Numerical Modeling and Economic Analysis of Ultrasonic-Assisted CO₂ Absorption Process for Offshore Application

Abstract

In the quest for net zero carbon emissions by 2050, Carbon Capture Utilization and Storage (CCUS) is indispensable. The development of more efficient CO₂ capture processes is essential. High-frequency ultrasonic irradiation is an emerging, intensified technique that can enhance the CO₂ absorption process. To advance this technology toward commercialization, it is crucial to conduct a thorough economic analysis to allow the identification of the key cost component. While equipment sizing is essential in this economic assessment, there is a lack of numerical models for estimating the size and power consumption of ultrasonic absorbers. This study introduces a numerical model for these predictions. The model was then used to determine the economic feasibility of this emerging technique against the packed bed columns based on capital expenditure (CAPEX), operational expenditure (OPEX), and unit technical cost (UTC) for 20 years of plant operation. According to the economic analysis, ultrasonic intensification requires 34% less CAPEX due to its compact design. Although its OPEX is 11% higher due to the additional electricity needed for the ultrasonic transducers, the UTC is still 3% lower than the conventional packed bed column, demonstrating a potential cost savings in implementing the ultrasonic irradiation-assisted technique during the CO₂ absorption process offshore.

1. Introduction

Carbon capture is one of the critical paths in the carbon capture, utilization, and storage (CCUS) solution towards a sustainable transition to net zero emissions and to overcome the global warming issue. It is essential to develop a more efficient CO₂ capture process that is at the same time economically feasible to commercialize. In the oil and gas industry, natural gas extracted from the field can often feature elevated CO₂ concentrations. Consequently, it is imperative to manage the surplus CO₂ effectively while safeguarding the natural environment. Acid gases such as CO₂ and H₂S must be removed from natural gas to prevent pipeline corrosion, meet sales gas calorific values, avoid crystallization during liquefaction, and protect humans from exposure to highly toxic H₂S gas [1,2,3,4]. Several technologies for acid gas removal from natural gas have been developed and commercialized, including membrane separation, cryogenic distillation, and solvent-based absorption processes [3,5,6].

Among these technologies, the acid gas absorption process using an amine-based solvent has been widely used in the oil and gas industries for decades. The chemical absorption technology demonstrates remarkably high separation efficiency (>90%) even at low carbon dioxide (CO₂) partial pressure with minimal hydrocarbon loss. The effectiveness of the amine-based absorption process is primarily driven by the chemical reaction occurring between the acid gas and the specific type of solvent employed within the absorber.

Methyldietanolamine (MDEA) is commercially used as the solvent for the CO₂ absorption process due to its promising characteristics such as high absorption capacity, low regeneration energy, low degradation rate, and being less corrosive as compared with primary and secondary amines [7,8,9]. However, the reaction rate between MDEA and acid gas such as CO₂ is slower as compared with the reaction between primary and secondary amines with CO_2, such as monoethanolamine (MEA) and diethanolamine (DEA) [4,8,10,11]. Due to this, piperazine (PZ), a cyclic diamine, is usually used with MDEA as the activator for CO₂ removal because of its rapid formation to form carbamate and bicarbamate with CO₂ [5,12]. The blended MDEA and PZ solvent (known as activated MDEA, or aMDEA) is usually employed to remove both CO₂ and hydrogen sulfide (H₂S) from natural gas during the sweetening process [9,13,14]. The aMDEA solvent was developed in the 1970s and patented by BASF for the CO₂ absorption process, with a removal efficiency higher than the traditional MEA and potassium carbonate solvents. Besides, the solvent requires only one-third of the energy consumption of conventional Benfield technology [14,15,16]. Aqueous aMDEA reacts directly with H₂S to form amine salt (methyldiethanolamine sulphide) as compared with CO₂, and it does not form carbamate [9,17]. Therefore, the presence of CO₂ will not affect the absorption of H₂S, even though the partial pressure of H₂S in the feed gas stream is much lower than CO₂.

Although this technology has been applied in acid gas sweetening for several decades, the conventional absorption column suffers several drawbacks, such as a high equipment corrosion rate, low CO₂ loading capacity, causing product off-spec, foaming, flooding, amine degradation, high energy consumption during regeneration, and excessive footprint and tonnage [12,18]. Ultrasonic irradiation is an emerging technology that can enhance gas-liquid mass transfer, enabling compact and lightweight designs, especially for offshore operations.

Ultrasonic irradiation technology has been studied widely to improve mass transfer for a wide variety of processes, such as biotechnology [19], chemical reactions and processes [20], wastewater treatment [19,21], microfluid systems [22,23], food technology [24], crude oil upgrading [25], and natural gas purification [26]. Ultrasonic technology has been widely used to enhance the mass transfer process due to its chemical and physical effects on the liquid medium [27]. The chemical effect of ultrasonic irradiation is also known as the sonochemistry effect, which is induced by the implosion of cavitation bubbles at high local pressure and temperature, causing the formation of free radicals [27]. These free radicals may enhance chemical reactions during the gas-liquid mass transfer process. Another phenomenon induced by ultrasonic irradiation in the liquid medium is the sonophysical effects, which refer to the formation of cavitation bubbles, acoustic streaming, an acoustic fountain, and atomization [27]. Figure 1 shows the schematic diagram of the sonophysical effects of ultrasonic irradiation in the liquid medium. The sonochemistry and sonophysical effects induced by high-frequency ultrasonic waves enhance mixing, stimulate radical formation, and increase the available surface area for mass transfer. This, in turn, results in higher removal efficiency.

Several experimental studies have been conducted to confirm the effect of ultrasonic irradiation on mass transfer enhancement in the gas-liquid absorption process. Tay et al. (2016) [29] investigated the effect of ultrasonic power up to 18 W on the CO₂ absorption process. Based on the experimental results, it was observed that the formation of an acoustic fountain and liquid atomization generated from a high ultrasonic power source can amplify the mass transfer absorption process by up to 80 times. Acoustic streaming provides better gas-liquid mixing, while an acoustic fountain increases the gas-liquid interfacial area for mass transfer. M. Yusof et al. (2019) [27] have conducted a continuous experimental study utilizing 1.7 MHz ultrasonic waves to assist CO₂ absorption in distilled water. The effect of gas flow rate, liquid flow rate, pressure, and voltage on absorption performance has been studied, and numerical optimization using Design Expert software has been conducted. At the optimum condition, the mass transfer coefficient of the continuous ultrasonic contactor system surpasses that of other contacting equipment, including bubble columns, stirred vessels, and counter-current-packed columns.

Akbari et al. (2017) [30] also conducted an experimental study to investigate the impact of 1.7 MHz ultrasound waves on micro-scale T-shaped glass microreactor gas-liquid contactors. Their research encompassed both physical and chemical absorption of CO₂ into deionized water and sodium hydroxide solutions, respectively. The findings from their study revealed a significant enhancement in mass transfer coefficient when ultrasound waves were utilized as compared with the silent system at various operating conditions.

Numerical simulation has gained prominence in the advancement of ultrasonic-assisted gas-liquid mass transfer technology. This approach offers a comprehensive understanding of the distinctive flow behaviors induced by high-frequency ultrasound waves, such as mixing, cavitation, and heat and mass transfer mechanisms [31,32,33]. For instance, Abolhasani et al. (2012) conducted a numerical study on the effect of high-frequency ultrasonic waves on the heat transfer rate [34]. The simulation results revealed that the 1.7 MHz ultrasound wave fostered enhanced fluid mixing and the generation of high-velocity flows, resulting in a more uniformly distributed temperature in a vessel. Moreover, the simulation findings were validated against experimental data, illustrating a robust agreement between the CFD simulation and the actual temperature measurements recorded during the experiments.

Another study led by Parvizian et al. (2012) used the CFD model to predict the complex flow pattern induced by the 1.7 MHz transducers in a novel ultrasound reactor [35]. The outcomes of their CFD simulation have shown the superior performance of the sonoreactor, which exhibited a notably more uniform velocity distribution in contrast to a traditional stirred tank operating at equivalent power consumption. The formation of a jet stream capable of improving liquid mixing can be induced by high-frequency ultrasound waves, even with lower power consumption.

Xu et al. (2016) introduced a numerical model to predict the formation of acoustic fountains by taking into account the influence of surface tension and ultrasound radiation pressure [36]. With this model, they predicted that the area of the acoustic fountain increased with the increase in ethanol concentration in the liquid medium. This effect stems from ethanol’s lower surface tension, density, and sound speed. Furthermore, numerical modeling has also been developed to determine the mass transfer coefficient for ultrasonic-assisted gas-liquid mass transfer. Researchers frequently employ the dynamic method of gassing-in and the logarithmic expression of the instantaneous pressure method to derive the mass transfer coefficient from experimental data, as previously demonstrated in multiple studies [29,37].

Based on previous experimental works, the effectiveness of the ultrasonic-assisted CO₂ absorption process has been well established, particularly in batch operations. Yet, for further advancement of this technology toward commercialization, a central challenge lies in cost reduction, encompassing both capital and operational expenses. Therefore, a comprehensive economic analysis is imperative to pinpoint the primary cost components of ultrasonic irradiation technology, enabling further cost optimization. One of the critical criteria for the economic analysis is equipment sizing, which will determine the capital expenditure (CAPEX) of the technology. However, the numerical model to predict the effective volume of the ultrasonic absorber is still lacking in the literature.

To the best of our knowledge, no literature to date has reported on the process simulation and economic analysis for the ultrasonic-assisted CO₂ absorption process. This paper presents a numerical model to predict the effective volume and energy consumption of the ultrasonic absorber using data from experimental studies. The predicted effective volume and energy consumption were further employed in process simulation to facilitate the economic comparison analysis between the ultrasonic-assisted CO₂ absorption system and conventional packed bed columns. Data from the process simulation was also used to estimate the operating expenditure (OPEX) for 20 years of operation. Finally, the Unit Technical Cost (UTC) was estimated to determine the economic feasibility of the ultrasonic absorber as compared with the conventional packed bed column.

2. Experimental Testing

2.1. Material

In this study, MDEA (purchased from Revlogi Materials, Puchong, Malaysia) and PZ (from Sigma Aldrich, Petaling Jaya, Malaysia) were mixed into a concentration of 46 wt% (39 wt% MDEA, 7 wt% PZ); the balance was distilled water and loaded with CO₂ through direct bubbling (to achieve 0.2 mol CO₂/mol amine loading). This mixture was used as the solvent for the ultrasonic-assisted CO₂ absorption process. The feed gas was prepared by mixing the pure CO₂ gas (supplied by Air Product, Kuala Lumpur, Malaysia) with pure nitrogen (N₂) gas (supplied by Air Product, Kuala Lumpur, Malaysia) based on the volumetric flow rate to meet the target composition of 25 vol% CO₂ and 75 vol% N₂. This mixture was used to replicate the composition of natural gas. Given that N₂ is an inert gas with lower solubility than CO₂, which is similar to methane (CH₄), substituting the flammable gas CH₄ with N₂ will have no discernible impact on the absorption performance [38,39].

2.2. Experimental Setup

An integrated pilot plant consisting of an ultrasonic-assisted absorption and solvent regeneration system was developed to study the performance of a continuous ultrasonic-assisted absorption process for the removal of CO₂ at various operating conditions. The schematic diagram and the process description were described in our previous paper [40]. The absorption process was conducted at 60 barg pressure and 76 °C temperature, and the solvent regeneration was performed at 1 barg pressure and 100 °C temperature.

2.3. Experimental Procedure and Analysis

Experimental tests were conducted to determine the effect of operating conditions such as gas flow rate, liquid flow rate, and ultrasonic power on the ultrasonic-assisted CO₂ absorption performance. The optimized operating conditions were selected based on the CO₂ outlet concentration (mol%), liquid-to-gas ratio (L/G) (gal/lbmol), mass transfer coefficient (K_Ga) (mol/m³.s.Pa), ultrasonic absorber effective volume (m³), and ultrasonic absorber power consumption (MW). CO₂ outlet concentration was measured using the infrared (IR) analyzer, and L/G and K_Ga were determined based on calculations as explained in our previous paper [40]. The ultrasonic absorber’s effective volume and power consumption were numerically determined and further described in Section 3.3 and Section 3.4.

Table 1. Operating conditions for experimental study.

Run	Parameters
	Gas Flow Rate (SLPM)	Liquid Flow Rate (LPM)	Ultrasonic Power (V)
1	20	0.2	30
2	17	0.2	30
3	15	0.2	30
4	17	0.2	25
5	20	0.3	30
6	20	0.3	25
7	20	0.4	30
8	20	0.2	25
9	20	0.4	25

provides the testing conditions for the experimental studies.

The titration method was used to determine the amine concentration and loading. For amine concentration determination, the samples were titrated with 0.5 N hydrochloric acid (HCl) [41]. 95 mL of distilled water was mixed with 5 g of amine sample and stirred at 400 rpm using the magnetic stirrer. The pH of the solution was determined using the pH meter (HANNA HI8424 Portable pH meter). The mixture was subsequently titrated using 0.5 N HCl until it reached a pH of 4.5. The weight of the amine sample, the pH of the solution before and after titration, and the volume of 0.5 N HCl solution used in the titration were recorded. The concentration of amine solution in wt% was calculated using the formula [41]:

$$\left(\frac{V_{HCl}\times N_{HCl}\times 9.102}{W_s}\right)=wt\% amine$$

(1)

where ${\mathrm{V}}_{\mathrm{HCl}}$ (mL) was the volume of HCl used to titrate the sample, ${\mathrm{N}}_{\mathrm{HCl}}$ was the normality of the HCl solution, and ${\mathrm{W}}_{\mathrm{s}}$ (g) is the weight of the sample.

For amine loading determination, the amine samples were titrated with 0.5 N potassium hydroxide (KOH) [41]. First, 125 mL of methanol was measured, and its pH was adjusted to 11.2 by adding a few drops of 0.5 N KOH. Furthermore, 20 g of the amine sample was weighed, mixed with the pH-adjusted methanol solution, and stirred at 400 rpm using the magnetic stirrer. The pH of the solution was determined using the pH meter (HANNA HI8424 Portable pH meter). The solution was then titrated with 0.5 N KOH until the pH of the solution returned to 11.2. The weight of the amine sample, the pH of the mixture before and after titration, and the volume of 0.5 N KOH used in the titration were recorded. The concentration (wt%) of acid gas in the amine solution was determined using the formula [41]:

$$\left(\frac{V_{KOH}}{W_s}-\frac{V_{KOH,f}}{W_{s,f}}\right)\times N_{KOH}\times 4.4=wt\% acid gas$$

(2)

where ${\mathrm{V}}_{\mathrm{KOH}}$ (mL) was the volume of KOH used to titrate the sample, ${\mathrm{V}}_{\mathrm{KOH},\mathrm{f}}$ (mL) was the volume of KOH used to titrate fresh solvent, ${\mathrm{W}}_{\mathrm{s},\mathrm{f}}$ (g) is the weight of fresh solvent, and ${\mathrm{N}}_{\mathrm{KOH}}$ is the normality of the KOH solution.

The acid gas loading (mol CO₂/mol amine) was calculated based on amine, and the acid gas concentration was determined using Equations (1) and (2):

$$\left(\frac{wt\% acid gas\times 2.068}{wt\% amine}\right)=Acid gas loading$$

(3)

3. Numerical Modeling of The Ultrasonic Absorber

3.1. Kinetic Reactions of CO₂ Absorption into PZ + MDEA + Water Blended Solvent

The absorption rate of CO₂ into the aqueous amine solvent mass transfer mechanism is represented using a rate-based steady-state model [42,43]. The main reactions that occur during CO₂ absorption into MDEA + PZ + water blended solvent include carbamate formation, bicarbamate formation, and MDEA-catalyzed hydration, as listed in R1–R5 in

Table 2. Reactions involved during CO₂ absorption into PZ + MDEA + water solvent.

No	Reaction Name	Reaction
R1	MDEA catalyzed hydration	${\mathrm{CO}}_2+\mathrm{MDEA}+{\mathrm{H}}_2\mathrm{O}\stackrel{}{\leftrightarrow }{ \mathrm{MDEAH}}^{+}+{\mathrm{HCO}}_3^{-}$
R2	Carbamate formation with PZ	${\mathrm{CO}}_2+\mathrm{PZ}+{\mathrm{H}}_2\mathrm{O}\stackrel{}{\leftrightarrow }{\mathrm{PZCOO}}^{-}+{\mathrm{H}}_3{\mathrm{O}}^{+}$
R3	Bicarbamate formation with PZ	${\mathrm{CO}}_2+{\mathrm{PZCOO}}^{-}+{\mathrm{H}}_2\mathrm{O}\stackrel{}{\leftrightarrow }\mathrm{PZ}{\left({\mathrm{COO}}^{-}\right)}_2+{\mathrm{H}}_3{\mathrm{O}}^{+}$
R4	PZ regeneration reaction	${\mathrm{PZCOO}}^{-}+{\mathrm{H}}_2\mathrm{O}+\mathrm{MDEA}\stackrel{}{\leftrightarrow }\mathrm{PZ}+{\mathrm{HCO}}_3^{-}+{\mathrm{MDEAH}}^{+}$

[5,14,43].

R1 in Table 2 shows the reaction of CO₂ with tertiary alkanolamines (MDEA) proposed by Donaldson and Nguyen [44]. This reaction mechanism entails the base-catalyzed hydration of CO₂. The mechanism suggests that tertiary amines cannot react directly with CO₂. In support of this concept, Versteeg and Van Swaaij (1988) [45] conducted a study on the absorption of CO₂ into non-aqueous (ethanol) solutions of MDEA and determined that solely physical absorption takes place in non-aqueous tertiary alkanolamine systems. Their findings reinforce the validity of the R1 mechanism.

PZ can react rapidly with CO₂ to form carbamate and bicarbamate through R2 and R3. Both reaction rates are much faster than R1; therefore, the main reactions during the CO₂ absorption process are the carbamate and bicarbamate formations [14]. PZ also can transfer the CO₂ to MDEA as a homogeneous activator through the PZ regeneration mechanism, as stated in R4 [14,15]. The ability of PZ to regenerate in the bulk solution in the presence of MDEA as a proton acceptor will help to maintain the absorption rate in the MDEA + PZ + Water blended solvent at a moderate level for a prolonged period, which is much higher as compared with MDEA + water or PZ + water solvent [14,16].

The chemical absorption of CO₂ into MDEA+PZ blended solvent can be depicted as a process involving gas absorption coupled with two parallel rapid pseudo-first-order reversible reactions [16,46]. The overall reaction rate is expressed in terms of the molar concentration of CO₂ and MDEA+PZ, as suggested by Xu et al. (1992) [16]:

$$r_{ov}=\left(k_{2,MDEA}{C}_{MDEA}+k_{2,PZ}{C}_{PZ}\right)\left[{CO}_2\right]$$

(4)

where ${\mathrm{C}}_{\mathrm{MDEA}}$ and ${\mathrm{C}}_{\mathrm{PZ}}$ was the free concentration of MDEA and PZ, respectively, and ${\mathrm{k}}_{2,\mathrm{M}\mathrm{D}\mathrm{E}\mathrm{A}}$ and ${\mathrm{k}}_{2,\mathrm{P}\mathrm{Z}}$ was the second-order rate constant for MDEA and PZ, respectively. However, in the bulk solution, it is difficult to measure the concentration of MDEA and PZ separately. Since the concentration of PZ in the blended solvent is minimal as compared with MDEA and the reaction of PZ to form carbamate and bicarbamate is faster as compared with the PZ regeneration mechanism [47], only the free concentration of MDEA was considered for the reaction rate constant calculation. In this case, the overall reaction rate constant, ${\mathrm{k}}_{\mathrm{O}\mathrm{V}}$, was simplified by using the coefficient kinetic constant, ${\mathrm{k}}_{2,\mathrm{M}\mathrm{D}\mathrm{E}\mathrm{A}}$ as follows:

$$r_{ov}=k_{ov}\left[{\mathit{CO}}_2\right]$$

(5)

$$k_{ov}=k_{2,MDEA}{C}_{MDEA}$$

(6)

The reaction rate constant for MDEA, ${\mathrm{k}}_{2,\mathrm{M}\mathrm{D}\mathrm{E}\mathrm{A}}$ (m³/kmol.s), was calculated based on the equation given by Haimour et al. (1987) [48]:

$$k_{2,MDEA}=8.741\times {10}^{12}exp\left(-8625/T\right)$$

(7)

The $C_{\mathrm{MDEA} }$(mol/L) was determined using the log-mean average of the free concentration of MDEA at the liquid inlet and outlet of each segment. This value was assumed to be constant for every stage in the ultrasonic absorber since the liquid flows in parallel mode to each of the stages:

$$C_{MDEA}=\frac{\left(C_{MDEA, in}-C_{MDEA,out}\right)}{\ln \left(\frac{C_{MDEA, in}}{C_{MDEA,out}}\right)}$$

(8)

3.2. Modeling of Ultrasonic CO₂ Absorption

The mass transfer between the gas and liquid phases in the ultrasonic absorber is described based on the two-film theory. The transport of CO₂ species begins with its diffusion from the bulk gas phase to the gas-liquid interface through the gas film. At this interface, the CO₂ absorption reaction takes place, and the reaction products then diffuse into the bulk liquid through the liquid film. These reactions can be classified into various kinetic regimes, which range from instantaneous, fast, intermediate, slow, or infinitely slow reactions [43].

The two-film theory considers equilibrium at the gas-liquid interphase, and the mass transfer resistance between the gas and liquid phases is added to get the overall resistance [49]. The overall mass transfer resistance of the CO₂ absorption process can be estimated using the resistance in series (RIS) model [43,50,51]:

$$\frac{1}{K_{G}a}=\frac{1}{k_g{a}_e}+\frac{k_l{a}_{e}E}{H_{C{O}_2}}$$

(9)

where ${\mathrm{K}}_{\mathrm{G}}\mathrm{a}$ (mol/m³.s.Pa) is the overall mass transfer coefficient, ${\mathrm{k}}_{\mathrm{g}}{\mathrm{a}}_{\mathrm{e}}$ (1/s) is the gas phase mass transfer coefficient, ${\mathrm{k}}_{\mathrm{l}}{\mathrm{a}}_{\mathrm{e}}$ (1/s) is the liquid phase mass transfer coefficient, ${\mathrm{H}}_{\mathrm{C}\mathrm{O}2}$ (Pa.m³/mol) is the Henry’s law constant, and ${\mathrm{E}}_{ }$ is the chemical enhancement factor of aMDEA. For the CO₂-(MDEA+PZ) reactions, it is assumed that the reactions are fast pseudo-first-order reversible reactions occurring within the liquid film only [16,46]. In this case, the CO₂ absorption into aMDEA solvent was considered liquid-film control. Therefore, the gas transport resistance has a negligible effect on ${\mathrm{K}}_{\mathrm{g}}\mathrm{a}$. The overall mass transfer coefficient was determined by Equation (10) below [50]:

$$K_{G}a=\frac{k_l{a}_{e}E}{H_{C{O}_2}}$$

(10)

The overall CO₂ absorption rate at each segment can be expressed as follows:

$$N_{CO2}=K_g{a}_{ }\left(P_{CO2}-P_{CO2}^{ *}\right)$$

(11)

where ${\mathrm{P}}_{\mathrm{C}\mathrm{O}2} \left(\mathrm{Pa}\right)$ was the CO₂ partial pressure and ${\mathrm{P}}_{\mathrm{C}\mathrm{O}2}^{ *}$ was the equilibrium CO₂ partial pressure. Since the kinetic of the reaction was fast, ${\mathrm{P}}_{\mathrm{C}\mathrm{O}2}^{ *}$ is negligible [43,52,53]. Combining Equations (10) and (11) will define the CO₂ absorption rate at each segment as:

$$N_{CO2}=\frac{k_l{a}_{e}E}{H_{CO2}}{P}_{CO2}$$

(12)

The ${\mathrm{P}}_{\mathrm{C}\mathrm{O}2}$ was determined using the log-mean average of CO₂ partial pressure at the inlet and outlet of each stage, $\mathrm{i}$ [5]:

$$P_{{\mathit{CO}}_2,i}=\frac{\left(P_{C{O}_2,i, in}-P_{C{O}_{2,}i,out}\right)}{\ln \left(\frac{P_{C{O}_2,i, in}}{P_{C{O}_{2,}i,out}}\right)}$$

(13)

The CO₂ mass transfer enhanced by the absorption reactions in the liquid phase is defined by using the enhancement factor ($\mathrm{E}$), which is the ratio of the absorption rate with and without the chemical reactions [5,42,46]. The enhancement factor, $\mathrm{E}$, was determined using the equation that was introduced by Wellek et al. (1978) [54], as shown in Equation (14). $\mathrm{E}$ was dependent on the Hatta number (Ha) and infinite enhancement (${\mathrm{E}}_{\mathrm{i}\mathrm{n}\mathrm{f}}$).

$$E=1+\frac{1}{{\left[{\left(\frac{1}{E_{inf}-1}\right)}^{1.35}+{\left(\frac{1}{E_1-1}\right)}^{1.35}\right]}^{\frac{1}{1.35}}}$$

(14)

where,

$$E_{inf}=1+\frac{ D_{MDEA}{C}_{MDEA}}{b_{MDEA}{D}_{CO2l}{C}_{CO2i}}$$

(15)

$$E_1=\frac{Ha}{\tan \mathrm{h}\left(Ha\right)}$$

(16)

$$Ha=\frac{\sqrt{D_{CO2l }\left(k_{OV}\right)}}{k_l^o}$$

(17)

where ${\mathrm{D}}_{\mathrm{MDEA}}$ (m²/s) was the molecular diffusivity of amine in the liquid, which was 0.5 m²/s in this study. $\mathrm{b}$ was the stoichiometric factor of the reaction, which was 1, ${\mathrm{D}}_{\mathrm{C}\mathrm{O}2\mathrm{l} }$(m²/s) was the molecular diffusivity of CO₂ in the liquid, which was 9.77 × 10⁻⁹ m²/s, ${\mathrm{C}}_{\mathrm{C}\mathrm{O}2\mathrm{i}}$ was the CO₂ molar concentration at the interphase, $\mathrm{Ha}$ was the Hatta number, ${\mathrm{k}}_{\mathrm{O}\mathrm{V}}$ was the overall reaction rate constant given by Equations (6)–(8), and ${\mathrm{k}}_{\mathrm{l}}^{\mathrm{o}}$ was the liquid physical mass transfer coefficient. The ${\mathrm{k}}_{\mathrm{l}}^{\mathrm{o}}$ was determined based on the experimental study conducted by Tay et al. (2016) [29]. They performed the ultrasonic-assisted physical CO₂ absorption into the water at high pressure, and the ${\mathrm{k}}_{\mathrm{l}}^{\mathrm{o}}$ based on their study was 0.014 m/s. The liquid phase mass transfer coefficient ${\mathrm{k}}_{\mathrm{l}}{\mathrm{a}}_{\mathrm{e}}$ for the ultrasonic-assisted CO₂ absorption process into MDEA+PZ solvent was determined from the K_Ga value of the experimental testing using Equation (10).

3.3. Modeling of the Ultrasonic Absorber Effective Volume

The model was developed to determine the effective volume of the ultrasonic absorber based on the mass balance method with the following assumptions:

• The operation is in a steady state.
• The fast absorption reactions occur in the liquid film at the gas-liquid interface.
• The liquid flow rate is constant throughout the absorber.
• The total pressure in the absorber is constant.
• Heat loss to the surroundings is negligible.
• Vaporization of water and MDEA+PZ is not considered in the mass conservation equation.
• The reaction of hydrocarbon and MDEA+PZ is ignored.

Using the input parameters from experimental studies, such as the liquid mass transfer coefficient (k_la_e), K_Ga, and L/G, the model was used to predict the effective volume of the ultrasonic absorber.

The CO₂ concentration in the gas phase along the height of the ultrasonic absorber was determined based on the steady-state one-dimensional mass conservation equation [43]:

$$\frac{d{N}_{C{O}_2}}{dz}=\frac{d\left(G{Y}_{C{O}_2}\right)}{dz}=N_{{\mathit{CO}}_2}$$

(18)

where G was the total gas flow rate per unit cross-sectional area of the ultrasonic absorber, ${\mathrm{Y}}_{{\mathit{CO}}_2}$ was the mol ratio of CO₂ in the gas phase, ${\mathrm{N}}_{{\mathrm{CO}}_2}$ was the CO₂ absorption rate at each stage, and $\mathrm{d}\mathrm{z}$ was the incremental height of the ultrasonic absorber from the bottom to the top. Figure 2 illustrates the schematic diagram of the ultrasonic absorber in the infinitesimal element for mass balance.

The total height of the ultrasonic absorber can be calculated using the following equation:

$$z={{\displaystyle \int }}_{y2}^{y1}\frac{Gdy}{K_{G}a{P}_T\left(y_{CO2}-y_{CO2}{}^{*}\right)}$$

(19)

where ${\mathrm{y}}_{\mathrm{C}\mathrm{O}2}$ was the CO₂ mole fraction in the gas phase, ${\mathrm{y}}_{\mathrm{C}\mathrm{O}2}{}^{*}$ was the equilibrium molar fraction, and ${\mathrm{P}}_{\mathrm{T}}$ was the total pressure. The CO₂ concentration profile at different heights of the ultrasonic absorber can be determined from the mass balance based on the CO₂ absorption rate. The total height required to achieve the target CO₂ concentration at the product gas was computed by the iteration method. Figure 3 shows the simplified flowchart of the ultrasonic absorber model to determine the ultrasonic absorber height. The model was solved by calculating the chemical enhancement factor (E) and absorption rate (N_CO2) at each segment, as explained in Section 3.2. The CO₂ composition for each segment was calculated from the MDEA+PZ CO₂ loading at the inlet and outlet of the segment.

Once the height of the ultrasonic absorber has been numerically determined, the effective volume can be calculated using the following equation:

$$V_{eff}=\frac{\pi D^2}{4}zN$$

(20)

where $\mathrm{D}$ (m) was the ultrasonic absorber internal diameter (ID) and $\mathrm{N}$ was the number of ultrasonic absorber modules. Due to fabrication constraints, the ultrasonic absorber ID was limited to a maximum of 1.5 m.

3.4. Determination of Ultrasonic Absorber Energy Consumption

The ultrasonic absorber energy consumption was estimated based on the ultrasound intensity obtained from the experimental studies:

$$U_I=\frac{{\left(P_{US}\right)}^2}{1000R{V}_R}$$

(21)

where ${\mathrm{U}}_{\mathrm{I}}$ was the ultrasound intensity (kW/m³), ${\mathrm{P}}_{\mathrm{U}\mathrm{S}}$ was the ultrasound power (V), $\mathrm{R}$ was the power supply circuit resistance (Ω), and ${\mathrm{V}}_{\mathrm{R}}$ was the ultrasonic absorber volume (m³). In this study, the circuit resistance was 8 Ω and the ultrasonic absorber volume was 6.70 × 10⁻⁴ m³. Maintaining consistent ultrasound intensity is imperative during technology scale-up, as the performance of the ultrasonic absorber is highly dependent on this critical parameter.

The ultrasonic absorber energy consumption can be determined using:

$$E_{US}=\frac{U_I\times V_{eff}}{1000}$$

(22)

where ${\mathrm{E}}_{\mathrm{U}\mathrm{S}}$ was the ultrasonic absorber energy consumption (MW).

4. Process Simulation and Economic Analysis

Economic analysis was carried out to evaluate the potential of ultrasonic-assisted CO₂ absorption technology against conventional packed columns. Process simulation was carried out using Aspen HYSYS V10 software to estimate the CAPEX and OPEX for both technologies. The economic evaluation was conducted by activating the costing engine in the Aspen HYSYS software. By activating the economic module, the process simulation results were automatically transferred to the Aspen Capital Cost Estimator (ACCE) for further mapping of unit operations to equipment and equipment sizing using default-assigned mapping and sizing algorithms.

4.1. Process Simulation

The process simulation for CO₂ absorption was conducted for two (2) cases. The first case uses the conventional packed column as the acid gas removal unit (AGRU), and the second uses the ultrasonic absorber to replace the AGRU. The case study for process simulation was based on the typical offshore natural gas sweetening process facility that contains 19.22 mol% of CO₂ in the feed gas stream with a target removal efficiency of 83.4% for bulk CO₂ removal. Detailed information on this case study is listed in

Table 3. Key specification of the selected case study.

Feed Gas	Gas Flow Rate	10,856 kmol/h @ 218 MMscfd
	Temperature	35 °C
	Pressure	59.8 barg
	Composition	19.22 mol% CO2 0.02 mol% H2S 0.06 mol% H2O 80.7 mol% Light and heavy hydrocarbon
	Gas Flow Rate	10,856 kmol/h @ 218 MMscfd
	Temperature	35 °C
	Pressure	59.8 barg
Product Gas	Temperature	86 °C
	Pressure	58.9 barg
	Composition	3.2% CO2 27 ppm H2S
Solvent	Composition	35 wt% MDEA, 6 wt% PZ, 59 wt% water
	Lean Amine Loading	0.2 mol/mol
	Rich Amine Loading	0.36–0.39 mol/mol
Ultrasonic Absorber Properties	No of Modules	10
	Gas Flow rate to each module	21.8 MMscfd

.

The same feed gas and product gas specifications are used for the packed column and ultrasonic absorber process simulations. The performance of the AGRU unit was simulated using the Amine property package. The solvent circulation rate was determined based on the L/G. The L/G for the conventional packed column was obtained from the heat and material balance of the case study process plant, which was 193 gal/lbmol CO₂ removed. For the ultrasonic absorber, the L/G was determined from the experimental run. In the process simulation, the equipment installed weight and cost were determined, together with the total energy from the pumps, heater, and cooler in the overall acid gas removal process. Other information that was obtained from the process simulation includes the total amount of CO₂ captured, the total amount of solvent, and the water top-up in the amine regeneration process. This information would be utilized to estimate the OPEX.

The process flow diagram for the process simulation is shown in Figure 4. The process consists of three main unit operations, which are the AGRU (packed column or ultrasonic absorber), high-pressure (HP) flash vessel, and low-pressure (LP) flash vessel. The acid gas absorption process occurs at the AGRU to remove the CO₂ in the feed gas from 19.22% to 3.2% and other components as provided in Table 2. This absorption process occurs at high pressure (59.8 barg), and the pressure drop across the AGRU was assumed to be less than 1 bar. The rich amine solvent leaving the AGRU was sent to the HP flash vessel and Coalescer operating at 8–9 barg to recover the hydrocarbon loss. The rich amine was regenerated by heating the solvent to 90–119 °C to release the acid gas from the amine at the LP Flash vessel operating at 1 barg. The regeneration temperature was adjusted to meet the target regenerated lean amine of 0.2 mol CO₂/mol amine loading. The regenerated amine was cooled down using cooling water in a shell and tube heat exchanger and recycled back to the AGRU. Since the ultrasonic absorber unit was not readily available in the Aspen HYSYS software, the efficiency of the absorption column unit, including the number of trays, was tuned to match the ultrasonic absorber’s experimental performance.

4.2. CAPEX Estimation

The installed cost and weight for all unit operations in the process simulation were based on the Icarus technology, except for the AGRU (packed column and ultrasonic absorber). The size of the conventional packed column was obtained from the absorber column data sheet of the case study.

Table 4. Dimension of conventional packed column [55].

Dimension	Value
Inner diameter (ID)	4.9 m
Height	32.6 m
Volume	614.8 m3
No. of unit	1
Installed weight	1210.3 tonne

summarizes the details of the packed column.

For the ultrasonic absorber, the effective volume was determined numerically, as explained in Section 2.2. The total volume was assumed to be 30% more than the calculated effective volume as a result of contingencies. The ultrasonic absorber weight was estimated based on a typical column density of 2.04 tonne/m^3, and the installed weight was assumed to be 30% more than the equipment weight.

The CAPEX for the CO₂ absorption process was the sum of all equipment installed costs, including the structure cost for offshore operations, with a 30% contingency. For the AGRU, the equipment cost was estimated based on a commercial absorber column price in 1999, and the value is updated to the year 2021 using the Chemical Engineering Plant Cost Index (CEPCI), where [56]:

$$Cost{ }_{Column, 2021}=Cos{t}_{Column, 1999}\times \frac{CEPC{I}_{2021}}{CEPC{I}_{1999}}$$

(23)

The cost index for 1999 and 2021 was 390.6 and 750, respectively [57]. The cost of the AGRU was then calculated using the cost-capacity equation [58]:

$$Cos{t}_{AGRU}=Cos{t}_{Column,2021}{\left(\frac{Q_2}{Q_1}\right)}^x$$

(24)

where ${\mathrm{Q}}_1\left({\mathrm{m}}^3\right)$was the capacity of the commercial absorber column and ${\mathrm{Q}}_2 \left({\mathrm{m}}^3\right)$ was the capacity of AGRU, for which the cost was to be determined in this study. $\mathrm{x}$ defines the relationship between the capacities, where in this study the value was 0.6. This value indicates that larger capacity was less costly due to economies of scale.

For the ultrasonic absorber equipment cost, the cost of the ultrasonic transducers was added to the cost of the AGRU column. Due to confidentiality, the number and unit price of the ultrasonic transducers will not be disclosed. The installed cost for the AGRU was assumed to be 30% higher than the equipment cost due to additional engineering, insurance, and administration costs [56].

The structure cost for the offshore operation was estimated based on the total equipment installed weight, including the piping, instruments, and solvent weight. Piping and instrument weight were assumed to be 50% of the equipment installed weight. The total solvent weight was estimated by assuming that 50% of the vessel’s volume was filled with liquid. An additional 10% of the solvent weight was also included for the solvent weight in the piping during operation. The structure cost was calculated based on a typical commercial cost for a jacketed leg platform, which was USD 36 k/tonne.

4.3. OPEX Estimation

The OPEX for the CO₂ absorption process, which consists of electricity cost, initial solvent cost, solvent top-up, water top-up, maintenance cost, and transducer change-out cost (only for ultrasonic absorbers), was calculated yearly. The OPEX was estimated for the total lifetime of the plant, which was assumed to be 20 years, and the total annual hours of operation for the plant in this study was 8000 h/year [11,56]. The maintenance cost was assumed to be 5% of the total equipment installed cost.

The electricity cost was estimated from the total energy consumption for the CO₂ absorption process obtained from the Aspen HYSYS process simulation. The electricity generated by the gas turbine was assumed to power the pump, heater, and ultrasonic absorber. The energy required for the plant operation was converted to power consumption costs by multiplying the fuel gas consumption rate by the sales gas price of 3 USD/MMBTU.

Another important expenditure for the plant is the initial cost of the solvent and the annual solvent top-up cost. The initial solvent cost was estimated by multiplying the total solvent weight with the commercial solvent price of 4350 USD/tonne. Over the course of continuous operation, the removal efficiency of the plant will decrease due to solvent degradation, the formation of heat-stable salts, and the accumulation of contaminants. Yearly amine change-out at a rate of 4% from its initial cost was recommended to maintain the CO₂ removal performance. Besides, water top-up was also required to maintain the solvent concentration and viscosity at the optimum condition. Some of the water might evaporate during the solvent regeneration process and need to be replaced. The rate of water top-up was determined from the HYSIS process simulation, and the yearly cost was estimated based on the commercial demineralized water cost of RM10.10/m³.

For the ultrasonic absorber, there was another additional cost to be considered, which was the transducer change-out cost. Over time, some transducers, springs, and o-rings might wear and tear. Therefore, scheduled maintenance and replacements must be conducted to maintain the transducer’s performance. Due to this, a yearly change-out at the rate of 7.5% from the initial cost of the transducer was proposed starting in the 2nd year of the operation.

4.4. Unit Technical Cost (UTC) Calculation

Unit technical cost (UTC) was defined as the cost incurred for removing a ton of CO₂ based on 20 years of operation. The amount of CO₂ removed was determined from the process simulation. The total cost was inclusive of CAPEX and OPEX. The UTC can be calculated as follows [51,59]:

$$UTC=\frac{\left(CAPEX+OPEX\right)}{Tonne of {\mathit{CO}}_{2}Removed}$$

(25)

5. Results and Discussions

5.1. Effect of Ultrasonic Power

The effect of ultrasonic irradiation power on ultrasonic absorber performance is shown in Figure 5. The experimental studies were conducted at 25 V and 30 V ultrasonic power using a 0.2 LPM liquid flow rate at 17 and 20 SLPM gas flow rate. In general, the ultrasonic absorber performance at 30 V ultrasonic irradiation power was superior to that at 25 V. The CO₂ outlet and L/G were about 10% lower as the ultrasonic irradiation power increased from 25 V to 30 V, while the K_Ga increased by about 5%.

Ultrasonic power can enhance the mass transfer of CO₂ from the gas phase into the liquid phase by intensifying the physical interaction between the CO₂ molecules and the aMDEA solvent [33]. The intensified sonophysical enhancement, such as acoustic streaming and acoustic fountains, leads to better mixing and more interfacial area for mass transfer to occur [27,29,40]. The acoustic streaming force and fountain flow rate are directly proportional to the ultrasonic power; thus, the CO₂ absorption efficiency increases as the ultrasonic power increases. Furthermore, acoustic cavitation generates localized hotspots and high-pressure zones, creating favorable conditions for the CO₂ absorption reaction with aMDEA. The increased temperature and pressure can enhance the reaction rate and promote carbamate formation, the chemical complex produced from the chemical reaction between CO₂ and aMDEA solvent. This can lead to faster absorption kinetics and improved overall absorption efficiency.

Similar enhancement trends are observed at two gas flow rates of 17 and 20 SLPM. However, the performance enhancement at 17 SLPM was higher than at 20 SLPM. Even though a higher gas flow rate introduced more CO₂ molecules into the ultrasonic absorber, which explained the reduced L/G at a higher gas flow rate due to more CO₂ removed (refer to Figure 5a), the reaction rate between aMDEA and CO₂ in the feed gas was not fast enough, and the sonochemistry effect from the high-frequency ultrasonic irradiation was not able to significantly enhance the chemical reaction. Therefore, the CO₂ absorption reaction is limited by the gas residence time in the ultrasonic absorber. Consequently, the target CO₂ outlet of 6.5 mol% could not be achieved at 20 SLPM even at 30 V ultrasonic power (refer to Figure 5b), and K_Ga was slightly reduced (refer to Figure 5c).

5.2. Effect of Liquid Flow Rate

The effect of liquid flow rate on ultrasonic absorber performance is demonstrated in Figure 6. The experimental testing was conducted at 25 V and 30 V ultrasonic power using a 20 SLPM feed gas flow rate. The liquid flow rate was varied from 0.2–0.4 LPM. From the graphs, it is observed that the liquid side mass transfer resistance was not significant in the ultrasonic absorber. The increased liquid flow rate did not significantly enhance the overall CO₂ absorption performance. The increased liquid flow rate introduces more amine molecules for the absorption process, which should increase the solvent absorption capacity. However, the opposite trend was observed as the liquid flow rate increased from 0.2 to 0.4 LPM in the ultrasonic absorber. The discrepancy was probably because the CO₂ absorption performance of the ultrasonic absorber was highly dependent on the reaction rate between the aMDEA and CO₂. As the liquid flow rate increases, the liquid retention time in the ultrasonic absorber reduces and limits the reaction time for CO₂ absorption into the aMDEA solvent.

Similar to the previous section, the increase in ultrasonic power from 25 V to 30 V can further enhance the CO₂ absorption process, resulting in a lower CO₂ outlet concentration and a higher K_Ga value (refer to Figure 6a,b). However, the improvement in L/G was insignificant, at less than 5% on average (refer to Figure 6c). Since lower L/G was preferred as it contributes to lower solvent circulation rates, lower solvent pumping energy, and heater power consumption for amine regeneration, maintaining the liquid flow rate at 0.2 LPM was more favorable.

5.3. Effect of Gas Flow Rate

The effect of gas flow rate on ultrasonic absorber performance is illustrated in Figure 7. The experimental runs were conducted using 30 V ultrasonic power and a 0.2 LPM liquid flow rate. The gas flow rate varied from 15 to 20 SLPM. Increasing the gas flow rate from 15 to 17 SLPM introduces more CO₂ molecules, enhancing the rate at which CO₂ molecules contact the aMDEA solvent and promoting faster absorption that leads to higher CO₂ removal efficiencies. This explains the increase of K_Ga (refer to Figure 7a) and the reduction of L/G (refer to Figure 7b).

However, the gas flow rate also affects the contact time between the gas and the solvent. If the gas flow rate is higher than the optimal condition, it tends to decrease the gas residence time in the absorber and reduce the CO₂ molecules to be absorbed into the solvent [52]. Consequently, at lower contact times, the absorption capacity of the solvent may not be fully utilized, resulting in lower CO₂ capture efficiencies, and the target CO₂ outlet of 6.5 mol% was not able to be met as the gas flow rate further increased to 20 SLPM (refer to Figure 7c). The CO₂ outlet increased by 31%, K_Ga was reduced by 2%, and L/G increased by 13% at a 20 SLPM gas flow rate. A similar trend was observed by other researchers for CO₂ absorption using AMP as a chemical solvent [60,61].

Based on these findings, the gas flow rate influences the absorption efficiency of CO₂ into the aMDEA solvent. Balancing the gas flow rate is essential to achieving optimal absorption rates while considering the mass transfer rate and contact time aspects of the process. In this study, the optimum gas flow rate for the ultrasonic absorber was 17 SLPM.

5.4. Prediction of Ultrasonic Absorber Effective Volume and Energy Consumption

The effective volume and energy consumption of the ultrasonic absorber were determined using the numerical modeling approach as described in the earlier section. The model was developed to predict the ultrasonic absorber’s effective volume and energy consumption from the experimental runs. Figure 8 shows the predicted effective volume based on the experimental run performance. From the graphs, it is observed that the ultrasonic absorber effective volume was inversely proportional to the K_Ga obtained from the experimental runs, as explained in Equations (19) and (20) of the developed model. A higher K_Ga value indicates higher absorption efficiency per unit volume, thus a higher CO₂ absorption rate at each segment of the ultrasonic absorber, as explained in Equation (11) [40]. As the absorption efficiency increased, less volume was required to achieve the target CO₂ removal, leading to a more compact ultrasonic absorber size.

The CO₂ absorption efficiency increased as the ultrasonic power increased due to stronger sonophysical and sonochemistry effects to enhance gas-liquid mass transfer. As a result, the effective volume at 17 SLPM and 20 SLPM gas flow rates using 30 V ultrasonic power was about 10% and 8% lower than 25 V, respectively (refer to Figure 8a). Gas flow rate showed the most significant effect on the ultrasonic absorber’s effective volume (refer to Figure 8b). The effective volume was reduced by 15% as the gas flow rate increased from 15 SLMP to 17 SLPM, owing to more CO₂ molecules being introduced and absorbed into the aMDEA solvent, leading to higher K_Ga. Further increase in gas flow rate above 17 SLPM reduced the ultrasonic absorber performance due to the limited retention time for CO₂ absorption reactions. This behavior was similar to increasing the liquid flow rate (refer to Figure 8c). Thus, limiting the liquid flow rate to 0.2 LPM is more beneficial.

Figure 9 shows the predicted energy consumption of the ultrasonic absorber based on the predicted effective volume and ultrasound intensity from the experimental testing. From Figure 9a, even though increasing the ultrasonic power from 25 V to 30 V enhanced the CO₂ absorption performance, this led to a 32% increase in ultrasonic absorber energy consumption. The trade-off between compact size and minimal energy consumption is evident in Figure 8a and Figure 9a, which showcase the predicted effective volume and energy consumption from the model, respectively.

Specifically, at 17 SLPM gas flow rate, the ultrasonic absorber with the smallest effective volume using 30 V of ultrasonic power requires 30% more energy consumption than at 25 V. Conversely, at lower ultrasonic power (25 V), the ultrasonic absorber’s effective volume increased by 10% compared with 30 V due to reduced mass transfer intensification. This significant trade-off becomes apparent solely through the application of numerical modeling, enabling the prediction of effective volume and energy consumption.

Furthermore, implementing high ultrasonic power for the CO₂ absorption process may require specialized equipment and additional costs. Therefore, it is important to consider the scalability and practicality of using high ultrasonic power in large-scale industrial applications. Minimizing the energy consumption for the ultrasonic absorber while maintaining its compact design is necessary for further scale-up and commercialization of the technology.

The effect of gas and liquid flow rates on energy consumption in the ultrasonic absorber closely paralleled their impact on the effective volume (refer to Figure 9b,c). Elevated gas flow rates (exceeding 17 SLPM) and liquid flow rates decreased ultrasonic absorber performance. This decline can be attributed to the constrained retention time available for CO₂ absorption reactions, ultimately resulting in escalated energy consumption.

Table 5. Summary of effective volume and energy consumption.

Run	Parameters			Responses
	Gas Flow Rate (SLPM)	Liquid Flow Rate (LPM)	Ultrasonic Power (V)	Effective Volume (m3)	Energy Consumption (MW)	KGa (×10−6 mol/m3.s.Pa)	L/G (gal/lbmol)
1	20	0.2	30	208.52	35.11	4.75	146.69
2	17	0.2	30	201.45	33.92	4.86	156.35
3	15	0.2	30	236.80	39.87	4.09	181.69
4	17	0.2	25	222.66	26.04	4.40	165.35
5	20	0.3	30	226.19	38.09	4.23	228.79
6	20	0.3	25	254.47	29.76	3.83	242.57
7	20	0.4	30	222.66	37.49	4.43	303.33
8	20	0.2	25	226.19	26.45	4.37	153.40
9	20	0.4	25	243.87	28.52	4.02	313.97

summarizes the responses, including the ultrasonic absorber’s effective volume and energy consumption, for all the experimental runs in this study. Based on this table, the energy consumption for Run 4 is the lowest and deemed the most optimum operating condition for the ultrasonic-assisted CO₂ absorption process in this study. The response based on this run, including the L/G and K_Ga, is further used in the process simulation and economic analysis.

5.5. CAPEX Comparison

Table 6. Installed cost and weight for the packed column and ultrasonic absorber from process simulation.

Equipment	Packed Column		Ultrasonic Absorber
	Installed Cost (USD)	Installed Weight (tonne)	Installed Cost (USD)	Installed Weight (tonne)
Cooler	754,200	111.132	631,500	91.680
Pump A	1,967,600	127.081	1,717,400	108.337
Coalescer	385,900	59.070	364,900	53.669
Pump B	456,400	35.205	401,800	29.883
LP Flash	622,200	76.153	553,200	67.538
Heater	548,500	83.097	479,600	72.275
HP Flash	775,500	117.856	714,900	118.193
AGRU	11,960,000	1210.3	15,079,877.8	512.85
Total	17,470,300	1819.9	19,943,177.8	1054.4

shows the equipment list, installed cost, and weight for the conventional packed column and ultrasonic absorber obtained from the process simulation. This information was used to calculate the CAPEX.

Table 7. CAPEX comparison between packed column and ultrasonic absorber.

	Packed Column	Ultrasonic Absorber
Installed Equipment Cost (mil USD)	17.470	19.94
Structure cost (mil USD)	131.05	78.61
Contingency @ 30% (mil USD)	44.56	29.57
Total CAPEX (mil USD)	193.08	128.12

shows the CAPEX comparison for both the packed column and ultrasonic absorber based on the process simulation. From the CAPEX comparison, it is observed that the ultrasonic absorber process requires 34% less CAPEX as compared with the conventional packed column process. Due to the enhanced mass transfer by ultrasonic irradiation, the ultrasonic absorber exhibits a compact design, resulting in reduced equipment weight. Consequently, this weight reduction contributes to lower structure costs for offshore operations.

5.6. OPEX Comparison

Table 8. Comparison of power consumption cost.

Parameters	Packed Column	Ultrasonic Absorber
Pump (MW)	8.08	6.90
Heater (MW)	107.30	94.14
Absorber (MW)	0.00	26.04
Total Energy (MW)	115.38	127.08
Power Consumption cost (USD/day)	74,880	82,368

compares the power consumption costs for the packed column and ultrasonic absorber. The pump and heater energy requirements for the packed column were much higher as compared with the ultrasonic absorber due to the packed column having a higher solvent circulation rate as compared with the ultrasonic absorber. 12–14% energy savings (from the heater and pump) were obtained by the ultrasonic absorber for having a lower L/G due to higher removal efficiency. However, the ultrasonic absorber requires 26.04 MW of electricity to power up the ultrasonic transducers, compared with the zero-energy requirement for the commercial packings to enhance the gas-liquid mass transfer area. Due to this, the power consumption cost for the ultrasonic absorber was 10% higher than the conventional packed column. The highest energy consumption was required for the heater to regenerate the solvent for both the packed column and ultrasonic absorber.

Table 9. OPEX Comparison between packed column and ultrasonic absorber.

Criteria	Packed Column	Ultrasonic Absorber
Power Consumption (mil USD)	499.20	549.12
Solvent Top-up (mil USD)	7.13	4.71
Demin Water top-up (mil USD)	2.66	2.99
Maintenance and repair (mil USD)	17.47	19.94
Transducer Change-out (mil USD)	0.00	8.65
Total OPEX (mil USD)	526.46	585.42

highlights the OPEX comparison between conventional packed columns and ultrasonic absorbers based on this study. From the table, it is observed that the ultrasonic absorber requires about 11% higher OPEX as compared with the packed column. This is because the ultrasonic absorber incurs additional costs related to power consumption for energizing the ultrasonic transducer and for transducer change-outs. Even though ultrasonic irradiation can enhance the gas-liquid mass transfer that leads to lower CAPEX, this technology requires higher OPEX than the conventional packed column.

5.7. UTC Comparison

Figure 10 and Figure 11 show the total cost distribution for the packed column and ultrasonic absorber, respectively. When analyzing the overall cost distribution, it becomes evident that the highest expense was attributed to power consumption, with the structure cost ranking second for the packed column and ultrasonic absorber process. This shows that UTC is highly affected by overall energy consumption and equipment weight. Reducing energy consumption and equipment weight will greatly improve the UTC of the technology, thus making it more economically feasible for commercialization. The energy consumption of the ultrasonic absorber surpasses that of the packed column due to the additional energy required for powering the ultrasonic transducer, along with the energy needed for the pump and heater. However, the mass transfer enhancement by ultrasonic irradiation significantly reduced the volume and weight of the ultrasonic absorber, making the structure cost lower than the conventional packed column.

Table 10. UTC comparison between packed column and ultrasonic absorber.

Criteria	Packed Column	Ultrasonic Absorber
CAPEX (mil USD)	193.08	128.12
OPEX for 20 years (mil USD)	526.46	583.34
UTC (USD/Tonne CO2)	56.61	54.67

compares UTC between the packed column and the ultrasonic absorber. Despite the ultrasonic absorber having approximately 11% higher OPEX than the packed column, its UTC remains 3% lower than the conventional packed column. This cost advantage is primarily due to the ultrasonic absorber’s compact design, which effectively reduces CAPEX by minimizing structure costs. In this study, the economic analysis clearly indicates the potential for cost savings by replacing the conventional packed column with an ultrasonic absorber for offshore operations. The potential for cost savings can be further maximized by reducing the OPEX of the ultrasonic absorber, making them comparable to those of the packed bed column.

Another commercially used technology for CO₂ capture, especially for offshore operations, is membrane technology [62]. Membrane technology is renowned for its modular and compact design, making it the foremost choice for CO₂ capture in offshore operations where footprint and equipment weight constraints are notably restrictive. The reported UTC for CO₂ capture using membrane technology ranges from 22.76–118.9 USD/ton CO₂ removed depending on the flow configuration in the membrane module and the requirement of sweep gas, vacuum pump, or feed gas compression to enhance the CO₂ removal efficiency [63]. Based on these reported values, the economic potential of solvent-based technology, either using the packed column or an ultrasonic absorber as the contactor, has not yet surpassed that of membrane technology. Nevertheless, the choice of an appropriate CO₂ capture technology for commercial application may also hinge on additional factors, including the CO₂ concentration at the feed gas, feed gas pressure, tolerance for hydrocarbon losses, and the presence of other contaminants in the feed gas.

6. Conclusions

In this work, a numerical model was developed to predict the effective volume and energy consumption of the ultrasonic absorber based on experimental studies at various operating conditions. The effects of ultrasonic power and liquid and gas flow rates were investigated. Findings from the experimental studies and numerical modeling confirmed that Run 4, which operated at 25 V ultrasonic power, 0.2 LPM liquid flow rate, and 17 SLPM gas flow rate, is the most optimum condition for the ultrasonic-assisted CO₂ absorption process because the energy consumption at this condition was the lowest, which was 26.04 MW with an effective volume of 222.66 m³. The economic analysis was conducted to compare the economic feasibility of this technology against the conventional packed bed column.

This technology demonstrates a potential 34% reduction in CAPEX compared with the conventional packed bed column. This is attributed to its ingeniously compact design, resulting in decreased equipment weight and lower structural costs, which is particularly advantageous for offshore operations. While the ultrasonic transducers impose an additional electricity demand, leading to an 11% increase in OPEX relative to the packed column, the overall UTC for the ultrasonic-assisted CO₂ absorption process remains 3% below that of the conventional packed column.

Therefore, it is concluded that there is a potential cost savings in implementing ultrasonic irradiation technology to improve the existing packed column for acid gas removal. To further maximize the economic advantages of this technology, energy optimization, such as heat integration, water and solvent recovery systems, and transducer power system optimization, is recommended for future work.