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Adsorptive separation by thermal parametric pumping part I: Modeling and simulation

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Abstract

A detailed model for the recuperative parametric pumping is presented. The model includes intraparticle mass transfer resistance, axial diffusion and non-linear equilibrium represented by Langmuir equation. The sensitivity studies shows that process performance strongly increases when cycle time increases and φ B /φ T ratio and particle size decreases. It also shows that bottom and top dead volumes do not influence much the process performance. Evolution of the histories of concentrations and temperatures, the bed performance from cycle to cycle and the bed dynamics at the cyclic steady state have been discussed.

The model revealed itself as useful to simulate the behavior of the recuperative parametric pumping process and was applied to predict optimal experimental results for the system phenol-water/Duolite ES-861 (Part II).

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Abbreviations

a i (z*, ϑ):

coefficients of the trial solution

a w :

specific area of wall, m−1

b :

separation parameter

C :

solute concentration in the fluid phase, kg/m3

C E :

initial (feed) solute concentration, kg/m3

c pf :

heat capacity of the fluid, kJ/(kg.K)

C p :

solute concentration in the pores, kg/m3

c s :

heat capacity of the adsorbent, kJ/(kg.K)

d :

column diameter, m

D ax :

axial dispersion coefficient, m2/s

D m :

molecular diffusion coefficient, m2/s

D P :

pore diffusivity, m2/s

d p :

particle diameter, m

f H :

humidity factor for the adsorbent (kg dry resin/kg wet resin)

G f :

fluid mass flowrate, kg/(m2.s)

h k :

length of subintervalk

h we :

wall heat transfer coefficient, kJ/(m2.s.K)

(−ΔH):

heat of adsorption, kJ/kgmol

H i (g k ):

Hermite polynomials over the subintervalk

j D :

Chilton Colburn factor

K(T):

slope of linear isotherm

K ae :

axial thermal conductivity, kJ/(m.s.K)

K f :

film mass transfer coefficient, m/s

K L :

parameter of the Langmuir isotherm, m3 solution /kg solute

k 0 :

parameter of the modified Langmuir isotherm, m3 solution /kg solute

L :

bed height, m

m(T):

mass capacity parameter

n :

number of cycles

N D :

number of mass transfer units for pore diffusion

N f :

number of film mass transfer units

N hw :

number of wall heat transfer units

Pe:

mass Peclet number

Pe h :

thermal Peclet number

q :

adsorbed solute concentration, kg solute /kg dry resin

Q :

flowrate in the column, m3/s

Q hc :

flowrate in the hot half cycle, m3/s

Q cc :

flowrate in the cold half cycle, m3/s

Q ∞ :

maximum adsorbent capacity, kg solute /kg dry resin

(Qπ/w):

reservoir displacement volume, m3

r :

radial coordinate, m

R :

ideal gas constant, kJ/(kgmol.K)

R 0 :

particle radius, m

Re:

particle Reynolds number

Sc:

Schmidt number

Sh:

Sherwood number

t :

time, s

t c :

cycle time, s

t cc :

cold half cycle time, s

t hc :

hot half cycle time, s

T :

temperature, K

T a :

ambient temperature, K

T cc :

cold temperature, K

T hc :

hot temperature, K

u :

superficial velocity, m/s

u cn :

concentration wave velocity, m/s

u i :

interstitial velocity, m/s

u th :

thermal wave velocity, m/s

u*:

normalized radial coordinate

u * k :

inferior limit of subintervalk

u +1/* k :

upper limit of subintervalk

V U :

volume percolated in upward flow, m3

X :

normalized fluid phase concentration

X p :

normalized fluid concentration in the pores

z :

spatial coordinate, m

z*:

normalized axial coordinate

〈〉:

average value

ξ h :

thermal capacity parameter

ε :

bed porosity

ε p :

intraparticle porosity

φ B ,φ T :

fractions of theQπ/ω that are withdrawn as bottom and top products, respectively

v :

kinematics viscosity, m2/s

ρ ap :

apparent density of the adsorbent, kg/m3

ρ f :

density of the fluid, kg/m3

ρ s :

density of the adsorbent, kg/m3

ρ h :

wet density of the adsorbent, kg/m3

ϑ :

normalized time

ω :

frequency of temperature change

τ :

space time, s

τ p :

tortuosity factor

π/ω :

duration of half cycle

E :

entrance

BP:

bottom product

cc:

cold half cycle

hc:

hot half cycle

0:

initial

TP:

top product

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Author notes

  1. Licínio M. Ferreira

    Present address: Chemical Engineering Department, University of Coimbra, 3000, Coimbra, Portugal

Authors and Affiliations

  1. Lab. of Separation and Reaction Engineering, School of Engineering, University of Porto, 4099, Porto Codex, Portugal

    Licínio M. Ferreira & Alírio E. Rodrigues

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  1. Licínio M. Ferreira
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  2. Alírio E. Rodrigues
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Ferreira, L.M., Rodrigues, A.E. Adsorptive separation by thermal parametric pumping part I: Modeling and simulation. Adsorption 1, 213–231 (1995). https://doi.org/10.1007/BF00704225

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