Page 491 - Water and wastewater engineering

12-8 WATER AND WASTEWATER ENGINEERING

TABLE 12-1
General forms of time-dependent membrane flux equations
Flux equation Linearized form Comments
kt
(a) J t J 0 e ⎛ J ⎞ Flux declines exponentially as
t
ln ⎜ ⎝ J ⎠ ⎟ kt foulants accumulate. Flux
assumed to drop to zero at
0
infinite time, which may not
occur in practice.
(b) J t J ss (J 0 J ss )e kt ⎛ J J ⎞ Similar to Eq. (a), except flux
t
ss
ln ⎜ ⎝ J J ⎠ ⎟ kt drops to a steady-state flux J ss
at t infinite time.
ss
0
n
(c) J t J 0 (kt) ⎛ J ⎞ Cannot be used for initial stages
t
()
ln ⎜ ⎝ J ⎠ ⎟ n ln kt of filtration because infinite
flux is predicted at time t 0.
0
Sometimes expressed as a
function of the volume of
permeate (kt V) instead of as a
function of time.
(d) J t J 0 ln ⎛ J ⎞ n ln 1 kt) The series resistance model can be
t
(
1 ( kt) n ⎜ ⎝ J ⎠ ⎟ written in this form with n 1.
0
Source: Adapted from MWH, 2005.
TABLE 12-2
Blocking filtration laws
Flux equation Major features and assumptions
Pore sealing (complete blocking filtration law) • Models blockage of the entrance to pores by particles
retained at the membrane surface.
J J e (1.5CJ t/ d ) • Each retained particle blocks an area of the membrane
P
P
0
0
t
surface equal to the particles cross-sectional area.
c concentration of particles • Flux declines in proportion to the membrane area that
has been covered.
• No superposition of particles occurs. Each particle lands
on the membrane surface and not on other particles, so
flux reaches zero when a monolayer of particles has been
retained.
Internal pore constriction (standard blocking • Models the reduction of the void volume within the
filtration law) membrane.
J 0 • Assumes the membrane is composed of
J t
(1 CJ t/L ) 2 cylindrical pores of constant and uniform
0
P
diameter.
L membrane thickness, m • Particles deposit uniformly on the pore walls; pore
volume decreases proportionally to the volume of
particles deposited.
(continued)