Multi-Scale Digital Twin Framework with Physics-Informed Neural Networks for Real-Time Optimization and Predictive Control of Amine-Based Carbon Capture: Development, Experimental Validation, and Techno-Economic Assessment

Abstract

Carbon capture and storage (CCS) is essential for achieving net-zero emissions, yet amine-based capture systems face significant challenges including high energy penalties (20–30% of power plant output) and operational costs ($50–120/tonne CO₂). This study develops and validates a novel multi-scale Digital Twin (DT) framework integrating Physics-Informed Neural Networks (PINNs) to address these challenges through real-time optimization. The framework combines molecular dynamics, process simulation, computational fluid dynamics, and deep learning to enable real-time predictive control. A key innovation is the sequential training algorithm with domain decomposition, specifically designed to handle the nonlinear transport equations governing CO₂ absorption with enhanced convergence properties. The algorithm achieves prediction errors below 1% for key process variables (R² > 0.98) when validated against CFD simulations across 500 test cases. Experimental validation against pilot-scale absorber data (12 m packing, 30 wt% MEA) confirms good agreement with measured profiles, including temperature (RMSE = 1.2 K), CO₂ loading (RMSE = 0.015 mol/mol), and capture efficiency (RMSE = 0.6%). The trained surrogate enables computational speedups of up to four orders of magnitude, supporting real-time inference with response times below 100 ms suitable for closed-loop control. Under the conditions studied, the framework demonstrates reboiler duty reductions of 18.5% and operational cost reductions of approximately 31%. Sensitivity analysis identifies liquid-to-gas ratio and MEA concentration as the most influential parameters, with mechanistic explanations linking these to mass transfer enhancement and reaction kinetics. Techno-economic assessment indicates favorable investment metrics, though results depend on site-specific factors. The framework architecture is designed for extensibility to alternative solvent systems, with future work planned for industrial-scale validation and uncertainty quantification through Bayesian approaches.

1. Introduction

The global imperative for industrial decarbonization has placed significant pressure on energy-intensive sectors to reduce greenhouse gas emissions while maintaining operational efficiency [1]. The petroleum refining industry, contributing approximately 4% of global industrial emissions, faces particular challenges in implementing effective decarbonization strategies [2]. Carbon capture, utilization, and storage (CCUS) technologies have emerged as important components of comprehensive emissions reduction approaches, offering the capability to capture 90–99% of CO₂ from point sources [3,4].

According to the International Energy Agency’s (IEA) 2025 CCUS Projects Database, operational CO₂ capture capacity reached approximately 50 million tonnes (Mt) as of Q1 2025, with projections indicating potential expansion to 430 Mt by 2030 [5]. However, this capacity remains below the levels required in net-zero emissions scenarios, highlighting the need for continued technology development and deployment [6]. Only approximately 20% of announced 2030 capture capacity has reached Final Investment Decision (FID), suggesting that economic and operational barriers continue to impede widespread adoption [7].

Post-combustion capture using aqueous amine solutions, particularly monoethanolamine (MEA) at 30 wt% concentration, remains among the most commercially deployed approaches, with extensive industrial experience [8]. However, the technology faces economic challenges: specific reboiler duties typically range from 3.2 to 4.2 GJ/tonne CO₂, imposing energy penalties of 20–30% on power plant output, while capture costs of $50–120/tonne CO₂ often exceed carbon pricing in many jurisdictions [9,10]. These challenges motivate the development of advanced optimization frameworks to improve energy efficiency and reduce operational costs.

1.1. Bridging from Conventional Methods to Intelligent Optimization

Traditional approaches to carbon capture optimization have relied on three primary methodologies: molecular-scale simulations for thermophysical property prediction, process-scale models for flowsheet optimization, and equipment-scale computational fluid dynamics (CFD) for detailed flow field analysis. While each methodology provides valuable insights at its respective scale, significant limitations emerge when applied to real-time optimization scenarios [11,12].

Molecular dynamics simulations, using tools such as LAMMPS and GROMACS, can predict diffusion coefficients and solubility parameters with high accuracy but require 24–72 h per calculation, making them unsuitable for online applications [13]. Process simulation tools (Aspen Plus, gPROMS) provide system-level optimization but typically require 5–30 min per steady-state solution and may struggle with real-time transient disturbances [14,15]. CFD simulations offer detailed spatial resolution but demand 4–8 h on high-performance clusters, precluding their use in closed-loop control [16].

Table 1. Comparison of conventional simulation methods for carbon capture systems with reported performance metrics.

Method	Computation Time	Accuracy	Spatial Resolution	Real-Time Capability
Molecular Dynamics	24–72 h	High (<5% error)	Atomic scale	Not feasible
Process Simulation	5–30 min	Medium (5–10%)	Lumped/staged	Limited
CFD Simulation	4–8 h	High (<3% error)	Continuous 3D	Not feasible
PINN Surrogate	<100 ms	High (<1% error)	Continuous 3D	Feasible

quantifies these limitations with reported computational times and accuracy metrics from the literature.

This computational gap motivates the integration of physics-informed machine learning approaches with digital twin technology. PINNs can encode the governing physics from these conventional methods while achieving inference speeds compatible with real-time control, effectively bridging multi-scale information into an operational framework [17,18].

1.2. Digital Twin Technology in Industrial Applications

Digital Twin (DT) technology has received increasing attention as an approach for addressing operational challenges in industrial processes [19,20]. A digital twin can be defined as a virtual representation of a physical system that maintains data exchange with its physical counterpart, enabling simulation, prediction, and optimization of system behavior [21,22]. The technology has evolved from early product lifecycle management applications to encompass real-time sensor integration and machine learning-enhanced prediction capabilities [20].

The digital twin market in the oil and gas sector was valued at EUR 102.33 million in 2023 and is projected to grow substantially through 2032 [23]. Research suggests that DT implementation may achieve energy savings of up to 30% in some industrial applications, though results vary significantly depending on implementation context [24,25]. Recent reviews have identified maturity levels for digital twin implementation ranging from descriptive visualization through autonomous optimization [26,27,28]. Current industrial adoption remains predominantly at informative and predictive levels, with autonomous implementations representing a smaller fraction of deployments [29].

Despite the current limitations in widespread industrial adoption, several factors justify the pursuit of DT frameworks for carbon capture applications. First, the energy-intensive nature of amine regeneration (representing 70–80% of operational costs) creates strong economic incentives for even modest efficiency improvements [30]. Second, the inherent variability in flue gas composition and flow rates from industrial sources necessitates adaptive control strategies that static optimization approaches cannot provide [14]. Third, regulatory requirements for emissions reporting and carbon credit verification increasingly demand real-time monitoring and documentation capabilities that digital twins naturally provide [31]. Finally, the declining costs of IoT sensors and edge computing now make real-time DT implementation economically viable at scales previously considered impractical [32].

1.3. Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have emerged as a methodology for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training [33]. The approach addresses some limitations of purely data-driven methods—including extrapolation challenges and inability to guarantee physical consistency—while potentially reducing data requirements compared to traditional machine learning [17,18].

The PINN framework uses automatic differentiation to compute partial derivatives of network outputs, enabling evaluation of PDE residuals at collocation points throughout the computational domain [34]. Recent advances include sequential training approaches for hyperbolic transport equations [35], domain decomposition methods for large-scale problems [36], and conservative formulations for flow applications [37]. Applications to CO₂ storage have shown promising results, with hybrid approaches achieving R² values exceeding 0.95 for plume prediction in reservoir simulations [38,39,40].

1.3.1. PINN Applications in Separation and Absorption Systems

While PINNs have been extensively applied to subsurface flow and reservoir simulation, their application to gas-liquid absorption systems presents unique challenges and opportunities. The coupled nature of mass transfer, heat transfer, and chemical reaction in amine-based capture systems creates stiff equation systems that traditional numerical methods struggle to solve efficiently [15]. Recent studies have demonstrated PINN effectiveness for similar reactive transport problems, achieving 50–100× speedup over finite element methods while maintaining accuracy within 2% [41,42].

The choice of sequential training over other PINN training strategies (e.g., curriculum learning, adaptive collocation, multi-fidelity approaches) is motivated by the hyperbolic nature of the convection-dominated transport in absorber columns. Standard PINN training struggles with sharp gradients and wave propagation, often failing to capture the correct physics without special treatment [43]. Sequential training addresses this by decomposing the time domain into segments, allowing the network to progressively learn the solution evolution. Comparative studies have shown that sequential training achieves 3–5× faster convergence and 40% lower final loss values compared to single-domain training for similar transport problems [35,44].

1.3.2. Recent DT-PINN Integrations in Process Engineering

The integration of PINNs with digital twin frameworks has gained momentum across process engineering applications. In chemical reactor systems, DT-PINN approaches have achieved 15–25% improvements in yield optimization for continuous pharmaceutical manufacturing [45]. For energy systems, hybrid physics-data models within digital twins have demonstrated 20–30% reductions in energy consumption for building HVAC systems [26]. In petroleum refining, digital twins incorporating physics-informed surrogates have enabled predictive maintenance with 85% accuracy in fault detection [32].

Table 2. Recent DT-PINN integrated applications in process engineering fields.

Application Domain	Key Metrics	Speedup	Reference
Chemical Reactors	15–25% yield improvement	1000×	[45]
HVAC Systems	20–30% energy reduction	500×	[26]
Petroleum Refining	85% fault detection	2000×	[32]
CO2 Storage	R2 > 0.95 for plume prediction	5000×	[40]
This Work	18.5% energy reduction	10,000×	–

summarizes recent DT-PINN applications in related fields, providing context for the present work’s positioning.

1.4. Research Gaps and Objectives

Despite advances in both DT and PINN technologies, several gaps remain in their application to carbon capture systems:

• Limited integration of multi-scale modeling approaches within digital twin frameworks for CCS applications [11,12];
• Insufficient validation of PINN implementations against experimental pilot plant data, with most studies relying on numerical benchmarks [46,47];
• Limited techno-economic analysis of combined DT-PINN implementations with sensitivity to key assumptions [30,48];
• Gap between research demonstrations and industrial deployment readiness [29,31];
• Need for surrogate models achieving inference times compatible with real-time control requirements [49,50];
• Lack of systematic comparison between PINN training strategies for absorption system modeling [44,51];
• Insufficient treatment of sensor noise and operational disturbances in DT implementations [52].

This study addresses these gaps by developing a multi-scale framework integrating PINN-based surrogate models with digital twin architecture for carbon capture optimization. To the authors’ knowledge, this represents one of the first comprehensive integrations of these technologies specifically for amine-based CCS systems with multi-level validation including experimental data.

The primary objectives are to:

• Develop a hybrid PINN-Digital Twin framework for amine-based CO₂ capture systems incorporating multi-scale modeling;
• Design and validate a sequential training algorithm achieving prediction errors below 1% compared to CFD simulations for the cases studied;
• Demonstrate computational speedups enabling real-time optimization applications;
• Quantify energy efficiency improvements under representative operating conditions;
• Conduct techno-economic analysis with appropriate sensitivity assessment;
• Compare sequential training performance against alternative PINN training methods;
• Provide mechanistic explanations for sensitivity analysis findings.

2. Materials and Methods

2.1. Multi-Scale Framework Architecture

The proposed framework integrates four modeling scales—molecular, process, equipment, and digital twin—connected through a central Physics-Informed Neural Network engine (Figure 1). This architecture enables information flow between scales: molecular simulations provide thermophysical properties to process models, which inform equipment-scale CFD boundary conditions; the digital twin layer provides optimization feedback.

Inter-Scale Data Flow and Integration

Figure 2 provides a detailed schematic of data flow between modeling scales. The integration follows a hierarchical approach where each scale provides specific parameters to subsequent scales:

• Molecular → Process: Diffusion coefficients ($D_{C{O}_2-MEA}$, $D_{C{O}_2-H_{2}O}$), Henry’s law constants, activity coefficients, and viscosity correlations are computed from molecular dynamics and passed as property packages to process simulation.
• Process → Equipment: Stream conditions (flow rates, compositions, temperatures) from converged flowsheets serve as boundary conditions for CFD simulations. Heat and mass transfer coefficients from correlations inform source terms.
• Equipment → PINN: CFD solutions provide training data and validation benchmarks. Velocity fields, concentration profiles, and temperature distributions form the supervised learning dataset.
• PINN → Digital Twin: Trained surrogate models enable real-time inference. Gradient information from the PINN supports optimization through backpropagation.

Figure 2. Detailed data flow schematic showing specific parameters exchanged between modeling scales. Molecular simulations provide thermophysical properties; process models establish operating boundaries; CFD generates training data; the PINN enables real-time inference for digital twin optimization.

Figure 2. Detailed data flow schematic showing specific parameters exchanged between modeling scales. Molecular simulations provide thermophysical properties; process models establish operating boundaries; CFD generates training data; the PINN enables real-time inference for digital twin optimization.

Table 3. Multi-scale simulation framework components.

Scale	Tool	Parameters	Time	Outputs
Molecular	LAMMPS, GROMACS	Force fields, T, P	24–72 h	D, solubility
Process	Aspen Plus V14	Flows, compositions	5–30 min	Duties, $\eta$
Equipment	ANSYS Fluent	Geometry, mesh	4–8 h	u, C, T fields
Digital Twin	PINN + IoT	Sensors, setpoints	<100 ms	Optimal controls

summarizes the simulation tools, key parameters, and output variables across modeling scales.

2.2. Process Description

The amine-based CO₂ capture process comprises two packed columns—absorber and regenerator—with heat integration (Figure 3). Flue gas containing 10–15 vol% CO₂ enters the absorber bottom, contacting lean amine solution flowing counter-currently. The exothermic absorption releases approximately 84 kJ/mol. Rich amine is preheated and enters the regenerator where thermal stripping at 110–120 °C releases captured CO₂. Regenerated lean amine is cooled and recycled.

Table 4. Process simulation specifications for amine-based CO₂ capture unit.

Parameter	Value/Specification
Absorber Column
Column type	Packed bed with Mellapak 250Y
Column diameter	1.2 m
Packing height	12 m
Number of theoretical stages	15
Operating pressure	1.0–1.2 bar
Gas inlet temperature	40–45 °C
Regenerator Column
Column diameter	0.8 m
Packing height	8 m
Operating pressure	1.5–2.0 bar
Reboiler temperature	110–120 °C
Solvent System
Solvent	Monoethanolamine (MEA), 30 wt%
Lean loading	0.20 mol CO2/mol MEA
Rich loading	0.45–0.50 mol CO2/mol MEA
L/G ratio	2.5–3.5 kg/kg
Solvent circulation rate	50–70 m3/h
Performance Targets
CO2 capture efficiency	≥90%
Specific reboiler duty	3.2–3.8 GJ/tonne CO2
Flue gas CO2 content	10–15 vol%
Flue gas flow rate	10,000–15,000 Nm3/h

provides process specifications used in this study.

Experimental Setup and Measurement Uncertainties

The pilot-scale validation data were obtained from a 12 m packed column facility.

Table 5. Experimental conditions and measurement uncertainties for pilot-scale validation.

Parameter	Value/Range	Uncertainty
Operating Conditions
Flue gas flow rate	10,000–15,000 Nm3/h	±2%
Liquid flow rate	50–70 m3/h	±1.5%
Inlet CO2 concentration	10–15 vol%	±0.2 vol%
Inlet gas temperature	40–45 °C	±0.5 °C
Instrumentation
Temperature sensors	Type K thermocouples	±0.5 K
CO2 analyzers	NDIR (0–20% range)	±0.1% of reading
Flow meters	Coriolis type	±0.1%
pH sensors	Online electrode	±0.02
Sampling Protocol
Steady-state criterion	<2% variation over 30 min	–
Data acquisition rate	1 Hz	–
Number of test conditions	24 operating points	–
Replicate measurements	3 per condition	–

details the experimental conditions and instrumentation specifications.

2.3. Physics-Informed Neural Network Architecture

The PINN component provides surrogate predictions of the coupled PDEs governing CO₂ absorption (Figure 4). The architecture employs a multi-output fully-connected network with shared hidden layers.

2.3.1. Governing Equations

The governing equations describe the coupled transport phenomena in the absorber column. The mass balance for CO₂ (Equation (1)) incorporates convection (first term on LHS), molecular and turbulent diffusion (first term on RHS), and the chemical reaction sink (second term on RHS). In the packed column, the effective diffusivity $D_{eff}$ accounts for both molecular diffusion and dispersion effects induced by the packing geometry [15]:

$${\displaystyle \frac{\partial C}{\partial t}}+\mathbf{u}·\nabla C=D_{eff}{\nabla }^{2}C+R(C,T,\left[\mathrm{MEA}\right])$$

(1)

The energy balance (Equation (2)) couples thermal transport to the reaction system. The left-hand side represents accumulation and convective transport of thermal energy. The right-hand side includes conductive heat transfer (through the effective thermal conductivity $k_{eff}$, which incorporates packing effects) and the exothermic heat release from CO₂ absorption ($\Delta H_{rxn}\approx -84$ kJ/mol for MEA) [8]:

$$\rho C_p\left({\displaystyle \frac{\partial T}{\partial t}}+\mathbf{u}·\nabla T\right)=k_{eff}{\nabla }^{2}T+(-\Delta H_{rxn})·R$$

(2)

The reaction rate follows the zwitterion mechanism (Equation (3)), which is the accepted kinetic model for CO₂-MEA systems. This two-step mechanism involves initial formation of a zwitterion intermediate followed by deprotonation. The rate constants $k_2$ (zwitterion formation), $k_{-1}$ (zwitterion reversion), and $k_3$ (deprotonation by base) are temperature-dependent Arrhenius expressions [53]:

$$R={\displaystyle \frac{k_2\left[{\mathrm{C}\mathrm{O}}_2\right]\left[\mathrm{MEA}\right]}{1+\frac{k_2}{k_{-1}}+\frac{k_2\left[\mathrm{MEA}\right]}{k_3}}}$$

(3)

The momentum equation (Equation (4)) governs velocity field evolution through the packed bed. Beyond standard Navier-Stokes terms, the packing resistance ${\mathbf{F}}_{packing}$ is modeled using the Ergun equation or packing-specific correlations that account for pressure drop through structured or random packings [16]:

$$\rho \left({\displaystyle \frac{\partial \mathbf{u}}{\partial t}}+\mathbf{u}·\nabla \mathbf{u}\right)=-\nabla P+{\mu }_{eff}{\nabla }^2\mathbf{u}+\rho \mathbf{g}+{\mathbf{F}}_{packing}$$

(4)

where C is CO₂ concentration, T is temperature, $\mathbf{u}$ is velocity, $D_{eff}$ is effective diffusion coefficient, R is reaction rate, $\rho$ is density, $C_p$ is heat capacity, $k_{eff}$ is thermal conductivity, $\Delta H_{rxn}$ is heat of reaction (84 kJ/mol), and ${\mathbf{F}}_{packing}$ represents packing resistance.

2.3.2. Boundary Conditions for CFD and PINN Training

The CFD simulations used to generate PINN training data employed the following boundary conditions:

• Gas inlet (bottom): Velocity inlet with uniform profile, specified CO₂ concentration (10–15 vol%), temperature (40–45 °C)
• Liquid inlet (top): Mass flow inlet with MEA concentration (30 wt%), lean loading (0.20 mol/mol), temperature (40 °C)
• Gas outlet (top): Pressure outlet at atmospheric conditions
• Liquid outlet (bottom): Pressure outlet, allowing backflow
• Column walls: No-slip for velocity, adiabatic for temperature, zero-flux for species

These boundary conditions are embedded in the PINN through the boundary loss term ${\mathcal{L}}_{BC}$, with 5000 boundary collocation points distributed across inlet, outlet, and wall surfaces.

2.3.3. PINN Loss Function

The total loss function combines data-driven and physics-informed components:

$${\mathcal{L}}_{total}={\lambda }_{data}{\mathcal{L}}_{data}+{\lambda }_{PDE}{\mathcal{L}}_{PDE}+{\lambda }_{BC}{\mathcal{L}}_{BC}+{\lambda }_{IC}{\mathcal{L}}_{IC}$$

(5)

where:

$$\begin{array}{cc}\hfill {\mathcal{L}}_{data}& ={\displaystyle \frac{1}{N_d}}\sum _{i=1}^{N_d}{∥{\widehat{\mathbf{y}}}_i-{\mathbf{y}}_i∥}_2^2\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill {\mathcal{L}}_{PDE}& ={\displaystyle \frac{1}{N_r}}\sum _{j=1}^{N_r}{\left|\mathcal{R}\left({\mathbf{x}}_j\right)\right|}^2\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill {\mathcal{L}}_{BC}& ={\displaystyle \frac{1}{N_b}}\sum _{k=1}^{N_b}{∥\mathcal{B}\left({\widehat{\mathbf{y}}}_k\right)-{\mathbf{g}}_k∥}_2^2\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill {\mathcal{L}}_{IC}& ={\displaystyle \frac{1}{N_0}}\sum _{l=1}^{N_0}{∥{\widehat{\mathbf{y}}}_l(t=0)-{\mathbf{y}}_0∥}_2^2\hfill \end{array}$$

(9)

The weighting coefficients $\lambda$ are adaptively updated using gradient normalization [43].

Table 6. PINN hyperparameters and training configuration with selection rationale based on systematic sensitivity analysis.

Parameter	Value	Rationale
Hidden layers	4	Grid search over 2–8 layers; 4 layers minimized validation loss while avoiding overfitting (see Section 2.3.4)
Neurons per layer	64	Tested 32, 64, 128, 256; 64 neurons achieved <1% accuracy loss vs. 256 with 4× faster training
Activation function	tanh	Required for smooth second-order derivatives in PDE residuals; ReLU caused gradient discontinuities
Optimizer	Adam	Adaptive learning rate
Initial learning rate	${10}^{-3}$	Standard starting point
Learning rate schedule	Decay to ${10}^{-5}$	Fine convergence
Batch size	1024	GPU optimization
Training epochs	25,000	Convergence criterion
${\lambda }_{data}$ (initial)	1.0	Reference weight
${\lambda }_{PDE}$ (initial)	0.1	Prevents physics terms from dominating early training before data fit established
${\lambda }_{BC}$, ${\lambda }_{IC}$	1.0	Solution uniqueness
Collocation points ($N_r$)	50,000	Interior domain coverage
Boundary points ($N_b$)	5000	Boundary representation

presents the hyperparameter configuration.

2.3.4. Hyperparameter Sensitivity Analysis

A systematic hyperparameter sensitivity study was conducted to justify the final architecture configuration. Figure 5 summarizes the results across key hyperparameters.

For network depth, validation loss decreased from $3.2\times {10}^{-3}$ (2 layers) to $1.2\times {10}^{-3}$ (4 layers) but showed no significant improvement beyond 4 layers while training time increased linearly. For network width, 64 neurons per layer achieved comparable accuracy to 256 neurons (within 0.8%) but with 4× faster training. The tanh activation was essential for accurate PDE residual computation; ReLU and its variants produced non-smooth second derivatives that degraded physics loss convergence.

The initial ${\lambda }_{PDE}=0.1$ was determined through the gradient normalization approach of Wang et al. [43], which balances gradient magnitudes across loss components during early training. Higher initial values caused the network to overfit to physics constraints before establishing a reasonable data fit, resulting in slower overall convergence.

2.3.5. Sequential Training Algorithm

To address challenges with nonlinear transport equations, we employ sequential training with domain decomposition (Algorithm 1).

Algorithm 1 Sequential Training PINN with Domain Decomposition

Require:  Training data $\mathcal{D}$, time domain $[0,T]$, number of segments $N_s$ Ensure:  Trained PINN model ${\mathcal{N}}_{\theta }$  1: Initialize network weights $\theta$  2: Divide time domain: $\Delta t=T/N_s$  3: for $k=1$ to $N_s$ do  4:     Define time segment: $t\in \left[\right(k-1)\Delta t,k\Delta t]$  5:     Sample collocation points in current segment  6:     if $k>1$ then  7:         Use previous segment solution as initial condition  8:     end if  9:     for epoch $=1$ to $E_{max}$ do   10:         Compute predictions: $\widehat{\mathbf{y}}={\mathcal{N}}_{\theta }(\mathbf{x},t)$   11:         Compute PDE residuals via automatic differentiation   12:         Calculate total loss ${\mathcal{L}}_{total}$   13:         Update adaptive weights using gradient normalization   14:         Update parameters: $\theta \leftarrow \theta -\alpha {\nabla }_{\theta }{\mathcal{L}}_{total}$   15:         if ${\mathcal{L}}_{total}<{ϵ}_{tol}$ then   16:            break   17:         end if   18:     end for   19: end for   20: return  ${\mathcal{N}}_{\theta }$

2.3.6. Comparison with Alternative PINN Training Methods

To contextualize the sequential training approach, we compared its performance against three state-of-the-art PINN training methods (Table 7):

• Standard PINN: Single-domain training without temporal decomposition
• Adaptive Collocation (RAR-D) [51]: Residual-based adaptive refinement with dynamic resampling
• Curriculum Learning [54]: Gradually increasing problem complexity

Table 7. Comparison of PINN training methods for CO₂ absorber modeling.

Method	Final Loss	Training Time (h)	R2 (Temperature)	Convergence Issues
Standard PINN	8.5 × ${10}^{-3}$	4.2	0.942	Gradient pathology near inlet
RAR-D Adaptive	2.1 × ${10}^{-3}$	3.8	0.978	Oscillatory loss curves
Curriculum Learning	1.8 × ${10}^{-3}$	3.5	0.982	Requires manual schedule
Sequential (This work)	1.2 × ${10}^{-3}$	2.5	0.991	None observed

Table 7. Comparison of PINN training methods for CO₂ absorber modeling.

Method	Final Loss	Training Time (h)	R2 (Temperature)	Convergence Issues
Standard PINN	8.5 × ${10}^{-3}$	4.2	0.942	Gradient pathology near inlet
RAR-D Adaptive	2.1 × ${10}^{-3}$	3.8	0.978	Oscillatory loss curves
Curriculum Learning	1.8 × ${10}^{-3}$	3.5	0.982	Requires manual schedule
Sequential (This work)	1.2 × ${10}^{-3}$	2.5	0.991	None observed

The sequential training approach achieved the lowest final loss and highest accuracy while requiring the least training time. The key advantage stems from its natural handling of the hyperbolic transport character; by solving progressively in time, information propagates correctly from inlet to outlet without the spurious gradient pathologies that plague single-domain approaches [43].

2.4. Digital Twin Implementation

Algorithm 2 describes the real-time optimization loop.

Algorithm 2 Digital Twin Real-Time Optimization Loop

Require:  Trained PINN surrogate ${\mathcal{N}}_{\theta }$, sensor data stream $\mathcal{S}$ Ensure:  Optimal setpoints ${\mathbf{u}}^{*}$  1: Initialize: Load PINN model  2: loop  3:     Read and validate sensor data: ${\mathbf{x}}_{meas}\leftarrow \mathcal{S}$  4:     Noise Filtering: Apply exponential moving average with $\alpha =0.3$  5:     State Estimation: $\widehat{\mathbf{y}}\leftarrow {\mathcal{N}}_{\theta }\left({\mathbf{x}}_{meas}\right)$  6:     Anomaly Detection:  7:     if $\parallel \widehat{\mathbf{y}}-{\mathbf{y}}_{meas}\parallel >{\delta }_{anomaly}$ then  8:         Trigger alert and log event  9:     end if   10:     Optimization:   11:        ${min}_{\mathbf{u}}J\left(\mathbf{u}\right)=E_{reboiler}\left(\mathbf{u}\right)+\gamma ·Penalty\left(\mathbf{u}\right)$   12:         Subject to: ${\eta }_{capture}\ge 0.90$   13:         ${\mathbf{u}}^{*}\leftarrow argminJ\left(\mathbf{u}\right)$ using L-BFGS-B   14:     Rate Limiting: Constrain $\parallel \Delta \mathbf{u}\parallel \le {\mathbf{u}}_{max\_rate}·\Delta t$   15:     Control Action:   16:     if $\parallel {\mathbf{u}}^{*}-{\mathbf{u}}_{current}\parallel >{\delta }_{deadband}$ then   17:         Send setpoint update to DCS   18:     end if   19:     Wait for next cycle ($\Delta t_{sample}=100$ ms)   20: end loop

Sensor Noise Handling and Disturbance Rejection

Industrial sensor measurements contain noise and occasional outliers that can destabilize real-time optimization. The framework implements a multi-layer robustness strategy:

• Signal conditioning: Raw sensor readings pass through an exponential moving average filter with $\alpha =0.3$, balancing noise rejection against response lag.
• Outlier detection: Measurements exceeding 3$\sigma$ from the 60-s rolling mean are flagged and replaced with predicted values from the PINN.
• Rate limiting: Setpoint changes are constrained to physically achievable rates (e.g., ±5% per minute for L/G ratio) to prevent actuator saturation.
• Deadband logic: Small optimization adjustments (<${\delta }_{deadband}$) are suppressed to reduce control valve wear and process variability.

Table 8. Framework robustness under simulated disturbances and sensor anomalies.

Disturbance Type	Magnitude	Recovery Time	Performance Impact
Sensor noise (Gaussian)	$\sigma =5\%$	N/A (filtered)	<0.5% efficiency loss
Sensor dropout	10 s duration	2 control cycles	No capture violation
Flue gas flow step	±20% step	45 s	Capture maintained >89%
CO2 concentration ramp	+5% over 5 min	Tracks smoothly	Capture maintained >90%

summarizes the robustness testing results under simulated sensor failures and process disturbances.

2.5. Validation Methodology

The PINN model undergoes a four-level validation:

• Analytical verification: Comparison with known solutions for simplified cases;
• CFD benchmark: Comparison with ANSYS Fluent simulations across 500 test cases;
• Experimental validation: Comparison with pilot-scale absorber data;
• Industrial assessment: Comparison with operational plant data (ongoing).

Transient Validation Protocol

To address real-time optimization requirements, the PINN was validated under transient conditions representative of industrial operation (

Table 9. Transient validation results under dynamic operating conditions.

Test Scenario	Disturbance	RMSE	Max Error	Response Match
Flue gas flow step	±20% step	1.8 K	4.2 K	94%
CO2 concentration ramp	+5%/min	0.018 mol/mol	0.032 mol/mol	92%
L/G ratio change	±10% step	0.8% capture	1.5%	96%
Combined disturbance	Flow + conc.	2.1 K	5.1 K	91%

). Test scenarios included step changes in flue gas flow, ramp changes in CO₂ concentration, and combined disturbances.

The response match metric quantifies how well the PINN predicts the temporal evolution of key variables during transients, computed as the cross-correlation between predicted and measured time series.

3. Results

3.1. PINN Training Convergence

Figure 6 presents training convergence over 25,000 epochs. The total loss decreased from approximately 1.0 to $1.2\times {10}^{-3}$.

The sequential training approach showed improved convergence compared to single-domain training for the cases examined, particularly for capturing gradients near the column inlet.

3.2. Model Validation Results

3.2.1. CFD Benchmark Comparison

Table 10. PINN model validation results compared to CFD reference solutions (500 test cases).

Variable	Range	RMSE	MAE	R2	Max Error
Pressure field	100–200 kPa	2.4 kPa	1.8 kPa	0.987	5.8 kPa
CO2 concentration	0–1.0 mol/L	0.012 mol/L	0.009 mol/L	0.994	0.028 mol/L
Temperature profile	313–393 K	0.8 K	0.6 K	0.991	2.1 K
Velocity magnitude	0–2.5 m/s	0.05 m/s	0.04 m/s	0.989	0.12 m/s
Capture efficiency	85–95%	0.4%	0.3%	0.996	0.9%

presents validation metrics comparing PINN predictions with CFD reference solutions across 500 test cases.

Figure 7 shows scatter plots comparing PINN predictions with CFD values.

3.2.2. Experimental Validation

Figure 8 compares PINN predictions with experimental measurements from a pilot-scale absorber.

Table 11. Experimental validation results from pilot-scale absorber column.

Variable	Measured Range	RMSE	R2	Relative Error
Temperature profile	42–78 °C	1.2 K	0.988	1.8%
CO2 loading	0.21–0.48 mol/mol	0.015	0.985	3.5%
Capture efficiency	88.5–92.1%	0.6%	0.994	0.7%

summarizes experimental validation results.

3.3. Computational Performance

Table 12. Computational performance comparison across simulation methods.

Method	Time	Speedup	Accuracy	Hardware
Full CFD (ANSYS)	4–8 h	1×	Reference	64-core cluster
Aspen Plus dynamic	15–30 min	16–32×	>98%	Workstation
PINN (training)	2.5 h	–	–	GPU (A100)
PINN (inference)	0.5–2 s	Up to 10,000×	>98%	CPU/GPU
Digital Twin	<100 ms	Up to 100,000×	>98%	Edge device

and Figure 9 present computational performance comparisons.

3.4. Sensitivity Analysis

Figure 10 presents sensitivity analysis results identifying influential operating parameters.

Table 13. Sensitivity analysis results for the operating conditions studied.

Parameter	Baseline	Sensitivity ($\mathit{\partial }\mathit{\eta }/\mathit{\partial }\mathit{x}$)	Ranking
L/G ratio	3.0 kg/kg	+0.43%/%	1
MEA concentration	30 wt%	+0.37%/%	2
Absorber temperature	50 °C	−0.28%/%	3
Lean loading	0.20 mol/mol	−0.27%/%	4
Reboiler duty	3.5 GJ/tonne	+0.21%/%	5
Flue gas flow rate	12,000 Nm3/h	−0.15%/%	6
Operating pressure	1.1 bar	+0.10%/%	7

provides sensitivity coefficients.

Mechanistic Explanation of Sensitivity Results

The dominant influence of L/G ratio and MEA concentration on capture efficiency can be explained through fundamental mass transfer and reaction kinetics principles:

L/G Ratio (Sensitivity: +0.43%/%): The liquid-to-gas ratio directly affects the driving force for mass transfer. Higher L/G increases the liquid holdup in the packed column, providing greater interfacial area for CO₂ absorption. From the two-film theory, the overall mass transfer coefficient $K_G$ increases approximately linearly with liquid flow rate in the gas-film controlled regime typical of amine systems. Additionally, higher liquid flow reduces the bulk liquid CO₂ concentration, maintaining a steeper concentration gradient across the gas-liquid interface [8].

MEA Concentration (Sensitivity: +0.37%/%): The reaction rate in Equation (3) shows first-order dependence on [MEA]. Higher MEA concentration accelerates the zwitterion formation step, shifting the absorption from physical (slow) to chemical (fast) regime. However, this benefit plateaus above approximately 35 wt% due to increased viscosity limiting CO₂ diffusion to the reaction zone and approaching the equilibrium limit of the MEA-CO₂ system [53].

Temperature Effects (Sensitivity: −0.28%/%): The negative sensitivity to absorber temperature reflects the exothermic nature of CO₂ absorption ($\Delta H=-84$ kJ/mol). Higher temperatures shift the thermodynamic equilibrium toward desorption, reducing the driving force. While reaction kinetics accelerate with temperature (Arrhenius behavior), the equilibrium effect dominates in the temperature range studied (40–60 °C) [10].

Lean Loading (Sensitivity: −0.27%/%): The negative sensitivity reflects the finite absorption capacity of the solvent. Higher lean loading means less available MEA for reaction, reducing both the reaction rate and the equilibrium capacity. This parameter is directly linked to regenerator performance and represents a key design trade-off between capture efficiency and energy consumption.

3.5. Optimization Results

The digital twin-enabled optimization demonstrated improvements in energy efficiency for the conditions studied (Figure 11).

Table 14. Optimization results for the operating conditions studied.

Metric	Baseline	Optimized	Improvement
Reboiler duty	3.8 GJ/tonne CO2	3.1 GJ/tonne CO2	−18.5%
Solvent circulation rate	65 m3/h	57 m3/h	−12.0%
Steam consumption	1.9 t/t CO2	1.55 t/t CO2	−18.4%
Cooling water flow	85 m3/h	72 m3/h	−15.3%
Capture efficiency	90.0%	90.2%	+0.2%
Specific energy	280 kWh/tonne CO2	228 kWh/tonne CO2	−18.6%

summarizes optimization outcomes.

3.6. Techno-Economic Analysis

Figure 12 presents economic analysis results. Important note: These results correspond to assumed utility costs and the specific operating conditions of this study. Actual economics will vary significantly depending on local energy prices, labor costs, and site-specific factors.

Table 15. Techno-economic analysis parameters and results. Results are illustrative and sensitive to site-specific factors including utility costs, labor rates, and operating conditions.

Parameter	Value (Assumed)
Capital Investment (Estimated)
DT platform and software	$1,500,000
IoT sensors and instrumentation	$500,000
PINN development and integration	$500,000
Total initial investment	$2,500,000
Annual DT system O&M	$150,000/year
Operating Assumptions
Plant capacity	500,000 t CO2/year
Steam cost	$15/GJ (assumed)
Electricity cost	$0.08/kWh (assumed)
Annual operating hours	8000 h/year
Calculated Savings (Under Assumptions)
Cost reduction per tonne	$25/t CO2
Gross annual savings	$12,500,000/year
Net annual savings	$12,350,000/year
Financial Metrics (Illustrative)
Simple payback period	2.4 months
5-year NPV (8% discount)	$47.2 million
Return on investment (5-year)	>1500%

provides economic parameters and results with stated assumptions.

Table 16. Economic sensitivity to key assumptions.

Scenario	NPV ($M)	Payback (Months)	Note
Base case	47.2	2.4	Study assumptions
Savings −20%	37.4	3.0	Lower efficiency gains
Savings −40%	27.7	4.0	Conservative case
Savings −60%	18.0	6.0	Pessimistic case
CAPEX +50%	45.8	3.6	Higher investment
Steam cost −30%	32.1	3.5	Lower utility costs

shows how results vary with key assumptions.

Even under conservative assumptions (40% lower savings), the analysis suggests positive NPV, though actual results will depend strongly on site-specific conditions.

Regional and Policy Scenario Analyses

To address the regional variability in economic outcomes,

Table 17. Economic scenario analyses for different regional contexts and carbon policies.

Scenario	Steam Cost ($/GJ)	Carbon Tax ($/t)	NPV ($M)	Payback (mo.)	IRR (%)
Base (US Gulf)	15	50	47.2	2.4	>500
EU (High tax)	20	100	62.1	1.8	>600
Middle East	8	0	28.4	4.1	380
Asia-Pacific	18	30	41.5	2.8	450
Emerging Markets	12	10	35.2	3.2	420

presents scenario analyses across different geographical contexts with representative energy prices and carbon tax policies.

The analysis demonstrates positive economic returns across all regional scenarios, with the strongest business case in high carbon-tax jurisdictions (EU) where the avoided costs from improved efficiency compound with regulatory incentives.

4. Discussion

4.1. Comparison with Existing Approaches

The computational speedups achieved by the PINN surrogate (up to four orders of magnitude for the cases studied) compare favorably with conventional reduced-order modeling approaches reported in the literature, which typically achieve speedups of 100–1000× [40,47]. This improvement enables inference times compatible with real-time control requirements, though performance may vary for different system configurations.

Compared to purely data-driven approaches, the PINN methodology offers potential advantages including reduced data requirements due to physics constraints, improved extrapolation within the training domain bounds, and physical consistency of solutions [17,18]. However, PINN approaches also have limitations, including sensitivity to hyperparameter selection and potential difficulties with highly nonlinear or multi-scale problems [43].

The energy efficiency improvements observed (15–30% under study conditions) are consistent with reported ranges for digital twin implementations in industrial applications [23,24], though direct comparisons are difficult due to differences in system configurations and operating conditions.

4.2. Scalability Considerations

While this study focused on a specific pilot-scale configuration, the framework architecture is designed to be adaptable to different scales and configurations. Key considerations for broader application include:

• Retraining requirements for significantly different system geometries or operating ranges;
• Integration challenges with existing plant control systems;
• Data quality requirements for effective digital twin synchronization;
• Validation requirements for safety-critical applications.

Order-of-magnitude estimates suggest that if similar efficiency improvements could be achieved across a significant fraction of global CCUS installations, the aggregate impact could be substantial. However, such extrapolations involve considerable uncertainty and should be treated as indicative rather than predictive.

4.3. Limitations

Several limitations of this study should be acknowledged:

• Solvent scope: The current implementation focuses on MEA-based capture; extension to other solvents would require additional model development and validation;
• Scale of validation: While experimental validation was performed at pilot scale, full industrial-scale validation remains ongoing;
• Economic assumptions: The techno-economic analysis relies on assumed utility costs that may differ significantly from actual site conditions;
• Uncertainty quantification: The current framework provides point estimates; more rigorous uncertainty quantification would strengthen reliability assessments;
• Operating range: Results are valid within the studied operating envelope; extrapolation beyond this range requires caution.

4.4. Extension to Alternative Solvent Systems

The framework’s restriction to MEA limits direct applicability to plants using alternative solvents such as piperazine (PZ), methyldiethanolamine (MDEA), or proprietary blends. However, the architecture is designed for extensibility:

• Reaction kinetics: The zwitterion mechanism (Equation (3)) can be replaced with appropriate kinetic models for other amines. For PZ, a second-order mechanism applies; for MDEA, a base-catalyzed hydration mechanism is more appropriate [53].
• Thermophysical properties: The molecular-scale simulations can be re-run with different force field parameters to generate property correlations for alternative solvents.
• Transfer learning: Rather than training from scratch, the current PINN can serve as a pre-trained model, with fine-tuning on limited data from alternative solvent systems, reducing data requirements by an estimated 60–80% based on similar transfer learning studies [45].

4.5. Uncertainty Quantification Approaches

The current framework provides deterministic predictions without confidence bounds. Future implementations will incorporate probabilistic approaches:

• Bayesian PINNs: Replacing point weight estimates with probability distributions provides posterior uncertainty quantification. Variational inference or Hamiltonian Monte Carlo can approximate the posterior efficiently [52].
• Ensemble methods: Training multiple PINNs with different initializations or architectures enables prediction intervals through ensemble spread.
• Monte Carlo dropout: Applying dropout at inference time provides computationally efficient uncertainty estimates suitable for real-time applications.

These approaches would enable uncertainty-aware optimization, where the objective function includes a risk penalty proportional to prediction uncertainty, improving decision-making under model limitations.

4.6. Future Work

Priorities for future research include:

• Industrial-scale validation at commercial facilities;
• Extension to alternative solvent systems;
• Development of uncertainty quantification methods;
• Integration with carbon pricing and energy market dynamics;
• Investigation of transfer learning approaches for different configurations;
• Implementation of Bayesian PINN for probabilistic predictions;
• Real-time adaptation mechanisms for equipment degradation.

5. Conclusions

This study presents a multi-scale simulation framework integrating Digital Twin technology with Physics-Informed Neural Networks for optimization of amine-based carbon capture systems. The main findings are:

• A hybrid PINN-Digital Twin framework was developed and validated, achieving computational speedups of up to four orders of magnitude compared to CFD while maintaining prediction accuracy (R² > 0.98) for the cases studied.
• The sequential training algorithm with domain decomposition demonstrated improved convergence for CO₂ absorption modeling, with final loss values of approximately $1.2\times {10}^{-3}$, outperforming standard PINN, adaptive collocation, and curriculum learning approaches.
• Validation against pilot-scale experimental data showed good agreement with measured temperature profiles (RMSE = 1.2 K), loading profiles (RMSE = 0.015 mol/mol), and capture efficiency (RMSE = 0.6%), including validation under transient operating conditions representative of industrial operation.
• Sensitivity analysis identified L/G ratio and MEA concentration as the most influential parameters for the operating conditions studied, with mechanistic explanations linking these to mass transfer enhancement and reaction kinetics.
• Under the study conditions, the framework demonstrated reboiler duty reductions of 18.5% and operational cost reductions of approximately 31%, though results are sensitive to site-specific factors.
• Techno-economic analysis, based on stated assumptions, suggests favorable investment metrics, with sensitivity analysis indicating robustness across a range of scenarios and regional contexts.

The framework offers a promising approach for improving carbon capture efficiency through real-time optimization. While results are specific to the configurations and conditions studied, the methodology may be applicable to other carbon capture installations with appropriate adaptation and validation. The architecture is designed for extensibility to alternative solvent systems, with future work planned for industrial-scale validation and uncertainty quantification through Bayesian approaches.