Jakob Kjøbsted Huusom

We present in this study a methodology to apply the radiative transfer equation (RTE) and the Monte Carlo ray tracing algorithm coupled with photon mapping (MCRT-pm) to the case of a tubular photobioreactor with external, point-like artificial illumination. The RTE is used to provide an analytical solution to the case of direct illumination by the photobioreactor light sources, while the MCRT-pm computes the diffuse contribution of the scattered light. The combined application of both techniques results in the formulation of an irradiance field that spans the three spatial coordinates of the photobioreactor volume, without incurring in the overestimation of the dark volume at the photobioreactor core associated with the Lambert-Beer law. Moreover, by avoiding simplifications such as single scattering or the diffusion approximation, our methodology remains applicable to any cellular shape and biomass concentration range. Thus, it emerges as a highly capable tool to aid and guide the design and optimization of illumination configurations for photobioreactors.

Fouling is a persistent issue in industrial heat-transfer equipment, increasing energy demand and reducing efficiency. This is also true in the dairy industry where falling-film evaporators are central to powder production. Most dynamic models, however, neglect gradual fouling, limiting predictive accuracy during extended operation. As a result, model-based control can become unreliable when fouling becomes significant. The dynamic models by Bojnourd et al. [1] are widely used but assume clean-surface operation. While this captures short-term thermal behavior, it cannot represent the progressive decline in heat-transfer performance caused by fouling. Díaz-Ovalle et al. [2] introduced a fouling-layer model that explicitly describes the growth of a fouling deposit over time. Building on this concept, the present work incorporates a simple dynamic fouling model for falling-film evaporators and validates it using industrial data from a four-effect evaporator using thermal vapor recompression. Two fouling-modelling strategies are evaluated: a mechanistic fouling layer model and an empirical model describing the observed loss in heat-transfer efficiency. The fouling layer model substantially reduces prediction error, demonstrating that it captures the dominant fouling behavior. Although the empirical model fits all observed discrepancies, it lacks predictive capability and therefore cannot be applied for model-based prediction or control.

Hybrid process models are increasingly used for real-time decision support in dynamic operations, where models must remain reliable under changing operating conditions. In such settings, models are often required to extrapolate beyond previously observed batch trajectories, yet conventional validation strategies may fail to reveal weaknesses in extrapolative behavior. This work investigates the effect of hybrid model structure on extrapolative performance using a pilot-scale batch crystallizer as a test case. A structured set of mechanistic and hybrid models is evaluated using nested batchwise leave-one-out cross-validation (NBLOOCV), in which entire batches are withheld to assess extrapolation across operating regimes. For this specific application, the results show that hybrid models employing simple linear correction terms consistently outperform more flexible neural network–based formulations under extrapolation, despite comparable training performance. For the studied process, the findings highlight the importance of validation strategies that reflect intended model use and demonstrate that modest, physically consistent hybridization provides a robust and interpretable basis for operational decision support.

Digital transformation in established chemical facilities is often hindered by infrastructure gaps, unclear return on investment, and a lack of organizational readiness. While data-driven soft sensors offer significant potential for real-time quality monitoring, their adoption is often constrained by systemic limitations. This paper presents an implementation strategy for a soft sensor at an industrial tar distillation facility to estimate the pitch softening point. Rather than treating technical and organizational limitations as blockers, they are treated as design boundaries that define a stepwise deployment roadmap.A baseline linear model was developed to run within the existing SCADA system, achieving a prediction accuracy of 58% within tolerance. This provides a zero-cost early alarm system for production consistency without requiring new hardware. The study further identifies the specific technical infrastructure requirements, including data pipelines and memory modules, needed to transition to more advanced nonlinear models, thereby achieving 92% accuracy. This approach enables stepwise, sustainable digitalization by aligning technical development with the infrastructure investment required for digital maturity.

To advance the progress of membrane materials and process development, accurate prediction of membrane performance has to be efficiently optimized. Such optimization is challenging when sustainable materials such as hydrophilic biopolymers from renewable resources are used on mixed matrix membrane (MMM) fabrication. The predictions of MMM using phenomenological modified Maxwell models are often locally dependent with high uncertainty levels. In this work, we systematically developed a hybrid model architecture using a delta model design pattern to enhance the prediction of the permeability of chitosan-based MMM for CO2/N2 separation and gain insight in the design of new sustainable membrane separation processes. The parametric model baseline is focused on the modified Maxwell equation including temperature dependence, involving the estimation of two interpretable parameters: void thickness (i.e. the interaction between the components of the membrane matrix) and the rigidification of the dispersed phase in the continuous matrix, with increasing level of complexity. A sequential combination of global and local optimization methods, yielded the best parametric model performance, reducing error by up to an order of magnitude. Then, a multilayer perceptron neural network (MLPNN) is trained using the output error of the parametric model and the introduction of additional experimental input variables. The hybrid model significantly improves the accuracy of gas permeability predictions while keeping interpretability by clarifying input-output correlations of properties not captured by the Maxwell model. This way, this approach can be used to understand the structure-functional relationship of novel membranes and facilitate the development of sustainable membranes and membrane processes.

Testbed and pilot facilities allow studies in real-world conditions—especially when scale matters. They often bring together universities and industry partners across borders, creating a space where collaboration thrives.

Digital twins and digital shadows are frequently used terms by industry and academia to describe data-centric models that accurately depict a physical system intended for process monitoring and control. Processes restricted by a low degree of automation rely greatly on operator competencies in key decision-making; a digital shadow can here assist as a guidance tool [1-4]. This work presents a practical implementation of a digital shadow to support operators running a pilot scale-packed batch distillation column at the Technical University of Denmark (DTU) primarily used in education and teaching activities [5]. This operation is selected due to inherent unsteady process dynamics that are controlled by a set of manual valves, which the student operator must continuously balance to meet purity constraints without disrupting the operation. This realisation employ a modular software architecture, separated into four distinct modules compiled into Docker images and independently deployed. These facilitate real-time connection with the equipment via OPC-UA endpoints, process model analysis via HTTP/HTTPS requests, and a dashboard UI presenting the data accessible through any web browser. The final module is realised as a Python package that stores thermodynamic models and is published on the internal GitLab registry for more straightforward utilisation across multiple projects. The advantages of this implementation strategy are flexibility and speed, allowing for continuously updating process models and directly employing them in various projects.