Pulse analysis - Principles of Chemical Separations with Environmental Applications - page 295

We can show that:

z
V (1

µ 1 ( z ) = µ 1 (0)

+ + δ 0 )

1

1 − α

α

+ ρ p K a
β

δ 0 = β

;

+ δ 0 ) 2
V 2

2 z
V

D 0
α

(1 V 0

α

µ 2 ( z ) = µ 2 (0) + δ 1 + V =

1 1 2 1

D i +

ρ p
β

K a
k a +

R 2

+ ρ p
β

− α
α

β
15

5
k p R

δ 1 = β K a

i

a e

δ a = contribution to concentration profile spreading due to adsorption

δ i = spreading due to pore diffusion

δ e = spreading due to mass transfer between particle and interstitial fluid.

Application of the method
1 Perform several pulse injections with variation in V .
2 Plot µ 1 vs z/V . The slope (Figure C.4) is (1

+ δ 0 ). Use the result to obtain a value for

K a .
3 The analysis will depend on the operating range of flowrates. D 0 can depend on V in
certain regimes (Figure C.5).
The pulse injection results can be plotted in the form shown in Figure C.6 or, if D 0 = γ V ,

as shown in Figure C.7 to determine the operating range.
The result of the above plots is a value for δ 1 which can be obtained from the intercept.

We need to perform additional experiments to isolate the contributions of

δ a , δ i , and δ e .

SLOPE=1+d 0

∆µ′

V

Figure C.4