## 2 Related work  
### Distillation Process-Related Models  
Debutanizer columns are an important part of several processing units in oil refineries. Therefore, the objective of the online composition of debutanizer outlet streams is to maximize the production of LPG while meeting the corresponding quality standards. Currently, the quality of the debutanizer output is measured via laboratory analysis. Hence, changes in the quality are identified only upon the analysis of the sample, which may take several hours. Therefore, to maintain the quality of the product within the predefined specifications, it is of imperative importance to predict the top and bottom outputs of the debutanization process precisely [2]. To realize this objective, Ref. [3] identifies three major approaches to develop the required models: (i) first-principle (a.k.a. fundamental) models, which consider mass, energy, and momentum principles and equations to provide a forecast; (ii) machine learning models, which are created by training an algorithm on input-output data of the process; and (iii) hybrid models, which combine both the fundamental and the empirical models. First-principle models involve sets of non-linear differential equations (usually in the order of \(10^{2}\) or \(10^{3}\) non-linear differential equations) and a comparable number of algebraic equations [4; 5]. The equations usually take into account the global balance of matter, partial balances of matter, pressure, temperature, flow, reflux policies, and the relationship between component concentrations at different levels of the distillation column [3; 6]. Although additional information regarding the structure of the distillation column can further enhance such models (e.g., the number of trays in a column or the column hydraulics [7]) with the increasing computational complexity of such models. To alleviate the computational needs, simplified distillation column models have been proposed [8; 9], at the expense of an increased error whose applicability often restricted to a single column [10]. These models are usually implemented in Advanced Process Control systems (APC), such as a Multivariable Model Predictive Control (MPC), for managing relevant process variables and their dynamics. The equations mentioned above govern the control logic between variables. Algorithms that perform matrix computations are used to solve such system dynamic models with multiple variables simultaneously. In addition to their computational complexity, the usefulness of such models is constrained to the model assumptions, e.g., sensor colocation points [11]. Data-driven models provide an alternative modeling approach for developing the forecast models [12]. In particular, machine learning models are developed based on the prior knowledge of the physical processes for creating good features of model outputs. The models are trained with the collected data from the actual operations of the unit: (1) The raw data are transformed into a dataset for developing models which perform features that reflect different dynamic features for the raw data variables; (2) Through the developed models, observed outputs are generated through the feature vectors. Through such model features, the machine learning models can accurately learn non-linear features from the data, even when some noises exist in the data [13]. Hybrid models arise from the combination of the first-principle and data-driven models [14]. Such models are used to retain the theoretical knowledge of the process, which is mirrored in equations. In contrast, the data-driven models can augment such knowledge using data, and can be used to model parts of the process that are hard to formulate and would otherwise require overly complex first-principle models [3; 15]. Hybrid models have been implemented widely in various chemical processes such as batch distillation [16], reactive distillation [17], and polymerization process [18; 19]. However, only a handful of models have been implemented in continuous distillation columns.