chapter 7. polarization phenomena & membrane fouling (part...
TRANSCRIPT
Chang-Han Yun / Ph.D.
National Chungbuk University
November 18, 2015 (Wed)
Chapter 7. Polarization Phenomena & Membrane Fouling
(Part I)
2 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
Contents
Contents Contents
7.5 Flux Characteristics in Pressure Driven Membrane Operation
7.4 Pressure Drop
7.3 Turbulence promoters
7.2 Concentration Polarization in Pressure Driven Processes
7.1 Introduction
7.6 ∼ 7.8 Concentration Polarization Model
3 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.1 Introduction
Concentration polarization and Fouling ⇨ flux↓over time
In MF/UF : very severe
In gas separation and pervaporation : less severe
<Figure 7-2> Overview of various types of resistance
towards mass transport across a membrane in
pressure driven processes.
<Figure 7-1> Flux behavior as a function of time.
Resistance
Rp : Pore blocking
Ra : Adsorption
Rm : Membrane
Rg : Gel layer forming
Rcp : Concentration polarization
4 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.1 Introduction
Additional resistances on the feed side to the transport ⇨ cause of flux decline
Concentration polarization(Rcp)
Adsorption(Ra)
Gel layer formation(Rg)
Plugging of the pores(Rp)
※ Feed quality and process ⇨ determine the extent of these phenomena
Convective flux through the membrane
(7-1)
For pressure driven processes(MF, UF, NF, RO)
(7-2)
※ In the ideal case, Rtot = Rm (the membrane resistance)
5 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.1 Introduction
Concentration polarization resistance(Rcp)
Retained solutes ⇨ accumulated at near membrane surface
⇨ concentration of retained solutes near membrane↑ ⇨ form resistance
Gel layer resistance(Rg)
Concentration of the accumulated solute molecules = so high
This mainly happens when the solution contains proteins.
Pore-blocking resistance(Rp) and Adsorption resistance(Ra) in porous membrane
Some solutes to penetrate into membrane and block pores ⇨ Rp
Finally leading to adsorption phenomena
Adsorption : on membrane surface as well as within pores themselves
6 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
Solvent : permeate through the membrane
Solutes : (partly) retained by the membrane
Solute balance at steady state
Convective transport of solute
(bulk → membrane surface)
= permeation through membrane
+ diffusive back flow(membrane → bulk)
(7-3)
cp < cb ⇨ Concentration polarization
<Figure 7-3> Membrane separation; the basic concept.
<Figure 7-4> Concentration polarization.
7 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
Integrate Eq(7-3) with boundary conditions
BC 1 : x = 0 → c = cm
BC 2 : x = δ → c = cb
(7-4)
(7-5)
Mass transfer coefficient(k), (7-6)
Define intrinsic retention(Rint), (7-7)
Eq(7-5) → (7-8)
Concentration polarization modulus : cm/cb
J↑ ⇨ cm/cb ↑
Rint↑ ⇨ cm/cb ↓
k↓ ⇨ cm/cb ↑
8 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
When the solute is completely retained by the membrane (Rint = 1.0 and cp = 0) :
Eq(7-5) and Eq(7-8) ⇨ (7-9)
※ Basic equation for concentration polarization
• Membrane part ⇨ Flux (J)
• Hydrodynamics ⇨ Mass transfer coefficient (k)
Mass transfer coefficient(k) dependency on hydrodynamics of the system
Sherwood number (Sh)
(7-10)
Where Re = Reynolds number, (7-11)
Sc = Schmidt number, (7-12)
a, b, c and d = constants
ν = kinematic viscosity, η = dynamic viscosity, dh = hydraulic diameter
v = flow velocity, L = length of the tube or channel, D = diffusion coefficient
9 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
Hydraulic diameter(dh)
For a pipe (hollow fibers, capillary membranes or tubular membranes)
dh = 4 A/S = 4 (π/4)∙d2/π∙d = d
For a rectangular slit (plate-and-frame) of height(h) and width(w)
dh = 4 w∙h/2(w+h) = 2 w∙h /(w+h)
Eq(7-10) → k = f(v, D, η, ρ, module configuration(dh, L))
Important parameters : v, D
if module configuration = constant ⇨ k = f (v, D)
MF and UF when comparison with RO or gas separation and pervaporation
D of macromolecules(or SS) = low
fluxes = relatively high
Appearance Laminar Turbulent
Tube Sh = k∙dh/D = 1.62 (Re∙Sc∙dh/L)0.33 Sh = 0.04 Re0.75 Sc0.33
Channel Sh = 1.85 (Re∙Sc∙dh/L)0.33 Sh = 0.04 Re0.75 Sc0.33
[Table 7-1] Mass transfer coefficients in various flow regimes
Concentration Polarization of MF = severe
10 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
To minimize concentration polarization
Flux (J)↓
Mass transfer coefficient (k)↑
To enhance Mass transfer coefficient(k)
Diffusion coefficient(D)
※ increased only by increasing temperature
Flow(solvent) velocity(v)↑
※ Flux of solvent↑ ⇨ Polarization↑
Module configuration to increase turbulence
※ Reynolds number(Re) : Turbulent flow > Re = 2,000 > Laminar flow
Concentration Polarization↓
k↑
<Figure 7-5> Fully developed laminar and
turbulent velocity profiles in a pipe or slit.
11 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
To increase of turbulence
velocity↑
using turbulence promoters to break the boundary layer
• adapting corrugated membranes
• pulsating flow
feed temperature↑ ⇨ D of solutes↑, η of solvent↓ ⇨ k↑ ⇨ Polarization↓
12 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes
Concentration profile
Pressure driven process
• Convective process
• Solute retained
Concentration driven process
• Diffusive process
• Fast solute permeating
7.2.1 Concentration
Profile
Transport Mechanism Process Resistance Concentration Profile
Convective transport
(Solute retained)
MF
UF
NF
RO
rm > rbl <Figure 7-4> or
<Figure 7-6a>
Diffusive transport
Gas separation
Pervaporation
Dialysis
Carrier mediated transport
rm < rbl <Figure 7-6b>
rm > rbl ⇨ developing concentration profile
rm < rbl ⇨ developing concentration profile
13 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes 7.2.1 Concentration
Profile
<Figure 7-6> Concentration profiles
in membrane processes
a) convective transport
b) diffusive transport
Membrane operation Influence Origin
RO
UF
MF
gas separation
pervaporation
electrodialysis
dialysis
diffusion dialysis
carrier mediated transport
moderate
strong
strong
(very) low
low
strong
low
low
moderate
k large
k small / J large
k small / J large
k large / J small
k large / J small
-
J small
J small / k large
J large※ / k large
[Table 7-2] Consequences of concentration polarization
14 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.2 Concentration Polarization in Pressure Driven Processes 7.2.1 Concentration
Profile
Process Concentration
Polarization
Flux
(J)
Permeating
Species
Diffusivity
(m2/sec)
k
(= D/δ)
MF or UF Severe High Macro
solutes 10-10 ∼ 10-11 Low
RO Less severe Lower Micro
solutes 10-9 Higher
Gas separation
Pervaporation Low or negligible Low
Micro
solutes 10-4 ∼ 10-5 High
Dialysis
Diffusion dialysis Not generally severe Low
Micro
solutes 10-9 Higher
Concentration polarization of pervaporation compared with gas separation
J : Pervaporation < Gas separation
k : Pervaporation < Gas separation
※ VOC removal from water : c = very low & selectivity = very high ⇨ show more severe effect
Plate-and-frame or Spiral wound module
Spacer materials ⇨ turbulence↑ ⇨ k↑
Concentration polarization :
Pervaporation > Gas separation
※ Facilitated membrane and Membrane contactors : Moderate ※ Electrodialysis : very severe
15 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.3 Turbulence promoters
Hydrodynamic performance ⇨ characterize k
Flow conditions (v, η, ρ, D) and module geometry ⇨ determine k by correlations
Turbulence promoters
Mass transfer↑
Correlation through Sherwood Number(Sh) when k ≠ f(spacer)
Sh = k∙dh/D = 0.0096 Re0.5 Sc0.6 (7-14)
<Figure 7-7> Schematic drawing of a spacer (upper figure) and a spacer filled channel (lower figure).
k↑(ex, feed spacer in spiral wound module)
Δp & Energy↑ k↑
concentration polarization↓(wall concentration↓) J↑
16 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.3 Turbulence Promoters
Mass transfer coefficient(k) when spacer is adapted for laminar flow region(Re < 2000)
(7-15)
where Δl is the distance between successive corrugations
<Figure 7-7> Schematic drawing of a flow channel with turbulence promoters
17 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.4 Pressure Drop
Well developed flow (7-16)
Fanning Equation (relation between Δp ↔ v) for a channel and a straight pipe
Δp = f (S∙L / A) 0.5 ρv2 (7-17)
where L = length of the tube, ρ = density of the liquid (fluid), v = flow velocity
f = friction factor, S = circumference, A = cross-sectional area
Pressure drop by introducing an spacer or turbulence promoter
(7-18)
where Δl = distance between successive turbulence promoters
[Table 7-3] Friction factors in various systems
Shape
Flow Region Channel Tube
Laminar f = 24 Re-1 f = 16 Re-1
Turbulent f = 0.133 Re-0.25 f = 0.079 Re-0.25
Fiction factor = f(Re) weakly
in turbulent region
⇨ Δp = f(v) strongly in turbulent region
18 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.5 Flux Characteristics in Pressure Driven Membrane Operation
Water flux for pure water through a porous membrane in pressure driven processes
(7-19)
where Rm = hydrodynamic resistance of the membrane
Hydrodynamic permeability, Lp = 1 / η∙Rm ⇨ J = LpΔp
Hydrodynamic resistance Rm = membrane constant ≠ f(feed composition or pressure)
Water flux for solution through a porous membrane in pressure driven processes
J ∝ Δp before finite Δp
J = constant after finite Δp
J∞ = Limiting flux = f(cb, k)
where cb = concentration in the bulk of the feed
k = mass transfer coefficient
(7-20)
from (7-9)
J ∝ Δp for pure water
<Figure 7-9> Flux as a function of Δp both for
pure water and for a solution.
19 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.5 Flux Characteristics in Pressure Driven Membrane Operation
(7-20)
Slope = - k
<Figure 7-11> Limiting flux (J∞) plotted as a function of the logarithm of the bulk concentration.
<Figure 7-10> The flux as a function of the applied
pressure for different cb and different k.
Feed concentration(cf)↑ at constant k ⇨ J∞↓
Mass transfer(k)↑ at constant cf ⇨ J∞↑
Typical for UF
Lesser extent for MF
Not for RO
Description of concentration polarization
Same for both UF and RO formally
Difficulty : UF > RO
(∵ properties of concentrated
macromolecular solutions)
20 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.6 Gel Layer Model
Concentration polarization in UF : very severe
flux through the membrane = high
diffusivity of the macromolecules = rather low
retention is normally very high
Gel concentration
depends on
independent of the bulk concentration
Gel formation
reversible or irreversible
very important factor in membrane cleaning
solute concentration at surface
= very high
<Figure 7-12> Concentration polarization and gel layer formation.
• Size
• Shape
• Chemical structure
• Degree of solvation
21 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.6 Gel Layer Model
Gel layer model
Good model for theory of concentration polarization and limiting flux behavior in UF
Describing the occurrence of limiting flux
<Assume> Solute = completely retained by the membrane
Δp↑ ⇨ Solvent flux(Jw↑) until a critical concentration ⇨ reach at gel concentration(cg)
Δp↑ further ⇨ gel layer = become thicker and/or compacter
• Resistance of the gel layer (Rg)↑ to solvent transport ⇨ constant flux
• Gel layer becomes the limiting factor in determining flow
Total resistance (see <Figure 7-12>)
Gel layer resistance(Rg) + Membrane resistance(Rm)
(7-21)
<Assume> Gel concentration = constant across gel layer
Slope = - k
Intercept on the abscissa (J∞ = 0) = ln(cg) <Figure 7-13> J∞ verse ln(cb)
22 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.6 Gel Layer Model
Drawbacks of gel layer model
cg = not constant
= f(cb, cross flow velocity)
cg for a given solute = varying widely
k = assumed to be constant
D of the macromolecular solute = f(concentration)
Gel formation phenomena = Different from characteristics of macromolecule
proteins = form a gel easily
dextranes = do not gel so easily even at very high concentrations
23 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.7 Osmotic Pressure Model
J = high
Rejection = high
k =low
the flux equation
(7-22)
Here, ΔP = hydraulic pressure difference
Δπ = osmotic pressure difference
cm (not by cb) ⇨ determine Δπ
Relationship between concentration ↔ π
For dilute low MW solutions ⇨ linear relationship(van't Hoff relationship)
In general, exponential rather than linear
π = a∙cn (7-23)
where a = constant
n = exponential factor > 1
concentration of macromolecule
at surface = very high
osmotic pressure cannot
be neglected anymore
24 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.7 Osmotic Pressure Model
For semi-dilute or concentrated polymer solutions : n > 2
a and n = f(MW, type of polymer)
Another expression for non-ideality : virial expansion
(7-24)
Non- linear relationship between flux ↔ ΔP
By combining Eq(7-23), Eq(7-22) and Eq(7-9)
(7-25)
(7-26)
<Figure 7-14> Schematic drawing of π as a function
of the concentration for various values of n.
25 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.7 Osmotic Pressure Model
Combining Eq(7-23) and (7-25), and substituting the result into Eq(7-26) leads to
(7-27)
or (7-28)
Two extreme cases
• Δπ = very high ⇨ ∂J/∂ΔP → 0
ΔP ↑ ⇨ J = not increase : J∞ region
• Δπ → 0 ⇨ ∂J/∂ΔP = 1/ (η Rm)
Multiplying with η Rm to Eq(7-28) ⇨ two dimensionless numbers :
(7-29)
and (7-30)
where superscript o : pure solvent
26 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.7 Osmotic Pressure Model
ηRm(∂J/∂ΔP)
Ratio between slope of the plot of J versus ΔP and that of pure solvent flux(Jo) versus ΔP
Measurement of effectiveness of ΔP
Maximum slope = (∂J/∂ΔP)o
At high ΔP
• ∂J/∂ΔP ↓ ⇨ Rm (∂J/∂ΔP) ↓ : effectiveness of an increase in ΔP↓ (Rm ↑ or η Rm ↑ in fact)
• Δπ↑
(Δπ n)/( η Rm k)
Ratio between osmotic pressure resistance
and membrane resistance
<Figure 7-15> Effectiveness of pressure increase as a function of the
ratio between the osmotic resistance and the membrane resistance.
Rm↑
Rm (∂J/∂ΔP) ↓
27 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.7 Osmotic Pressure Model
Influence of Δπ as a function of ΔP
Eq(7-25) ⇨ J as a function of ΔP(<Figure 7-16>)
J∞ can be attained at even lower pressures at low Rm than that in <Figure 7-16>
<Figure 7-16> Calculated values of J plotted as a function of the applied ΔP
at varying cb and the following parameters:
a=100; n=2; Rm=5×105 bar∙sec/m; k=2×10-6
cb
28 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.7 Osmotic Pressure Model
Relationship between Gel layer model ↔ Osmotic pressure model
Gel layer model
• Plot of J versus In(cb) ⇨ straight line (slope = -k)
Osmotic pressure mode
• Eq(7-25) ⇨ similar J versus In(cb) relationship, (7-31)
• Rm↓ ⇨ (Δπ n)/(η Rm k) ≫ 1 ⇨ the right-hand side of Eq(7-31), ∂J/∂ln(cb) = slope = -k
J∞ = 0 ⇨ ΔP = Δπ, High values of (Δπ n) / (η Rm k) ⇨ J↓ (∵ osmotic pressure effects)
Factors leading to high (Δπ n) / (η Rm k)
• High ΔP or Low Rm ⇨ High J
• High bulk concentration(cb)
• Low mass transfer coefficient(k)
• High value of n(macromolecular solute)
<Figure 7-17> Flux J∞ as a function of the
concentration in the bulk, cb.
29 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.8 Boundary Layer Resistance Model
<Assume> 100 % rejection of solutes and steady-state
Convective flow of solute towards membrane surface = Diffusive flow back to bulk of feed
∴ 100% rejection ⇨ average velocity of the solute molecules in the boundary layer = zero
Boundary layer resistance model(<Figure 7-18>)
Concentration↑ ⇨ hydrodynamic resistance in boundary layer (Rbl)↑
Rbl & Rm ⇨ solute flux(J) with assuming no gelation
(7-32)
Boundary layer = considered concentrated solution
Permeability(P) of stagnant layer = f(c, MW of solute)
• Rbl for macromolecular (UF) : much greater
• Rbl for low MW (RO) : lower relatively
P of the solvent = f[distance(x)] where 0<x<δ
(∵ concentration profile in boundary layer)
<Figure 7-18> Schematics of boundary layer resistance model.
30 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.8 Boundary Layer Resistance Model
phenomenological Darcy equation
osmotic gradient
(driving force for solvent flow in boundary layer)
Integration over the boundary layer leads to
(7-34) where (7-35)
Simplifying Eq(7-34) ⇨ (7-36)
Sedimentation measurement ⇨ Permeability (P) ⇨ Rbl
permeability ↔ sedimentation coefficient
(7-37)
Where v1 = partial molar volume of the solvent
v2 = partial molar volume of the solute
c = solute concentration.
volume flux, (7-33)
<Figure 7-19> Correlation between the sedimentation of
a solute and the permeation of a solvent.
31 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.8 Boundary Layer Resistance Model
Ultracentrifugation ⇨ Sedimentation coefficient(s)
(7-38)
where dr/dt = sedimentation velocity of that particle
ω2r = acceleration in centrifugal field
Concentration dependence of sedimentation coefficient
(7-39)
Substitution of Eq(7-37) → Eq(7-35)
(7-40)
(7-41)
<Assume> 100 % rejection ⇨ c(x) = cb exp (J∙x / D) (7-9)
32 Chapter 7. Polarization Phenomena & Membrane Fouling Chungbuk University
7.8 Boundary Layer Resistance Model
Since integration of P(x)-1 over the boundary layer gives
<Assume> diffusion coefficient D = constant ≠ f(c)
(7-42)
Substitution of Eq(7-9) → Eq(7-41) and integration over the boundary layer gives:
(7-43)
⇨ ΔP, J, Rm, cb, k, s and D ⇨ calculate Rbl
Error in k ⇨ large effect on the calculated Rbl ⇨ need exact k ⇨ difficult for application
(∵ since cm is related to k via an exponential function)
※ Boundary layer resistance model = osmotic pressure model on the point of concept
(7-44)
※ Difficulties in practical use : boundary model > osmotic model
(Independent measurements are essential for both models.)