Tham khảo tài liệu 'robotics process control book part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Examples of Dynamic Mathematical Models 35 Figure Scheme of a distillation column Co - condenser Bo - reboiler 1 . i . k . j . h - tray number. R F i 1 cxi 1 R F i c xi ẠG . cyi yi G i c V Si Hxr c xi Ạ G c yi-1 Figure Model representation of i-th tray. 36 Mathematical Modelling of Processes c. . cx I - liquid molar fraction of a more volatile component Hyi Hxi - vapour and liquid molar hold-ups on i-th tray. Mass balance of a more volatile component in the liquid phase on the i-th tray stripping section is given as Hxi X R F cxi 1 Cxi G cyi-1 cvyi at where t is time. Under the assumption of equilibrium on the tray follows cVyi cyi f Cxi Mass balance of a more volatile component in the vapour phase is dCyi v Hyi dt G cyi cyi We assume that vapour molar hold-up is small and the following simplification holds cyi cvyi and the i-th tray is described by Hxi x R F cxi 1 _ cxi G f cxi-1 f cxi at Mass balance for fc-th tray feed tray can be written as Hxk Rcxk 1 FcxF - R F cxk G f cxk-1 - f cxk at where cxF is a molar fraction of a more volatile component in the feed stream. Mass balances for other sections of the column are analogous j-th tray enriching section Hxj R cxj 1 - cxj G f cxj-1 - f cxj h-th tray top tray Hxh R cxD - cxh G f cxh-1 - f cxh at Condenser HxC dt R D cxD G f cxh where D - distillate molar flow cxD - molar fraction of a more volatile component in condenser HxC - liquid molar hold-up in condenser. first tray Hxi R F cx2 - cxi G f cxw - f cxi at where cxw is molar fraction of a more volatile component in the bottom product. Examples of Dynamic Mathematical Models 37 Figure A nonisothermal CSTR. Reboiler HxW dW R F cx1 - WcxW - G f cXW where w is a molar flow of the bottom product and HxW is the reboiler molar hold-up. The process state variables correspond to a liquid molar fraction of a more volatile component on trays in the reboiler and the .
