Optimization-Based Approach to Process Synthesis for Process

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An optimisation-based approach to process synthesis for process intensification: Synthesis of reaction-separation processes Hanns Kuhlmann, Heiner Veith, Marcel Moeller, Kieu-Phi Nguyen, Andrzej Górak, and Mirko Skiborowski Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02225 • Publication Date (Web): 21 Dec 2017 Downloaded from http://pubs.acs.org on December 26, 2017

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Industrial & Engineering Chemistry Research

An optimisation-based approach to process synthesis for process intensification: Synthesis of reaction-separation processes. Hanns Kuhlmann,† Heiner Veith,† Marcel Möller,† Kieu-Phi Nguyen,† Andrzej Górak,‡,† and Mirko Skiborowski∗,† †TU Dortmund University, Department of Biochemical and Chemical Engineering, Laboratory of Fluid Separations, Emil-Figge-Strasse 70, 44227, Dortmund, Germany ‡Lodz Technical University, Department of Environmental and Process Engineering, Department of Heat and Mass Transfer, ul. Wólcza´ nska 213, 90924 Lodz, Poland E-mail: [email protected]

Abstract Process synthesis and intensification are powerful tools for the development of costand energy-efficient chemical processes. However, even though their combination maximises the potential for improvements, they are mostly applied separately. The current article presents the extension of a phenomena-based process synthesis method by an aditional building block for reactor network synthesis and reactive separations. The method facilitates the automatic generation of thermodynamically feasible phenomenabased flowsheet variants by means of superstructure optimisation, which are subsequently translated into equipment-based flowsheets taking into account classical as well as intensified equipment. By composing a flowsheet from mass and energy transfer phenomena instead of pre-defined unit operations, counter-intuitive solutions and

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significant improvements can be achieved. In the current contribution, the capabilities of the method are demonstrated using the transesterification of propylene carbonate with methanol as a case study. The resulting optimal flowsheet represents a combination of integrated and hybrid separation steps for overcoming the intrinsic limitations of this system. The obtained result presents significant cost saving potential compared to those flowsheet variants previously generated by an alternative process synthesis method.

1

Introduction

Conceptual process design, as an initial step during process development, represents one of the most important and complex tasks in chemical engineering. The special importance results from the fact that the decisions made in this early phase determine the major share of the overall costs of the final process 1 . The most important subtask of conceptual process design is process synthesis (PS), which determines the choice of process technologies and their interconnection in order to generate an economically and environmentally favorable process flowsheet. While it has been argued that there is not a single, logic and universal sequence of steps to PS 2 , a remarkable number of different PS methods have been developed in order to systematise PS, such as the well-known hierarchical approach presented by Douglas 3 and Smith and Linnhoff 4 . In order to support the process engineer in generating flowsheet variants, the process design problem is decomposed into subtasks and potential solutions to each task are derived based on heuristic rules 5,6 or analysing thermodynamic insights 7 . Opposed to such a systematic, but iterative procedure, also a simultaneous approach, based on mathematical models of the flowsheet variants and a computer-based optimisation tool can be followed in order to find the best performing solution. Such an optimisation-based PS approach can either be based on a combination of a derivative-free optimisation approach and a commercial process simulator, as first proposed by Gross and Roosen 8 or by an appropriate superstructure model and the direct solution of an according mixed integer nonlinear 2


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programming (MINLP) problem 9,10 . Since the resulting problems are complex to set up and solve 11 , a systematic generation and refinement approach, as in the PS framework presented by Recker et al. 12 presents a reasonable compromise to efficiently address the PS problem. In most of the available PS methods, the generated flowsheet variants are composed of classical unit operations. However, the concept of process intensification (PI) relies on new and innovative apparatuses and unconventional combinations of existing ones, offering significant economical and ecological improvements 13 . PI methods therefore often address debottlenecking of existing processes rather than the design of new processes. However, the biggest impact of PI on process economics and environmental sustainability is to be expected when considered already in the early phase of PS 14 . In order to enable the consideration of PI during PS, one option is the extension of the portfolio of unit operations by intensified equipment. As an example, Holtbruegge et al. 15 collected a database of several conventional and intensified processing techniques such as hybrid and reactive separations and subsequently extended and automated the thermodynamic insight approach 7 . The resulting flowsheet variants can further be evaluated by an optimisation-based design approach, taking into account intensified equipment such as dividing wall columns 16 , hybrid separation processes 17 , and even complete flowsheets for reaction and separation 12 . However, since the consideration of PI principles mostly results in highly integrated processes and the simultaneous consideration of various phenomena, the simulation and optimisation of these process variants demands specialised solution approaches, severely complicating the consideration in PS. One alternative is to perform PS on a lower, more abstract level of aggregation. An extremely low level of aggregation is applied in the elementary process function concept suggested by Freund and Sundmacher 18 and Peschel et al. 19 , in which the best possible process performance is evaluated based on arbitrary modifications of a single representative fluid element performed over the residence time by mass and energy fluxes. While this level of aggregation offers the largest potential for PI and provides an upper bound for improved process performance, the translation into a distinct process design is complex

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and the application was yet constrained to the reaction section for process design. The idea of phenomena-based PS method builds on the composition of a process from the underlying fundamental mechanisms each unit operation is based upon and therefore theoretically is able to represent any kind of chemical process 20–23 . In order to achieve a manageable combinatorial complexity, meaningful combinations of single phenomena (such as mass and heat transfer during phase contacting) can be combined to so-called phenomena building blocks (PBBs) 24–26 . By arbitrarily combining different kinds of PBBs and/or the targeted enhancement of specific phenomena, equipment-specific limitations can be overcome and PI is achieved on the phase and transport scale, the operation and equipment scale as well as the process and plant scale according to the classification of Freund and Sundmacher 27 and Lutze and Sudhoff 28 . In our recent publication, we introduced an automated version of such a phenomena-based PS method, which generates intensified flowsheet variants based on a superstructure of PBBs that are subsequently translated into specific equipment 29 . In contrast to previously presented similar approaches 30,31 , the current method builds on rigorous thermodynamic models, avoiding simplifications that might render the final flowsheet infeasible. While the method was initially introduced with the restriction to separation process design for the case study of ethanol dehydration, this publication addresses a simultaneous design of a reaction and separation process. Thereby, different degrees of integration, including reactive separations, such as reactive distillation and membrane reactors are taken into account. While such a full integration is oftentimes considered superior to an external combination of reaction and separation, the opposite was demonstrated repeatedly (e.g. Recker et al. 12 , He et al. 32 , Urselmann and Engell 33 ). In order to account for the different options, the novel Reactor-Network(RN)-PBB is introduced. This PBB presents a superstructure model for a reactor network that comprises arbitrary combinations of non-isothermal continuously stirred tank reactors (CSTRs), plug flow reactors (PFRs) as well as differential side stream reactors (DSRs). Based on the combination of the RN-PBB with different (reactive) separation PBBs, the

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PS method is capable of generating flowsheet variants with different degrees of integration. Consequently, reactor network synthesis is combined with PI-focused, phenomena-based PS, allowing for a simultaneous consideration of sequential reaction and separation as well as reactive separation processes or a combination of both. After briefly summarising the general framework of the phenomena-based PS approach in Section 2, the reactor network synthesis approach is described in further detail in Section 2.4 for which the new RN-PBB is introduced. The application of the extended PS method is finally demonstrated for a complex case study comprising a transesterification reaction in Section 3.

2

Phenomena-based process synthesis approach

In our previous publication 29 , a multi-step framework for PS was proposed and described in detail, the principle of which is depicted in Figure 1 and outlined in the subsequent sections. The aim of the developed framework is the generation of phenomena-based flowsheet variants based on the combination of PBBs, followed by a subsequent translation into real equipment. Each PBB comprises meaningful combinations of phenomena such as mixing, reactions, energy and mass transfer. These PBBs are therefore similar to the concept of ”aggregated units” introduced by Gavrila and Iedema 34 or the ”simultaneous phenomena building blocks” by Lutze et al. 25 . Performing PS on this level of aggregation bears the advantage of designing flowsheet variants without considering equipment-specific constraints and pre-defined structures of known unit operations 35 . Consequently, a high potential for PI is enabled through an arbitrary combination of PBBs as well as the targeted enhancement of specific phenomena by choosing appropriate equipment in the course of the translation process.

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Figure 1: Process synthesis framework divided into five subsequent steps.

2.1

Process Synthesis Framework

The first step of the presented framework defines the PS problem by specifying the available feed stream(s), the desired product stream(s), potential chemical reactions as well as available utility streams. Additionally, the objective function for optimisation is defined and thermodynamic models and kinetic data of the involved components are collected. In the second step, promising PBBs for each reaction and/or separation step are identified by exploiting thermodynamic insights in order to limit the PS problem size, making use of a modified version of the automatic screening tool developed by Holtbruegge et al. 15 as well as potential information from a reference design. In the third step, the generation of PBB-based flowsheet variants is performed based on a superstructure of the selected PBBs. Figure 2 illustrates the general representation of the superstructure containing the PBBs as basic element, which are interconnected by a distribution network consisting of streams, mixers and splitters 36 . The PBB models are implemented in the equation-based simulation software Aspen Custom Modeler (ACM)® and connected to built-in procedures, which access the databases and property calculation routines of Aspen Properties® . Each PBB in the superstructure is substituted by a specific entity in the course of the optimisation, whereas the generic mixers allow for modifications of pressure, temperature and phase state of the entering stream through addition or removal

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of heat and eletrical power. The generic combination of PBBs allows for the exploitation of integration on various levels, e.g. thermal coupling as well as hybrid and reactive separation processes.

Figure 2: Upper section: Scheme of a generic superstructure of nP BB PBBs with nF feed and nP product streams. Lower section: Scheme of a PBB with corresponding mixers and splitters.

The superstructure entails a set of continuous and discontinuous design degrees of freedom (DDoF), which determine the activation/deactivation of the PBBs as well as their interconnection and operating variables such as operating pressures. These DDoF are optimised with respect to the specified objective function in order to automatically generate PBBbased flowsheet variants and find the best performing one among them. The optimisation problem is addressed by a memetic optimisation algorithm, which combines an evolutionary strategy for the exploration of the search space and the optimisation of the discrete DDoF with a deterministic optimisation algorithm for the local refinement of continuous variables. The performance of different flowsheet variants is evaluated and compared based on the objective function Ω, which provides an estimation of the operating costs as well as 7



selected investment costs of each element of the superstructure. A meaningful estimation of investment costs is only possible in case specific equipment can already be fixed or needs to be considered because a major impact on the economic performance is to be expected. Furthermore, user defined penalty functions are added, which e.g. penalise the deviation from a desired product purity specification. Details on the objective function are provided in the Supporting Information. In the fourth step, the best performing PBB-based flowsheet variants are further translated into equipment-based flowsheets, considering conventional as well as intensified equipment. For the translation, at first a reformulation to rate-based models is performed, whereas characteristic mass and energy transfer coefficients are correlated with cost functions and considered as additional DDoF during a local optimisation of the flowsheet. Based on the results, an investigation of equipment size and cost is performed to identify suitable equipment and decide whether the use of intensified equipment such as rotating packed beds (RPB) is expected to be beneficial. In the last step of the framework, the necessary equipment-specific correlations for a rigorous calculation of hydrodynamics as well as reaction, mass and energy transfer kinetics are gathered and detailed rate-based models are applied for evaluating the most promising equipment-based flowsheet. Since the process flowsheet is already fixed at this stage, the last step is considered as optional for a detailed design of the process. A detailed description of the different steps of the framework, including the optimisation approach, the translation procedure and the mathematical models is given in the initial publication 29 . The following subsection will provide a brief overview of the pre-existing PBBs, while the novel RN-PBB is introduced and validated in the subsequent section.

2.2

Phenomena building blocks

In the current version, the vapour-liquid-(VL-) and liquid-liquid-(LL)-PBB describe the single- or multistage contacting of a vapour and liquid phase or two immiscible liquid phases, 8


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respectively. Furthermore, the vapour-permeation-(VP-) and pervaporation-(PV-)PBB describe the contacting of two vapour phases and one vapour with one liquid phase, respectively, which are separated by a selective membrane. For each of these PBBs it is optional to implement chemical reactions in the involved phase(s), allowing for the synthesis of reactive separation processes. The VL-PBB and VP-PBB were introduced in detail in the preceding publication 29 . The LL- as well as the PV-PBB are very similar to these two building blocks and will be further elaborated in a future contribution in combination with an additional suitable case study to demonstrate the application. The feasibility of the generated PBB-based flowsheet variants is warranted by the consideration of rigorous thermodynamic models for each PBB. Thermodynamic equilibrium is exploited as idealised assumption of perfect mixing and 100% efficiency, unless facilitated transport requires the consideration of transport kinetics (e.g. for membrane separations). Thereby, mass and energy transport are assumed to be limited by intrinsic non-idealities such as phase equilibria only, not by equipment-specific limitations such as non-ideal mass or energy transfer. In case of reactions, however, equilibrium does not necessarily represent the ideal state. As an example, incomplete conversion in the reaction step could be beneficial in terms of operating costs caused by a subsequent separation, which requires the consideration of reaction kinetics during PS. This is especially important in case of multiple competing reactions, since they have a decisive influence on the selectivity towards a certain component. However, in case of single equilibrium-limited reactions, the assumption of reaction equilibrium can still be a meaningful measure for simplification of the optimisation problem, which is established case-dependent.

2.3

Reactor network synthesis

The optimal choice of a reactor network can be determined by different methods, including superstructure optimisation. Nevertheless, the probably best known reactor network synthesis method is the attainable region concept, which was initially developed by Horn 37 . 9



This concept allows to determine all attainable product compositions for a given feed by means of a graphical or geometrical analysis, taking into account arbitrary combinations of mixing and different basic reactor concepts 38 . While Glasser et al. 39 applied this method to isothermal systems with constant volume restricting the analysis to combinations of CSTRs and PFRs, Feinberg and Hildebrandt 40 focused on DSRs for synthesising reactor networks. Especially the boundary of the attainable region is of particular interest, as it represents the maximum concentrations that can be achieved by the reactor network 41 . Based on a mathematical study of the underlying reaction system, Feinberg and Ellison 42 provided a method for determining the maximum number of CSTRs that need to be considered in order to accurately determine this boundary. While presenting a very helpful tool for process analysis, the attainable region concept also presents some limitations in the context of PS. Especially when investigating non-isothermal reactor networks, the graphical study of the attainable region is limited 43 . In this case, the attainable compositions are not only defined by reaction and mixing, but also by external heat transfer. In combination with multiple reactions, this results to a multi-dimensional space, which cannot be analysed graphically. Therefore, Zhou and Manousiouthakis 43 combined the IDEAS framework 44,45 with a shrink-wrap algorithm in order to determine the attainable region for non-isothermal reactor networks. Even if the attainable region can be accurately and efficiently determined, it provides only information on the maximum achievable product compositions and not the attributed costs. It yet provides an excellent tool for process analysis, in order to determine the existence of a feasible solution. One of the first methods establishing a superstructure for the optimisation of reactor networks was proposed by Aris 46 , who applied dynamic programming for a combination of CSTRs and PFRs. Jackson 47 studied the influence of the flow configuration on the performance of a reactor network superstructure consisting of PFRs, which are connected by side streams. This superstructure method was modified by Achenie and Biegler 48 using axial dispersion reactors for the synthesis of complex reactor networks with external heat ex-

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change. Kokossis and Floudas 49 presented an extensive superstructure consisting of CSTRs and PFRs, which are approximated as a cascade of CSTRs. Furthermore, different feeding, recycling and bypassing strategies were included in order to realise complex flow configurations. Further methods have been proposed, combining stochastic optimisation and mathematical programming in order to solve the reactor network synthesis problem on the basis of general superstructures of CSTRs and PFRs 50–53 . However, in most of these methods some sort of model simplification is established in order to reduce the computational effort such as the quasi linear programming method applied by Soltani and Shafiei 53 . One major advantage of such superstructure optimisation approaches is the fact that the number of considered reactors is variable and that a distinct objective function, other than the maximum product composition, can be implemented. Furthermore, non-isothermal reactor networks for complex reaction systems containing multiple consecutive and parallel reactions can be determined without specific modifications. However, the resulting MINLP problems can become severely complex to solve.

2.4

Novel Reactor-Network-PBB

Taking into account the structure of the introduced PS method, the implementation of a superstructure-based reactor network model presents a straight forward extension that is expected to work well with the memetic optimisation approach, considering the positive results reported in literature 50–53 . The novel RN-PBB is therefore based on a combination of the basic reactor concepts, CSTR, PFR and DSR, whereas the latter are approximated by a series of CSTRs in accordance with the CSTR equivalence principle introduced by Feinberg and Ellison 42 . As such, the novel RN-PBB extends the portfolio of (reactive) separation PBBs, introduced in the preceding work 29 and summarised in the previous section. The novel RN-PBB models a generic reactor network consisting of an arbitrary interconnection of non-isothermal CSTRs, PFRs and DSRs for single-phase reactions. It has potentially 11



two input streams and one output stream, and comprises the phenomena reaction and mixing in vapour or liquid phase, stream mixing and separation as well as external heat transfer. As illustrated in Figure 3, the RN-PBB is subdivided into a series of nRN discrete elements, whereas each one contains a single CSTR and a subsequent PFR, which is approximated by means of a series of nCST R CSTRs. Besides the reactor models, each discrete element contains two mixers upfront the reactors and two splitters, which enable the distribution of the side stream (feed 1) to any CSTR and PFR or a bypass of the discrete element.

Figure 3: Scheme of the RN-PBB with a generic discrete element consisting of one CSTR and one PFR.

All q ∈ {1, . . . , (nCST R + 1)} CSTRs in each discrete i ∈ {1, . . . , nRN } are modelled by means of an energy balance, component balances for each component j ∈ {1, . . . , nC } and a

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summation constraint

out n˙ out RN,CST Ri,q · zRN,CST Ri,q,j , in Reac n˙ in RN,CST Ri,q · zRN,CST Ri,q,j + rRN,CST Ri,q,j · VRN,CST Ri,q =

(1)

in out ˙ ex n˙ in ˙ out RN,CST Ri,q · hRN,CST Ri,q + QRN,CST Ri,q = n RN,CST Ri,q · hRN,CST Ri,q ,

(2)

nC X

out zRN,CST Ri,q,j = 1.

(3)

j=1

Therefore, the ingoing and outgoing streams of each CSTR are characterised by molar in in flow rate, composition and specific enthalpy (n˙ in RN,CST Ri,q , zRN,CST Ri,q,j , hRN,CST Ri,q and out out n˙ out RN,CST Ri,q , zRN,CST Ri,q,j , hRN,CST Ri,q ). The changes caused by the CSTR are determined Reac from the reaction rate rRN,CST Ri,q,j and the hold-up, which is denoted by VRN,CST Ri,q and

indirectly considered as a DDoF. Consequently, the existence of a reactor can be modelled without the necessity of additional integer variables by simply allowing for hold-ups above or equal to zero. The expression of the reaction rate depends on the reaction kinetic and is therefore specific for the case of application. Besides the hold-up for each CSTR, the pressure pRN is also considered as a DDoF but is assumed constant in the complete RNPBB. Modifications of the pressure are important to allow for variations of the temperature while considering and avoiding potential (partial) phase transition. The required specific enthalpies are calculated by means of built-in Aspen Properties® procedures

in in hin RN,CST Ri,q = f (TRN,CST Ri,q , pRN , z RN,CST Ri,q ),

(4)

out out hout RN,CST Ri,q = f (TRN,CST Ri,q , pRN , z RN,CST Ri,q ),

(5)

which inherently consider the heat of reaction in terms of the variation of the specific enthalpies. Additional heat (Q˙ ex RN,CST Ri,q ) can be supplied to or withdrawn from each CSTR out in order to adjust its temperature. Therefore, the temperature of each CSTR TRN,CST Ri,1 out and PFR TRN,P F Ri are considered as DDoF of the RN-PBB as well. The temperature of all

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CSTRs that are approximating a PFR is however restricted to equal to the PFR temperature out out (TRN,CST Ri,2 = . . . = TRN,CST Ri,n

CST R +1

out = TRN,P F Ri ). Ideal heat transfer is assumed during

the generation of flowsheet variants in order to exploit the full potential of the RN-PBB. The total external heat added to or withdrawn from each PFR Q˙ ex RN,P F Ri is calculated by summation of the heat transfer for all embedded CSTRs

Q˙ ex RN,P F Ri =

nCST R +1 X

Q˙ ex RN,CST Ri,q .

(6)

q=2

Furthermore, the split factors of each splitter r in discrete i ξRN,Si,r are considered as DDoF, which allow for the distribution of the first feed among the CSTR and PFR. The balance equations of both splitters for each discrete i ∈ {1, . . . , nRN } are n˙ in ˙ out,1 ˙ out,2 RN,Si,r = n RN,Si,r + n RN,Si,r ˙ in n˙ out,1 RN,Si,r RN,Si,r = ξRN,Si,r · n

, r = 1, 2, , r = 1, 2.

(7) (8)

The variable n˙ in RN,Si,r denotes the inlet molar flow rate of splitter r in discrete i, whereas n˙ out,1 ˙ out,2 RN,Si,r and n RN,Si,r are the outlet molar flow rates directed to the subsequent splitter and mixer, respectively. No modification of the composition and temperature is performed by the splitter. The split factor of the second distributor of the last discrete ξRN,SnRN ,2 is set to zero in order to obtain only one product output stream for the entire RN-PBB. For each mixer, component and energy balances are considered, while no reaction is considered to occur in the mixer. Each CSTR and PFR is characterised by their specific residence times (τRN,CST Ri,1 , τRN,P F Ri ) which are considered as DDoF. For the PFR, the total residence time is equally divided among all embedded CSTRs

τRN,CST Ri,q =

τRN,P F Ri nCST R

, q = 2, . . . , (nCST R + 1),

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(9)

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resulting also in approximately equal hold-ups for each of the CSTRs. The residence time of Reac each CSTR τRN,CST Ri,q is used to calculate its volume VRN,CST Ri,q whereas the total volume Reac of the PFR VRN,P F Ri is calculated as the sum of the embedded CSTRs

Reac VRN,CST Ri,q =

Reac VRN,P F Ri

=

τRN,CST Ri,q · n˙ out RN,CST Ri,q ρmolar,out RN,CST Ri,q

nCST R +1 X

, q = 1, . . . , (nCST R + 1),

Reac VRN,CST Ri,q .

(10)

(11)

q=2

In order to optimise the reactor network, an objective needs to be specified, which aligns with the previously introduced form of the objective function for the phenomena-based PS 29 . In order to prevent excessive reaction volumes, an additional share for investment costs is considered for the RN-PBB besides the operating costs for heating or cooling for each of the implemented reactors. Details on the cost calculation for the RN-PBB can be found in the Supporting Information.

2.5

Validation of the RN-PBB

In order to demonstrate the capability of determining promising reactor networks with the novel RN-PBB in combination with the presented PS approach, the application for two well known test reaction systems is further demonstrated. These are the Van de Vusse 54 and the Denbigh 55 test reaction systems, which have been investigated by various reactor network design methods. For the subsequent investigations, a single RN-PBB was optimised with the current method, taking into account the specific reaction kinetics, whereas energy balances were neglected due to the simplified reaction schemes without any information on real components.

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2.5.1

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Van de Vusse Test Reaction System

The van de Vusse reaction system illustrated in Figure 4 comprises one parallel and one consecutive reaction of general components A, B, C and D 54 . This test reaction was investigated multiple times to quantify the performance of reactor network synthesis methods 49,52,56,57 . For the investigation, a single feed stream of 1 L s−1 of pure A is set according to Jin et al. 52 . Component B represents the target product of this reaction.

Figure 4: Van de Vusse reaction system with reaction rates. Table 1 summarises the two different scenarios considered for this reaction, as well as the Reac resulting composition of the target product xB and the overall hold-up VRN , which were

considered as alternative objective functions for the optimisation. The product composition determined in the first scenario is fixed in the second scenario. Table 1: Two different optimisation scenarios for the van de Vusse reaction. Scenario

nRN [-]

nCST R [-]

xB [mol mol−1 ]

3 VReac RN [m ]

Objective

1 2

2 2

2002 2002

0.68745 0.68745

2.628 · 10−4 2.601 · 10−4

Maximise xB Reac Minimise VRN

In order to demonstrate that a large model can be handled, a very large number of 1000 CSTRs was chosen for approximating each PFR, even though a significantly smaller number should suffice. The optimal reactor network resulting for the first scenario is illustrated in Figure 5 and comprises a CSTR that is partially bypassed as well as a subsequent PFR. The obtained product composition of xB = 0.68745 mol mol−1 and the reactor network design is in excellent agreement with the best reported result that was presented by Jin et al. 52 . The 16


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resulting reactor network for the second scenario has a similar structure, but results in a slightly reduced overall hold-up, while producing the same product composition. In both scenarios, one CSTR and one PFR were discarded during the optimisation.

Figure 5: Optimal reactor network for setup 1 of the van de Vusse reaction.

2.5.2

Denbigh Test Reaction System

The Denbigh test reaction system 55 , which has also been investigated as test case for other reactor network synthesis methods 49,52 , comprises one parallel and two consecutive reactions involving the generalised components A, B, C, D and E as demonstrated in Figure 6. For the investigation, a single feed at 100 L s−1 of pure A is assumed 52 . Furthermore, component C is considered as the target product. The temperature independent reaction rates are given in Figure 6 as well.

Figure 6: Denbigh reaction system with reaction rates.

Table 2 summarises the two different scenarios considered for this reaction, as well as Reac the resulting composition of the target product xC and the overall hold-up VRN , which

were considered as alternative objective functions for the optimisation, whereas the product composition determined in the first scenario is fixed in the second scenario.

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Table 2: Two different optimisation scenarios for the Denbigh reaction. Scenario

nRN [-]

nCST R [-]

xC [mol mol−1 ]

3 VReac RN [m ]

Objective

1 2

3 3

1001 1001

0.62096 0.62096

124.49 27.27

Maximise xC Reac Minimise VRN

The resulting optimal reactor networks for both scenarios are illustrated in Figure 7. Although the superstructure allows for the use of three sequential combinations of a CSTR and a PFR, the optimal reactor network obtained for scenario one contains only one PFR followed by two CSTRs. This results equals the result determined by Jin et al. 52 using a global optimisation approach. In the second scenario, the reactor network is modified by exchanging the last CSTR by a PFR, whereas the total required reaction volume and consequently the investment costs are significantly reduced.

Figure 7: Optimal reactor networks for scenario 1 (top) and scenario 2 (bottom) of the Denbigh reaction.

Further details and an interpretation of the results of the two test reaction systems are provided in the Supporting Information.

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3

Case Study: Transesterification of propylene carbonate

In order to illustrate the capabilities of the developed PS method, it is applied to a complex case study considering the transesterification of propylene carbonate (PC) with methanol (MeOH) to di-methyl carbonate (DMC) and 1,2-propanediol (PDO), which has been extensively investigated theoretically as well as experimentally by Holtbruegge et al. 58–62 . Both DMC and PG have versatile chemical properties as well as several large-scale applications, with e.g. DMC being used in the production of electrolytes for lithium ion batteries 63 and PDO as a solvent in various cosmetics and as de-icing fluid for aircrafts 64,65 . In the final contribution of Holtbruegge et al. 62 , several intensified flowsheet variants were developed on an expert-knowledge basis and optimised individually by means of a combination of a memetic optimisation algorithm and a simulation model in ACM® , which considered experimentally validated rate-based models of the involved unit operations. The resulting intensified flowsheet variants showed a significant economic potential over the considered base-case design. The results of this study therefore serve as reference for the current investigations in which the potential benefits of the developed PS method are to be evaluated. The subsequent sections present the application of the five successive steps of the introduced PS method.

3.1

Step 1: Problem definition and analysis

The key to the desired conversion is an exothermic chemical-equilibrium limited transesterification reaction that is illustrated in Equation 12. The reaction occurs in the presence of the homogeneous catalyst sodium methoxide 66 . The reactants PC and MeOH are converted into the two target products DMC and PDO.

P C + 2M eOH DM C + P DO

19


(12)


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The reaction equilibrium and kinetics have been experimentally investigated and modelled by Holtbruegge et al. 66 . The reaction rate

r(T ) = νj · ka (T ) · wcat · V

Reac

·

1 M

3

· aP C · a2M eOH −

1 · aDM C · aP DO , Ka (T )

(13)

is described by means of an activity-based approach as a function of the stoichiometric coefficient νj and the activity of each component aj , as well as the catalyst mass fraction wcat , the average molar mass M , the reaction volume V Reac , the reaction rate constant ka (T ) and the equilibrium constant Ka (T ). The reaction rate constant is further expressed by an Arrhenius equation in order to account for its temperature dependency

ln(ka (T )) = 24.73 − 3494.63 · T −1 ,

(14)

while the influence of the temperature on the activity-based chemical equilibrium constant Ka is described as ln(Ka (T )) = −5.41 + 1145.25 · T −1 .

(15)

For consistency reasons the same thermodynamic property models that were used by Holtbruegge et al. 62 were applied for the current study as well, making use of the built-in procedures of ACM® . In specific, the UNIQUAC gE model was used in order to describe the non-ideality of the liquid phase 67 , whereas ideal behaviour of the vapour phase was assumed. For details on the applied thermodynamic models and the parameters, refer to the paper of Holtbruegge et al. 62 . The mixture exhibits a non-reactive binary azeotrope between the product component DMC and the substrate MeOH, which occurs at a composition of wM eOH =0.701 kg kg−1 and represents the lowest boiling point of the system 68 . The atmospheric boiling point temperatures of the azeotrope and the components are given in Table 3.

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Table 3: Pure component and azeotrope boiling point temperatures at atmospheric pressure. National Institute of Standards and Technology 69 . AZ[MeOH/DMC] Boiling point temperature [K]

336.8

MeOH DMC 337.7

363.2

PC

PDO

513.1

460.3

For PS, the desired product purities of 0.999 kg kg −1 for DMC and = 0.990 kg kg −1 for PDO at an annual production capacity of 13,600 t DMC are specified in accordance with the scenario considered by Holtbruegge et al. 58 as well.

3.2

Step 2: Selection of PBBs

In order to identify a subset of suitable PBBs, one of the flowsheet variants from Holtbruegge et al. 62 was analysed and decomposed. The translation of the reference flowsheet into a PBB-based version is illustrated in Figure 8. This translation does not only allow for the analysis of different suitable PBBs and the minimum number of required PBBs to depict the flowsheet, but can further be used for a comparison with novel flowsheet variants determined by the developed PS method, taking into account the same objective function.

Figure 8: Left: Reference flowsheet adapted from Holtbruegge et al. 62 . Right: PBB-based representation of the reference flowsheet (Dark grey: reactive section, Liquid, Vapour). 21



In this process variant, the feed streams are introduced into a reactive distillation column that converts the substrates to a large extend, while producing the desired PDO product as bottom product as well as the low-boiling azeotrope as the top product. Inside the stripping section, DMC is transferred to the vapour phase and removed to the top of the column, such that the reactive distillation column overcomes the reaction equilibrium limitations of a reactor without additional separation. The high-boiling homogeneous catalyst enters the column with the MeOH feed and is considered non-volatile 62 . Consequently, the reaction is considered to be limited to the stripping section, which is furtheron referenced as reactive section. In order to achieve a high conversion of PC in the reactive distillation column, MeOH is fed in excess to the column. In order to achieve also a high conversion of MeOH, it has to be recovered from the top product and recycled to the column. DMC presents the second valuable product of the process that has to be produced at the specified purity. In this configuration, a hybrid separation process consisting of a distillation column and a hydrophilic VP membrane is used to perform the MeOH-DMC separation. Based on the decomposition of the process, it becomes obvious that four (reactive) VL-PBBs and at least one VP-PBB are required to generate the PBB-based reference flowsheet. The PS problem is divided into the two subprocesses Reaction-Separation and DMC Purification according to Figure 8. The target products of the first subprocess are PDO at the specified purity and a second product at approximately azeotropic composition of DMC and MeOH. Two feed streams enter the process, a pure PC feed and a MeOH feed that comprises fresh MeOH (twice the amount of PC to consider the stoichiometry of the reaction) and recycled MeOH from the DMC Purification subprocess containing a minor DMC impurity. The amount and composition of the recycle stream is estimated from the reference flowsheet. The first product of the Reaction-Separation subprocess is specified as feed stream for the DMC Purification subprocess. The target products of that subprocess are DMC with the specified purity as well as the MeOH recycle stream to the Reaction-Separation subprocess. In the following, these two subprocesses are addressed as independent PS tasks, whereas their

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fixed interconnection allows for a subsequent reintegration of the best solutions into a single flowsheet. While this results in a limitation of the design space, it allows for a reasonable simplification of the overall PS problem to be efficiently addressed by the current PS method using rigorous PBB models. It also provides insight in how far the single subprocesses could be modified, which would be interesting for a retrofit design. Based on the local optimisation of the PBB-based representation of the reference flowsheet, the resulting TAC estimates are also introduced in Figure 8. These values serve as a reference for the evaluation of the new flowsheet variants that are to be developed by the PS method. For the Reaction-Separation subprocess, the analysis of the reference flowsheet reveals that two VL-PBBs with activated liquid-phase reaction suffice to obtain the desired products. In the following, VL-PBBs with simultaneous reaction in the liquid phase are labeled as VL-RPBB. For the application of the PS method, the novel RN-PBB is additionally considered in order to allow for the generation of the sequential arrangement of reaction and separation, reactive separation or a combination of both. As a further simplification, it is assumed that reaction equilibrium is reached in the reaction and for each stage of a reactive separation. For the DMC Purification subprocess, VL-PBBs and VP-PBBs are used in the reference flowsheet and are therefore considered for the PS method. The separation performance of the VP-PBB requires a kinetic model for which the experimentally validated model from Holtbruegge et al. 60 ,61 for the hydrophilic membrane Pervap1255-30 from Sulzer Chemtech Ltd. is considered. Details on the applied solution-diffusion model are given in the publications of Holtbruegge et al. 60 ,61 , whereas a short summary is provided in the Supporting Information.

3.3

Step 3: Generation of PBB-based flowsheet variants

After the selection of suitable PBBs for the two subprocesses, the PS method was applied to derive PBB-based flowsheet variants based on the optimisation of the superstructure with respect to an economic objective which primarily considers the operating costs 29 . For the 23



definition of the superstructure, the number of PBBs has to be defined, taking into account a compromise between structural flexibility and the complexity of the optimisation problem, which grows exponentially with the number of PBBs. Therefore, a maximum number of four VL-PBBs and two RN-PBBs was specified for the Reaction-Separation subprocess, whereas a maximum number of two VL-PBBs and two VP-PBBs was specified for the DMC Purification subprocess. Further specifications and the results of the PS method are described individually for each subprocess.

3.3.1

Reaction-Separation subprocess

In addition to the maximum number of PBBs for the specification of the superstructure, also a minimum number of one VL-PBBs was specified, since a RN-PBB alone would not be able to satisfy the product specifications. The distribution network further considered the two feed streams, whereas stream splitting was restricted to splitters subsequent to VLPBBs in order to avoid unnecessarily complex flowsheets. Besides the selection of PBBs and their interconnection, the activation of the liquid phase reaction in the VL-PBBs as well as the operating temperature of the RN-PBBs, being limited between 40 ◦ C and the boiling point temperature of the mixture, were considered as DDoF during the optimisation. Penalty terms were added to the objective function to account for a violation of the product specifications. Further details on the parameters of the evolutionary strategy as well as the penalty functions are provided in the Supporting Information. The evolutionary strategy operated on a population of 10 individuals for 955 generations, resulting in the evaluation of 9550 solution vectors, which passed the structural screening procedure. The optimisation process was stopped since the objective function of all individuals remained within a pre-defined tolerance of 5 % over a period of 100 generations. While the initialisation of such an optimisation problem is extremely challenging, since no sequence of PBBs is specified upfront and the single PBBs can be strongly integrated, the developed structural screening and initialisation procedure 29 performed well.

24


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Overall, 59 % of the evaluated solution vectors that passed the structural screening resulted in converged and locally optimised flowsheet evaluations. Out of the converged flowsheet variants, 245 satisfied the imposed purity specifications. However, not all of these flowsheet variants are structurally different. The generic definition of the superstructure leads to the generation of structurally equivalent flowsheets, for which the solution vector is different, but only the order of selected PBBs is exchanged without influencing the general topology and functionality of the flowsheet. Considering only the type and number of selected PBBs and the distribution of the feed streams, it can be concluded that for this subprocess, at least 38 structurally different flowsheet variants were generated, which satisfied the purity constraints. The best performing one is illustrated in Figure 9.

Figure 9: Best result of the superstructure optimisation for the first subprocess (Dark grey: reactive section, Liquid, Vapour)

25



Although up to four VL-PBBs and two RN-PBBs could be used, the best flowsheet variant is composed of only two VL-R-PBBs. The PC feed enters the liquid input of VLR1 and the MeOH feed that of VL-R2. The main difference to the reference flowsheet is the modification of feed position and the reaction in both VL-R-PBBs, which entails that catalyst is provided with the PC feed rather than the MeOH feed. These modifications result in high concentrations of both reactants in the liquid phase and especially in VL-R1, where most of the conversion is achieved. In the reference flowsheet, the reactive distillation column requires a high reflux ratio in order to ensure a high concentration of the the lowboiling reactant MeOH in the stripping section. This results in increased operating costs due to the high reboiler duty. Nevertheless, this suboptimal solution considered by Holtbruegge et al. 62 was also a consequence of the low solubility of the homogeneous catalyst in PC, which therefore had to be introduced with the MeOH feed. The results of the PS method show that a reduction of the TAC by 39 % compared to the reference flowsheet would be possible if this restriction could be overcome. The technical feasibility of the catalyst distribution will be addressed during the translation into equipment-based flowsheets in Section 3.4. Figure 10 shows two additional flowsheet variants that were generated by the PS method, each including two VL-R-PBBs and one RN-PBB. In both flowsheet variants, the VL-RPBBs are present in a configuration equivalent to a reactive distillation column. While the RN-PBB is included as a typical side stream reactor in flowsheet variant a), it presents a classical pre-reactor in flowsheet variant b). While being inferior to the previously presented best solution, these configurations also result in estimated TAC savings of 33 % and 24 % compared to the reference flowsheet.

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Figure 10: Alternative flowsheet variants for the first subprocess. (Dark grey: reactive section, Liquid, Vapour).

3.3.2

DMC Purification subprocess

In order to be split the azeotrope, one of the VP-PBBs was always activated. Furthermore, the distribution network considered a single feed stream, whereas stream splitting was again restricted to splitters subsequent to VL-PBBs. In addition to the potential condensation of the product stream after each VP-PBB, the continuous DDoF were confined to a feed pressure between 1.5 bar and 5.0 bar, a permeate pressure between 0.02 bar and 0.15 bar and the retentate factor, which is the ratio of retentate to feed flowrate, between 0.30 and 0.99. Refer to Kuhlmann and Skiborowski 29 for further details on the models and the Supporting Information for further details on the specification of the evolutionary strategy. After the structural screening, a total of 4280 solution vectors were evaluated in the course of the optimisation. Again, the optimisation process was stopped due to the fulfillment of the aforementioned termination condition. The performance of the screening and initialisation approach even was slightly better for this optimisation problem. Overall, more than 72 % of the solution vectors that passed the structural screening procedure resulted in converged 27



and locally optimised flowsheet evaluations. Out of the converged flowsheet variants, 1403 satisfied the imposed purity specifications. However, only at least 12 of them represent different flowsheet structures, taking into account the analysis of selected PBBs and feed streams. This can be attributed to the larger flexibility offered by the increased size of the superstructure. The best performing flowsheet variant is illustrated in Figure 11.

Figure 11: Best result of the superstructure optimisation for the second subprocess ( Liquid, Vapour). Again, the general structure of the flowsheet appears to be similar to the reference flowsheet containing one VP-PBB and two VL-PBBs. However, the interconnection of the PBBs is distinctively modified, feeding not only the first product from the Reaction-Separation subprocess and part of the vapour outlet stream of VL1 to the VP-PBB, but also the complete vapour outlet stream of VL2. The MeOH-rich permeate of the VP-PBB is condensed and recycled to the Reaction-Separation subprocess. The DMC-rich retentate is fed to the vapour input of VL1, other than in the reference flowsheet, where it is condensed and fed to the liquid input of VL2. Overall, the flowsheet appears like a distillation column with the 28


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VP membrane connected via side streams. A significant reduction of the reboiler duty is achieved, resulting in a reduction of the TAC by 14 % compared to the reference flowsheet. An investigation of the single modifications shows that the savings can mainly be attributed to the absence of the retentate condensation, which as a single modification of the reference flowsheet results in TAC savings of 12 %. However, this also proofs that both modifications have a positive effect, as an additional 2 % savings can be achieved by the sidestream configuration.

3.4

Step 4: Translation into equipment-based flowsheets

While the PBB-based flowsheet variants promise significant saving potential compared with the PBB-based translation of the reference flowsheet, a more detailed comparison based on equipment-based flowsheets needs to be conducted in order to validate these saving potentials considering detailed equipment-specific models and constraints, as well as an updated objective function with distinct cost correlations for the selected equipment. This subsection first deals with the identification of suitable equipment for the translation into equipment-based flowsheets, considering the translation procedure introduced in Kuhlmann and Skiborowski 29 . The evaluation of these equipment-based flowsheets is performed in the subsequent subsection in step five of the PS method.

3.4.1

Reaction-Separation subprocess

The best PBB-based flowsheet for the Reaction-Separation subprocess indicated in Figure 9 is composed of two VL-R-PBBs for which in a first step, the equilibrium-based model was transformed to a rate-based model. Besides the continuous DDoF, also the combined mass transfer coefficient kL A was optimised. This variable represents a combination of the volume of the VL-R-PBB, the effective interfacial area as well as the liquid-side overall volumetric mass transfer coefficient, which was assumed to be equal for all components in this step. Furthermore, the assumption of chemical equilibrium was replaced by a detailed 29



description of the reaction rate, taking into account Equations 13 to 15, whereas the liquidphase reaction volume of the VL-R-PBBs VVReac,L was considered as DDoF as well. Based L on the results and a database of characteristic ranges for various vapour-liquid contacting equipment, so-called design windows were derived and the minimum dimensions of each type of equipment were calculated, which are necessary for providing the required liquid-phase reaction volume. Refer to Kuhlmann and Skiborowski 29 for further detail on the translation procedure. The results are summarised in Table 4, while illustrations of the corresponding design windows are provided in the Supporting Information. Table 4: Relevant information for translating the best flowsheet of the first subprocess. Variable

VL-R1

VL-R2

V˙ VVL [m3 h−1 ] kL A [m3 s−1 ] ρL [kg m−3 ] ρV [kg m−3 ] [m3 ] VVReac,L L

7387 0.0485 908 1.35 5.98

7561 0.3977 887 1.26 18.86

Based on the analysis of the design windows, the spray column, packed columns with structured or random internals for both VL-R-PBBs as well as a tray column for VL-R2 were evaluated as feasible equipment. Based on the estimated equipment dimensions, an estimation of the corresponding investment costs was performed and the results are indicated in Figure 12. The results show that a spray column should present the most economic choice for VL-R1, while a tray column would be an economic choice for VL-R2. Both are advantageous compared to the packed column due to the ease of implementing a larger liquid phase reaction volume, while operating without or with less expensive internals. However, considering the benefits of implementing several PBBs in a single equipment, the translation of both VL-R-PBBs into a single spray column is favoured.

30


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Figure 12: Investment cost comparison for both VL-R-PBBs of the first subprocess.

3.4.2

DMC Purification subprocess

The same translation procedure was applied to the best PBB-based flowsheet for the DMC Purification subprocess indicated in Figure 11. Table 5 summarises the results for both VL-PBBs obtained after the optimisation. These results are further processed for the identification and sizing estimation of suitable equipment. Table 5: Relevant information for translating the best flowsheet of the second subprocess. Variable

VL1

VL2

V˙ VVL [m3 h−1 ] kL A [m3 s−1 ] ρL [kg m−3 ] ρV [kg m−3 ]

2508 0.0030 975 1.97

276 0.0097 975 2.21

Based on the evaluation of the design windows, for which illustrations are provided in the Supporting Information, an RPB, a spray column and a packed column with structured or random internals were identified as suitable equipment for both VL-PBBs. Furthermore, a tray column presents an additional option for VL2. The investment cost estimates for the different equipment options, which are illustrated in Figure 13, show that a packed 31



column with structured internals presents the most economic solution for both VL-PBBs. The packed column with structured internals is comparably small and favoured in terms of mass transfer and hydrodynamics compared to the spray column. The RPB would allow for further size reduction, but at significantly increased costs due to the more complex design. Consequently, a structured packed column was selected as translation of both VL-PBBs.

Figure 13: Investment cost comparison for both VL-PBBs of the second subprocess.

Besides the VL-PBBs, the PBB-based flowsheet further contains a VP-PBB, which already presents a rate-based model for a specific membrane. The translation procedure was therefore concerned with the selection of a specific type of membrane module, making a selection based on a decision tree, which takes into account considerations related to membrane fouling, operating pressure as well as membrane material. Details on the decision tree are provided in Kuhlmann and Skiborowski 29 where it is detailed in the Supporting Information. For the current case study a capillary module, a hollow fine fiber module, a plate-and-frame module as well as spiral wound membrane module were determined as suitable options. For ease of comparability, a plate-and-frame module was selected, since this type of module was also considered by Holtbruegge et al. 62 .

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3.5

Step 5: Optimisation of equipment-based flowsheets

Based on the results from the translation procedure, detailed non-equilibrium equipment models with equipment-specific correlations for calculating hydrodynamics as well as mass and energy transfer were set up in order to determine an optimal equipment-based process design. The two subprocesses were furthermore combined to a single flowsheet, for which the two VL-PBBs of each subprocess were represented by distillation columns. However, instead of implementing a model for a spray column for the Reaction-Separation subprocess, both columns were modelled as packed columns, in order to allow for a direct comparison with the reference flowsheet, taking into account the same models as used by Holtbruegge et al. 62 . The models were implemented in ACM and are briefly summarised in the following.

3.5.1

Simulation models

The (reactive) distillation columns were modelled by means of non-equilibrium stage models, considering Sulzer BX structured packings. Heat and mass transfer was described based on the two-film theory assuming thermodynamic equilibrium at the phase interface only. Mass and energy transfer coefficients, as well as pressure drop, liquid hold-up and interfacial area were calculated using equipment-specific correlations. Due to the homogeneously catalysed reaction, the calculation of liquid hold-ups is of special interest. Therefore, besides the liquid hold-up of the packing, it was also calculated for the liquid distributors and the reboiler as well. The column diameter was calculated based on the assumption of a fixed maximum gas capacity factor of 1.5 P a0.5 . Furthermore, the detail level of the model enabled the application of rigorous cost models which facilitate a reliable estimation of investment and operating costs. The full physical model was previously validated based on pilot-scale experiments by Holtbruegge et al. 66 . The vapour permeation was described by means of a solution-diffusion based model, which applies an axial discretisation of the membrane 70 . The membrane process was assumed to 33



be composed of plate-and-frame modules that provide a membrane area of 50 m2 each, such that the total required membrane area is achieved by numbering up of identical modules. Furthermore, the pressure drop on the retentate and permeate side are considered. The local flux of the considered Pervap1255-30 membrane was described based on correlations for the permeance of each component derived by Holtbruegge et al. 60 in combination with the partial pressure difference as description of the driving force. Furthermore, all heat exchangers, pumps and compressors were modelled and investment costs as well as operating costs for the different utilities were considered for the description of the overall costs of the process. For a detailed description of the cost calculation, it is referred to the work of Holtbruegge et al. 62 .

3.5.2

Final translated flowsheet

The final translated flowsheet was set up according to the results of the translation and an initial operating point was established based on the results obtained for the optimised PBBbased flowsheets. Based on this initial solution, a local economic optimisation was performed taking into account the same objective function as considered by Holtbruegge et al. 62 , which combines the total annualised costs of the process with penalty functions, that try to enforce certain equipment-specific restrictions, such as maximum membrane temperature or minimum liquid load in the distillation columns. The results of this local optimisation, including the final values for the DDoF and characteristic dimensions are illustrated in 14.

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Figure 14: Final translated and optimised flowsheet design. The boxes provide relevant data as well as the dimensions and DDoF, which were varied during local economic optimisation of the flowsheet (framed by dashed lines) (Dark grey: reactive section, Liquid, Vapour).

While the process represents mainly the results of the translation, an additional modification is introduced to respect the limited solubility of the homogeneous catalyst in PC. As indicated by the PBB-based process design (Section 3.3), feeding the low boiling substrate MeOH below the high boiling substrate PC provides a significant economic incentive, as far as homogeneous catalyst is present in the intermediate section. However, since the homogeneous catalyst is only soluble in MeOH and delivered as a solution with a concentration of 30 wt-% in MeOH 71 , an additional MeOH+catalyst feed is introduced to the top of the column. The complete MeOH recycle and the major share of the fresh MeOH are however introduced to the column below the PC feed. In order to provide the same amount of catalyst as Holtbruegge et al. 62 , 168.60 kgh−1 of a MeOH solution containing 30 wt-% catalyst is added to the reflux stream of the reactive distillation column. In the reactive distillation column, PC is almost completely converted and PDO is obtained in the bottom product with the desired purity. The top product contains the binary azeotrope of MeOH and DMC, which is fed to the VP membrane. The VP membrane process selectively separates MeOH as permeate that is recycled to the reactive distillation column.

35



The retentate serves as vapour feed of the second distillation column, which is operated at the same pressure as the VP retentate. As in the PBB-based process, the complete vapour stream from the stripping section is removed and mixed with the vapour streams from the partial condensers of both columns, before serving as feed to the VP membrane. As indicated in Figure 14, a special feed distributor that allows passage of the liquid while removing the vapour of the stripping section is required for the second distillation column. Alternatively, the column could be split into two separate sections. The second target product DMC is obtained with the desired purity as bottoms product of this column.

3.5.3

Conclusive economic comparison

While representing only the results of a local optimisation, the economic performance of the final translated flowsheet is further compared to that of the four intensified flowsheet variants that have been optimised by the memetic optimisation approach by Holtbruegge et al. 62 . The results are further analysed in respect to the sequential arrangement of a CSTR followed by a rather complex distillation sequence, which was used as reference process by Holtbruegge et al. 62 . The final economic comparison of all flowsheet variants is given in Figure 15, whereas the most promising ones developed by Holtbruegge et al. 62 are a reactive dividing wall column (RDW) combined either with a pressure swing distillation (PrS) or a VP process for separating the binary azeotrope between MeOH and DMC.

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Figure 15: Economic comparison of all flowsheet variants investigated by Holtbruegge et al. 62 (Sequential, RD + PrS, RD + VP, RDW + PrS, RDW + VP) with the one generated with the developed PS method (RD + VP mod.).

The final cost comparison shows that the RD + V P (mod) flowsheet, which represents the final translated flowsheet originating from the current PS method, provides the best performance, cutting the TAC of the sequential reference process by more than half. Compared to the RD + V P flowsheet, which was deemed best by Holtbruegge et al. 62 , a further reduction in TAC of 39 % is achieved. Besides the cost reduction, the rigorous simulation reveals that also the column diameter of the reactive distillation column is reduced significantly compared to the RD + V P flowsheet due to the reduction of the vapour load. Consequently, not only operating, but also investment cost of the process are reduced. Nevertheless, the proposed catalyst feeding strategy needs to be validated in order to warrant the technical feasibility of the resulting process design. After all, the economic incentive is sufficient to investigate the design in more detail. A reactive DWC, as present in the best process variants considered by Holtbruegge et al. 62 , provides further potential for intensifying the final process design determined by the current PS method. While in principal, a DWC can be determined by the developed PS method based on an interconnection of several VL-PBBs, the decomposition into the Reaction37



Separation and DMC Purification subprocesses prohibits an automated identification. This illustrates the limitation of the design space that results from the decomposition, which however facilitates to efficiently address the complex overall PS problem with the current PS method. Nevertheless, the aggregation of the two distillation columns to a dividing wall column can be performed subsequently.

4

Conclusion

The current article presented the extension and application of a novel model-based method for phenomena-based process synthesis to reaction-separation processes. The method facilitates the automatic generation of thermodynamically feasible phenomena-based flowsheet variants by means of a superstructure optimisation considering a variety of phenomena building blocks (PBBs). Neglecting equipment-specific limitations in a first step, innovative flowsheet variants are obtained taking into account different aspects of process intensification, including the integration of reaction and separation as well as hybrid separation processes. The current article extended the previously introduced process synthesis method 29 by introducing a Reactor-Network-PBB that allows for the consideration of various reactor network configurations. Furthermore, the application in combination with different (reactive) separation PBBs to a challenging process synthesis case study, which is the transesterification of propylene carbonate with methanol, was investigated. The demonstrated results impressively show the benefits of performing process synthesis on a lower level of aggregation than predefined unit operations. By neglecting or at least softening equipment-specific constraints, it is possible to exploit the maximum economic potential for a given problem. In the considered case study, the generation of flowsheet variants relied on the same basic elements as the reference flowsheet and still significant cost savings were achieved. It was demonstrated that the developed process synthesis method can identify innovative solutions that exceed those developed based on expert knowledge, even in case process intensification was already

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considered in the first place. Yet, the complexity of the superstructure optimisation approach, taking into account a large degree of structural flexibility as well as thermodynamically sound models of the PBBs, limits the size of the considerable process synthesis problems. The applied decomposition approach provides a means to keep the overall complexity in a manageable range, but can lead to the exclusion of promising solutions such as the reactive dividing wall column, which was previously proposed by Holtbruegge et al. 62 . Future work will be directed towards the expansion of the feasible problem size, as well as the extension of the portfolio of PBBs e.g. by a Pervaporation-PBB, which also includes reactions and is therefore able to represent a membrane reactor based on the extraction principle.

Acknowledgement The PS approach is developed within a research project funded by Akzo Nobel Industrial Chemicals B.V. for which financial support is gratefully acknowledged.

Supporting Information Available The supplementary information contains information on the objective function, validation of the RN-PBB as well as economic models, superstructure setups, translation procedure and thermodynamic property data for the case study.

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Nomenclature Abbreviations ACM : CST R: DDoF : DM C: DSR: LL: M eOH: M IN LP : P BB: P C: P DO: P F R: P I: P S: P rS: PV : RDW : RN : RP B: V L: V P:

Aspen Custom Modeler Continuously stirred tank reactor Design degree of freedom Di-methyl carbonate Differential side stream reactor Liquid-liquid Methanol Mixed integer nonlinear programming Phenomena building block Propylene carbonate 1,2-Propanediol Plug flow reactor Process intensification Process synthesis Pressure swing distillation Pervaporation Reactive dividing wall column Reactor network Rotating packed bed Vapour-liquid Vapour permeation

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Latin letters A, B, C: aef f : ai : AV P : cp : CostC : CostH : CurB C: D: fc : h: H: ∆hLV S : ka : Ka : kL : kL A: M: nC : nCST R : nF : nmin gen :

nP : nP arents: nP en: nP BB :

Empirical parameters Effective interfacial area Activity of component i Membrane area Specific heat capacity Cooling agent costs Steam costs Currency exchange rate Diameter Depreciation factor Specific enthalpy Height Heat of evaporation of steam Activity-based reaction rate constant Activity-based chemical equilibrium constant Liquid-side overall mass transfer coefficient Fused mass transfer variable (= kL · aef f · VV L ) Average molar mass Number of components Number of CSTRs for approximation of a PFR Number of feed streams Number of compared generations to check whether the termination condition is fulfilled Number of product streams Number of parent selection vectors Number of penalty functions Number of PBBs

41


[−] [m2 m−3 ] [mol mol−1 ] [m2 ] [kJ kg −1 K −1 ] [B C t−1 ] [B C t−1 ] [B C U S$−1 ] [m] [−] [kJmol−1 ] [m] [kJ kg −1 ] [kg 3 s−1 kmol−2 m−3 ] [−] [m s−1 ] [m3 s−1 ] [kmol kg −1 ] [−] [−] [−] [−]

[−] [−] [−] [−]


nRN : n: ˙ p: pDew : P: P enalty: ˙ Q: QV P : r: R: RR: S: T: TC : tOp : T AC: T IC: T OC: V: V˙ : w: wcat : x: z:

Number of discrete elements in the RNPBB Molar flowrate Pressure Dew point pressure Electrical power Penalty function Heat duty Molar permeance Activity-based reaction rate Radius Reflux ratio Differential selectivity Temperature Cooling agent temperature Time of operation Total annualised costs Total investment costs Total operating costs Volume Volume flowrate Mass fraction Catalyst mass fraction Molar fraction of liquid phase Molar fraction of component i

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[−] [mols−1 ] [bar] [bar] [kW ] [B C] [kW ] [mol h−1 m−2 bar−1 ] [mol s−1 ] [m] [kg kg −1 ] [−] [K] [K] [h] [B C a−1 ] [B C] [B C a−1 ] [m3 ] [m3 h−1 ] [kg kg −1 ] [kg kg −1 ] [mol mol−1 ] [mol mol−1 ]

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Greek letters ∆Ω: ν: ρ: ρmolar : τ: Ω: ξ:

Objective function tolerance Stoichiometric coefficient Mass density Molar density Residence time Fitness function Dimensionless factor

[B C a−1 ] [−] [kg m−3 ] [mol m−3 ] [s] [B C a−1 ] [−]

Subscripts CST R: MT : S: RN :

CSTR as part of the RN-PBB Mass transfer Splitter as part of the RN-PBB RN-PBB

0: ex: in: out: P i, j: Reac:

Reference state External Input stream Output stream Product i of subprocess j Reaction

Superscripts

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Figure 16: Table of Content graphic

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Optimization-Based Approach to Process Synthesis for Process

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