Model validation

To further evaluate the predictive capability of the model, additional CO2 absorption experiments were carried out under different operating conditions and the corresponding results were compared with the modeling ones. Since the thermal level significantly affects the reaction equilibrium and therefore the system dynamics, the capture process was carried out by changing the operating temperature to 20 °C (Exp. 2, Table 1). Especially when dealing with industrial scale absorption, the temperature is a parameter whose level is responsible for considerable energy consumption while operating at low temperatures is not always possible. Moreover, since the reactive absorption is an exothermic process, it is quite difficult to keep the temperature constant when large volumetric flow rate and reaction volumes are considered. Therefore, a model used to predict and describe the capture system dynamics should be efficient over a wide range of temperature. Fig. 5 deals with the comparison between experimental data and model predictions for the case of Exp. 2 where it is seen that the temperature change affects the capture system efficiency.

Fig. 5. Capture system efficiency, [NH3]0 = 1.0 M, T = 20 °C (Exp.2).

Fig. 5 shows how the reaction phase remains practically unchanged in terms of duration, with a slight increase of the corresponding values, due to the growth of the mass transfer rate with temperature. Nevertheless, the final decrease of η occurs more quickly than at 5 °C (Exp 1, Table 1) thus leading to values close to zero in 200 minutes. This is due to the considerable decrease of K3 (Table 3) that determines a faster accumulation of carbon dioxide into the liquid phase and the gas solubility reduction, due to the Henry constant decreasing, as shown in eq. (4), which causes the lowering of the saturation concentration. Accordingly, the reaction phase and the subsequent one are not negatively influenced by the temperature increase that, however, accelerates CO2 accumulation and the efficiency reduction in the process final phase. For this reason, Fig. 5 presents a narrower offset with respect to Fig. 2.

The model was further validated by predicting the experimental results obtained when simultaneously varying initial ammonia concentration and process temperature (Exp. 3 in Table 1). Specifically, the initial NH3 concentration was halved with respect to previous experiments (from 1.0M to 0.5M), while the temperature was set at 20 °C. The comparison between the model prediction and experimental results, in terms of capture efficiency, is reported in Fig. 6.

Fig. 6. Capture system efficiency, [NH3]0 = 0.5 M, T = 20 °C (Exp.3).

As expected, the halving of absorbent concentration has a remarkable influence on the reaction phase duration. In fact, the latter one is exclusively due to CO2 consumption by NH3 that prevents carbon dioxide accumulation within the solution. The lower is the initial concentration of ammonia, the faster is its consumption and the shorter is the reaction phase. Moreover, as also shown in Exp. 2 (Fig. 5), the temperature increase accelerates the solution saturation by attenuating the effects of secondary reaction phenomena and reducing the final mismatch between experimental and model results (Fig. 6).

The analysis of Fig. 5 and Fig. 6 shows the effectiveness and the reliability of the proposed mathematical model that is able to predict the absorption process dynamics despite the variation of the operating conditions. In Exp. 2 (R2=0.981,MSE=0.003) and Exp.3 (R2=0.975,MSE=0.003), respectively the data are fitted by the model curves quite well, by accurately describing the time evolution of the process efficiency. In particular, the developed model turns out to be able to predict how the temperature increase affects the process and to quantify the decrease of the reaction phase duration depending on the initial level of ammonia into the absorbent solution.

A validated model that effectively describes the reactive absorption process allows to gain important information in view of plant design. Based on the operating conditions, the time (hereafter called operation time) when the single absorber efficiency drops below a prescribed threshold can be evaluated. By computing, through the model, the operation time of a generic absorbent column, different plant configuration can be simulated. For instance, the model could be used to evaluate whether more columns should be operated in series, parallel or alternate configuration. Moreover, the “a priori” knowledge of the time evolution of the chemical composition might permit to properly design the regeneration process as well as eventual intermediate steps of carbonate salts production.

Based on the consideration above, Fig. 7 shows two possible industrial application of the proposed mathematical model, which considers the two most significant model results: the column operation time (t*) and the chemical composition analysis.

Fig. 7. Possible industrial applications of the proposed dynamic model.

To this aim, let us consider two capture columns working alternatively (section A, Fig. 7) with the CO2-rich feed initially flowing only into column (1). Once t* is selected depending upon operating conditions and threshold, the valve actuators can be programmed. The valve that controls the CO2-rich feed into the capture column (1) and the one controlling the CO2-rich feed into the capture column (2) can be closed and opened, respectively. Moreover, the valve that allows exhaust CO2-rich sorbent to flow in the regeneration column can be opened, without the use of real-time measurements.

In section B reports a potential application of the model related to its capability to predict the chemical composition of the solution is addressed. The CO2-rich sorbent solution can be seen as a raw material to synthetize carbonic salts in an intermediate production process whose yield also depends on the carbonic ion concentration. The proposed model could easily compute the chemical composition of the CO2-rich sorbent thus allowing one to utilize these data to design and optimize the carbonic salt production section.

As for the transposition of the results of this work at the industrial scale, it is worth mentioning that additional activities are required to simulate industrial conditions including suitable regeneration strategies depending upon the selected technologies where the knowledge of the corresponding hydrodynamics will affect the mass transfer coefficient values. However, the thermodynamics approach, adopted to describe the reactive absorption phenomenon, cannot be affected by the investigation scale since the speciation equations and the electroneutrality equation hold true even at larger scale. In addition, once the fluid dynamics is known, suitable expressions useful to evaluate the transfer coefficient can be identified while the mathematical structure of the proposed model equations remains unchanged.

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