Numerical Methods in Lagrangian Actinometry: Solving for a UV Reactor's Dose Distribution
Abstract:Lagrangian actinometry (LA) has been demonstrated to be an effective method for measurement of dose distributions delivered by UV reactors (Blatchley et al., 2006, 2008). A standardized protocol for application of LA is being developed so that any qualified organization could apply LA for validation or analysis of reactor behavior and performance. The numerical methods that are required for deconvolution of the UV dose distribution from an LA application are complex. This manuscript addresses in more detail the data analysis methods used to estimate a UV dose distribution from the experimental data collected from LA dose-response experiments and field tests. Data from LA experiments consist of error-contaminated fluorescence intensity (FI) distributions for populations of dyed-microspheres for both the dose-response experiments and field tests on UV reactors. The method used to determine the “best” dose distribution that is responsible for the observed FI distribution from a UV reactor involves the determination of a constrained linear least-squares solution to a linear system Ax ≈ f, where A is a m by n “data” matrix with m ≥ n that contains information about the dose-response behavior of dyedmicrospheres, x is an n-dimensional vector of unknown weights for a dose distribution, and f is an m-dimensional vector containing the FI distribution for a population of dyed-microspheres from a UV reactor field test. The development and formulation of this numerical method is presented, along with the results that are produced from the algorithm when applied to field samples generated from full-scale UV reactors. Dose distributions that were calculated by the numerical algorithm were subsequently integrated with the dose-response behavior of three microorganisms (coliphages MS-2 and T1, along with Cryptosporidium parvum) to predict the inactivation responses of these organisms. Predicted inactivation values estimated by LA for coliphages MS-2 and T1 were compared against their corresponding biodosimetrically measured inactivation responses.
Document Type: Research Article
Publication date: January 1, 2009
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