Enhancing the Efficacy of Adsorption-Based Carbon Storage Systems: A Finite Element Analysis Approach

Carbon capture and storage (CCS) technology transfers CO₂ emissions from fossil fuel consumption into secure geological storage [1]. CO₂ capture system uses a liquid sorbent to chemically react with CO₂ and form a solid material, which is then transported to a regeneration unit for decomposition. Instead of being a term, "carbon capture" in this study describes a process of capturing CO₂ from a gas stream [2]. CCS involves separating CO₂ from its source and storing it away from the atmosphere [3]. At present, CO₂ capture systems improve energy utilization and the purity of CO₂ capture [4]. CO₂ capture devices use a chemical reaction to reduce carbon gas emissions [5]. Carbon capture technologies include capturing CO₂ from fuel combustion or industrial processes [6]. Carbon capture units use polyethylenimine (PEI) or carbon sponges to capture carbon [7]. Carbon capture cartridges reduce CO₂ emissions produced by combustion processes, such as boilers or heaters. The components and functions of CO₂ capture equipment include a CO₂ capture tower packed with a CO₂ sorbent. However, specific information on carbon capture is not provided [8]. Carbon capture technology captures CO₂ from a variety of applications and power situations [9]. Figure 1 shows a CO₂ storage tank with steel walls.

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Figure 1. CO₂ storage tank with steel walls

Carbon capture, utilization, and storage (CCUS) technology in offshore facilities is use to reduce emissions and improve production efficiency [10]. Carbon capture is an important tool for decarbonizing the energy system and achieving global climate change targets. CO₂ is captured using various industrial processes. Safe CO₂ sequestration needs a dedicated measurement, monitoring, and verification program. CCS is a mitigation method, in which CO₂ emissions from industrial and power production are captured and stored underground to regulate the levels of greenhouse gases in the atmosphere [11]. CO₂ is captured using various devices, systems and methods to decrease CO₂ concentrations in the atmosphere on a global scale [12-14].

To meet climate objectives, global energy systems need to be restructured on a historic scale with ambition and speed. CCUS technologies are projected to play an important role in facilitating this transformation as part of a low-cost portfolio of technologies and tactics. Figure 2 provides a solution for significantly reducing emissions from critical industrial processes, such as the manufacturing of iron and steel, cement, and chemicals, all of which remain the foundation of contemporary civilizations. In the electricity industry, CCUS improves production diversification while addressing the risk of "lock-in" of emissions from existing infrastructure. CCUS also opens up new clean energy opportunities, such as low-carbon hydrogen production from fossil fuels for heating, transportation, and power generation. Almost all hydrogen production today is based on fossil fuels, most notably natural gas, with around 1,800 MW of output fitted with CCUS [15]. Critically, CCUS offers the infrastructure and know-how to accelerate the deployment of CO₂ removal technologies, such as bioenergy with carbon capture and storage (BECCS), and direct air capture.

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Figure 2. CO₂ capture and sequestration

Porous materials provide a safe technique for permanent storage because they allow safer transit from industry to long-distance storage sites without leaking. CO₂ stored in porous materials may be safely and easily accessed for a variety of uses.

3.1 Computational domain

The explored domain in present simulation is restricted to the 3D part of the elbow since numerical modeling of the entire elbow demands powerful and expensive computing resources, in addition to the excessively lengthy simulation required (Figure 3).

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Figure 3. Simulation required of modelling

Many models have the same fundamental operating system. Each type may be loaded with product and delivered as liquid or gas depending on the use. The next part goes into the theory underlying these procedures.

All procedures are completed using the control valves on the tank's underbelly. The valves are labeled so that they can be easily identified. The diagram and nomenclature demonstrate how the plumbing circuitry works for the specific model.

To improve tank filling, the following instructions should be obeyed:

1. Keep your transfer lines as short as feasible. Long insulated transfer lines cause larger fill losses and longer fill time.
2. A safety release mechanism must be installed in any line between two valves where liquid may become trapped.
3. Complete the filling procedure as quickly as feasible.
4. Do not allow the filling system pressure to go below 165 psig (11.6 Kg/cm²) to keep the temperature of liquid CO₂ from falling below the vessel's minimum design temperature. Before each fill, the vessel should be visually examined for damage, cleanliness, and appropriateness for the planned gas service. If damage is found (e.g., major dents, loose fittings, etc.), repair the item as quickly as feasible.

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(a)

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(b)

Figure 4. Computational domains (a) 2D-axisymmetric geometry, (b) 3D computational domain

Figure 4 illustrates the 2D and 3D computational domains, reflecting the dynamic nature of the simulation process, spanning from 0 to 3603 seconds. This duration encompasses CO₂ gas charging (0-1200 seconds), a holding phase (1201-2401 seconds), discharge (2402-3002 seconds), and a final hold-in phase (3003-3603 seconds).

3.2 Modeling equations

The modeling equations are central to the heat and mass transport simulation for CO₂ storage during the adsorption-desorption cycle in a fixed column with modified silica aerogels.

• A more plausible storage tank is employed as the computational domain.
• Darcy's law is used to charge CO₂ in storage tanks.
• Heat transfer between the bed and container walls is considered. The convective heat transfer between the outside wall and surrounds is also considered.
• The Dubinin-Astakhov (D-A) model, specifying the microspore volume carrying capacity of the adsorbent, is employed.
• Variation in esoteric heat of adsorption is based on the D-A model.

$\  { bulk }=\rho s(1-\varepsilon pellet)(1-\varepsilon b e d)$               (1)

$q\,  {CO}_2 \  { compoun }=\ {mCO}_2 \ { sorbed \,to } \frac{\  { compound }}{\ { mcompound }}+\ {V} \cdot \ {\rho gasCO}_2$                 (2)

$\begin{aligned}

& \rho  {CO_2}= \ {qCO_2} \  { compound } \cdot \rho { bulk }+ \  { pgasCO_2 }   \  

 \cdot(1-\ { εbed }) \  { εpellet } 

  + \  { pgasCO_2 }   \  { εbed }  

&

\end{aligned}$              (3)

$n_a=n_{\text {max }} \exp \left[-\left[\frac{R T}{\varepsilon}\right]^m {\ {ln }} \left(\frac{P_0}{P}\right)^m\right]$             (4)

$\varepsilon b e d=a+\beta T$                   (5)

Table 1. The specific conditions of heat flux

3.2.1 Conservation of momentum

Darcy's flow model predicts the total pressure distribution over time, yielding a time-dependent velocity field distribution.

Darcy's law, along with the continuity equation, produces mass and momentum conservation [16].

$\frac{\partial}{\partial t}\left(\varepsilon_b p c o_2\right)+\nabla \cdot\left(p c o_2 u\right)=Q_m$                (6)

$u=-\left(\frac{K}{\mu}\right) \nabla P$                    (7)

$Q_m=-M c o_2\left(1-\varepsilon_b\right)$ Psilica $\frac{\partial n_a}{\partial t}$             (8)

where, $\varepsilon_b$ represents the porosity of the adsorbent bed, $p \mathrm{co}_2$ is the fluid density, $u$ is the Darcy velocity of CO₂, $K$ is the permeability (m²), $\mu$ is the dynamic viscosity of the fluid, $Q_m$ is the mass source term that accounts for the mass contributed from the gas stage to the absorption phase in the form of volume per second, Psilica represents particle density, Mco₂ is the molecular volume of CO₂ gas.

Some significant hurdles must be addressed concurrently in order to achieve these traits. A large amount of adsorption bed is necessary to offset the high CO₂ emissions, which is one of the hurdles. It is significantly difficult because it is relatively expensive to build such a bed. Another hurdle is to attain reusability, selectivity, and high capacity simultaneously.

3.2.2 Energy conservation

The heat of the system is transported during the CO₂ adsorption process in porous medium via conduction and convection. The energy balance partial differential equation (PDE) can be expressed as follows [17]:

$\begin{aligned}

\frac{\partial}{\partial t}\left(\varepsilon_b p c o_2\right)+\nabla \cdot & {\left[p \operatorname{co}_2\left(-\frac{k}{\mu} \nabla P\right)\right] } 

 =-M \operatorname{co}_2\left(1-\varepsilon_b\right)  {\text{P}silica } \frac{\partial n_a}{\partial t}

\end{aligned}$             (9)

$q_{s t}=\alpha \sqrt{\ln \left(n_{\max } / n_a\right)}$                         (10)

$\begin{aligned}

& \left(\varepsilon_b p c o_2+p c o_2 n_a \ {Mco}_2 \ {Cpg}+\ {\text{P}silica} \,\ {Cps}\right) \frac{\partial T}{\partial t} +\mathrm{pcO}_2 \ {Cpg} \overrightarrow{\ {v}} \text {. } \nabla \ {T} =\nabla \cdot\left(K_{\text {eff }} \nabla T\right)+Q+\emptyset 

&

\end{aligned}$                (11)

$K_{\text {eff }}=\varepsilon_b K c o_2+\left(1-\varepsilon_b\right) K_{\text {silica }}$           (12)

$\begin{aligned}

Q=Q_a+Q_p= & \left(1-\varepsilon_b\right) \, {{\text P}silica} \frac{\partial n_a}{\partial t} q_{s t} +\gamma T\left[\varepsilon_b \frac{\partial p}{\partial t}+(\vec{v} \cdot \nabla) \mathrm{p}\right]

\end{aligned}$                (13)

where, $C p g$ is the specific heat capacity of $\mathrm{CO}_2, v$ is the Darcy velocity, $K_{\text {eff }}$ is the effective thermal conductivity, $Q$ is the energy source, including adsorption, $Q_a$ is the heat source, and $Q_p$ is the compression, $q$ is the esoteric heat of adsorption, and $\Phi$ is the viscous dissipation term. The volumetric thermal expansion coefficient $(\gamma)$ for ideal gases is characterized by the reciprocal of the temperature $(1 / \mathrm{T})$, denoted in inverse Kelvin.

To prevent CO₂ leakage, the adsorption bed should be reusable at least 1000 times. This ensures that CO₂ can be captured back. At the same time, the sorbent should be inexpensive to create, reducing the complexity of building an adsorption bed and allowing it to be widely used.

The adsorption bed should be able to continue absorbing CO₂ despite unexpected temperature, humidity, and pressure changes. An ideal sorbent should trap CO₂ with unlimited selectivity.

3.2.3 Boundary and initial conditions

The initial pressure within the system is set at 0.1 MPa. The velocity of the gas entering the system is maintained at 0.15 m/s. The initial temperature within the storage tank is established at 323 K, matching the inlet gas temperature. The heat flux across the boundary is $-h_t^*\left(T_{a m b}-T\right)$, where $T_{a m b}$ represents the ambient temperature, set at 293.15 K, and $h_t$ is the heat transfer coefficient, valued at 36 W/m²K.