Design, Simulation, and Comparative Analysis of a Carbonating Tower

Abstract

In many books, the Solvay process is mentioned as one of the most widely used processes for the production of sodium carbonate. However, on the contrary, no information has been found in the literature that allows for the availability of the functionality of thermodynamic, kinetic, physical, and physicochemical properties with temperature for the exothermic reactions that occur. As it is known, this type of reaction implies that the tower should be cooled. However, no information or heuristic has been found to assign or select the optimal stage for cooling. In this work, a carbonating tower is designed using a simulator to consider the aforementioned functionality, solely based on the input stream data. The beneficial effect of cooling on column performance is confirmed. Subsequently, a cooling mode is established, and the optimal stage to be cooled is determined. Additionally, a heuristic has been proposed to choose the best candidate stages to be cooled. Finally, a sensitivity study of sodium bicarbonate performance is conducted; the variation of concentration and temperature of the product stream is examined in response to changes in the temperature of the feed streams, and a nomogram is presented to solve the proposed study.

1. Introduction

The final product of a Solvay soda plant is sodium carbonate (Na₂CO₃). It is also known as trona, natron, barrilla, soda ash, Solvay soda, among other names. It can be found in nature or produced artificially. Sodium carbonate is used as a raw material for the saponification of fatty acids in the manufacture of soaps and detergents. It is also used as a flux in glass furnaces to produce glass containers, flat glass, insulation fibers, and glassware. As a source of alkalinity and sodium ions, it is used in the production of chemicals such as chromium compounds, pigments, and sodium bicarbonate. It is widely used in other industries and processes, including the paper industry, textile industry, metallurgy, mining, oil and gas, water treatment, food processing, etc. [1]. In addition to its traditional uses, it should be noted that sodium carbonate is an important component in the production of lithium carbonate. Briefly, after two previous stages of precipitation and purification of lithium-containing brine, in a final stage, lithium is precipitated as lithium carbonate from the purified brine by the addition of sodium carbonate [2].

According to the report [3], the “lithium triangle,” which is the geographical area located in South America, at the border of Argentina, Bolivia, and Chile, concentrates over 85% of the world’s reserves of this soft metal. Within the triangle, there are the salt flats of Uyuni (Bolivia); Olaroz-Cauchari, Salinas Grandes, Rincón, and Hombre Muerto (Argentina); and Atacama (Chile), among the largest ones.

In the work [4], there is an extensive development regarding the design and specification of all the equipment involved in the Solvay soda process. They consider a carbonating tower with a cooling stage but do not take into account the temperature functionality of all the properties in each stage of the tower. In the bibliography [5], a study can also be seen regarding the improved manufacturing of soda ash using the AspenPlus simulator. While the simulation of a real plant is presented, little to nothing is mentioned about the study of each stage. However, it is valuable to know that modeling with AspenPlus resulted in highly representative simulations of reality.

In many textbooks, the Solvay process is mentioned as one of the most widely used processes. However, on the contrary, no information has been found in the literature that allows for the availability of the temperature functionality of thermodynamic, kinetic, physical, and physicochemical properties. In that sense, the simulator used is the tool that allows us to overcome such drawbacks and conduct design and/or analysis studies.

This chapter deals with the design of a carbonating tower for the production of sodium bicarbonate. The model to be simulated is built based on the equipment models available in the simulator. In order to find a new design and considering a tower of 13 perforated plates, the only data taken into account are the flow rates and properties of the inlet streams. Once the tower is found, studies are conducted to determine whether or not to cool the column. Upon obtaining an affirmative response, the next step is to determine the best stage to be cooled. Based on the results obtained, a heuristic is proposed that considers the worst and best candidate stages to be cooled. Finally, taking into account the best tower found (tower with the cooled tray), the impact on the sodium bicarbonate yield due to variations in the temperature of the inlet streams is studied.

1.1 Solvay process

The discovery of the chemistry of the ammonia-soda process dates back to the early 1800s. Some British and French plants operated in 1840–1860, but without success. The aforementioned process is generally called the Solvay process because in 1865 Ernest Solvay started the first truly successful plant in Couillet, Belgium [6]. Then, in 1874, the first successful ammonia and soda plant was erected in England. The ammonia-soda process is the dominant technology used worldwide, which is why this process is selected for Solvay soda production. In this process, basically three stages are distinguished: the absorption stage, the carbonating stage and the ammonia recovery stage. The overall reaction is:

$${\text{CaCO}}_3+\text{2NaCl}\to {\mathrm{Na}}_2{\mathrm{CO}}_3+{\text{CaCl}}_2$$

However, this reaction is not carried out directly. The Solvay process uses an intermediate step. (NH₄)HC0₃ is formed to obtain Na₂C0₃ from NaCl and CaC0₃. The necessary ammonia (NH₃) is recycled. The reactive substances are calcium carbonate (main CO₂ generator), sodium chloride, and ammonia (intermediate component).

In the carbonating stage, more specifically, in the tower used for the production of sodium bicarbonate, the following reactions basically occur [7].

$${\mathrm{NH}}_3+{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_2\to \left({\mathrm{NH}}_4\right){\mathrm{HCO}}_3$$

$$\left({\mathrm{NH}}_4\right){\mathrm{HCO}}_3+\text{NaCl}\to {\mathrm{NH}}_4\mathrm{Cl}+{\text{NaHCO}}_3$$

The carbon dioxide used is obtained from the calcination of limestone and recovered during the decomposition of bicarbonate into sodium carbonate. Ammonia is introduced into the tower as a brine solution previously obtained in an absorption tower.

The carbonating tower acts as the heart of the Solvay process. Sodium bicarbonate is formed by the absorption of carbon dioxide in the ammoniacal brine. It is then washed, filtered, dried, cooled, and finally sieved. Filtration is carried out in a rotary filter, and for the drying or calcination stage, a steam-heated calciner is generally used, where the bicarbonate decomposes into sodium carbonate according to the reaction:

$${\text{2NaHCO}}_3\to {\mathrm{Na}}_2{\mathrm{CO}}_3+{\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$$

2. Carbonating tower design

2.1 Considerations

The absorption of carbon dioxide takes place with chemical reaction, and since the reactions that occur are highly exothermic, a cooling system is generally required for the column. On the other hand, while it is true that the absorption of a gas can be carried out in a packed or tray tower, in this case, only a tray tower can be considered since it would be more complicated to install the cooling circuit in a packed column, as well as extracting side streams for cooling purposes.

The product’s outlet temperature is adopted according to the report [8], which establishes that the ideal temperature is between 25°C and 30°C. Lower temperatures can cause salt or ammonium bicarbonate precipitation, while higher temperatures hinder the complete precipitation of the formed bicarbonate.

2.2 Hypothetical problem to be solved

The aim is to design a carbonating tower for which only the flow rates and compositions of the two inlet streams are known at the top and bottom. Additionally, the operating conditions, flow rates, and compositions of the outlet streams at the top (GASO) and bottom (BICARBO), as well as all physical design parameters of the column, hydraulic conditions of all trays, and installation costs, need to be calculated (Figure 1).

Figure 1.

Carbonating tower.

2.2.1 Data

A tower with 13 sieve trays is considered. Figure 1 shows the schematic of the simulated carbonating column. The ammoniacal brine stream (SALMU) enters at Tray 1, while the gas stream (GAS) enters at Tray 13. Flow rate, pressure, temperature, and composition information is provided in Table 1. The stream compositions have been obtained from [4].

Stream	GAS	SALMU
Mass Flow Kg/h	70,000	200,874
T [°C´]	60	25
Pressure Bar	2.5	1.0125
Mass Fraction		Mass Fraction
CO2	0.460274	NaCl	0.228948
CO	0.00468233	NH4OH	0.186464
N2	0.506162	H2O	0.584587
O2	0.0288817

Table 1.

Input streams data.

Assumption: a) The presence of a chemical reaction and the probable formation of sodium bicarbonate (solid) are considered based on the operating temperature of the trays.

Restriction: The temperature of the outlet stream, mainly containing sodium bicarbonate, must be within the range of [25, 30]°C.

2.3 Resolution methodology

To solve the problem, it is modeled and simulated using the AspenPlus simulator [9]. The calculation method for physicochemical properties is selected, the components are loaded, and input data for the inlet streams are entered. Then, runs are performed to verify the correct operation of the simulator and to ensure that the reactions proposed by the simulator align with those proposed in the literature (Table 2). With the correct model, initially, a simulation is performed without considering the internal column calculation. The desired results are obtained, and then the mentioned internal column design is added. It is verified that all trays operate correctly, costs are calculated, and the simulation is concluded.

Reaction	Type	Stoichiometry
1	Equilibrium	NH3 + H2O ↔ OH^− + NH4^+
2	Equilibrium	H2O + HCO3^− ↔ CO3^2− + H3O^+
3	Equilibrium	2 H2O + CO2 ↔ HCO3^− + H3O^+
4	Equilibrium	2 H2O ↔ OH^− + H3O^+
NaHCO3	Salt	NaHCO3 ↔ HCO3^− + Na^+
NH4HCO3	Dissociation	NH4HCO3 → HCO3^− + NH4^+
NH4CL	Dissociation	NH4CL → Cl^− + NH4^+

Table 2.

Chemical model.

2.4 Results

Table 3 presents the overall mass and energy balance as reported by the simulator. It is correct because the mass entering the tower is equal to the mass exiting. The simulator works with a precision greater than 10⁻⁶, so if the introduced mole fractions do not have equal or higher precision, small errors occur in the “Relative difference” column. Table 4 shows a portion of the information obtained after the simulation. It includes values of mass flow rate, density, enthalpy, average molecular weight of the stream, phase state, and operating conditions for each stream and component. Analyzing the top outlet stream (GASO), it is verified that no component is present in the gas phase that, a priori, is known not to exist under the operating conditions of the tower.

Total	Units	In	Out	Generated	Relative difference
Mole flow	kmol/hr	12,301,416	11,825,826	−299,2414	0,01433567
Mass flow	kg/hr	270,874,49	270,874,49		−3,74E-13
Enthalpy	MMkcal/hr	−680,1975	−680,1976		3,44E-08

Table 3.

Global mass and energy balance in the column.

Stream name	Units	GAS	SALMU	BICARBO	GASO
Stream Class		CONVEN	CONVEN	CONVEN	CONVEN
MIXED Substream
Phase		Vapor Phase	Liquid Phase		Vapor Phase
Temperature	C	60	25	25.3616	47.7403
Pressure	Bar	2.5	1.01253	1.1	1
Molar Vapor Fraction		1	0	0	1
Molar Liquid Fraction		0	1	0.980726	0
Molar Solid Fraction		0	0	0.0192741	0
Mass Vapor Fraction		1	0	0	1
Mass Liquid Fraction		0	1	0.925559	0
Mass Solid Fraction		0	0	0.0744415	0
Average MW		33.7875	19.6365	21.7507	26.7028
Mass Flows	kg/hr	70,000	200,874	197,248	73,626
H2O	kg/hr	0	136,621	126,910	4352.8
CO2	kg/hr	32219.2	0	85.4751	18895.5
CO	kg/hr	327.763	0	2.77842	324.985
N2	kg/hr	35431.4	0	252.067	35179.3
O2	kg/hr	2021.72	0	38.7442	1982.98
Na^+	kg/hr	0	18088.5	14070.3	0
CL-	kg/hr	0	27900.9	27900.9	0
NH4+	kg/hr	0	63.8135	5524.43	0
OH-	kg/hr	0	5.76E+01	3.84E-03	0
H3O+	kg/hr	0	4.92E-09	7.61E-05	0
NH3	kg/hr	0	18142.8	96.67	12890.5
NaHCO3	kg/hr	0	0	14683.5	0
NH4HCO3	kg/hr	0	0	0	0
NH4CL(S)	kg/hr	0	0	0	0
HCO3–	kg/hr	0	0	7364.75	0
CO3–	kg/hr	0	0	318.918	0

Table 4.

Global information of the carbonating tower designed.

When examining the results of the BICARBO stream, it is found that:

• The simulator not only presents it in the liquid phase but also reports that a liquid and solid phase coexist, as expected based on the outlet temperature.

• It exits at 25.4°C, therefore, the sodium bicarbonate exits at that temperature, and consequently, the required outlet temperature range of [25,30]°C is satisfied.

• It is composed of a liquid mass fraction (92.5%) and a solid mass fraction (7.5%). The mass fraction of the solid phase shows that it is composed solely of NaHCO₃ (14683.5 kg/h).

• 92.9% of the liquid water that entered has passed into this stream.

• No ammonium chloride or ammonium bicarbonate is formed.

• The inert components do not remain completely unchanged, but instead react in the liquid phase in proportion to their inlet composition: 0.8% CO, 0.7% N₂, and 1.9% O₂.

• Only 42% of the CO₂ is utilized.

Based on the above, we can conclude that the tower is operating correctly. However, the utilization of CO₂ could be improved by achieving a better flow rate ratio and maintaining correct hydraulic operating conditions.

The data regarding column sizing and the most important operating conditions are presented in Table 5. It should be noted that the spacing between trays is in accordance with what is observed in the literature (0.6 m). The trays function well, hydraulically, since none of them show weeping and a typical allowed value of 80% flooding is also respected.

Section starting stage	1
Section ending stage	13
Calculation mode	Sizing
Tray type	Sieve
Number of passes	1
Tray spacing [m]	0.6096
Section diameter [m]	3.27398
Section height [m]	7.9248
Section pressure drop [bar]	0.1517
Section head loss (Hot liquid height) [m]	1.30429
Trays with weeping	None
Maximum % jet flood	80.0006

Table 5.

Carbonating column design data.

Moreover, a cost table is also reported (Table 6) in which the total capital cost, operating cost and equipment cost (calculated by the simulator), among others, are highlighted. According to the above, it can be seen that a complete and detailed design of the carbonating column has been carried out knowing only the inlet streams.

Total capital cost [USD]	2,627,650
Total Operating Cost [USD/Year]	999,672
Total Raw Materials Cost [USD/Year]	0
Total Product Sales [USD/Year]	0
Total Utilities Cost [USD/Year]	35544.4
P.O. Period [Year]	0
Equipment Cost [USD]	254,500
Total Installed Cost [USD]	256,100

Table 6.

Costs of the designed column.

3. Impact of cooling on the performance of a carbonating column

At this point, the newly designed tower will be considered with an additional cooling stage. The cooling will be done as follows: part of the liquid will be extracted from stage 13, this stream will be cooled indirectly by an external heat exchanger and then re-enter stage 12 (Figure 2). The data, assumptions, and constraints are the same as those considered for the previous tower, which did not consider cooling. The problem is solved by adding the cooling condition to the model of the designed carbonating column.

Figure 2.

Carbonating column, streams, and cooling scheme.

3.1 Discussion and results

The basic sizing achieved is common to both columns and is presented in Table 5. The simulation results for the column with cooling are shown in Table 7. Both designs, with and without cooling, satisfy the requirement the outlet temperature of the liquid stream is within the desired range of [25–30]°C. Thus, the temperatures are 27.05°C and 25.36°C for the columns with and without cooling, respectively.

Stream name	Units	GAS	SALMU	BICARBO	GASO
Stream Class		CONVEN	CONVEN	CONVEN	CONVEN
MIXED Substream
Phase		Vapor Phase	Liquid Phase		Vapor Phase
Temperature	C	60	25	27.0485	50.026
Pressure	Bar	2.5	2	1	1
Molar Vapor Fraction		1	0	0	1
Molar Liquid Fraction		0	1	0.9635029	0
Molar Solid Fraction		0	0	0.0364971	0
Mass Vapor Fraction		1	0	0	1
Mass Liquid Fraction		0	1	0.8638933	0
Mass Solid Fraction		0	0	0.1361067	0
Average MW		33.7875	19.6365	22.5265	27.176
Flujo Molar	kmol/hr	2.071.77	10.229.65	9.313.33	2.247.48
H2O	kmol/hr	0	7.586.28	6.998.02	188.2803
CO2	kmol/hr	732.0907	0	8.4931	322.9076
CO	kmol/hr	11.7015	0	0.891	10.8105
N2	kmol/hr	1.264.80	0	81.0838	1.183.71
O2	kmol/hr	63.1811	0	10.7223	52.4588
Na^+	kmol/hr	0	786.827	446.917	0
CL-	kmol/hr	0	786.977	786.977	0
NH4+	kmol/hr	0	0.87	401.796	0
OH-	kmol/hr	0	0.719	0	0
H3O+	kmol/hr	0	0	0	0
NH3	kmol/hr	0	1.067.98	177.736	489.315
NaHCO3	kmol/hr	0	0	339.91	0
NH4HCO3	kmol/hr	0	0	0	0
NH4CL(S)	kmol/hr	0	0	0	0
HCO3–	kmol/hr	0	0	59.825	0
CO3–	kmol/hr	0	0	0.956	0

Table 7.

Overall information on carbonating tower with cooling.

The total capital costs of the column with cooling and without cooling are correspondingly: USD 2,972,670 and USD 2,627,650, that is. the former is 13.1% higher. However, this difference decreases when comparing the operating costs, which are USD 1,029,020 per year for the column with cooling and USD 999,672 per year for the column without cooling. The column with cooling is only 2.9% more expensive, a value that could potentially be reduced or even eliminated with changes in column operation.

If the stoichiometry of the reactions involved is considered, it is found that one mole of carbon dioxide produces one mole of sodium bicarbonate. Therefore, by observing Tables 4 and 7, it can be seen that without cooling, 174.789 kmol/hr. of sodium bicarbonate is produced, while with cooling, 339.91 kmol/hr. is produced, representing a 94.5% increase with the latter. Furthermore, the amount of solid sodium bicarbonate produced in the cooled column is almost double compared to the other column, specifically 82.8% more. This information is interesting as the simulator reports that it is the only species in solid phase.

When analyzing the unreacted CO₂ exiting the column, it is observed that the column without cooling loses 33% more CO₂ compared to the column with cooling (Tables 4 and 7), which somehow corroborates the sodium bicarbonate production data.

Finally, it is interesting to examine the temperature profiles for both columns (Figure 3). In graph (a), both curves are monotonically increasing, with the outlet temperature of Tray 13 being lower than that of the other column in graph (b). In this graph, Trays 12 and 13 operate at practically the same temperature, which is the lowest throughout the column, namely 26.98°C and 27.05°C, respectively. This explains the higher amount of solid-phase sodium bicarbonate compared to the liquid phase and, as mentioned earlier, in a greater proportion than in the column without cooling.

Figure 3.

Temperature and composition profile of the carbonating tower. (a) Tower without cooling and (b) tower with cooling.

4. Optimal stage to cool in a carbonating column

As mentioned earlier, highly exothermic reactions occur in the carbonating column, especially due to CO₂ absorption. Therefore, it can be assumed that cooling the column is necessary, and indeed, as proven in the previous section, it results in improved sodium bicarbonate production.

Now, the goal is to determine, which stage of the carbonating column should be cooled to achieve the highest yield in NaHCO₃ production. All the data considered in the cooled column (Table 7) are adopted [10].

It should be noted that for the column design, only the flow rates and compositions of the two feed streams to the tower are considered. The liquid stream consisting of ammoniated brine (SALMU) previously obtained in an absorption tower within the same plant, enters Tray 1. The gas stream (GAS), obtained from the calcination of limestone and recovered during the decomposition of bicarbonate a).

into sodium carbonate in a Solvay soda plant, enters Tray 13. The product, NaHCO₃, is obtained in the liquid outlet stream (BICARBO), while the unreacted gases exit through the gas outlet stream (GASO).

4.1 Methodology for modeling cooling and finding the optimal stage

A 13-stage column is initially designed without cooling. Then, the condition of cooling in the last stage is added, and the problem is solved. The cooling process involves extracting a portion of the liquid from a stage, cooling it through an external heat exchanger, and reintroducing it to the same stage (Figure 4).

Figure 4.

Scheme of the stage to be cooled in the carbonating column.

Next, the amount of heat extracted is varied to achieve maximum NaHCO₃ production. Once this point is reached, all the design data is kept as parameters, and the same amount of heat is extracted from each stage of the column. In other words, a simulation is performed for each stage that is cooled. If all the variables are kept fixed and only the tray to be cooled is changed, the study will allow comparing the NaHCO₃ yield in each case and therefore choosing the best tray to be cooled.

4.2 Discussion and results

The search for the optimal stage was conducted by cooling from the first stage (Tray 1) to the last stage (Tray 13) in order to establish the finding of a global optimum. The graphical comparison of the mass flow rate of NaHCO₃ produced, based on the stage being cooled (Figure 5), reveals that when cooling Tray 11, the highest performance of the carbonating column is achieved: 28,584.93 kg/hr. of sodium bicarbonate. However, the difference with the adjacent trays is small. It is only 0.020% and 0.054% more efficient compared to cooling Tray 12 or Tray 10, respectively. Therefore, for practical purposes, either of these trays could be chosen without causing significant differences.

Figure 5.

Flow rate of NaHCO3 according to the cooled tray.

It is interesting to note that as the tray closest to the bottom of the column is cooled, the BICARBO temperature decreases but the GASO temperature increases (Figure 6). This is logical since the cooling stage is farther away from GASO and.

Figure 6.

Temperature of the outlet streams according to the cooled tray.

closer to BICARBO. Regarding the flow rates of the outlet streams, a similar behavior is observed. The flow rate of BICARBO decreases when cooling is applied to the trays near the column’s bottom, while the flow rate of GASO increases (Figure 7). This is consistent with the temperature profile seen before since, for example, if the GASO temperature is higher, this justifies the higher flow rate of that gaseous stream. The temperature of BICARBO is 27.3 °C compared to 27.05°C in the cooled tower and 25.36°C in the first non- cooled carbonating tower. This demonstrates that as the temperature in BICARBO increases, the concentration of sodium bicarbonate in BICARBO and the column’s performance also increase.

Figure 7.

Mass flow rate of the outlet streams according to the cooled tray.

On the other hand, the fact of keeping all the design variables of the column constant and only evaluating the number of plates to be cooled allows us to affirm that the result achieved is valid and the following heuristic could be proposed for the choice of the best stage to be cooled:

1. Discard the first and the last stage.

2. Discard as candidates all the stages from the second (from the top) to the one located in the middle.

3. The best candidate will be closer to the base of the column than to the middle of the column.

5. Sensitivity of the performance of a carbonating column to changes in temperature of the inlet streams

The objective of this study is to determine the impact on the NaHCO₃ performance due to changes in the temperature of the inlet streams. Three cases are studied:

1. The temperature of the liquid feed stream, SALMU, is changed in steps of 5 °C from 10 to 35°C while keeping the rest of the parameters constant.

2. The temperature of the GAS feed stream is changed in steps of 5°C from 30 to 80°C while keeping the rest of the parameters constant.

3. Simultaneous variation of a) and b).

To proceed, we choose the tower with the best performance among the ones studied here. Therefore, we select the column with tray 11 being cooled and conduct the sensitivity study. Firstly, we set the temperature of the GAS stream as a parameter and fix it at 30 °C. Then, we simulate for a temperature of 10 °C for the SALMU stream. Next, we move on to the next simulation: keeping the parameter value constant, we increment the temperature of the SALMU stream by a step increment of 5°C, that is. we take the value of 15°C. This process is repeated, taking the same parameter value and incrementing the SALMU stream temperature by the step value (5°C) for each new simulation, until we cover the entire proposed study interval: [10–35]°C (Figure 8). Therefore, a total of six simulations will be performed, considering the same parameter value.

Figure 8.

Evolution of NaHCO₃ mass fraction with temperature.

Subsequently, the parameter value is increased by a step of 5°C, and the aforementioned procedure is repeated. The parameter increment is done within a range of 30 to 80°C. At the end of the described process, a total of 66 simulations will have been conducted. Similarly, the procedure is followed to address the proposed objectives for case (b) (Figure 9) and (c).

Figure 9.

Relationship between NaHCO₃ mass fraction and temperature rise of the gaseous feed stream.

5.1 Sensitivity analysis results

When analyzing the results for case (a), it can be observed that the production of NaHCO₃ decreases as the T_SALMU temperature increases (Figure 8), for all values of the T_GAS parameter. A similar behavior is observed when analyzing case b), where the production of sodium bicarbonate decreases as the T_GAS temperature increases, for all values of the T_SALMU parameter (Figure 9). It is interesting to note that in both cases, the evolution of the curves is nearly linear. Although the curves in Figures 8 and 9 may appear to be strictly straight and parallel at first glance, they are not strictly parallel. When comparing the slopes, it is evident that they are not parallel. In the best case, that is. the case with the highest concentration (T_GAS = 30°C, Figure 8), the slope of the curve is smaller than the slopes of the other curves. A similar situation is observed in Figure 9.

Furthermore, in the curve corresponding to the most favorable condition mentioned earlier (T_GAS = 30°C, Figure 8), it can be observed that for every 1°C increase in the T_SALMU temperature, the mass fraction of NaHCO₃ decreases by 1.0061 10⁻³, which is equivalent to a flow rate of 259.09 [Kg/h]/°C.

When analyzing the variation in T_GAS temperature (Figure 9) in the best case (T_SALMU = 10°C), it can be observed that the mass fraction of NaHCO₃ decreases by.

1.2003 10⁻⁴/°C, or in other words, the NaHCO₃ flow rate decreases by 29.342 [Kg/h]/°C. Therefore, the production of the column is more affected by changes in the temperature of the liquid feed stream than the gas stream. Quantitatively, the production of NaHCO₃ is eight times more affected by a one-degree celsius variation in the T_SALMU stream than in the T_GAS stream.

Figures 10 and 11 show the impact on the T_BICARBO due to the variation in the temperature of the liquid and gas feed streams. Increasing the temperature of these streams results in an increase in the temperature of the product stream in both cases. Considering the lower curve in Figure 10, for every 1°C increase in T_SALMU, the temperature T_BICARBO increases by only 0.064°C. A similar analysis based on Figure 11 shows a relationship of 0.044°C T(GAS)/°C T(BICARBO).

Figure 10.

Relationship between BICARBO stream temperature and liquid feed stream temperature rise.

Figure 11.

Relationship between the temperature of the BICARBO stream and the temperature rise of the gaseous feed stream.

Therefore, the variation of the liquid feed stream temperature (T_SALMU) impacts 45.6% more than the variation of the gaseous feed stream temperature (T_GAS), on the BICARBO product stream temperature (T_BICARBO).

In the study of case c), which involves the sensitivity analysis of sodium bicarbonate production due to simultaneous variations in the temperatures of the SALMU and GAS feed streams, the results found have been condensed into a graph (Figure 12). This graph illustrates the evolution of the temperature and mass fraction of NaHCO₃ in the BICARBO stream for any desired condition. Furthermore, the graph serves as a nomogram for the studied problem. Using the nomogram, one can obtain results for any combination of the variables studied without the need for simulation under those specific conditions.

Figure 12.

Simultaneous sensitivity study of temperature and concentration of the BICARBO stream.

For example, if one wants to determine the temperature and NaHCO₃ concentration when T_SALMU = 25°C and T_GAS = 75°C, they would locate 25°C on the x-axis, follow the mass fraction curves to find the one corresponding to 75°C, and read the approximate value of 0.134 (mass fraction of NaHCO₃) on the y-axis. Using the temperature curves, T_BICARBO can be estimated to be approximately 28°C. (Note: To satisfy operational restrictions, the graph excludes the portion of curves below 25°C.)

6. Conclusions

A carbonation tower has been designed for the production of sodium bicarbonate. The model to be simulated was built based on the equipment models of the simulator. The design is complete and includes the physical dimensioning of a column of sieve trays, the dimensioning of each tray, and the verification of the hydraulic operation of each one of them. It is important to point out that the use of the simulator has taken into account the calculation of the physicochemical and thermodynamic properties as a function of temperature of all the components present, which otherwise would not have been possible due to the scarcity of bibliographic information for this purpose. It also allows a quick calculation of all costs, namely: total capital cost, operating, service, and equipment costs, among others.

It is well-known that the carbonating process is exothermic, and therefore, the column should be cooled. This has been confirmed by the conducted study. It has been found that when a stage of the carbonating column is cooled, the total capital cost of the column is 13% higher than when the column is not cooled. However, the operating costs are similar, with only a 2.9% increase due to cooling. In return, there was a 35.3% improvement in the yield of sodium bicarbonate production.

Once the question of whether or not to cool a carbonating column is satisfied, the next question is how many stages should be cooled and which ones. In this regard, no study has been found in the literature that provides the answer. Therefore, this paper presents the results of the behavior and performance of each carbonating column according to the cooled stage. After analyzing the 13 trays of the studied column, it was found that the optimal stage to be cooled is tray 11. The result of the conducted study is limited by the input data and the cooling process used. However, on the other hand, the fact that all the design variables of the column were kept constant, and only the tray to be cooled was evaluated allows us to assert that the achieved result is valid as a global optimum.

Furthermore, it can be proposed as a heuristic that when choosing the stage to be cooled, it is advisable not to select the stages near the top or middle of the column but rather those closer to the bottom of the column.

From the sensitivity analysis of the NaHCO₃ yield in the carbonating column, it has been found that: (i) The concentration of NaHCO₃ decreases as the temperature of the feed streams increases and that the influence is eight times greater for variation of the temperature of the feed liquid stream than for variation of the temperature of the gaseous feed stream; (ii)The temperature of the liquid outlet stream (product) increases when the temperature of the feed streams, either one or both of them, increases; and (iii) The impact on the outlet temperature is 45.6% greater per degree celsius of temperature variation in the liquid feed stream compared to the variation in the gaseous feed stream.

Lastly, the sensitivity analysis allowed for the creation of a nomogram, which enables the determination of the conditions of the outlet stream, such as temperature and concentration, based on the temperatures of the inlet streams. Furthermore, it could easily be constructed to display all other variables of the column, including flow rate and concentrations of all species present in both outlet streams.

The findings presented in this study are valid for the given conditions and assumptions. However, the results may vary under different circumstances such as changing the type of column (e.g., having multiple passes or different sections), altering the conditions of the cooling process in the stage, modifying the percentage of flow rate to be cooled, and adjusting the amount of heat exchange, among other factors.

Acknowledgments

Special thanks to IntechOpen for their exceptional collaboration and invaluable support in the publication of this chapter. We would also like to extend our sincere gratitude to Universidad Nacional de Jujuy for their support of scientific research.

Thanks

I would like to thank my parents, my brother and sister John and Liliana, my son “Jaimito-Leo” and my wife Mechy, for their immense encouragement and love.