Filtration

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Process Engineering Guide:
GBHE-PEG-SPG-300

FILTRATION

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Process Engineering Guide:

FILTRATION

CONTENTS
0

INTRODUCTION

1

THE THEORY UNDERLYING FILTRATION PROCESSES

1.1

The Mechanism of Simple Filtration Systems
1.1.2
1.1.3
1.1.4
1.1.5

1.2

Cake Filtration
Complete Blocking
Standard Blocking
Intermediate Blocking

Cake Filtration – Models and Mechanisms
1.2.1 Classical Theory for the Permeability of Porous Cakes and Beds
1.2.2 The Rate of Filtration through a Compressible Cake – The
Standard Filtration Equation
1.2.3 The Compression or Consolidation of Filter Cakes – Ultimate
degree of dewatering
1.2.4 The Rate of Consolidation
1.2.5 Useful Semi-Empirical Relations for Constant Pressure and
Constant Rate Cake Filtration
1.2.6 Constant Pressure Filtration
1.2.7 Constant Rate Filtration
1.2.8 Multiphase Theory of Filtration

1.3

Crossflow Filtration

2

THE RANGE AND SELECTION OF FILTRATION EQUIPMENT
TECHNOLOGY
2.1
2.2
2.3
2.4
2.5
2.6

Scale
Solids Recovery, Liquids Clarification or Feed stream
Concentration
Rate of Sedimentation
Rate of Cake Formation and Drainage
Batch vs Continuous Operation
Solids Loading


2.7
2.8
2.9
2.10
2.11

3

SUSPENSION CONDITIONING PRIOR TO FILTRATION
3.1
3.2

4

Simple Filtration Aids
Mechanical Treatments

POST-FILTRATION TREATMENTS AND FURTHER DOWNSTREAM
PROCESSING

4.1

5

Further Processing
Aseptic or “Hygienic” Operation
Miscellaneous
Shear versus Compressional Deformation
Pressure versus Vacuum

Washing
4.1.1 Air-Blowing
4.1.2 Drying

TESTING AND CHARACTERIZATION OF SUSPENSIONS
5.1

Introduction – Suspension

5.2

Properties relevant to Filtration Performance
5.2.1 Pre-Filtration Properties of Suspension
5.2.2 Properties of Filter Cake
5.2.3 Laboratory Scale Filtration Rigs

5.3

Means of Monitoring Flocculant Dosage

5.4

Filter Cake Testing
5.4.1 Strength Testing (See also piston press described earlier)
5.4.2 Cake Permeability or Resistance
5.4.3 Rate of Cake Formation


6

EXAMPLES OF THE APPLICATION OF THE FORGOING PRINCIPLES

6.1
6.2
6.3

Dewatering of Calcium Carbonate Slurries
Dewatering of Organic Products – Procion Dyestuffs
Filtration of Biological Systems – Harvesting a Filamentous
Organism

REFERENCES

TABLES

FIGURES


0

INTRODUCTION
For the purposes of this process engineering guide, filtration will be
regarded as the process whereby solids are separated from liquids by the
use of a porous medium. This definition then deliberately excludes the
filtration of gas streams. Filtration together with gravity separation forms
the basis for nearly all unit operations to accomplish the dewatering of
suspensions [3-5]. It is therefore worthwhile considering the broad factors
that favor filtration over gravity separation methods for a given system [1].
Perhaps the most important of these involves the use of a porous medium
to effect the operation. The nature of the former may be tailored and
designed to best suit the requirements of both phases of the suspension
and the sort of dewatering action required. In contrast, all techniques
based on gravity separation are completely dependent upon the density
difference, ∆ρ, between solid and liquid phases. Since ∆ρ must be
regarded for many systems as an invariant, (It may be slightly perturbed
by a change in operating temperature), a small value for the quantity
almost Invariably means that gravity separation will prove difficult. This Is
often the case for biological particles (see Section 3.8). For such cases
filtration is then often to be preferred.
The penalty that has to be paid for this versatility of filtration process
design is usually greater expense and additional complexity when
continuous or automated operation is desired. It must be stressed that the
above statements are based on broad, generalized principles. For both
filtration and gravity separation, the ingenuity of solid/liquid separation
equipment designers has led to means of at least partly circumventing
many of the disadvantages associated with each [8].
The above definition of filtration encompasses a large number of
possible operations ranging from the clarification (or even sterilization> of
a very slightly loaded suspension to the removal of a product in the form of
a solid cake. Other variations permit filtration to be used as a thickening
operation where a feed stream is concentrated in the suspended phase
without the formation of a cake or the deposition of solids. Since this
section of the manual falls within the dewatering section, most emphasis
will be given to processes where it is the suspended phase that contains
the desired product and Is usually to be further processed. Clarification by
filtration will be discussed briefly but, for greater detail, the reader is
referred to the separate chapter on that subject (GBHE-PEG-SPG-400 Centrifugation) and to references [1,12]


Finally It is appropriate to set the context for the rest of this guide. In
Section 3.5.2 some of the basic, and largely classical, theory of filtration
will be presented. The range and selection of filtration equipment Is then
briefly discussed in Section 3.5.3. In this and all parts of this section
emphasis will be placed much more upon relating material properties to
the process design than in providing a comprehensive survey of the
available technology. To Illustrate process interactions, In Section 3.5.4 a
brief consideration is given to those operations most likely to follow
filtration in a complete process. In Section 3.5.5, methods for testing and
characterizing the filtration properties of suspensions are described
together with the interpretation of the results in terms of the theory
previously given. To conclude the section, examples are given of the
processing of suspensions containing inorganic, organic and “biological”
particles. It is hoped that these will illustrate many of the principles
previously developed.

1

THE THEORY UNDERLYING FILTRATION PROCESSES
The purpose of this part is to provide the necessary theory on which the
rest of the section is based. It is intended that each of the following topics
should be self-contained and can therefore be read in isolation. The theory
pertaining to washing and dewatering by air-blowing is postponed until
Section 3.5.4.
1.1 The Mechanism of Simple Filtration Systems
Various authors have proposed schemes for classifying the diverse
mechanisms that may operate during filtration operations. The simplest
classification for solids retaining systems discriminates between cases
where the solids build up on top of a cake and those where they are
retained within the filter medium. A useful classification based on this
approach was provided a long time ago by Hermans and Bredee [14] who
distinguished four mechanisms, which are sketched schematically in
Figure 1:


1.1.2 Cake Filtration (Figure 1(a))
This process involves the removal of solids by the formation of a filtered
“cake” on the surface of the medium. It Is the cake itself which effects the
subsequent filtration. Depending upon whether the suspended particles
are smaller or larger than the pores of the medium, this process Is usually
preceded by a bridging or straining process in order for cake formation to
ensue. Hermans and Bredee proposed the following equations to describe
the time dependence for cake filtration:

where

V is the volume of filtrate at time t, Qo. the Initial flow rate
and k an empirical constant.

Alternatively in terms of a mean (cumulative) flow rate, q(t):

Equations (1) and (2) clearly represent a gross oversimplification of the
cake filtration of real systems. Modified forms of these are presented In
subsequent sections. Graphical representations of Equations (l)-(2) are
shown In Figure 2(a).

1.1.3 Complete Blocking

(Figure 1(b))

This mechanism Involves a straining process either at the medium surface
or within Its internal structure. This implies that the solids particles are
larger than the. local size of the pores of the medium. This then results in
completing blocking of pores as the filtration proceeds with a linear
decrease in the flow rate with volume:


In surveying a large number of suspensions and filter media, Hermans
and Bredee found this type of filtration to be rather rare. It also falls to
yield a useful and physically plausible volume-time relationship when
integrated.
The concept of "complete blocking" as depicted in Figure l(b) still retains
some merit for classification purposes, however.
1.1.4 Standard Blocking (Figure l(c))
This is the mechanism most pertinent to depth filtration where particles
may pass through the pores of the medium but are retained by eventual
adhesion to it. Hermans and Bredee's model ascribed a "fouling" process
where the internal volume of the pores decreased linearly with V.
Thus they obtained equation (4).

Since the subject of deep bed filtrations falls outside the intended scope of
this guide, no further discussion of this mechanism or topic will be
presented. More Information may be found in the guide on clarification or
In the books by Svarovsky (Chapter 11 of [1] and Purchas (Chapters 3
and 6 of [12]. In addition, the role of the particle zero-potential has recently
been considered by Raistrick amongst others (J H Raistrick in [94]).
The equations (l)-(4) were developed to allow volume, flow rate and time
correlations to be tested for each mechanism under conditions of constant
pressure filtration. A simpler diagnostic means of distinguishing and
interpreting them was provided by the dependence of the rate of change
of total filtration resistance, r, (i.e. medium plus accumulated solids) with
filtration volume, dr/dV, with r. The three mechanisms described so far
were attributed the following dependence:


In order to encompass the sometimes observed relationship, dr/dV a r,
Hermans and Bredee's classification allowed for a fourth mechanism:
1.1.5 Intermediate Blocking
Where,

This mechanism may be physically viewed as being intermediate between
Figures l(b) and l(c).

1.2

Cake Filtration – Models and Mechanisms

In this section of the dewatering chapter, greater prominence will be given
to cake filtration than to the other mechanisms just described. In part this
reflects the frequency with which the formation and properties of a cake
dominates a separation operation. However, the other reason for this
emphasis derives from the necessity to understand and control the
influence of the suspension itself as opposed to the hardware; for a
properly conceived cake filtration the suspension properties are dominant
and the filtration medium of secondary importance.
Before presenting some of the basic theory for cake filtration it is important
to delineate the factors which relate to the fundamentals of dewatering
presented In Section 3.2. In general for a given cake filtration system one
might want to ask the following two questions:
(i)

What degree of dewatering Is attainable for a given suspension In a
cake filtration rig? How is this ultimate dewaterabillty influenced by
changes in the suspension, filtration conditions and driving
pressure?

(ii)

What are the kinetics of the filtration process, ie do they allow the
process to operate near to or at the ultimate limit as in (1) above.

In general theories describing the permeability of a cake or its rate of
deposition are very much aimed at addressing the second sort of
question.


However, when one is trying to understand, for example, the expression of
liquid in a filter press, it is the ultimate dewaterability that is usually critical
though kinetics may again be limiting. For a comprehensive understanding
of filtration processes It is therefore necessary to have a quantitative
picture of both the kinetics of the process and the maximum degree of
dewatering that can be obtained. Both these Issues will be tackled In the
following pieces of theory. Additional aspects of the theory of filter cakes
and sediments have been discussed In more detail by Tiller and other
workers [11].
Other relevant references may be found in the sedimentation section of
this chapter (3.3).
1.2.1 Classical Theory for the Permeability of Porous Cakes and
Beds
From an observation of the rate of flow of liquids through beds of sand,
Darcy [15] suggested an empirical correlation between the fluid velocity, u,
the pressure drop across the bed, ∆P, and the bed thickness, L. The
result, Darcy's Law, may be expressed in the simple form:

Some insight into the nature of the constant, K1, is gained by assuming a
result from the Poiseuille [16] Equation for the flow of a liquid through a
capillary tube of radius, r, and length, L:

This result enables equation (6) to be modified thus:

where the Influence of the fluid viscosity, Q, has been explicitly Included.
dimensions of (length) 2.

K2 has


A combination of the equations of Darcy and Polseuille together with the
Incorporation of two properties of the bed itself (SA and Ɛ, led to the
equation attributed to Kozeny and Carman [17-18]:

In this equation the bed properties SA and Ɛ represent the specific surface
area (m-1) and the fractional voidage, ie 1 - ɸ, where ɸ is the
dimensionless volume fraction of particles In the bed or filter cake.
The Kozeny-Carman Equation, although the precursor for the most
commonly used filtration equations, suffers from a number of restrictions
and oversimplifications. Basically It Is a sound description for the drainage
rate of viscous flow of a clear liquid through a porous bed of constant
permeability VULCAN VGP systems the permeability at a given point may
be a function of pressure drop, time and the height of that point within the
bed. Further discussion of these features is provided later. The constraint
of viscous laminar flow is also sometimes not strictly applicable In
practice. Where turbulence becomes significant a correction to the
rearranged equation may be made as follows, after Burke and Plummer
[20]:

This equation was derived for beds of uniform spherical particles of
diameter, d; hence SA = 6/d. It can be seen that the leading term for the
pressure drop per unit length is the simple, viscous Kozeny-Carman
contribution. The second term is the kinetics energy loss to the pressure
drop through turbulent flow. Whether such a kinetic energy modification is
necessary for a given bed and flow rate may be judged by a plot of the
Reynolds Number,


against permeability (eg Morgan's work with sintered metal pores [21].
Fortunately it Is often the case that the simpler, purely viscous treatment
of permeability Is sufficiently accurate for practical applications.

1.2.2 The Rate of Filtration through a Compressible Cake – The
Standard Filtration Equation
From the somewhat idealized equations for the permeability of porous
beds, a straightforward modification, to allow for medium resistance, Rm,
yields a general expression for cake filtration rates:

Rc, the cake resistance (units of m-l) may In turn be related to, w, the
weight of solids per unit volume of filtrate (kg rnm3) and a quantity, r, the
specific resistance of the cake (le resistance/weight of solids per unit area
or m kg-1):

As pointed out in (i) for many real systems it is necessary to take account
of the finite compressibility of the filter cake under an applied pressure. A
simple empirical correction to resistance has been very widely used
(1,12).


where ro is the specific resistance at zero pressure drop and the exponent
“s” is known as the compressibility factor. This factor ranges from 0 for a
perfectly incompressible material to unity a highly compressive cake. Thus
a general expression for the rate of cake filtration may be written as:

Equation (15) may be Integrated to yield the total filtration volume after a
specified time provided that the functional dependence of the flow rate or
the pressure drop with time is known. It is, however, once again very
important to note the simplifications and approximations that are Inherent
In this equation.
Firstly, It is very common to assume that the medium resistance, Rm,
is a constant in time. Physically this corresponds to no blinding or trapping
of solids within the medium, ie a complete absence of Hermans and
Bredee's mechanisms (ii), (iii) and (iv) of Section 3.5.2(a). In reality the
medium resistance is quite likely to change during the initial stages of
cake formation. Once a cake of any substantial thickness has been
formed, the cake Itself will largely prevent any further particulate matter
from reaching the filter medium or support.
Hence Rm will usually thereafter indeed be a constant unless further
solids are leached into the medium from the underside of the cake.
Thus it is often reasonable to treat Rm as a constant during the cake
filtration but it may prove erroneous to deduce its value from a
measurement of the resistance to "clean" suspension medium alone.
(For an alternative perspective to this Issue, see (b)(v).)
The specific cake resistance, r or r0 will not be a simple constant for a
given suspended phase and medium. It will depend critically upon the
colloidal properties of the suspension and the consequent structure of the
filter cake. It may also depend upon the mode and rate of cake lay-down.

Factors such as particle size and distribution, particle shape, particle
surface properties, the presence and nature of any flocculating agent, etc,
etc, will all strongly influence r. Thus there arises the ability to control the
filtration process by conditioning the suspension by the use of
pretreatments and filtration aids. These will be discussed in more detail
later. One further reservation concerning equations (14) and (15) must be
expressed. It should not be presumed that the simple power law
dependence of r on the pressure drop ΔP will apply over a very extended
range of pressures.

1.2.3 The Compression or Consolidation of Filter Cakes – Ultimate
degree of dewatering
Many of the physical principles pertaining to the consolidation process
have already been derived in previous sections of the manual (3.2 - 3.4).
The subject is sufficiently central to many filtration situations, however,
that an outline of the theory will be reproduced here. Consolidation of a
structured filter cake will occur during its laydown and the filtration process
proper. Additionally it may be exploited following cessation of the actual
filtration by the application of pressure to express liquid from the pores of
the cake. This latter may involve cake collapse, that is consolidation, or
displacement by gas. Pneumatic dewatering is briefly considered in a later
section (3.5.5(b)).
The ultimate attainable degree of dewatering of a filter cake through
consolidation is calculated by considering the two opposing forces on the
cake. On the one hand, above a certain solids content the cake will
possess a structural resistance to densification which may be quantified In
terms of Its uniaxial, compressional yield point, Py(ɸ). Methods for
measuring Py(ɸ) and a description of its application are given later. This
Internal resistance to densification operates against the externally applied
pressure differential across the filter cake, ΔP.
Consider a filter cake of solids finit undergoing constant pressure
consolidation. Initially, provided that Py(ɸ init) is less than the applied
consolidating pressure, ΔP, the cake will be compressed and liquid
expelled from it. As this process continues, the concentration of solids in
the cake, ɸ, and hence the function, Py(ɸ), will increase.


The compressional yield point, Py(ɸ), is in fact a very strong function of
solids content (see Examples 3.5.7) and at some later time it will be of
sufficient magnitude to match the applied pressure and consolidation will
cease. This defines that the ultimate degree of dewatering will occur
when:

when this condition Is reached the internal stresses of the cohesive cake
are large enough in magnitude to fully resist the applied pressure ΔP.
Thus predicting the ultimte dewaterability simply requires a knowledge of
the function Py($) and this may be measured by a simple laboratory scale
determination. Examples of this procedure are given later and in Section
3.2.6 of the manual.

1.2.4 The Rate of Consolidation
Equation (16) enables the easy estimation of an equilibrium degree of
dewatering for a given filter cake and consolidating pressure. The question
of how fast that ultimate solids content is attained is a more complicated
one involving additional physical factors such as the drag forces exhibited
by the consolidating network on the liquid being expressed from the cake.
A full analytical description of the kinetics of such processes are not
presently available.
The Consolidation Model of Buscall and White, based on the Yield Stress
(Py) concept applied to sedimentation, has already been discussed in
some detail in Sections 3.2 and 3.3. This model automatically incorporates
the ultimate dewatering limit of Equation (16) for consolidation. This
follows from the choice of constitutive equation relating the time evolution
of the concentration of solids in the cake (the substantive derivative) in
terms of the yield stress parameter:


A number of attempts have been made to couple equation (17) with
continuity equations in order to derive scaling relationships for the
physically distinct problem of filtration (cf the results for sedimentation,
Sections 3.2 and 3.3 of this chapter). Possible strategies are outlined in
references [25-273]. Although such an approach has not yet proved
entirely successful a number of comments may be made:
(1) As for sedimentation the equation (17) encompasses the notion that
the driving force for solid/liquid separation is attenuated by the elastic
stress in the cake as described by Py(ɸ).
(2) Thus at low driving pressures (ΔP), Py(ɸ)) the rate of cake
consolidation may be enhanced by manipulation of those factors (Sections
3.2.6 and 3.3) that reduce Py(ɸ). Strategies for suspension conditioning
may utilize this type of reasoning and are considered later in Sections
3.5.3 and 3.5.4.
(3) In contrast at relatively higher driving pressures (ΔP >> Py(ɸ)), the
main factors controlling consolidation will involve properties of the primary
particles such as drag coefficients, together with dynamic drag coefficients
for the network (λ(ɸ) in Equation (17)). The pore structure and cake
permeability will therefore be relevant and hence In this case the
controlling factors are similar to those affecting the specific cake
resistance as discussed earlier (3.5.2(b)).
Until such a time as a full analysis of filtration in terms of the yield stress
concept has proved possible, the kinetics of consolidation of filter cakes
will remain a largely experimental science with understanding being at
best qualitative. Possible experimental approaches to the problem are
given In Section 3.5.6 and examples discussed in Section 3.5.7.


1.2.5 Useful Semi-Empirical Relations for Constant Pressure
and Constant Rate Cake Filtration
Constant Pressure Filtration [1,10,12]
As a starting point, the general cake filtration equation, (15), is rearranged in the
following form:

Integration of this simple form of the equation allows the relationships between
filtrate volume, time and Instantaneous filtration rate to be deduced. The results
are:


Both the specific resistance and the medium resistance can be evaluated
from the general equation, (18), via a plot of reciprocal rate, dt/dV, as a
function of cumulative filtrate volume, V. Such a plot has a slope equal to
the first bracketted term In the equation from which r o may be evaluated
(at a given pressure); the intercept yields the medium resistance, Rm. It Is
quite common with cake filtrations for the extrapolated data to pass
through the origin such that the medium resistance Is negligible compared
with that of the cake. These simple principles are Illustrated schematically
in Figure 3. Likewise, for compressible cakes a series of reciprocal rate
versus cumulative volume at various pressures yields the relationship
between ΔP and specific resistance from which the exponent, S b of
equation (14) can be evaluated (see Figure 3).
Once the specific and medium resistances are known, from laboratory (or
plant) measurements of V-l versus V, the relations (19)-(22), and those
that follow for constant rate filtrations, may be applied In a predictive
fashion. It is, however, Important to recall the predictions and restrictions
that apply to equation (18) and were discussed in Section 3.5.2(b) (II). The
two most important caveats in this context involve the scaling up of the
quantities r o and Rm. The medium resistance Rm may be an important
parameter and may not hold the same value at plant-scale as measured in
the laboratory. Likewise, r o depends critically upon the mode of cake
formation and so also may vary with scale, Initial filtration rate.
1.2.7 Constant Rate Filtration
For a constant rate filtration, the pressure drop will increase as the cake
builds up. In practical situations there will be a limit to the magnitude of ΔP
that can be applied or tolerated. Hence it is necessary to know the
cumulative volume, V*, and time, t*, associated with a given limiting
pressure drop, ΔP*. The volume- time relationship is trivial: cumulative
volume is given by the product of the time and constant rate.
The other relations are again derived simply from equation
(15):


The equations (19)-(23) have been derived for strict conditions of constant
pressure or rate. In reality many dewatering configurations operate in
regimes which are intermediate between these two whereupon a more
involved numerical integration of equation (15) will be required in order to
derive volume-time relationships. A common configuration involving both
extreme cases utilizes constant rate filtration until the pressure drop has
reached Its maximum attainable (or tolerable) value whereupon the
filtration continues at constant pressure until the rate falls to an
unacceptable level.

1.2.8 Multiphase Theory of Filtration
The theory and equations that have been presented in outline here, have
long been accepted as a reliable though somewhat empirical description
of the cake filtration process. However, more recently (- 1975 onwards),
various workers have re-examined this so-called "two resistance*
approach (ie r and ), and contrasted its basis with an alternative
description, the "multiphase filtration theory" [22,23].

The latter Involves a lengthy derivation of equations based on a continuum
mechanics approach. This detail will not be presented here but may be
found In the references. Rather an outline of some of the results will be
discussed and compared with the "two resistance" formulation.
It is first worthwhile recapitulating on the Interpretation of data analyzed
via the *two resistance" approach. In essence this method attributes the
resistance to filtration to two additive contributions: that of the cake which
may be a function of time and pressure etc and that of the septum or
medium which is rigorously regarded as constant (and often negligible).
For this case a linear relationship between the inverse filtration rate V-l and
cumulative filtrate volume, V, Is taken to imply the following:
(1)

The local porosity and cake resistance are uniform.

(2)

The average porosity and cake resistance are constant.


Where non-linear reciprocal rate data is encountered, the following
conclusions are inferred from the apparent compressibility of the filter
cake:
(1)

lion-uniformity of local porosity and cake resistance.

(2)

Time and other dependence for average porosity and cake
resistance.

(3)

Dependence of cake resistance on slurry concentration, pressure
and septum.

In essence the “multiphase” description is based upon local continuity and
motion equations for both suspending and particulate phases In the cake
and septum. Application of dimensional arguments together with estimates
of the magnitude of the relevant groupings indicate which terms dominate
V-l. Briefly it is the pressure driven and drag forces that control the process
whilst inertial and viscous forces may be largely neglected. At the end of
the analysis the following multiphase cake filtration equation is gained:

where G Is a function of slurry concentration, solid and liquid densities, the
filter area (A), and the average porosity. For the case where the cake
height is a linear function of filtrate volume, V, G can be shown to be
Independent of V. Then the reciprocal rate equation depends upon the
three quantities:
K o (V) :- Septum permeability
J o (V) :- Septum pressure gradient
Po (V) :- Cake pressure drop
and now deviation from a linear relationship between V-l and V for
constant Po, are attributed to changes in the permeability and pressure
gradient developed In the septum and its Interface with the filter cake.
Willis et al have demonstrated that this theory is plausible by showing that
a given cake (formed by the filtration of a Lucite slurry> can be made to
undergo a transition from apparent “incompressible” to “compressible”
filtration merely by changing the nature of the septum.

In fact, Willis and co-workers cited only one experimental verification of
their theory and so It Is unwise to speculate on Its generality. Perhaps the
most important feature of the analysis Is that the attribution of non- linear
reciprocal rate data to “compressible” cake formation without further
corroborating evidence may prove fallacious if septum fouling, blinding or
compression Is occurring. Means of obtaining this corroborative evidence
and of quantifying cake compressibility without a septum present are
considered later in Section 3.5.6.

1.3

Crossflow Filtration [8 -44]
Although a detailed discussion of the various applications and some
variants of crossflow filtration will be provided in Section 3.9 of this manual
(“Pressure Driven Membrane Separation Processes”), a brief outline of the
principles will be given here, The basic objective of a crossflow
configuration is to achieve the limited dewatering of a suspension (or
solution> using a permeable membrane but without the retention or
immobilization of the solid phase. This is achieved by maintaining a
tangential flow of the suspension across the surface of the membrane.
Thus, Ideally, cake formation is totally avoided and the particulate phase
remains evenly distributed throughout the concentrating suspension as a
result of the convective effects of the flow [28,35,391.
At a simple level the first requirement for an understanding of crossflow
dewatering would be a model relating the permeate flux, ie the rate of
concentration to the primary process variables: temperature, driving
pressure, starting concentration and transmembrane velocity. For a
perfectly ideal case, the flux relationship could be simply derived from
treating the septum as a non-blocking bed of constant permeability. The
flux would then be directly proportional to the driving pressure gradient as
predicted by the Darcy or Kozeny-Carman relationships, equations (6)(9), In all real cases the behavior of the flux is by no means that simple.
An alternative approach that has been applied, also largely
unsuccessfully, Is to use some sort of modified cake filtration model. In
reality the factors that control the flux of permeate are various, subtle and
almost Inevitably time dependent and hence It Is no surprise that simple
models are Inappropriate. some useful generalizations may, however, be
made.


In many real examples of crossflow filtration, particularly In ultrafiltration
[31-37], the flux rate Is limited by a mechanism called concentration
polarization. This arises because the layers of suspension closest to the
membrane are those which suffer depletion from permeate. There Is
therefore a local increase In concentration (but not necessarily a “cake”)
which inevitably leads to a fall in the permeate flux.
Acting In opposition to this mechanism are the effects of diffusion and
laminar or turbulent convective flows. Clearly the diffusion process Is very
dependent on the size and nature of the particulate (or dissolved) phase.
Some useful relationships have been given to correlate the effects of the
various factors that may operate when this mechanism is dominant. The
following have been used for dewatering of biological suspensions by
ultrafiltration [32-33]:

It must be stressed that equations such as (25) and (26) are by no means
applicable to all crossflow situations.
In addition to the above problems Involving particle concentration gradient,
another common source of permeate flux decline is the phenomenon
referred to as "fouling" [35-36].

Fouling encompasses a whole series of processes whereby permeate flux
falls as a function of time as a result of changes in the membrane Itself.
Commonly these changes might Involve deposition of material on the
surface or interior of the membrane often leading to a time-dependent
decrease in Its porosity. Beyond these generalizations lies an enormous
number of experimental studies and observations but unfortunately there
Is as yet only relatively poor understanding of the phenomenon and how

to avoid It. Current active research Is being carried out in various centers
in the world with notable British contributions being made at Bath 1351
and at Varren Spring Laboratory - the latter under the auspices of a
BIOSEP project [39-41]. This project has utilized various electron
microscopy based investigations to probe the whereabouts of protein
foulants, identified by staining, during biological separations.

In the future, this sort of experiments should at least assist in the
elucidation of the mechanisms of fouling In various cases thereby enabling
the application of collold and surface science to avoid such problems.
Another engineering based strategy for reducing fouling, the deliberate
production of transmembrane, turbulent vortices, has recently been
investigated by Hltchell I951.
Again with respect to potential future developments, it is interesting to note
that developments are being made in new filtration-based dewatering
strategies involving the use of electric fields [38,40]. Examples of these
process operations Include electrophoresls, electrodecantation,
electroflltratlon, electro-osmosis and others.
Some of these will be discussed in more detail in Section 3.9. However, a
particularly worthwhile technology target In the present context involves
the concept of harnessing a dielectrophoretic effect to prevent fouling or
concentration polarization during crossflow filtration processes [40].


2

The Range and Selection of Filtration Equipment Technology [1,12]
It is not the purpose of this short section to attempt to provide a
comprehensive equipment selection guide for filtration-based solids/liquid
separation operations. There are already established sources for such
Information; see, for example, Chapter 9 of reference [12] and Chapter 20
of reference [1] . Rather it is intended to Indicate how an understanding of
both the properties of the material and the rest of the envisaged process
train will facilitate a choice from the available filtration-based options.
The main factors that Influence the choice of technology are:

2.1

Scale

The scale of the operation is not normally too stringent a constraint since
most devices are available in a range of sizes to handle a variety of
capacities. In ‘general, however, very small scale separations will not
usually command the most expensive filtration plant If thermal drying can
follow the mechanical dewatering stage. For high value feedstreams (e.g.
pharmaceuticals etc) other factors may override this option, however.


2.2

Solids Recovery, Liquids Clarification or
Feedstream Concentration

As a generalization most solids recovery dewatering operations will
Involve the formation of a filter cake whilst clarification (Chapter 4)
procedures will often avoid cake formation in order to maintain a high flux
of liquid. Where feedstream concentration is required two options arise.
Either a cake may be formed which Is then reslurried to a higher solids
content, or a continuous thickening process may be employed. Very often
a crossflow filtration arrangement will be appropriate for such a continuous
thickening arrangement.
2.3

Rate of Sedimentation

The rate of sedimentation of a suspension can have various effects on the
choice of filtration plant. For example a bottom fed rotary drum filter may
not be suitable for slurries containing a fraction of very large or very dense
particles since these may settle out to form a "heel" well before they can
be transported to the bottom of the drum. The sedimentation behavior Is
also often critical In determining the structure of a filter cake closest to the
septum. Thus If the initial filtration rate Is properly controlled, the bottom of
the cake consists of the largest, fastest settling solids which may help to
trap the finer end of the particle size distribution and thus reduce blocking
and blinding. A third area in which the suspension settling properties are
of paramount importance Is where a filtering centrifuge Is being
considered as dewatering device. For these machines, the mechanism of
operation entails a rapid settling of the solids phase In the centrifuge bowl
followed by flow of the supernatant through the, hopefully, porous bed.
The way In which this bed is formed and the properties that result will thus
depend on the settling characteristics of the suspension.


2.4

Rate of Cake Formation and Drainage

The rate at which the height of a filter cake rises can easily be assessed
using simple laboratory filtration tests (see next section). It will depend on
both the solids loading and the porosity and structure of the cake itself.
This property has obvious repercussions on the geometry and necessary
dimensions of suitable filtration equipment.
2.5

Batch vs Continuous Operation

This is clearly a critical question which must be addressed by looking at
the solids loading and rate of cake build-up, etc.
2.6

Solids Loading

As already explained, this factor will affect (Ill), (iv) and (v) above. In
addition it will strongly Influence the flow properties and hence the rate at
which the suspension can be presented to the filter If this proves to be
limiting.
2.7

Further Processing

It is necessary to consider the Influence of additional operations which
may either accompany the filtration or follow it in further downstream
processing. Possibilities include washing, air blowing and thermal drying.
The physical nature of the final product may also be relevant here (e.g. in
re-dispersible systems).

2.8

Aseptic or “Hygienic” Operation

When handling biological materials for pharmaceutical, food or other
products, the necessity to be able to clean and sterilize a filter my impose
particularly stringent demands. A detailed discussion of the relevant
Issues and the suitability of various filters (and other plant) to aseptic
operation Is given in the BIOSEP Report SAR 1 1401.


2.9

Miscellaneous

Various other factors are likely to Influence decisions about choice of
dewatering filter device. Of these the economics of the whole process Is
probably the most important. Such considerations will not be considered
here but are discussed In reference [45]. It is, however, worth pointing out
that process decisions cannot be taken on the basis of economic factors in
isolation. Very often physical constraints (e.g. those discussed in Section
3.5.2(b)) render an otherwise economically attractive strategy impossible.
In order to illustrate the influence of the factors described in (i) to (ix)
above, Table 1 presents an impression of the range of suitability for
commonly available filtration devices.
Having briefly considered the main factors influencing a choice of filtration
technology, a short discussion of two related topics is appropriate here.
These are the relative merits of dewatering by shear versus compression
and by vacuum versus positive applied pressure filtration.

2.10

Shear versus Compressional Deformation

During the latter stages of cake filtration, further dewatering is often
achieved by the application of direct mechanical pressure to the cake itself
- this Is the consolidation or expression process described In Section
3.5.2(b). Such a densification of the cake, In order to expel further
occluded liquid, may be promoted by either an applied shear or uniaxial
compressional deformation. For either case no change In the structure will
result until a critical stress, the yield stress, has been exceeded. Figure 4
compares the yield stress for both shearing cay) and uniaxial
compressional (Py) deformations for samples of BaC12-coagulated,
polystyrene latex suspensions. The latter provide a convenient model
which mimics a typical flocculated cohesive filter cake [46-47]. It can be
seen that shearing forces are effective (In the sense of exceeding the
relevant yield stress) at much smaller stresses (by some 1-2 orders of
magnitude); these shearing motions will often enable densification In their
own right via structural rearrangement and the concomitant collapse of the
cake structure. The advantages of dewatering by shear or a combination
of shear and compression are already exploited in many filtration rigs, e.g.
counter-moving belt filters [49], but there are almost certainly further gains
still to be made in this area.


2.11

Pressure versus Vacuum

There are a number of hardware-based factors which favor a choice of
pressure over vacuum filtration or vice versa and these are fairly simple to
assess. Thus, in general, positive pressure filtration, being capable of
yielding larger trans-septum driving forces, can yield greater filtration rates
and hence reduce the size of dewatering plant.
On the other hand vacuum filters have the advantage of simple
construction and ease of continuous discharge in operation. They are,
however, normally limited to total driving pressure drops of - 0.8 bar and,
In the normal way, unsuitable for the filtration of suspensions containing
volatile solvents.
The above factors relate to the actual filters. In addition, there are more
subtle factors, some of them less well understood, that pertain to
suspension properties. Of these the most important is the cake
compressibility. For a perfectly incompressible cake (s = 0) and a constant
pressure filtration, equation (20) indicates that the filtration time for a given
slurry volume is inversely proportional to the driving pressure. Thus
potentially large gains in rate may be expected by the use of positive
pressure drops greater than a bar compared with the vacuum
configurations. For compressible cakes (s > 0) the same equation predicts
that the advantage to be gained may be considerably attenuated by the
pressure dependence of the cake resistance. An assessment of cake
compressibility, for example by using the methods described later, Is
therefore highly desirable if the efficiency of increasing the trans-septum
pressure drop is to be predicted.
Finally, to illustrate the subtlety of some of these effects, attention Is
drawn to recent membrane (but not crossflow) filtration studies of Leaver
and Bewdick 1421. Studying the filtration of protein (USA) solutions these
workers have observed twice the permeate flux for vacuum compared with
positive pressure filtration even though the trans-membrane pressure
drops were apparently identical. The reason for this behavior is unclear,
but presumably involves some sort of membrane fouling.


3

Suspension Conditioning Prior to Filtration
Suspension conditioning may involve a simple mechanical treatment of
the suspension, the addition of a so-called filtration aid, or a combination
of both. The range of possible treatments may be conveniently divided into
these two categories:

3.1

Simple Filtration Aids
Using the term "filtration aid" in its broadest sense there are three general
classes of aid. The first class contains those pretreatment chemicals
which are added to modify the state of flocculation or coagulation of the
suspension prior to filtration [50,51].
Commonly these additives may be inorganic, e.g. Al or Fe salts or
polymeric, e.g. starches, gums, polyelectrolyte’s etc. The conventional
purpose of such aids is normally to enhance filtration via one of the
following:

(i)

Production of open aggregates so as to yield a porous filter cake thereby
achieving fast filtration rates [50-52].

(ii)

To yield strong aggregates so as to prevent wash-off and attrition; blinding
and septum fouling is therefore reduced [50-52].

(iii)

To improve the suspension rheology (Chapter 7).

(iv)

To modify the wetting behavior of the medium on the suspended phase.

It should, however, be borne in mind that if further, mechanical dewatering
of the filter cake by compression is ultimately to be sought, then factors (i)
and (ii) will later prove deleterious. A compromise must then be struck to
enable a structured cake that may be compressed under modest driving
pressures yet retain sufficient porosity during the actual filtration for
reasonable flow rates to ensue.
Since the selection and action of flocculants is discussed in detail in a
separate section of this chapter (3.7), no further mention of these will be
made here.

Additionally the reader may wish to refer to Chapter 2 (Sections 2.4 and
2.5) for details of flocculation mechanisms and the resulting floe
structures.
The other two classes of filter aids are the so-called *pre-coat" and "body
aid" additives (1, 12). The purpose of the former is obvious and serves to
provide an enhanced filter medium surface on which a cake may be laid
down. It is usually formed by re-circulating a pre-coat slurry through the
filter (typically a rotary vacuum device or similar) prior to the application of
the suspension of Interest. A Body Feed on the other hand is completely
mixed with the suspension requiring filtration before it reaches the filter
device. It serves to Increase the porosity of the developing filter cake (i.e.
Factor (i) above > and hence to lengthen the filter cycle time. An indication
of the efficiency of either pre-coat or body-feed filtration aids may be
gained by incorporating these additives in a small scale laboratory
filtration trial such as those described in Section 3.5.6, In the main the
function of the former may be assessed by its effect on the measured
septum resistance, The body-feed aid on the other hand should have the
effect of reducing the specific resistance of the filter cake.
The properties of some commonly encountered pre-coat and body-feed
filter aids are presented in Table 2. Further detailed discussion of the use
of these is provided in references [1, 12, and 52]. Finally it is worth noting
that surfactants are often employed in order to reduce the ultimate
moisture contents of filter cakes [53].
More information on this aspect of chemical pre-treatments may be found
in a later part of the chapter, Section 3.7.4


3.2

Mechanical Treatments
A large number of options are available for suspension pre-treatments that
do not necessarily involve inert or chemically active additives. The
following list, plus a few pertinent references, covers some of the most
commonly used methods:

(i)

Shear Treatment - often employed to reduce the apparent viscosity of the
suspension [46-48].

(II)

Degassing - more frequently employed prior to gravity separations. It may
be necessary before the filtration of certain biological products, however
(see Section 3.8).

(iii)

Suspension Ageing - like (i), (iv), (v), this technique is aimed at improving
filtration performance via a modification of the flocculated structure of the
suspension, e.g. in the manufacture of catalyst supports.

(iv)

Heat Treatment/Freeze Thaw I543.

(v)

Acoustic Methods - generally used for biological systems (see Section 3.8)
[55].
It is important to note the immense potential value of suspension
conditioning to filtration operations. The field of biotechnology covers
many examples where such conditioning has either a profound influence
on the process economics, or is absolutely essential to the Integrity of the
product. For example, to avoid protein denaturation, degassing may be an
imperative conditioning step. A full and valuable review of many aspects of
conditioning relevant to bio-separations is provided in BIOSEP SAR
Report "Primary Solid/Liquid Separation" [40].

Finally in terms of mechanical treatments it Is appropriate here to mention
for completeness a technology development program being carried out by
Batelle into "Combined Fields Separation Processes". The objective of this
sort of approach Is to identify combinations of separation means such as
electric and acoustic fields, such that synergistic advantages In
dewatering may be achieved.


In the cases of electro-acoustic and ultrasonic-assisted dewatering,
Batelle claim highly significant Improvements In the rate and degree of
filtration for suspensions containing particles such as coal, biological’s,
paper pulp and food materials. Unfortunately technical details are not yet
available though a number of patents have been filed. Although some of
these treatments do not strictly involve suspension conditioning, It Is clear
that there is considerable potential for the exploitation of filtration-based
processes combined with other separation fields in this way.
Post-Filtration Treatments and Further Downstream Processing [56]
An outline of the influence and theory of three typical post-filtration
operations, the washing of filter cakes. air blowing and thermal drying,
serves to illustrate process interaction with the filtration operation.

4.1

Washing [56, 59]
Filter cake washing is usually employed to effect a purification of the cake
by removing entrained soluble’s, or less frequently to recover the mother
liquor where the latter is of high value. The two main parameters of
interest are the quantity of wash liquor required to achieve the required
level of solute removal and the period of time taken for this degree of
washing to be attained.
Probably the simplest approach to calculating the required quantity of
wash liquor has been provided by Vakeman. He distinguishes between
filter cakes still holding filtrate in the voids, i.e., “saturated” cakes, and
those that have been blown dry, the unsaturated cakes. For both cases
Vakeman has analyzed the various mechanisms influencing the washing
process and produced charts of the fraction of recovered solute as a
function of the wash ratio, (i.e. the volume of wash liquor X the cake
voidage) and one other dimensionless parameter. These then permit a
very simple way of calculating the volume of wash liquor from small scale
laboratory tests. Further details are not relevant here but good accounts of
the use of the tests and theory, together with the charts, are provided in
the references [1,12,56-59].


Once the volume of liquor has been calculated, the washing time is very
straightforwardly estimated from the final filtration rate that was observed
following cake build-up. Inasmuch b both the wash time and volume
depend upon cake porosity and tortuosity, it will be appreciated that the
factors that influence the mode of cake lay-down (including the various
possible pre-treatments) will be very relevant to the washing performance.

4.1.1 “Air-Blowing”
The use of "air-blowing" as a method of dewatering filter cakes is strictly
not restricted to air alone; other gases or vapors, for example, nitrogen or
even steam may be used. For biological or food suspensions the latter
may provide an additional role for purposes of sterilization (see Section
3.5, 7(c)). The gas is propelled through the cake in a fashion appropriate
to the filtration mode, hence for vacuum driven systems atmospheric air is
commonly sucked through the cake (deliberately or otherwise) following
"breakthrough". With filter presses, pressure nutches etc, compressed air
is forced through the pores of the cake in order to displace as much
moisture as possible. By using heated air or nitrogen some additional
drying action is available; such techniques are, however, normally
restricted to small scale or high value products usually having special
problems of toxicity etc such that normal drying techniques are difficult to
apply*
The fundamental guiding principle in "air-blowing" is that the applied gas
pressure must be sufficient to overcome the capillary forces tending to
hold liquor within the pores of the cake (see Sections 3.2.9 and 3.5.7(a)).
Probably the best current model for this process has been provided by
Vakeman. Unfortunately, in terms of real operating experience, the
predictions that it provides are of limited accuracy even for near-ideal
systems containing hard particles of quasi-spherical geometry. Worse
than that, for suspensions of high aspect ratio particles (e.g. needles or
plates), or for compressible cakes or those prone to cracking, Wakeman's
method is of little practical value.
In terms of more empirical approaches, experimental work on a laboratory
or semi-technical scale can be used to make predictions of dewatering
time, final product moisture content and the air flow required. A number of
cautionary points should, however, be noted.


Since the final moisture content can be very sensitive to changes in the
particle size distribution and the way that the cake Is formed, it is very
Important to use identical material for the laboratory tests and to ensure
that factors such as air flow rate and cake thickness are reproduced as
closely as possible. Even so, as a "rule of thumb", it should be noted that
small scale characterization tests tend to yield an optimistic figure for final
moisture content since effects such as cake compression and cracking
tend to be more prevalent on large scale.
Further discussion of most of the above features as well as some more
practical examples are provided in the references [60-65].

4.1.2 Drying [67 -76]
It is not our intention to treat the subject of drying in any detail here.
However, a short discussion is included for completeness to highlight the
importance of considering the interaction between the filtration operation
and further downstream processes. It is hoped that a future release of the
Suspension Processing Manual will contain a more detailed chapter
(Chapter 10) based on those aspects of drying that will be alluded to In the
present context.
A general guiding principle that is invoked for most large scale dewatering
trains is to remove as much water as possible by mechanical means (i.e.
the filtration process here). This then minimizes the expenses of the
energy-intensive downstream drying operation. However, it is normally the
case that physical constraints imposed by the mechanical dewatering step
will intervene before the hypothetical economic optimum is reached (see
Section 3.10 - “Process Synthesis”).
There is a large literature, both Internal and external to the Company,
based on drying. A recent report by the FCMO drying team I661 described
three typical regimes of “paste preparation prior to a drying operation”:
a. Where there is no requirement for pipe flow. An example of this
situation is where a filter cake is discharged at high solids content
and is transported, perhaps by conveyor, to say an agitated
vacuum oven for final drying. It will be typical here to obtain the
maximum, physically-possible dewatering during the filtration.
b. Where a filter cake is re-slurried in order to deliver it by pipe flow to
typically a spray-drier. Clearly it is pointless in this case to

mechanically dewater to the ultimate physical limit. The filtration
step should be tailored towards facilitating the re-slurrying o f the
filter cake to a manageable suspension.
c. Where the paste is formed into a chosen, stable, physical shape to
accelerate the subsequent thermal drying. For such cases the
requirement of the filtration stage is to provide a paste with
rheological properties that allow this shaping process, e.g. by
extrusion. This situation is relevant to the formation of catalyst
supports and ceramic materials in general.
The sorts of interactions between mechanical and thermal dewatering
indicated in (a - c) above are variously discussed in the drying literature
[67-76]. It would appear, however, that relatively little Is known of how the
morphology of the filter cake influences the rate of thermal drying. For
example the relationship between, say, filter cake porosity and the
necessary residence time in an oven drier would be a useful one to
establish. Thus such Interactions would usefully be the subject of future
research. Finally the subject of drying as part of a solids Isolation process
is very critical when a redispersible solid is desired. This latter topic is
treated in detail in Chapter 13 of the manual.

5

Testing and Characterization of Suspensions
5.1

Introduction – Suspension

5.2

Properties relevant to Filtration Performance

In order to best utilize the principles and theory that have thus far been
presented, it is necessary to know as much as possible about the
"colloidal" properties of the suspension requiring filtration. Both the
properties of the pre-filtration suspension and those of any filter cake that
is formed are of importance. All or any of the following are likely to be
relevant:


5.2.1 Pre-Filtration Properties of Suspension
(i)

Suspension viscosity including any tendencies towards shear
degradation, thixotropic or any other structural modification
following shear flow 146-481.

(ii)

Suspension medium viscosity and wetting characteristics on the
solid (Chapter 2).

(iii)

Settling properties of the suspension, particularly the rate of
sedimentation. Relative density of solid phase. Floe size and
structure. (Chapter 2, References [50,5])

(iv)

The size distribution of particles and/or aggregates that are
present (Chapter 2).

(v)

The ease with which flocculated structure, and in particular the
above size distribution, may be modified by mechanical treatments
or inert/chemical additives. Such modifications will, of course, also
influence the other suspension properties above.

5.2.2 Properties of Filter Cake
(i)

The mechanical strength of the cake and hence its resistance
towards consolidation and the variation of this property with degree
of consolidation (Section 3.7, References [50-52]).

(ii)

The porosity of the cake as a function of voidage, that Is the
tortuosity of the path that supernatant must follow through the cake.
This property then is correlated with the cake resistances [51].

(iii)

The influence of mechanical treatments and additives to the
suspension and the actual filtration conditions, e.g. rate of cake laydown, on the cake strength and resistance.

Once a representative number of the above suspension properties has
been determined so as to enable a good understanding of its "colloidal"
behavior, the knowledge may be applied to the following targets:
(i)

Identification of the most appropriate plant and scale for the
filtration unit operation or suggestion of a better, alternative
dewatering means other than filtration (see Section 3.10).


(ii)

Optimization of the way that the operation is carried out. For
filtration this will include the choice of filtration conditions and
details of cycle time as well as their Impact on further downstream
processing.

(iii)

Prediction of optimal plant operation. Thus, for example, it is
essential to know what level of performance in terms of rate and
degree of dewatering can be expected under a given set of
conditions. This Is of paramount Importance for scaleup
calculations (see Section 3.2).

(iv)

Removal of process "bottlenecks" and correction of plant operating
problems. This again relies heavily on (iii) and the identification of
"benchmarks" for optimal performance.

(v)

To suggest where conditioning techniques 'and/or filtration aids
may be desirable or appropriate. Whereas the means and optimal
extent of pre-treatment should ideally be estimated from smallscale experimentation.

5.2.3 Laboratory Scale Filtration Rigs [77-80]
A number of small-scale rigs exist and these may be applied to the
measurement of filtration rates, filter cake properties and the Influence of
suspension properties on them. These rigs are commonly used for the
Initial derivation of data for scale-up purposes. If there is any doubt, they
may also be applied to the question of identifying the filtration mechanisms
of Section 3.5.2, although they are predominantly applied to cake filtration
tests.
Apparatus for measuring filtration rates on a small scale have been
described by various workers [77-80]. The rigs of Allen & Stone [77],
Gregory [78] and Bridger [80] are representative and of straightforward
construction. The Allen & Stone apparatus, is well automated and their
paper describes its mode of operation in detail. A reproduction from their
paper is given In Figure 5 from which the basic operating principles are
easily deduced. The original objective of the rig was to obtain data for
scale-up purposes. In contrast to this, the equipment of Gregory was
initially developed in order to assess the value of polymer flocculants as
additives to filtration slurries and to derive optimum polymer dosages by
experiment. The report of Brldger and Tadros uses a test rig to investigate

some fundamental aspects of the Influence of suspension properties on
the mechanistic details of cake filtration.
The "equilibrium" and kinetic aspects of the consolidation process
(Sections 3.2 and 3.5.2) may also be studied on a laboratory scale. Tests
may be carried out on a small-scale variable volume filter such as the
Piston press supplied by Triton Electronics, for example. With these
devices it Is possible to measure the solids content of a consolidating filter
cake as a function of pressure and also the rate at which this degree of
consolidation is approached. In the same vein a gas-pressure driven
pressure filter for laboratory scale tests from 0- "10 bar is now available
from Schenk.

5.3

Means of Monitoring Flocculant Dosage

The means of selecting appropriate flocculants and assessing optimal
dosages is dealt with more fully in Section 3.7 of this manual. However, a
recent addition to the range of portable, small-scale testing methods is
well worth a mention in the present context. The new test method is an online monitor for flocculation control [81-82]. Its operating principles are
based on the measurement of turbidity fluctuations In the flowing
suspension of interest. Gregory [82] has shown that the root mean square
fluctuation intensity can be related to the suspended particle size
distribution via a semiempirical relationship. This conclusion enables the
RMS signal to be used as a fast and sensitive Indicator of floe formation.
The device, marketed by Rank Brothers of Bottlsham, is relatively cheap
(ca $7.5K at the time of writing) and constructed in a way that makes it
ideal for portable use and for continuous monitoring. Gregory has
described applications where the device has been tested both in
clarification and in achieving flocculation of more concentrated
suspensions such as those requiring filtration. The method may also be
comfortably applied to suspensions that tend to foul the sample cell simply
by monitoring the ratio of both the RMS fluctuations and the average light
transmission. This ratio has been shown to be relatively invariant to the
deposition of modest quantities of material on the surfaces of the sample
cell. A recent ad hoc, trial of the Rank Brothers monitor has been made.
The device proved a sensitive indicator of flocculation In bacterial
suspensions to which high molecular weight cationic polyacrylamides had
been added. The response time was also fast demonstrating the potential
of such instruments as continuous dosage monitors.

5.4

Filter Cake Testing

For the general case of the suspension processing of fine solids the most
common application of filtration involves cake formation and treatment. It
is therefore appropriate to consider the parameters and means by which
the properties of the filter cake may be characterized. The three principal
properties that define the behavior of the cake are its strength, its
permeability or, conversely, resistance, and the rate at which it is laid
down. Methods for determining these will now be given.

5.4.1 Strength Testing (See also piston press described earlier)
This is relevant both to an understanding of the influence of the pressure
drop on the ordinary compressible cake filtration rate (as described by
equation (14)) and to the subject of compression dewatering following
filtration. Although a number of empirical measures of cake "strength"
exist, the most suitable and fundamental parameter to use is the uniaxial
modulus of compression, K [83] or the compressional yield function Py(Ø)
described earlier. The former my be defined In terms of the effect of
pressure on a cake volume (V) or concentration (Ø) change:

The modulus, K, is a very strong function, (K ~ Ø3-4 of concentration, Ø,
and depends upon the nature, shape and size distribution of the priory
particles as well as the structure of the cake and the Interparticle forces. K
Is related to the function Py(Ø) and is also very similar numerically to the
conventional infinitesimal modulus of shear G(Ø). This fact enables its
determination by straightforward laboratory techniques. (For further details
see Section 3.2,4.) Arguably the simplest of these to use is the Pulse
Shearometer Cell (Figure 8 of Section 3.3). This device enables the rapid
determination of G (~ K) for a small sample of slurry or filter cake by
measuring the propagation time of a low strain (~ 10-6) shear wave
between two discs mounted on piezo-electric crystals in the cell.
Calculation of G requires only the propagation speed of the wave, u (from
the disc spacing and propagation time), and the density, p, of the cake or
slurry:

The shearometry technique is generally restricted to the range 103 < G
< 106 dynes crn-2 but this is not usually a problem. Where cakes of higher
strength need testing an alternative strategy may be adopted by
measuring the compressional yield point, Py(Ø), in a centrifuge. The filter
cake must now be formed in situ from the slurry (to be filtered) in a
centrifuge tube.

A measurement of the height of the equilibrium sediment as a function of
gravitational field enables the evaluation of Py(Ø) over a range of
concentrations (Figure 9 of Section 3.3). The upper bound of Py(Ø)
measurable by this technique is constrained mainly by the gravitational
field that the centrifuge is capable of (safely) producing and the density of
the solid phase.
Measurements of either G or K may then be used to evaluate the
pressure, Pt, which must be applied to the cake in order to concentrate it
to concentrations, (Ø)*:

This then assumes a long enough contact time such that kinetics will not
prove limiting. That Is It represents the equality Ps = Py(Ø), the ultimate or
structural limit. For the centrifuge technique Py(Ø) may, in principle, be
calculated from a single experiment. Using the shearometer cell a series
of determinations at different slurry concentrations must be made. In both
cases equation (29) is solved either by graphical or numerical integration.
An example of the calculation is provided in the next section. Finally it may
be noted for completeness that K may also be measured directly In a
compression cell (84) but, for practical purposes, one of the two methods
described above is usually more straightforward and of sufficient
accuracy. For further clarification of the definition, interpretation and
measurement of G(Ø), K(Ø) and Py(Ø) the reader is referred to Section
3.2.


Filtration

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