Design and Optimisation of Batch Reactors

Transcription

1 Design and Optimisation of Batch Reactors Jinzhong Zhang Supervisor: Professor Robin Smith 2-1 XVII PIRC Annual Research Meeting 2000 In recent years, a methodology has been developed for the systematic design of chemical reactors which sets performance targets, predicting the maximum yield and selectivity for a given reaction system with its catalyst. Even the most complex systems can be analysed, involving multiphase reactors and complex heat transfer arrangements. The mixing patterns and heat transfer arrangements associated with the target provide the basis for the design to achieve the target. So far the technology has only considered continuous processes, which by definition are at steady state. By contrast, batch reactors are in a dynamic state. For batch reactors, the degrees of freedom to be optimised include feed addition policy (batch or semibatch), temperature profile through the batch, product takeoff and recycle policy and batch cycle time. This presentation will discuss how the previous methodology for continuous reactors can be adapted to the design and optimisation of batch reactors.

2 Outline 1. Introduction 2. Batch Reactor Model General Representation 3. Optimisation Methodology 3.1 Profile Based Approach 3.2 Stochastic Optimisation by Simulated Annealing 4. Case Studies 5. Conclusions and Future work 2-2 Design and Optimisation of Batch Reactors

3 1. Introduction 2-3 Design and Optimisation of Batch Reactors

4 Batch vs Continuous Why batch?! Nature of process/product! Scale-up from laboratory! Economic balance! Production scale! Long reaction times! Production flexibility Reactor Separation and Recycle System Heat Recovery System Heating and Cooling Utilities Water and Effluent Treatment Reactor plays a fundamental role in most chemical processes 2-4 Design and Optimisation of Batch Reactors

5 Benefits of Effective Reactor Design Technology! Yield and selectivity improvement! Raw material and waste reduction! Capital investment saving! Safety of operation enhancement In consequence,! The whole chemical process benefits from this 2-5 Design and Optimisation of Batch Reactors

6 Industrial Challenges Complex reactions in Note that! Biochemical processes! Fine and speciality chemicals! Pharmaceuticals! Polymer processing Most of the above processes are in BATCH mode! 2-6 Design and Optimisation of Batch Reactors

7 Industrial Challenges (cont d)! Multiphase reactions! Non-isothermal systems Compare with continuous reactor Batch reactors are always in a DYNAMIC state! 2-7 Design and Optimisation of Batch Reactors

8 Conventional Technology for Reactor Design! Scale-up directly from laboratory! Repeated simulation using CFD Heuristics! Simple cases! Contradictory guidelines Graphical methods! Simple reactions! Small systems If we cannot meet the challenges Lost opportunities Poor reactor designs 2-8 Design and Optimisation of Batch Reactors Many batch reactors are scaled up directly from laboratory equipment. More recently, designs have started to exploit simulation using computation fluid dynamics. Heuristics are based on physical arguments and experience. Although they are easy and fast to apply, and give us engineering insights, their application is limited to small problems, simple reaction schemes, simple kinetics and often they give contradictory guidelines. Graphical methods use the concept of attainable regions. The attainable region is the region of all feasible operating points for a given reaction scheme. For every feed point the various feasible operation points can be obtained through reaction, through mixing with other operating / feed points or through reaction and mixing. Different reactors result in different attainable regions. However, improvements in the overall performance cannot be realised without extending the attainable region of the problem, which can only be achieved by combining different types of ideal reactors, and exploiting the reaction and mixing patterns. So the graphic method is difficult to apply to a system of many components and complex reactions. Lack of proper methods can result in poor reactor design and lost opportunities.

9 Superstructure-based Approach for Continuous Reactor Design and Optimisation Optimal Solution Types Combinations Targeting Tools 2-9 Design and Optimisation of Batch Reactors A superstructure approach has been developed for the systematic design of continuous chemical reactors which sets performance targets, predicting the maximum yield and selectivity for a given reaction system with its catalyst. This approach enables simultaneous optimisation of structural and operational alternatives and is capable of addressing complex reaction systems. The optimal solution obtained can be used as a target.

10 Reactor Network for Multiphase Reactions Phase 1 Reactor Compartment Mass transfer Homogeneous reactor network Phase 2! Vipul L. Metha, PhD thesis, DPI, UMIST, 1998! REACTOR, V.1.2, DPI, UMIST 2-10 Design and Optimisation of Batch Reactors For multiphase reactions, the concepts of reactor compartment and shadow reactor are introduced. Within each compartment, homogeneous reactors are connected in series and parallel with each other. Reactor compartments in all phases are connected in the same manner. Each reactor compartment exchanges mass with the corresponding reactor compartments (shodow reactor compartments) in the other phases. This methodology for continuous reactor design has been successfully employed in the software, REACTOR, developed in DPI of UMIST.

11 However, all those technologies are developed for continuous processes but cannot tackle the problems caused by the inherently dynamic nature of batch processes 2-11 Design and Optimisation of Batch Reactors

12 Batch Reactor Design: Problem Statement Physical properties Physical parameters Phase equilibria Reaction kinetics Mechanism Kinetic parameters Mass transfer models Specifications Operational constraints Product specifications Process requirements Operation! Batch or semi-batch! Feed addition strategy! Batch cycle time! Temperature control! Recycle / discharge Equipment! Vessel volume! Agitator and baffles! Loading and discharge arrangements! Heat transfer 2-12 Design and Optimisation of Batch Reactors The problem for batch reactor design assumes basic information on reaction kinetics, mass transfer models and physico-chemical properties. The aim is to find the most promising reactor designs with objectives such as optimum yield and selectivity. Simultaneous evaluation of various operation conditions and equipment configuration is necessary at this stage. During optimisation, process requirements, specifications and operational constraints need to be considered.

13 Batch Reactor Design: Previous Work Objective functions Constraints Employ Pontryagin s maximum principle Employ standard NLP optimisation codes, i.e. SQP, GRG, etc Local optimum So far, both approaches can only be used for Simple reaction systems Homogenous systems Simple reactor configurations 2-13 Design and Optimisation of Batch Reactors So far, most research work done for batch reactor design and optimisation has attempted to find suitable mathematical methods to solve the batch reactor models which involve a set of differential equations. These methods include Pontryagin s maximum principle and some standard non-linear programming methods such as GRG (Generalised Reduced Gradient method) and SQP (Successive Quadratic Programming). However, these methods can only be used for simple reaction systems with homogeneous reaction and simple reactor configuration. This presentation will discuss a new methodology for batch reactor design and optimisation that is developed based on the superstructure-based approach for continuous reactor design.

14 2. Batch Reactor Model General Representation 2-14 Design and Optimisation of Batch Reactors

15 Ideal Batch Reactors and PFRs Feed Time Feed Time Batch Reactor Product Semi-batch Reactor Product PFR Micro-mixed PFR 2-15 Design and Optimisation of Batch Reactors The analogies between ideal batch reactors and plug flow reactors have long been used for the modelling of batch reactors.

16 Industrial Batch Reactors Batch reactor with external heat exchanger and recycle Batch reactor with vapour condenser and recycle 2-16 Design and Optimisation of Batch Reactors However, few industrial batch reactors can be described accurately enough as ideal batch reactor models.

17 Industrial Batch reactors Cross-flow filter Liquid in Gas in Reaction gas Batch feed Reaction autoclave Reaction mixer Reaction pump Reaction heat exchanger Product Liquid and dissolved gas out Buss loop reactor Cocurrent downflow contactor reactor 2-17 Design and Optimisation of Batch Reactors There are even more complex configurations for batch reactors in use in industry.

18 Schematic Diagrams of Batch Reactor Feed Recycle Feed Recycle Pressure Pressure Heat Volume Heat Volume Temperature Temperature Discharge Batch cycle time Discharge All the variables shown vary with reaction time 2-18 Design and Optimisation of Batch Reactors From these industrial reactors, some common design variables can be extracted. Those include feed addition policy (batch or semi-batch), temperature profile through the batch, reaction pressure, product takeoff and recycle policy and batch cycle time.

19 Elements of Batch Reactor Models The following elements need to be considered! Time intervals! Reactor compartments! Phase interactions Mass transfer! Variable profiles during reaction time Feed rate in semi-continuous mode Temperature policy Pressure policy Recycle/discharge 2-19 Design and Optimisation of Batch Reactors

20 Homogeneous Reactions in Batch Reactor Feed i Feed j Splitter Product Reactor compartment Time interval 1 Mixer Time interval i Time interval n Total discharge! Steady state assumption within each time interval! Properties of each reactor compartment are identical! Number of time intervals can be set by users! Length of each time interval changes based on the whole reaction time 2-20 Design and Optimisation of Batch Reactors Based on the investigation of industrial batch reactors, a superstructure model of a batch reactor is developed firstly in a single phase. This superstructure is built along the batch cycle time rather than a superstructure with physical connections. The batch cycle time is discretised into a number of time intervals. The reactor compartment in each time interval connects to the reactor compartments in the time intervals which are immediately before and after it through splitters and mixers. Unlike the superstructure of a continuous reactor, all the reactor compartments in the superstructure of a batch reactor are indentical as they represent the same reactor vessel at different periods of time. The scale of a batch reactor superstructure is flexible because the number of time intervals can be set by users to meet the requirements of different cases. The length of each time interval changes based on the whole reaction time. The structural changes of the superstructure may generate different operating mode (batch or semi-batch), different reactor configrations which include reactors with or without recycle and/or dischage. on the other hand, this superstructure model also embeds the operating variables such as temperature, flowrate, pressure. This superstructure model of batch reactors enables the simultaneous optimisation of batch reactors. The mixing arrangement at this stage is restricted to a well-mixed vessel. Later work will enlarge the options to consider a wider variety of mixing patterns.

21 Multiphase Reactions Feed Phase i Product Feed Product Phase j Time interval 1 Time interval i Time interval j Time interval n Mass transfer within the same time interval only 2-21 Design and Optimisation of Batch Reactors To extend the superstructure for multiphase reactions, an identical homogeneous superstructure can be built in each phase. Mass transfer only takes place between compartments in the same time intervals due to the irreversibility of time.

22 Virtual Superstructure of Mutiphase Batch Reactor Feed i Phase 1 Feed j Splitter Product Reactor compartment Mixer Total discharge Feed i Phase 2 Feed j Splitter Product Reactor compartment Time interval 1 Mixer Time interval i Time interval n Total discharge 2-22 Design and Optimisation of Batch Reactors A virtual superstructure model for batch reactors is then developed that embeds all key variables for batch reactor design for a well-mixed device. This model can be used for multiphase, nonisothermal, dynamic reactors. However, the nonlinear nature caused by complex kinetics still needs to be tackled by suitable optimisation techniques. 'Virtual' here means that this superstructure does not pysically exist but only exists in the time dimension.

23 This superstructure model of batch reactors converts the dynamic optimisation problem into structural optimisation problem which decides! The existence of streams and units! The parameter values corresponding to each stream or unit The task now becomes how to optimise them SIMULTANEOUSLY 2-23 Design and Optimisation of Batch Reactors

24 3. Optimisation Methodology 2-24 Design and Optimisation of Batch Reactors

25 3.1 Profile Based Approach 2-25 Design and Optimisation of Batch Reactors Here we present a method known as the Profile Based Approach developed for dynamic process optimisation.

26 Units vs Profiles Irrespective of control valves and heat transfer units How to determine optimal profile for each variable? Variables Variable 1 Variable 2 Variable 3 Time 2-26 Design and Optimisation of Batch Reactors First, we assume the design and optimisation of a dynamic process can be divided into two steps. In the first step, the profiles of control variables are generated and optimised. Then, in the second step, by using the optimised profiles as their desired values or set points we move on to the design of a mechanical system to follow the desired trajectories.

27 Previous Work ---- Profile Generation by Piecewise Constant Approximation Correct optimal profile, u(t) u(t) u(0) Piecewise constant approximation u(0),..., u(4) u(1) u(2) u(3) Time 2-27 Design and Optimisation of Batch Reactors The conventional method to generate the profiles for the variables of a dynamic process is to integrate the differential equations in the corresponding mathematical model using some traditional numerical methods such as the Runge-Kutta method.

28 Profile Implementation Rather than generate profiles by integrating differential equations u(t) We propose Impose a shape of profile directly for each variable Time 2-28 Design and Optimisation of Batch Reactors

29 Profile Search for Optimisation Then, evaluate the objective values for each set of imposed profiles Objective values Search profiles with different! Shapes! Start and end conditions Profiles The optimal profiles can then be found 2-29 Design and Optimisation of Batch Reactors

30 Realisation of Profiles Feasible search region Feasible search region with imposed profiles Constraints can be imposed onto the profile search region to make sure the optimal profiles are realisable 2-30 Design and Optimisation of Batch Reactors However, some profiles that are theoretically feasible are not realisable in practice. The method readily takes account of the practical constraints and other design and/or operation specifications by limiting the search region.

31 Profile Based Approach (PBA) Apply initial profiles Simulation Evaluation Apply different profiles Criteria Optimal Profiles! Optimal solutions can be reached by profile search! This approach can be applied for other dynamic optimisation processes! Optimisation engine is needed 2-31 Design and Optimisation of Batch Reactors The basic procedure of the Profile Based Approach starts from a set of initial feasible profiles that are simulated and evaluated in terms of the objective function and validation of constraints. An iterative loop within the algorithm is applied to search different profiles. Each set of profiles is subject to the specific criteria that decide whether the optimal has been reached or not.

32 3.2 Stochastic Optimisation by Simulated Annealing Optimisation Engine for the Profile Based Approach 2-32 Design and Optimisation of Batch Reactors

33 Variables Variable 1 Variable 2 Variable 3 Similar objective values Time Variables Variable 1 Time Variable 3 Variable2 And many other different profiles... Similar objective values can be obtained by different operating conditions 2-33 Design and Optimisation of Batch Reactors In practice, different combinations of profiles of variables may give similar objective values. So a desired optimisation approach should be able to handle the process models and deliver not only the performance limits of the system but also a set of designs with performances close to the target.

34 Targeting vs Optimality Optimal Solution replaced with... Objective Promising area Design variables targets and design options Employ stochastic optimisation instead of deterministic optimisation techniques 2-34 Design and Optimisation of Batch Reactors Instead of identifying only one 'optimal solution' to the design problem, the approach should be able to identify the performance target of the system and deliver different designs that can approach the targets closely.

35 Stochastic Optimisation by Simulated Annealing! Exploits analogies with statistical thermodynamics! Guarantees optimality, regardless of initialisation - because of the randomised nature of the search: the initial guess is soon forgotten - because of the mathematics behind simulated annealing the final solution is a stochastic optimum! Implementation of simulated annealing - States - Moves and perturbations - Acceptance criteria - Annealing schedule Subject to specific cases 2-35 Design and Optimisation of Batch Reactors

36 Perturbation Moves for Batch Reactor Optimisation Decision Levels Feed Changes Structural Changes Temperature Changes Amount Profile Reactor Compartment Streams Batch Cycle Time Recycle Discharge! This move tree is based on the virtual superstructure model! The probability of each move can be set by users to bias the random search process 2-36 Design and Optimisation of Batch Reactors Possible changes are made to the superstructure in order to obtain a new state. These changes are called perturbation moves in the simulated annealing algorithm. The upper level moves include lower level sub-moves. Each move has corresponding probability which is used to bias the stochastic search procedure that can be based on engineering insight for specific cases.

37 Design and Optimisation Framework Problem specific properties Design parameters Simulator Material balances Energy balances (A) Objective Evaluate (B) Constraints Perturbation Moves Continuous changes Discrete changes Simulated Annealing Optimiser Accept / Reject / Terminate Optimal solutions Non-linear optimisation 2-37 Design and Optimisation of Batch Reactors The stochastic experiment starts from an initial structure which is subsequently perturbed to a new state that is simulated and evaluated in terms of the objective function and violation of constraints. This new state is then either accepted as the starting point for the next perturbation or rejected, in which case the previous structure is perturbed again. New states with improved objectives are always accepted if they do not violate the constraints. Other states are accepted with some probability depending on the performance degradation experienced by the system and the progress of the annealing process. During the search, states of degraded performance are accepted so that local optima can potentially be passed by instead of terminating the search. The search reveals a stochastic optimum associated with confidence levels established from a multitude of stochastic experiments. The nonlinear optimisation then finely tunes the solutions suggested by stochastic optimisation by further optimising the continuous variables, including batch cycle time and total feed.

38 Design Implementation and Validation Process data and specifications Optimisation Detailed simulation Experimentation Industrial process 2-38 Design and Optimisation of Batch Reactors The proposed approach should be understood as part of an overall procedure that includes detailed simulation and validation stages with the real process. The procedure aims to cut down the with trial and error, instil confidence and develop design targets and incentives.

39 4. Case Studies 2-39 Design and Optimisation of Batch Reactors

40 Case Study 1: Parallel Reaction Scheme r 1 = k 1 C A C B A + B C (desired product) 2B D (unwanted product) r 2 = k 2 C B 0 k 1 = l mol -1 s -1 0 k 2 = l mol -1 s -1 E 1 = J mol -1 E 1 = J mol -1 Feed and Reaction Conditions N A = 0.1 kmol N B = 0.1 kmol temperature bounds 40 o C T 120 o C Jackson R, Senior MG, et al, Chem. Eng. Sci., 26(1971) Garcia V, M Cabassud, et al, Chem. Eng. J. 59(1995) Design and Optimisation of Batch Reactors This case study is employed to validate the proposed method.

41 Problem Description Objective function: Fractional yield of C from B Investigate under the following conditions! Fixed batch cycle time! Isothermal operation at different temperature! Different feed policy Results compared with those of Garcia et al. (1995) Garcia V, M Cabassud, et al, Chem. Eng. J. 59(1995) Design and Optimisation of Batch Reactors

42 First simulation at the same conditions as Garcia et al -----Validation of method Batch cycle time (s) Temperature ( O C ) Feed policy Garcia et al This work Batch 46.02% 46.36% Constant flow rate B 81.09% 82.18% Batch 47.64% 47.89% Constant flow rate B 84.14% 85.16% Garcia V, M Cabassud, et al, Chem. Eng. J. 59(1995) Design and Optimisation of Batch Reactors

43 Now optimise without constraints on feed addition 1 Batch cycle time (s) 3600 Temperature ( O C ) 120 Feed policy Garcia et al Feed profile of B 83.06% This work 98.06% Feed profile of B 86.12% 99.07% Garcia V, M Cabassud, et al, Chem. Eng. J. 59(1995) Design and Optimisation of Batch Reactors

44 ! Simulation results from the method presented in this work are consistent with the non-linear programming method! The non-linear programming method loses opportunities during optimisation The advantages from simultaneous optimisation are demonstrated by the following case studies 2-44 Design and Optimisation of Batch Reactors

45 Case Study 2: Consecutive-parallel Reaction Scheme A + B R (desired product) B + R S (unwanted product) r 1 = k 1 C A C B r 2 = k 2 C R C B k 0 1 = 1667 l mol -1 s -1 k 0 2 = 1667 l mol -1 s -1 E 1 = J mol -1 E 2 = J mol -1 Feed and Reaction Conditions N A = 0.1 kmol N B = 0.1 kmol temperature bounds 302 O C T 352 O C Burghart A and J Skrzypek, Chem. Eng. Sci., 29(1974) Garcia V, M Cabassud, et al, Chem. Eng. J. 59(1995) Design and Optimisation of Batch Reactors

46 Results of Garcia et al Fractional yield of R from B: 86.7% at batch cycle time 6000s Garcia V, M Cabassud, et al, Chem. Eng. J. 59(1995) Design and Optimisation of Batch Reactors

47 Fraction of total B Results of This Work Temperature o C Feed flowrate of B Temperature Profile Time intervals Time intervals Optimised result: Fractional yield of R form B: 97.5% at batch cycle time 6000s Compared to 86.7% for Garcia et al Design and Optimisation of Batch Reactors

48 Results Selection Feed policy Yield + around % Temperature profile Solution is not unique, select the most controllable one 2-48 Design and Optimisation of Batch Reactors As mentioned previously, different conditions may give similar objective values. The optimisation techniques can generate a set of solutions around the target from which we can choose the most controllable one.

49 Sensitivity Analysis for Key Variables Fractional yield of R from B Batch cycle time (s) The capability to optimise all the key variables simultaneously makes sensitivity analysis easy, which can bring physical understanding and engineering opportunities Design and Optimisation of Batch Reactors

50 Case Study 3: Synthesis of -Chlorocarboxylic Acids [( ) ] L L L ( 1 L ) MC4A DC4A C4A Cl2 r = y k + k C + k k C + k C + k C r k rc = L Cl ( 522. ) ( ) T T k = e k = e k = y = Cl 2 + C 4 A MC 4 A + HCl 2Cl 2 + C 4 A DC 4 A + 2HCl C 4 A - -monochlorobutanoic acid, DC 4 A -, -dichlorobutanoic acid 2 Catalyst molar fraction 3 Salmi T, Paatero E, Fagerstolt K, Chem. Eng. Sci., 48(1993), pp Design and Optimisation of Batch Reactors The chlorination of Butanoic Acid involves two reactions that both take place in the liquid phase. The reactions are auto-catalytic in terms of the concentration of the desired product a-monochlorobutanoic acid. The kinetic model for the reaction scheme is complex and numerically unstable to solve. The rate of the production of by-product is proportional to the rate of production of the desired product and the chlorine concentration in the liquid phase. The reactions in the liquid phase are accompanied by the absorption of chlorine and desorption of HCl. Both reactions are found to be in slow reaction regime.

51 Problem Data Feed and Reaction Conditions! P = 10 bar! Liquid feed: 13.3 kmoles of C4 A! Gas feed: 100 kmoles of Cl2! Temperature bounds: 100 O C T 500 O C Phase equilibria and mass transfer! HCl2 = H HCl = bar! a = m 2 /m 3, g = 0.5, L = 10-4 m! DCl2 = 6.66*10-9 m 2 /sec, D Cl2 = 8.45*10-9 m 2 /sec Film model for mass transfer Salmi T, Paatero E, and Fagerstolt K, Chem. Eng. Sci., 48(1993), pp Romanainen and Salmi T, Chem. Eng. Sci., 47(1992), pp Design and Optimisation of Batch Reactors The pressure in the reactor is assumed to be constant. Solubility data for both chlorine and HCl, and density of the pure components were taken from the literature. Mass transfer coefficient values were calculated from the experimental data available for pure component diffusivities through a film model.

52 Objective: Optimise Fractional yield of MC 4 A to C 4 A! Batch cycle time! Feed addition rate (semi-batch)! Temperature simultaneously 2-52 Design and Optimisation of Batch Reactors

53 Results Illustration Fraction of total Cl Feed addition rate of Cl 2 Temperature o C Time intervals Time intervals! No recycle, all unreacted and produced gas is discharged, final batch time at 1.03hr! Following the above operating conditions, the fractional yield of MC 4 A to C 4 A can reach 99.7% Temperature profile Design and Optimisation of Batch Reactors

54 Alternative Operating Conditions Feed addition rate of fresh Cl Recycle percentage of gas phase Temperature profile Yield at 99.7% Batch cycle time at 0.9hr Design and Optimisation of Batch Reactors

55 Results and Improvements Reactor & operating mode Fractional yield of MC 4 A to C 4 A! Counter current packed bed (continuous) 66.7%! Mechanically agitated vessel (continuous) 71.7%! Bubble column (continuous) 69.9%!Semi-batch with constant addition rate of Cl 2 (optimised) and constant temperature(optimised) 72.3%!Semi-batch with constant addition rate of Cl 2 (optimised)under optimised temperature profile 72.3%!Semi-batch with optimal addition rate of Cl 2 under optimised temperature profile 99.7% 2-55 Design and Optimisation of Batch Reactors

56 5. Conclusions and Future work 2-56 Design and Optimisation of Batch Reactors

57 Conclusions! Design and optimisation methodology for batch reactors has been developed - Multiphase - Non-isothermal - Different feed addition policies - Different recycle/discharge arrangements - Batch cycle time!validated by different applications! Optimisation framework for dynamic processes 2-57 Design and Optimisation of Batch Reactors Besides the successful application in batch reactor design, the optimisation methodology presented here might prove useful for the optimisations of other dynamic processes.

58 Future Work I!Include different reactor configurations - Mixing - Heat transfer units etc Design and Optimisation of Batch Reactors

59 Future Work II!Design and optimise batch reaction and separation processes simultaneously etc Design and Optimisation of Batch Reactors

60 Future Work III! Design and optimisation when chemistry and kinetics unknown A, B, C? A, B, C, E, F, G! If we only know what we put in and what we get out, how can we optimise the system? Develop model of reaction chemistry and reactor design simultaneously 2-60 Design and Optimisation of Batch Reactors