Filtration, 1. Fundamentals

Abstract

The article contains sections titled: 1. Terminology 2. Filtration Models 2.1. Calculation of the Pressure Drop over the Filter Medium and/or the Filter Cake 2.1.1. Definition of Filter Resistance and Cake Permeability: The Darcy Equation 2.1.2. The Equation of Kozeny and Carman 2.2. Cake Filtration 2.2.1. The “Cake Filter Equation” 2.2.2. Evaluation of Experiments with Linear Diagrams 2.2.2.1. Linear Diagram in the Differential Form 2.2.2.2. Linear Diagram in Integrated Form 2.2.2.3. Example 2.2.2.4. Deviations from Linearity 2.2.3. Compressible Cake Filtration 2.3. Blocking Filtration and other Modes of Filtration 2.3.1. Complete Blocking Filtration 2.3.2. Intermediate and Standard Blocking Filtration 2.3.3. Simplified Evaluation of Experimental Data 2.4. Depth Filtration 2.4.1. Depth Filtration Mechanisms 2.4.2. Cleaning and Sizing of Deep Bed Filters 2.5. Cross‐Flow Filtration 3. Washing of Filter Cakes 3.1. Basic Effects, Mass Balances 3.2. Example of Experimental Results 3.3. Test Procedures and Pitfalls 3.4. “Intermediate” Deliquoring before Cake Washing 4. Deliquoring of Filter Cakes 4.1. Deliquoring by Gas Pressure 4.1.1. Equilibrium Saturation of Filter Cakes 4.1.2. Kinetics of Deliquoring by Gas Pressure 4.1.3. Approximate Solution for Coarse, Incompressible Cakes 4.1.4. Practical Scale‐Up of Deliquoring by Gas Pressure 4.1.5. Shrinking and Cracks in Filter Cakes 4.2. Deliquoring by Expression 5. Optimal Filtration Cycle Time 6. Interparticle Forces and Forces Between Particles and Filtermedia, DLVO Theory 7. Mathematical Simulation of Filtration and Cake Formation 8. Handling of “Unfilterable” Suspension 8.1. Optimization of Upstream Steps (Crystallization, Precipitation) 8.2. Application of Flocculants (Polyelectrolytes) 8.3. Adaptation of pH 8.4. Checking of Alternatives to Cake Filtration 8.5. Use of a Filter Aid

Parameter Estimation for Incompressible Cake Filtration: Advantages of a Modified Fitting Method

“…However, substituting K m = m / V for K in Eq. , where m is the filter cake mass at the end of filtration, the equation stays the same, only r takes the meaning of r m , i.e., the mass‐specific resistance , . This was meant when we mentioned earlier that the height‐ and mass‐specific form are equivalent and that we do not limit the generality of our approach due to the primary focus on height‐specific filter cake resistances.…”

“…During the whole separation process, the accumulated liquid mass at the filter outlet is measured by an automatic scale. Using either the filter cake height at the end of filtration or the mass of separated matter together with the collected liquid volume, converted from the mass using the density, as a function of time, the parameters cake resistance and medium resistance can be calculated [1,2].…”

“…In the next section, the mathematics behind this calculation procedure is described. So far, it is only noted that the already mentioned standard method is based on a linear representation of the measured data and a corresponding linear model formulation that is fitted to these data points [1,2,17]. In our opinion, such strategies were very helpful to evaluate experimental data manually on paper sheets; however, current computer tools make them obsolete.…”

“…(8) or (9) is used for fitting it to the experimental data and determining R M and r. Before moving on to the parameter fitting strategy, a remark is made on the specific resistance r. As mentioned, here r is considered as height-specific; therefore, also the final cake height H is included in the factor K. However, substituting K m = m/V for K in Eq. (4), where m is the filter cake mass at the end of filtration, the equation stays the same, only r takes the meaning of r m , i.e., the mass-specific resistance [1,2]. This was meant when we mentioned earlier that the height-and mass-specific form are equivalent and that we do not limit the generality of our approach due to the primary focus on height-specific filter cake resistances.…”

“…Resistance of cake and medium cause pressure drop in the fluid phase and, therefore, influence the filtration setup, such as choice of filter apparatus and suitable pumps as well as integration of filtration into the larger process. As long as filter cakes can be considered incompressible, these two parameters are indeed decisive and are the only descriptors to be determined by parameter fitting as all others are known from the experimental conditions [1,2]. Filter cakes can be considered incompressible depending on their material properties and the operation conditions.…”