Lesson 26. Types and Rate of Filtration

26.2 Types of filtration

Based on the mechanism, following four types of the filtration are known.

26.2.1 Surface filtration: It is a screening action by which pores or holes of the medium prevent the passage of solids. The mechanisms, straining and impingement are responsible for surface filtration. For this purpose, plates with holes or woven sieves are used. Example is cellulose membrane filter.

26.2.2 Depth filtration: This filtration mechanism retains particulate matter not only on the surface but also at the inside of the filter. This is aided by the mechanism entanglement. It is extensively used for clarification. Examples are ceramic filters and sintered filters.

 Advances in sintered metal filters:

• Filtration technology utilizing sintered metal media provides excellent performance for separation of particulate matter. Sintered metal filter media are widely used in the chemical process, petrochemical and power generation industries.

• Advances in filtration technology include the development of continuous processes to replace old batch process technology. Liquid/solids filtration using conventional leaf filters is messy and hazardous to clean and require extended re-circulation time to obtain clean product. Traditional gas/solids separation systems such as cyclones, Electro static precipitators and disposable filters are being replaced by sintered fiber metal filtration systems.

• Sintered metal filters should be operated within the design parameters to prevent premature blinding of the media due to fluctuations in process operations. Use of flow control assures the filter will not be impacted with a high flow excursion. Filter efficiency increases as the filter cake forms. The cake becomes the filter media and the porous media acts as a septum to retain the filter cake. Filter cakes can be effectively washed in-situ and backwashed from the filter housing. A gas assisted pneumatic hydro pulse backwash has proven to be the most effective cleaning method for sintered porous metal filters.

• Sintered metal filters can be fully automated to eliminate operator exposure and lower labour costs while providing reliable, efficient operation.

Case study of depth filtration:

Several forces have driven changes in filtration technology during the last couple of decades, including environmental concerns, the health and safety of winery workers, and wine quality. The major active component in traditional depth filtration is diatomaceous earth, which has several major problems. First, it is difficult to dispose of because it does not decompose. Second, it can cause symptoms similar to coal miners' "black lung" disease when inhaled over long periods of time. In the United States this problem can be overcome by using cross flow filtration. The main benefit of cross flow filtration is that it uses a membrane with an absolute pore size to clarify wine without the need for media to act as the sieve for removal of particles from wine.

Example of cross flow filtration

• Nanofiltration is a recent membrane filtration process used most often with low total dissolved solids water, with the purpose of softening and removal of disinfection by-product precursors such as natural organic matter and synthetic organic matter.

• It is a cross-flow filtration technology which ranges somewhere between ultra filtration and reverse osmosis. The nominal pore size of the membrane is typically below 1 nanometer, thus Nanofiltration. Nanofilter membranes are typically rated by molecular weight cut-off rather than nominal pore size. The transmembrane pressure required is considerably lower than the one used for RO, reducing the operating cost significantly. However, NF membranes are still subject to scaling and fouling and often modifiers such as antiscalants are required for use.

 26.2.3 Ultra filtration: Ultra filtration is a pressure-driven membrane transport process that has been applied, on both the laboratory and industrial scale. Ultra filtration is a separation technique of choice because labile streams of biopolymers (proteins, nucleic acids & carbohydrates) can be processed economically, even on a large scale, without the use of high temperatures, solvents, etc. Shear denaturation can be minimized by the use of low shear (e.g., positive displacement) pumps.

 Following types of ultra filtration membranes are used prominently:

• Asymmetric skinned membranes made from synthetic polymers by the "phase-inversion" methods.

• Inorganic membranes, utilizing inorganic porous supports and inorganic colloids, such as ZrC*2 or alumina with appropriate binders.

• Melt-spun, "thermal inversion" membranes.

• "Composite" and "dynamic" membranes with selective layers formed in situ.

 26.2.4 Cake filtration: By this filtration mechanism, the cake accumulated on the surface of the filter is itself used as a filter. A filter consists of a coarse woven cloth through which a concentrated suspension of rigid particles is passed so that they bridge the holes and form a bed. Example is cake made from diatomite. This cake can remove sub micrometer colloidal particles with high efficiency.

 26.3 Rate of Filtration

The analysis of filtration is largely a question of studying the flow system. The fluid passes through the filter medium, which offers resistance to its passage, under the influence of a force which is the pressure differential across the filter. Thus, we can write the familiar equation:

Rate of filtration = driving force/resistance

Resistance arises from the filter cloth, mesh, or bed, and to this is added the resistance of the filter cake as it accumulates. The filter-cake resistance is obtained by multiplying the specific resistance of the filter cake that is its resistance per unit thickness, by the thickness of the cake. The resistances of the filter material and pre-coat are combined into a single resistance called the filter resistance. It is convenient to express the filter resistance in terms of a fictitious thickness of filter cake. This thickness is multiplied by the specific resistance of the filter cake to give the filter resistance. Thus the overall equation giving the volumetric rate of flow dV/dt is:

dV/dt = (AΔP)/R

As the total resistance is proportional to the viscosity of the fluid, we can write:

R = μr(Lc + L)

Where, R is the resistance to flow through the filter, Δ is the viscosity of the fluid, r is the specific resistance of the filter cake, Lc is the thickness of the filter cake and L is the fictitious equivalent thickness of the filter cloth and pre-coat, A is the filter area, and ΔP is the pressure drop across the filter.

 If the rate of flow of the liquid and its solid content are known and assuming that all solids are retained on the filter, the thickness of the filter cake can be expressed by:

Lc = wV/A

where w is the fractional solid content per unit volume of liquid, V is the volume of fluid that has passed through the filter and A is the area of filter surface on which the cake forms.

The resistance can then be written;

                                                              R = μr[w(V/A) + L)]                                               (7.6)

and the equation for flow through the filter, under the driving force of the pressure drop is then:

                                                       dV/dt = AΔP/μr[w(V/A) + L]                                             (7.7)

Eq. (7.7) may be regarded as the fundamental equation for filtration. It expresses the rate of filtration in terms of quantities that can be measured, found from tables, or in some cases estimated. It can be used to predict the performance of large-scale filters on the basis of laboratory or pilot scale tests. Two applications of Eq. (7.7) are filtration at a constant flow rate and filtration under constant pressure.

 26.3.1 Constant-rate Filtration: In the early stages of a filtration cycle, it frequently happens that the filter resistance is large relative to the resistance of the filter cake because the cake is thin. Under these circumstances, the resistance offered to the flow is virtually constant and so filtration proceeds at a more or less constant rate. Eq. (7.7) can then be integrated to give the quantity of liquid passed through the filter in a given time. The terms on the right-hand side of Eq. (7.7) are constant so that integration is very simple:

 dV/Adt = V/At = ΔP/μr[w(V/A) + L]

or

                                                   ΔP = V/At x μr[w(V/A) + L]                                              (7.8)

 From Eq. (7.8) the pressure drop required for any desired flow rate can be found. Also, if a series of runs is carried out under different pressures, the results can be used to determine the resistance of the filter cake.

 26.3.2 Constant-pressure Filtration: Once the initial cake has been built up, and this is true of the greater part of many practical filtration operations, flow occurs under a constant-pressure differential. Under these conditions, the term ΔP in Eq. (7.7) is constant and so,

 μr[w(V/A) + L]dV = AΔPdt

and integration from V = 0 at t = 0, to V = V at t = t

μr[w(V2/2A) + LV] = AΔPt

and rewriting this

tA/V = [μrw/2ΔP] x (V/A) + μrL/ΔP

                                          t / (V/A) =   [μrw/2ΔP] x (V/A) + μrL/ΔP                                  (7.9)

Eq. (7.9) is useful because it covers a situation that is frequently found in a practical filtration plant. It can be used to predict the performance of filtration plant on the basis of experimental results. If a test is carried out using constant pressure, collecting and measuring the filtrate at measured time intervals, a filtration graph can be plotted of t/(V/A) against (V/A) and from the statement of Eq. (7.9) it can be seen that this graph should be a straight line. The slope of this line will correspond to μrw/2ΔP and the intercept on the t/(V/A) axis will give the value of μrL/ΔP. Since, in general, μ, w, ΔP and A are known or can be measured, the values of the slope and intercept on this graph enable L and r to be calculated.

Last modified: Saturday, 5 October 2013, 10:32 AM