Analytical modelling of steady-state filtration process in an automatic filter with continuous “back-flushing” operation M. Meireles1, M. Prat2, A. Ramadane, G.Estachy3 1Laboratoire de Génie Chimique, LGC/UMR 5503, CNRS/UPS/INP, Toulouse, France, meireles@chimie.ups-tlse.fr 2Institut de Mécanique des Fluides de Toulouse, IMFT, UMR 5502 CNRS/UPS/INP, Toulouse, France ; prat@imft.fr 3Alfa Laval Moatti SAS, La Clef Saint Pierre, 10 Rue du Maréchal de Lattre de Tassigny, 78997 Elancourt Cedex, France ; guillaume.estachy@alfalaval.com Keywords. Automatic - filter – self-cleaning – clogging – pressure - drop INTRODUCTION The specificity of an “automatic filter” is to use a “permanent” filtering medium with a self-cleaning device. It is required by some applications that need extent maintenance intervals and limited operation costs (typically: operated for Marine applications to remove particles from lube or fuel oils in diesel engines). The ability to cleaning generally implies the use of a 2D filtering medium, at the opposite of disposable cartridges filters. In the case of Alfa Laval Moatti filters, the self-cleaning operation is permanent, and ensured by a continuous back-flushing circulation through part of the filtering medium: the filtering mesh lays horizontally into a disctype frame, itself separated into M+1 angular sectors by radial ribs. The assembly of two of these plate frames constitutes a “filtering element”, which openings force the flow across the filtering mesh. A stack of several filtering elements makes a “filtering unit” (providing specified filtering area), forming at the same time M+1 independent “columns”. In each element, the polluted flow passes through M sectors and deposit particles onto the filtering mesh (“filtration mode”). In the same time, a tiny part of the clean liquid is being back-flushed through 1 sector -isolated by mean of a rotating distributor-, removing solids from it (“back-flushing mode”). The clogging mechanisms of a filtering medium simply crossed by a flow charged in solid particles are described in the bibliography. It is question here to adapt those “filtration models” to the system scale and specificities, and especially to couple them with a “back-flushing model” that introduces the influence and efficiency of the periodic cleaning. The objective of the study is then to develop an analytical model predicting the Pressure Drop through a filter operating in steady-state (periodic) regime. That could provide some knowledge on the clogging mechanisms involved and on the influence of different parameters such as: filter mesh characteristics (size, porosity …), system adjustments (element design, flow used for back-flushing, rotating speed …) and operating conditions (flow, viscosity, pollution concentration/size distribution …) METHODS The problem requires a multi-scale approach from the particle/mesh unit cell size up to the scale of a complete filter, with intermediate scales of “sector“ and “element“. We first studied the flow pattern in a section of disc type element for both filtration and back-flushing modes. Then a mathematical model based on common accepted formulas for flow through screen and simplified capture mechanism has been proposed to account for the impact of the collection of particles onto the screen filter on the pressure drop. Finally the general model is completed with introduction of the “back-flushing“ model accounting for periodic cleaning of each sector, wether“ perfect“ or “imperfect“. We made a comparison of the calculated pressure drop variation with experimental tests and discussed the impacts of assumptions RESULTS 1/ Hydrodynamics through a section of one sector: came to the conclusion that the filtration velocity can be considered as uniform spatially. This greatly simplifies the modeling of clogging. More, a mono-dimensional model could be settled there (correlated by 3-D CFD results). This 1-D model will allow for relatively simple determination of particle residence time in back-flushing mode. 2/ Filtration: 2 possible clogging mechanisms at mesh scale a) screen clogging b) cake filtration As no direct evaluation through experiments (e.g. visualization or filtration tests) is available at the mesh scale, we developed models at the sector scale and tested them against available data from filter scale experiments. Results are consistent with the assumptions of screen filtration model (a) therefore this is retained in the following as regards the modelling of back-flushing Screen Clogging Model Cake filtration Model 8000 > 25 microns Cake Filtration Model Press Drop (Pa) Press. Drop (Pa) 800 Experimental data 600 > 28 microns 400 6000 Experimental data 4000 2000 200 0 0 2500 0 2000 4000 Time ( s) 6000 3500 4500 5500 6500 Time (s) 3/ Back-flushing model: assuming the “screen clogging model“ and re-using the hydrodynamics model settled in 1/, the back-flushing model calculates the trajectory and then the “exit time“ of any particle initially laying on the mesh at a distance X 0 from the sector intlet (or outlet in back-flush orientation). If ∆t is the time the sector is being back-flushed, L the radial distance from inlet to outlet, and Xb the initial position of the last particle which has time to exit in ∆t, then the ratio Xb/L, hereafter called “αb“ may represent the “efficiency“ of backflushing, i.e the proportion of clean area (or open holes) on the screen at the end of backflushing operation. Xb is found by iterative computing 4/ Filtration model translated to the element scale and coupled with back-flushing model: the periodic and steady state conditions introduced in equations of screen model capture defined in 2/ plus the coupling on the “αb“ parameter defined in 3/ allowed to sort out formulas for Pressure drop VS. Time and flow rate repartition in the different sectors of one element CONCLUSION Some experimental results compared to 2 basic filtration models derivate from bibliography (screen filtration/cake filtration) allowed a clear identification of the clogging mechanisms involved in such kind of filters. It permitted to develop the model presented here, which computes the pressure drop versus time at the element scale, taking into account the influence of the periodic back-flushing and its efficiency. Some strong assumptions (particle-capture mechanisms for instance) or limitations (steady-state regime) deserve to be refined in further studies to gain a better understanding of filtration and back-flushing mechanisms REFERENCES Etude et modélisation du colmatage d'un filtre plissé/11-03-2005 / Thèses INP Toulouse/ Benmachou, Kader Berman A.S, “Laminar flow in channels with porous walls”, Journal of Applied Physics, Page 1232, (1953). Oxarengo, L., Schmitz, P., Quintard, M, Chemical Engineering Science, 59, 1039-1051, 2004. K.C Ting; R.J. Wakeman, V.Nassehi, Filtration, 6, (3), 2006. A semi-analytical model for gas flow in pleated filters /Chemical Engineering Science, Volume 65, Issue 9, 1 May 2010, Pages 2835-2846 / M. Rebaï, M. Prat, M. Meireles, P. Schmitz, R. Baclet