This study presents different approaches for introducing mixed integer problems into a meta-heuristic algorithm. The algorithms are developed to address the simultaneous design and optimization of a heat pump unit. A distinction is made between integer variables such as nominal tube diameters and the adsorbent employed in the process. The choice of adsorbent is named as a "key variable" due to its high impact on the process. To optimize the selection of these "key variables", a branched version of Particle Swarm Optimization (PSO) is presented and compared with the non-Branched version and a deterministic solver (IPOPT). Advanced Convergence Criterion is also implemented to mitigate the computational effort of these approaches. In the studied cases, Branch_PSO presents a higher degree of consistency and can even outperform the traditional PSO in simultaneous process optimization and material screening. However, its computational effort in cases with a large number of branches might be... [more]

In this study, we propose a method to uniquely determine robust operating conditions for simulated moving bed (SMB) chromatography, an essential continuous liquid-phase separation technique in the pharmaceutical industry, in the form of explicit algebraic equations. The proposed method incorporates process robustness-defined as the probability of meeting the target purities under flow-rate uncertainty due to pump errors-without requiring computationally expensive dynamic simulations. In a computational demonstration, the method achieved a joint probability of 0.960 for simultaneously attaining 99.9% purity in both extract and raffinate products.

Simulated Moving Bed (SMB) chromatography is widely used for a variety of separations, yet, when applicable, these systems are typically operated using offline optimization strategies. Over time, process degradation and unforeseen disturbances may cause SMB units to deviate from the calculated optimal conditions, reducing overall performance. Real-Time Optimization (RTO) offers a promising solution by continuously monitoring and adjusting operating conditions to maintain optimal performance, despite such perturbations. However, experimental implementation of RTO in industrial SMB processes is costly and requires significant interdisciplinary coordination.To address this challenge, a virtual framework is proposed for the preliminary development of a model-based RTO system. The methodology employs a virtual plant-model pair, in which a representative plant model generates in silico experimental data, while a structurally distinct predictive model reproduces these results. Structural mism... [more]

Power-to-ammonia (P2A) provides a carbon-free alternative to conventional ammonia production by replacing fossil-based feedstocks with electrolytic hydrogen and nitrogen from air separation. For decentralized P2A systems, pressure swing adsorption (PSA) offers a flexible alternative to cryogenic air separation. However, its industrial implementations are largely proprietary, and open, first-principles models capable of simulating its cyclic, nonlinear transport are scarce in literature. This work presents a first-principles, dynamic, one-dimensional model of a PSA superstructure for nitrogen generation, formulated with thermodynamically consistent equations of state, coupling multicomponent mass, energy, and momentum balances with kinetically limited adsorption on carbon molecular sieves. The resulting system of partial differential-algebraic equations is semi-discretized using the finite volume method, integrated using diagonally implicit Runge-Kutta methods, and cyclic steady states... [more]

We present a steady-state, optimization-based techno-economic study of a continuous fluidized temperature-swing adsorption (TSA) system for post-combustion CO2 capture from biomass-derived flue gas, using two adsorption stages and one desorption stage with integrated heat-pump thermal management. The GAMS/CONOPT4 model couples molar and energy balances, Toth adsorption equilibrium, fluidized-bed hydrodynamics and literature cost correlations. Optimization yields CO2 purity of 96% v/v and 95.5% recovery at low, safe pressures with particle Reynolds numbers of 2-11, indicating near-minimum-fluidization operation. The nominal capture cost is 87 USD/tonCO2 with an internal rate of return of 42%; utilities comprise 49% of annualized costs and the adsorption compressor dominates equipment capital. Disabling the heat pump increases modeled capture cost to 124 USD/tonCO2, highlighting the heat pump's decisive role in reducing energy demand and costs. Adding adsorption stages lowers modeled cos... [more]

Magnetic Inductive Swing Adsorption (MISA) is a carbon dioxide capture process similar to Temperature Swing Adsorption that uses direct electromagnetic heating instead of classic heating systems for the regeneration step of the process. However, the lack of validated dynamic models hinders process optimization. This work introduces an open-source MISA model in the IDAES framework, incorporating Specific Absorption Rate (SAR) physics (SAR ? B²) to capture electromagnetic heating. Binary Sips isotherm parameters for Fe3O4@HKUST-1 were fitted to experimental data, achieving high statistical agreement (R2 > 0.996, RMSE < 0.022 mol/kg). Comprehensive validation was performed against adsorption isotherms, dynamic breakthrough curves, and desorption profiles. The model predicts breakthrough time with only 9% error and saturation time with 6% error. Crucially, the coupled thermal transport and SAR heating model capture temperature evolution during desorption within 5% error across all field st... [more]

Early-stage system-level assessment of emerging technologies is essential for achieving climate neutrality and a circular economy; however, such assessments are often constrained by the lack of representative life cycle inventory data. In thermal energy systems, performance strongly depends on scale, making direct application of laboratory- or bench-scale experimental data potentially misleading in life cycle assessment (LCA). This study investigates the influence of experimental scale on system-level evaluation using a zeolite-based thermal energy storage (TES) system as a case study.LCAs were conducted using performance data from laboratory-, bench-, and pilot-scale experiments and compared with predicted commercial-scale performance derived from numerical simulations. The TES system stores waste heat via water vapor desorption from zeolite and generates pressurized steam using a moving-bed with indirect heat exchanging system. Heat recovery ratios of 36%, 50%, and 61% were obtained... [more]

This study presents the modeling and operation optimization of an adsorption heat storage to improve the supply of renewable heat to a house. The system configuration is an open system with water being carried by an air flow and adsorbed on zeolite 13X beads in a packed bed. A numerical model is developed based on mass and energy balances, using a Langmuir adsorption isotherm and a Linear Driving Force (LDF) mass transfer equation. The model is implemented in Pyomo and solved with the NLP solver IPOPT. A sensitivity analysis on the discretization parameters is performed to choose a good compromise between accuracy and computational time. The chosen model is then validated against experimental data from the literature, with a mean absolute percentage error less than 5%. The dynamic optimization of the operation of the system to satisfy a heat demand is then performed. The trajectory for the inlet fluid velocity is optimized in several heat demand scenarios. The results show that this nu... [more]

Direct Air Capture (DAC) is a negative emissions technology whose performance is inherently linked to ambient conditions, which directly affect its primary feed stream (air). A common simplification in DAC model simulations is the use of fixed weather conditions, which can bias the predicted performance under weather variability. In response, this study quantifies the impact of local meteorological variability and temporal weather aggregation on the performance of DAC units. Building on a previously developed and validated 1D mechanistic model of a fixed-bed Steam-assisted Temperature Vacuum Swing Adsorption (S-TVSA) DAC process, we simulate its operation using weather data from the Met Office station at Buchan (UK), near the Saint Fergus terminal - a strategic hub for Carbon Capture and Storage (CCS) activities in Scotland. A two-branch methodological framework is developed combining optimization and forward simulations. Operating conditions are optimized using a multi-objective genet... [more]

This document includes the configuration design codes and the data produced from the simulation of Magnetic Inductive Swing Adsorption. Furthermore, the document also consists of the surrogates produced for the optimisation study. This reduces the installation of IDAES/Pyomo/PETSc in a new conda environment.

SUPPORTING INFORMATION for the work "Particle Swarm Optimization for simultaneous design and optimization of heat pumps considering Mixed Integer problems", submited to ESCAPE 36.

This document provides the Supplementary Material for the study titled: Virtual Plant–Model Pair as a Step Towards Real-Time Optimization of a Simulated Moving Bed System. The work has been submitted to the peer-reviewed proceedings of the 36th European Symposium on Computer-Aided Process Engineering (ESCAPE 2026).

Digital supplementary material for the ESCAPE 36 submission "Modeling and Simulation of Nitrogen Generation by Pressure Swing Adsorption for Power-to-Ammonia". Contains relevant model parameters from the literature.

Isotherm data for CO2 and N2 adsorption for Fe3O4@HKUST1 (MOF) and Mass and Energy balance equations for Magnetic Inductive Swing Adsorption system.

Shipping is the backbone of global freight. However, due to its currently strong reliance on fossil fuels, it accounts for 3 % of global greenhouse gas emissions, highlighting both the need and challenge of achieving the required rapid decarbonization. Over the past decade, Onboard carbon capture and storage (OCCS) has gained interest as a potential mitigation strategy while alternative fuels continue to develop. However, several capture technologies could be considered to capture the resulting CO2. In order to identify the most promising ones, this study performs a screening of different capture technologies (including absorption, membrane-assisted liquefaction, adsorption-assisted liquefaction, calcium-looping) through the case of a combination carrier under retrofit and newbuilding scenarios.
Overall, the results indicate that retrofit installations can reduce CO2 emissions by at least 45 %, even when using the existing ship power system. Once the utility (heat and power) is assum... [more]

The transition to renewable energy sources, such as biogas, requires purification processes to separate methane from carbon dioxide, with adsorption-based methods being widely employed. Accurate simulations of these systems, governed by coupled PDEs, ODEs, and algebraic equations, critically depend on precise parameter determination. While traditional approaches often result in significant errors or complex procedures, optimization algorithms provide a more efficient and reliable means of parameter estimation, simplifying the process, improving simulation accuracy, and enhancing the understanding of these systems. This work introduces an Artificial Intelligence-based methodology for estimating the isotherm parameters of a mathematical phenomenological model for fixed-bed experiments. The separation of CO2 and CH4 is used as case study. This work develops an algorithm for parameter estimation for the system's mathematical model. The results show that the validated model has a close fit... [more]

The efficient separation of carbon dioxide (CO2) and methane (CH4) is crucial for chemical processes, including biogas upgrading and natural gas purification. Metal-organic frameworks (MOFs) have gained significant attention as promising adsorbents for these processes due to their high porosity and tunable structures. Estimating the adsorption capacity of MOFs is essential for screening high performing adsorbents. While molecular simulations are commonly used to estimate the adsorption capacities, their computational intensity acts as a bottleneck in screening MOF adsorbents. In this study, we propose a machine learning (ML)-based framework for the high-throughput prediction of adsorption isotherms for CO2 and CH4 in MOFs. A graph neural network (GNN) model was developed to predict adsorption capacities, effectively replacing the time-consuming molecular simulations. The GNN model processes the structural graphs of MOFs, capturing their spatial configurations, such as surface structure... [more]

Recent advancements in material design have made adsorption a more energy-efficient alternative to traditional thermally driven separation processes. Accurate modelling of adsorption thermodynamics is crucial for designing and operating equilibrium-limited adsorption systems. High-quality open-source packages like PyIAST, PyGAPsare available for processing adsorption data in Python. They provide a robust set of features for processing and analysing isotherms. However, they have no support for automatic differentiation and are not targeted for performance. Langmuir.jl addresses these limitations by leveraging Julia's composable and differentiable programming ecosystem. Langmuir.jl includes tools for processing adsorption thermodynamics data—loading data, fitting isotherms with most often used models, predictive multicomponent adsorption through Ideal Adsorption Solution Theory (IAST) — and, importantly, enabling accurate derivative calculations through Julia's automatic differentiation... [more]

By capturing carbon dioxide from biomass flue gases, energy processes with negative carbon footprint are achieved. Among carbon capture methods, the fluidized temperature swing adsorption (TSA) column is a promising low-pressure alternative, but it has been developed on small scales. This work aims to model, simulate and optimize a fluidized TSA multi-stage equilibrium system to obtain a cost estimate and a conceptual design for future process scale up. A mathematical model described adsorption in multiple stages, each with a heat exchanger, coupled to the desorption operation. The model was based on elementary macroscopic molar and energy balances, coupled to pressure drops in a fluidized bed designed to operate close to the minimum fluidization velocity, and coupled to thermodynamics of adsorption equilibrium of a mixture of carbon dioxide and nitrogen in solid sorbents (the Toth equilibrium isotherm was used). The complete fluidized TSA process has been optimized to minimize costs,... [more]

Integrated Carbon Capture and Conversion (ICCC) technologies offer an efficient alternative to conventional Carbon Capture, Utilization, and Storage (CCUS) methods by simultaneously capturing and converting CO2 into value-added chemicals. Dual-function materials (DFMs) are particularly promising due to their capability to integrate adsorption and catalysis in a single step, thereby reducing both energy consumption and associated costs. This study models the dynamic behavior of CO2 adsorption within a laboratory-scale packed-bed reactor employing DFMs. The mathematical model incorporates momentum, mass, and heat transfer equations, implemented using COMSOL Multiphysics v5.6, and evaluates various axial dispersion models (ADMs) and mass transfer coefficients (MTCs). The results indicate that the Rastegar-Gu ADM, combined with an MTC of 8.3 × 10-2 s-1, provides the most accurate representation of breakthrough and saturation times, as well as the total quantity adsorbed. Furthermore, relat... [more]

The transition to renewable energy sources, such as biogas, requires purification processes to separate methane from carbon dioxide, with adsorption-based methods being widely employed. Accurate simulations of these systems, governed by coupled PDEs, ODEs, and algebraic equations, critically depend on precise parameter determination. While traditional approaches often result in significant errors or complex procedures, optimization algorithms provide a more efficient and reliable means of parameter estimation, simplifying the process, improving simulation accuracy, and enhancing the understanding of these systems.
This work introduces an Artificial Intelligence-based methodology for estimating the isotherm parameters of a mathematical phenomenological model for fixed-bed experiments. The separation of CO₂ and CH₄ is used as case study. This work develops an algorithm for parameter estimation for the system's mathematical model. The results show that the validated model has a close fi... [more]

Metformin, widely prescribed to treat type 2 diabetes for its effectiveness and low cost, has raised concerns about its presence in aqueous effluents and its potential environmental and public health impacts. To address this issue, xerogels were synthesized from resorcinol and formaldehyde, with molar ratios ranging from 0.05 to 0.40. These xerogels were thoroughly characterized using FT-IR, SEM, TGA, and TEM analyses. Batch adsorption experiments were performed with standard metformin solutions at concentrations of 50 and 500 mg/L, varying pH, and temperature to determine the adsorption isotherms of the synthesized xerogels. The adsorption data revealed a maximum adsorption capacity of 325 mg/g at pH 11 and 25 °C. Quantum chemical calculations revealed that electrostatic interactions govern metformin adsorption onto xerogels. The xerogels’ adsorption capacity was evaluated in competitive systems with CaCl2, NaCl, MgCl2, and synthetic urines. Reuse cycles demonstrated that xerogels cou... [more]

This study addresses the environmental and health hazards posed by Pb(II) and iodine, two significant contaminants. The objective was to explore the adsorption of these substances from aqueous solutions using biochar derived from the leaf midribs of the date palm through a slow pyrolysis process. The pyrolysis was conducted in two stages within a vacuum furnace: initially at 300 °C for 1 h followed by overnight cooling, and then at 600 °C with a similar cooling process. The resulting biochar was characterized for its microstructural features and functional groups using scanning electron microscopy (SEM) and Fourier transform infrared (FT-IR) spectroscopy. It exhibited a porous structure with large numbers of pores (20 to 50 μm in size) and functional groups including O-H, C-H, and C=C, which are integral to its adsorption capabilities. For the adsorption studies, a 100 ppm Pb(II) ion solution was treated with varying amounts of biochar (20, 40, 60, and 80 mg) for 24 h. In parallel, iod... [more]

Glyphosate, a broad-spectrum herbicide, poses a potential threat to human health and the ecosystem due to its toxicity. In this study, iron-based water treatment residuals (Fe-WTRs) were employed for glyphosate removal. The adsorption kinetics, isotherms, and thermodynamics, as well as the effects of pH, Fe-WTR particle size, and temperature, were explored. The results show that Fe-WTRs are an effective adsorbent for glyphosate adsorption, and the maximum uptake capacity was recorded as 30.25 mg/g. The Fe-WTR surface was positively charged, and low-valent iron dominated under acidic conditions, favoring glyphosate adsorption. Furthermore, smaller Fe-WTR particles (<0.125 mm) showed a faster absorption rate and 20% higher adsorption capacity than larger particles (2−5 mm). The kinetic analysis indicated that the adsorption process exhibits a two-step profile, conforming to the pseudo-second-order model, and the thermodynamic analysis indicated that it is a spontaneous, endothermic, a... [more]

The global increase in antibiotics consumption has caused hazardous concentrations of these antimicrobials to be present in soils, mainly due to the spreading of sewage sludge (or manure or slurry) and wastewater, and they could enter the food chain, posing serious risks to the environment and human health. One of these substances of concern is cefuroxime (CFX). To face antibiotics-related environmental pollution, adsorption is one of the most widely used techniques, with cost-effective and environmentally friendly byproducts being of clear interest to retain pollutants and increase the adsorption capacity of soils. In light of this, in this work, three low-cost bioadsorbents (pine bark, oak ash, and mussel shell) were added to different soil samples (at doses of 12 and 48 t/ha) to study their effects on the adsorption of CFX. Specifically, batch experiments were carried out for mixtures of soils and bioadsorbents, adding a range of different antibiotic concentrations at a fixed ionic... [more]