Model-free approach for inferring residence time distribution and its applications

Residence Time Distribution (RTD) is an important concept for optimizing chemical processes, but conventional RTD studies have limitations, such as being sensitive to experimental errors, oversimplifying the system, or being computationally expensive. This study proposes a novel numerical algorithm that accurately and robustly computes the RTD based on data points without assuming any predetermined model. The proposed method employs B-spline regression analysis with fixed-point iteration (FPI), a technique commonly used in the field of rheology to calculate the relaxation time spectrum. Our algorithm estimates accurate RTDs using B-spline regression analysis and guarantees non-negative RTD values using the FPI method. We use simulation data, both error-free and error-included, to verify the optimal conditions of the algorithm. We identify the optimal conditions of the algorithm, confirming that it can accurately compute RTDs regardless of the shapes of the input function and the RTD. Through experimental and CFD data, we verify that the algorithm computes consistent RTDs regardless of the input function when sufficient data are provided. Our RTD calculation algorithm can calculate RTD regardless of any input data and does not use a predefined model, so it is expected to be effectively utilized in RTD analysis of complex systems such as twin-screw extruders, stirred tank reactors, and pharmaceutical manufacturing systems.