Filtration

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This article is about Conventional Filtration, for crossflow filtration see Crossflow filtration.

Filtration is a process by which most or all solid particles in a liquid-solid suspension fluid are separated from the fluid by passing the fluid through a porous medium barrier. In conventional filtration (as opposed to crossflow filtration) the incoming fluid, or feed, flows perpendicular to the porous medium. A layer of solids continues to build with time over the surface of the medium, while the flux of the feed through the medium approaches a zero asymptote. In bioprocessing, filtration is an early processing step during the recovery phase. It may be employed, for example, to retrieve a target product in solution from an undesired solid mass of freshly ruptured cells. Filtration is of particular value because it allows for an effect means of volume reduction, a crucial tool in early processing.

The Processes

Filtration, as discussed above, deals with the separation of solids in suspension from liquids. A barrier, called the filter medium or septum, catches solid particles too large to pass through this medium on a first side as liquids and fine, very small solid particles pass to a second side side. On the first side, the solids form a continuously thickening layer known as a filter cake. As this cake increases in thickness, the flux of material, or filtrate, through the filter medium, decreases, approaching a horizontal asymptote at zero. It is therefore necessary to occasionally stop filtration and remove the cake, or systematically clean the filter during filtration, in order to continue a process of filtration for an extended period of time. Several methods and devices have been devised that allow for this filter cleaning while operating, as well as mechanisms permitting easy removal of filtered solids from the filtering machinery.

In mathematical modeling, filter cakes are often treated as non-compressible. Unfortunately, that is not the case. Several factors, including the pressure gradient of the driving force, if applicable, may cause the filter cake to partially collapse. This can make determining the height and resistance of the cake difficult, which in turn renders other variables such as flux and processing time indeterminate.

Design and Operation

There are four categories of filtration as divided by driving force: gravity, vacuum, pressure and centrifugal force. The last may also be considered a form of centrifugation, and will not be discussed in great detail here. Types of filtration may also be classified by mechanism (sorted by whether solids are stopped at the surface of a cake or trapped within pores of a medium), by objective (sorted by whether a dry solid, clarified liquid, or both are sought), by operating cycle (sorted by whether filtration is continuous or intermittent), or by nature of the solids. For simplification, only classification by driving force, with specific reference to exemplary machinery will be discussed here.

Gravity filtration

The simplest form of filtration uses only the force of gravity to drive a fluid through a porous medium. Because this driving force is relatively weak, the filtrate must be of low viscosity and generally dilute. The medium is placed orthogonal to the force of gravity and parallel to the ground. An excellent example of such filtration may be found in the common place household drip coffee filter, in which a layer of coffee grounds acts as a pre-established filter cake and the thin paper of the coffee filter is the the filter septum. Liquid coffee streams through the septum into a collecting pot below; coffee grounds remain trapped on the upper side of the septum. Such gravity filters my also be used in industry on a larger scale, for example, the sand gravity filter, however, with only gravity as the driving force, these filters tend to be too slow to meet the demands of industry.

Vacuum filtration

An example of a rotating drum vacuum filter from US Pat. 2,379,754

A vacuum filter operates by creating a lower pressure on the distal side of the medium with respect to the incoming feed. A vacuum may provide a substantial pressure difference sufficient to filter a filtrate too viscus for a gravity filter to handle. It can also produce a fairly dry solid and provide a means for washing the precipitate. Examples of vacuum filters include the leaf filter, the Buchner funnel, and rotating drum vacuum filters. Leaf filters are a staple of this design. Essentially, the leaf with a low internal pressure due to vacuum is immersed in the filtrate mixture until a think layer of cake has built up on the surface of the leaf. The leaf is then transferred to a washing tank, where wash is draw through the leaf until a slight internal pressure is applied to the leaf, removing the cake. In another example, drums with filter media on the outer face, and an internal vacuum, are partially immersed in and rotated through the filtrate mixture, picking up a layer of precipitate. As the drum rotates out of the mixture, the precipitate is washed off the surface and collected. Most vacuum filters operate continuously.

Pressure filtration

Several plates and filters from an example of a filter press from US Pat. 2,390,628

If a higher pressure is required than can be achieved via vacuum filtration, such as in the instance that an especially viscous liquid is being filtered or filter-aid cannot be used to ease the filtration (see below), a pressure filter may be employed. In pressure filtration, the filtrate is driven through the filter by positive pressure on the feed side of the filter. While there are several forms of pressure filters, the filter press largely dominates the field. Often taking the form of the plate-and-frame filter or the similar plate filter, the filter press is comprised of a series of plates and frames between which the filtering medium is arranged such that the plates tightly stack one against the next, forming small chambers in between. Channels for filtrate or wash and clarified fluid or soiled wash run along the top and bottom of the plate stack. Near the top and bottom of each plate are holes which may alternately be shut to force filtrate or wash entering one hole to flow through the medium to exit an alternate hole on the side of the filter distal to the side from which the filtrate entered. After filtrate has run through the filter press for a time, cake builds up on one side of the filters. the holes may alternately be plugged and wash forced through the device to clean the cake from the system. Pressure filtration tends to have high energy demands and be messy, however, it is capable of separating solid-liquid suspensions that other forms of filtration are simply not capable of addressing.

Principles and theory

In most cases of conventional filtration, a solid suspension fluid, or filtrate, is flowed against a porous medium by application of a pressure gradient across the medium, wherein the solids in the suspension too large to pass through the medium become trapped on one side of the medium, building up in a layer called a cake, of sometimes more specifically filter cake. The flow of the liquid filtrate through the porous medium, which is a bed of solids, may be described by Darcy's Law written in the form:

${\frac {1}{A}}{\frac {dV}{dt}}={\frac {\Delta p}{\mu _{o}R}}$

wherein A is the cross-sectional area of the medium through which the fluid flows, V is the volume of filtrate, t is the time, Δp is the change in pressures across the medium and cake, μ_o is the is the viscosity of the filtrate, and R is the combined (in series) resistance of the filter medium ("R_M") and filter cake ("R_C"), which is:

$R=R_{M}+R_{C}$.

The cake resistance may further be described in terms of the specific cake resistance α the the following form:

$R_{C}=\alpha \rho _{c}\left({\frac {V}{A}}\right)$

wherein ρ_c is the mass of dry cake solids per unit volume of filtrate.

Darcy's Law for the flow of the liquid filtrate through the bed of solids porous filter medium and cake may therefore be rewritten as:

${\frac {1}{A}}{\frac {dV}{dt}}={\frac {\Delta p}{\mu _{o}\left(\alpha \rho _{c}\left({\frac {V}{A}}\right)+R_{M}\right)}}$

This equation may be integrated with an initial condition of zero filtrate at time zero to yield:

${\frac {t}{\frac {V}{A}}}={\frac {\mu _{o}\alpha \rho _{c}}{2\Delta p}}\left({\frac {V}{A}}\right)+{\frac {\mu _{o}R_{M}}{\Delta p}}$

which may also be rewritten in term of the filtrate density ρ, the ratio of the mass of dry cake solids to the mass of feed c, and the ratio of the mass of wet cake to the mass of dry cake w:

${\frac {t}{\frac {V}{A}}}={\frac {\mu _{o}\alpha \rho c}{2\Delta p\left(1-wc\right)}}\left({\frac {V}{A}}\right)+{\frac {\mu _{o}R_{M}}{\Delta p}}$

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