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10ο ΠΑΝΕΛΛΗΝΙΟ ΕΠΙΣΤΗΜΟΝΙΚΟ ΣΥΝΕΔΡΙΟ ΧΗΜΙΚΗΣ ΜΗΧΑΝΙΚΗΣ, ΠΑΤΡΑ, 4-6 ΙΟΥΝΙΟΥ, 2015.

SYNTHESIS AND DESIGN OF MULTIPHASE CHEMICAL AND BIOCHEMICAL REACTORS

Georgios P. Panayiotou1, Aikaterini D. Mountraki1,2, Antonis C. Kokossis1

1School of Chemical Engineering, National Technical University of Athens (NTUA), Heroon Polytechniou 9,Zografou Campus GR-15780, Athens, Greece

2Compagnie Industrielle de la Matière Végétale (CIMV), 109, Rue Jean Bart - Diapason A - F-31670 Labège,

France

ABSTRACT

In recent years, the chemical reactor has been elevated to the position of being arguably the most important unit

to optimize within a chemical process plant. The growing demand for “green products” has contributed to therapid development of biorefineries. The fractionation of biomass and its conversion to products is the objective

of recently developed chemistries which are still under research in order to be optimized. The design of

contemporary biochemical reactors is mainly based on the existing experience and heuristics in conventional

reactors. The diversity of feedstock, along with the complicated activity of the microorganisms used, imposes

new uncertainty factors for the design of the bioreactors. The new objectives are centered around cleantechnology and are namely: (1) to give as far as possible only the desired product, (2) to reduce by-products and

pollution, (3) to minimize the inhibition factors, and (4) to intensify processing in order to improve economics.

This work presents a superstructure-based simulated annealing approach to the synthesis of reactor networks in

an equation-oriented environment. Mass transfer correlations are introduced for different types of reactor

showing a notable impact on the selection of the design of the reactor. An example in algae bioreactors is also

discussed, highlighting the wide range of application of the method proposed.

ACKNOWLEDGEMENT

The EC (Reneseng-607415 FP7-PEOPLE-2013-ITN) is gratefully acknowledged for supporting this work.

INTRODUCTION

The reactor design was the objective of the chemical industry well before the first process design methods were

developed. The first systematic approach used for optimization for reactor design is dated back in 1960 by Aris

(1960). The first reactors were single phase and the development of multiphase reactor network synthesisreceived attention only after the late 90’s. Approaches to optimal homogeneous reactor network synthesis

include the geometric attainable region (AR) method (Hildebrandt & Glasser, 1990; McGregor et al, 1999), the

optimization reactor network superstructures using mixed integer non-linear mathematical programming

(MINLP) (Kokossis & Floudas, 1990; 1994) or a combination of the two (Balakrishna & Biegler 1992;

Lakshmanan & Biegler, 1996). AR applications are severely limited for problems of higher dimension and

inappropriate for the case of multiphase systems whereas the non-linear process models cause uncertainty about

the quality of designs obtained from the mathematical programming-based approaches. Moreover, both

strategies lead to only a single design candidate. Realizing these shortcomings Marcoulaki and Kokossis (1999)

introduced stochastic techniques to superstructure search, that allow to provide robust performance targets as

well as a set of potential design candidates with close-to-target performances. Hillestad (2004) proposed a new

model formulation that composed of both CSTR and PFR model equations and an optimal control problem was

solved by using a steepest descend method. More recently Jin et al (2012) presented a double-level optimization

method which combines linear programming and stochastic optimization approach according to the character of

the reactor network model based on CSTR.

All the methods described have studied their application to conventional reactions. The introduction of

biorefineries has industrialized new chemistries, revealing a lack of available designing techniques and methods

for the biorefinery processes. Next challenge is the third generation biorefineries, where algae process is aheterogeneous system with complex mass transfer and hydrodynamic behavior. This paper introduces the

optimization of a superstructure representation of ideal reactor units involving CSTRs and PFRs as proposed by

Kokossis and Floudas (1990) for the full conceptual design of multiphase chemical and biochemical reactors.

The objective of this study is to develop a systematic superstructure framework for the synthesis and design of

biorefineries process. The mathematical model of the optimization problem is enriched with mass transfer

correlations for different real reactor designs, investigating the impact of these correlations to the final design

decision. A wide range of correlations is available in the literature for various kinds of reactors such as agitatedvessels, sieve plate reactor, bubble column reactors, sparged reactors and packed column reactors (Schluter et al,

1992; Kawase et al, 1992; Linek et al, 2012). Two case studies are presented: (1) The modified Denbigh

reaction, presented by Linke and Kokossis (2003), and (2) the case of a new biorefinery example, the cultivation

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of algae for the production of lipids. The proposed method can be applied for the synthesis, design, and

optimization for both, conventional and non-conventional processes since it is fully adjustable to any type of

process.

PROBLEM DESCRIPTIONFor a given chemical process, the input data include the raw materials, the reaction kinetics, and the

thermodynamic properties. The mathematical model is an improved version of the systematic framework based

on Simulated Annealing (SA) algorithm for the synthesis, design, optimization and superstructure representation

of complex network reaction systems (Kokossis & Floudas, 1990). The synthesis framework includes the

following stages:

1. Targeting stage: At the end of this stage the initial structure of the superstructure representation is created

using the shadow reactor superstructure; where for each reactor unit is consisted by two parallel blocks, the

reactor taking account for the one phase and the shadow reactor taking account for the other phase(s).

2. Screening and design stage: This stage evaluates the results of the targeting stage and screen the options that

have a positive impact on the system.

3. Analysis stage and validation.

The superstructure (Fig. 1) is composed from the two types of basic reactors units: ideal CSTRs and ideal PFRs.

The horizontal connection is calculated by the mass balances, while the vertical connection depends on the mass

transfer between the two phases (iph i↔ iph j). The transport phenomena are very important in multiphase

reactor network. For every different type of reactor, different mass transfer coefficients are calculated and may

include anaerobic biofilms, agitated vessels, sieve plate reactors, bubble column reactors, sparged reactors, pack

column reactors.

Figure 1. Superstructure representation

The great importance of the framework is that it identifies the maximum achievable efficiency of the resulting

optimum reactor network, providing useful information about

i.

The number and type of reactorsii. The desired mass transfer correlation for each type of reactor

iii. The volumes of reactors

iv. The appropriate feeding, mixing, recycling and bypassing strategy and

v. The optimal values of the flowrates, compositions and yields.

CASE STUDIES

The proposed method can be applied to a wide range of reactor types. Scoping for highlighting its applicability, atheoretical and a biorefinery example is illustrated. The selected correlations for the above mentioned reactor

types are introduced into the general optimization problem. The objective function maximizes the yield.

Theoretical example

The reaction selected is the theoretical Denbigh reaction which is used mainly for network analysis, simplifying

very complex reactions such as parallel reactions, series (or consecutive) reactions, independent reactions, series-

parallel reactions, triangular reactions. It is very promising for the simulation and reaction network design of

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complex nonlinear biorefinery reaction such as the algae cultivation for the production of chemicals. It can be

analyzed to four reactions (Eq.1-4) as shown below (Mehta, 1998):

A+2F B + 2H r 1=k 1CLACLFCLF k 1=10

−ℎ− (1)

A+F D + H r 2=k 2CLACLF k 2=5

(

−)

ℎ− (2)B+F C + H r 3=k 3CLBCLF k 3= 2

−ℎ− (3)

B+2F E + 2H r 4=k 4CLBCLFCLF k 4= 1 (

−)

ℎ− (4)

The impact of mass transfer coefficient on the reactor network is examined through the study of fixed mass

transfer coefficient and the case of a free selection based on the correlations for the type of the reactor.

Case A: K L = 330

In the first case the mass transfer coefficient is set 330 for all the types of reactors. The results on Table 1

indicate that the reactor network does not change, resulting in an optimum configuration of PFR reactors for both

phases.

Table 1. Results of theoretical reaction for constant K L

Case B: K L = Free Selection

Table 2 presents the results in the case where the mass transfer coefficient is freely selected, restricted only by

the type of reactor. It is observed that the configuration PFR-PFR is also preferred most of the times. In this case

though, alternative configurations also start to arise, with a small penalty in the objective function.

Table 2. Results of theoretical reaction for free selection K L

Biorefinery example

The example chosen is the cultivation of algae for the production of lipids. Deliberately, algae is not often

studied computationally due its complex and nonlinear nature of the Monod equations which characterize best

the reaction occurs during algal growth, as a result of the photosynthesis of the algae. Algal growth kinetics cancharacterized using the Langmuir equation. The mechanism behind the algal growth is biosorption which more

like chemisorption rather than physical absorption. Algae biomass can characterize as weakly acidic ion

exchanger. The process of biosorption it is strongly pH-depended. Biosorption occurs when biomass (dead or

alive) binds with passive cations. An application of this process is the biological and cheap removal of toxic

metals from industrial waste waters. The reaction mechanism of biosorption process is very complex due to the

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fact that involves ion-exchange complexation, electrostatic attraction and microprecipitation while metal ion

binding takes place. Spirulina is chosen for this example since it is the algae with the biggest amount of

information available.

The algal cultivation usually takes place in four kinds of reactors (Slegers, 2014): raceway pond, horizontal

tubes, vertically stacked horizontal tubes, flat panels. The most commonly reactor used is the raceway pond.Recent experimental studies shown that the mixing baffles created have important impact on the yield of the

reactor (Slegers, 2014). Consequently, this can be simulated as Denbigh reactor represented by sub-CSTRs for

every mixing buffer Flat panel PBR reactor type. Table 3 shows the algae species which were chosen in this case

study and the standard values which were used in the simulation.

Table 3. Standard Values of the algae species used in simulations (Slegers, 2014)

Thalassiosira pseudonana:

= 10 −

= 269 −

= 0.05 −

Phaeodactylum tricornutum:

= 1 −

= 75 −

= 0.05 −

For the maximum algae growth a conversion yield is measured by the conversion efficiency of the light energy

into biomass and denoted as PE (“photosynthetic efficiencies”) (Slegers, 2014). The maximum attainablefeasible conversion is 9%. However, for each type of reactor applies different average PE conversion; i.e. for

raceway ponds 1.5%, for horizontal tubes 3%, for flat plats 5%. The overall chemical reaction equation used to

simply the photosynthesis process which occurs during algal growth is characterized by the Monod growth

model which is presented below (Eq. 8, 9):

106 + 16 − + 4

− + 122 → + 138 (8)µ = µmaxS/(Ks + S) (9)

Where μ is the concentration (growth) of the biomass component () and S the concentration

of . The results are realistic since the maximum feasible algal growth yield ratio was achieved before the

point (point 5 on Fig. 2) where concentration starts decreasing. The algorithm initially converged at annealing

temperature 129 degrees C implying that it could undergone further optimization to give, finally, an objectivevalue of 6.96 percent yield ratio (desired product molar flowrate over feed molar flowrate), represented by point

4 at Fig. 2, with final annealing temperature below two degrees C.

Figure 2. Algal Growth vs Time

CONCLUSIONS AND FUTURE WORK

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The results of the case studies reconfirm the reliability of the framework to adapt with flexibility and high level

of accuracy. Not only, has it enabled the reactor design of the conventional chemical processes with linear

simple kinetics but also it has facilitated the synthesis and design of biochemical processes with complex

reaction mechanisms. From this study it has been proven that for the algae growth and fermentation, the

Michaelis – Menten kinetics (Monod equation) which applies to most biochemical processes can be accuratelysimulated. The latest version of the framework which is proposed in this study enables the real design of

biochemical reactors with interactive mass transfer coefficients adapted for each case. Future work will automate

this framework to enable the user the fast and easy input of reaction equations and kinetics and the feed re-

characterization.

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