“…Due to the continuous addition and removal of material from the upstream and downstream process, continuous-stirred tank reactor (CSTR) equations were utilized to model the RTD of molecules throughout the process (Fogler, 2006). This approach has been utilized extensively by pharmaceutical, oil, fertilizer, and polymer industries typically utilizing dyes, ions, or radioactive molecules for the tracer (Ben Abdelouahed et al, 2016;Bhaskar & Singh, 2018;Boskovic & Loebbecke, 2008;Orsi et al, 2009;Sharma et al, 2016;Sugiharto et al, 2009;Youssef et al, 2017). An alternative approach for RTD characterization of screw extruders utilized anthracenebearing substance as a fluorescent tracer demonstrating improved Nomenclature: C i , C 1 , C 2 , C 4 , C 6 , concentration of tracer at t = 0 (i) and at time t for bioreactor (1), permeate (2), pre-SPTFF hold tank (4), and post-SPTFF hold tank (6); C is , C i × % seiving for the post-bioreactor models including permeate, pre-SPTFF and post-SPTFF hold tanks for a tracer impacted by filter sieving; F, flowrate in and out of the bioreactor; t, time in hours; V, V2, bioreactor volume (V) and permeate volume in the ATF filter (2); τ, V/F; τs, (Tank volume × (1−PCV)/Volumetric flowrate)/% sieving.…”