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
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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.
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