(52b) Machine-Learning Based Pressure Drop Prediction for Structured Column Packings

Distillation and absorption columns serve as crucial components in a wide array of applications within the chemical industry such as petroleum refining, exhaust gas cleaning or carbon capture. To improve mass transfer, these columns are in many cases equipped with random or structured column packings to ensure intimate contact between gas- and liquid-phase.

An essential challenge in packed column design is the prediction of gas-side pressure drop. High pressure drop leads to increased energy consumption, thereby negatively impacting operational costs. For constant gas load, pressure drop is lowered for increased apparatus cross-section, but an excessively large apparatus will result in high investment costs. Therefore, accurate prediction of pressure drop is essential for optimizing packed column design.

Many semi-empirical models for the prediction of pressure drop in packed columns have been developed in the past, for example Stichlmaier et al. (1989), Billet and Schultes (1991 and 1999) or Mackowiak (2010). The main drawback of current modeling approaches is that they are reliant on one or more empirical parameters. Laborious experimental campaigns are necessary to derive these empirical parameters before a column packing can be described with a given model. It is generally not possible to simply infer empirical model parameters of one column packing from those of another.

An alternative to semi-empirical physics-based models is the use of machine learning (ML) methods. ML is a subfield within the expansive domain of artificial intelligence that enables automatic pattern recognition within a dataset without the need to explicitly specify physical relationships between the considered quantities. In addition to its capability for deriving highly accurate predictions, ML can be used to assess the importance of input features, thereby enhancing the understanding of the examined system.

The objective of this research is to derive a modeling approach for the prediction of pressure drop in structured column packings that fully eliminates the need for empirical model parameters. Once the model is calibrated, packing pressure drop can be predicted directly from geometric packing descriptors, without the need for further measurements. In particular, the proposed model can be used to calculate dry and irrigated pressure drop of novel packing geometries not included in the original dataset.

The methodology is divided into two main parts: In the first part, dry pressure drop of different structured column packings is determined experimentally as a function of gas load. In the second part, a ML meta-model is built on top of the already established pressure drop model of Mackowiak (2010). The Mackowiak model requires only a single packing-specific parameter called the packing form factor. Within the proposed approach, the ML-model is used to derive a packing’s form factor directly from packing geometry. Only then is the Mackowiak model used to calculate dry and irrigated pressure drop.

For the experimental part of this work, dry pressure drop of various structured column packings with different geometries and packing materials is measured in dependence of gas velocity. Measurements are carried out in a polypropylene column with 422 mm inner diameter and packed heights of up to 1.8 m. Gas velocity is varied between 0.5 and 5 m/s while ambient air is used as gas phase for all experiments. In total, about 30 different structured packings are characterized with the described methodology. In the next step, the obtained dry pressure drop measurement results are used to evaluate the form factor of each of the packings investigated. This is done through fitting the Mackowiak model to the measurement data by manipulating the form factor until best fit (least squares method) is achieved. Once the form factor is determined, the Mackowiak model is found to reproduce the measured data for dry pressure drop with very high accuracy (R² = 0.99).

Next, ML methodology is employed to predict the packing form factor (model target) from packing geometry (model features). For this, a dataset comprising of 9 features related to packing geometry descriptors (porosity, specific area, corrugation angle, channel side length, channel angle), packing material (metal/plastic/ceramic), packing surface structure (smooth/wavy) and packing perforations (hole diameter, hole spacing) is used. The dataset further contains the packing form factors obtained in the experimental part of this work. For further considerations, the data is normalized and standardized. As algorithm selection may impact the accuracy of target predictions, various models such as support vector machines (SVM), random forest (RF), and Extreme Gradient Boosting (XGB) are explored to select the most suitable algorithm. The results show that especially the RF and XGB algorithms yields remarkably accurate model predictions with corrugation angle, packing perforations, channel angle and porosity having the greatest impact on pressure drop. The results of leave-one-out cross-validation suggest that even the form factor of packings not included in the original dataset can be calculated with good accuracy (R² > 0.8) Partial dependence plots are used to assess the effect of individual model features on pressure drop as well as possible interactions between features.

Currently, this study has three main limitations. First, the dataset used for developing the modeling approach currently comprises of about 30 structured packings. To further improve prediction accuracy, the inclusion of additional structured packings in the dataset is beneficial. Second, it has not yet been investigated how the proposed approach could be applied to random packings. Due to the random arrangement of individual packing elements, it is not as straightforward to derive geometric descriptors for a random packing bed as it is for structured packings. Third, the current study is focused only on column packing pressure drop. For an overall evaluation of processes involving packed columns, other properties such as specific liquid hold-up, interfacial area or mass transfer coefficients must additionally be considered.

In conclusion, this research aims to predict pressure drop in structured column packings by introducing a novel ML-based meta-modeling approach. Using the proposed procedure, the packing form factor is calculated directly from the structured packing’s geometric properties. From this, the Mackowiak model is used to predict pressure drop. The findings indicate that the proposed approach effectively predicts pressure drop in structured column packings. The elimination of empirical parameters and the ability to apply this methodology to a wide range of structured packings offer significant advantages compared to current modeling approaches.