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An optimisation-based approach to process synthesis for process intensification: General approach and application to ethanol dehydration Hanns Kuhlmann, and Mirko Skiborowski Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02226 • Publication Date (Web): 24 Aug 2017 Downloaded from http://pubs.acs.org on August 27, 2017

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Industrial & Engineering Chemistry Research

An optimisation-based approach to process synthesis for process intensification: General approach and application to ethanol dehydration. Hanns Kuhlmann∗ and Mirko Skiborowski TU Dortmund University, Department of Biochemical and Chemical Engineering, Laboratory of Fluid Separations, Emil-Figge-Strasse 70, 44227, Dortmund, Germany E-mail: [email protected]

Abstract Process synthesis and intensification are well-known and powerful tools for the development of chemical processes with improved energy and cost efficiency. However, even though a combination of both provides the most potential for exploiting these improvements, process synthesis still focusses on classical unit operations, while intensified process options are rather delayed and considered mainly for retrofit. This does not only limit the result of process synthesis, but also impedes the application of intensified process options, as they need to justify additional investment for process modification. In order to reveal improved process options and reduce the barrier for intensified processes, the current article presents a process synthesis approach which generates thermodynamically feasible phenomena-based flowsheets by means of superstructure optimisation. The approach provides maximum flexibility for integrating and modifying the involved phenomena building blocks, which only afterwards are interpreted and translated into equipment that represents the final process. Innovative ∗

To whom correspondence should be addressed

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hybrid process configurations and intensified equipment can thereby be synthesized automatically in conceptual design. The current article introduces the general concept and the implementation for an initial set of phenomena building blocks. Successful application of the approach is demonstrated for the non-reactive but thermodynamically non-ideal case study of ethanol dehydration.

1

Introduction

Conceptual process design is one of the most important, but also most complex tasks in chemical engineering. The decisions made in this early phase of process development account for up to 80 % of the overall costs of the final process 1 . Especially process synthesis (PS), which is the choice of process technologies and their interconnection to determine possible flowsheet variants for achieving a specific task, is of upmost importance in determining an economic and environmentally favorable process design. Yet most PS methods are focusing on the classical concept and set of unit operations. According to Stankiewicz and Moulijn 2 ,3 , the concept of process intensification (PI) especially comprises novel equipment and processing techniques that offer substantial improvements in (bio)chemical manufacturing and processing. Nevertheless, it is mostly neglected in this early phase and rather applied subsequently to single separation and/or reaction steps for debottlenecking existing processes. However, the biggest impact of PI can be made, if it is integrated with PS and considered already in the early process development phases. This was already indicated by Moulijn et al. 4 who argued that a friendly symbiosis will be beneficial for the design of innovative and energy and resource-efficient future process plants. Despite the vast number of definitions for PI, which generally consider it as a tool for achieving substantial improvements of process economics and sustainability, there have been several attempts to classify PI principles according to different levels or scales 4–7 , which allow for an obvious connection to PS. This connection was recently elaborated by Lutze and Sudhoff 8 , who use the distinction into the fundamental and molecular scale, the phase and transport 2 ACS Paragon Plus Environment

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scale, the operation and equipment scale and the process and plant scale, which were initially introduced by Freund and Sundmacher 9 . While van Gerven and Stankiewicz 6 expect the largest impact of PI on the lowest scale, improvements on the fundamental and molecular scale are mainly obtained by improvements in chemistry and kinetics, changing reaction pathways and catalyst selection, as well as improving mixing in order to give each molecule the same processing experience. Building up on an established chemistry, PS methods mainly address the challenges concerned with the three scales on top of the fundamental and molecular scale. This includes the selection of the optimal technology in terms of involved phases and contacting of these phases, the equipment implementing that technology and the combination of the different involved technologies to depict the final process flowsheet. In order to allow for the consideration of intensified equipment and process options, either unit operation based PS methods need to be extended by the multitude of additional intensified options or PS needs to be performed on a lower level of aggregation. Promoting a task-oriented rather than equipment oriented approach, Siirola 10 argued that the design of abstract processes allows for the identification of the configuration that is the closest to ideal process conditions, not limited to a given set of equipment. While such an abstract approach seems more complex as such, Mangold et al. 11 already argued that the use of model libraries defined below the level of unit operations provides advantages in model flexibility, reusability, complexity and cost. Although several tools for process modelling on an abstract level below the concept of unit operations have been developed, as e.g. Model.LA 12 , PROMOT 13 or ModKit 14 , modelling and design of processes on an abstract level has not prevailed so far. Nevertheless, especially the idea of retrofitting and designing process flowsheets by means of a phenomena-based approach has been repeatedly promoted in literature 7,15–17 . Phenomena are the fundamental mechanisms any chemical process or unit operation is based on and as such PS building up on the combination of different phenomena can generate any kind of chemical process. However, the combinatorial complexity of a PS problem on the basis of phenomena is practically not traceable. Therefore Arizmendi-Sánchez and Sharratt 18 and



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Lutze et al. 19 promoted to compose process options on the basis of phenomena building blocks (PBBs), which already present a combination of different phenomena that usually are linked together, such as mass and heat transfer in case of phase contacting. While both authors present impressive results for exemplary case studies, the presented methods start with the analysis of a given base case process design, which is subsequently transposed into a phenomena-based representation, forming the basis for the subsequent intensification. In order to allow for a grassroot PS approach, building on the principle of PBBs, the current article proposes an optimisation-based approach. It is specifically developed to handle the combinatorial complexity that is encountered when allowing for a generic combination of the PBBs and the numerical complexity that comes with the consideration of rigorous thermodynamic models in order to avoid previous simplifications that might render the final design infeasible. In order to accurately classify the current method the following section first presents a brief review of PS methods, focussing on the consideration of PI. Subsequently, Section 3 presents the general framework for generating PBB-based flowsheet variants, while Section 4 and 5 provide a detailed description of the applied superstructure, the mathematical models and the developed optimisation approach. The procedure for translating the PBB-based flowsheets into real equipment is further elaborated in Section 6. Finally, the application of the developed PS method is demonstrated for the case study of ethanol dehydration in Section 7, before Section 8 presents a conclusion and an outlook.

2

Review of process synthesis methods

The major objective of PS methods is the generation of flowsheet variants for a given design problem. Even though it is well known that systematic PS methods can lead to cost savings of up to 60 %, in industrial practise PS is usually performed by means of a knowledgebased approach building on the experience of a team of accomplished experts 20 . While this procedure has been established for decades with unequivocally satisfying results the design


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space is always limited by the knowledge, experience and creativity of the involved experts. But most of all, the number of finally considered process variants is limited by the time frame of the project. In order to expand the design space and accelerate the development process, many systematic PS approaches have been developed to aid the team of experts in the development process. Nevertheless, as pointed out in the introduction, the number of PS methods readily considering PI is still limited. The existing PS methods can be divided according to the level of aggregation of the building blocks of which the flowsheet is constructed (see Figure 1).

Figure 1: Levels of aggregation of the elements used for generating flowsheet variants. Furthermore, they can be classified concerning their solution strategy into hierarchical, knowledge-based and optimisation-based PS methods. While hierarchical methods decompose the PS task into subsequent problem analysis and screening steps for flowsheet feasibility and performance, optimisation-based PS methods try to determine the best performing flowsheet variant directly from a superstructure embedding all potential variants. The classical concept of unit operations represents the highest level of aggregation, as it directly takes into account of a certain type of equipment, like the distillation column indicated in Figure 1. Flowsheet generation on this level is straightforward and can build up on available computer-based models, which consider the constraints of existing apparatuses and therefore enable detailed calculation of mass and energy transfer, hydrodynamics and cost functions. The hierarchical heuristic approach developed by Douglas 21 is still the most 5 ACS Paragon Plus Environment


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prominent approach to PS and a classical example for a unit operation based PS method. The PS methods developed by d’Anterroches and Gani 22 and Tula et al. 23 , which interpret the PS problem analogous to a Computer Aided Molecular Design (CAMD) problem 24 , perform the initial selection of feasible process options based on the thermodynamic insights approach developed by Jaksland et al. 25 . While the application of hierarchical, knowledgebased methods is mostly straightforward, only few methods account for the integration of PI principles, such that improved solutions are easily missed. Interestingly, an extension of the thermodynamic insight approach of Jaksland et al. 25 which considers a multitude of PI options was recently presented by Holtbruegge et al. 26 . Their algorithmic evaluation scheme takes into account hybrid and reactive separation processes as well and provides an important step towards the consideration of PI options in PS. The limitation to classical unit operations holds for most mathematical programming approaches as well. However, the optimisation of a superstructure that embeds all conceivable combinations of unit operations relevant for a certain PS problem bears the advantage to overcome the problem of a too narrow design space 27 . However, it has to be considered that the initial superstructure needs to be set up in advance and the optimal solution can be found only inside of this fixed search space of pre-defined unit operations 27–29 . For PS, large and flexible superstructures are usually preferred, whereby simplified performance models are used to reduce the problem complexity. While this allows for the identification of a proven optimal solution, the result might not reflect reality accurately and even feasibility is not warranted 30 . One potential solution to handle the combinatorial complexity of a large design space and apply rigorous models is a decomposition into subsequent steps, as proposed in the PS framework by Marquardt et al. 31 . Through combination of suitable methods for different unit operations, this approach can also efficiently address the synthesis of hybrid separation processes, as demonstrated by Skiborowski et al. 32 .

While some efforts have been made on the unit operation level to include hybrid and


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reactive separation processes in PS 26,32 , a more promising approach to include PI in PS is based on a lower level of aggregation, considering processes as combination of fluid elements or phases. This disassembly is illustrated in Figure 1, showing the contacting between phases in a section of a distillation column, as well as a single fluid element in one of these phases. By manipulating the physico-chemical phenomena at this lower level of aggregation in an arbitrary way, without considering any equipment-specific constraints, the best possible performance can be evaluated. Therefore, PS on this lower level of aggregation by direct manipulation of the underlying phenomena enables the highest potential for PI during PS. Focussing on the optimisation of reaction performance Freund and Sundmacher 5 and Peschel et al. 33 followed exactly this idea to generate flowsheet variants for innovative reactor concepts and reactive separations. Considering that most PI principles represent the combination and targeted enhancement of specific mass and energy transfer phenomena 7 , several phenomena-based PS methods have been developed that follow this idea. An early representative is the knowledge-based PS method developed by Gavrila and Iedema 34 , which addresses reactor network design by combining desirable phenomena to so-called aggregated units. Another approach is the process retrofitting method by Arizmendi-Sánchez and Sharratt 18 , which analyses and improves a given process in terms of the involved phenomena using an extensive library of phenomena building blocks (PBBs). The PS method developed by Lutze et al. 19 builds on a database of phenomena that are combined to simultaneous PBBs, from which phenomena-based flowsheet variants are generated by a series of screening steps and connection rules. Further development of this approach has recently been fostered in the work of Babi et al. 35 , who extended the method by the translation of phenomena-based flowsheets to innovative designs and an additional sustainability analysis. While PS methods on this lower level of aggregation promote the exploitation of PI options and optimisation-based methods provide the potential to handle the extended design space, the complexity of the resulting optimisation problem presents a significant challenge.



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Previous methods, as those presented by Papalexandri and Pistikopoulos 36 and Linke and Kokossis 37 therefore apply simplified models for the separation, in order to handle the combinatorial complexity of the problem. However, such model simplifications might result in infeasible solutions. Consequently, an accurate description of the separation performance is desirable in order to ensure process feasibility in the course of PS. The current contribution therefore combines several of the aforementioned ideas. Similar to the ideas of Gavrila and Iedema 34 and Lutze et al. 19 , meaningful combinations of different phenomena, such as chemical reactions, mass and energy transfer, etc. constitute the PBBs of which the processes are composed. These PBBs either consider a distinct description of mass transfer or rigorous thermodynamic equilibrium models to verify the feasibility of the resulting PBB-based flowsheet variants. These are further translated into specific equipment, considering hybrid and integrated processes, as well as intensified equipment. Reactive separations, which are the main subject of a subsequent publication, can be identified by the current approach as well.

3

Process Synthesis Framework

Similar to previous PS methods considering PI 19,38 , a multi-step framework is proposed, which in accordance to Figure 2 starts with with an initial problem definition and selection of PBBs. Subsequently, PBB-based flowsheet variants are generated based on idealised PBBs, taking into account either operation at thermodynamic equilibrium or mass transfer without consideration of driving force limiting effects. The most promising PBB-based flowsheet variants are finally translated to real equipment-based flowsheets, taking into account conventional as well as intensified equipment. This two-step synthesis approach is motivated by the fact that PI solutions approach ideal performance in such a way that the according assumptions of e.g. thermodynamic equilibrium are more valid than for conventional equipment 18 . Nevertheless, thermodynamic feasibility is warranted in the PS steps. While the


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general approach was already introduced in Kuhlmann and Skiborowski 39 , all five steps are outlined in the subsequent subsections with a focus on the two PS steps in Sections 4 and 6.

Figure 2: PS framework divided into five subsequent steps.

3.1

Step 1: Problem definition and analysis

In the first step, the PS problem is defined by specifying the available feed stream(s), the desired product stream(s), possible chemical reactions as well as available utility streams. Furthermore, the objective function for the optimisation is defined (e.g. costs, energy consumption) and thermodynamic models and kinetic data are collected.

3.2

Step 2: Selection of PBBs

Suitable PBBs for each reaction and/or separation step are identified to set up the PS problem. For this task a modified version of the automatic screening tool developed by Holtbruegge et al. 26 is applied. Instead of identifying suitable unit operations for each reaction and/or separation step, the results from the analysis of the physicochemical properties is used to identify suitable PBBs. In case a reference case design is available, this information is taken into account as well. Based on this pre-selection of suitable PBBs, a final selection is performed by the user, taking into account preferences and experience. Further detail on the implementation of available PBBs is given in Section 4.2.



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3.3

Step 3: Generation of PBB-based flowsheet variants

In order to automatically generate PBB-based flowsheet variants and determine the most promising ones, a superstructure is set up based on the selection of suitable PBBs from step 2. The superstructure is represented by means of the state-space approach 40 , as illustrated in Figure 3. The basic elements of the superstructure are the PBBs, which are interconnected by a distribution network of mixers and splitters. The resulting optimisation problem that determines which PBBs are used and how they are connected, represents a complex MINLP problem which is optimised with respect to the objective function defined in step 1. The generic combination of PBBs allows for strongly integrated designs, including thermal coupling, hybrid and reactive separation processes. Consequently, this PS step addresses PI on the process and plant as well as the operation and equipment level 8 , while warranting process feasibility through the underlying thermodynamic models and respected process specifications. Further details on the PBBs, the superstructure and the applied optimisation approach are presented in Sections 4 and 5.

3.4

Step 4: Translation into equipment-based flowsheets

The most promising PBB-based process variants are further investigated considering mass and energy transfer limitations in order to evaluate a suitable implementation by means of different equipment, either conventional or intensified. Building on detailed rate-based models and a local optimisation of the resulting flowsheet, suitable equipment is determined considering mass and energy transfer coefficients as degrees of freedom, within ranges defined by a database of conventional and PI equipment 7 . The optimisation is therefore used for the identification and preliminary sizing of suitable equipment, taking into account process specific constraints for the equipment. The translation process considers both single PBBs as well as their potential integration and fosters PI on the operational and equipment level as well as the phase and transport level 8 . In case a combination of PBBs cannot be represented by means of given equipment, the design of new equipment might become attractive. The 10 ACS Paragon Plus Environment

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procedure for the translation is further elaborated in Section 6.

3.5

Step 5: Optimisation of equipment-based flowsheets

In the final step, a detailed design of the most promising equipment-based flowsheet is determined using detailed equipment-specific correlations and constraints. Depending on the type of equipment and the available data, targeted experiments might become necessary. This step can be considered optional and should be performed prior to a final implementation of the resulting process in order to provide a detailed sizing and design of the process.

4

Superstructure model

The superstructure, which enables a generic connectivity between the feed and product streams of the process as well as all potential PBBs, is illustrated in Figure 3. Connections are established inside the distribution network between splitters for each incoming and mixers for each outgoing stream. An important feature of the superstructure model is that the type of PBB presents an additional design degree of freedom (DDoF) in the optimisation, such that the PBB illustrated in Figure 3 represents a template for each available type of PBB, containing up to two input and output streams. The distribution network model is introduced in Section 4.1, while the specific types of PBB considered in the current work are introduced in Section 4.2. While a non-reactive system is investigated in the case study of this work (see Section 7), the PBB models are readily presented for reactive systems, which are subject of a subsequent publication.



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Figure 3: 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. This type of superstructure has the advantage that it only needs to include a maximum number of PBBs that are considered simultaneously in the process. A fixed choice of PBB types would require the same number of PBBs for each type being present in the superstructure, resulting in a significantly increased size of the superstructure model 1 . Nevertheless, the selection of each PBB type and their interconnections still presents a very complex combinatorial problem that has to be solved in combination with the strongly nonlinear PBB models in order to determine process designs that satisfy the process specifications while minimising/maximising the given objective function. Therefore, a specific solution approach has been developed, which excludes most structurally infeasible combinations by means of a rule-based screening procedure prior to a stepwise initialisation and optimisation procedure. The solution approach is further elaborated in Section 5.


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4.1

Distribution network model

As illustrated in Figure 3 each PBB has up to two input and output streams, which are connected with the mixer and splitter nodes of the distribution network. While the splitter nodes perform mainly a distribution of the entering stream, the generic mixers also allow for a modification of the thermal state of the mixed stream. Thereby, mechanical work and heat can be added or withdrawn in order to modify the temperature, pressure and phase state of the stream, prior to entering the main element of a PBB. These modifications can account for specific constraints depending on the type of PBB. While also each feed stream is connected to a splitter and each product stream is connected to a generic mixer node of the distribution network, the splitter and mixer models are further introduced for a general PBB entity.

4.1.1

Splitter

Each splitter distributes the PBB output stream among the different mixers in the distribution network. However, in order to avoid severe branching, the distribution is limited to a maximum of two mixers k ∈ {1, . . . , 2nP BB + nP } by means of two binary variables Ψasplit,k,l and Ψbsplit,k,l for each splitter l ∈ {1, . . . , 2nP BB + nF }. An additional binary variable Ψselect split,l further limits the distribution to the mixer selected by Ψasplit,k,l only, avoiding any distribution for the specific PBB output stream. This additional binary variable is used to limit the number of active splitters in the process to maximum number of nsplit . The outgoing streams of any splitter in the distribution network

n˙ DN k,l

=

   Ψa

split,k,l

b · ξsplit,l · n˙ in ˙ in split,l + Ψsplit,k,l · (1 − ξsplit,l ) · n split,l

  Ψasplit,k,l · n˙ in split,l

, Ψselect split,l

, Ψselect split,l = 1

(1)

= 0,

are therefore determined by selection of the binary decision variables Ψasplit,k,l , Ψbsplit,k,l and Ψselect split,l for all k mixers and l splitters, as well as the continuous split ratios ξsplit,l for all l



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splitters. Additional constraints account for the restrictions on the number of splitters and the distribution to at most two mixers: 2nPX BB +nP k=1 2nPX BB +nP

Ψasplit,k,l = 1,

(2)

Ψbsplit,k,l = 1,

(3)

k=1

Ψasplit,k,l + Ψbsplit,k,l ≤ 1, 2nPX BB +nF

Ψselect split,l ≤ nsplit .

(4) (5)

l=1

Since streams are distributed only, the composition, temperature and pressure of the streams leaving the splitter equal those of the stream entering the splitter.

4.1.2

Generic mixer

All streams entering a mixer are first mixed based on the material and energy balance for the mixer 2nPX BB +nF l=1 2nPX BB +nF l=1 2nPX BB +nF

n˙ DN ˙ out k,l = n mix,k ,

(6)

in out n˙ DN ˙ out k,l · zmix,k,l,j = n mix,k · zmix,k,j ,

(7)

in out ˙ n˙ DN ˙ out k,l · hmix,k,l + Qmix,k = n mix,k · hmix,k ,

(8)

l=1

in in for which n˙ DN k,l , zmix,k,l,j and hmix,k,l are the molar flow rate, molar fraction of each component

j ∈ {1, . . . , nC } and the specific enthalpies of the stream directed from splitter l to mixer k. out out The variables n˙ out mix,k , zmix,k,j and hmix,k denote the molar flow rate, composition and specific

enthalpy of the stream leaving the mixer. Modifications of the thermal state of the mixed out stream are considered directly through manipulation of the temperature Tmix,k and pressure


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pout mix,k of the mixed stream, in terms of the specific enthalpies out out out hout mix,k = f (Tmix,k , pmix,k , zmix,k ),

(9)

which are computed by Aspen Properties® routines. The required energy for the modification is considered in the energy balance as external heat Q˙ mix,k .

4.2

Specific type of PBB

Each type of PBB contains specific information about input/output constraints, flow direction and mixing condition of the involved phase(s) as well as material and energy balances. While this article introduces the PBB types Inactive, Vapour-Liquid (VL) and Vapour Permeation (VP), which are used for the considered case-study, further PBB types and their application to appropriate case-studies will be introduced in subsequent contributions. These include the PBB types Liquid-Liquid (LL), which models counter-current contacting of two immiscible liquid phases, and the PBB type Reactor-Network (RN), which models a generic reactor network.

4.2.1

Inactive

The PBB type Inactive equates each input and corresponding output stream and represents the case of no mass transfer and reaction, which is of special importance for the initialisation of the flowsheet model once a new optimisation is started. The initialisation procedure is described in detail in Section 5.3.

4.2.2

Vapour-Liquid-PBB

The PBB type VL, illustrated in Figure 4, describes either co-current or counter-current contacting of a liquid and a vapour phase. Additional constraints for the mixer nodes assure



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the correct phase state for each entering stream. The VL-PBB combines the phenomena ideal mixing in the vapour and liquid phase, phase contacting, mass and energy transfer and phase separation as well as potential reactions in both phases. While co-current contacting is modeled by a single equilibrium stage, counter-current contacting is modeled by a cascade of thermodynamic equilibrium stages.

Figure 4: VL-PBB including discretisation scheme and important variables. In accordance with the assumption of ideally mixed phases and mass and energy transfer, each equilibrium stage is modelled by means of the well known MESH equations, considering mass balances and equilibrium conditions for each equilibrium stage i ∈ {1, . . . , nV L } and component j ∈ {1, . . . , nC } Reac,L n˙ LV L,i−1 · xV L,i−1,j + n˙ trans · rVL L,i,j · VVReac,L = n˙ LV L,i · xV L,i,j , V L,i,j + ΨV L L,i

(10)

Reac,V n˙ VV L,i+1 · yV L,i+1,j − n˙ trans · rVV L,i,j · VVReac,V = n˙ VV L,i · yV L,i,j , V L,i,j + ΨV L L,i

(11)

LE yV L,i,j = KVV L,i,j · xV L,i,j ,

(12)


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as well as enthalpy balances and summation constraints

n˙ LV L,i−1 · hLV L,i−1 + Q˙ trans ˙ LV L,i · hLV L,i , V L,i = n

(13)

n˙ VV L,i+1 · hVV L,i+1 − Q˙ trans ˙ VV L,i · hVV L,i , V L,i = n

(14)

nC X j=1 nC X

xV L,i,j = 1,

(15)

yV L,i,j = 1.

(16)

j=1

In the current form, the mass and energy balances for the liquid and vapour phase are ˙ trans linked by a stream of transferred mass n˙ trans ˙ LV L,i , xV L,i,j V L,i,j and energy QV L,i . The variables n and hLV L,i as well as n˙ VV L,i , yV L,i,j and hLV L,i define the liquid and vapour molar flow rate, composition and specific enthalpies for each stage. Possible reactions in the liquid and vapour phase are indicated by the binary variables ΨReac,L and ΨReac,V , which emulate the VL VL presence of a catalyst, while the extent of a reaction is modelled by the reaction rates rVL L,i,j and VVReac,V . These and rVV L,i,j as well as the liquid and vapour hold-up for a stage VVReac,L L,i L,i are calculated by dividing the total liquid and vapour hold-up of the VL-PBB VVReac,L and L VVReac,V , which are considered as DDoF of the VL-PBB, by the number of stages L

VVReac,L L , nV L V Reac,V = VL . nV L

VVReac,L = L,i

(17)

VVReac,V L,i

(18)

The necessary distribution coefficients and specific enthalpies

LE = f (TV L,i , pV L , xV L,i,j , yV L,i,j ), KVV L,i,j

(19)

hLV L,i = f (TV L,i , pV L , xV L,i ),

(20)

hVV L,i = f (TV L,i , pV L , y V L,i ),

(21)



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are calculated by means of Aspen Properties® routines. The operating pressure pV L as well as the binary decision variables are DDoF of the VL-PBB. For the first stage, the incoming liquid stream (n˙ LV L,0 , xV L,0,j and hLV L,0 ) matches the stream from the liquid mixer of the VL-PBB, while the incoming vapour stream of the last stage (n˙ VV L,nS +1 , yV L,nS +1,j and hVV L,nS +1 ) matches the stream from the vapour mixer of the VLPBB. Accordingly, the outgoing vapour stream from the first stage (n˙ VV L,0 , yV L,0,j and hVV L,1 ) and the liquid stream from the last stage (n˙ LV L,nS , xV L,nS ,j and hLV L,nS ) represent the streams entering the splitters of the VL-PBB. It is important to note that the VL-PBB can represent any kind of single section gas-liquid contacting equipment. In order to represent e.g. a single feed distillation column, two VL-PBBs have to be connected. The feed is introduced into one of the intermediate mixers and the outgoing streams are partly recycled back to the opposing phase, which represent the reflux and boil-up streams. In order to further reduce the computational complexity and perform a reasonable model reduction, an approximation of the equilibrium-stage model by means of an orthogonal collocation on finite elements (OCFE), in accordance with the work of Stewart et al. 41 , has been applied to the VL-PBB as well. While significantly reducing the number of VLE and enthalpy computations, the OCFE approach potentially introduces the problem of overshooting composition profiles due to the polynomial approximation of the trajectory, which can result in convergence problems. Further details about the application of this approach are provided in the Supporting Information.

4.2.3

Vapour-Permeation-PBB

The PBB type VP, illustrated in Figure 5, models mass transfer between two co-current or counter-current (not illustrated) vapour phases separated by a semipermeable membrane. The entering feed stream and a potential sweep gas stream are the input streams, while the retentate and permeate are the outgoing streams of the PBB. The VP-PBB combines


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the phenomena ideal mixing in both vapour phases, phase contacting with the membrane, mass transfer through the membrane and potential reactions in both phases. Additional constraints for the mixer nodes assure that the feed is superheated to 30 K above its dew point temperature in order to avoid condensation of the retentate 42 . The degree of superheating can however easily be changed based on the considered membrane or introduced as additional DDoF during optimisation. For an idealised and equipment independent performance modelling, neither temperature and concentration polarisation nor pressure drop are considered.

Figure 5: VP-PBB including discretisation scheme and important variables. Mass transfer through the membrane is modeled by a solution diffusion type model, while the membrane is axially discretised to account for the changing fluxes along the membrane length. For each discrete element i ∈ {1, . . . , nV P } the transmembrane flux model and the component balances for the retentate and permeate side are evaluated for each component



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j ∈ {1, . . . , nC } n˙ trans V P,i,j = QV P,i,j · DFV P,i,j ,

(22)

Ret n˙ Ret ˙ trans V P,i−1 · yV P,i−1,j + n V P,i,j · AV P,i + Reac,Ret Ret = n˙ Ret ΨReac,Ret · rVRet V P,i · yV P,i,j , P,i,j · VV P,i VP

(23)

P erm n˙ PV erm ˙ trans P,i−1 · yV P,i−1,j − n V P,i,j · AV P,i + erm erm erm P erm ΨReac,P · rVP P,i,j · VVReac,P = n˙ PV erm P,i · yV P,i,j , VP P,i

(24)

in combination with the summation conditions nC X

yVRet P,i,j = 1,

(25)

erm yVP P,i,j = 1.

(26)

j=1 nC X j=1

The transmembrane flux n˙ trans V P,i,j is calculated based on a thermodynamic model for the driving force DFV P,i,j and an empirical model for the membrane permeance QV P,i,j . These depend on the membrane type and the system under consideration. Refer to the case study in Section 7 for an example. The retentate and permeate streams are characterised by the Ret molar flow rate and composition for each discrete n˙ Ret ˙ PV erm V P,i and yV P,i,j as well as n P,i and erm . Similar to the VL-PBB, possible reactions in both phases are indicated by the binary yVP P,i,j erm variables ΨReac,Ret and ΨReac,P , while the extent of a possible reaction is modelled by the VP VP P erm reaction rates rVRet P,i,j and rV P,i,j as well as the retentate and permeate hold-up for a discrete erm and VVReac,P , which are calculated analogous to Equations 17 and 18. VVReac,Ret P,i P,i Ret The incoming retentate stream of the first discrete (n˙ Ret V P,0 and yV P,0,j ) equals the stream from

the feed mixer of the VP-PBB. The VP-PBB can be operated with or without a sweep gas on the permeate side. In case a sweep gas is used, the the incoming permeate stream of P erm the first discrete (n˙ PV erm P,0 and yV P,i,j ) matches the stream from the sweep mixer of the VP-


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PBB. In case no sweep gas is used, n˙ PV erm P,0 is zero. Accordingly, the outgoing retentate and Ret P erm permeate streams from the last discrete (n˙ Ret ˙ PV erm V P,nV P , yV P,nV P ,j , n P,nV P , yV P,nV P ,j ) represent the

streams entering the splitters of the VP-PBB. The membrane area of each discrete AV P,i is determined from the variable total membrane area AV P and the number of discrete elements as

AV P,i =

AV P . nV P

(27)

Instead of modifying the total membrane area, which may vary significantly for different applications, the retentate factor ξVRet P , describing the amount of retentate with respect to the total feed molar flowrate

ξVRet P =

n˙ Ret V P,nV P n˙ Ret V P,0

(28)

is modified. While the membrane area results from the solution of the governing model, the retentate factor is well scaled between 0 and 1. P erm The DDoF of the VP-PBB are the operating pressures for both phases (pRet V P and pV P ), the

use of a sweep stream, the membrane area, as well as the binary decision variables and the hold-ups of both phases in case of reactions taking place. Furthermore, a binary decision variable ΨCond determines if the final permeate stream is condensed in order to avoid high VP costs for compression in further processing steps. Therefore, the permeate stream can be condensed, compressed as a liquid and evaporated again in the generic mixer nodes. The heat duty for condensation Q˙ Cond is calculated as VP

Q˙ Cond VP

=

   n˙ PV erm P,n

VP

P erm,V · hPV erm,L ˙ PV erm P,nV P · hV P,nV P P,nV P − n

  0 , ΨCond VP = 0


, ΨCond VP = 1

(29)


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with the specific enthalpies

P erm,boil P erm hPV erm,L , pV P , xPV erm P,nV P ) P,nV P = f (TV P

(30)

P erm P erm P erm hPV erm,V , pV P , yV P,nV P ) P,nV P = f (TV P

(31)

being again calculated by Aspen Properties® routines. A model reduction by means of orthogonal collocation allows for a simplification of the VP-PBB model and can be applied in a similar form as described in the work of Skiborowski et al. 43 . In contrast to the experience with the collocation approach for the VL-PBB, no problems caused by overshooting approximations are known.

4.3

Cost evaluation

In order to not only generate feasible PBB-based flowsheets that satisfy the process specifications, but also evaluate and optimise the performance, a quantification of this performance needs to be defined as objective function. The selected objective function

min

Ω=

nX P BB

T OCP BB,m +

m=1

fc ·

nX P BB

T OCmix,k +

k=1 2nPX BB +nP

T ICP BB,m +

m=1 n P en X

2nPX BB +nP

! T ICmix,k

+

k=1

P enaltyn

(32)

n=1

reflects the economic performance of the process in combination with a set of nP en penalty functions, which strongly penalise solutions that do not satisfy the purity specifications. The latter have to be introduced, since the applied optimisation approach (see Section 5) cannot handle inequality constraints. The economic part of the objective function represents operating costs of the PBBs and the mixers (T OCP BB,m and T OCmix,k ) associated with the use of utilities and investment costs T ICP BB,m and T ICmix,k which are depreciated to an annual


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share by the depreciation factor fc . There are no costs attributed to stream splitting. Since PS is performed on the level of PBBs, the final type of equipment is not yet specified and as such, a meaningful estimation of investment costs is not possible and therefore avoided unless a specific equipment can already be fixed or needs to be considered because a major impact on the economic performance is to be expected. Consequently, the economic performance is largely quantified by the operating costs of the process. The operating costs T OCmix,k include the power consumption for an optional pressure increase and the cooling water or steam consumption, in case additional heat transfer is necessary. While the required amount of steam and cooling water is determined based on the heat duty and a logarithmic mean temperature difference, four cases are distinguished, concerning an optional pressure increase depending on the thermal state of the in- and outlet streams. As illustrated in Figure 6, compression of the liquid stream is preferred over expensive compression of a vapour stream as long as not only the compression of a vapour stream is required. In order to account for the temperature level at which the heat is transferred, different utilities are introduced. As an example, three pressure levels for steam are available, from which the lowest possible option is selected. Further information is provided in the Supporting Information. The operating costs for the pressure change are determined based on the required power consumption independent of the specific case. However, even though decisions on specific equipment are avoided in the PBB-based flowsheet design, the costs for a compressor present a major impact factor on the process economics and as such the costs of the compressor are considered in the investment share T ICmix,k , while the investment costs for heat exchangers and pumps are neglected at this level.



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Figure 6: Four different cases for calculating the power consumption for a pressure increase in the mixer.

Since the auxiliary equipment, which consumes the utilities, is considered as part of the generic mixer nodes and equipment specific investment costs are not considered for the PBB-based flowsheet synthesis, the PBBs do not contribute investment costs T ICP BB,m and operating costs T OCP BB,m , unless a specific type of equipment or material is already fixed and should be considered. The latter is the case for the membrane separation considered in the PBB type VP-PBB. A full replacement of the membrane material every four years is considered and additional operating costs are considered in case of the aforementioned option of permeate condensation. Detailed information concerning the economic performance model are provided in the Supporting Information.

5

Optimisation Approach

By treating the PBBs in the superstructure as a template for which the selection of a specific type determines the distinct set of model equations, the optimisation problem represents a mixed form of a generalised disjunctive programming (GDP) problem 44 and a classical MINLP problem that is characterised by the large quantity of binary decision variables. While the use of disjunctions for the PBB models has obvious advantages in terms of model


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size reduction, a tailored optimisation approach is required in order to solve the resulting optimisation problem. Therefore, a memetic algorithm, consisting of an evolutionary algorithm that addresses the combinatorial complexity and handles the disjunctions and a local deterministic optimisation approach that minimises the objective function by modifying the operating conditions, is proposed. This combination does not only allow for an effective handling of the disjunctions, but combines the advantage of the population-based algorithm to perform a global search, with the efficient local improvement of a deterministic optimisation algorithm 45 . The basic steps of the optimisation approach are illustrated in Figure 7.

Figure 7: Structural illustration of the developed optimisation approach.

In this work, an evolutionary strategy with plus-selection (ES), which is implemented in Visual Basic for Applications® with a graphical user interface in Microsoft® Excel® , is combined with the deterministic Nelder-Mead algorithm 46 that is part of the built-in optimisation tool in Aspen Custom Modeler (ACM)® . In each generation of the ES new individuals are generated based on the common evolutionary operators and characterised by a solution vector that is further described in Section 5.1. If this vector passes a structural screening procedure (see Section 5.2), which is implemented to avoid the evaluation of structurally infeasible designs, the vector is translated into a process model that is implemented in the equation-based simulation environment ACM® . This also provides the advantage of 25 ACS Paragon Plus Environment


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utilising the aforementioned property databases and Aspen Properties® routines, expanding the range of application of the approach. Nevertheless, prior to optimisation of the resulting process model, simulation runs need to be performed, started with an initialisation procedure that is described in Section 5.3. For each type of PBB, specific initialisation procedures are implemented in order to improve convergence of the process model, which is mandatory due to the complexity of the integrated process models and the nonlinearity of the underlying thermodynamic property models. The optimisation process is stopped as soon as the objective function of all individuals remains within a defined tolerance ∆Ω over a period of at least nmin gen generations. The applied values are listed in Section 7.

5.1

Generation of a Solution Vector

The ES represents a population-based search strategy, in which new individuals, represented by a solution vector, are generated by different recombination and mutation mechanisms inspired by natural evolution. New generated individuals compete with the parent generation and the best set of individuals forms a new generation, whereas the population size remains constant. A more elaborate description of the principle of ES is e.g. given by Weicker 45 who also provides a more elaborate description of the mutation and recombination operators applied for the current ES. These operators include a full range mutation, with a large-scale random specification of the DDoF, and a near space mutation, with a small-scale modification in the vicinity of the parent value for the DDoF. Furthermore, an arithmetic crossover, which generates the new value based on the average value of the three best individuals of the previous generation and the direct parent, as well as a simple crossover, which selects the DDoF value based on one of the three best individuals of the previous generation or the direct parent are included. A more elaborate description of the single operators is provided in the Supporting Information as well. Whenever a new solution vector is generated, one of these operators is randomly selected for each of the DDoF. In contrast to typical ES, the probabilities for the selection of a specific operator are not automatically updated by 26 ACS Paragon Plus Environment

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means of self-adaption mechanisms in the course of the optimisation process. Instead, they are pre-defined such that full range modifications are preferred in the beginning to explore the search space, while in a later phase the focus is placed on the other operators to exploit known promising regions of the search space. The exact values of these probabilities are defined individually for each case study. The general solution vector of an individual

, . . . , ΨPnPBB ], . . . , [ΨPnPBB , [ΨP1,1BB , . . . , ΨP1,nBB v s =(Y1P BB , . . . , YnPPBB BB ,nn BB ,1 BB 1,bin

P BB ,bin

P BB P BB [ξ1,1 , . . . , ξ1,n ], . . . , [ξnPPBB , . . . , ξnPPBB 1,cont BB ,1 BB ,nn

P BB ,cont

],

],

[Ψa1,1 , . . . , Ψa1,2nP BB +nF ], . . . , [Ψa2nP BB +nP ,1 , . . . , Ψa2nP BB +nP ,2nP BB +nF ], [Ψb1,1 , . . . , Ψb1,2nP BB +nF ], . . . , [Ψb2nP BB +nP ,1 , . . . , Ψb2nP BB +nP ,2nP BB +nF ], Ψselect , . . . , Ψselect 1 2nP BB +nF , ξ1 , . . . , ξ2nP BB +nF )

(33)

BB contains discontinuous DDoF YmP BB and ΨPm,o , which define the type of the PBB as well P BB as their discontinuous optimisation variables, and continuous DDoF ξm,p , which define the

operating variables of each PBB. Thereby, the total number of discontinuous and continuous optimisation variables nm,bin and nm,cont depends on the type of PBB. For every PBB, the characteristic variables for the corresponding splitters (Ψak,l , Ψbk,l , Ψselect , ξl ) in the distribul tion network are also part of the solution vector. However, it is important to note that not only the set of equations for a specific PBB is altered by modification of YmP BB , but also the number and type of specific DDoF of this PBB, other than those related to mixer and splitter nodes, differ between the different types. In order to cope with this flexibility P BB in terms of the continuous DDoF, the ξm,p values do not represent the exact value of the

DDoF, but rather a relative position of this value in between the lower and upper bounds, P BB such that 0 ≤ ξm,p ≤ 1 for all these values.

While the optimisation of a generic superstructure that allows for all possible choices of PBB types and their interconnection certainly contains the best possible configuration, it



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also results in a hardly traceable and severely complex optimisation problem. In order to limit the combinatorial complexity to some extent, structural restrictions can be imposed by limiting the choices for PBB types in the set for YmP BB for a specific PBB. Furthermore, the interconnection of PBBs may be restricted by discarding some of the connections in the distribution network, fixing some of the corresponding binary decision variables. Nevertheless, such restrictions should only be introduced in a reasonable fashion, e.g. taking into account the results from the preliminary mixture analysis described in Section 3. In order to avoid a tedious evaluation of infeasible flowsheet structures, an additional structural screening procedure is triggered as soon as a solution vector has been generated.

5.2

Screening of Structural Variables

While the generic definition of the superstructure offers a maximum flexibility, structurally invalid flowsheets, which e.g. do not provide a consistent path from the feed streams to the product streams, are part of the search space and should be discarded prior to a detailed investigation. Therefore, solution vectors are screened prior to a detailed evaluation and potentially recreated unless all of the following criteria are fulfilled: 1. Check of required PBB input streams For each type of PBB it is tested if the stream distribution according to the binary decision variables for the splitter nodes fits the input requirements for the specific type of PBB.

2. Pre-evaluation of direct recycles A direct recycle, which redirects an output stream of a PBB to an input stream of the same PBB, is only valid if the output stream is split and not totally recycled. Stream distributions that are therefore prohibited are illustrated as cases 1.1-1.4 in Figure 8. Furthermore, in order to limit the occurrence of equivalent structures, recycling is


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limited to the split stream of a product stream (dashed lines in cases 2.1-3.4 in Figure 8) from a PBB, while the split stream may also not be the sole input stream (case 3.2). While illustrated for a PBB with two input and output streams, considering the first product stream, these screening criteria apply for the other product stream and PBBs with only one input stream as well.

Figure 8: Valid and invalid direct recycle structures for PBBs with two input and output streams.

3. Prohibit mixing of PBB output streams In order to avoid backmixing an additional screening criterion is that the splitter nodes of both product streams may not distribute those streams to the same mixer nodes. 4. Guarantee a consecutive path from the feed streams to the product streams While the first three screening criteria are easily evaluated and already exclude a lot of infeasible structures, they do not guarantee a consecutive path from the feed to the product streams, such that e.g. isolated recycles as illustrated in Figure 9 still pass the screening criteria. In order to avoid the evaluation of such infeasible structures as well, the calculation of a simplified mass balance for the flowsheet is performed in an implementation in Visual Basic for Applications® . In case this mass balance cannot be solved, isolated recycles or dead ends in the process structure are expected.



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Figure 9: Example of a flowsheet variant containing an isolated recycle between PBB1 and PBB2.

These screening criteria are evaluated in the presented order and in case any of the criteria is violated, the solution vector is recreated and procedure is started again. As soon as a solution vector is validated, it is passed to the detailed evaluation described in the next section.

5.3

Simulation and Evaluation

After clarifying the structural feasibility of the PBB-based flowsheet design associated with the solution vector, the next step is a detailed evaluation of the resulting flowsheet. Therefore, a simulation model is generated in ACM® and a sequence of initialisation steps is performed in order to obtain a steady state solution. This step is of major importance and at the same time of severe complexity, since unlike common simulation models in a commercial simulator, the structure of the process is not known a-priori and there are no unit operation specific initialisation procedures available. Therefore, the model is built in a sequence of steps, starting with the sheer flowsheet structure, which has been checked in the final screening step, and gradually adding information to finally obtain the desired modelling depth. This general sequence of initialisation steps is illustrated in Figure 10.


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Figure 10: Initialisation sequence to obtain the desired modelling depth.

In the beginning, each flowsheet is composed of PBBs of the type Inactive and all types of mass and energy transfer as well as reactions are deactivated in order to determine an initial mass balance. After evaluating this initial flowsheet, the PBB types are set according to the solution vector (step 1), which was generated by the ES. Model reduction by OCFE is activated for each supported PBB type (step 2) and the flowsheet is evaluated again. The successive step 3 is distinguished according to the respective PBB type. While the activation of mass and energy transfer is straightforward for the VP-PBB, three different methods are implemented for the VL-PBB, which are specifically chosen based on the rate of convergence observed for the respective application. The simplest method is the activation of mass and energy transfer in all equilibrium stages at once. Alternatively, the VL-PBB is first reduced to a single equilibrium stage followed by the successive adding of stages, whereas all values of the previous stage are copied to the new one. A steady state simulation run is started each time after copying the values, whereas this procedure is repeated until the desired total number of stages is reached. The third method also activates mass and energy transfer for



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all stages at once, but at the same time the outputs of all mixers in the flowsheet are fixed followed by a steady state simulation run. Consequently, in a first step the PBBs are evaluated independently which increases the chance of convergence since the influence of recycle streams is disabled. Afterwards, the difference between the fixed and the calculated mixer output is gradually reduced to zero by applying the built-in homotopy tool of ACM® . If the subsequent simulation is not converged, a second attempt without OCFE is started (step 4a) in order to overcome problems caused by inaccurate approximation of the composition profiles in the OCFE model, as described in Section 4.2.2. In case the evaluation is successful, potential chemical reactions are gradually activated making use of the homotopy tool (step 4b). The final result of the initialisation process is transferred to the next step Local Optimisation.

5.4

Local Optimisation

After obtaining a steady state solution for the PBB-based flowsheet in the preceding step, the continuous variables of the solution vector are further optimised in accordance with the objective function, making use of the built-in Nelder Mead algorithm in ACM® , while all discontinuous DDoF are fixed. Therefore, the general flowsheet structure is fixed at this instance, while the distribution of split streams as well as heat duties, mechanical energy and other continuous DDoF, which primarily modify the operating conditions are optimised. This does not only aid the ES in form of a memetic algorithm, but also results in significant improvements of the objective function, reducing the process costs, but also reducing the penalty terms and therefore complying with the purity constraints. Finally, the value of the objective function is returned to the ES, where it is used to generate new individuals. Note, that the ES handles all variables as discrete decisions, including the continuous DDoF, for which the total range of values is discretised, taking e.g. the set of [0, 0.25, 0.5, 0.75, 1] for the range of [0, 1]. This results in a significant reduction of the search space for the ES. The final 32 ACS Paragon Plus Environment

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values for the DDoF are determined in the course of the local optimisation. Therefore, the refined continuous variables are also not returned to the ES as e.g. in the memetic algorithm developed by Urselmann and Engell 47 .

6

Translation of PBB-based flowsheets to equipmentbased flowsheets

During the generation of the PBB-based flowsheet variants, ideal mixing, mass and heat transfer are assumed. While the underlying models used for PS are based on rigorous thermodynamics and therefore warrant a general degree of feasibility, they do not allow for a detailed design and rating of the process, which requires the identification of suitable equipment. For a translation of the PBB-based flowsheets to specific equipment in step 4 of the PS framework (Figure 2), these idealised assumptions are now relaxed. Consequently, kinetics of mass and energy transfer as well as size/volume constraints are considered, e.g. taking into account the size of a skid mounted mobile plant. Therefore, initially the most promising PBB-based flowsheet models are reformulated to rate-based models. These models are optimised in order to determine a set of optimal mass and potentially reaction rate coefficients, taking into account a tradeoff relation that correlates the rate coefficients with investment costs. The latter has been derived based on a literature survey. Taking into account the results of this optimisation, suitable equipment is finally selected based on sizing calculations in accordance with a database of conventional and intensified equipment. Since the VP-PBB already represents a rate-based model for a specific membrane, the translation procedure is reduced to the selection of a suitable membrane module based on a decision tree, which takes into account considerations related to membrane fouling, operating pressure as well as membrane material. While the decision tree is provided in the Supporting Information, the translation procedure is further outlined for the VL-PBB. Other PBBs and the according translation information will be introduced in future contributions. 33 ACS Paragon Plus Environment


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6.1

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Reformulation to rate-based models

The important information necessary for identifying suitable equipment for the VL-PBB are the vapour and liquid volume flow rates as well as the overall mass transfer coefficients. The volume flow rates are determined from the mass flow rates using density information obtained with Aspen Properties® routines. Mass transfer kinetics are introduced based on the two film model, whereas a simplified approach based on bulk phase concentrations and overall mass transfer coefficients without considering interface concentrations is applied 48,49 . Consequently, Equations 12 and 19 are substituted with:

molar n˙ trans · (xEQ ˙ i,total · xV L,i,j , V L,i,j = kL,i,j · aef f · VV L,i · ρL,i V L,i,j − xV L,i,j ) + n

(34)

V LE xEQ V L,i,j · KV L,i,j = yV L,i,j ,

(35)

n˙ i,total =

nC X

n˙ trans V L,i,j ,

(36)

j=1 LE KVV L,i,j = f (TV L,i , pV L , xEQ V L,i , y V L,i ),

(37)

ρmolar = f (TV L,i , pV L , xV L,i ), L,i

(38)

for all non-equilibrium stages i ∈ {1, . . . , nV L } and components j ∈ {1, . . . , nC }. Here, the interfacial molar flow rate n˙ trans V L,i,j of component j is determined by two contributions. The diffusive part is determined as the product of a liquid-side overall mass transfer coefficient kL,i,j , an effective interfacial area aef f , the volume of the non-equilibrium stage VV L,i , the molar density of the liquid ρmolar and the difference between a liquid composition xEQ L,i V L,i,j in equilibrium with the bulk vapour composition yV L,i,j and the liquid bulk composition xV L,i,j . The second term represents convective transport and is depicted by the product of the total interfacial molar flow rate n˙ i,total and the bulk liquid composition. The equilibrium LE distribution coefficient KVV L,i,j and the liquid density ρmolar are determined based on Aspen L,i

Properties® routines, based on the compositions and the temperature and pressure. Both the effective interfacial area aef f and the liquid-side overall mass transfer coefficient


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kL,i,j depend on the specific equipment and are usually determined based on dedicated empirical correlations taking into account hydrodynamics and transport properties like diffusion coefficients and surface tensions. Since a specific equipment is to be selected at the end of the translation procedure, a pragmatic simplification is made by lumping the volume of a non-equilibrium stage VV L,i , the effective interfacial area aef f and the liquid-side overall mass transfer coefficient kL,i,j together to a single optimisation variable kL A. Since this simplification implicates equal mass transfer coefficients for each component (kL,i,1 = . . . = kL,i,nC ), this assumption should be checked for multi-component systems and weighting factors for the different components might be introduced to compensate significant deviations. In order to determine an optimal kL A value, a tradeoff between improved mass transfer rates and increasing investment costs needs to be introduced. Therefore, an additional cost function is introduced to the objective function in Equation 32. The cost function

T ICV L = 833950 B Cs m−3 · kL A + 441930 B C,

(39)

is derived from sizing and investment cost correlations, as well as representative kL and aef f values published for various vapour-liquid contacting equipment 42,50 . The modified flowsheet model is then again optimised, taking the structure of the preceding PBB-based flowsheet as fixed and performing a minimisation of the modified objective function using the Nelder Mead algorithm. In addition to the revision of the DDoF from the PBB-based flowsheet, furthermore the characteristic information for the investigation of the equipment sizing, the vapour flow rates V˙ VVL , the kL A value, as well as mean densities for both phases ρL and ρV are obtained. In case a reaction takes place in one of the phases, the total liquid and/or vapour hold-up VVReac,L and VVReac,V are considered as additional DDoF. L L



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6.2

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Equipment size investigation and investment cost calculation

In order to derive equipment specific size information from the results obtained by the ratebased model optimisation, a graphical method is suggested. It builds on a database of typical published equipment-specific operating ranges, considering loading limitations in terms of vapour velocities uVV L as well as information on suitable ranges for kL aef f and the specific liquid hold-up LV L . Since values for the specific vapour hold-up are not readily available, they are not provided here. Table 1 summarises the values of various vapour-liquid contacting equipment, considered for the translation of VL-PBBs.

Table 1: Typical ranges of uV and kL aef f for vapour-liquid contacting equipment. VL-equipment Tray column 42,50,51 Packed column (random) 42,50,51 Packed column (structured) 50–52 Spray col42,50,53 umn Rotating packed bed (RPB) 50,54,55

uV,min VL [m s−1 ]

uV,max VL [m s−1 ]

0.29

2.42

0.29

2.91

0.10

4.36

0.30

1.20

0.10

20.00

kL amax ef f [s−1 ]

kL amin ef f [s−1 ] ·

1.15 10−2 5.09 10−4 5.09 10−4 1.25 10−3 1.30 10−2

· · · ·

1.00 10−1 1.35 10−1 1.35 10−1 1.35 10−2 2.50 10−1

L VL [−] · · · · ·

0.70 0.15 0.15 0.20 0.30

Based on these ranges, the minimum and maximum dimensions of each equipment are determined. In general, the volume ranges are determined by min/max

VM T

kL A

=

max/min

,

(40)

kL aef f

while the ranges for the specific cross-sectional area ACS , characteristic diameters DM T and


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equipment heights HM T are derived for the different types of columns as min/max

ACS

min/max

DM T

V˙ VVL

, V,max/min uV L q min/max = 4 · ACS /π,

=

(41) (42)

min/max

min/max HM T

=

VM T

max/min

.

(43)

ACS

In case a reaction takes place in one of the phases, the minimum required equipment min volume for providing sufficient hold-up VReac is calculated based on the required reaction

volume and typical specific hold-up values by

min VReac

VVReac,L L = LV L

(44)

min exceeds the required equipment if a liquid-phase reaction takes place. In case VReac

volume for pure mass transfer VMmin T , Equation 40 is replaced by

min VMmin T = VReac ,

VMmax T =

kL A . kL amin ef f

(45) (46)

For RPBs, the sizing information is derived in accordance with Sudhoff et al. 54 , calculating the ranges for the inner and outer radius Ri,Rotor and Ro,Rotor , as well as the height of the rotor HRotor as



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V˙ VVL

0.5 ρ 0.25 V

Ri,Rotor = 0.437 · ρL v u u V min/max min/max MT , Ro,Rotor = t max/min 2 · π · HRotor min/max

HRotor

= 0.625 ·

,

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(47)

(48)

V˙ VVL V,max/min

π · Ri,Rotor · uV L

.

(49)

Together with additional sizing guidelines from Gudena et al. 56 and Woods 42

3 ≤

HM T ≤ 30, DM T

(50)

Ro,Rotor ≤ 1 m,

(51)

HRotor ≤ 0.85, Ro,Rotor

(52)

limiting the ratio of column height to diameter, as well as the rotor sizes for an RPB, equipment specific design windows are derived, which can be visualised graphically. Figure 11 illustrates such a design window and the different limitations for a randomly packed distillation column. If no suitable design window can be determined for a certain type of equipment, this type can be excluded from further investigation.

Figure 11: Exemplary design window for a randomly packed distillation column.


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For further investigation, the derived design parameters are augmented by surcharge factors according to the work of Gudena et al. 56

Htotal,Column = HM T · 1.5,

(53)

Dtotal,Column = DM T ,

(54)

Ro,total,RP B = Ro,Rotor · 1.5,

(55)

Htotal,RP B = HRotor · 1.5,

(56)

in order to account for extra space, e.g. for liquid distributors in columns or the motor and housing of a RPB. Finally, these design parameters are checked against given size/volume limitations, e.g. for mobile or off-shore implementations, and the investment costs of each suitable equipment are calculated in order to select the most promising one. Further information on the investment cost calculation is provided in the Supporting Information. Note that this translation procedure is one step towards the selection of suitable equipment, while a final design for a specific equipment should be based on dedicated calculations, making use of a multi-component mass transfer model, such as the Maxwell-Stefan approach 57 , in combination with equipment-specific correlations.

7

Case Study: Dehydration of ethanol

In order to demonstrate the developed PS method, it is applied to the well-known, but industrially relevant case study of ethanol dehydration. While this binary mixture might seem simple, the separation of this azeotropic mixture demands the use of a rigorous thermodynamic model and allows to demonstrate the capability of the PS method to determine interesting solutions without providing any initial process structure. The following subsections describe the application of the five step approach introduced in Section 3 in a step-by-step fashion.



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7.1

Step 1: Problem definition and analysis

Two scenarios with different feed composition, product purities and capacity are investigated. The problem specifications are set according to the publications of Roth et al. 58 and Gudena et al. 56 in order to obtain comparable results and are summarised in Table 2. The first scenario represents a large-scale purification of an already concentrated ethanol stream 58 , while the second scenario is representative for a decentralised production of ethanol from a lignocellulosic feedstock 56 . While no size/volume restrictions are assumed for the first scenario, space limitations of commercial motor vehicles (CMV) (height: 4.27 m, width: 2.60 m, length: 14.63 m) 59 are assumed for a ”plant-on-a-truck” concept for the second scenario, in order to facilitate an on-site purification of ethanol at farms.

Table 2: Two different scenarios for the dehydration of ethanol 56,58 . F eed ScenariowEtOH [kg kg −1 ]

spec wEtOH [kg kg −1 ]

spec wH2O [kg kg −1 ]

m ˙ EtOH [t a−1 ]

1 2

0.996 0.997

0.990 0.999

197250 4289

0.719 0.050

Thermodynamic property data is calculated by Aspen Properties® routines, describing the non-ideality of the liquid phase by means of the NRTL model 60 . Further information on the thermodynamic property models is provided in the Supporting Information. For the evaluation of the objective function defined by Equation 32, the capital charge factor is fixed to 10 % for a depreciation period of ten years. In order to satisfy the product specifications, penalty terms are introduced that are given in the Supporting Information, together with the specific ES setup for both scenarios.

7.2

Step 2: Selection of PBBs

In order to identify suitable PBB types for the given PS problem, the modified version of the automatic screening tool developed by 26 is applied. Based on the screening of pure 40 ACS Paragon Plus Environment

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component property data the following PBB types are suggested for both scenarios: VL-PBB in combination with suitable MSA, VL-PBB in combination with PV- or VP-PBB, VL-PBB on different pressure levels, single PV- or VP-PBB as well as LL-PBB in combination with suitable MSA. As far as possible, the introduction of additional components to the system is to be avoided and therefore the first and last option with a MSA are initially discarded. While in principle both, a PV as well as a VP membrane can be used for the dehydration of ethanol, only the VP-PBB is selected for further consideration as representative membrane process, as it avoids temperature polarisation and allows for a closer comparison with the results obtained by Roth et al. 58 . VL-PBBs on different pressure levels are not further considered here since it was shown in previous studies that in many cases pressure swing processes are economically inferior compared to membrane-based hybrid processes for the dehydration of EtOH 61 .

7.3

Step 3: Generation of PBB-based flowsheet variants

In accordance with the pre-selection of PBB types in the previous step, the automatic generation and ranking of different PBB-based flowsheet variants is performed by means of the superstructure optimisation approach. Before presenting the results for the two considered scenarios, first the setup of the superstructure is summarised.

7.3.1

Setup of the superstructure model

In order to model the VP-PBB, a suitable membrane needs to be selected and a thermodynamic model for the driving force DFV P,i,j , as well as an empirical model for the membrane permeance QV P,i,j need to be provided. Here, a polyimide membrane produced by WhiteFox Technologies Ltd. is selected and the driving force and permeance are described by the difference in partial pressure and an empirical correlation provided by Roth and Kreis 62 . The membrane is axially divided into nV P = 30 discrete elements and the corresponding values for each discrete element i ∈ {1, . . . , nV P } and each component j ∈ {1, . . . , nC } are 41 ACS Paragon Plus Environment


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calculated as

Ret DFV P,i,j = pPV erm P,i,j − pV P,i,j ,

QV P,i,j = Q0V P,j · exp

−EA,j R · TVRet P,i

(57) ! .

(58)

The necessary parameters Q0V P,i,j and EA,j are provided in the Supporting Information. For modelling the VL-PBB, a total number of nV L = 30 equilibrium stages is assumed. This number presents a compromise between computational effort and feasibility of the separation. For the sake of model reduction, an OCFE approximation by means of 3 finite elements with 3 internal collocation points is applied, resulting in a significant reduction of the model complexity, having to solve the MESH equations for only 9 instead of 30 stages per VL-PBB. However, in order to obtain the final results which are demonstrated here, the OCFE approximation is deactivated and the MESH equations are solved for all of the 30 stages of each VL-PBB. Consequently, potential deviations caused by the OCFE approximation are avoided. It is important to note that this number of equilibrium stages does not represent a final process design. It shall only be sufficient to allow for a desired separation in the synthesis step, while providing the necessary accurate description of the thermodynamic restrictions. The actual sizing of equipment is considered in the translation step, for which the objective function is also refined. Consideration of the number of equilibrium stages as DDoF already in the synthesis step is in principle possible, but would require the introduction of investment costs in the objective function and as such the consideration of specific equipment. Without such modification of the objective function, the best possible solutions will always exploit the maximum number of available equilibrium stages. Setting up the superstructure, it has to be guaranteed that it is rich enough to cover the flowsheet of the optimal design, but especially when using rigorous models, it has to be as tight as possible to decrease the complexity of the resulting optimisation problem 63 . Therefore, a compromise had to be made between a generic superstructure allowing for all possible


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connections of a large number of different PBBs and a dedicated superstructure with too few possible choices. Especially by introducing too many PBBs, the number of possible flowsheet variants rises exponentially. Therefore, for this case study, the superstructure comprises four PBBs, featuring a maximum number of two VP-PBBs and two VL-PBBs. Furthermore, one of the PBBs is fixed to the type VP-PBB dictating the use of a membrane in order to overcome the azeotrope. In order to check for the exclusion of superior solutions and the effect on the computational effort, another superstructure with six PBBs is set up for scenario one and the results are reported as well. The distribution network further considers a single feed stream and two product streams. Stream splitting is further restricted to the splitters subsequent to the VL-PBB. Allowing for arbitrary stream splitting resulted in highly interconnected complex configurations which did not provide any benefit concerning the quantification of process economics. In addition to the potential condensation of the product stream after the VP-PBB, the continuous DDoF are bound by confining the feed pressure to a range between pRet V P,0 ∈ [1.5 bar, 5.0 bar], the permeate pressure between pPV erm P,nV P ∈ [0.02 bar, 0.15 bar] and the retentate factor between ξVRet P ∈ [0.30, 0.99]. These lower and upper bounds of the continuous optimisation variables are established based on a preliminary sensitivity analysis.

7.3.2

Flowsheet variants for scenario 1

For the first scenario, the termination condition introduced in Section 5 was fulfilled after 798 generations, which means that 7980 solution vectors passed the structural screening procedure and were evaluated in the course of the optimisation. Overall, 35 % of the solution vectors that passed the structural screening procedure resulted in converged and locally optimised flowsheet evaluations. The low convergence rate results from the complexity of the model in combination with the generic process structure which prohibits an exploitation of the structure for the initialisation, as well as problems resulting from the OCFE approxi-



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mation at high purities. It will be shown in Section 7.3.3, that the convergence rate can be increased significantly by the extension of the initialisation procedure that accounts for a re-evaluation without the OCFE approximation, in case convergence cannot be reached in the first run. Out of the converged flowsheet variants, 614 satisfied the imposed purity specifications. However, it should be noted that in fact 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 scenario, at least 18 structurally different flowsheet variants were generated, which satisfied the purity constraints. One of the results, which is however not one of the most promising ones, is illustrated in Figure 12. The VL-PBBs are connected in a countercurrent configuration with a liquid and a vapour recycle, representing the structure of a typical distillation column. The top product is dehydrated using a sequence of two VP-PBBs representing a two-stage vapour permeation process, whereas the permeate of the first stage is fed to the distillation column and the permeate of the second stage is recycled to the membrane feed. It therefore represents the typical distillation-based hybrid process investigated e.g. by Roth et al. 58 . This process results in a total heat requirement of 15.42 M W , a total cooling requirement of 12.12 M W and a TAC estimate of 4898 kB Ca−1 and is further addressed as reference case for scenario one.


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Figure 12: Reference case for scenario 1 of the case study of ethanol dehydration. ( Vapour)

Liquid,

The best flowsheet variant that was generated in the course of the optimisation is illustrated in Figure 13. It consist of a single VL-PBB and two VP-PBBs, whereas instead of recycling the permeate of the second VP-PBB, it is mixed with the feed stream and fed into the VL-PBB. This results in an increase in the water concentration of the VL-PBB inlet stream which further results in a reduction of the boil-up ratio. Consequently, the energy consumption is significantly reduced compared to the reference case, resulting not only in a reduction of the heat and cooling requirement by 20 % and 30 % respectively, but also in a reduction of the TAC estimate by about 18 %. While this cost reduction is mainly caused by the reduced heat requirement, no significant increase in membrane area is required. The result of the PBB-based PS is further supported by the study of Vane and Alvarez 64 who



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proposed and investigated in detail a hybrid membrane-assisted vapour stripping process, which shows a high resemblance with the PBB-based flowsheet demonstrated here.

Figure 13: Best flowsheet variant for scenario 1 of the case study of ethanol dehydration. Liquid, Vapour

In order to investigate the influence of the size of the superstructure, especially the number of PBBs, on the quality of the solution and the computational effort, an additional optimisation of a superstructure with six PBBs was performed. The choice of the PBB type was restricted to a maximum of three VL-PBBs and three VP-PBBs, whereas one of the PBBs was fixed to VP-PBB. The termination condition was fulfilled after 1104 generations, which means that 11040 solution vectors were evaluated. Thereby, a similar convergence rate as mentioned before was achieved. The best flowsheet variant that was generated equals the one shown in Figure 13. In general, the number of flowsheet variants that benefit from the enlarged superstructure and can compete with the reference case shown in Figure 12 is very small. Only 2 % of the flowsheet variants which showed improved performance compared to the reference case are composed of more than two VL-PBBs and/or two VP-PBBs. Most 46 ACS Paragon Plus Environment

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of the flowsheet variants have similar structures such as the one shown in Figure 13 but use three VP-PBBs whereas one of them usually has a negligible membrane area, making its effect superfluous. Therefore, it can be concluded that for this case study, the computational effort is increased significantly for the increased superstructure size without generating a better solution, indicating that the superstructure with four PBBs is sufficiently sized for this case study.

7.3.3

Flowsheet variants for scenario 2

Following the same approach as for the first scenario, the termination condition was fulfilled after 1084 generations, which means that 10840 solution vectors were evaluated. By modifying the initialisation procedure as mentioned before, overall 52 % of the evaluated solution vectors that passed the structural screening resulted in converged and locally optimised flowsheet evaluations. Due to the increase of the purity constraint in comparison to scenario 1, the number of flowsheet variants satisfying them was reduced to 199. Out of these flowsheet variants, at least 15 were structurally different, taking into account the type and number of selected PBBs and the distribution of the feed streams only. This time, a fixed flowsheet that was proposed by Gudena et al. 56 serves as reference case. This flowsheet consists of a combination of two vapour permeation stages with a stripper configuration consisting of three RPBs. For comparison with the PBB-based process flowsheets obtained from the optimisation, this reference case is initially translated into a PBB-based flowsheet. The three RPBs are directly translated into single VL-PBBs and the feed stream is introduced between the first two VL-PBBs. Additionally, the vapour product of the stripper configuration is fed to the VP-PBB sequence, whereas the permeate streams are recycled to the VL-PBB. The results are illustrated in Figure 14. This process results in a total heat requirement of 1.60 M W , a total cooling requirement of 0.98 M W and a TAC estimate of 487 kB Ca−1 .



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Figure 14: Reference case for scenario 2 of the case study of ethanol dehydration. Vapour

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Liquid,

The best PBB-based flowsheet obtained from the superstructure optimisation is illustrated in Figure 15. While showing some resemblance in the overall structure, only a single VL-PBB and VP-PBB are utilised. Furthermore, the VL-PBB is equipped with a reboiler and a condenser. Compared to the reference case, the total heat and cooling requirement is reduced by 24 % and 2 % respectively, resulting in a reduction of the TAC estimate by 21 %. The main reason for this reduction is the elimination of recycle streams from the VP-PBB to the VL-PBB which cause a major share of the heat requirement of the reference case. However, since both the permeate and retentate of the VL-PBB need to satisfy the purity 48 ACS Paragon Plus Environment

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specification in this design, a minor increase in total membrane area results in comparison to the reference case.

Figure 15: Best flowsheet variant for scenario 2 of the case study of ethanol dehydration. Liquid, Vapour

While the same components are to be separated in both scenarios, only at different compositions, it is interesting to note that different PBB-based flowsheets are determined as most promising options in the course of the optimisation. In order to check the validity of the results, the best flowsheet variants for the first and second scenario have therefore been explicitly tested for the other scenario, taking into account the fixed structure while optimising the continuous DDoF. The comparison of the results revealed that the best flowsheet variants obtained for each scenario are indeed the best performing ones, as indicated in Table 3.



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Table 3: Comparison of the results of both scenarios for the case study of ethanol dehydration.

7.4

TAC [kB Ca−1 ]

Scenario 1

Scenario 2

Best flowsheet variant Reference case Best flowsheet variant (other scenario)

4023 4898

387 487

4032

487

Step 4: Translation into equipment-based flowsheets

Furthermore, the translation of the most promising PBB-based flowsheet variants into equipmentbased flowsheets was performed.

7.4.1

Translation of scenario 1

The most promising PBB-based flowsheet for the first scenario was illustrated in Figure 13. After reformulation of the equilibrium-based model to a rate-based model and the optimisation of the continuous DDoF, a target kL A-value is determined for the VL-PBBs and design windows are derived for each type of equipment considered in the database. The relevant information from the optimisation is summarised in Table 4, while the corresponding design windows are illustrated in Figure 16.

Table 4: Relevant information for translating the best flowsheet of scenario 1. Variable

Value

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

25064 0.066 856 0.896

Obviously, there is no suitable design window for the tray column while only very small design windows result for the spray column and the RPB, such that they are not considered


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further. The design windows of the structured and randomly packed columns are very similar, however, the minimal dimensions of the structured packed column are slightly lower due to the increased mass transfer efficiency. Consequently, the investment cost calculation yields 1.80 · 106 B C for the randomly packed column and 1.17 · 106 B C for the structured packed column, which is why the latter is selected for representing the VL-PBB.

Figure 16: Design windows obtained for the VL-PBB of the best flowsheet variant of scenario 1. Selecting a column design with structured packing, a height of the column between 6.5 m and 85.5 m and a diameter between 1.4 m and 3.7 m can be extracted from the design window. Obviously, this result does not replace a detailed sizing. However, in order to show the general validity of the results obtained from the superstructure model and the translation method, the flowsheet is set up in Aspen Plus® using the rate-based RadFrac model to simulate the stripping column and a tuned separator model to represent the VP-membrane performance. To determine an appropriate sizing, a Sulzer© Mellapak™250.X packing is selected and the Packing Sizing and Packing Rating functions of Aspen Plus® are applied. In order to achieve the same separation performance in terms of product compositions, a column diameter of 2.02 m and a column height of 6.96 m are determined, both lying well 51 ACS Paragon Plus Environment


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in the ranges determined by the translation method. More specific, the dimensions of this column lie in the bottom left corner of the design window determined by the translation method (compare Figure 16) and the stream compositions obtained by the PBB-model are consistent with the Aspen Plus® simulation.

7.4.2

Translation of scenario 2

Again, the most promising PBB-based flowsheet illustrated in Figure 15 is selected for the translation into an equipment-based flowsheet. The relevant information obtained after reformulation of the PBB-based model to a rate-based model and the optimisation of the continuous DDoF is summarised Table 5. Table 5: Relevant information for translating the best flowsheet of scenario 2. Variable

Value

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

2821 0.073 909 0.749

The design windows derived for the different types of equipment are further illustrated in Figure 17. Because of the alternative feed and product specifications and unlike the first scenario, this time for each equipment choice suitable design windows are determined.


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Figure 17: Design windows obtained for the VL-PBB of the best flowsheet variant of scenario 2.

However, as indicated in the initial problem specification, the final design should be applicable for a decentralised production and as such additional space limitations of a CMV are assumed for a ”plant-on-a-truck” concept. The size ranges derived from the design windows are therefore summarised in Figure 18 and compared with the space limitations of the CMV.



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Figure 18: Ranges of apparatus height and width of the VL-PBB of scenario 2. TC: tray column, PC: packed column, SC: spray column, RPB: rotating packed bed.

Obviously, especially the maximum height of a CMV presents a limiting factor, resulting in a direct discard of a spray column. A tray column and both packed columns might be feasible with their minimum heights derived from the design windows lying just below the maximum height. However, the best fit to the additional space limitations of a CMV is given by the RPB, for which the full range of heights lies completely below the size constraint, while also most of the range for widths satisfies the CMV limitation. Consequently, the RPB appears to be the most promising option for a final design, which is why a final comparison based on investment costs is not performed.

7.5

Step 5: Optimisation of equipment-based flowsheets

For a final design and sizing, the most promising equipment-based flowsheet should be determined by detailed rate-based models building on equipment-specific correlations and constraints, as well as a thorough consideration of process hydrodynamics. This step is out of the scope of this contribution, which should provide process concepts and a quantification of performance estimates for a dedicated investigation. A final design can be performed by means


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of an optimisation-based approach taking into account a superstructure of a fixed flowsheet structure with variable equipment sizes and operating conditions, such as e.g. demonstrated by Roth et al. 58 for similar flowsheet variants as determined in this contribution.

8

Conclusion

The current work introduced a novel model-based method for process synthesis, which facilitates an automatic generation of flowsheet variants by superstructure optimisation using a combination of a stochastic and deterministic algorithm. The basic elements of the generic superstructure are so-called phenomena building blocks, which represent an aggregation of different mass and energy transport phenomena that are not necessarily linked to a certain type of equipment. A special feature of the current method that distinguishes it from preceding methods is the consideration of rigorous thermodynamics for each of the phenomena building blocks. This warrants thermodynamic feasibility of the resulting flowsheet variants and makes the method applicable to complex mixtures exhibiting thermodynamic limitations such as azeotropes and distillation boundaries. The mostly generic combination of the phenomena building blocks allows for the generation of highly integrated and especially hybrid flowsheet variants, presenting process intensification on the process and plant scale. Process intensification on the operation and equipment scale is further pursued in the subsequent translation of the phenomena building blocks to specific equipment, taking into account conventional as well as intensified equipment. The applicability of the method was demonstrated using the dehydration of ethanol as a case study, showing that it is possible to automatically generate conventional as well as innovative flowsheet variants, which are able to outperform known solutions. Validity of the results was analysed by a comparison between superstructures of different sizes, also analysing the computational effort of increasing the search space, as well as a detailed rate-based model analysis for one of the investigated scenarios taking into account a rate-based model of a



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packed distillation column in Aspen Plus® . The latter comparison also demonstrated that the graphical translation method provides reasonable information to analyse the suitability of the different types of equipment. Future work extends the portfolio of available phenomena building block models, specifically demonstrating the applicability to reactive systems, taking into account reactor networks and reactive separations. Furthermore, the application of the process synthesis method to more complex case studies, also involving a selection of mass separating agents will be demonstrated. Both extensions requiring an adequately detailed description that would have exceeded the current article, which primarily introduced the method and a first selection of phenomena building blocks. Although the results of the case study demonstrate the benefits and the potential of the developed method, the high number of required solution vectors and generations also indicates the limitations of the current implementation. The current implementation provides a very convenient and user-friendly connection to the portfolio of physical property models, as well as the available databases of Aspen Properties® . However, the solution of the optimisation problem might significantly benefit from a transfer to a dedicated modelling and optimization environment, such as GAMS or AMPL, which provide automatic differentiation and highly sophisticated solvers for all kinds of mathematical programming problems.

Figure 19: For Table of Contents Only


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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 model reduction, evolutionary operators as well as economic models and thermodynamic property data for the case study. This material is available free of charge via the Internet at http://pubs.acs.org/.

Nomenclature Latin letters



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aef f : ACS : AV P : CostC : CostEl : CostH : CostV P : cp : D: DFV P : EA : fc : h: H: HRotor : ∆hLV S : kL : kL A: KVV LLE : m: ˙ nC : nF : nmin gen :

nP : nP arents : nP BB :

Effective interfacial area Cross-sectional area VP membrane area Cooling agent costs Electricity costs Steam costs VP membrane costs Specific heat capacity Diameter VP driving force for mass transfer Activation energy Depreciation factor Specific enthalpy Height Axial height of RPB rotor Heat of evaporation of steam Liquid-side overall mass transfer coefficient Fused mass transfer variable (= kL · aef f · VV L ) VL-distribution coefficient in VL-PBB Mass flowrate Number of components 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 PBBs


[m2 m−3 ] [m2 ] [m2 ] [B C t−1 ] [B C kW h−1] [B C t−1 ] [B C m−2 ] [kJ kg −1 K −1 ] [m] [bar] [J mol−1 ] [−] [kJmol−1 ] [m] [m] [kJ kg −1 ] [m s−1 ] [m3 s−1 ] [mol mol−1 ] [ta−1 ] [−] [−] [−]

[−] [−] [−]

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nP en : nsplit : nV L : nV P : n: ˙ p: PCompr : PP ump : P enalty: ˙ Q: QV P : r: R: Ri,Rotor : Ro,Rotor : T: tOp : T AC: T IC: T OC: V˙ : V: vs: w: x: y: wj : xj : yj : Y: z:

Number of penalty functions Number of active splitters Number of discrete elements in the VLPBB Number of discrete elements in the VPPBB Molar flowrate Pressure Power consumption of compressor Power consumption of pump Penalty function Heat duty Molar permeance Reaction rate Ideal gas constant Inner radius of RPB rotor Outer radius of RPB rotor Temperature Time of operation Total annualised costs Total investment costs Total operating costs Volume flowrate Volume Solution vector Vector of mass fractions Vector of molar fractions in liquid phase Vector of molar fractions in vapour phase Mass fraction of component j Molar fraction of component j in liquid phase Molar fraction of component j in vapour phase PBB type Molar fraction


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


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Greek letters ∆Ω: : κ: ρ: ρmolar : Ω: ξ: Ψ:

Objective function tolerance Hold-up Heat capacity ratio Mass density Molar density Objective function Dimensionless factor Integer variable

[B C a−1 ] [m3 m−3 ] [−] [kg m−3 ] [kmol m−3 ] [B C a−1 ] [−] [−]

Subscripts c: EtOH: h: H2O: i: j: k: l: m: mix: MT : n: o: p: R: split: V L: V P:

Cooling Ethanol Heating Water Indicator of discrete element Indicator of component Indicator of mixer Indicator of splitter Indicator of PBB Mixer Mass transfer Indicator of penalty function Indicator of discontinuous optimisation variable Indicator of continuous optimisation variable Rotor of an RPB splitter VL-PBB VP-PBB


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Superscripts 0: a, b: boil: Cond: DN : EQ: in: L: max: min: out: ∆p: P erm: Q: Reac: Repl: Ret: select: spec: trans: V: V LE:

Reference state Selection of mixer Boiling Condensation Distribution network Equilibrium Input stream Liquid Maximum Minimum Output stream Pressure increase Permeate of VP-PBB Heat transfer Reaction Membrane replacement Retentate of VP-PBB Selection of splitter Product specification Interfacial flowrate Vapour Vapour-liquid equilibrium

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