Presentation is loading. Please wait.

Presentation is loading. Please wait.

d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 1 1 PSE Summer School 2012 Process Simulation and.

Similar presentations


Presentation on theme: "d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 1 1 PSE Summer School 2012 Process Simulation and."— Presentation transcript:

1 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 1 1 PSE Summer School 2012 Process Simulation and Optimization of Chemical Plants DAAD Summer School 2012, Mexico Sponsorship: DAAD German Academic Exchange service

2 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen (Process Optimization with MOSAIC an short introduction) Prof. Dr.-Ing. habil. Prof. h.c. Dr. h.c. G. Wozny Problem formulation Examples MOSAIC Process Simulation and Optimization of Chemical Plants Part III

3 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 3 Process Simulation and Optimization Solution methods Overview heuristic Rules, short cut Methods, trial and error, Sensitivity studies Direct Methods Discretisation of the manipulated variables, Discretisation of the manipulated variables and the state variables, - SQP (Sequentially Quadratic Programming) (very general, often used z.B. Aspen, Bayer, BP, ICI, Linde,... ) direct Search (z.B. genetic Algorithm, Simulated Annealing,...) Optimization GAMS® ROMEO gOPT MOSAIC

4 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 4 Process Simulation and Optimization Problem formulation F: Objective Function measure of goodness min F(x,u) s.t. y = {0,1} f(dx/dt, x, u, y) = 0 g(x, u, y) 0 x min x x max u min u u max x: state variables (after discretization) u: manipulated variables (peace wise constant) f: equality equation Model equation MESH) g: inequality constraints (physical constraints or from construction e.g. F-Factor for Distillation) y: Integer variable

5 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 5 Process Simulation and Optimization Problem formulation with uncertainties x: state variable (after Discretisation) u: manipulated variable (peace wise constant) min F(x,u) f: Model equation (MESH) : stochastic Variable (distribution given) g: probability restrictions g(x,u, ) = P { (x,u, ) ) } > p s.t. f(dx/dt,x,u, ) = 0 g(x,u, ) 0 x min x x max u min u u max Werk, S.; Barz, T.; Arellano-Garcia, H.; Wozny, G.: Performance Analysis of Shooting Algorithm in Chanced Constrained Optimization, PSE 2012, Singapore July

6 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 6 Process Simulation and Optimization A simple example: min F(x,y) with: F = x 2 + y 2 Equality constraints x + y = 1 F/ x = 0 -> x = 0 F/ y = 0 -> y = 0 With Constraints: x y F=const x+y=1 : F = x 2 + y 2 = x 2 + ( 1 - x ) 2 F/ x = 0 = 2x -2 ( 1 - x) Without constraints: Introduction constraints

7 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 7 7 Process Simulation and Optimization Lagrangsche Multiplicator F = x 2 + y 2 = Minx + y - 1 = 0 Add the constraints ( = 0) F = x 2 + y = x 2 + y 2 + ( x + y - 1 ) = Minimum! Now: 3 equations, 3 Unknown F / x = 0 = 2 x + Solution: Formulate the objective function Formulation of equality constraints (Balance equations), … F / y = 0 = 2 y + F / = 0 = x + y - 1 (that is the equality constraint)

8 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 8 Process Simulation and Optimization Start up Feed Top product Bottom product Q cond Q reb t = 0 : column cold and emty t = t 1 : reboiler switch on t = t 2 : vapor at top of the column t = t 3 : reflux switch on t = t 4 : all streams > 0 t = t 5 : column in steady state reflux

9 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 9 Process Simulation and Optimization Example: start up Min ( t start up ) Subject to:f ( dx/dt, x, u, t ) = 0 (MESH – Model equation) g (dx/dt, x, u, t ) 0 (vapour load, liquid load...Process constraint) x min x x max (Variable constraint); u min u u max ; (manipulated variables) + start up conditions, Initialization Objective Function

10 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 10 Process Simulation and Optimization Example: start up - many products - complex procedure - low Frequency -> less Training - different Solutions - Basis: PhD Thesis Ch. Kruse, 1995 Main column PhD Thesis E. Reuter, 1995, Batch distillation with reaction PhD Thesis P. Li, 1997, Batch distillation with Reaction PhD Thesis M. Flender, 1998, Column with side streams PhD Thesis R. Schneider, 199, Three phase distillation PhD Thesis K. Löwe, 2000, Two pressure column system PhD Thesis Wang 2001, Batch distillation PhD Thesis F. Reepmeyer 2004 Reactive distillation homogeneous PhD Thesis Tran Trung Kien, 2004 Three Phase distillation with decanter PhD Thesis F. Forner, 2007 Reactive Distillation heterogeneous min t start up (aim)

11 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 11 Process Simulation and Optimization conventional Strategy Switch over attime t=? from R1= to R2 and Q2 Feed F zFzF V Q FC LC TC W F xBxB B LC xDxD L=u 1 D FFC Start t = 0: R = L/D = Q = Q1 Switch over at Time t=0 to the steady state values R2 and Q2 and then wait

12 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 12 Process Simulation and Optimization modified Strategy Switch over at time t=? from R1 = 0 and Q1 to R2 and Q2

13 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 13 Process Simulation and Optimization Derivation of the modified Strategy F, x F D, x D B, x B VL HU x B = x B0 - K p ( 1- e -t/T ) HU dx B dt = F x F - D x D - B x B D = V - L F = D + B K P = F F + (K-1) (V-L) x D = K x B HU=const., V=const., F=const. K=const. with Balance volume

14 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 14 Process Simulation and Optimization modified Strategy Concentration x B stat BBum xtxMint Optimised

15 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 15 Process Simulation and Optimization Feed Distillate Bottomproduct j n Condenser Reboiler D, x D B, x B F, x F Balance volume 1 condenser j-1 Balance volume j Balance volume n reboiler Feed LjLj L j-1 L j+1 VjVj V j+1 j+1 D B j tray

16 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 16 Process Simulation and Optimisation Objective function modified Strategy X (concentration, molar fraction) not measurable in real Plant Therefore Temperature choosen

17 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 17 Process Simulation and Optimization Pilot plant Bottom product Column data: diameter70 mm Packing high 2,5 m NTS28 ( Fa. Sulzer) Reflux ratio 1,5 pressure150 mbar Reboiler duty525 W reboiler Hold-up 0,002 m**3 Distillate Feed C6=27,9% C8=72,1% F=4,0 kg/h C6=99,98% C8=99,7% Side stream

18 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 18 Process Simulation and Optimization Pilot plant time MT

19 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 19 Process Simulation and Optimization

20 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 20 Process Simulation and Optimization

21 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 21 Process Simulation and Optimization time in Minutes Start up: conventional Strategy

22 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 22 Start conditions Steady state Feed stream:4 kg/h Feed concentration: 27,9% Feed temperature: 85 o C Distillate concentration:99.98% Bottom concentration:0,3% ? Time optimal problem: min t f [R(t), Q(t)] With model equations x D (t f ) 1 0 x B (t f ) 0,003 0,1 R(t) 20 0 Q(t) 1 Optimal Strategy Reflux ratio Reboiler duty Process Simulation and Optimization

23 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 23 Process Simulation and Optimization

24 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 24 Process Simulation and Optimization Experimental results Without side stream, two products Reduction of start up time: 93 % * * In comparison with the conventional procedure Time in minutes MT in °C Conventional strategy Optimised strategy

25 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 25 Process Simulation and Optimization Conclusion Derivation of a time optimal start up procedure Model validation Column with and without a side stream % deviation between Simulation - Experiment ca. 2% Time reduction 54% for the side stream column conventional 366 min modified 168 min ( remark: reflux ration infinity -> 360 min ) outlook: Transfer to complex column systems (DFG ), DAAD Transfer to reactive distillation (Project sponsored by AIF ) Transfer to plant wide start up investigations

26 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 26 Process Simulation and Optimization Conclusion: - empirical Optimization is sometimes suitable but not general - Basic: Process model, deep Process knowledge - Optimization methods (objective function, constraints, mathematical methods,... - Applications in Industry not often up to now - New research trends in PSE (stochastic Optimization, online Optimization, MIDO)

27 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 27 MOSAIC Optimization with MOSAIC

28 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 28 Concept Optimization Das Internet gPROMS Aspen Custom Model GAMS Matlab Program Custom Export Docu 1Docu 2 Docu 3Docu 4 Docu 5 Optimization results

29 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 29 Modeling systematic Process Simulation and Optimization Min ( J) Subject to:f ( dx/dt, x, u, t ) = 0 ( e.g. MESH – Model equation) g (dx/dt, x, u, t ) 0 (vapour load, liquid load...Process constraint) x min x x max (Variable constraint); u min u u max ; (manipulated variables, constraints) + Initialization ( at time 0) General Formulation: Objective Function (cost, time, profit, energy, waste, …) equilibrium constraints

30 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 30 Optimization Evaluate the equation system Compose the equation system If needed enter new model equations Define the notation Workflow: Requirements: - Extend existing MOSAIC elements - Define the optimization statement, based on an evaluation - Keep compatibility - New symbols (, <,...) can not be defined - Code generator for different optimizer

31 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 31 NLP – Problem formulation Constrained Optimization: minf(x) s.t.h(x) = 0 g(x) 0 More general: minf(x) s.t.c (x) = 0 x L x x U Non equality constraints moved to equality constrains c(x) -> any equation system from the MOSAIC library Non equality constraints Equality constraints (Model eq.)

32 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 32 NLP Example – Hughes 1981 Min: Model equations - Equality constraints:

33 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 33 Implement model in MOSAIC Notation Equations Define Variables Initial Evaluation

34 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 34 Reuse model as constrains

35 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 35 Formulate the statement

36 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 36 Formulate the statement

37 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 37 Code export Matlab Gams

38 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 38 Solution F(x) = x i=1 = x i=2 =

39 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 39 Inequality constrains - example B A Objective: Min (P = 2(A + B)) Inequality constrains: Stay in box x o R o x o B - R o y o R o y o A - R o No overlaps (x o=1 – x o=2 ) 2 + (y o=1 – y o=2 ) 2 (R o=1 + R o=2 ) 2 (x o=1 – x o=3 ) 2 + (y o=1 – y o=3 ) 2 (R o=1 + R o=3 ) 2 (x o=2 – x o=3 ) 2 + (y o=2 – y o=3 ) 2 (R o=2 + R o=3 ) 2 Variables: x,y - CoordinatesP - Perimeter R - RadiusA - Height o - Number of circleB - Width

40 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 40 Equality constrains B A Objective: Min (P = 2(A + B)) Equality constrains: Stay in box No overlaps Variables: x,y - Coordinates P - Perimeter R - Radius A - Height i - slack index c - Slack variables B - Width o - circle index

41 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 41 Define optimization parameter A B

42 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 42 Solution Local optimum Matlab – fmincon Global Minimum NEOS Server - LINDOGLOBAL 1 3 B A P = A = B = 6 P = A = B = GAMS – CONOPT P = A = B = 7.464

43 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 43 Additional Examples in MOSAIC

44 d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 44 Challenges reuse of models multi scale applications data base models + meta data (ontology) large nonlinear dynamic systems mixed integer dynamic highly nonlinear systems transfer to applications experiment design model discrimination transfer to real world applications


Download ppt "d|b|t|a Fachgebiet Dynamik und Betrieb technischer Anlagen 1 1 PSE Summer School 2012 Process Simulation and."

Similar presentations


Ads by Google