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4 Introduction where z is the distance coordinate, t is the time, v is the interstitial velocity of the gas, c the concentration of the adsorbate in the fluid phase, and q ̄ is the adsorbate concentration in the adsorbent particle. Under the assumption that the flow is represented by an axially dispersed plug flow, the differential mass balance of the fluid phase is described by: D δ2c+ δ(vc)+δc+1−ε·δq=0 (1.1) Lδz2 δz δt ε δt where DL is the axial dispersion coefficient, and ε is the void volume in the column. The first term in equation 1.1 describes variation in concentration of the adsorbate in fluid phase if axial dispersion is occurring in the column [3]. The second term describes variation of concentration along the column due to convective flow. The third term represents variation of concentration in time, and the last one the adsorption (or uptake) rate in the adsorbent. The adsorption rate is a function of concentration in both the adsorbent and in the gas: δq=f(q, c) (1.2) δt The adsorption rate equation used to describe the adsorption systems studied in this work is the one described by the linear driving force approximation [4]: δq=k(q∗ - q) (1.3) δt where q is the adsorbate loading, q∗ the adsorbate loading in equilibrium with the fluid phase, and k is the mass transfer coefficient, which measures how fast the molecules diffuse and adsorb into an adsorbent. For a column loaded with spherical adsorbent particles having radius R, and subjected to a step-change in adsorbate concentration, the initial and boundary conditions for the column are: t < 0, q(R, 0, z) = c(0, z) = 0 (1.4) t ≥ 0, c(t, 0)= c0 (1.5) To obtain the solution for the breakthrough curve is necessary to solve equations 1.1 and 1.3, together with the boundary conditions described by equations 1.4 and 1.5. Under the assumptions of isothermal plug flow systems in which a single trace com- ponent with linear adsorption isotherm is adsorbed, the analytic solution for the break- through profile is given by the Klinkenberg equation [5]: c1 √√ξ√τ c=2·erfc( ξ- τ- 8 - 8) (1.6) (1.7) 0 ξ = kKzmax · 1−ε vεPDF Image | Structured Zeolite Adsorbents for PSA Applications
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