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A. Derivation of The Energy Balance Equation ( Ncomp ) ∂∑ ∂T εt ∂t T CiCvi + (1 − εb)ρsCps ∂t i=1 ( Ncomp ) ∂∑ ∂T +ρs(1 − εb)∂t T QiCpi i=1 + DR2 ρwCpw ∂t (A.11) ( Ncomp ) ∂∑ ∑∂Qi ] +∂z UT =λ∂2T i=1 [Ncomp CiCpi − (1 − εb)ρs (−∆Hi) ∂t ∂z2 Here, εt and DR2 are defined as εt = εb + (1 − εb)εp ( ∆d)2 DR2=1+ w −1 D (A.12) (A.13) Next, we perform differentiation by parts on the first five terms of Eq. A.11 to separate the T differential terms from the rest to get the following equation, [ Ncomp (Ncomp ) Ncomp ∂∑∂∑∂∑ ] εt [ i=1 ∂t CiCpi + ∂z ∑ ∂T +(1−εb)ρs∂t QiCpi εt∂t [ Ncomp U CiCpi i=1 T i=1 CiCvi +(1−εb)ρsCps Ncomp ∑ ] i=1 i=1 ρs(1 − εb) QiCpi + DR2 ρwCpw i=1 ∂T ∂t (A.14) + − U CiCpi i=1 =λ∂2T ∂z2 [ Ncomp ] ∑ ∂T ∂C Ncomp ∂z +εtRT ∂t −(1−εb)ρs ∑ ∂Qi ] 202 i=1 (−∆Hi) ∂tPDF Image | Operation and Control of Pressure Swing Adsorption Systems
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