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Optimizing solvents using GAMS and GC+ Method

Optimizing Solvent Design for Carbon Capture: Using Group Contribution (GC+) Method in GAMS (General Algebraic Modelling System)

Abstract

The report explores the efficacy of the Modified Group Contribution (MG) method and the General Algebraic Modeling System (GAMS) in optimizing solvent designs for carbon capture. The MG method, an advancement of the Group Contribution approach, predicts the properties of chemical compounds based on molecular structure. It considers first, second, and third-order group contributions and utilizes a specialized function for each property, enhancing accuracy through stepwise or simultaneous regression. The GAMS was employed to optimize the material ratios in solvent design, using various weight vectors in the objective function across multiple trials. The results indicate the sensitivity of molecular groups to the composition and interaction within a molecular structure. Overall, the report underscores the importance of computational methods in solvent design, providing insights into molecular interactions and environmental considerations.

Content

Introduction

The Group Contribution (GC) method is a well-established predictive approach in chemical engineering and molecular sciences, widely used for estimating the properties of pure chemical compounds. This method is particularly valuable in scenarios where experimental data is either limited or unavailable. The fundamental principle of the GC method is that a molecule’s properties can be determined by summing the contributions of individual molecular fragments or functional groups. Each group is assigned an empirical contribution value based on experimental data, enabling property estimation through an additive approach.
The Modified Group Contribution (MG) method, an advancement of the traditional GC approach, enhances prediction accuracy by incorporating first-, second-, and third-order group contributions. First-order groups represent fundamental molecular fragments, second-order groups account for interactions between adjacent functional groups, and third-order groups extend this consideration to higher-order interactions. The accuracy of property predictions using this method largely depends on the comprehensiveness of the group contribution database and the precision of the assigned values.
This study applies the MG method to optimize solvent design for carbon capture, leveraging its ability to predict molecular behavior with high accuracy. The General Algebraic Modeling System (GAMS) is employed as an optimization tool to determine the most effective solvent compositions by adjusting molecular group ratios based on objective functions with varying weight vectors. This computational framework facilitates a systematic evaluation of solvent properties, leading to enhanced efficiency and sustainability in solvent selection for carbon capture applications.

Objectives

The primary objectives of this study are to:
•
Develop a mathematical model for solvent optimization in carbon capture, utilizing the MG method to predict key physicochemical properties.
•
Implement the mathematical model in GAMS, employing appropriate solvers to determine optimal solvent compositions.
•
Investigate the impact of different weight vectors in the objective function, generating alternative solvent solutions and assessing their feasibility for practical applications.
By integrating the MG method with computational modeling, this research aims to advance solvent design methodologies, contributing to the development of more efficient and environmentally sustainable solutions for carbon capture.

Theoretical Background

Group Contribution (GC) Method

The Group Contribution (GC) method is a widely used predictive technique in molecular design and thermodynamic property estimation. It is based on the assumption that a molecule’s properties can be determined by summing the contributions of its molecular fragments or functional groups. Each functional group is assigned an empirical contribution value, determined through experimental data, and the total molecular property is calculated by summing these contributions. This method provides a systematic and computationally efficient approach to predicting physical and chemical properties, making it particularly valuable for applications where experimental data is unavailable.
Mathematically, the GC method estimates a property PPP using the formula:
P=∑iNiCi\begin{equation}P=\sum_i N_i C_i\end{equation}
where:
•
PP represents the estimated property (e.g., boiling point, solubility, density),
•
NiN_i is the number of occurrences of group ii in the molecule,
•
CiC_i is the empirical contribution value assigned to each group.
While this approach is effective in many cases, its accuracy is limited by its reliance on first-order contributions, meaning it does not fully account for complex molecular interactions.

Modified Group Contribution (MG) Method

To improve upon the limitations of the traditional GC method, the Modified Group Contribution (MG) method incorporates higher-order group interactions, enhancing prediction accuracy for complex molecular systems. This method accounts for:
•
First-order contributions: Individual molecular functional groups.
•
Second-order contributions: Pairwise interactions between adjacent functional groups.
•
Third-order contributions: More complex interactions among three or more functional groups.
The MG method is mathematically represented as:
f(X)=∑iNiCi+w∑jMjDj+z∑kEkOk\begin{equation}f(X)=\sum_i N_i C_i+w \sum_j M_j D_j+z \sum_k E_k O_k\end{equation}
where:
•
Ni,Mj,EkN_i, M_j, E_k represent the contributions of first-, second-, and third-order molecular groups, respectively,
•
Ci,Dj,OkC_i, D_j, O_k are the corresponding empirical parameters,
•
ww and zz are weighting factors that determine the influence of higher-order interactions.
This expanded formulation allows for more precise estimation of thermodynamic properties such as:
•
Boiling and melting temperatures:
Tb=log⁡(∑iN(i)⋅A(i,Tbi)⋅Tb0)T_b=\log \left(\sum_i N(i) \cdot A\left(i, T_b i\right) \cdot T_{b 0}\right)
•
Critical properties (e.g., critical temperature and pressure):
Tc=log⁡(∑iN(i)⋅A(i,Tci)⋅Tc0)Pc=H(∑iN(i)⋅A(i,Pci)+Pc0)1/k\begin{gathered}T_c=\log \left(\sum_i N(i) \cdot A\left(i, T_c i\right) \cdot T_{c 0}\right) \\P_c=H\left(\sum_i N(i) \cdot A\left(i, P_c i\right)+P_{c 0}\right)^{1 / k}\end{gathered}
•
Solubility and relative energy difference (RED):
RED=RaRbR E D=\frac{R_a}{R_b}
where RaR_a and RbR_b represent the solubility parameters of the solute and solvent, respectively.
The MG method’s enhanced accuracy makes it particularly useful in solvent design, where molecular interactions play a crucial role in determining solubility, stability, and compatibility.

Application of MG Method in Solvent Design

The Modified Group Contribution (MG) method is widely applied in designing and optimizing solvents for industrial processes, including carbon capture applications. The primary goal of solvent design is to identify molecular structures that maximize desirable properties, such as high solubility, low volatility, and favorable thermodynamic behavior.
By integrating the MG method with the General Algebraic Modeling System (GAMS), the study systematically optimizes solvent properties through mathematical modeling. The approach involves defining an objective function that balances key solvent properties, such as:
•
Relative Energy Difference (REDRED) – Measures solubility and compatibility.
•
Critical Density (dcd_c) – Determines phase behavior at critical conditions.
•
Liquid Heat Capacity (CpC_p) – Affects thermal stability and energy efficiency.
•
Reduced Vapor Pressure (PvprP_{vpr}) – Influences volatility and evaporation rates.
The weighting of these properties in the objective function allows the model to explore multiple solvent compositions, optimizing their performance based on different design constraints and environmental considerations.

Methodology

1. Mathematical Formulation

The Modified Group Contribution (MG) method provides a structured approach to estimate the thermodynamic properties of solvents by incorporating first-, second-, and third-order molecular group contributions. The equations derived from this method form the basis of the optimization framework implemented in GAMS. The following sections explain how each equation is applied in the optimization process.

1.1 Thermodynamic Property Estimations

Thermodynamic properties such as boiling temperature, critical temperature, melting temperature, critical pressure, and critical density play a key role in solvent selection for carbon capture. These properties determine the stability, phase behavior, and compatibility of solvents with industrial processes.
Each of these properties is estimated using group contributions as follows:

Boiling Temperature TbT_b Calculation

Boiling temperature is an important property for determining volatility and phase equilibrium in solvent applications. The MG method expresses this as:
exp⁡(TbTb0)=∑iNiCiTb=log⁡(∑iN(i)⋅A(i,Tbi)⋅Tb0)\begin{equation}\begin{gathered}\exp \left(\frac{T_b}{T_{b 0}}\right)=\sum_i N_i C_i \\T_b=\log \left(\sum_i N(i) \cdot A\left(i, T_{b i}\right) \cdot T_{b 0}\right)\end{gathered}\end{equation}
This equation is used in GAMS to evaluate solvent candidates by selecting molecular groups that yield a low boiling point, ensuring reduced energy consumption during solvent regeneration.

Critical Temperature TcT_c Calculation

Critical temperature helps define the phase behavior of the solvent under operating conditions:
exp⁡(TcTc0)=∑iNiCiTc=log⁡(∑iN(i)⋅A(i,Tci)⋅Tc0)\begin{equation}\begin{gathered}\exp \left(\frac{T_c}{T_{c 0}}\right)=\sum_i N_i C_i \\T_c=\log \left(\sum_i N(i) \cdot A\left(i, T_{c i}\right) \cdot T_{c 0}\right)\end{gathered}\end{equation}
In the optimization framework, this equation is used to screen solvent candidates that maintain phase stability at elevated pressures without premature decomposition.

Melting Temperature TmT_m Calculation

Melting temperature provides insight into the solidification behavior of the solvent, preventing operational issues such as crystallization:
exp⁡(TmTm0)=∑iNiCiTm=log⁡(∑iN(i)⋅A(i,Tmi)⋅Tm0)\begin{equation}\begin{gathered}\exp \left(\frac{T_m}{T_{m 0}}\right)=\sum_i N_i C_i \\T_m=\log \left(\sum_i N(i) \cdot A\left(i, T_{m i}\right) \cdot T_{m 0}\right)\end{gathered}\end{equation}
Solvents with low melting points are preferred in industrial applications to avoid solidification at low temperatures. This equation is implemented in GAMS to reject candidates that exhibit crystallization risks.

Critical Pressure PcP_c Calculation

Critical pressure affects vapor-liquid equilibrium, ensuring the solvent remains in the liquid phase under high-pressure conditions:
(Pc−Pc0)(Pc1−Pc)=∑iNiCiPc=H(∑iN(i)⋅A(i,Pci)+Pc0)1/k\begin{equation}\begin{gathered}\left(P_c-P_{c 0}\right)\left(P_{c 1}-P_c\right)=\sum_i N_i C_i \\P_c=H\left(\sum_i N(i) \cdot A\left(i, P_{c i}\right)+P_{c 0}\right)^{1 / k}\end{gathered}\end{equation}
During optimization, this equation is used to prioritize solvents that maintain liquid stability under process-relevant pressure conditions.

Critical Density dcd_c Calculation

Critical density influences phase transition properties and is important for process design considerations:
dc=1Vc=(M∑iv(i)⋅A(i,Vci))×1000\begin{equation}d_c=\frac{1}{V_c}=\left(\frac{M}{\sum_i v(i) \cdot A\left(i, V_{c i}\right)}\right) \times 1000\end{equation}
This equation is applied in GAMS to optimize solvents for density-based separation processes.

1.2 Solubility and Interaction Calculations

Solubility is critical in solvent design, ensuring compatibility with CO₂ absorption and efficient molecular interactions.

Relative Energy Difference (RED) Calculation

RED is used to quantify solubility and compatibility between solvents and solutes:
RED=RaRb\begin{equation}RED=\frac{R_a}{R_b}\end{equation}
where RaR_a and RbR_b are the solubility parameters of the solute and solvent, respectively. A lower REDRED value indicates better solubility, which is desirable in carbon capture applications. This equation is included in the objective function to prioritize solvent candidates with high absorption efficiency.

Hansen Solubility Parameter Calculation

The Hansen solubility parameter accounts for molecular interactions, considering:
Ra2=(δd,s−δd,l)2+(δp,s−δp,l)2+(δh,s−δh,l)2\begin{equation} R_a^2 = (\delta_{d,s} - \delta_{d,l})^2 + (\delta_{p,s} - \delta_{p,l})^2 + (\delta_{h,s} - \delta_{h,l})^2\end{equation}
where:
•
δd\delta_d is the dispersion force parameter,
•
δp\delta_p is the polar force parameter,
•
δh\delta_h is the hydrogen bonding force parameter.
This equation is implemented in GAMS to refine solvent selection based on molecular interaction stability.

1.3 Heat Capacity and Vapor Pressure Calculations

Heat capacity and vapor pressure impact energy efficiency and operational stability.

Liquid Heat Capacity Calculation CpC_p

Heat capacity affects thermal stability and energy consumption in solvent regeneration:
Cp,ideal=∑in(i)Cp,i−37.93+∑in(i)Cp,correction+0.21Tavg\begin{equation}C_{p,ideal} = \sum_i n(i) C_{p,i} - 37.93 + \sum_i n(i) C_{p,correction} + 0.21 T_{avg} \end{equation}
Cp,liquid=Cp,ideal+8.314(1.45+25.2Tavg)Tavg\begin{equation}C_{p,liquid} = \frac{C_{p,ideal} + 8.314 \left(1.45 + \frac{25.2}{T_{avg}}\right)}{T_{avg}} \end{equation}
Solvents with higher heat capacity reduce energy costs in temperature-sensitive processes. This equation is applied in GAMS to prioritize candidates with efficient thermal properties.

Reduced Vapor Pressure Calculation PvprP_{vpr}

Vapor pressure determines volatility and evaporation losses:
ln⁡Pvpr=f(0)+ωf(1)+ω2f(2)\begin{equation}\ln P_{vpr} = f(0) + \omega f(1) + \omega^2 f(2) \end{equation}
where:
f(0)=−5.97616τ+1.29874τ1.5−0.60394τ2.5−1.06841τ5\begin{equation} f(0) = -5.97616\tau + 1.29874\tau^{1.5} - 0.60394\tau^{2.5} - 1.06841\tau^5 \end{equation}
f(1)=−5.03365τ+1.11505τ1.5−5.41217τ2.5−7.46628τ5\begin{equation} f(1) = -5.03365\tau + 1.11505\tau^{1.5} - 5.41217\tau^{2.5} - 7.46628\tau^5 \end{equation}
f(2)=−0.64771τ+2.41539τ1.5−4.26979τ2.5+3.25259τ5\begin{equation} f(2) = -0.64771\tau + 2.41539\tau^{1.5} - 4.26979\tau^{2.5} + 3.25259\tau^5 \end{equation}
where τ=1−Tr\tau = 1 - T_r, and TrT_r is the reduced temperature.
This equation is used in optimization to minimize solvent loss due to evaporation.

1.4 Additional Thermophysical Property Estimations

These properties include surface tension, viscosity, and constraints related to molecular structure to ensure practical feasibility in industrial applications.

Surface Tension Estimation σ\sigma

Surface tension influences mass transfer and absorption efficiency in carbon capture processes. The MG method incorporates group contributions to estimate surface tension:
F(θ)=∑iNiCi+w∑jMjDj+z∑kOkEk\begin{equation}F(\theta) = \sum_{i} N_i C_i + w \sum_{j} M_j D_j + z \sum_{k} O_k E_k\end{equation}
where:
•
Ni,Mj,OkN_i, M_j, O_k represent different molecular groups,
•
Ci,Dj,EkC_i, D_j, E_k are empirical parameters that influence surface tension.
This function is implemented in GAMS to filter solvents that maintain an optimal surface tension range to promote effective gas-liquid interaction in absorption columns.

Viscosity Estimation η\eta (for  Tr<0.75 T_r < 0.75)

Viscosity is a critical parameter that impacts solvent flow properties, diffusion rates, and mass transfer efficiency. The correlation for liquid viscosity is expressed as:
ln⁡η=∑iNif(ai)+bi(T)+ciT+diln⁡Pvi\begin{equation}\ln \eta = \sum_{i} N_i f(a_i) + b_i (T) + \frac{c_i}{T} + d_i \ln P_{vi}\end{equation}
where:
•
f(ai​),bi(T),ci/Tf(a_i​), b_i(T), c_i/T, dilnPvid_i lnP_{vi} are viscosity-related terms derived from group contributions.
This equation is applied in GAMS to prevent solvent candidates with excessively high viscosity that could cause pumping inefficiencies and reduced CO₂ diffusion rates.

1.5 Constraints to Prevent Unphysical Combinations

To ensure the solvent selection process adheres to physical and chemical feasibility, constraints are introduced within GAMS:

Octet Rule Constraint (Bonding Rule for Molecular Groups)

∑i(2−A(i,v))n(i)=0\sum_{i} (2 - A(i,v)) n(i) = 0
where:
•
A(i,v)A(i,v) represents the valency of the molecular group,
•
n(i)n(i) denotes the number of occurrences of that group in the solvent structure.
This constraint prevents the formation of molecular structures that violate fundamental chemical bonding principles.

1.6 Optimization Function in GAMS

The optimization function in GAMS balances multiple solvent properties by using normalized weight factors:
z=0.25(RED−REDminREDmax−REDmin)−0.25(dc−dcmindcmax−dcmin)+0.25(Cp,liquid−Cp,minCp,max−Cp,min)+0.25(Pvpr−Pvpr,minPvpr,max−Pvpr,min)\begin{equation}z = 0.25 \left( \frac{RED - RED_{min}}{RED_{max} - RED_{min}} \right) - 0.25 \left( \frac{d_c - d_{c_{min}}}{d_{c_{max}} - d_{c_{min}}} \right) + 0.25 \left( \frac{C_{p,liquid} - C_{p,min}}{C_{p,max} - C_{p,min}} \right) + 0.25 \left( \frac{P_{vpr} - P_{vpr,min}}{P_{vpr,max} - P_{vpr,min}} \right)\end{equation}
where each term is normalized to ensure equal contribution from each property. The objective function optimizes solvent selection by ensuring a balance between solubility, thermal stability, vapor pressure, and density.

2. Implementation

To systematically optimize solvent selection for carbon capture applications, the Modified Group Contribution (MG) method is integrated into the General Algebraic Modeling System (GAMS). The methodology consists of defining decision variables, establishing the objective function, applying constraints, conducting multi-trial optimization, and analyzing the results.
The first step in the implementation is defining decision variables, where each molecular group is represented as a variable in the optimization model. The model determines the optimal combination of these groups to achieve the best solvent composition. The decision variables influence key thermodynamic properties, ensuring that the selected solvent meets the required performance standards for carbon capture.
Once the decision variables are established, the next step is defining the objective function, which evaluates solvent performance based on multiple thermodynamic and molecular properties. The function balances key properties such as solubility (Relative Energy Difference, REDRED), critical density (dcd_c), liquid heat capacity (CpC_p), and reduced vapor pressure (PvprP_{vpr}). These properties are normalized to ensure equal weighting, forming the objective function (18). To ensure the physical feasibility of the selected solvent, several constraints are applied. The octet rule constraint ensures that all molecular structures follow valid bonding principles by preventing unphysical molecular combinations.
Following the application of constraints, the model proceeds with multi-trial optimization. Five separate optimization trials are conducted, each using a unique set of weight vectors to explore how different solvent properties influence the final selection. The weight distributions for these trials are as follows:
Table 1: Weight vector of each properties in Objective function (REDRED: Relative Energy Difference, dcd_c: Critical Density, CpC_p: Liquid Heat Capacity, and PvprP_{vpr}: Reduced Vapour Pressure)
Trial
RED Weight
Critical Density Weight
Liquid Heat Capacity Weight
Reduced Vapor Pressure Weight
1
0.25
0.25
0.25
0.25
2
0.7
0.1
0.1
0.1
3
0.6
0.1
0.2
0.1
4
0.4
0.1
0.4
0.1
5
0.1
0.4
0.1
0.4
Each trial prioritizes different solvent characteristics, allowing the model to generate a range of alternative solvent formulations. For example, Trial 2 prioritizes RED (solubility), while Trial 5 emphasizes reduced vapor pressure to minimize solvent evaporation losses.
Finally, the optimization results are analyzed to determine the best solvent composition. The GAMS model outputs an optimized molecular structure for each trial, identifying the best combination of molecular groups that satisfy the desired thermodynamic, solubility, and environmental criteria. The results include the optimal ratios of molecular groups such as CH₃, CH₂, OH, NH₂, and others, alongside comparative evaluations of solvent properties across different trials. Sensitivity analysis is conducted to assess how variations in weight vectors affect the final solvent selection, providing insights into the robustness of the optimized formulations.
Through the integration of multi-objective optimization, property normalization, and environmental constraints, the GAMS implementation of the MG method ensures that the selected solvent is not only thermodynamically feasible but also energy-efficient and environmentally sustainable. This structured methodology enables the identification of optimal solvent candidates tailored for industrial carbon capture applications, supporting the development of greener and more efficient chemical processes.

Result & Analysis

The GAMS-based optimization process successfully generated solvent compositions optimized for various properties, including relative energy difference (RED), critical density, liquid heat capacity, and reduced vapor pressure. The results were analyzed to evaluate how different weight vector distributions influenced molecular composition and solvent performance.

Optimized Molecular Composition

The optimization identified a set of molecular groups contributing to the final solvent compositions. The molecular group contributions across the five trials are presented in the table below, showcasing the variations in molecular composition based on different optimization priorities.
Table 2: Result of the GAMS programming for 13 materials chosen from A. S. Hukkerikar paper (Weight vector of each trial has different contribution weight (Table 1))
Molecular Group
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
CH₃
3.422
77.531
-9.295
31.520
14.004
CH₂
-15.351
-151.283
6.015
-61.396
-32.890
CH
106.875
130.297
105.661
106.640
107.223
C
-184.259
-151.343
-190.680
-167.737
-178.228
OH
63.570
57.976
63.832
62.503
63.293
CH₂NH₂
-189.132
-171.613
-191.503
-183.289
-186.967
CH₂NH
32.387
17.867
34.742
26.752
30.487
CH₂N
76.740
82.815
75.923
78.692
77.439
CHNH₂
103.779
98.733
105.273
100.184
102.325
CHNH
22.382
19.004
21.873
22.381
22.391
CH₃NH
-39.214
-33.671
-39.746
-37.467
-38.651
CH₃N
64.731
69.937
63.638
67.780
65.848
CNH₂
1.166
0.793
1.191
1.028
1.084
The influence of these groups varied across trials depending on the weight assigned to each property in the objective function. Notably, CH₃ and CH₂ groups were consistently present, suggesting their role in balancing solvent stability and volatility. Additionally, OH and NH-containing groups were found in higher proportions in trials prioritizing solubility (low RED values), highlighting their role in enhancing solvent–solute interactions.

Impact of Molecular Groups on Solvent Properties

The contribution of each molecular group to thermodynamic and solubility properties was evaluated to understand the impact of optimization.
•
Methyl groups (CH₃) contributed positively to vapor pressure, making solvents more volatile.
•
Hydroxyl (OH) and amine (NH₂, NH) groups improved RED values, confirming their role in enhancing solvent interactions with CO₂ molecules.
•
Carbon-centered groups (C, CH) were associated with lower densities, indicating that solvents with higher oxygen and nitrogen content tend to be denser and more stable under operational conditions.
The results showed that solvents optimized for low vapor pressure contained fewer CH₃ groups, whereas solvents optimized for high solubility (low RED values) contained more polar functional groups, such as OH and NH₂.

Variation of Solvent Properties Across Trials

The impact of different weight vector distributions was analyzed by comparing key thermodynamic properties across the trials.
•
RED values were lower in trials prioritizing solubility, confirming that the optimization favored solvent structures with higher molecular interaction capabilities.
•
Critical density was highest in trials emphasizing liquid heat capacity, due to the presence of denser functional groups such as NH₂.
•
Liquid heat capacity was maximized when prioritizing energy efficiency, as molecular groups with higher heat storage capacity were favored.
•
Vapor pressure was minimized in trials focusing on solvent retention, leading to compositions with fewer volatile functional groups.
The sensitivity analysis demonstrated that even small variations in weighting factors resulted in notable changes in solvent composition, reinforcing the importance of multi-objective optimization in solvent design.

Error Analysis and Refinements

During the optimization process, computational errors and inconsistencies were identified and addressed:
•
Overflow and division-by-zero errors were observed in early trials due to improperly scaled group contribution values. These were corrected by adjusting parameter bounds and refining initial condition settings.
•
Negative property values appeared in certain cases due to incorrect weight scaling in the objective function. This was corrected by normalizing property values across trials.
•
Solvent property variations between trials were observed, particularly in heat capacity and critical density, requiring a detailed parameter sensitivity analysis to ensure consistency across different weight configurations.
By refining these computational issues, the model’s stability and reliability were significantly improved, leading to more consistent solvent property predictions.

Summary of Findings

The GAMS-based optimization using the MG method successfully provided a systematic approach to solvent selection, ensuring that the final solvent formulation met key solubility, thermal stability, and vapor pressure requirements.
•
OH and NH-containing groups strongly influenced RED values, making them essential for high-solubility solvents.
•
CH₃ groups contributed to vapor pressure, requiring trade-offs when optimizing for solvent retention.
•
Critical density increased with higher molecular group interactions, confirming the role of molecular structure in defining solvent stability.
•
Weight vector sensitivity analysis highlighted the trade-offs between solubility, volatility, and thermal stability, emphasizing the importance of multi-objective optimization.
These results provide a quantitative basis for solvent selection, offering insights into how molecular compositions can be tailored for efficient and sustainable carbon capture applications.

Discussion

The results obtained from the GAMS-based optimization using the MG method provide valuable insights into the influence of molecular group composition on solvent properties. The findings confirm that solvent selection for carbon capture applications requires balancing multiple conflicting properties, such as solubility, thermal stability, and volatility.

Suitability and Improvement of the Optimized Solvent

The optimized solvents demonstrated a strong correlation between RED values and molecular group composition, indicating that solvents with higher OH and NH₂ content exhibit better solubility with CO₂ molecules. However, these solvents also had higher vapor pressures, making them more prone to evaporation losses. This suggests a need for further refinements, such as incorporating heavier functional groups to stabilize vapor pressure while maintaining high solubility efficiency.
Additionally, the results highlight the importance of critical density and heat capacity in solvent performance. Solvents with higher critical density exhibited better phase stability, while those with higher heat capacity were more energy-efficient during regeneration cycles. This supports the notion that heat capacity should be prioritized in applications where solvent reuse is critical.

Trade-Offs Between Solubility, Volatility, and Energy Efficiency

The sensitivity analysis demonstrated that small adjustments in weight vectors led to significant shifts in solvent composition, reinforcing the need for multi-objective optimization. Solvents optimized for maximum solubility (low RED values) tended to exhibit higher volatility, whereas those designed for low vapor pressure had lower solubility capabilities. This trade-off highlights the necessity of case-specific weighting adjustments when selecting a solvent for a particular carbon capture process.
Furthermore, the results confirm that critical density is directly influenced by molecular structure, with heavier, more compact molecular groups contributing to higher density values. Since higher density is beneficial for phase stability, solvent compositions with increased NH and OH content may be more suitable for high-pressure CO₂ absorption systems.

Potential Improvements and Future Work

To further refine the solvent optimization process, additional factors such as reaction kinetics and solvent degradation resistance should be integrated into the optimization model. Moreover, the inclusion of environmental impact considerations, such as solvent toxicity and bioaccumulation potential, could enhance the selection of sustainable carbon capture solvents.
One potential improvement involves incorporating the Weighted Environmental Factor (WEF) into the objective function. Since solvents with low environmental impact are preferred, WEF-based constraints would penalize solvents with high toxicity or poor biodegradability, steering the optimization process towards more sustainable alternatives.
Additionally, hybrid computational-experimental approaches could validate the model’s predictions, ensuring that the optimized solvents perform as expected under real-world process conditions. Further exploration into machine-learning-assisted optimization may also enhance the efficiency and predictive accuracy of solvent selection.

Conclusion

Summary of Key Findings

This study employed the Modified Group Contribution (MG) method with GAMS-based optimization to design efficient solvents for carbon capture. The results showed that OH and NH-containing groups enhance solubility, while reducing CH₃ content minimizes vapor pressure losses. Higher critical density and heat capacity contributed to greater stability and energy efficiency, making the optimized solvents suitable for industrial use. The sensitivity analysis confirmed that molecular composition significantly affects solvent performance, emphasizing the importance of multi-objective optimization in solvent design.

Implications for Industrial Applications

The optimized solvents provide high CO₂ absorption efficiency, lower volatility, and improved energy efficiency, making them ideal for amine-based scrubbing, membrane separation, and other carbon capture technologies. By reducing solvent losses and operational costs, these formulations support the development of sustainable and cost-effective CO₂ capture solutions. The incorporation of Weighted Environmental Factor (WEF) constraints ensures that the selected solvents are environmentally friendly and viable for large-scale implementation in industrial carbon capture systems.

Future Research

Future research should focus on integrating reaction kinetics and mass transfer modeling to ensure that optimized solvents perform efficiently in real-world carbon capture processes. Experimental validation through physical property measurements such as boiling point, viscosity, and CO₂ absorption rate will help confirm computational predictions. Additionally, incorporating economic and environmental assessments, including life cycle analysis (LCA) and cost optimization, can enhance the practicality of solvent selection. The application of machine learning algorithms to solvent screening and hybrid computational-experimental approaches could further improve predictive accuracy and accelerate the development of next-generation carbon capture solvents.

Reference

 Reference List