Reaction of Carbon Dioxide Gas Absorption with Suspension of Calcium Hydroxide in Slurry Reactor

Chemical phenomena involving three phases (solid, liquid, and gas) are often found in the industry. Carbonate (CaCO 3 ) is widely used in industries as a powder-making material in the cosmetic industry, a pigment in the paint industry, and filler in the paper and rubber industry. This research aim to study the ordering process carbonate deposits (CaCO 3 ) from the absorption process of CO 2 gas with Ca(OH) 2 suspension. The absorption reaction of CO 2 gas with Ca(OH) 2 suspension was carried out in a stirred slurry tank reactor. Initially, the reactor containing water was heated to a certain temperature, then Ca(OH) 2 was added to the reactor. Furthermore, CO 2 gas with a certain flow rate and temperature (according to the reactor temperature) is flown with the help of a gas distributor. Samples were taken every 1 min until the concentration of Ca(OH) 2 could not be detected (completely reacted). The variables in this study were: stirrer rotation speed (5.66711.067 rps), CO 2 gas flow rate (34.0127–60.5503 c/s), and temperature (30–50°C). The mass transfer coefficient and the reaction rate coefficient were determined by minimizing Sum of Squares of Errors (SSE). This experimental process follows a dynamic regime. A dimensionless number relationship for the gas-liquid mass transfer for the value range is Re 1 = 18928.76-38217.20, Sh = 0.07928 Re g0.4383 Re l0.4399 Sc 0.6415 with an error of 5.19%. The dimensionless number relationship for solid-liquid mass transfer is Sh = 0.0001179 Re g0.4674 Re l0.5403 Sc 1.444 with an error of 7.31%. The relationship between the reaction rate constant and the temperature in the 30-50 °C range can be approximated by the Arrhenius equation, namely k r = 1771000 e -2321.4/T cm 3 /mgmol/s with an error of 3.63%.

CaCO3 is mainly used as a filler material in paint, plastic, paper, food, ceramics, medicine, and other industries [5].It is widely found in nature in the form of limestone; however, due to its low purity, the level of refinement is not sufficient for use in industries.
CaCO3 preparation can be done by a three-phase reaction using a stirred slurry tank reactor.Compared to other threephase reactors, the stirred slurry tank reactor has several advantages, such as simple construction and design, good heat transfer performance, online catalyst addition and removal, and equitable interphase mass transfer rates with low energy input [6].Calcium-based sorbents for adsorption of CO2 are significant matter due to their potential variety of application fields to decrease CO2 greenhouse gas and have been improved with diverse structures and compositions to enhance the adsorption capacity [7].Many previous studies have focused on the synthesis of CaCO3 through the reaction of carbon dioxide and calcium hydroxide.Jin et al. [8] studied the effect of ethanolamine concentration, reaction temperature, reaction pressure, and reaction time on the polymorphs of CaCO3.Liendo et al. [9] investigated the effect of gas flow rate and initial CaCO on the synthesis of CaCO3 through the carbonation route in a continuously Stirred Bubble Reactor and a Packed Bed Reactor Shirsath et al. [10] investigated the effect of Ca(OH)2 slurry concentration, CO2 flow rate, Ca(OH)2 slurry flow rate on the particle size and morphology of CaCO3.Made et al. [11] studied the production of CaCO3 from natural CaO into nano-sizes with varying concentrations of Ca(OH)2.Kamba et al. [12] synthesized pure CaCO3 nanocrystals using a high-pressure homogenizer (HPH).The reaction CO2 and slurry of Ca(OH)2 was controlled by diffusion and reaction in the low temperature range and controlled by diffusion in the high temperature range [13].However, no study has investigated the correlation of dimensionless numbers on gas-liquid mass transfer coefficients from the manufacturing of CaCO3.Therefore, this study aims to determine mass transfer, coefficients, rate constants, and dimensionless numbers from the production of precipitated CaCO3 by CO2 absorption using Ca(OH)2.

2-1-Material Preparation
CO2 with a purity of 99.98% was obtained from PT. Samator Gas Industry, Yogyakarta, Indonesia.Ca(OH)2 having purity of 96% and an average grain size of 0.0005 cm was obtained from UD Organic, Yogyakarta, Indonesia.

2-2-CaCO3 Production
A tank with a width of 1 cm and an inner diameter of 12.64 cm which was equipped with four baffles was used as a reactor.A pitched blade turbine with a diameter of 5.34 cm was used as a stirrer.The used gas distributor was in the form of a pipe ring with a diameter of 7.8 cm and a hole distance of 0.5 cm.A diagram of experimental instruments is presented in Figure 1.

Figure 1. A scheme of experimental setup using a stirred tank reactor
The reactor tank was filled with 2 L of distilled water, then it was heated at a temperature of 30-50 °C.The water bath which was passed by the CO2 gas pipe was heated so that the gas flow temperature was the same as the reactor temperature.10 g of Ca(OH)2 was fed into the reactor.The stirrer was varying at rotation rates of 5.667 rps to 1.067 rps to form a saturated solution of Ca(OH)2.The gas valve was opened at flow rate variation of 34.0127 cm/s to 60.5503 cm/s and inflated in the reactor with the help of a gas distributor.In every 1 min, the sample was taken to analyze the remaining Ca(OH)2 concentration.The experiment was stopped after the Ca(OH)2 content had finished reacting which was indicated by the colour of the sample that did not change to pink when the phenolphthalein (PP) indicator was dropped.

3-1-Effect of Stirrer Speed
Experiments were carried out by varying the stirring speed, CO2 flow rate (CA), and temperature towards the changes of Ca(OH)2 concentration (CB) in the reactor during the reaction.The stirring speed was varied by observing visually during the experiment the homogeneity of the solution and the presence of vortices.The rate of gas flow cogitated the rate of absorption of the liquid against the gas, while the temperature was started from the ambient temperature with an interval of 5 °C.Sampling every 1 min was the fastest time that allows sampling and detection of the presence of Ca(OH)2 in the sample.
The stirrer speed varied from 5.667 to 1.067 rps, while other variables were kept constant.In this process, the greater stirring reduced the mass transfer barrier of Ca(OH)2 to water which led to more reacted Ca(OH)2.Besides, the increase in stirring rate would enhance the interfacial area, therefore, the Ca(OH)2 dispersion in water becomes more complete.This phenomenon is consentient with the previous result conducted by [9] who stated that the low stirring speed led to the low mass transfer, while the high stirring rate accelerated the mass transfer rate.
Figure 2 shows the correlation between the Ca(OH)2 concentration with the time at different stirring speeds.It indicates that the longer the stirring would decrease the concentration of Ca(OH)2 in the solution.If the stirring rate was increased for the same period, the decrease in the concentration of Ca(OH)2 would also increase.The largest decrease in the rate occurred at the highest stirring speed of 9.467 rps.This phenomenon is consentient to the previous result conducted by Fan et al. [14] who stated that the low stirring speed led to the low mass transfer, while the high stirring rate accelerated the mass transfer rate.The values of liquid-gas mass transfer coefficient (klag) and solid-liquid mass transfer coefficient (ks) on the variation of stirring speed were calculated using the Hooke-Jeeves method.The relationship between the stirring rate and the klag and ks variables is shown in Figure 3.The approximation errors of Equations 1 and 2 were 3.41% and 4.39%, respectively.
The value of the klag increased by the increase of stirring.This phenomenon shows that higher stirring speed leads to the smaller mass transfer barrier of CO2 gas into the water, as a result, higher klag and larger amount of CO2 diffused into the water can be obtained.Babou et al. [15] stated that increasing the stirrer speed resulted in a reduction of particle size.The decrease in the particle size with the increase in stirring speed can expand the formation of the huge number of small nuclei, thus, generating much larger particles.

3-2-The Effect of CO2 Gas Flow Rates
Flowrate varied from 34.0127 to 60.5503 cm/s to determine the effect of CO2 flow rate.Increasing the flow rate of CO2 would accelerate the reduction of Ca(OH)2, especially for the rates between 9.925-11.883mL/s.The correlation of the concentration of Ca(OH)2 at various CO2 gas flow rates, including both the experimental data and calculation is shown in Figure 4. Figure 4 shows that the higher the gas flow rate, the concentration of Ca(OH)2 reduced faster.The result indicates that a higher gas flow rate leads to the larger swelling of the CO2 gas which diffuses as carbonic acid (H2CO3), then carbonic acid will be broken down into H+ and CO3= and reacted with the dissolved Ca(OH)2.A lower CO2 flow rate with conventional stirring may give a beneficial state for the formation of plate-like particles [10,16].CO2 gas flow rate also affects reaction time, percentage phase, and crystal size.Increasing CO2 gas flow rate decreases the particle size [17].
The concentration of Ca(OH)2 in the simulation was close to the experimental data with an average error ranging 0.12-8.84%.This result proved that the process can be approached by existing mathematical models.The relationship between klag and ks on changes in the flow rate of CO2 gas can be seen in Figure 5.
with the approximation error of Equations 3 and 4 were 2.22% and 7.79%, respectively.
The enlarged gas flow rate of CO2 would increase the dissolution turbulence hence, it would have the same tendency (pattern) as the change in the stirring speed.

3-3-Effect of Changes in Reaction Temperature
The effect of the reaction temperature was carried out at temperature of 30-50°C, while other variables were kept constant.At 35°C, the concentration of Ca(OH)2 was lower than the one at the temperature of 30 °C.After that, the Ca(OH)2 concentration enhanced with an increase in temperature.This phenomenon occurred because, at temperatures between 30-35°C, the reaction equilibrium has reached.The increase in temperature decreased the formation of CaCO3 [18].
As shown in Figure 6, temperature affected the reaction rate.Temperature changes affected the decrease of the concentration of Ca(OH)2 in the solution.Temperature increase had a relatively smaller effect on reducing Ca(OH)2 concentration than the stirring speed and the CO2 gas flow rate.This case happened because the higher the temperature, the smaller the amount of solid Ca(OH)2 and CO2 gas dissolved in the water.Temperature increase can increase the particle size which can be described by the competition existing between the nucleation and crystalline growth phases.At low temperatures, the nucleation rate is greater than the crystalline growth, thus, generating small particles sizes.On the contrary, the high temperature produces the larger particle sizes [15].

Figure 6. The relationship between the concentration of Ca(OH)2 mgmol/cm 3 with time at various temperatures
The optimization results of the reaction rate constants at various temperatures can be seen in Table 1. with a mean error of 3.63%.

Table 1. Optimization of kr at various temperatures
The ratios of the reaction rate constant for the difference in temperature increase of 10°C were: 1.277 (3040°C), 1.2672 (35-45°C), and 1.2578 (40-50°C).The results showed that the rate constant ratios were less than 1.5 at the temperature difference of 10°C.
.      * (6) When viewed from the existing resistance, the changes can be seen in Table 2.As shown in Table 2, the dominant regime for this experiment is the gas-liquid mass transfer regime, which can be seen from the overall reaction rate constant.The value of 1/klag was greater than the values of PA/(HCB * ksas) and 1/(krCB * ).Although the resistance to gas-liquid mass transfer is the most influential parameter, however, the magnitude of the resistance to the reaction rate cannot be neglected because its value was only half of the gas-liquid mass transfer resistance.

3-4-The Relationship between the Dimensionless Number at Various Gas-liquid Mass Transfer Coefficient
The author declares that there is no conflict of interests regarding the publication of this manuscript.In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.
The mass transfer rate from gas to liquid is affected by many factors, such as bubble diameter, gas flow rate, liquid physical properties, and stirring speed.This effect can be reflected by the relationship between Sherwoods number (Sh), gas Reynolds number (Reg), liquid Reynold's number (Rel), and Schmidt's number (Sc).The number relationship approach was carried out by an analysis of dimensionless number which results in Equation 7. Sh = 0.07928 Reg 0.4383 Rel 0.4399 Sc 0.6415 (7) with an average error of 5.19%.Equation 7shows that the higher the Rel the faster the stirring will increase the Sh.This is due to the phenomenon that faster stirring cycle results in the smaller mass transfer barrier of CO2 gas into the water.Therefore, klag increases, which finally enhances the amount of CO2 diffused into the water.Larger amount of CO2 gas that diffuses into the water leads to larger formation of H2CO3 Reg increases following the increase of CO2 gas flow rate acceleration that causes the increase of solution turbulence.As the result, a same pattern with the change of stirring speed was obtained.However, the effect of the change in stirring is slightly greater than the increase in flow velocity on the clag value klag.
Reduction of Sc will decrease the Sh.An increase of the temperature change would increase the coefficient of gas diffusivity in the liquid y(D) and decrease the Sc because Sc is inversely proportional to the temperature.The relationship between Sh, Reg, Rel, and Sc on various clag values are presented in Table 3.The power of Re at a dimensionless number group equation can be used to indicate the appropriate regime.This is expressed as the Reynolds index, which was obtained from the variation of the Re at a fixed temperature.If the Reynolds index value is close to zero, it includes a viscous chemical or dynamic regime.If the value is between 0.5 and 0.8, it is called a turbulent dynamic regime for the fixed interface.If the index is between 3 and 5, the characteristic is the dynamic regime for the free interface [20].When following these limitations, as the process has a Reynolds index close to 0.5, therefore, it can be included in the dynamic regime category for the free interface.This is following the review regime based on Q10 which states that this process is a dynamic regime.

3-5-The Relationship between the Dimensionless Number at Various Solid-liquid Mass Transfer Coefficient
The solid-liquid mass transfer coefficient as reflected in the change in Sh as a function of the Reg, Rel, and Sc is shown in Equation 8; Sh = 0.0001179 Reg 0.4674 Rel 0.5403 Sc 1,444 (7) with an average error of 7.31%.
The power of the Sc in this experiment was 1.444.According to the literature that the rank of the Sc is less than 1.This difference may be caused by the factors that affect Sc which is not measured directly (experimental variable) but from the literature review.The values of Equation 8 on various ks data is shown in Table 4.The change in the increase of the Reynolds number of liquid was indicated by an increase in the stirring speed which would increase the Sherwood number.The increase in stirring speed facilitates the breakdown of Ca(OH)2 into Ca ++ and OH =.The dispersed Ca 2+ in the water increased resulting in an increase of the ks.The same thing will happen in the increase of the Reynolds number of gas with an increasing flow rate of CO2 gas.Increasing the temperature change will result in a higher and a decrease in the Sc because Sc is inversely proportional to the diffusivity.A decrease in temperature will decrease the ks.
From the calculation, the Reynold index is 0.6.The index is between 0.5 and 0.8, therefore, this process has dynamic regime characteristics for fixed interfaces.These results are consistent with the review of gas-liquid mass transfer coefficients, which categorize this process as a dynamic regime for the fixed interface.
The rate constant in this study is almost the same with the previous research conducted by Fernianti [21] regarding the reaction of solid CO2 and CaCO3 gas in a stirred tank slurry reactor at a temperature range of 2045°C, namely kr1 = 1.47×10 6 e -2290 / T cm 3 /mgmol•s and kr2 = 1767.75e -2021.35/ T s -1 .
In the previous research conducted by Vasconceles et al. [20] stated that the gas-liquid mass transfer analysis for high Re in the bubble reactor has Reynold's power, namely: Sh = 1.13 Re 1/ 2 Sc 1/2 , whereas, the boundary layer theory for laminar velocity follows the Froessling equation for the solid form Sh = c Re 1 /2 Sc 1 / 3 .The c value is close to 0.6 or other experiments get a value between 0.42 and 0.95.
In the gas-liquid reaction experiment with a solid catalyst, the reaction takes place quickly with a Rel was greater than 25, hence, the solid-liquid mass transfer coefficient equation is as follows [22].ks = 0.6 (DA/dp) Rel 1/2 Sc 1/3 (9) When compared with this process, it turns out that the Reynold index has almost the same value as the equation above and belongs to the same regime, namely the dynamic regime for the fixed interface.This means that the experimental results have the same trend as the previous experiment.

4-Conclusion
This experiment was carried out to explore the effect of stirring speed, CO2 flow rate, and temperature on the synthesis of CaCO3 during the reaction of CO2 and Ca(OH)2.Increasing stirring speed decreased the concentration of Ca(OH)2.thus, the formation of CaCO3 also gets dropped.Reduction of Ca(OH)2 concentration occurs faster as rising of CO2 flow rate.The increase in temperature lowers the formation of CaCO3.A mathematical model can be applied to the experimental process, as proved by simulations that approach experimental data.This experimental process follows a dynamic regime.A dimensionless number relationship for the gas-liquid mass transfer for the value range Re1 = 18928.76-38217.20,Sh = 0.07928 Reg 0.4383 Rel 0.4399 Sc 0.6415 with an error of 5.19%.The dimensionless number relationship for solid-liquid mass transfer is Sh = 0.0001179 Reg 0.4674 Rel 0.5403 Sc 1.444 with an error of 7.31%.The relationship between the reaction rate constant and the temperature in the 30-50 °C range can be approximated by the Arrhenius equation, namely, kr = 1771000 e -2321.4/Tcm 3 /mgmol•s with an error of 3.63%.

Figure 2 .Figure 3 .
Figure 2. The relationship between the concentration of Ca(OH)2 with time at a various stirring speed

Figure 4 .
Figure 4.The relationship between the concentration of Ca(OH)2 in mgmol/cm 3 with time at various gas flow rates

Figure 5 .
Figure 5.The relationship between ln klag and ln ks with ln N The equations that represent Figure 5 are: klag = 0.9616 v 0.6028 (3) ks = 0.8744 v 0.6244 (4) the relationship between the constant rate of reaction and temperature in the Arrhenius equation: kr = 1.771 × 106 e -2321.4/ T cm 3 /mgmol/s 5

Table 4 . Relationship between Sh (experimental data and calculation), Reg, Rel, and Sc on various ks values
ag Area of boundary gas-liquid per unit volume of liquid, cm 2 /cm 3 as Area of boundary solid-liquid per unit volume of liquid, cm 2 /cm3