International Journal of Chemical Engineering

Research Article

Feasibility of Batch Reactive Distillation with Equilibrium-Limited Consecutive Reactions in Rectifier, Stripper, or Middle-Vessel Column

Table 2

Model equations of vessel path for single-reaction systems.
Nonreactive 𝑑 𝑥 𝑖 𝑑 𝑡 = 𝐷 ( 𝑥 𝑖 − 𝑥 𝐷 , 𝑖 ) + 𝑊 ( 𝑥 𝑖 − 𝑥 𝑊 , 𝑖 ) − 𝐹 𝑑 ( 𝑥 𝑓 𝑑 , 𝑖 − 𝑥 𝑖 ) − 𝐹 𝑤 ( 𝑥 𝑓 𝑤 , 𝑖 − 𝑥 𝑖 )
Reactive, 𝜈 𝑇 = 0 𝑑 𝑋 𝑖 𝑑 𝑡 = 𝐷 ( 𝑋 𝑖 − 𝑋 𝐷 , 𝑖 ) + 𝑊 ( 𝑋 𝑖 − 𝑋 𝑊 , 𝑖 ) − 𝐹 𝑑 ( 𝑋 𝑓 𝑑 , 𝑖 − 𝑋 𝑖 ) − 𝐹 𝑤 ( 𝑋 𝑓 𝑤 , 𝑖 − 𝑋 𝑖 )
Reactive, 𝜈 𝑇 ≠ 0 𝜈 𝑈 = 𝑈 1 − 𝑇 𝜈 r e f 𝑥 r e f and
𝑈 𝑑 𝑋 𝑖 = 𝑋 𝑑 𝑡 𝐷 ⋅ 𝑖 ⋅ ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 r e f ) ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 𝐷 , r e f ) − 𝑋 𝐷 , 𝑖 + 𝑋 𝑊 ⋅ 𝑖 ⋅ ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 r e f ) ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 𝑊 , r e f ) − 𝑋 𝑊 , 𝑖 − 𝐹 𝑑 ⋅ 𝑋 𝑖 ⋅ ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 r e f ) ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 𝑓 𝑑 , r e f ) − 𝑋 𝑓 𝑑 , 𝑖 − 𝐹 𝑤 ⋅ 𝑋 𝑖 ⋅ ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 r e f ) ( 1 − ( 𝜈 𝑇 / 𝜈 r e f ) ⋅ 𝑥 𝑓 𝑤 , r e f ) − 𝑋 𝑓 𝑤 , 𝑖 − 𝑋 𝑖 ⋅ 𝜈 1 − 𝑇 𝜈 r e f ⋅ 𝑥 r e f ⋅ 𝜈 𝑇 ⋅ ∫ c o l u m n 𝑑 𝜉 𝑑 𝑡 𝑑 ℎ + 𝑈 ⋅ 𝑋 𝑖 ⋅ 𝜈 𝑇 𝜈 r e f ⋅ 𝑑 𝑥 r e f 𝑑 𝑡