Chemical Process Operating Region

Transcription

1 Inherently Safer Design Oriented Segregation of Chemical Process Operating Region Wang Hangzhou, Yuan Zhihong, Chen Bingzhen * Zhao Jinsong, Qiu Tong, He Xiaorong, Institute of Process System Engineering, Tsinghua University

2

3 Outline Introduction Methodology/Algorithm Case Study Industrial Application Flow-sheet Analysis Conclusions

4 Introduction Chemical Process: Nonlinear dynamics Limit cycles Oscillations Chaos Input/output multiplicities Limit process operation and process control Impose adverse effects on safety/product quality

5 Importance of stability Industrial statistics show that about 70% of the industrial accidents are caused by human errors. These abnormal events have significant economic, safety and environmental impact. Venkatasubramanian V, Rengaswamy R, Yin KKavuri S N. A review of process fault detection and diagnosis Part I: Quantitative model-based methods. Computers & Chemical Engineering, 003, 7(3): Accident Pyramid

6 Inherently safer operation For insurance of running chemical process safely, to develop a method for designing processes that are inherently safer -with the focus on disturbances having the potential for hazardous responses--is a problem of common interest.

7 Nonlinear Analysis Inherent characteristics Stability and controllability are two important inherent characteristics of a process in terms of its operability. More integrated among various units Tighter restrictions on environmental/safety Academia Industry Nonlinear Analysis Inherently safer design

8 Inherently safer design Stability

9 Inherently safer design Controllability Variable changes with time Variable x Nonminimum phase Minimum phase Initial value Target value Controllability Time t

10 Bifurcation theory α= -0.5 α= 0 α= 0.5 dy yy dt dx x dt The system s characteristics changes with its parameter variation. It is important to identify singularity points where the change of a reacting system ss stability characteristics occurs. From: Phase portrait showing Saddle-node bifurcation

11 Methodology

12 Stability of steady-state point Lyapunov stability d x Fx ( ) Differential Equations dt,solution is x(x 0, t) x(0) = x0 0, 0, when x x, 1 0 x(x 1, t) x(x 0, t), t0,then x(x 0, t) isstable Lyapunov method linear system Nonlinear system Linear expansion near steady state point (1)If all eigenvalues of A have negative real parts, then the system is stable. ()If one of the eigenvalues has a positive real root, the system unstable. (3)If there are no eigenvalues with positive real part, but there is a single real zero, The solution of the system stem is stable, but not asymptotically stable. dx i dt f ( x, x,, x ) ( i 1,,..., n) i 1 n n f ( x, x,, x ) a x X ( x, x,, x ) i 1 n ij j i 1 n i1 (1) If there are no eigenvalues with positive real part, but there is a single real zero, then the stability depends on higher order terms. () If all eigenvalues have negative real parts, then the steady-state point is stable. (3) If one of the eigenvalues has a positive real part, then the steady state is unstable.

13 Singularity theory based stability analysis method Differential Equations Steady state solution lti curve Calculate steady state curve Select the first steady state point Determine the Find singularity points stability of the point Select the next steady state point The stability is the same as the prior point Jacobian matrix is singular N Y Mark this singularity point Determine stabilities of points in both sides of singularity point N Determine the singularity of prior point Y Determine the stability of the point According to the determine result establish the stability region Are there any steady state points Y N Stop Algorithm diagram Wang Hangzhou, Chen Bingzhen, et al. Singularity theory based stability analysis of reacting systems. 10th International Symposium on Process Systems Engineering,009,Salvador,Bahia,Brazil

14 Stability analysis When q c =0.3,q=3 solutions of system x 1 x x 3 x 4 stability A Stable B unstable C stable ntration of B) x (Dimensionless concen q c =0.3 (Dimensionless cooling water flow rate) A B C stablie unstable q (Dimensionless feed flow rate) Converge to steady state point Deviation from the steady state Variable changes with time under different disturbances (Point A, Stable steady state point ) Variable changes with time under different disturbances (Point B, unstable steady state point )

15 Singularity theory based controllability analysis method Calculate steady state curve Obtain the zero dynamics Find singularity points for zero dynamics Y Determine stabilities of points in both sides of singularity point N N Y According to the determine result establish the minimum i phase behavior region Algorithm diagram N Y Yuan zhihong, Chen Bingzhen, et al. Controllability analysis for chemical processes based on singularity it theory. 5th International Symposium on Design, Operation and Control of Chemical Processes, 010, Singapore

16 Controllability analysis Indicator for controllability Minimum/nonminimum phase: non-minimum phase Minimum phase

17 Algorithm The detailed steps are as follows: 1 Set up dynamic mathematical modeling of the chemical process described by differential algebraic equations (DAEs). Solve the DAE, based on the extended homotopy continuation algorithm, to obtain all the steady states. 3 Obtain the zero dynamics of the chemical process.

18 Algorithm 4 Determine the characteristics of the steady states (stable or unstable), based on singularity theory and bifurcation theory. 5 Solve eigenvalues of the Jacobian of zero dynamics to determine whether the zero dynamics are stable or unstable. 6 Segregate the whole operating range into distinct zones, based on the results obtained from steps 4 and 5.

19 Case Study Exothermic CSTR with reactions A B C Mole and Energy balances: dc Q A ( C Af C A) k 1( T ) C A dt V dcb Q ( C Bf C B ) k ( T ) C B k 1( T ) C A dt V dt Q ( H A) ( H B) UA ( T f T ) k 1 ( T ) C A k ( T ) C B ( T T c ) dt V Cp Cp CpV dtc Qc UA ( Tcf Tc ) ( T Tc ) dt V c Cp cv c

20 Analysis results q c =0.3 (Dimensionless cooling water flow rate) 0.9 stablie unstable q c =0.3 (Dimensionless cooling water flow rate) stablie unstable (Dimensionless con ncentration of A) x (Dimensionless con ncentration of B) x q (Dimensionless feed flow rate) q (Dimensionless feed flow rate) Stability of dimensionless concentration of A Stability of dimensionless concentration of B 1. Calculate singularity point to divide steady state solution curve.. Determine several point to judge stability. Wang Hangzhou, Chen Bingzhen, et al. Singularity theory based stability analysis of reacting systems. 10th International ti Symposium on Process Systems Engineering,009,Salvador,Bahia,Brazil

21 Zero dynamic system Zero dynamic equations:. 1 1 ( )( x f ysp 1 ) 1 ( x 1f 1 )( ( ) Sysp 1 1 ( ) 1 ) y x sp1 f. ( ysp 1xf ){ [ 1 1( ) ysp 1 ( ) S] ( ysp )]} [ 1 1( ) ysp 1 ( ) S]( x3f ) y x y x sp 1 f sp 1 f

22 Operating zone segregation 1. stable minimum phase. unstable minimum phase 3. stable non-minimum i phase

23 Operating space segregation Dimensionless concentration of product Dimensionless temperature of reactor 1. stable minimum phase. unstable minimum phase 3. stable non-minimum phase

24 Industrial Case Study Liquid catalytic oxidation of toluene CH 3 COOH ß» ¼Á + H O + O R 1 n[c6h5ch 3] R R4 CHCH CHCHO CHCOOH R 3 R C H CH OH C H COOH 5 C H O

25 k k k k k e e e e e R E R E E E E n n n n n n n n R R R R n / 60 Model E1 RT n11 n ( 1/1000) ( /1000 3/1000) R k e C C C E RT n1 n 0 ( 1/1000) ( /1000) R k e C C E3 RT n31 n ( 1/1000) ( /1000 3/1000) R k e C C C E4 RT 4 04 R k e ( C /1000) n41 E5 RT n51 n ( 3/1000) ( 4 /1000) R k e C C H 1 H 5 H 1000(0.106T 516.1) H 1000( T 71.5) 1 3 H 1000( 0.019T 50.49) 4 H 1000(0.0759T 111.3) 5 Cp T Cp T T Cp T T Cp T T Cp T T Cp Cp M 9 M M 108 M 1 M 1 M 9 6 Cp m c Cp c Cp1C 1CpC Cp3C3 Cp4C4 Cp5C5 Cp6C CM CM CM CM CM CM H V( RH R H R H R H R H ) r T Tf Tc Tcf Hx UA dc1 Q ( C 10 C1) ( R1R R3) dt V d C Q ( C 0 C ) R R 4 dt V d C 3 Q ( C 30 C 3) R 3 R 5 dt V d C Q 4 ( C C 40 4) R R 4 5 dt V d C5 Q ( C 50 C 5) R 5 dt V dc6 Q ( C 60 C 6) R 1 dt V dt Q Hr Hx ( T f T ) dt V Cp V d Tc Qc Hx ( Tcf Tc ) dt V CpV m c c c c

26 Analysis results Realistic industrial operating point -----Unstable non-minimum phase behavior Unstable minimum phase behavior Wang Hangzhou, Chen Bingzhen, He Xiaorong, Zhao Jinsong, Qiu Tong. Modeling, simulation and analysis of the liquid-phase catalytic oxidation of toluene, Chemical Engineering Journal, 010,158():0-4.

27 Analysis results Realistic industrial operating point -----Unstable non-minimum phase behavior Unstable minimum phase behavior

28 I Nonlinear Analysis Tool Temperature T (K) LP 340 P1 LP1 F cw = Initiator volumetric flowrate F I (m 3 /h) P FI = unstable stable unstable LP stable 0.7 Temperature T (K) H LP3 P LP4 LP Monomer volumetric flowrate F (m 3 /h) P1 Conversion rate x Adiabatic temperature rise B = 14.0, heat transfer coefficient =.0 LP LP1 H unstable stable P Damkohler criterion Da P (kmol/m 3 ) Initiator concentration C I LP1 Volume flow rate of cooling medium F c = (m 3 /h) LP unstable stable T c (K) Jacket temperature LP1 Volume flow rate of cooling medium F c = (m 3 /h) LP unstable stable Monomer concentration C m (kmol/m 3 ) LP1 Volume flow rate of cooling medium F c = (m 3 /h) LP unstable stable Monomer volume flow F t (m 3 /h) x Monomer volume flow F t (m 3 /h) x Monomer volume flow F t (m 3 /h) x 10-3

29 Flow-sheet Case Study F, T, C r A F0, T0, CA0 F, T, CA F1, T1, CA 1 F, T, CA Operating variables:f 0 F 3 F r

30 Model A A A Chemical reactions Model E1 E dt1 F0 Fr H 1 RT H 1 RT1 ( T 0 T 1 ) ( T T 1 ) k 10e C A 1 k 0e C A 1 dt V 1 V 1 Cp C p k1 E 3 B H 3 RT Q 1 1 k30e C A1 k Cp CpV 1 U E 1 E E 3 dc A1 F0 F r RT1 RT1 RT1 k ( C A0 C A1) ( C A C A1) k10e C A1 k0e C A1 k30e C A1 3 R dt V1 V1 E1 dcb1 F0 F r RT1 ( C B 0 C B1) ( C B C B1) k10e C A1 dt V1 V1 E1 E dt F1 F3 H 1 RT H RT ( T1 T ) ( T03 T ) k10e C A k0e C A dt V V Cp Cp E 3 H 3 RT Q k30e C A Cp CpV E1 E E 3 dc A F1 F 3 RT RT RT ( C A1 C A) ( C A03 C A) k 10 e C A k 0 e C A k 30 e C A dt V V E1 dc B F1 F 3 RT ( C B1 C B ) ( C B 03 C B ) k 10 e C A dt V V

31 Analysis results

32 Analysis results Maximum conversion rate point: Unstable None minimum phase

33 Comparison Stability and controllability Stability and controllability changed after CSTR in series

34 Conclusions For a process, the steady state solutions change when the operating parameters vary, at the same time system s stability and phase behavior change. system s stability and phase behavior should be considered totally, as the system s contained equipment / subsystem differ from that contained in the system in terms of these features. It is important to account for the trade-offs between stability, controllability and profitability or product quality when selecting a set of normal design/operating g parameters.

35 Thank You! Institute of Process System Engineering, Tisnghua University