Bayesian Deconvolution of Vessel Residence Time Distribution

Abstract

Residence time distribution (RTD) within vessels is a critical aspect for the design and operation of continuous flow technologies, such as hydrothermal synthesis of nanomaterials. RTD affects product characteristics, such as particle size distribution. Tracer techniques allow measurement of RTD, but often cannot be used on an individual vessel in multiple vessel systems due to unsuitable exit flow conditions. However, RTD can be measured indirectly by removal of this vessel from the system and deconvoluting the resulting detected tracer profile from the original trace of the entire system. This paper presents three models for deconvolution of RTD: BAY an application of the Lucy-Richardson iterative algorithm using Bayes’ Theorem, LSQ an adaptation of a least squares error approach and FFT a Fast Fourier Transform. These techniques do not require any assumption about the form of the RTD. The three models are all accurate in theoretical tests with no simulated measurement error. For scenarios with simulated measurement error in the convoluted distribution, the FFT and BAY models are both very accurate. The LSQ model is the least suitable and the output is very noisy; smoothing functions can produce smooth curves, but the resulting RTD is less accurate than the other models. In experimental tests the BAY and FFT models produce near identical results which are very accurate. Both models run quickly, but in real time control the runtime for BAY would have to be considered further. BAY does not require any filtering or smoothing here, and so potentially there are applications where it might be more useful than FFT.