Carbon Dioxide Gasification of Biochar: A Sustainable Way of Utilizing Captured CO₂ to Mitigate Greenhouse Gas Emission

Abstract

This study proposes CO₂ gasification of biochar as a potential carbon utilization pathway for greenhouse gas emission reduction. It aims to evaluate the effects of CO₂ concentration on carbon and CO₂ conversion and output CO yield. It also performs kinetic analysis, using the volume reaction model, to determine the activation energy and pre-exponential factor. The operating conditions utilized include gasification temperatures of 700, 800, and 900 °C; inlet CO₂ concentrations of 15%, 30%, 45%, and 60% by volume (N₂ balance); and a CO₂ flow rate of 5 L/min. Carbon dioxide gasification of biochar was performed in a fixed bed batch reactor, and the composition of the output gases was analyzed. Increases in the temperature and inlet CO₂ concentration both resulted in an increase in carbon conversion, with the maximum carbon conversion of 57.1% occurring at 900 °C and a 60% inlet CO₂ concentration. The results also showed that CO₂ conversion increased against temperature but decreased with an increasing inlet CO₂ concentration. The maximum CO₂ conversion of 76% was observed at 900 °C and a 15% inlet CO₂ concentration. An activation energy in the range of 109 to 117 kJ/mol and a pre-exponential factor in the range of 63 to 253 s⁻¹ were determined in this study.

1. Introduction

Energy production in the US is largely sourced from fossil fuel (petroleum, natural gas, and coal), nuclear energy, and renewable energy. In 2022, fossil fuel accounted for 79% of the total energy production in the US [1]. The use of fossil fuels leads to the emission of greenhouse gases (GHGs). GHGs include carbon dioxide (CO₂), methane (CH₄), nitrous oxide (N₂O), and industrial gases like hydrofluorocarbons (HFCs), perfluorochemicals (PFCs), sulfur hexafluoride (SF₆), and nitrogen trifluoride (NF₃). In a 2021 report on US emissions, it was seen that GHG emissions totaled 6340 million metric tons (14.0 trillion pounds) of carbon dioxide equivalents [2]. Sustainable goal number 13 states that urgent action must be taken to combat climate change and its impact [3]. In conjunction with this goal is the 2015 Paris agreement [4], which advocates for efforts to be made to limit the temperature rise to 1.5 $°\mathrm{C}$ above pre-industrial levels. In order to achieve sustainability goals and to prevent the negative effects of climate change, decarbonization of all sectors is paramount. In pursuit of this decarbonization agenda, alternative sources of energy like wind, solar, biomass, etc., are being explored. With fast-growing global economies and world populations, however, energy demands continue to increase. This means that fossil fuel will still need to play a major role in meeting the current energy demands. To that end, carbon capture and storage (CCS) technologies have been implemented to reduce CO₂ emissions in the atmosphere.

With the implementation of CCS technologies comes the need to utilize the captured CO₂. Several utilization pathways exist. For example, captured CO₂ is used in curing concrete, producing algae-based products like biofertilizers, and producing carbonated drinks and beverages. Captured CO₂ is also useful in the production of fuels and chemicals. The use of CO₂ to produce fuel is largely implemented in two ways: the direct hydrogenation of CO₂ and indirect production, where CO₂ is converted into an intermediary product and then synthesized. In direct hydrogenation, hydrogen is added to CO₂, without first converting it into an intermediary product, to produce methane, methanol, and other chemicals [5]. The direct hydrogenation pathway, however, is very costly, as CO₂ is not chemically active to react with hydrogen. The indirect pathway, on the other hand, is more attractive seeing that CO₂ is first converted into carbon monoxide (CO), a more chemically active product with multiple uses. While CO can be used to manufacture various organic and inorganic chemicals, the indirect pathway focuses on synthesizing CO and hydrogen in a Fischer–Tropsch (FT) reactor. When CO and H₂ are combined, it is called synthesis gas, usually known as syngas. The FT synthesis of syngas, which is a very well-known process, can be used to produce methanol and various hydrocarbons, including bio-jet fuel, biodiesel, etc.

The main challenge with this indirect pathway is the conversion of CO₂ into CO. Some options exist, like the reverse water–gas shift (RWGS) process, methane reforming, and electrochemical conversion. While the aforementioned approaches are highly energy-intensive, a promising approach is the CO₂ gasification of biochar to produce CO. Biochar is a porous, carbon-rich waste material which can be obtained from either pyrolysis or the gasification of biomass. Pyrolysis-based biochar is superior compared to gasification-based biochar. CO₂ gasification of biochar is a unique approach because it achieves two things simultaneously: carbon emission reduction, through the utilization of captured CO₂, and efficient waste disposal since waste material is the fuel source.

There are several factors that can influence the CO₂ gasification yield, some of which include feedstock type, operating temperature, inlet CO₂ concentration and flow rate, etc. These factors have been studied by various researchers. For example, Sadhwani et al. [6] studied CO₂ gasification using southern pine at temperatures from 700 to 934 $°\mathrm{C}$ and a 100% inlet CO₂ concentration using a fluidized bed gasifier. They reported increasing the CO concentration from 6.0% vol at 700 $°\mathrm{C}$ to 11.3% vol at 934 $°\mathrm{C}$. Shen et al. [7] studied CO₂ gasification using woody biomass at temperatures of 700 and 800 $°\mathrm{C}$ and an inlet CO₂ concentration of 15% CO₂ (air balance) in a small-scale autothermal gasifier. They reported CO concentrations of 20 and 40% vol at 700 and 800 $°\mathrm{C}$, respectively. Cheng et al. [8] performed a numerical study using woodchips at temperatures of 875 to 950 $°\mathrm{C}$ and inlet CO₂ concentrations of 20%, 40%, 60%, and 80% CO₂ (air balance) via the Eulerian method. They reported CO concentrations of 10%, 14%, 18%, and 15.7% vol at 20%, 40%, 60%, and 80% inlet CO₂ concentrations, respectively. Hu et al. [9] performed 100% CO₂ gasification using rice straw at temperatures of 700, 800, 900, and 1000 $°\mathrm{C}$ in a thermogravimetric analyzer (TGA). They reported CO concentrations of 16%, 21%, 40%, and 43% vol at 700, 800, 900, and 1000 $°\mathrm{C}$, respectively and kinetic parameters such as an activation energy of 155.7 kJ/mol and a pre-exponential factor of 1.72 × 10⁵ s⁻¹. Wang et al. [10] studied kinetic analysis of the CO₂ gasification of pine sawdust and wheat straw via the volume reaction model (VRM). They reported activation energies of 140.7 and 163.5 kJ/mol and pre-exponential factors of 2 × 10⁵ and 4.22 × 10⁴ s⁻¹ for pine dust and wheat straw, respectively. Pacioni et al. [11] performed a TGA study on coffee grounds and sawdust via the VRM. They reported activation energies of 185.8 and 211.7 kJ/mol and pre-exponential factor values of 3.32 × 10⁵ and 7.93 × 10⁶ s⁻¹ for coffee grounds and sawdust, respectively. Beagle et al. [12] performed CO₂ gasification of coal and oak using a TGA via the random pore model (RPM). They reported activation energy values of 100.4 and 127.9 kJ/mol and pre-exponential factor values of 319 and 44.9 s⁻¹ for pine dust and wheat straw, respectively.

While numerous studies have been reported, as highlighted above, to understand factors such as the feedstock type and operating temperature, few studies have been reported on understanding the effect of CO₂ concentration on carbon conversion and product yield, which is the focus of this study. Understanding this effect is important because the captured CO₂ from various sources and industries has various CO₂ concentrations. This study adds value to the existing literature by reporting elaborately on the output gas composition and performing a detailed kinetic analysis at the laboratory scale using a fixed bed batch reactor.

2. Materials and Methods

2.1. Materials

Kingsford biochar (Kingsford, Belle, MO, USA) was purchased from a commercial supplier and used as the feedstock for this study. The biochar, which came in large chunks, was further sized and sieved to a particle size of 1 to 3 mm. A small particle size is important to allow high heat and mass transfer as the gasification reaction occurs.

2.2. Feedstock Analysis

2.2.1. Proximate and Ultimate Analysis

To analyze the feedstock (Kingsford biochar), proximate and ultimate analyses were performed. The proximate analysis determined the fixed carbon, volatile matter, ash, and moisture contents in the sample. The ultimate analysis, on the other hand, was used to determine the elemental composition, such as the carbon, hydrogen, nitrogen, oxygen, and sulfur content in the sample. The proximate and ultimate analyses help to determine the physical and chemical properties of the feedstock, thus enabling researchers to predict the quantity of feedstock needed and perform the necessary yield calculations. The proximate and ultimate analyses of the Kingsford biochar sample were performed by Hazen Research Inc. (Golden, CO, USA), and the results are shown in

Table 1. Proximate and ultimate analyses of Kingsford biochar.

Ultimate Analysis (wt.%, daf)					Proximate Analysis (wt. %)				HHV (MJ/kg)
C	H	N	O	S	Volatile Matter (db)	Moisture (wb)	Fixed Carbon (db)	Ash (db)
57.53	2.53	0.31	23.79	0.19	35.74	4.95	46.49	17.77	17.22

.

2.2.2. SEM Analysis

Scanning electron microscopy (SEM) is a technique that uses electrons, as opposed to light, to create images. This occurs by means of a focused beam of electrons scanning the surface of the material. The Phenom™ XL G2 Desktop SEM, purchased from Thermo Fisher Scientific (Waltham, MA, USA), was used for this analysis. To prepare the sample for SEM, a carbon dot was placed on the SEM pin stub, and the biochar sample was placed on the carbon dot surface. The sample was securely fixed to the pin stub by means of aluminum strips and placed in the sample holder. The sample holder was placed in the SEM machine, and the analysis was carried out. The images were taken with magnification ranging from 810× to 5600×, and an energy-dispersive X-ray spectroscopy (EDS) analysis was performed. The results are discussed in Section 3.1.

2.3. Experimental Setup and Procedure

2.3.1. Experimental Setup

The experimental setup is shown in Figure 1. To run the CO₂ gasification experiment, the major apparatus needed include a fixed bed batch reactor, a split furnace, a mass flow controller/meter, impinger-bottle-based glass condensers, a pre-cooler, an electric gas cooler, and a gas analyzer. The fixed bed reactor is a stainless steel, one-inch inner diameter reactor that holds the biochar bed on a wire mesh in the middle of the reactor. The split tube furnace TVS 1200 (Carbolite Gero, Newtown, PA, USA) is used to provide heat to the reactor, alongside a Carbolite Gero 301 temperature controller, with a maximum operating temperature of 1200 °C. The mass flow controller (Model GFC17, Aalborg Instruments, New York, NY, USA) is used to control the flow rate of the supplied gases from the nitrogen and CO₂ gas cylinders. The condenser setup, which included a set of three impinger bottles (500 mL each), U-tube and L-tube adapters, stainless steel clamps, and an insulated coolant reservoir, was purchased from Apex Instruments (Apex, Centennial, CO, USA) and customized in house. A Coleman flip lid cooler (Coleman, Wichita, KS, USA) was used as the pre-cooler. The mass flow meter (Model FMA-1601A, Omega, Norwalk, CT, USA) was used to measure the flow rate of the output gas. The electric gas cooler (Model 2000, NOVA Analytical Systems, New York, NY, USA) was used to provide further cooling and ensure a steady flow of the output gas through the gas analyzer by means of an in-built pump system. The gas analyzer (Model 700 P-4C, NOVA Analytical Systems, New York, NY, USA) was used to analyze the composition of the produced gas, such as CO₂, CO, H₂, and CH₄.

2.3.2. Experimental Design

In this study, the three independent parameters are inlet CO₂ flow rate, gasification temperature, and inlet CO₂ concentration. A CO₂ flow rate of 5 L/min, temperatures of 700, 800, and 900 °C, and inlet CO₂ concentrations of 15%, 30%, 45%, and 60% (N₂ balance) were used in this study. The experiments were run twice for validation purposes, resulting in a total of 24 experiments.

2.3.3. Operating Procedure

Initially, a known quantity of biochar (in this case, 52.5 g) was loaded into the reactor. The biochar sat on the wire mesh support in the middle of the reactor, forming a fixed bed of biochar. The reactor was securely placed in the split tube furnace, and the top and bottom of the reactor were insulated with 2-inch fiber glass to prevent any heat loss. The reactor outlet was connected to the condenser, which was built using three impinger bottles, clamps, U-tubes, and an insulated container. The condenser outlet was connected to the pre-cooler inlet, and the pre-cooler outlet was connected to the mass flow meter inlet. In between the pre-cooler and the mass flow meter is a filter to prevent impurities (particulates) from entering the flow meter. The outlet of the mass flow meter was connected to the inlet of the electric gas cooler, and the outlet of the electric gas cooler was connected to the inlet of the gas analyzer.

Before CO₂ gasification, the biochar goes through a preheating process, where nitrogen is allowed to pass through the biochar for about 30 to 45 min (in total) until the electric furnace attains the set temperature. A bypass connection was installed on the reactor, with an exhaust pipe, in order to remove all the volatile matter without allowing it to pass through the condenser. The valve at the condenser inlet is opened when the gasification experiment is about to start. Once equilibrium temperature is achieved, the nitrogen supply is stopped, and CO₂ gas is introduced to initiate the gasification experiment. As soon as the CO₂ gas supply is introduced, the bypass valve is closed, and the condenser inlet valve is opened. Thus, the produced syngas flows through the condenser to the gas analyzer, where the concentrations of CO₂, CO, H₂, and CH₄ are measured. The concentration of the produced gas is recorded using a DAQ system. The experiment is allowed to run for approximately 30 min after the CO₂ is introduced. After 30 min of operation, the CO₂ gas cylinder is turned off, and the bypass valve is opened. The DAQ system is stopped, all the devices, including the electric gas cooler, gas analyzer, flow meters, etc., are disconnected from power, and the reactor is allowed to cool down for about 3 to 4 h. Once the reactor is cooled, the leftover char is collected, measured, and stored in a Ziploc bag for further analysis.

2.4. Kinetic Analysis

The volume reaction model (VRM) is selected for the kinetic analysis because it is widely used by researchers for biochar gasification. The VRM, also known as the volumetric or homogenous model, does not account for the structural changes in the biochar sample during the gasification reaction. However, it assumes that the reaction occurs at all active sites, which are uniformly distributed across the char particles, both inside and outside [10]. This model is basically a simplification of the gas–solid heterogeneous reaction, as noted by Pacioni et al. [11]. The expression for the gasification reaction rate as predicted by the VRM is shown in Equation (1).

$$\frac{dx}{dt}=k_{VRM}\ast (1-x)$$

(1)

where $\frac{dx}{dt}$ is the gasification reaction rate, $k_{VRM}$ is the rate constant from the volume reaction model, $x$ is carbon conversion.

Studies show that the apparent reaction rate constant is more suitable for predicting the kinetics of the gasification experiment, as it accounts for the reaction order, chemical reaction controls, and the concentration of the output gas [13]. Using a simplified Dutta and Wen model [14], the gasification rate can be expressed as:

$$\frac{dx}{dt}=k_{app}\ast \frac{P}{RT}\ast (1-x)$$

(2)

where $\frac{dx}{dt}$ is the gasification reaction rate, $k_{app}$ is the apparent rate constant (L/mol·s), $P$ is the pressure of the output gas (atm), $R$ is the universal gas constant (L·atm·K⁻¹·mol⁻¹), $T$ is temperature ($K$), and $x$ is carbon conversion.

To calculate the apparent reaction rate constant, Equation (2) must be linearized first (as shown in Equation (3)); then, the slope of the graph plotted with the linear equation will be used to determine the apparent rate constant. The plots based on Equation (3) are shown in Section 3.7.1.

$$-\mathit{ln}\left(1-x\right)=k_{app}\ast \frac{P}{RT}\ast t$$

(3)

where $\frac{dx}{dt}$ is the gasification reaction rate, $k_{app}$ is the apparent rate constant (L/mol·s), $P$ is the pressure of the output gas (atm), $R$ is the universal gas constant (L·atm·K⁻¹·mol⁻¹), $T$ is temperature ($K$), and $x$ is carbon conversion.

Upon calculating the apparent rate constant from each model, the Arrhenius equation (Equation (4)) can be utilized to calculate the activation energy $E_a$ and pre-exponential factor $A_0$.

$$k_{app}=A_0{e}^{\frac{-E_a}{RT}}$$

(4)

where $R$ is the molar gas constant (L·atm·K⁻¹·mol⁻¹), $T$ is temperature (K), $E_a$ is the activation energy (kJ/mol), $A_0$ is the pre-exponential factor, $k_{app}$ is the apparent rate constant.

The linearized form of Equation (4) is denoted in Equation (5).

$$\mathit{ln}\left(k_{app}\right)=\frac{-E_a}{R}\frac{1}{T}+ln\left(A_0\right)$$

(5)

where $R$ is the molar gas constant (L·atm·K⁻¹·mol⁻¹), $T$ is temperature (K), $E_a$ is the activation energy (kJ/mol), $A_0$ is the pre-exponential factor, and $k_p$ the rate constant.

Based on Equation (5), the graph of “$ln\left(k_{app}\right)$ vs. $1/T$” is plotted, and the slope represents $\frac{-E_a}{R}$, while the y-intercept represents $ln\left(A_0\right)$. These calculations are carried out, and the plots made are shown in Section 3.7.2.

3. Results and Discussion

As stated above, the objectives of this study are to understand the effect of CO₂ concentration on carbon conversion and product yield and to perform kinetic analysis using the volume reaction kinetic model to determine important parameters such as the activation energy, reaction rate, and pre-exponential factor.

3.1. SEM Analysis

SEM analysis of the biochar sample showed that the biochar is a very porous material, as depicted in Figure 2. During the gasification process, CO₂ gas flows into these pores, encouraging surface reaction.

The gray surfaces are carbon, while the white surfaces represent ash, as shown in Figure 2c. From the proximate analysis of the biochar, shown in Table 1 (Section 2.2), the biochar contains about 48% carbon, hence the surface of the material being mostly gray. The proximate analysis also indicates an ash content of 18%, hence the presence of the white surfaces. Ash comprises elements such as oxygen, carbon, calcium, phosphorus, and silicon. An EDS analysis performed on the white region showed some of these elements, which validated the presence of ash.

3.2. Effects of Temperature on CO Concentration

The main reaction, the Boudouard reaction, is an endothermic reaction; hence, energy is needed for the reaction to take place. The effects of temperature on CO concentration are shown in Figure 3. For all the tested concentrations of inlet CO₂, the concentration of CO in the output gas increases as temperature increases. In Figure 3a (15% inlet CO₂ concentration), the concentrations of CO at the 5 min mark are 3.2, 10, and 19.3% vol at 700, 800, and 900 $°\mathrm{C},$ respectively. In Figure 3b (30% inlet CO₂ concentration), the concentrations of CO are 4.6, 17.2, and 26% vol at 700, 800, and 900 $°\mathrm{C}$, respectively. In Figure 3c (45% inlet CO₂ concentration), the concentrations of CO are 5.4, 21.6, and 31.4% vol at 700, 800, and 900 $°\mathrm{C}$, respectively. In Figure 3d (60% inlet CO₂ concentration), the concentrations of CO are 5.3, 22.5, and 34% vol at 700, 800, and 900 $°\mathrm{C}$, respectively. The 5 min mark was chosen to ensure consistent comparisons by avoiding initial data variations. Ultimately, a similar trend is seen for each CO₂ inlet concentration, whether 15%, 30%, 45%, or 60% CO₂. As the temperature increases, the concentration of CO in the output gas is expected to increase. This is because an increase in temperature will result in more free energy available to favor reactions. Gibbs free energy describes the amount of energy available in a system to do work. Gibbs free energy is given by Equation (6). As temperature increases, $∆G°$ becomes more negative, indicating the presence of more free energy.

$$∆G°=∆H°-T∆S°$$

(6)

where $∆G°$ is the Gibbs free energy (kJ/mol); $∆H°$ is enthalpy change (kJ/mol); $T$ is temperature (kJ/mol); $∆S°$ is entropy change (kJ/mol).

In addition, the CO concentration generally decreases with time at all temperatures. Once CO₂ is introduced into the gasification chamber at the start of the experiment, the CO₂ molecules move into the carbon active sites on the biochar and sponsor chemical reactions, resulting in the peak CO concentrations. Over time, the biochar is consumed, resulting in fewer vacant active sites and a gradual decrease in the carbon concentration, resulting in a decrease in the CO concentration. A similar trend in the effect of temperatures on the CO₂ gasification of southern pine was reported by Sadhwani et al. [6]. They reported CO concentrations of 6, 7.3, 9.8, and 11.3 at 700, 790, 850, and 934 $°\mathrm{C}$, respectively, having performed 100% CO₂ gasification of southern pine. Another study by Hu et al. [9] reported a similar trend in the CO concentration values of 16, 21, 40, and 43% vol at 700, 800, 900, and 1000 $°\mathrm{C}$, respectively, for 100% CO₂ gasification of sewage sludge. A second run of these experiments is shown in Figure A1.

3.3. Effects of Inlet CO₂ Concentration on CO Concentration

An increase in the inlet CO₂ concentration led to an increase in the CO concentration. An increase in the inlet CO₂ concentration increases the CO₂ partial pressure. As the CO₂ partial pressure increases, the number of effective collisions between reactant molecules increases, leading to higher char reactivity. The effects of the inlet CO₂ concentration on the CO concentration are shown in Figure 4. For different operating temperatures, the concentration of CO in the output gas has an increasing trend as the inlet CO₂ concentration increases. As shown in Figure 4a (700 $°\mathrm{C}$), the concentrations of CO at the 5 min mark are 3.2, 4.6, 5.4, and 5.3% vol at 15%, 30%, 45%, and 60% inlet CO₂ concentrations, respectively. In Figure 4b (800 $°\mathrm{C}$), the concentrations of CO are 10, 17.2, 21.6, and 22.5% vol for 15%, 30%, 45%, and 60% inlet CO₂ concentrations, respectively. In Figure 4c (900 $°\mathrm{C}$), the concentrations of CO are 19.3, 26, 31.4, and 34% vol for 15%, 30%, 45%, and 60% inlet CO₂ concentrations, respectively.

When the inlet CO₂ concentration increases, more CO₂ is available for chemical adsorption at the carbon active sites of the char. When the carbon concentration decreases and fewer vacant active sites are present as a result, the CO concentration is expected to decrease with time. For example, in Figure 4c, the peak CO concentrations are observed during the first 5 min; afterward, the CO concentrations for the 45 and 60% inlet CO₂ concentrations start to merge. This is indicative of the fact that even though more CO₂ was available in the case of 60%, there were fewer vacant active sites and a lower carbon concentration to sponsor the reaction. The number of active sites of the biochar decreases primarily due to the consumption of the biochar’s carbon content over time.

A similar trend in the effect of the inlet CO₂ concentration using woodchips was reported by Cheng et al. [8], wherein they stated CO concentrations of 10, 14, 18, and 15.7% vol for inlet CO₂ concentrations of 20, 40, 60, and 80% (air balance), respectively, across a temperature range of 875 to 950 $°\mathrm{C}$. Another study undertaken by Shen et al. [7] on woody biomass using CO₂ (air balance) reported CO concentrations of 20 and 40% vol for 700 and 800 $°\mathrm{C}$, respectively. Although a similar trend of an increasing CO concentration with an increasing inlet CO₂ concentration is seen in the study carried out by Cheng et al. [8], they noted that they did not observe increases at a 60% inlet CO₂ concentration. A second run of these experiments is shown in Figure A2.

3.4. Effects of Temperature and Inlet CO₂ Concentration on Carbon Conversion

Carbon conversion describes how much carbon in the biochar is converted into CO during the reaction time, in this case 30 min. To calculate the carbon conversion, the difference between the initial biochar mass and the instantaneous mass was divided by the initial mass, as shown in Equation (7).

$$x=\frac{w_0-w_t}{w_0}$$

(7)

where $x$ is carbon conversion; $w_0$ is the initial weight of the char (g); $w_t$ is the instantaneous weight of the char (g).

As discussed in Section 3.2 and Section 3.3, the CO concentration increases as temperature and the inlet CO₂ concentration increase. Therefore, carbon conversion increases as both the temperature and inlet CO₂ concentration increase. In Figure 5, the carbon conversion of the biochar varying against temperature and CO₂ inlet concentration is shown. While the carbon conversion is at a low of 5.3% at 700$°\mathrm{C}$ and a 15% inlet CO₂ concentration, the carbon conversion at 900 $°\mathrm{C}$ and a 60% inlet CO₂ concentration is 57.1%. The recommended operating conditions therefore to maximize carbon conversion are a temperature of 900 $°\mathrm{C}$ and above and an inlet CO₂ concentration of 60%.

3.5. Effects of Temperature on CO₂ Conversion

CO₂ conversion describes how much CO₂ is converted into a desirable product such as CO during the reaction. The CO₂ conversion was calculated using Equation (8), where the difference in the moles of CO₂ at the inlet and outlet is divided by the moles of CO₂ at the inlet. As temperature increases, the CO₂ conversion is expected to increase. This is because the main reaction that sponsors this conversion is the Boudouard reaction, which is endothermic in nature. An increase in temperature therefore will result in more CO₂ being converted into CO.

$${CO}_2 Conversion=\left(1-\frac{n_{{CO}_2,out}}{n_{{CO}_2,in}}\right)\ast 100\%$$

(8)

where $n_{{CO}_2,out}$ is the moles of CO₂ at the outlet; $n_{{CO}_2,in}$ is the moles of CO₂ at the inlet.

The effects of temperature on CO₂ conversion are shown in Figure 6. For the different inlet CO₂ concentrations, the conversion of CO₂ increases as temperature increases. In Figure 6a (15% inlet CO₂ concentration), the CO₂ conversion at the 5 min mark is 18.1, 48, and 76% at 700, 800, and 900 $°\mathrm{C}$, respectively. In Figure 6b (30% inlet CO₂ concentration), the CO₂ conversion is 11.1, 47, and 53% at 700, 800, and 900 $°\mathrm{C}$, respectively. In Figure 6c (45% inlet CO₂ concentration), the CO₂ conversion is 10.1, 42, and 53% at 700, 800, and 900 $°\mathrm{C}$, respectively. In Figure 6d (60% inlet CO₂ concentration), the CO₂ conversion is 7.4, 34, and 47% at 700, 800, and 900 $°\mathrm{C}$, respectively. Across all the inlet CO₂ concentrations, the trend is similar, with the highest CO₂ conversion of 76% occurring at 900 $°\mathrm{C}$ and a 15% inlet CO₂ concentration.

Though CO₂ conversion increases with temperature, the CO₂ conversion at a specific temperature decreases with time, as shown in Figure 6. This occurs due to the fact that there is less carbon (in the biochar) to react with the CO₂ molecules, as carbon is being consumed over time during the experiment. The absence of vacant active sites results in less CO₂ conversion over time. A second run of these experiments is shown in Figure A3.

3.6. Effects of Inlet CO₂ Concentration on CO₂ Conversion

To understand how the inlet CO₂ concentration affects the CO₂ conversion, it is important to study how the equilibrium constant ($k_p$) varies at different partial pressures. For a chemical reaction involving gases, the pressure exerted by the gases can be used to calculate the equilibrium constant for varied partial pressures of gases. The equilibrium constant, $k_p$, can therefore be expressed as the ratio of the partial pressure of the products to the partial pressure of the reactants, as denoted in Equation (9).

$$k_p=\frac{P_{products}}{P_{reactants}}$$

(9)

where $k_p$ is the equilibrium constant; $P_{products}$ is the partial pressure of the products; $P_{reactants}$ is the partial pressure of the reactants.

An increase in the inlet CO₂ concentration leads to an increase in the partial pressure of CO₂. This increase in partial pressure results in a lower $k_p$, signifying that the reverse reaction is being favored at a higher CO₂ concentration. When the reverse reaction is favored, that means the CO₂ conversion efficiency is lower.

The effects of the inlet CO₂ concentration on CO₂ conversion are shown in Figure 7. For different operating temperatures, CO₂ conversion decreases as the inlet CO₂ concentration increases. In Figure 7a (700 $°\mathrm{C}$), the CO₂ conversion at the 5 min mark is 18.1, 11.1, 10.1, and 7.4 for 15, 30, 45, and 60% inlet CO₂ concentrations, respectively. In Figure 7b (800 $°\mathrm{C}$), the CO₂ conversion is 48, 47, 42, and 34% for 15, 30, 45, and 60% inlet CO₂ concentrations, respectively. In Figure 7c (900 $°\mathrm{C}$), the CO₂ conversion is 76, 53, 53, and 47% for 15, 30, 45, and 60% inlet CO₂ concentrations, respectively. Across all temperatures, the CO₂ conversion decreases as the inlet CO₂ concentration increases.

The decrease in the $k_p$ values as the inlet CO₂ concentration increases indicates that the CO₂ conversion is lower at higher inlet concentrations of CO₂. Another reason for this trend is due to a phenomenon called the CO inhibition effect. In a chemically controlled surface reaction, there are three subsequent processes that can take place: (1) chemical adsorption of CO₂ on the solid surface, (2) the surface reaction of CO₂ with the carbon in the char, and (3) the desorption of the product, CO, from the solid surface [15,16]. When the adsorption of CO₂ is the rate controlling step, an increase in CO₂ partial pressure will lead to an increase in the reaction rate. When the desorption of CO from the solid surface, however, is the rate controlling step, an increase in CO₂ partial pressure will not affect the char’s reactivity, and thus CO₂ conversion decreases. This is called the CO inhibition effect.

The highest CO₂ conversion occurs at a CO₂ inlet concentration of 15%. Knowing that the highest CO₂ conversion occurs at a 15% CO₂ concentration is beneficial because it implies that flue gases that are captured at low CO₂ concentrations can be used directly for the gasification process. This eliminates the need for carbon sequestration and therefore saves costs. It is worth noting that there are other impurities that may need to be removed before the captured CO₂ is ready for use for gasification. A second run of these experiments is shown in Figure A4.

3.7. Determination of Kinetic Parameters

In this section, the steps and calculations employed to determine the gasification rate constant, as well as the activation energy and pre-exponential factor, are discussed.

3.7.1. Determining the Gasification Rate Constant (k_app)

Having calculated the carbon conversion $x$ using Equation (7) (discussed in Section 3.4), Equation (3) (discussed in Section 2.3) is used to calculate the apparent rate constant (k_app). The graphs of “$-\mathit{ln}\left(1-x\right)$ vs. time” for 15%, 30%, 45%, and 60% inlet CO₂ concentrations are shown in Figure 8. In Figure 8, the plots for the different temperatures are shown alongside the equations for the lines. A second run of these experiments is shown in Figure A5.

To avoid unstable data and improve the accuracy, the graphs shown in Figure 8 were truncated to only include data points from 4 min to 13 min. The resulting slope, which represents “$k_{app}\ast \frac{P}{RT}$”, as discussed in Equation (16), was used to calculate the apparent rate constant. The values for $k_{app}$ for each experiment are recorded and shown in

Table 2. Apparent rate constants at different temperatures and inlet CO₂ concentrations.

Inlet CO2 Concentration	${\mathit{k}}_{\mathit{a}\mathit{p}\mathit{p}}$ at Different Temperatures (L/mol·min)
	$700 °\mathbf{C}$	$800 °\mathbf{C}$	$900 °\mathbf{C}$
15%	0.122	0.518	1.192
30%	0.172	0.865	1.649
45%	0.193	0.839	1.897
60%	0.182	0.916	2.094

. The $k_{app}$ values shown in Table 2 are the average values from two runs of each experiment for validation purposes.

3.7.2. Determining the Activation Energy and Pre-Exponential Factor

Once $k_{app}$ is calculated, ln ($k_{app}$) can be calculated and plotted against temperature based on Equation (5), as discussed in Section 2.3. The slope of the graph will represent $\frac{-{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}$, while the y-intercept will represent ln(${\mathrm{A}}_0$). The graphs of “ln($k_{app}$) vs. temperature” are shown in Figure 9, and the activation energy (${\mathrm{E}}_{\mathrm{a}}$) and pre-exponential factor (${\mathrm{A}}_0$) values are outlined in

Table 3. Kinetic parameters from present study.

Inlet CO2 Concentration	Activation Energy (kJ/mol)	Pre-Exponential Factor (s−1)
15	109	63
30	108	87
45	109	105
60	117	253

. These values in Table 3 are the average values from two runs of each experiment for validation purposes.

The activation energy reported in this study was within the range of 108 to 117 kJ/mol. Since the activation energy describes the minimum amount of energy needed to sponsor a chemical reaction, it should stay about the same regardless of temperature and concentration variations. The closeness in values reported in this present study is a sign of accuracy. The activation energy values reported by other researchers were comparable. For example, 140.7 and 163.5 kJ/mol [10], 185.8 and 211.7 [11], and 100.4 and 127.9 kJ/mol [12].

4. Conclusions

As a contribution to sustainability goal number 13, this study proposes an efficient carbon utilization pathway, where captured CO₂ can be used in the gasification of biochar (a carbon-rich waste material) to produce useful fuels and chemicals. With the captured CO₂ coming at various concentrations, this study aimed to investigate the effects of the CO₂ concentration on the carbon conversion and product yield, alongside performing kinetic analysis, using the volume reaction model, to determine important parameters such as the activation energy and pre-exponential factor. The parameters employed in this study include gasification temperatures of 700, 800, and 900 $°\mathrm{C}$; inlet CO₂ concentrations of 15, 30, 45, and 60% by volume (N₂ balance); and an inlet CO₂ flow rate of 5 L/min.

A positive correlation was observed between temperature, inlet CO₂ concentration, and carbon conversion efficiency. In other words, an increase in the temperature and inlet CO₂ concentration resulted in an increase in the carbon conversion efficiency, with the maximum conversion of 57.1% occurring at 900 $°\mathrm{C}$ and a 60% inlet CO₂ concentration.

The study also revealed that the CO₂ conversion increased with temperature but decreased with an increasing inlet CO₂ concentration. The maximum CO₂ conversion reported in this study is 76%, occurring at 900 $°\mathrm{C}$ and a 15% inlet CO₂ concentration.

The activation energy was found in the range of 109 to 117 kJ/mol and the pre-exponential factor found in the range of 63 to 253 s⁻¹ in this study.

This study explains the relationship between the inlet CO₂ concentration and carbon conversion and demonstrates that the CO₂ gasification of biochar is a viable pathway for utilizing captured CO₂ to produce useful fuels and chemicals. The advantage of this process is that efficient waste disposal takes place simultaneously since the feedstock is waste material. Another important finding in this study is that the CO₂ conversion is higher at lower inlet concentrations of CO₂. This implies that flue gases captured at low CO₂ concentrations can be used directly for gasification. This eliminates the need for carbon sequestration and therefore saves costs. It is worth noting that there are other impurities that may need to be removed before the captured CO₂ can be used for gasification. The kinetic parameters calculated in this study can be used by engineers in their design process to perform scaled-up gasification studies and optimize clean energy production. While this study is performed using a batch-type gasification process and operated at a maximum temperature of 900 $°\mathrm{C}$, future studies could employ a continuous gasification process and higher temperatures of 1000 to 1200 $°\mathrm{C}$.