Engenharia Química - Graus de Liberdade em Operações Unitárias

Unit FjT P Aij ai Fj FjT1 P1 FjT2 P2 A1j T1 P1 F1 T1 P1 x11 xc1 F2 T2 P2 x12 xc2 F3 T3 P4 x13 xc3 A2j T2 P2 Asj Ts Ps Block Degrees of Freedom Typical Valid Assignment Unit Relationships Splitter Mixer s split fractions Heatercooler Adiabatic heat exchanger c1 c1 c1 c2 3 c1 c2 c2 c2 sc 1 1 Q 1 Q 1 UA 1 1 1 1 1 1 Q s s sc 2s 1 c 2 c 2 sc 2s 1 c 2 sc 2s 1 s c 1 2c 4 c 4 c 2 s 1 s 3c 2 c 2 2c 2 1 2c1 2 2c2 2 2 c1 c2 c3 c1 c2 7 c 2 c 2 c 2 c 2 c1 2 c1 2 c2 2 c2 2 c 2 c 1 c 2 c1 c2 3 c 2 c 2 c 1 å ai 1 i Ti T Total Mass balance Mass balance Mass balance hot fluid Mass balance cold fluid Energy balance Energy balance Energy balance hot fluid Energy balance cold fluid Pressure relations Total Feed s 1 Split fractions Total Total Design Q UATLM Pi P c c M M Feeds Feed P Q or Tout c 1 Feeds P1 P2 Q or UA 1 Q 1 2 3 1 2 Flash Valve Q 1 1 1 1 c 4 3c 2 1 2c 2 c 1 c 3 c 1 2c 3 Mass balance Mass balance Isoenthalpic H1 H2 Energy balance Equilibrium P2 P3 T2 T3 Total c 1 c 2 2c 3 c 2 c 2 c 2 c 2 Total c c c Feed P Q or Vapor fraction Feed P or P2 2c 3 Degrees of freedom of some common unit operations MARTÍN M M Introduction to Software for Chemical Engineers 2 ed CRC Press 2019 786 p ISBN 9781138324213 1 η 1 W 1 1 2 2 Pump Compressor turbine 2c 2 c 1 c 3 2c 2 2 c 2 c 4 c 1 c 2 Mass balance Mass balance Mechanic energy balance c 2 c 2 c 2 c 2 c 1 c 2 Total Total 1 1 1 c c Feed P or P2 Feed P or P2 Efficiency Energy balance Isoentropic S1 S2 1 Q 1 Q Stoichiometric reactor Q Ni Ni0 å nij ξji Ni N0 å nij ξj 2c 2 1 r c 1 c r 4 c 1 Mass balance c 2 c 2 rξj c 1 Total 1 c Feed reactions extent Pout Reactor duty Energy balance j 1 j 1 r r i 1 c Equilibrium reactor 2c 2 c c 4 c c 2 c 2 c Total c Feed P T in the reactor Equilibrium chemical potential å nij mi0 RT 1n fi T P xi 0 j 1 r i 1 c 1 VR Kinetic reactor Q 2c 2 r 2 c 1 c r 5 c 1 Mass balance c 2 c 2 rri c 1 Total 1 c Feed P heat volume r reaction rates Energy balance fi fi0 riVR fi fi0 riVR Degrees of freedom of some common unit operations Actual compressors turbines are not really isentropic Efficiency η ΔHsΔHactual is usually assumed Feed refers to the complete feed specification component molar flows plus P and T c 2 specifications If a kinetic reactor is possible specify the P in the reactor ie CSTR or a relation for pressure drop along the reactor typical in PFR