Improved Analysis and Understanding of the Petlyuk Distillation - PDF document

1 Improved Analysis and Understanding of the Petlyuk Distillation Column by Ivar J. Halvorsen and Sigurd Skogestad Norwegian University of Science and Technology (NTNU) Department of Chemical Engineering Paper 5a, presented at The 4th Topical conference on Separations Science and Technology Session T1005 - Distillation and Modelling and Process II Friday, November 5, 1999, at 2:00 PM in Monte Carlo Theatre - Wyndham Anatole AIChE Annual Meeting, Dallas TX 31. Oct - 5. Nov 1999 Email: Sigurd.Skogestad@chembio.ntnu.no, Ivar.J.Halvorsen@ecy.sintef.no Web: http://www.chembio.ntnu.no/users/skoge http://www.chembio.ntnu.no/users/ivarh NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 2 Motivation and Objectives • The Petlyuk Arrangement can save large amounts of energy- and also capital costs (A typical number of 30% is reported, but up to 50% is possible) • It is 50 years since Wright’s patent (1949) • It is 25 years since Petlyuk presented the energy savings results (1965) • Usage of Petlyuk arrangement is still limited. Why? • Usual reasons given: “Difficulties in design and difficulties in control?” Objective: • Understand how the energy usage is affected by disturbances, manipulative variables and product purity specifications. • Focus on operation. NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November

3 Introduction: 3-component separation: Conventional configurations: INDIRECT SPLIT (ISV) DIRECT SPLIT (DSL) A A AB ABC B ABC B BC C C NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 4 Prefractionator Arrangements: The Petlyuk The prefractionator does the easy arrangement split (A/C) A A Pre- AB AB fractionator Main column ABC B ABC B B BC BC C C “Fully Thermally Coupled Columns” Saves 20-50% NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November

5 “Petlyuk” in a single shell: The Dividing Wall Column: Condenser Extra DOF: L Liquid split (R l ) A (B) 3 Top product L 1 =L*R l 1 4 Feed B (AC) A,B,C Side product 2 5 Extra DOF: “The Dividing Wall” Vapour split (R V ) V 6 V 2 =V*R v Reboiler C (B) Bottom product NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 6 Minimum Energy for the Petlyuk Column Very simple minimum boilup expression (Fidkowski 1986, Westerberg 1989): α A z A α C z C   petlyuk ( ) , (1)   = max - - - - - - - - - - - - - - - - - - - – 1 – q - - - - - - - - - - - - - - - - - - - α A ϕ 1 ϕ 2 α C min – –   Underwood roots ( ϕ ) from: α A z A α B z B α C z C ( ) - - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - - - - - = 1 – q α A ϕ α B ϕ α C ϕ – – – (2) α A > ϕ 1 > α B > ϕ 2 > α C Assumptions: • Infinite number of stages • Constant relative volatility • Constant molar flows • Sharp product splits (pure products) NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November

7 Minimum energy: Operation in the flat region between the preferred split in prefractionator and a balanced main column Main column Main V (energy) column A Balanced main L column A+ β B V min ( β ) upper β ABC B Prefractionator V 1 V 1 V 1,min ( β ) C+(1- β )B lower Preferred split C V β β P β R NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 8 Solution surface for boilup ( V ) as a function of the remaining DOFs ( R l ,R v ) for sharp splits V ( R l ,R v ): Contour plot of V(R l ,R v ) Our Contribution: 1 C3 0.9 0.8 Extended the expression C4 to operation outside 0.7 R * At balanced the flat region main column Vapor split R v 0.6 P * C2 0.5 At preferred prefractionator split 0.4 Optimal operation z f =[0.33 0.33 0.33 ] line, V =100% 0.3 α =[4.00 2.00 1.00 ] q = 0.5 0.2 V =300% C1 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Liquid split R l The energy consumption increase rapidly when the operation is not exactly at the minimum energy region (which is on PR). Important: When PR is large, one DOF ( R l or R v ) may be kept constant!!! NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November

9 COMPUTATION OF THE ENERGY CONSUMPTION OUTSIDE THE FLAT REGION: V ( R l ,R v ) Characteristic corner edges : Contour plot of V(R l ,R v ) C1: At preferred split 1 The contour C3 C2: Left branch of V 1,min ( β ) 0.9 segments are straight lines 0.8 C3: Balanced main column C4 0.7 R * At balanced main column C4: Right branch of V 1,min ( β ) Vapor split R v 0.6 P * C2 0.5 At preferred prefractionator split V 1 0.4 Optimal operation z f =[0.33 0.33 0.33 ] C3 line, V =100% 0.3 α =[4.00 2.00 1.00 ] q = 0.5 C4 0.2 V =300% C1 C2 R 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Liquid split R l P C1 PR: Minimum energy region β NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 10 Column sections at minimum reflux for 3 main cases: : Over-refluxed Case 1: β P < β R : Minimum reflux Case 3: β P = β R R Q P P Q R Case 2: β P > β R R P=Q=R P Q NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November

11 Contour plot of theoretical savings as function of feed composition compared to the best of the conventional configurations. B Medium difficult separation Case: α =[4.00 2.00 1.00], q = 1.00 Maximum saving is 35.6% for 0.8 z f =[0.50 0.18 0.32] Molfraction of B 0.6 5% Contour lines V ISV =V DSL β P = β R 0.4 NOTE! The largest savings is achieved 0 3 when the preferred split coincide 0.2 25 3 30 5 with a balanced main column 0 2 2 2 5 0 15 5 1 C 0.2 0.4 0.6 0.8 A Molfraction of A NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 12 Important observations for high purity operation of the Petlyuk column: 2-point on-line optimization is required in the following situations: • For operation close to the boundary region In particular for difficult separations 1-point on-line optimization is sufficient: • For operation further away from the boundary, but note that the control strat- egies may be different dependant on the particular side. No optimizing control is required: • For very small feed variations and other disturbances (impossible in practice) • Can be sufficient for easy separations (But then the potential savings are small!) NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November

13 Computing: Very simple analytic functions, realized in Matlab: The minimum energy solution is just a function of α , z and q • V min =f ( α ,z,q ) at the operating points P*=f( α ,z,q ), R*=f( α ,z,q ) • P* and R* are defined by the degrees of freedom ( R l ,R v ) (Which fully determines all internal flows) The most complex operation is computing the Undewood roots, (finding the roots of a 3.rd order polynomial) Example: Each triangular plot shown is computed at ~1200 grid points in z. CPU-time is < 10 seconds on 200MHz Pentium CPU. The full solution surface f( V,R l ,R v , α ,z,q )=0 is computed via the corner points: • Ci=f i ( V, α ,z,q ), for V>V min , (i=1-4) • An arbitrary operating point • V =f( Rl,Rv, α ,z,q )=f( R l ,R v ,C1,C2,C3,C4) • Note that we get a full solution surface for every set of α ,z,q NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November 14 Summary of Underwood’s Equations for Minimum Energy Calculations Top and bottom equa- Feed equation tions has the “real” - “Top section” w i,T gives common roots φ and ψ α i w i T ∑ , V T = - - - - - - - - - - - - - - - - - - - “ V min ”-roots ϕ ( α i φ ) – Underwood: i When one or more pairs φ i ψ i , + 1 coincide, then φ i ψ i ϕ i , and w i,F =Fz i,F = = + 1 α i z i ∑ V=V min ( ) 1 – q = - - - - - - - - - - - - - - - - - - - ( α i ϕ ) – i F ,z,q Usage: 1. Compute ϕ from “feed eq” “Bottom section” 2. Specify 2 DOF variables. α i w i B 3. Use every “active” ϕ -root in ∑ , V B w i,B = - - - - - - - - - - - - - - - - - - - - V T -V B =(1-q)F ( α i ψ ) – “top or bottom” eq. and compute i V min and all recoveries w i,B =w i,T -Fz i,F Note: “Active” roots are between the distributed components NTNU Department of Chemical Engineering AIChE Annual Meeting 1999, Dallas TX, 31. October-5. November