Flue gas cleaning by periodic absorption

Simulations and designs are presented of conventional and periodic SO 2 absorption from exhaust gases using salt water as absorption solvent. Operating conditions resemble those of a maritime operation, involving relatively small amounts of SO 2 , so the separation is in the linear region. The advantages of periodic operation, as already demonstrated for conventional distillation remain valid for absorption processes: Less tall towers, than staged towers are possible, or substantially less salt water is required for the process employing periodic cycling.


| INTRODUCTION
There is a renewed interest in separations based on periodically, or cyclically, operated trays. Studies in the later years 1,2 have confirmed that periodic separations can provide several advantages over conventional column separations. 3 Promising experimental studies are published within periodic distillation 1,4 and stripping. 5,6,7 Therefore, expanding the concept of periodic operation to related column separations is of interest.
We consider absorption as opposed to distillation and/or stripping. The latter operations have received more attention in the literature. Perhaps, because these typically operate with higher stripping factor values (near unity for distillation 8 and 1.4 for stripping 9 ), which enhances the benefits one can reap from the Lewis Case 2 effect. 8 Periodic absorption has received considerably less attention in the literature. However, several important green transition chemical engineering operations are based on absorption, so while the effects are less strong here (for typical absorption factors 9 near 1.4), it is important to also address this operation in order for it to benefit from periodic operation.
Absorption is widely used for cleaning flue gases. In the maritime sector, exhaust gas cleaning systems (EGCS) are employed to clean exhaust gases in different configurations. Between 2007 and 2011, 80% of the fuel used in commercial shipping was low-grade fuel containing high amounts of sulfur emitting large amounts of SO 2 , NO x , CO 2 , CO, aerosols with particle matter (PM) during combustion. 10,11 In more recent years, efforts have been made to reduce the environmental impact of shipping, where especially SO 2 and NO x pose a significant threat to the environment and to human health. 12 Solutions for combined SO 2 and NO x emission reduction are rather complex and costly, and most processes are still in the development stage. 13 Therefore, separate systems are more likely to achieve emission reductions. Reduction of NO x emissions can be achieved by use of natural gas as fuel, or by exhaust gas recirculation (EGR) where the exhaust gas is recirculated back into the air intake. This lowers the oxygen intake and increases CO 2 , slowing the combustion and reduces the temperature, thus lowering NO x emissions. 14 However, removing NO x from the exhaust gas is usually still necessary. A common technique is selective catalytic reduction (SCR). 11,14 EU regulations dictate that as of 2015, ships must use fuels with a sulfur content of no more than 0.1% in certain areas and as of 2020 fuels with sulfur content of no more than 0.5% are allowed in European waters. However, fuels with higher sulfur contents are still allowed if proper exhaust cleaning systems are installed. 15 One way to comply with the regulations is to use low-sulfur fuel containing less than 0.1% sulfur. However, this type of fuel is rather expensive, 13 and supply is also an issue as the refining capacity of low-sulfur fuel is currently insufficient. 11,14 An alternative is flue gas desulfurization (FGD). One technique used in the maritime sector is wet open-loop scrubbing, where seawater is pumped up and contacted with the exhaust gas in a scrubber column. In the scrubber, the SO 2 is absorbed as sulfate in the sea water which is discharged back into the sea.
High sulfur-containing fuels usually contain around 3.5% sulfur 11,13 as this is the current worldwide sulfur limit. 10 Current scrubbers are capable of reducing sulfur content to below that of untreated exhaust gas from fuel containing the regulatory limit of <0.1% with SO 2 reductions of 95%-99%. 11,13,14 In addition, an economic study shows that the use of high sulfur fuel with a scrubber to clean the exhaust gas has a cost advantage over use of low sulfur fuel without a scrubber. 11 Plate and packed columns with liquid distributors are usually used during absorption applications like scrubbing. 9 Much like in distillation and stripping, absorption (or scrubbing) could be operated periodically with the same advantages. Regarding scrubbers on ships, the advantage of fewer trays and a smaller column might be even more significant due to their weight of up to 55 tonnes. 14 No investigations of the possibility of periodic operation mode in such absorption applications seem to have been made previously. This article is structured as follows. First, we identify the separation specifications and the phase equilibrium criteria. Then we calculate the performance of a conventionally operated scrubber. This is followed by setting up the model for and calculating the performance of a periodically operated scrubber. Performances will be compared, and finally, we will discuss the results and make conclusions to bring closure. For the studies we employ staged systems (as opposed to systems with structured packings). This is in order to illustrate and quantify the advantages of periodic cycling more precisely. Packed columns tend to dominate in applications requiring small diameters, whereas staged systems are more used for larger diameters. Wankat 16 mentions 2 ft (roughly 60 cm) as a rough value of demarcation.

| SYSTEM DESCRIPTION
In order to determine the possible advantages of periodic operation mode in FGD, the number of necessary trays of an absorption column is determined for conventional and periodic operation mode. This is done using an exhaust gas composition from a typical two-stroke diesel engine running on high sulfur-containing fuel of 3.5% sulfur. The goal is to lower the sulfur concentration in the gas to levels less than that of untreated fuel containing the regulatory limit of 0.1%.

| Equilibrium data
The solubility of dilute SO 2 in seawater, from SO 2 + N 2 mixtures have been determined by Rodríguez-Sevilla et al. 17 over a temperature ranging from 278.15 to 318.15 K, and SO 2 partial pressures range from 0.050 to 1.5 kPa. We have processed and reproduced their data at 25 C and (near) atmospheric pressure for the dilute "linear" region, as shown in Figure 1. Note that for this article, only the dilute "linear" region is considered. The equilibrium data shows a linear trend, with some scatter, at low concentrations of SO 2 , as confirmed by the trendline. Therefore, the equilibrium between SO 2 in the liquid and vapor phase can be described by Here the equilibrium constant, K SO2 ¼ 5:82, has been chosen as the result of extrapolating the quadratic fit of (y,x)-data to zero. Note that the processing of the Py/x data as a function of x gives a value near 4 (as shown). For final designs, it would be appropriate to gather more experimental data than what is present here. Also, models beyond the linear case would be appropriate. Note that the purpose here is mainly comparative, so the conclusions are expected to be valid even though the approach is simple. In fact, the conclusions reached with a simple model are more likely to be generalizable. proportional to the sulfur content of the fuel. 19 Therefore, the exhaust gas entering the column from an engine fueled with 3.5

| Compositions and flows
sulfur-% fuel contains y Nþ1,SO2 ¼ 6 Á 10 À4 Á 3:5 2:2 The treated exhaust gas must be cleaner than the untreated exhaust gas from a diesel engine running on 0.1 sulfur-% fuel. 15 Thus, the maximum allowed average outlet SO 2 mole fraction is The inlet liquid is pure seawater, so x 0,SO2 ¼ 0. The liquid outlet mole fraction of SO 2 , x N,SO2 , can be determined by closing an SO 2 balance, once the flows have been specified. The aqueous solubility of SO 2 is significantly larger than that of N 2 , O 2 , NO 2 , and CO 2 , which are the other main components of the exhaust gas. Therefore, it seems justified to assume that only SO 2 transfers among the phases. The vapor flow for the conventional operation mode is defined first. The exhaust gas amount from the two-stroke diesel engine at 90% engine load is V = 77.35 mol/s. 18 At atmospheric pressure and 298.15 K this would for an ideal gas correspond to 1.9 m 3 /s. As the entering liquid is clean (x 0,SO2 ¼ 0), the minimum liquid flow, L min , can be found from the K-factor using the following equation 9 F I G U R E 1 Equilibrium data for SO 2 in seawater at 25 C and at atmospheric pressure Using the vapor flow and the equilibrium constant found earlier, Giving an absorption factor, 9  During the VFP shown in Figure 3 (left), the liquid hold ups remain on every tray by the vapor thrust passing upward through the column.
During the LFP shown in Figure 3 (right), the vapor flow is interrupted, and the liquid hold ups are transferred to the trays below. The hold up on the bottom tray (here N) is drained as the liquid product, and the feed is added to the top tray (here 1). The mechanism of liquid transfer is a topic of its own. 5 We will not delve deeply into the specifics here, since the purpose is mainly comparative. The total flows over one periodic period must match the total flow of conventional operation over the same time span in order to make an adequate comparison. That is, the L/V ratio must remain unchanged. The time of the LFP is here assumed to be set to t LFP = 3 s, as this is a nearly realistic time for the liquid to be drained from one tray to another, whilst the VFP is set to t VFP = 97 s. Thus, the vapor flow for periodic operation is The increase in vapor flow compared to the conventional vapor flow is due to the shorter time span at which the vapor flow is uninterrupted. The liquid flow becomes The liquid hold up, M, has numerically the same value, though in units of mol. Thus, the liquid and vapor amounts entering the column over one period are the same for conventional and periodic operation mode, and therefore, the L/V ratio should be the same for both situations to be comparable. Finally, the liquid outlet composition may be specified. An SO 2 balance is The parameters and specifications for the calculations and simulations to determine the theoretical number of stages are summarized in Table 1.

| CONVENTIONAL OPERATION
The

| PERIODIC OPERATION
Design of a periodic absorption system cannot be made graphically with a McCabe-Thiele diagram as was the case for the conventional system. In the following section, a model describing the system is set up, followed by a description of the design method, and finally giving the obtained design. The model and design method resemble the design method for distillation columns presented by Patrut 1 and previously by Toftegaard. 21

| Assumptions
The model and simulations are made under the following assumptions: • Perfect mixing on each tray

| Model setup
The total molar hold up on tray k, M k , is the sum of all component hold ups. However, the molar hold up is assumed constant, so it does not change over time. The only hold up that changes over time is that of SO 2 , M k,SO2 , as the SO 2 is absorbed by the liquid over time. The mole fraction of SO 2 in the liquid phase is given by the following relation where the total hold up P j M k,j henceforth will be denoted M as this is assumed constant throughout. The mole fraction of SO 2 in the vapor phase above each tray can then be calculated by use of the K-factor, where (as shown) K SO2 ¼ 5:82.

| Vapor flow period
During the VFP, as the liquid remains on the trays, only vapor flows.
From the vapor phase, SO 2 is continuously absorbed into the liquid. Therefore, the liquid hold up of SO 2 increases over time. The increase of SO 2 hold up in the liquid equals the decreased amount of SO 2 in the vapor over the tray. For tray k, this may be expressed by an SO 2 balance, For the top tray, k = 1, the change of liquid hold up of SO 2 is the difference between the SO 2 amount entering the top tray and the amount leaving the column As for the bottom tray, the change of liquid hold up of SO 2 is the difference between the SO 2 amount entering the column and the amount leaving the bottom tray Note that the principle is the same for all trays in the column.
where the superscript (V) denotes the end of the VFP and (L) denotes the end of the LFP, respectively.

| Design method
The design method of the scrubber column implemented here is analogous to the design methods of Patrut 1 and Toftegård. 22 Here the total hold up and the liquid mole fraction of SO 2 are specified. From here, the development of the SO 2 hold up on tray N over time is found by integrating Equation (16) Figures 6 and 7, respectively. Figure 6 shows the liquid mole fractions of SO 2 on each tray over four cycles, and Figure 7 shows the vapor mole fractions of SO 2 on each tray over four cycles.
The simulation was first conducted only with one tray, tray N (red). As   Table 2.

| Tray efficiencies
The reason behind the decrease of necessary liquid feed when operating periodically compared to conventionally can be explained by an increase in tray efficiencies. Tray efficiencies can be treated in different ways, as discussed by a set of reference works listed. 4,6,8 Here, we consider the tray efficiency during conventional operation 9 to be where y k is the average vapor mole fraction leaving the tray, y kþ1 is the vapor mole fraction entering the tray and y Ã k is the vapor mole fraction in equilibrium with the liquid leaving the tray. When using the graphical McCabe-Thiele method to determine the number of theoretical trays, the tray efficiencies are usually assumed to be unity. In other words, the actual vapor mole fraction leaving the tray is assumed to be at equilibrium with the liquid leaving the tray. For periodic operation, the point efficiency is also assumed to be unity, because the vapor is assumed to be at equilibrium with the liquid on the tray at any given time. The expression for tray efficiency during periodic operation is analogous to that of conventional operation 4 where y k is the time-averaged vapor mole fraction leaving the tray during the VFP, y kþ1 is the time-averaged vapor mole fraction entering the tray during the VFP and y In addition, the space required for scrubbers is an issue. The higher tray efficiencies calculated above explain the potential reduction of tray numbers. A reduction of three trays can appear to be a small number. However, out of seven trays, it is of the order 40%. Two important opposing aspects to consider when designing a suitable scrubber are size and absorbent consumption. In the present context, reducing the liquid consumption is also an aspect of interest. Up to 2% of the power generated from diesel engines on vessels is consumed by the connected scrubbers where most of the power consumption is associated with seawater pumping. 14 Thus, there is a trade-off between power consumption and size/weight considerations. The higher tray efficiencies also explain the reduced need for seawater pumping for the absorption. As shown in ing what the point efficiencies really are. Therefore, we believe the current approach-recognizing its limitations-is sufficient for the present purpose. Therefore, we believe that the present approach is a sensible guideline. It remains an open question, whether the magnitude of one advantage is sufficient to make a breakthrough for a given technological concept. Several considerations are important: An economic model, robustness of operation, controllability, ease of maintenance, simplicity of equipment, availability of vendors/ producers will need to be considered to come closer to an answer.
We provide here initial quantitative assessment of such an operation and throw light on certain aspects of it.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.