The efficiency in reducing the NOx gases is about 80–90% (Carucci et al. 2009; Jiang et al. 2020; Lao et al. 2020) which makes SCR technology the best viable option for NOx reduction. Currently, urea solution is commonly used in commercial vehicles as an ammonia precursor (Shin et al. 2020). In aqueous urea SCR, the amount of urea converted into ammonia is uncertain. Also, the control of urea injection is complicated and often has problems with deposition inside the pipes at colder temperatures (Börnhorst et al. 2019). Solid ammonium salts are the best alternative to urea solution that act as ammonia carriers that are stable and have higher ammonia release per unit mass. The different ammonia cursors for solid-SCR (SSCR) are solid urea, ammine chloride of strontium (Li et al. 2017; Liu and Tan 2020) and calcium, ammonium carbonate, and ammonium carbamate (Kurien and Srivastava 2019). Ammonium carbonate (ACN) and ammonium carbamate (ACM) are the most preferred salts due to their operating temperature range, ease of availability, and storage and can be easily implemented into the current SCR systems (Kim et al. 2014; Peitz et al. 2014). ACN (NH4–CO3–NH4) is a hygroscopic, water-soluble, white crystalline salt, containing a strong odor of ammonia. Upon heating, the salt converts initially into ammonium bicarbonate which further decomposes to carbon dioxide and water. The molecular weight of ACN and ACM are 96.09 and 78.07 g/mol, respectively (Peitz et al. 2014). The ammonia storage capacity is, respectively, 20.8 mol and 25.8 mol per kg (Fulks et al. 2009; Kim et al. 2014). In terms of mass, NH3 gas of 0.35 g and 0.436 g is obtained from 1 g of ACN and ACM, respectively. ACM is preferred to ACN for NH3-SCR as it does not generate H2O and a better pressure of NH3 is developed easily at lower temperatures. NH3/CO2 ratio is an important factor to be considered as both these gases can combine and readily form a carbamate (Fulks et al. 2009). Kim et al. have investigated the thermal degradation study of ACM and assessed its effect on the pressure release (Kim et al. 2020). However, in their study, only a single heating rate of 5 K/min was used and the effect of different rates of heating was not analyzed. Very few studies have addressed the investigation of solid ammonium carbonate as an ammonia carrier for SCR systems. Also, lacuna exists in terms of the experimental data regarding thermal dissociation parameters of ACN. Changes in the heating rate have significant effects on the reaction rates and temperature at which the rate is a maximum. This paper aims to estimate the activation energy of ammonium carbonate using TGA/DSC analysis and compare the results obtained with ammonium carbamate. The comparison shall provide insights as to which compound is more suitable for use in NH3-SCR systems. Also, relationship between the heating rate and the temperature at which the highest rate of reaction is observed will be derived.

Kinetics of dissociation

Thermal dissociation of ammonium carbonate

The dissociation of ammonium carbonate can be kinetically modeled using the reaction rate of the salt using Arrhenius constants (Mohan and Dinesha 2022). The solid salt sublimates to ammonia gas due to the application of heat and the rate of the reaction can be represented as a product of two parameters given by Eq. (1) (Fogler 2006).

$$\gamma = - \frac{{{\text{d}}m}}{{{\text{d}}t}} = Am_{0} \left( {1 - X} \right)^{n} e^{{ - E_{a} /{\text{RT}}}}$$
(1)

where \(\gamma\) is the rate of the reaction, \(A\) is the pre-exponential (frequency) factor in s−1, \(E_{a}\) is the activation energy in J/mol, and \(R\) is the universal gas constant, 8.314 J/mol−K. \(X\) is the fraction of the salt converted to gas. The order of the reaction, \(n\), is obtained using the shape index as discussed by Kissinger (1957). The slope \(- \frac{{{\text{d}}m}}{{{\text{d}}t}}\) is calculated using finite difference approximation of the order \(O\left( {\Delta t^{2} } \right)\) (central differencing).

Experimental setup

ACN is a colorless, crystalline solid having a molecular formula, (NH4)2CO3, and a molecular weight of 96 g/mol which is soluble in water. The ACN samples of laboratory reagent grade were locally procured which had a purity of more than 98%. Its density is 1,500 kg/m3 and had a melting point of 58 °C. Thermogravimetric analysis (TGA) was carried out in this study using a Q50 analyzer. The samples were taken into the test chamber, which was filled with nitrogen gas. Three separate samples (Sample 1, 2, and 3) were subjected to different heating rates, \(\emptyset\) of 2 K/min, 4 K/min, and 8 K/min, respectively, to ascertain the weight loss of ACN. The amount of mass lost due to thermal degradation was measured against time. The resulting data were used to estimate the average activation energy and pre-exponential factor for dissociation of ACN. Another separate sample (Sample 4) was taken into a Q200 analyzer for differential scanning calorimetry. The sample was heated in the test chamber filled with nitrogen gas. Changes in the heat flow were measured against the temperature rise. The result of DSC was used to assess the stability of ACN and to identify the shape index for determining the order of the reaction. Weights of samples 1, 2, 3, and 4 measured 11.324 mg, 14.677 mg, 15.976 mg, and 4.2 mg, respectively.

Results and discussion

DSC analysis

Sample 4 was taken into DSC Q200 and checked for endothermic behavior. Figure 1 shows the heat flow against temperature for a heating rate of 4 K/min. The DSC curve is now used to identify the shape index of the peak formation, using the values of a and b as shown in Fig. 1. From Fig. 1, the shape index, S is calculated as \(\frac{a}{b} = 0.29\) (Kissinger 1957; Simon Fraser University 2013), and further the order of the reaction, \(n\) is calculated as \(n = 1.26\sqrt S\) = 0.6825. This value is further used in kinetics equations for estimating the activation energy.

Fig. 1
figure 1

A graph of endothermic heat flow against temperature for ammonium carbonate obtained from differential scanning calorimetry (DSC)

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TGA analysis

Samples 1, 2, and 3 were subjected to TGA for heating rates of 2, 4, and 8 K/min, respectively. Figure 2a shows the conversion of the salts from room temperature. The final mass of the salts corresponding to 2, 4, and 8 K/min was 0.00015 mg, 0.00026 mg, and 0.00018 mg, respectively. Figure 2b shows the derivative weight (in %/K) indicating the maximum peak temperatures (\(T_{p}\)) at which the slope changes its sign. The derivative plot indicates the point of the greatest rate of change against temperature on the weight loss curve. From the figure \(T_{p}\) values for samples 1, 2, and 3 are 95.98 °C, 118.3 °C, and 128.15 °C, respectively. At these temperatures, the rate of change of mass of the salts is a maximum. This data are useful in controlling the rate of reaction ACN using heating rate and operating temperature. For example, when a high release of ammonia is desired, with an available heating rate of 4 K/min, ACN will have to be operated in the vicinity of 118 °C, which is the \(T_{p}\) at that heating rate. Figure 3 shows the Arrhenius plot of \(\ln \left[ {\left( { - \frac{{{\text{d}}m}}{{{\text{d}}t}}} \right)\left( {\frac{1}{{m_{0} \left( {1 - X} \right)^{n} }}} \right)} \right]\) against \(1000/T\). A first-order linear equation is fitted to each heating rate. The fitted line had high values of R2 of 0.9922, 0.9967, and 0.9971. The slope and intercept of the fitted regression model are used to calculate the activation energy and pre-exponential factor that are shown in Table 1. Even when the material and the reaction are the same, the literature has shown that there is a difference in activation energy with respect to heating rate (Dingcheng et al. 2018).

Fig. 2
figure 2

a Extent of conversion, X and b derivative plot obtained from thermogravimetric analysis of ammonium carbonate

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Fig. 3
figure 3

Arrhenius plot obtained for three different heating rates and the fitted linear equation

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Table 1 Activation energy and pre-exponential factor obtained for ammonium carbonate
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The results obtained are similar to the values obtained by Lee et al. (2013) who obtained activation energy of 75.49 kJ/mol. Fulks et al. (2009) have reported that the ammonia release energy from ammonium carbonate is 109 kJ/mol. The rate of the reaction for ACN can be thus be derived as

$$\gamma = - \frac{{{\text{d}}m}}{{{\text{d}}t}} = m_{0} \left( {8.88 X 10^{7} } \right)\left( {1 - X} \right)^{0.6825} e^{ - 9308.4/T}$$
(15)

In the current study, the highest rate of reaction obtained for the heating rates of 2, 4, and 8 K/min is obtained at temperatures of 95, 117, and 126 °C, respectively. The corresponding salt conversion (\(X\)) is obtained as 0.64, 0.68, and 0.67, respectively. Figure 2b shows the derivative plot that shows the peak temperature \(T_{p}\). The peak temperature corresponds to a point where the derivative of \(\left( { - \frac{{{\text{d}}m}}{{{\text{d}}t}}} \right)\) changes its sign. The values of \(T_{p}\) obtained for 2, 4, and 8 K/min are 96, 118, and 128 °C, respectively. These temperatures are the same as that seen for the highest rate of reaction. Also, the values of \(T_{p}\) and the highest rate of dissociation are observed when the extent of conversion, is about 66% (\(X_{{\text{p}}} = 0.66\)) of the initial mass. It can be concluded that the peak temperature is obtained when the mass of the sample is reduced to 1/3rd of the initial mass (\(m_{{\text{p}}} = m_{0} /3\)); or \(\left( {1 - X_{p} } \right) = 1/3\).

The peak temperature is observed when the slope \(- \frac{{{\text{d}}m}}{{{\text{d}}t}}\), reverses the sign. It can be obtained by differentiating Eq. (1) with respect to time and equating it to zero as shown in Eq. (2).

$$\frac{{\text{d}}}{{{\text{d}}t}}\left( { - \frac{{{\text{d}}m}}{{{\text{d}}t}}} \right) = \frac{{\text{d}}}{{{\text{d}}t}}\left[ {Am_{0} e^{{ - \frac{{E_{a} }}{{{\text{RT}}}}}} \left( {1 - X} \right)^{n} } \right]$$
(2)

On further simplification, Eq. (2) reduces to

$$0 = Am_{0} e^{{ - \frac{{E_{a} }}{{{\text{RT}}_{p} }}}} \left( {1 - X_{p} } \right)^{n} \left[ {\frac{n}{{\left( {1 - X_{p} } \right)}}\left( { - \frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p} + \frac{{E_{a} \emptyset }}{{{\text{RT}}_{p}^{2} }}} \right]$$
(3)
$$\frac{n}{{\left( {1 - X_{p} } \right)}}\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p} + \frac{{E_{a} \emptyset }}{{{\text{RT}}_{p}^{2} }} = 0$$
(4)

\(\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p}\) is the rate of the extent of conversion at the peak temperature \(T_{p}\). By substituting the value, \(\left( {1 - X_{p} } \right) = 1/3\), and rearranging, we can get an expression for \(T_{p}\) as a function of \(\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p}\) as

$$T_{p} = \sqrt {\frac{{E_{a} \emptyset }}{{3{\text{Rn}}\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p} }}}$$
(5)

The peak temperatures obtained for heating rates 2, 4, and 8 K/min are 96, 118, and 128 °C, respectively. The derivative of conversion with respect to time, \(\frac{{{\text{d}}X}}{{{\text{d}}t}}\), at these peak temperatures is calculated using central differencing equations as 0.0011, 0.002, 0.0036 s−1, respectively. The slopes of \(\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p}\) showed a linear relationship with the heating rates. To simplify the expression further, \(\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p}\) is expressed as a function of \(\emptyset\) as shown in Eq. (6).

$$\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p} = 0.0251\emptyset + 0.0003$$
(6)

Equation (6) is a simple linear approximation of \(\left( {\frac{{{\text{d}}X}}{{{\text{d}}t}}} \right)_{p}\) as a function of \(\emptyset\) and hence is associated with errors. A correction factor is now introduced (\(12.48 - 96.87\emptyset\)), which is also a function of \(\emptyset\) and appended to Eq. (20). Hence the equation for \(T_{p}\) for \(\emptyset = \left( {2,8} \right)\) is now modified as

$$T_{p} = \left( {12.48 - 96.87\emptyset } \right) + \sqrt {\frac{{E_{{\text{a}}} \emptyset }}{{3{\text{Rn}}\left( {0.0251\emptyset + 0.0003} \right)}}}$$
(7)

The values of \(T_{p}\) estimated using Eq. (7) for heating rates of 2, 4, and 8 K/min are 95.54, 118.67, and 127.77 °C, which is very close to the experimentally obtained peak temperatures. With the known values of activation energy and shape index, the peak temperature for a given heating rate can be estimated or vice versa. This approach is very helpful in designing the heating circuit in the SCR system.

The activation energy obtained in this work is compared with the results of Kim’s study (Kim et al. 2020) on ACM. Figure 4 shows the comparison of conversion obtained in the current work with results obtained from Kim et al. (2020). ACM decomposes completely for a heating rate of 5 K/min. In comparison, a similar curve is obtained for ACN decomposition in the current study for a slower heating rate of 2 K/min. Prima facie shows that degradation of ACN occurs at a lower ramp rate of heating as compared to ACM. Considering the waste heat available from hydrocarbon combustion, this information is useful for implementing Solid SCR systems. NH3 release energy for ACN is also higher compared to that of ACM (Fulks et al. 2009). For ACN, the solid to gas reaction involves one additional mole of water vapor also as a product. Hence, the activation energy would be higher than that of ACM. The values of activation energy for ACM reported in the literature are between 57.2 and 66.9 kJ/mol (Y. Kim et al. 2020; Lee et al. 2013) which are lower than ACN. Hence, ACN requires a much rapid heating rate as compared to ACM for the same rate of conversion.

Fig. 4
figure 4

TGA curves of ACN from the present study in comparison with ACM (Kim et al. 2020)

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ACM also has a higher partial pressure of NH3 compared to ACN. ACM can produce 15% (vol.) more NH3 vapors than ACN for the same heat available. Another important factor is that the solid reaction of ACN produces one mole of water vapor which is absent in the case of ACM dissociation. The combustion products will be carrying water vapors in the exhaust line and it will form deposits on the inner surfaces. This condition is persistent even if ACM is used as the precursor. In terms of cost, ACM is expensive by at least 2.5–3 times the cost of ACN, which is significant.

Conclusions

This paper experimentally investigates the thermal degradation and chemical kinetics studies of ammonium carbonate as a solid ammonia carrier for use in an NH3-SCR system in a CI engine. The rate of the reaction is obtained as

$$\gamma = - \frac{{{\text{d}}m}}{{{\text{d}}t}} = m_{0} \left( {8.88 \times 10^{7} } \right)\left( {1 - X} \right)^{0.6825} e^{ - 9308.4/T}$$

The highest rate of the reactions is obtained when the mass of the sample is reduced to 1/3rd of the initial mass at a temperature \(T_{p}\). Expression for peak temperature, \(T_{p}\) for heating rates, \(\emptyset = \left( {2,8} \right)\) is derived and calculated. This enables the estimation of the peak temperature regime for any given heating rate.