(529e) Gray-Box Soft-Sensor Modeling of Vessel Interior Temperatures across Different Liquid Supply Angles

Soft sensors are valuable tools in the chemical industry for providing real-time interior data, especially when physical sensors are difficult to install inside chemical facilities. One key application can be temperature prediction inside tanks or reactors, which can inform the control systems to reduce unnecessary energy consumption by preventing overheating or excessive cooling. However, existing soft sensor models are often tailored to specific supply conditions, limiting their adaptability to varying industrial scenarios. Recently, a gray-box soft sensor model was proposed, capable of predicting interior temperatures across different supply temperatures and flow rates [1]. However, its performance under varying supply angles remains unexplored.

This study investigates the model’s applicability across different supply angles. Temperature data were collected from water experiments using a straight or dual-angled nozzle. Each nozzle was tested in both a heating process (50 °C supply, 10 °C initial) and a cooling process (10 °C supply, 35 °C initial) at a flow rate of 770 mL/min (residence time ≈ 6 min). Model predictions at three interior locations were evaluated using Mean Absolute Error (MAE) and Maximum Absolute Error (MaxAE). MaxAE is calculated with the moving average of experimental and predictive temperatures and first 40 s ignored.

Results show that in the heating process, MAE and MaxAE remain below 0.6 °C and 1.7 °C, respectively, regardless of the nozzle shape used for training. In the cooling process, MAE is a bit larger reaching 0.7 °C, while MaxAE can rise up to 2.8 °C in the initial period (40 s -120 s). However, if this initial period is ignorable, MaxAE is below 2.0 °C for the subsequent 780 s. Flow visualization results suggest that early-stage discrepancies arise from differing flow dynamics under varying supply angles.

These findings demonstrate that this gray-box model can generalize across supply angles and contribute to energy-efficient thermal management in the chemical industry, with potential applications in HVAC field as well.

References

[1] Xu, F., Wang, J., Sakai, Y., Sabu, S., Kanayama, H., Zhang, Satou, D., Kansha, Y., Gray-box virtual sensor with constraints for predicting room temperature in cooling and heating modes. Build. Environ. 273 (2025), 112729.