A Batch Reactor Heat Recovery Problem description Challenge - PowerPoint PPT Presentation

Heat Recovery Challenge Problem J. Jäschke Introduction A Batch Reactor Heat Recovery Problem description Challenge Problem Simulations Discussion Conclusions Johannes Jäschke, Sigurd Skogestad Department of Chemical Engineering NTNU Trondheim, Norway Trondheim, 9. June 2012 J. Jäschke Trondheim, 9. June 2012 1

Heat Recovery Outline Challenge Problem J. Jäschke Introduction Problem Introduction 1 description Simulations Discussion Problem description 2 Conclusions 3 Simulations Discussion 4 Conclusions 5 J. Jäschke Trondheim, 9. June 2012 2

Heat Recovery Introduction Challenge Problem J. Jäschke Introduction Optimizing real processes consists of 2 parts: Problem description Optimization problem 1 Simulations Formulating the problem Discussion Minimum Solving it systematically, often using a model Conclusions Implement the solution in the real process 2 This presentation: Challenge problem to test Optimization Implementation Discussion J. Jäschke Trondheim, 9. June 2012 3

Heat Recovery Introduction Challenge Problem J. Jäschke Introduction Some challenges when optimizing real systems Problem Optimization part description Non-linearity Simulations Non-convexity Discussion Integer variables Conclusions Non-smoothness Time-varying systems (Dynamic systems) Implementation part Missing information Uncertainty Disturbances (parametric uncertainty) Noise Structural model mismatch Temporal uncertainty J. Jäschke Trondheim, 9. June 2012 4

Heat Recovery Heat recovery challenge problem Challenge Problem J. Jäschke Ttarget Introduction Qheater Problem Tmix description 9 10 q1 q2 q3 q4 q5 q6 q7 q8 q9 q10 T1 T1 T1 T1 T1 T1 T7 T8 T8 T10 Simulations Th10in Th10 qh10 Discussion Th9 qh9 Th9in 7 8 Conclusions qh8 Th8in Th8 qh7 Th7 Th7in 5 6 Th6in Th6 qh6 Th5 qh5 Th5in 3 4 qh4 Th4in Th4 qh3 Th3in Th3 1 2 qh2 Th2in T2 qh1 Th1 Th1in T0 q0 Objective: Adjust split to maximize Tmix J. Jäschke Trondheim, 9. June 2012 5

Heat Recovery Heat recovery challenge problem Challenge Problem J. Jäschke Hot flow rates Introduction [m 3 /min] 0.05 Problem Ttarget Qheater 0 description Tmix 0 200 400 600 800 1000 1200 1400 9 10 time [min] q1 q2 q3 q4 q5 q6 q7 q8 q9 q10 [m 3 /min] T1 T1 T1 T1 T1 T1 T7 T8 T8 T10 0.05 Th10in Th10 qh10 0 Simulations Th9 qh9 Th9in 7 8 0 200 400 600 800 1000 1200 1400 time [min] qh8 [m 3 /min] Th8in Th8 0.05 qh7 Discussion Th7in Th7 5 6 0 0 200 400 600 800 1000 1200 1400 Th6in Th6 qh6 time [min] [m 3 /min] Th5in Th5 qh5 0.05 Conclusions 3 4 Th4in Th4 qh4 0 0 200 400 600 800 1000 1200 1400 qh3 Th3in Th3 1 2 time [min] [m 3 /min] 0.05 qh2 Th2in T2 0 Th1in Th1 qh1 0 200 400 600 800 1000 1200 1400 T0 time [min] q0 [m 3 /min] 0.05 0 Cold flow rate and temperature 0 200 400 600 800 1000 1200 1400 time [min] [m 3 /min] 0.05 Total cold flow rate 0 0.1 0 200 400 600 800 1000 1200 1400 [m 3 /min] time [min] [m 3 /min] 0.05 0.05 0 0 200 400 600 800 1000 1200 1400 0 0 200 400 600 800 1000 1200 1400 time [min] [m 3 /min] 0.05 time [min] ° C] Cold stream temperature 0 0 200 400 600 800 1000 1200 1400 Temperature [ time [min] [m 3 /min] 80 0.05 0 60 0 200 400 600 800 1000 1200 1400 time [min] 0 200 400 600 800 1000 1200 1400 time Hot stream temperatures 200 ° C 100 0 1 2 3 4 5 6 7 8 9 10 Hot stream J. Jäschke Trondheim, 9. June 2012 6

Heat Recovery Heat recovery challenge problem Challenge Problem Batch discharge J. Jäschke Flow rate: Introduction  0 for t < t s Problem   � description q j ∆ p j t j sj ≤ t ≤ t j si + t j hi ( t ) = k i for h i i ei Simulations  t > t j si + t j 0 for  ei h head Discussion Conclusions t j si Start time of discharge j t j ei End time of discharge j ( h j i = 0) Pressure drop at valve ∆ p j i = ρ g ( h j i + h head ) Level during discharge j Adh j dt = − q j i i J. Jäschke Trondheim, 9. June 2012 7

Heat Recovery Heat exchangers Challenge Problem J. Jäschke out in Introduction T T hi hi Problem q hi description Simulations q 0i Discussion Conclusions T T 0 i SS-assumption: Heat transfer Energy balances ∆ T log , i = ( T h , i − T 0 ) − ( T in hi − T i ) Q i = q 0 i ( T i − T 0 ) log ( T h , i − T 0 ) Q i = q hi ( T in hi − T out ( T in hi − T i ) hi ) � 0 . 8 � q hi ( t ) Heat transfer UA i ( q hi ) = UA 0 i q h 0 i Q i = UA ( q hi )∆ T log , i J. Jäschke Trondheim, 9. June 2012 8

Heat Recovery Splitter and mixer Challenge Problem J. Jäschke Introduction Splitter f q T Problem 1 0 1 T i = T 0 description f q T q 2 0 2 0 Simulations q i = f i q 0 f q T Discussion i 0 i N Conclusions � f i = 1 f q T N 0 N i = 1 Mixer N T q T mix = 1 � 1 1 q hi T i T q q 0 2 2 i = 1 q 0 T T q N i i mix � q 0 = q i T q i = 1 N N J. Jäschke Trondheim, 9. June 2012 9

Heat Recovery Objective function and heater Challenge Problem J. Jäschke Introduction T Problem target description Simulations Heater duty Discussion Conclusions q 0 T mix � � Q heat ( t ) = q 0 c p T target − T mix ( t ) Objective: � 24 h min Q heater ( t ) dt f i 0 J. Jäschke Trondheim, 9. June 2012 10

Heat Recovery Open-loop Simulation – equal f i Challenge Problem J. Jäschke Equal fractions in all parallel branches Mixing temperature Introduction 200 Problem description ° C] 150 Simulations Temperature [ Discussion 100 Conclusions 50 0 0 200 400 600 800 1000 1200 1400 time [min] Heater Duty 600 400 kW 200 0 0 200 400 600 800 1000 1200 1400 time [min] J. Jäschke Trondheim, 9. June 2012 11

Heat Recovery Open-loop Simulation – equal f i Challenge Problem J. Jäschke Introduction Problem description Equal fractions in all parallel branches Simulations Cold stream split 1.2 Discussion 1 Conclusions 0.8 0.6 0.4 0.2 0 −0.2 0 200 400 600 800 1000 1200 1400 time [min] � 24 h J = Q heat dt = 35005 . 17 MJ 0 J. Jäschke Trondheim, 9. June 2012 12

Heat Recovery “Optimization” Challenge Problem J. Jäschke Definition Introduction An active branch is a branch connected to a no-zero hot Problem description stream Simulations Discussion Idea Conclusions q i = f i q 0 assign flow only to active branches f i , active = 1 / n active f i , inactive = 0 if no branch is active, then f i = 1 / n total J. Jäschke Trondheim, 9. June 2012 13

Heat Recovery “Optimized” Challenge Problem Mixing temperature J. Jäschke 200 Introduction ° C] 150 Problem Temperature [ description 100 Simulations Discussion 50 Conclusions 0 0 200 400 600 800 1000 1200 1400 time [min] Heater Duty 600 400 kW 200 0 0 200 400 600 800 1000 1200 1400 time [min] J. Jäschke Trondheim, 9. June 2012 14

Heat Recovery “Optimized” Challenge Problem J. Jäschke Introduction Cold stream split Problem description 1 Simulations Discussion 0.5 Conclusions 0 0 200 400 600 800 1000 1200 1400 time [min] � 24 h J = Q heat dt = 25364 . 11 MJ 0 J. Jäschke Trondheim, 9. June 2012 15

Heat Recovery Discussion Challenge Problem J. Jäschke Implementation of “optimal solution” Introduction Very simple Problem description Assumption: Only hot flows measured Simulations Clearly sub-optimal Discussion Conclusions Optimization Nonlinear problem Time-varying Static optimization at each time instant Suboptimal policy Temperatures not used. Piecewise constant f i Large improvement 35 , 005 . 17 MJ = ⇒ 25 , 364 . 11 MJ J. Jäschke Trondheim, 9. June 2012 16

Heat Recovery Conclusions Challenge Problem J. Jäschke Nonlinear optimization problem: Sub-optimal solution Introduction Simple implementation Problem description Simulations For true optimal solution: Discussion More information required Conclusions Temperatures Flow rates Estimate unmeasured parameters ( UA 0 ) Future work Improve “optimization” algorithm Include temperature measurements Time varying f i Assume flows are not measured Modify problem Add buffer tank before split J. Jäschke Trondheim, 9. June 2012 17

Heat Recovery Challenge Problem J. Jäschke Introduction Problem description Simulations Discussion Thank you ! Conclusions A simulink model will be made available on http://www.nt.ntnu.no/users/skoge/ publications/2012/BatchChallenge J. Jäschke Trondheim, 9. June 2012 18