Catalysts 2021, 11, 1190. https://doi.org/10.3390/catal11101190 www.mdpi.com/journal/catalysts Article Six Flux Model for the Central Lamp Reactor Applied to an Ex‐ ternal Four‐Lamp Reactor Fernando J. Beltrán *, Francisco J. Rivas and Juan F. García‐Araya Departamento de Ingeniería Química y Química Física, Instituto Universitario de Investigación del Agua, Cambio Climático y Sostenibilidad (IACYS), Universidad de Extremadura, 06006 Badajoz, Spain; fjrivas@unex.es (F.J.R.); jfgarcia@unex.es (J.F.G.‐A.) * Correspondence: fbeltran@unex.es; Tel.: +34‐924‐289387 Abstract: One of the difficulties of establishing the intrinsic kinetics of photocatalytic oxidation pro‐ cesses is due to the complex mathematical formula used to determine the rate of photon absorption. To solve this problem, some models have been proposed and checked, such as the Six Flux Model (SFM) confirmed in central lamp photoreactors. External lamp photoreactors are also one of the most used configurations to study the photocatalytic oxidation of contaminants in water, and com‐ plex mathematical solutions have been reported to solve the rate of photon absorption. In this work, SFM Equations already reported for the central lamp photoreactor have been adapted to determine the rate of photon absorption in an external four‐lamp photoreactor. The results obtained show slight differences from those of the Monte Carlo method. Additionally, once the rate of photon ab‐ sorption was validated, the intrinsic rate constant and scavenging factor of the photocatalytic oxi‐ dation of some contaminant compounds from results already published have been determined. Keywords: volumetric rate of photon absorption; six flux model; external lamp photoreactor; pho‐ tocatalytic oxidation kinetics; scavenging factor; water organic contaminants 1. Introduction It is well known that Advanced Oxidation Processes (AOPs), are the only technolo‐ gies capable of destroying water contaminants at ambient conditions due to the high oxi‐ dizing power of hydroxyl radicals generated in these processes [1,2]. Photocatalytic oxi‐ dation (PCO) of water contaminants with ozonation and Fenton oxidation are some of the advanced oxidation processes that have attracted a lot of research interest in the last two decades [3–7]. In this century, literature shows more than 6700 papers on this subject; a figure similar to that of ozonation or Fenton processes, with about 7100 and 5500 papers, respectively, according to the Scope database. PCO consists of the irradiation of semicon‐ ductor material to produce positive (holes) and negative (electrons) charges when the en‐ ergy of radiation at least equals the band gap energy of the semiconductor [8]. Strong oxidant holes and reducing electrons then migrate from the valence and conduction bands, respectively, to the surface of the catalyst to directly, in the case of holes, or indi‐ rectly, through species formed from them (hydroxyl, superoxide radicals, etc.), react with the organics present in water [9]. It is evident that absorption of energy is the key step of PCO. The knowledge of the rate of photon absorption is fundamental to establishing the contaminant oxidation rate. The main variables affecting the photon absorption rate con‐ cern the geometry of the reacting system (photoreactor), the intensity of radiation and the optical properties of the catalyst, among others [10,11]. When solving the photocatalytic oxidation rate of any contaminant, the radiation transfer equation and the mass balance of the target compound and, in some cases, fluidodynamic aspects are needed, with the former as the most difficult step to be solved [12]. Literature has already reported compli‐ cated mathematical models to solve the radiation transfer equation or algorithms based Citation: Beltrán, F.J.; Rivas, F.J.; García‐Araya, J.F. Six Flux Model for the Central Lamp Reactor Applied to an External Four‐Lamp Reactor. Catalysts 2021, 11, 1190. https:// doi.org/10.3390/catal11101190 Academic Editor: Roberto Fiorenza Received: 15 September 2021 Accepted: 28 September 2021 Published: 29 September 2021 Publisher’s Note: MDPI stays neu‐ tral with regard to jurisdictional claims in published maps and institu‐ tional affiliations. Copyright: © 2021 by the authors. Li‐ censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con‐ ditions of the Creative Commons At‐ tribution (CC BY) license (http://crea‐ tivecommons.org/licenses/by/4.0/).