Optimizing the operation of a direct-flow filtration device

Abstract

Direct-flow filtration is a common technique for filtering impurities from a fluid using a porous-walled channel or a pipe, one end of which is closed off with a cap. Pure fluid flows out of the porous walls, while impurities are left in the channel. Such systems are composed of a series of individual porous channels or pipes stacked in close proximity. We develop a mathematical model for the flow in a 2D filtration channel and a 3D pipe, with a capped end, to describe the behaviour within a direct-flow device. We study the axial dependence of the transmembrane pressure (TMP) across the membrane walls on the imposed flux, wall permeability and the proximity of the neighbouring fibres. The mathematical models derived are used to predict the operating regimes of the device that maximize the spatial uniformity in the TMP and thus optimize the use of the entire membrane area. We show how a large portion of the available membrane area is not used when the fibres are packed too closely together, with the majority of the filtration behaviour being localized near to the impermeable capped end; this leads to inefficient filtration. We quantify the device performance by examining the uniformity of the filtration across the length of the device and the output of the filtered fluid for a given operating pressure.

Pressure driven inside feed (PDI) hollow fibre filtration: Optimizing the geometry and operating parameters

“…Before displaying results indicating the influence of void fraction, fibre diameters and other parameters an overview of the pressure profiles is given using the parameter with parallel that used in [8] where: = area in the shell side area in the lumen side Fig. 6 shows three patterns of pressure profiles.…”

“…1). In classical dead-end filtration the flow and filtration direction are both normal to the membrane surface, while in crossflow mode the flow is parallel to the membrane surface with permeation being orthogonal to the feed flow [8]. The modern water membrane market is based on the use of Direct-flow, which combines a filtration cycle operated in dead end with a regular intermittent backwash.…”

“…In particular there are limited entries for the PDI format as given in Table 2 which includes some results for crossflow. A recent mathematical study developed a dimensionless model to explore the variation in the axial dependency of TMP and predict the operating regimes of the device that maximize the spatial uniformity in TMP and thereby optimize the use of the entire membrane area [8]. However it did not take the wall thickness into account and covered a limited set of module geometric parameters.…”

“…. In contrast to previous work [8], this approach examines the transmembrane pressure difference (TMP) profiles established by the fluid mechanics in units with realistic industrially relevant dimensions.…”

“…The fluid velocity in direction is , and velocity along the fibre length direction is . As explained in previous paper [8], the Reynolds number of our current model is reconsidered as = (2 )/ , where is the density of the fluid (taken to be water), is the typical axial velocity where the average is used in Reynolds number calculation, and is the kinematic viscosity. With imposed average flux of 70 Lmh, the Reynolds number calculated with the above values of length and radius is 131, the reduced Reynolds number = (10 −2 ) ≪ 1 [5].…”