A digital twin is a virtual representation of a physical process, continuously updated with real-time data from its physical counterpart. This link between the two entities (physical and digital) needs to be dynamic, allowing for the simulation, analysis, and monitoring of the physical asset, enabling optimized decision-making for maintenance and operational improvements. Classical model-based approaches are typically demanding in terms of running time and memory and can hardly accommodate real-time changes in operating conditions. This limits, to some extent, their application in complex real-time scenarios. Reduced-order modeling (ROM) is an essential step that enables digital twinning by incorporating measured data into the loop and ensuring that the surrogate is swiftly computed and updated. In this study, we examine several techniques for ROM of dynamical processes, including extensions of the classical methods known as operator inference (OpInf) and sparse identification (SINDy). These methods are evaluated for their ability to model and control the dynamic operation of the case study, e.g., a catalytic Power-to-X reactor; this is a key technology for converting renewable electricity into synthetic fuels or platform chemicals. Power-to-X systems are essential for long-term energy storage and mitigating the mismatch between intermittent renewable generation and demand. We show how snapshot data collected during process operation can be used to extract valuable information. This is used for controlling and predicting the complex processes that faithfully describe the physics of the catalytic carbon dioxide methanation reactor under a variety of parameters and conditions. By evaluating the accuracy and computational efficiency of these methods, we aim to identify suitable reduced-order predictive surrogate models tailored to the challenging application under study. If time permits, discussions on robustness to noisy or hidden/incomplete data will be added, and also on including a nonlinear convolutional neural network (CNN) decoder to enrich the reconstruction capabilities.