Bayesian deconvolution of vessel residence time distribution

Huddle, Thomas; Langston, Paul; Lester, Edward

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 (Cabanas, Darr et al. 2000). 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 (Richardson 1972, Lucy 1974) using Bayes’ Theorem, LSQ an adaptation of a least squares error approach (Blackburn 1970) 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.

Citation

Huddle, T., Langston, P., & Lester, E. (2018). Bayesian deconvolution of vessel residence time distribution. International Journal of Chemical Reactor Engineering, 16(4), https://doi.org/10.1515/ijcre-2016-0219

• Journal Article Type: Article
• Acceptance Date: Oct 9, 2017
• Online Publication Date: Oct 21, 2017
• Publication Date: Apr 1, 2018
• Deposit Date: Oct 17, 2017
• Publicly Available Date: Oct 22, 2018
• Journal: International Journal of Chemical Reactor Engineering
• Print ISSN: 1542-6580
• Electronic ISSN: 1542-6580
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 4
• DOI: https://doi.org/10.1515/ijcre-2016-0219
• Keywords: Residence Time Distribution; Deconvolution; Bayes’ Theorem; Least Squares; FFT
• Public URL: https://nottingham-repository.worktribe.com/output/962147
• Publisher URL: https://www.degruyter.com/view/j/ijcre.ahead-of-print/ijcre-2016-0219/ijcre-2016-0219.xml