Non-isothermal Reactors10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 11: Non-isothermal Reactors, equilibrium limitations, and stability This lecture covers: Derivation of energy balances for ideal reactors; equilibrium conversion, adiabatic and non-adiabatic reactor operation. Non-isothermal Reactors dNN streams N rxnsi=+∑∑FVim,,cvυilr dtlml==11stoichiometstoichiometric ric coefficient coefficient r - depends on concentration l- T - catalyst dUtotaldVNs∑treamscv+=PHcvconc()TFtotal+Q+W+(other energy termsdx dtmmm s) m=1flow work extensive intensive heat do work Æ Wshaft work s negative work expansion work If small control volume, pressure constant. In 1cvV has a fixed P other control volumes P2 P1 P1≠ P2 Figure 1. Schematic of a PFR with small control volumes, each with a fixed P. PFR has many small control volumes, each with its own constant P. For isothermal – Q adjusted to keep T constant – Practical – have big cooling bath – or just operate at a particular temperature found after reactor built ⇒ not a good strategy, for design we want to know ahead of time – before assumed uniform T, actually have hot spots Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Where is T? In Utotal and . cvrTl() dUtotal totalN streamstotalcvdU=+cvdT∑⎛⎞dU⎜⎟cvdNi dt dT dti=1⎝⎠dNidtheat capacity intensive substitute for of system contribution of each species dNi dt Want dY= FY() dtAssume ideal mixtures UNtotalcv≈∑iU i()Tcvextensive intensive dUtotalcv=UTic() dNviIf P=Constant (Isobaric) NdHtotald()U+PV dU dP dV==+VP+ dt dt dt dt dt0dUtotalcvdV+ Pcvdt dt↓ dHtotaldtAssume isobaric, all ideal mixtures, neglecting K.E., P.E., other energies ⎛⎞N speciesdTN streams N⎜⎟∑∑NCcvip,,i=−∑speciesFim()Hi()TmHi(Tcv)⎝⎠imdti N∑∑streams N rxns−+HTic()vVcvυi,lrl()TcvQ+Wsil ∑υ,() i lHTi cv≡ΔH stoichiometric coefficient rxn()Tcvil10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 11 Prof. William H. Green Page 2 of 4 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].N streams N rxns−=∑∑HTi()cvVcvυi,lrl()Tcv−∑Vr()T ΔH cv l cv rxn()Tcvil ll Assume QU≅−A()T T (conduction) acvarea of contact 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 11 Prof. William H. Green Page 3 of 4 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. coolant heat reactor transfer coefficient Ws≈ 0 (As a stirrer, heat negligible) If designing engines W. s≠ 0 Now just put into MATLAB and solve Chapter 8 in Fogler – lots of special case equations – be careful of assumptions Special case: Start up CSTR to a steady state want to know ultimate T dTN streams N speciescv=≅0(∑∑FH()T)−H(T)−∑Vr dtim,i m i cv cv lΔHrxn+UA(Ta−Tcv)milAll depend on TCV When we reach steady state, no more accumulation FF−+rV=0 at steady-state Ai,,n Aout A See Fogler: 8.2.3 If just one reaction, one input stream, one output stream, and the system is at steady-state: UA()TT−+=ai∑FX,,inputCpi(TT−in) AFHAo()−ΔrxnIn this special case, conversion and T linear 1 reaction making heat as product is made. When ΔH =(-) Exothermic, reactor is hotter than cooling reactor (heat transfer rxnimportant) (+) Endothermic, reactor must be heated so that reaction will run GT()≡−(ΔHrxn)(−rAV FAo) Generation ⎛⎞⎛⎞F⎜⎟R()TC=+∑ii, nUA⎜⎟pi,⎜⎟1()T−T c⎝⎠FFAo⎜⎟∑i,,inC⎜⎟ p i⎝⎠K Heat removal K = 0 Adiabatic K = Big Cooling KTai+TTnc= 1+K R()T linear with T GT()→ constant at high T - not linear with T •• • ()GT T ()R T rxnH−Δ Three steady-state solutions cool a lot Figure 2. Graph of G(T) versus T. Three steady-state points are shown where R(T) intersects with the heat of reaction. With multiple steady states must consider stability. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 11 Prof. William H. Green Page 4 of 4 Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month