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We assume that the concentration of CO2 does not measurably change after leaving the bed and therefore a Danckwert’s3 boundary condition given by ∂ci =0 at z=L (2.7) ∂z is applied to the bed outlet. Depending on whether an adsorption or desorption half cycle is being modeled, either a constant feed concentration or a no-flow boundary condition is used at the bed inlet, respectively. The energy balance for this system is written ρ ∂us +ε′∂cfuf +ε∇(⃗vc u )+ε∇q +εP·∇⃗v=0 (2.8) b∂t ∂t ff f where the energy flux, internal energies of both the fluid and solid-phase, and the enthalpy of the fluid-phase are represented by qf = −k∇T (2.9) (2.10) (2.11) (2.12) (2.13) (2.14) where and uf ≡hf −PVf us = (Cps + Cpxn) (T − Tref ) − λ n hf =Cpy(T−Tref) Cpx =xiCpfi i Cpy =yiCpfi i The walls of the adsorbent bed are assumed to be insulated, and the bed inlet is modeled as either insulated or having a constant feed temperature depending on the half-cycle being simulated. At the bed outlet the boundary condition for the energy balance is ∇T=0 at z=L (2.15) 11PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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