Development of an Optimization-Based Framework ... - ACS Publications

Article pubs.acs.org/IECR

Development of an Optimization-Based Framework for Simultaneous Process Synthesis and Heat Integration Qingyuan Kong* and Nilay Shah Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom S Supporting Information *

ABSTRACT: With the increasing attention toward renewable platform chemicals, a considerable amount of reaction pathways are being investigated for the potential of scale-up and industrialization. Heat integration, as a key feature in the field of process engineering, needs to be taken into consideration when developing preliminary reaction networks producing value-added products. In this study, we introduce an optimization-based framework for the simultaneous process synthesis and heat integration with the goal of finding the most profitable biobased platform chemical and its production pathways from a number of alternatives. A process superstructure that consists of master reaction stages and lower-level separation stages is introduced to demonstrate the theory. With a novel variable discretization approach, the problem is formulated as a mixed integer linear programming model to determine the optimal reaction pathways and separation sequences along with the heat integration cascade using simple data. The solutions to the problem reveal key information of the optimal flowsheet such as the maximum economic performance the process can achieve and the minimum cooling and heating duties required resulting from the heat integration analysis. A case study is presented to illustrate the applicability of the proposed approach. power more efficiently.9 Recent developments in biorefinery industries have led to commercialized production of biopolymers,10 biofuels,11 and various biochemicals.12 Companies such as BASF are also switching their focus to more sustainable biobased products.13 Nevertheless, most of the production routes of the biobased platform chemicals that have been discovered are still at laboratory scales with only a few promising processes being evaluated for scale-up.14−16 In the future, as technologies develop, more biobased platform chemicals with appropriate properties will become available to replace current petrochemicals, and the need for design methodologies for corresponding processes will grow simultaneously.17 For the scale-up and design of a well-known process, the procedure normally follows heuristic-based approaches (e.g., Douglas18), which enables one to acquire insightful information of the process, such as economic potential, energy consumption, and environmental impact. It generally involves the design of a chemical reaction network, separation synthesis, and heat integration analysis.19 While such procedures are already demanding for well-known processes in terms of resource and time investment,20 it is even more ambitious for novel proposed pathways. Furthermore, building a new production plant without comparing alternatives can potentially cause nonprofitability and eventually closure of production.21 Therefore, an optimization-based process synthesis

1. INTRODUCTION The use of fossil resources for the production of fuels and commodity chemicals has been the focal point of discussion for the past few decades. It was anticipated that the total amount of fossil fuels (coal, natural gas, and oil) available on earth can support current and future needs for at least another hundred years.1 However, as much of the conventional oil has run out, exploration of oil has moved on to areas that involve drilling in less hospitable environments with more advanced technologies, which, as a result, is leading to an increase in the cost of oil extraction.2 Moreover, most of the global oil comes from relatively few countries leading to concerns about the security of supply and future increases in already volatile oil prices.3 In addition, the vast consumption of fossil fuels has dramatically increased the level of greenhouse gas in the atmosphere over the years.4 These preceding factors coupled with the increasing global energy demand underline the urgent need to develop sustainable alternatives for fossil resources. Among all the potential renewable feedstocks, cellulosic biomass has been identified as the most promising replacement for fossil fuels5 to meet both chemical and energy demands while reducing environmental impact6 and carbon footprint.7 Cellulosic biomass is composed of three major constituents, namely, lignin, cellulose, and hemicellulose, and can be converted to value-added bioproducts through biorefinery processes.8 A biorefinery system plays a similar role in the bioprocessing industry to that of the oil refinery in the crude oil industry. It utilizes biological, physical, and thermochemical conversion technologies to produce biofuels, biochemicals, and © XXXX American Chemical Society

Received: Revised: Accepted: Published: A

February 8, 2017 March 24, 2017 April 12, 2017 April 12, 2017 DOI: 10.1021/acs.iecr.7b00549 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Conceptual diagram of the process superstructure.

impact. Bao et al.36 also developed a shortcut method for the preliminary synthesis of process-technology pathways based on simple material balances. Moreover, the authors have already established an optimization based framework for the process synthesis of optimal reaction networks integrated with distillation sequencing.37 Although these methods may have high parametric uncertainties, the results are accurate enough to serve as a guidance for future research and follow-on process development activities. However, it is important to note that none of the abovementioned conceptual frameworks included simultaneous heat integration, which as a key part of process engineering19,38−40 was proven to significantly increase the energy efficiency of chemical processes.41−44 This is also the case in recent emerging biorefinery industries. For example, Ng et al.45 developed a nonlinear modular optimization framework for the simultaneous process synthesis and energy integration for sustainable biorefineries. Meanwhile, Elia et al.46 proposed a threestage nonlinear decomposition framework to generate a novel heat exchange and power recovery network (HEPN) for any large-scale process. It was subsequently modified to be used for the simultaneous process synthesis heat and power integration in thermochemical coal, biomass, and natural gas to liquids (CBGTL) facility.47 Nevertheless, nonlinear programming can give rise to large-scale nonconvex problems which in general are very difficult to solve, and it is not easy for other users who are not familiar with optimization to determine the global optimum of the problem. To overcome this limitation, this paper presents a state-of-the-art mixed integer linear programming (MILP) model for the synthesis of reaction pathways and separation sequences with simultaneous heat integration.

framework is necessary for the screening of all potential reaction and separation alternatives to identify the optimal products and its associated flowsheet in the very first phase of the process design. Optimization-based approaches as a mathematical tool for process synthesis have been well developed over the past decades.22−25 Recent efforts have been focused on the modification and application of those conceptual methodologies. For instance, Kim et al.26 developed a system-level methodology for the synthesis and evaluation of a wide range of biomass-to-fuel strategies based on cost drivers, followed by sensitivity analysis to determine the effects of major parameters. Tan et al.27 presented a fuzzy multiobjective optimization approach to evaluate land use, water, and carbon footprint arising from the bioenergy production systems. In addition, the trade-offs between environmental impact and economic potential of different biorefinery processes were studied by different groups with the assistance of multiobjective optimization.28,29 Despite the fact that these methods can provide rather accurate and convincing results, they rely heavily on the maturity of individual reaction pathways and processing technologies.29−33 However, the level of information required for these types of approaches is too high when considering newly developed processes, which may only have limited information, e.g., basic reaction and component data. To deal with such problems, several conceptual optimization methods were developed for the preliminary screening and assessment of potential reaction networks. For instance, Ulonska et al.34 extended the reaction network flux analysis (RNFA),35 an effective estimation model, to evaluate various biofuel candidates and their associated production processes with respect to cost and environmental B

DOI: 10.1021/acs.iecr.7b00549 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article


outlet bypass stream Qnext k , the temperature of the flow is adjusted to match the reactor temperature of the next stage (Tk+1) via a heat exchanger prior to mixing (mixk); (v) the direct removal stream of the reaction outlet (QRi,k) is assumed to be cooled to ambient temperature (T⌀) by a cooler; (vi) the distillate of each column is condensed via a total condenser with cooling duty of ΔECk,l while the bottom stream exits via a partial reboiler with heating duty of ΔERk,l; and (vii) finally, the BR top/bottom direct removal streams (f TR i,k,l/f i,k,l) of each column are cooled to ambient temperature and the temperatures of distillation products that enter the next reaction stage ( f Tout i,k,l / Bout f i,k,l ) are adjusted to TRe k+1 before mixing. 3.2. General Approach. On the basis of the principle of Douglas,18 heat integration must follow two rules: (1) heat can be transferred from hot streams in one temperature interval (i.e., T1 ≤ t ≤ T2) to cold streams in that same interval; (2) to ensure driving force for heat transfer, each hot stream temperature should be reduced by the minimum approach temperature before intervals are constructed. As mentioned above, the temperature variable is discretized to form a new index t ∈ T. As a result, two new sets of binary variables known as the interval temperature integer variables ( ys stream and ye stream ) are t̂ t̂ introduced in this paper to identify the respective temperatures of inlet and outlet streams of each heat exchanger (i.e., if the temperature of the inlet stream of the heat exchanger is at t, then ys stream = 1, and 0 otherwise). The temperature interval of t̂ = 1 if the temperature range each heat exchanger (TIstream t includes temperature point t) is determined via a binary expression. Normally, temperature intervals are modified before being used for heat integration analysis (i.e., subtraction by the minimum approach temperature for hot streams). However, unlike normal heat integration problems, the stream property (hot or cold) is underdetermined in this case and can only be determined after the problem is solved. Therefore, instead of evaluating the heat surplus directly over the modified intervals, actual heat surpluses of each stream (SHAstream ) at different t temperatures are first calculated:

This work is an extension of the authors’ previous work37 with several modifications. First, instead of having temperature as a continuous variable, it is discretized to be used as a new set domain to maintain the model’s linearity. Second, heat exchangers are implemented wherever enthalpy change occurs, in different streams, distillation columns, or reactors (Figure 1). Moreover, the energy saving potential of the process is quantified through automatic heat integration analysis, and the resulting minimum cooling and heating duties are matched by the auxiliary utilities available (Sections 3.1−3.6). Finally, utility costs are included in the objective function to evaluate the effect of simultaneous heat integration to the process economy (Section 3.7). A case study is then presented along with sensitivity analysis to demonstrate the functionality of the model (Sections 4 and 5).

2. PROBLEM STATEMENT The synthesis problem addressed is stated as follows: given a set of feedstock platform chemicals (i ∈ Ifeedstock) and laboratory or other scale data for reactions (j ∈ J) starting from that chemical, synthesize an optimal process that meets a certain objective (e.g., maximum economic potential, minimum energy consumption). Distillation is used as the main separation technique due to its maturity.48 The characteristics of each reaction (e.g., conversion, selectivity, and temperature) and boiling point of each reactant/product involved are gathered from the literature and other databases. Other properties of the components such as market value, heat of formation, heat of evaporation, and latent heat, if unknown, are all estimated via a group contribution method.49 Heat integration is performed based on the principle developed by Douglas18 but takes place simultaneously rather than sequentially. The conceptual design procedure is intended to quickly scan all process alternatives to identify the most promising product and its production route while providing the heat integration cascade of the process. The results of this work, although preliminary, can be of help to set the future direction for current research studies and facilitate detailed techno-economic analysis.

SHA tstream = FCptstream TItstream , ∀ t

(1*)

where is the flow heat capacity of each master stream defined as the sum of the product of the flowrate and specific heat capacity of all components in each stream at temperature t (note here that all equations with * are bilinear equations which can be formally linearized to fit in the MILP model). The adjusted cascaded heat surpluses (SHstream ) based on the stream t property (HOTstream as a variable) are simply: FCpstream t

3. PROBLEM FORMULATION 3.1. Superstructure Formulation. The process superstructure concept is presented as Figure 1. The material balances, separation rules, and the concept of master reaction stages k ∈ K along with associated distillation stages l ∈ L have already been discussed previously.37 In this extended method, heat exchangers are installed for the cooling or heating of various streams prior to mixing or right after splitting points. Apart from energy change in those heat exchangers, enthalpy change of reactors (ΔEk), cooling duty of condensers (ΔECk,l), and heating duty of reboilers (ΔERk,l) are taken into consideration for the heat integration as they also play important roles in the heat cascade. The general concepts, as illustrated in Figure 1, are as follows: (i) the addition stream of each stage k (Ai,k) is first heated to match the reaction temperature of that stage (TRe k ) before entering the mixer (mixk); (ii) enthalpy change of each reaction is calculated by performing the energy balance around the reactor which consequently is subject to either constant cooling or heating to remain isothermal; (iii) the temperature of the separation inlet stream (Qsepin i,k ) is adjusted to be equal to the boiling point of the lightest component in the stream by a heat exchanger before entering the separation system; (iv) on the other hand, for the reactor

SHtstream = −SHA tstream , ∀ all cold streams, t

(2)

SHtstream = SHA tstream + Tgradient , ∀ all hot streams, t

(3)

where Tgradient is the minimum approach temperature allowed for energy to transfer between streams. 3.3. Reactor Heat Surplus. Each reaction stage operates at a certain temperature (TRe k ) which is determined by the temperature of the reaction that occurs in that stage (TRj). Therefore, a new set of binary variables known as the interval temperature integer variable of each reaction (x̂j,t) are introduced first to identify the binary expression of each reaction temperature, i.e., if reaction j occurs at temperature t, the binary variable x̂j,t = 1, and 0 otherwise:

xĵ , TR j = 1, ∀ j C

(4) DOI: 10.1021/acs.iecr.7b00549 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research exothermicity into consideration, is thus given as

The interval temperature integer variable of that reaction stage (ŷk,TRj) is equal to x̂j,TRj only if reaction j occurs in stage k (i.e., yj,k = 1), and only one temperature can be assigned to each reactor, i.e., yk̂ , t ≥ xĵ , t + yj , k − 1, ∀ j , k , t

∑ yk̂ ,t

SHkRe, t = SHAkRe, t + Tgradient EXOk − SHAkRe, t (1 − EXOk), ∀ k , t (14*)

where EXOk is a binary variable defined as the exothermicity of each reaction stage and is constrained as follows:

(5)

≤ 1, ∀ k (6)

t

The actual temperature of each reaction stage k (TRe k ) is thus written as TkRe =

∑ t ·yk̂ ,t , ∀ k

in Therefore, the temperature of the inlet flow to the reactor (Qi,k ) Qin is preheated to TRe . The binary variable y is defined so that k k,t Re yQin k,t = 1 for all temperatures t within the range of 0 °C ∼ Tk :

ykQin ≥ ykQin , ∀ k, t ,t ,t+1

(9)

+ HoVi , t )ykQin Q iin, k , ∀ k ,t

i,t

∑ (Cpi ,t

+ HoVi , t )ykQout Q iout ,∀k ,k ,t

i,t

(10)

ykCD ̂ ,l ,t =

1 − Niin, k , l + (11*)

i

TopCTi , k , l ≤ Niin, k , l , ∀ i , k , l

(18)

(19) (20)

∑ TopCTi ,k ,l ≤ SAk ,l , ∀ k , l

(21)

i

These three equations essentially state that for an active distillation column (eq 21), if component i exists in the column (eq 20) and all other components i′ that have lower boiling points than that of i are not present (eq 19), then component i is the lightest component in that stage, i.e., TopCTi,k,l = 1. In addition, condensers and reboilers are only operational (SAk,l = 1) at theirs assigned temperatures in the columns that are active (i.e., ∑t yk̂RB ≤ SAk,l , ∀ k , l and ∑t ykCD ̂ , l , t ≤ SAk , l , ∀ k , l ). ,l ,t The utility requirements of the condenser (ΔECk,l) and the reboiler (ΔERk,l) are related by the energy balance around each column which is defined as follows:

(12)

where ΔHR⌀j is the standard heat of reaction j, T⌀ is the temperature under standard conditions and is set to be equal to the ambient temperature, ξj,k is the extent of reaction j in stage k, and ΔEk is the enthalpy change of reaction stage k. The actual heat surplus of each reaction stage at temperature t (SHARe k,t) is defined as follows: SHAkRe, t = −ΔEk ·yk̂ , t , ∀ k , t

∑ Niin′ ,k ,l ≥ 1 − TopCTi ,k ,l , ∀ i , k , l i ′< 1

j

∑ Cpli(Q iout T ⌀) = ΔEk , ∀ k ,k

(17)

CD where ŷk,l,t is the interval temperature integer variable of each condenser and TopCTi,k,l is the binary variable used to identify the component with the lowest boiling point each active column (i.e., TopCTi,k,l = 1 if component i is the lightest component in column l of k), which is defined as the following:

∑ Cpli(Q iin,kT ⌀) − Ekin + ∑ ΔHR j⌀ξj ,k + Ekout −

∑ TopCTi ,k ,lBpMi ,t , ∀ k , l , t i

Qin with yQout k,t = yk,t as reactions are isothermal. Now the energy balance of each reaction stage is simply

i

∑ Ybi ,k ,lBpMi ,t , ∀ k , l , t

where Ybi,k,l is the binary variable used for the selection of the heavy key in each separation stage (i.e., Ybi,k,l = 1 if component i is the heavy key in column l of k) and BpMi,t is defined so that BpMi,t = 1 if the boiling point of component i is t, 0 otherwise. The second assumption is that the operational temperature of each condenser is identical to the boiling point of the lightest component (i.e., most volatile component) in that column to allow total condensation of all components in the distillate:

*where Cpi,t accounts for both liquid and gaseous phase specific heat capacity of component i at temperature t and HOVi,t is the latent heat of vaporization of component i at temperature t (HOVi,t = latent heat of component i if the temperature is equal to the boiling point of component i, 0 otherwise). Similarly, the relative flow energy of the reaction outlet stream (Eout k ) is formulated as follows: Ekout =

(16)

i

By assuming the reference temperature in this work to be 0 °C, the relative flow energy (Eink ) of the reaction inlet stream, which also takes account of the energy change involved in evaporation of different substances, is thus given as follows:

∑ (Cpi ,t

1 − EXOk ≥ yj , k , ∀ k , j ∈ EndoR

yk̂RB = ,l ,t

(8)

ykQin ≥ yk̂ , t , ∀ k , t ,t

Ekin =

(15)

3.4. Reboilers and Condensers. For the analysis of reboiler and condenser utilities, two key assumptions are first made. The first one is that the operational temperature of the reboiler is set to be equal to the boiling point of the heavy key component of that column to ensure that none of the nonheavy key components are returned to the column via boil-up. Therefore, the interval temperature integer variable of each reboiler (ŷRB k,l,t) is defined as follows:

(7)

t

EXOk ≥ yj , k , ∀ k , j ∈ ExoR

(13*)

In order to fit the heat surplus of each reaction into the overall heat integration analysis, each reaction is either treated as a hot stream (exothermic) or cold stream (endothermic) and releases or absorbs energy at one particular temperature. The reaction stage heat surplus (SHRe k,t), which takes the reactor’s

ΔER k , l = −ΔECk , l + EkfT, l + EkfB, l − Ekfin ,l , ∀ k , l

(22)

where and are the relative flow energy of the distillate and bottom product, respectively, defined as the sum of the product of the corresponding flowrate ( f Ti,k,l/f Bi,k,l) and liquid Efk,lT

D

Efk,lB


Article

Industrial & Engineering Chemistry Research specific heat capacity (Cpli) of component i multiplied by the operational temperature of the condenser (TCD k,l ) and reboiler (TRB k,l ): EkfT, l

=

∑

fiT, k , l CpliTkCD ,l ,

∀ k, l (23*)

i

EkfB, l =

of each master stream are defined either by the user or the model, i.e.,

∑ fiB,k ,l CpliTkRB,l , ∀ k , l

(24*)

i

where the operational temperatures of the condenser and reboiler can be written in terms of the interval temperature integers (i.e., RB RB CD TkCD , l = ∑t t · yk̂ , l , t , ∀ k , l and Tk , l = ∑t t · yk̂ , l , t , ∀ k , l ). These two equations are bilinear and can be integrated into the methodology by linearization. On the other hand, the relative flow energy of the inlet stream to each distillation column (Efin k,l ) is calculated through the following equation: Ekfin ,l =

∑ f iin,k ,l CpliTkfin,l , ∀ k , l

where is the inlet flowrate of component i to separation stage l of k and Tfin k,l is the temperature of that stream. For the inlet stream to the whole separation system (f ini,k,l=1), the initial temperature is dependent on the temperature of the reaction which may need adjustment to ensure that all components in the stream are in the liquid phase. As mentioned above in Section 3.1, the temperature after the adjustment is equal to the boiling point of the lightest component in the stream, which, in fact, is also equal to the operating temperature of the condenser CD of that column (i.e., Tfin k,l=1 = Tk,l=1). In the case where l > 1, each in separation inlet stream ( f i,k,l>1) comes from either from the top (temperature is equal to the lightest component’s BP) or bottom product (temperature is equal to the heavy key’s BP) of previous separation stages. As a result, the flow temperature (Tfin k,l ) is always equal to the boiling point of the lightest component in that stream and requires no temperature adjustment CD (i.e., the relation: Tfin k,l = Tk,l always holds for any l > 1). The cooling duty (ΔECk,l) for a total condenser is calculated based on Douglas18 and is simply given as follows:

CD CD SHkCD , l , t = SHAk , l , t + Tgradient = −ΔECk , lyk̂ , l , t + T

gradient

TskQnext = TkReNkQnext , ∀ k

(31*)

TekQnext = TkRe+ 1NkQnext , ∀ k

(32*)

TskQsepin = TkReNkQsepin , ∀ k

(33*)

Qsepin TekQsepin = Tkfin ,∀k , l = 1Nk

(34*)

TskQR = TkReNkQR , ∀ k

(35*)

TekQR = T ⌀NkQR , ∀ k

(36*)

,∀k ∑ t ·ysk̂Mstream ,t

(37)

t

TekMstream =

,∀k ∑ t ·yek̂Mstream ,t

(38)

t

with both of the binary variables constrained so only one temperature point can be selected for active streams (i.e., ∑t ysk̂ Mstream ≤ NkMstream , ∀ k and ∑t yek̂Mstream ≤ NkMstream , ∀ k ). Among ,t ,t those four types of streams, addition streams are assumed to be cold whereas ROR streams are set to be hot. On the other hand, RON and ROS streams are either hot streams if the exit temperature of the heat exchanger is lower than that of the inlet or cold streams otherwise, i.e.,

where Rf is the reflux ratio and hvi is the heat of evaporation of component i. Similarly to the reaction stages, substances in condensers act as heat sources whereas those in reboilers act as heat sinks at their respective temperatures, so they can be treated as hot and cold streams, respectively. As a result, the expressions for the CD heat surplus of each condenser (SHk,l,t ) and reboiler (SHRB k,l,t) in RB terms of the actual heat surplus (SHACD /SHA ) at each k,l,t k,l,t temperature t are written as: RB RB SHkRB , l , t = − SHAk , l , t = −ΔER k , lyk̂ , l , t , ∀ k , l , t

(30*)

TskMstream =

(26)

i

TekA = TkReNkA , ∀ k

where are binary variables that represent the existence of each master stage stream (i.e., NMstream = 1 if there is flow in k that stream). The respective binary expressions for the starting and ending interval temperature integers of each master stage stream, ys Mstream and ye Mstream , are thus given as follows: ̂ ̂ k,t k,t

in f i,k,l

ΔECk , l = −∑ (Rf + 1)fiT, k , l hvi , ∀ k , l

(29)

NMstream k

(25*)

i

TskA = T ⌀NkA , ∀ k

TskQnext − TekQnext ≤ M ·HOTkQnext , ∀ k

(39)

TekQnext − TskQnext ≤ M(1 − HOTkQnext ), ∀ k

(40)

HOTkQnext ≤ NkQnext , ∀ k

(41)

TskQsepin − TekQsepin ≤ M ·HOTkQsepin , ∀ k

(42)

TekQsepin − TskQsepin ≤ M(1 − HOTkQsepin), ∀ k

(43)

HOTkQsepin ≤ NkQsepin , ∀ k

(44)

HOTMstream k

where = 1 if that stream is a hot stream, 0 otherwise. On the basis of the above information, the temperature interval where each stream is located (TIMstream ) can be deterk,t mined (i.e., if the streams’ starting temperature is T ( ys Mstream ) ̂ k,T and exits the heat exchanger at temperature T + x ( ye Mstream ̂k,T+x ), = 1 for all T ≤ t ≤ T + x). For user defined cold TIMstream k,t streams and streams with HOTMstream = 0: k

(27*)

, ∀ k, l, t (28*)

3.5. Master Stage Streams (Mstream). There are in total four types of streams in each master stage k (Mstream) that may require temperature adjustment, namely, the addition stream (Ai,k), reactor outlet bypass to the next master stage sepin (RON-Qnext i,k ), to the separation stage (ROS-Qi,k ) and to direct R removal (ROR-Qi,k). As mentioned in Section 3.1, the inlet (Tsstream ) and outlet temperatures (Testream ) of the heat exchanger k k

Mstream TIkMstream = TIkMstream − yek̂Mstream , ∀ k, t ,t , t − 1 + ysk̂ , t ,t−1

On the other hand, TIkMstream ,t E

=

TIMstream k,t

TIkMstream ,t−1

(45)

is defined as follows for hot streams:

+ yek̂Mstream − ysk̂ Mstream , ∀ k, t ,t ,t−1

(46)


Article

Industrial & Engineering Chemistry Research The flow heat capacity of each master stream (FCpMstream ) is k,t simply FCpkMstream = ,t

∑ Mstreami ,k Cpi ,t i

+

∑ Mstreami ,kHoVi ,t , i

∀ k, t

(47)

(48*)

=

TR TkCD , l Nk , l ,

∀ k, l

(53*)

Re Tout TekTout , l = Tk + 1Nk , l , ∀ k , l

(54*)

RB Bout TskBout , l = Tk , l Nk , l , ∀ k , l

(55*)

Re Bout TekBout , l = Tk + 1Nk , l , ∀ k , l

(56*)

Dstream FCpk,l,t =

, ∀ k, l ∑ t ·ysk̂Dstream ,l ,t t

TekDstream = ,l

, ∀ k, l ∑ t ·yek̂Dstream ,l ,t t

≤ NkDstream , ∀ k, l ∑ ysk̂Dstream ,l ,l ,t

−

≤

M ·HOTkTout ,l ,

i

(67)

(68*)

3.7. Objective Function. In this work, the main objective is to obtain the optimum process flowsheet with the highest economic potential, which accounts for the energy cost after heat integration. Normally, an optimal or near optimal heat exchanger network exhibits the following characteristics: (a) minimum utility cost; (b) minimum number of heat exchanger units; and (c) minimum investment cost for heat exchangers. However, it is possible to have conflicts among these characteristics. Therefore, it is assumed in this paper that (a) has precedence over (b) and (b) over (c).50 The general expression for the objective function is given as follows: EP 3 = EP 2 − energy cost

(69)

Z = max EP 3

(70)

where EP2 is the economic potential of the process based on the analysis of the raw material and separation cost and has been discussed previously.37 The energy cost, on the other hand, includes the total cost of both cooling water (CWCT) and steam (SCT), i.e., energy cost = CWCT + SCT

(57)

(71)

In order to calculate the total cost of utilities, the total heat surplus at each temperature t (SHTotal ) is first calculated via the t following equation:

(58)

Qsepin ) ∑ (SHkRe,t + SHkA,t + SHkQnext + SHkQR ,t , t + SHk , t k Bout TR BR ∑ (SHkRB,l ,t + SHkCD,l ,t + SHkTout , l , t + SHk , l , t + SHk , l , t + SHk , l , t ) k ,l

(60)

,∀t

In addition, the stream properties of Tout and Bout streams are determined by the following constraints: TekTout ,l

∑ Dstreami ,kHoVi ,t ,

SHAkDstream = FCpkDstream TIkDstream , ∀ k, l, t ,l ,t ,l ,t ,l ,t

+

t

TskTout ,l

+

and the actual heat surplus (SHADstream ): k,l,t

SHtTotal =

≤ NkDstream , ∀ k, l ∑ yek̂Dstream ,l ,l ,t

∑ Dstreami ,k Cpi ,t ∀ k, l, t

(59)

t

(66)

i

where NDstream are binary variables that represent the existence k,l of each distillation stage stream. The respective binary expressions for the starting and ending interval temperature integers of each distillation stream, ys Dstream ̂ k,l,t and ye Dstream , are thus given as follows: ̂ k,l,t TskDstream = ,l

(65)

The flow heat capacity of each distillation stream (FCpDstream ): k,l,t

(52)

CD Tout TskTout , l = Tk , l Nk , l , ∀ k , l

(64)

hot streams

(51*)

⌀ BR TekBR , l = T Nk , l , ∀ k , l

Bout Bout TekBout , l − Tsk , l ≤ M(1 − HOTk , l ), ∀ k , l

Dstream TIkDstream = TIkDstream − ysk̂Dstream , ∀ k, l, t , ,l ,t , l , t − 1 + yek̂ , l , t ,l ,t−1

(50)

RB BR TskBR , l = Tk , l Nk , l , ∀ k , l

(63)

cold streams

(49*)

⌀ TR TekTR , l = T Nk , l , ∀ k , l

Bout Bout TskBout , l − Tek , l ≤ M · HOTk , l , ∀ k , l

Dstream TIkDstream = TIkDstream − yek̂Dstream , ∀ k, l, t , ,l ,t , l , t − 1 + ysk̂ , l , t ,l ,t−1

3.6. Separation Stage Streams (Dstream). The top or the bottom product of each distillation column can have three end destinations: (i) the inlet streams to subsequent separation Ts stages ( f i,k,l,l′ /f Bs i,k,l,l′), which as mentioned above do not require any heating or cooling; (ii) the direct removal streams ( f TR i,k,l/ ), which are cooled before storage (top/bottom removal f BR i,k,l streams); and (iii) the streams that enter the next reaction Bout stage ( f Tout i,k,l /f i,k,l ), which may require temperature adjustment to match the temperature of the reactor (top/bottom out streams). The following sections present the heat surplus formulation of the distillation products in detail. The inlet (TSDstream ) and outlet temperatures (TeDstream ) of k,l k,l the heat exchanger of each distillation split stream are given as follows: TskTR ,l

(62)

whereas TR and BR streams are defined by the user to be hot streams. Similar to eqs 45 and 46, the temperature interval of the heat exchangers of each distillation stream is given as:

The actual heat surplus of each master stage stream (SHAMstream ) is given as k,t SHAkMstream = FCpkMstream TIkMstream , ∀ k, t ,t ,t ,t

Tout Tout TekTout , l − Tsk , l ≤ M(1 − HOTk , l ), ∀ k , l

∀ k, l

(72)

The cascaded heat (CHt) at each temperature interval t is thus: CHt =

(61)

,∀t ∑ SHtTotal ′ t ′> t

F

(73) DOI: 10.1021/acs.iecr.7b00549 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article


Figure 2. Proposed reaction network reaction. Reactions R3 and R4, R5 and R6, and R9 and R10 are all competitive reactions. Optimal reaction network is outlined with the dashed circle.

as p-cymene,53 perillic acid,54 and even polymers55 thanks to its competitive price, biodegradability, and low toxicity. With more and more reaction pathways becoming available at the laboratory scale in the future, it would be of great interest to researchers that one can identify the optimal process configuration from a number of potential candidate reactions, which is sustainable and commercially competitive to be further investigated for detailed design at larger production scale. Therefore, in this work, the proposed method is applied on the given reaction network37 shown in Figure 2 to demonstrate the model’s applicability (Table S1 in the Supporting Information provides the data for all reactions involved). In this case study, it is assumed that the hypothetical plant can process 15 000−20 000 t/year of limonene with an annual operational time of 8500 h. The costs of steam and cooling water are taken to be $11.2 per 106 kJ and $3.91 per 106 kJ, respectively.56 The reflux ratio of each distillation column, which is given in eq 26, is initially assumed to be 1.3 and is subject to further sensitivity analysis to determine its impact on the optimal solution. In addition, thermodynamic properties of the components in Figure 2 are estimated via various group contribution methods57−59 and are summarized in Table S2 of the Supporting Information. (The standard heats of formation of different components are used to calculate the standard heat of each reaction). Furthermore, the temperature is initially discretized into intervals of 10 °C to save computational effort (e.g., the reaction temperature of R11 is at 65 °C, which lies in the seventh interval), and intervals of 5 °C and 2 °C are also analyzed for comparison in the sensitivity analysis. 4.2. Initial Solutions. The optimal reaction network identified by the model is shown as the network within the dashed envelope of Figure 2 with carvacrol (H) being selected as the optimal product. In general, reaction No.4 is chosen to be the first step over the others that originate from limonene (A) to produce the intermediate product carvone (E). Meanwhile, reaction No. 3 also takes place as a competitive reaction to produce the byproduct limonene oxide (D). Pure carvone is separated from limonene oxide to undergo further isomerization to form the final product carvacrol. Both carvacrol and

The minimum heating duty required for the system (Qhot min) is provided to the cascade to neutralize the temperature interval t with the largest energy deficit and is formulated as follows: hot CHtafterheating = CHt + Q min ,∀t

(74)

CHtafterheating ≥ 0

(75)

(Qcold min )

The minimum cooling duty of the system is measured as the cooling duty required to meet the largest heat surplus of the cascade given as follows: cold CHtaftercooling = CHtafterheating − Q min ,∀t

(76)

CHtaftercooling ≤ 0

(77)

CHaft terheating

CHaft tercooling

where and each represents the cascaded heat surplus of each temperature interval after minimum heating and cooling are provided to the process, respectively. The total cost of cooling water and stream are thus given as follows: cold CWCT = CWC unitQ min

(78)

hot SCT = SC unitQ min

(79)

Overall, the objective function (eq 70) together with the constraints from eqs 2−79 form a mixed integer linear programming (MILP) model which can be solved globally using the optimization solver CPLEX in GAMS (version 24.2.3) to obtain the optimal process configuration and the grand composite curve of the integrated process. To illustrate the proposed approach, a case study is solved in the following sections.

4. CASE STUDY 4.1. General Information. D-Limonene is a renewable chemical with numerous applications in the cosmetics, medicine, perfume, and food industries.51 It is currently being produced as a side product from the citrus juice industry at >60 000 t/year.52 Recently, extensive research has been carried out to study the possibility for limonene to be used as a platform chemical for the synthesis of higher value chemicals such G


Article


Figure 3. Optimal process flowsheet of the case study; all flowrates are in the unit of mol/min (temperature intervals of 10 °C).

increasing the number of temperature intervals, which would improve the resolution of the results. The top and bottom products of column k2-l1 containing pure carvone and carvacrol, respectively, are cooled to 20 °C prior to storage. The optimal economic potential is $20.8 million per annum with an annual utility cost of $0.275 million. The grand composite curve of the whole process is given in Figure 4. The

limonene oxide are sold at their market prices. The corresponding optimal process flowsheet with heat exchangers implemented is shown in Figure 3. There are 15 utility streams in total. As can be seen, the fresh feed of limonene (A) is first heated from 20 to 80 °C to match the operational temperature of reactor k1, where R3 and R4 take place. The reactor outlet, which is composed of a mixture of limonene oxide (D) and carvone (E), is initially at 80 °C and then heated to 200 °C before entering the subsidiary distillation column. The reboiler and condenser of the first column (k1-l1) operate at 240 and 200 °C, respectively. The distillate containing pure limonene oxide leaves the condenser at 200 °C and is cooled to 20 °C prior to storage. On the other hand, the bottom product, carvone, exiting the reboiler at 240 °C, is cooled to 80 °C to match the operational temperature of the second reactor (80 °C) and is mixed with the fresh feed of carvone (also preheated to 80 °C) before entering the second reactor. The product of the second reactor, which consists of both carvone and carvacrol (H), leaves the reactor at temperature of 80 °C and is preheated to 240 °C prior to separation. One thing to note here is that the boiling points of components E and H are very close (231 and 238 °C, respectively) and are both located in the 24th interval in the case of a temperature interval of 10 °C. As a result, the reboiler and condenser of the second column both operate at 240 °C, which is normally not allowed for any distillation columns. Nevertheless, this special scenario is acceptable to serve as an estimated solution to the complex model. On the other hand, the situation can be resolved by

Figure 4. Grand composite curve (ΔT = 10 °C).

optimal solution indicates that the minimum heating and cooling required for the system is 313 kW and 1407 kW, respectively, with a pinch point at 240 °C. The total utility H


Article

Industrial & Engineering Chemistry Research saving compared with the case where there is no heat integration (i.e., all the energy required is provided by auxiliary utilities) is around 40%. The initial solutions are further analyzed by performing sensitivity analysis in Section 5. 4.3. Column Pressure Modification. However, it is noticed that the energy integration potential is relatively low due to a high pinch point caused by the fact that there is a reboiler operating at 240 °C which consumes all of the auxiliary heating provided. On the other hand, the large leap in cascaded heat from 80 to 70 °C indicates that two highly exothermic reactors both operate at 80 °C and release far more energy than any other streams. To match the reboiler heating duty with the cooling duty induced by the reactors, the pressures of the distillation columns are reduced to lower the operating temperatures of reboilers and condensers by 170 °C. The resulting grand composite curve is shown in Figure 5.

Figure 6. Grand composite curve for the sensitivity analysis on the interval size with original TRj and Rf = 1.3.

the resolution of the results and can be an issue for distillation columns with close operational temperatures of the reboiler and condenser. One can also argue that a more accurate solution can be obtained if the interval is small enough. Therefore, sensitivity analysis is performed on the interval size to evaluate the validity of the initial interval size. The interval size is first set to 5 °C before being further reduced to 2 °C, and the grand composite curves for each of the three cases are shown in Figure 6. Solutions to key variables, such as the pinch point, the minimum cooling and heating requirement for the system (Qcooling and Qheating min min ), are summarized in Table 2. It is shown Table 2. Summary of Key Variables for Cases with Different Interval Sizes Figure 5. Grand composite curve (ΔT = 10 °C) with column depressurizition.

As can be seen, the new pinch point is at 80 °C and a significant amount of heat produced by reactors is utilized by low pressure reboilers at 70 °C. As a result, the minimum cooling duty required of the process is reduced from 1407 to 1143 kW (an 18.7% drop), whereas the heating duty drops from 313 to 21.3 kW (a 93% improvement). In summary, the economic potential of the low pressure process is $20.9 million per annum with an annual utility cost of $0.144 million. The total energy savings is improved from 40% to approximately 69%.

Table 1. Summary of Problems Sizes and Solving Time for Cases with Different Interval Sizes number of variables

number of equations

solving time (s)

ΔT = 10 ΔT = 5 ΔT = 2

26 684 50 044 114 284

62 700 115 814 261 876

33.9 105.9 710.4

Qcooling (kW) min

Qheating (kW) min

pinch point (°C)

ΔT = 10 ΔT = 5 ΔT = 2

1406 1407 1413

313 306 307

240 230 230

that the pinch points shift from 240 to 230 °C for both of the later cases. The two temperature points of the ΔT = 10 °C case where there is a large transition in cascaded heat (200 and 70 °C) shift slightly downward. These changes can be interpreted as follows: with a reduced interval size, more points are evaluated by the solver, thus providing a more precise value for the cascaded heat of each point. On the other hand, changing the size of the temperature interval would barely affect both the minimum cooling and heating duties, due to the following facts in this case study: (i) the whole heat integration network is below the pinch; (ii) the largest heat surplus and deficit of the process integration network are caused by the highly exothermic reactions and high temperature reboilers; and (iii) the reactors and reboilers operate at different temperatures that are not affected by the resolution of the temperature interval. Also, the sensitivity analysis indicates that changing the interval size does not alter the optimal process flow diagram. Therefore, the assumption of the temperature interval of ΔT = 10 °C is valid for the analysis of the overall utility requirement of this particular process. Nevertheless, more precise solutions can always be acquired by narrowing the interval size if solution time is not an issue for researchers. 5.2. Reflux Ratio. In reality, the reflux ratio of each column is calculated based on the minimum reflux ratio which can be

5. SENSITIVITY ANALYSIS 5.1. Interval Size. In the above case study, the original problem with temperature interval size of 1 °C takes hours to solve, whereas by increasing the size of each temperature interval from 1 to 10 °C, the solution time is reduced from hours to minutes (shown in Table 1). However, it may lower

cases/ variables

cases/variables

I


Article


process. The reason for this is that, as reflux ratio increases, both the reboiler and condenser of each column will process more fluid, increasing the utility requirements for each unit (eqs 22 and 26). Overall, changing the reflux ratio will affect the overall process economics, but the influence can be considered negligible, and it does not alter the optimal flowsheet of the process. Therefore, it would be safe to use reflux ratio as a parameter for the preliminary analysis. 5.3. Reaction Temperature. Another parameter that requires sensitivity analysis is the reaction temperature of each reaction (TRj). Since the data for all reactions are gathered from the literature, most of which are at laboratory scale, the conditions of each reaction, if scaled up, may vary from the original literature value. As a result, it is necessary to identify the impact that reaction temperature has on the heat integration analysis and the optimal process configuration. As illustrated in Figure 8, each of the original reaction temperatures (TRj0) is first brought down by 20 °C (dotted line) and then increased to TRj0 + 20 °C (gray line). The results indicate no change on the process utility and the pinch temperature (Table 4). This is

obtained via complex correlations such as Underwood’s equation.60 However, the nonlinearity of the equation will overcomplicate the problem at this stage of design. Therefore, instead of having the reflux ratio as a decision variable, it is assumed in this paper that the reflux ratios for all columns are the same and the value is set to be 1.3 (Rf 0) initially. To examine the model’s sensitivity to this assumption, the same method is performed on the same case but with 10% change in the reflux ratio (i.e., Rf = 0.9Rf 0 or Rf = 1.1Rf 0). The cascaded heat for the three scenarios is given in Figure 7. As the reflux ratio increases from

Table 4. Summary of Key Variables for Cases with Different Reaction Temperatures

Figure 7. Grand composite curve for the sensitivity analysis on the reflux ratio (Rf) with original TRj and (ΔT = 10 °C).

Table 3. Summary of Key Variables for Cases with Different Reflux Ratios Qcooling (kW) min

Qheating (kW) min

pinch point (°C)

Rf = 1.17 Rf = 1.3 Rf = 1.43

1390 1406 1422

297 313 329

240 240 240

Qcooling (kW) min

Qheating (kW) min

pinch point (°C)

TRj = TRj0 − 20 TRj = TRj0 TRj = TRj0 + 20

1406 1406 1406

313 313 313

240 240 240

due to the fact that, even with different reaction temperatures, the active reactions of the optimal solution still operate way below the pinch temperature. However, as mentioned above, the temperatures which the large transition of the grand composite curve starts from and ends with are dependent on the temperatures of the active reactions in the optimal solution. Therefore, it is shown in the diagram that changing the reaction temperatures from TRj0 − 20 °C to TRj0 + 20 °C also shifts the turning point (Point A) from TRj0 − 20 to TRj0 + 20 °C, whereas the end of the large leap (Point B) varies from TRj0 − ΔT − 20 to TRj0 − ΔT + 20 °C with ΔT being the interval size. This suggests that if the reaction temperature is low enough (i.e., cooling water does not satisfy the minimum approach temperature), an alternative cooling agent may be

1.17 to 1.43 (10% each time), the overall grand composite curve shifts slightly toward the right, meaning increased cascaded heat at each temperature. In addition, the minimum cooling and heating duties required are also increased (Table 3), thus leading to a rise in the overall utility cost of the

cases/variables

reaction temperature (°C)

Figure 8. Grand composite curve for the sensitivity analysis reaction temperature (TRj) with (ΔT = 10 °C) and Rf = 1.3. J



Article

■

used to maintain the reactors at isothermal conditions. Overall, for cases with a lower pinch point or reactions operating around the pinch point, it is possible to improve the optimal solution (i.e., reducing utility requirement) by varying the reaction temperatures. Nevertheless, in this case, neither the process economy nor the flowsheet are affected by the change in reaction temperatures.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b00549. Reaction and component data are included in Tables S1 and S2; group contribution method for the estimation of the market values of various components is briefly explained (PDF)

■

6. CONCLUSIONS AND OUTLOOK In this paper, an extension of the authors’ previous work37 has been introduced for the automatic conceptual design and simultaneous process synthesis with heat integration. The aim of this work is to investigate the effect of heat integration on the energy consumption while screening for the most promising biobased chemical and its production route from alternative candidate products and reaction pathways. The modified process superstructure is presented with the addition of heat exchangers. New sets of constraints are added to the original mixed integer linear programming (MILP) optimization formulation to track and evaluate the energy change of each stream. The continuous temperature variable is discretized to maintain the model linearity. The objective is to maximize the economic potential of the process subject to constraints that include the screening of reaction pathways, separation sequencing, heat integration, and product selection. The proposed optimization model was tested using a case study which involves the reaction pathways starting from the popular bioderived D-limonene. Good quality global optimum solutions were obtained from a single model including the optimal flowsheet, process economic potential, pinch temperature, and minimum cooling and heating duties. The initial results showed that energy savings due to simultaneous heat integration was close to 40% for this particular case which was further improved to approximately 69% when distillation columns are operated at a lower pressure. Several sensitivity analyses were performed in order to validate the assumptions made on the model. The sensitivity analysis showed that the optimum process configuration is not affected by varying the size of the temperature interval, reflux ratio, and reaction temperatures. On the other hand, variations in reflux ratio and temperature interval size do have an impact, although small, on the overall process utility requirement. The pinch temperature, however, only changes when reducing the size of the temperature interval. In summary, the solutions of the case study illustrate the ability of the proposed method to generate the optimal process flowsheet with simultaneous heat integration. This model at this stage has already shown great potential for the process synthesis of innovative reaction networks. It can provide valuable results given limited information of the reactions and help researchers to eliminate unnecessary risks at the earliest stage of process design. To build upon this work, a more sophisticated and well-calibrated case study will be used to further demonstrate the model’s applicability to other industrial scale problems. Moreover, alternative separation technologies such as precipitation, filtration, and solvent extraction will be explored for the model to be able to identify and separate components with different phases such as gas/liquid and liquid/solid mixtures. Furthermore, the capital costs of individual units will be taken into consideration. By doing so, it will allow the model to accommodate more complicated problems.

AUTHOR INFORMATION

Corresponding Author

*(Q.K.) E-mail: [email protected]. ORCID

Qingyuan Kong: 0000-0002-8892-7235 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The support of the EPSRC under Grant EP/L017393/1, “Sustainable Polymers” is gratefully acknowledged. NOMENCLATURE

Indices Descriptions

i j k l t p

Components Reactions Master Stages Separation Stages Discretized temperature points Discretized split fraction points

SuperscriptMstream (Master stage streams)

A Qnext Qsepin QR

Addition streams to each reaction stage Reactor outlet bypass to next reaction stage Reactor outlet to the separation system Reactor outlet bypass to direct removal

SuperscriptDstream (Lower level separation stage streams)

Tout Distillate of each distillation column to next reaction stage TR Distillate to direct removal of each distillation column Bout Bottom product of each distillation column to next reaction stage BR Bottom product to direct removal of each distillation column Binary Variables

x̂j,t ŷk,t yQin k,t

yQout k,t

EXOk Dstream ys Mstream / ys k,l,t ̂ ̂ k,t

K

= 1 if the reaction temperature of j is at t; 0 otherwise = 1 if the temperature of reaction stage k is at t; 0 otherwise = 1 for all temperature t within the range of 0 °C to the temperature of the reactor inlet stream at stage k; 0 otherwise = 1 for all temperature t within the range of 0 °C to the temperature of the reactor outlet stream at stage k; 0 otherwise = 1 if reactor stage k is exothermic; 0 otherwise = 1 if the starting temperature of the stream is at t; 0 otherwise DOI: 10.1021/acs.iecr.7b00549 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article


ye Mstream / ye Dstream ̂ ̂ k,t k,l,t

SCT SCunit SHTotal t

= 1 if the end temperature of the stream is at t; 0 otherwise = 1 if the inlet temperature of the heat exchanger of the stream is higher than the outlet temperature; 0 otherwise = 1 if temperature point t lies within the starting and end temperature of the stream; 0 otherwise = 1 if the boiling point of component i is at t; 0 otherwise = 1 if component i is the one with the lowest boiling point in separation stage l of k; 0 otherwise = 1 component i exists in the inlet stream to separation column l of stage k; 0 otherwise = 1 if component i is chosen as the heavy key at separation stage l and in master stage k; 0 otherwise = 1 if the flowrate of the stream is not zero; 0 otherwise

HOTMstream /HOTDstream k k,l Dstream TIMstream /TIk,l,t k,t

BpMi,t TopCTi,k,l Nfin i,k,l Ybi,k,l NMstream /NDstream k k,l

CHt CHaft tercooling CHaft tercooling Qcold min Qhot min

Other Variables Used in This Paper (explained in more detail in the authors’ previous work37)

yj,k = 1 if reaction j occurs in reaction stage k; 0 otherwise SAk,l = 1 if column l of k is active; 0 otherwise

■

Continuous Variables

Ai,k ΔECk,l ΔERk,l ΔEk Eink Eout k Efk,lT Efk,lB Efin k,l TRe k TCD k,l TRB k,l TsMstream /TsDstream k k,l TeMstream /TeDstream k k,l SHAMstream /SHADstream k,t k,l,t SHMstream /SHDstream k,t k,l,t Dstream FCpMstream /FCpk,l,t k,t EP3

EP2 Z energy cost CWCT CWCunit

Total steam cost of the process Unit cost of steam Total heat surplus of the process at temperature t Cascaded heat of the process at temperature t Cascaded heat after minimum heating is provided at temperature t Cascaded heat after minimum heating and cooling are provided at temperature t Minimum cooling duty required of the process Minimum heating duty required of the process

Flowrate of component i added to the master mixing stage k Condenser cooling duty of column l at stage k Reboiler heating duty of column l at stage k Isothermal energy change of reaction stage k Flow energy of the inlet stream to reactor at stage k Flow energy of the outlet stream of reactor at stage k Flow energy of the distillate of column l at stage k Flow energy of the bottom product of column l at stage k Flowrate energy of the separation inlet stream to column l at stage k Reaction temperature of each reaction stage k Operating temperature of condenser in column l of k Operating temperature of reboiler in column l of k Temperature of streams prior to heat exchangers Temperature of streams leaving heat exchangers The actual heat surplus of different streams The heat surplus used for heat integration analysis of each stream Flow heat capacity of the streams Economic potential of the process including energy cost Economic potential of the process without energy cost Objective function Total energy cost of the process Total cooling water cost of the process Unit cost of cooling water

REFERENCES

(1) Council, N. R. Sustainability in the Chemical Industry: Grand Challenges and Research Needs - A Workshop Report; The National Academies Press: Washington, DC, 2005; p 206. (2) Beattie, A. 5 Biggest Risks Faced By Oil And Gas Companies. http://www.investopedia.com/articles/fundamental-analysis/12/5biggest-risks-faced-by-gas-and-oil-companies.asp (accessed November 16, 2016). (3) U.S. Energy Information Administration. Annual Energy Review 2001; U.S. Department of Energy; 2011. (4) Murphy, T. Declining Fossil Fuel Supplies and the Energy Trap; 2011. http://oilprice.com/Energy/Energy-General/Declining-FossilFuel-Supplies-And-The-Energy-Trap.html. (5) Naik, S. N.; Goud, V. V.; Rout, P. K.; Dalai, A. K. Production of first and second generation biofuels: A comprehensive review. Renewable Sustainable Energy Rev. 2010, 14 (2), 578−597. (6) Bridgwater, A. V. Renewable fuels and chemicals by thermal processing of biomass. Chem. Eng. J. 2003, 91 (2−3), 87−102. (7) Hill, J.; Nelson, E.; Tilman, D.; Polasky, S.; Tiffany, D. Environmental, economic, and energetic costs and benefits of biodiesel and ethanol biofuels. Proc. Natl. Acad. Sci. U. S. A. 2006, 103 (30), 11206−11210. (8) Harmsen, P. F. H.; Huijgen, W. J. J.; Bermúdez López, L. M.; Bakker, R. R. C. Literature Review of Physical and Chemical Pretreatment Processes for Lignocellulosic Biomass; Energy Research Centre of the Netherlands: 2010. (9) Fernando, S.; Adhikari, S.; Chandrapal, C.; Murali, N. Biorefineries: Current Status, Challenges, and Future Direction. Energy Fuels 2006, 20 (4), 1727−1737. (10) Šprajcar, M.; Horvat, P.; Kržan, A. Biopolymers and Bioplastics: Plastics Aligned with Nature; 2012. (11) International Energy Agency. IEA Energy Technology Essentials: Biofuel Production; 2007. (12) Contractors, D. S. E. Biochemical Production Plants. http:// www.dsengineers.com/en/sectors-of-activities/bio-based-products/ biochemical-production-plants.html (accessed November 2, 2016. (13) Hardcastle, J. L. Commercial-Scale Biochemical Production Plant Online. Environmental Leader Environmental & Energy Management News; July 23, 2015. (14) Becker, J.; Lange, A.; Fabarius, J.; Wittmann, C. Top value platform chemicals: bio-based production of organic acids. Curr. Opin. Biotechnol. 2015, 36, 168−175. (15) Isikgor, F. H.; Becer, C. R. Lignocellulosic biomass: a sustainable platform for the production of bio-based chemicals and polymers. Polym. Chem. 2015, 6 (25), 4497−4559. L


Article


(38) Papoulias, S. A.; Grossmann, I. E. A structural optimization approach in process synthesisII. Comput. Chem. Eng. 1983, 7 (6), 707−721. (39) Duran, M. A.; Grossmann, I. E. Simultaneous optimization and heat integration of chemical processes. AIChE J. 1986, 32 (1), 123− 138. (40) Lang, Y. D.; Biegler, L. T.; Grossmann, I. E. Simultaneous optimization and heat integration with process simulators. Comput. Chem. Eng. 1988, 12 (4), 311−327. (41) Yoon, S.-G.; Lee, J.; Park, S. Heat integration analysis for an industrial ethylbenzene plant using pinch analysis. Appl. Therm. Eng. 2007, 27 (5−6), 886−893. (42) Beninca, M.; Trierweiler, J. O.; Secchi, A. R. Heat integration of an Olefins Plant: Pinch Analysis and mathematical optimization working together. Braz. J. Chem. Eng. 2011, 28, 101−116. (43) Peng, F.; Cui, G. Efficient simultaneous synthesis for heat exchanger network with simulated annealing algorithm. Appl. Therm. Eng. 2015, 78, 136−149. (44) Viswanathan, M.; Evans, L. B. Studies in the heat integration of chemical process plants. AIChE J. 1987, 33 (11), 1781−1790. (45) Ng, R. T. L.; Tay, D. H. S.; Ng, D. K. S. Simultaneous Process Synthesis, Heat and Power Integration in a Sustainable Integrated Biorefinery. Energy Fuels 2012, 26 (12), 7316−7330. (46) Elia, J. A.; Baliban, R. C.; Floudas, C. A. Toward Novel Hybrid Biomass, Coal, and Natural Gas Processes for Satisfying Current Transportation Fuel Demands, 2: Simultaneous Heat and Power Integration. Ind. Eng. Chem. Res. 2010, 49 (16), 7371−7388. (47) Baliban, R. C.; Elia, J. A.; Floudas, C. A. Optimization framework for the simultaneous process synthesis, heat and power integration of a thermochemical hybrid biomass, coal, and natural gas facility. Comput. Chem. Eng. 2011, 35 (9), 1647−1690. (48) Gorak, A.; Sorensen, E. Distillation: Fundamentals and Principles; Elsevier Science: 2014. (49) Joback, K. G.; Reid, R. C. ESTIMATION OF PURECOMPONENT PROPERTIES FROM GROUP-CONTRIBUTIONS. Chem. Eng. Commun. 1987, 57 (1−6), 233−243. (50) Biegler, L. T.; Grossmann, I. E.; Westerberg, A. W. Systematic methods of chemical process design; Prentice Hall PTR: 1997. (51) Ciriminna, R.; Lomeli-Rodriguez, M.; Demma Cara, P.; LopezSanchez, J. A.; Pagliaro, M. Limonene: a versatile chemical of the bioeconomy. Chem. Commun. 2014, 50 (97), 15288−15296. (52) Lange, B. M., Biosynthesis and Biotechnology of High-Value pMenthane Monoterpenes, Including Menthol, Carvone, and Limonene. In Biotechnology of Isoprenoids; Schrader, J., Bohlmann, J., Eds.; Springer International Publishing: Cham, 2015; pp 319−353. (53) Martín-Luengo, M. A.; Yates, M.; Martínez Domingo, M. J.; Casal, B.; Iglesias, M.; Esteban, M.; Ruiz-Hitzky, E. Synthesis of pcymene from limonene, a renewable feedstock. Appl. Catal., B 2008, 81 (3−4), 218−224. (54) Ferrara, M. A.; Almeida, D. S.; Siani, A. C.; Lucchetti, L.; Lacerda, P. S. B.; Freitas, A.; Tappin, M. R. R.; Bon, E. P. S. Bioconversion of R-(+)-limonene to perillic acid by the yeast Yarrowia lipolytica. Braz. J. Microbiol. 2013, 44 (4), 1075−1080. (55) Byrne, C. M.; Allen, S. D.; Lobkovsky, E. B.; Coates, G. W. Alternating Copolymerization of Limonene Oxide and Carbon Dioxide. J. Am. Chem. Soc. 2004, 126 (37), 11404−11405. (56) Mascia, M.; Ferrara, F.; Vacca, A.; Tola, G.; Errico, M. Design of heat integrated distillation systems for a light ends separation plant. Appl. Therm. Eng. 2007, 27 (7), 1205−1211. (57) Zábranský, M.; Růzǐ čka, V. Estimation of the Heat Capacities of Organic Liquids as a Function of Temperature Using Group Additivity: An Amendment. J. Phys. Chem. Ref. Data 2004, 33 (4), 1071−1081. (58) Bureš, M.; Majer, V.; Zábranský, M. Modification of Benson method for estimation of ideal-gas heat capacities. Chem. Eng. Sci. 1981, 36 (3), 529−537. (59) Verevkin, S. P.; Emel'yanenko, V. N.; Diky, V.; Muzny, C. D.; Chirico, R. D.; Frenkel, M. New Group-Contribution Approach to Thermochemical Properties of Organic Compounds: Hydrocarbons

(16) Corma, A.; Iborra, S.; Velty, A. Chemical Routes for the Transformation of Biomass into Chemicals. Chem. Rev. 2007, 107 (6), 2411−2502. (17) Simmons, B. A.; Loque, D.; Blanch, H. W. Next-generation biomass feedstocks for biofuel production. Genome Biology 2008, 9 (12), 242−242. (18) Douglas, J. M. Conceptual design of chemical processes; McGrawHill: 1988. (19) Nishida, N.; Stephanopoulos, G.; Westerberg, A. W. A review of process synthesis. AIChE J. 1981, 27 (3), 321−351. (20) Gnansounou, E.; Dauriat, A. Techno-economic analysis of lignocellulosic ethanol: A review. Bioresour. Technol. 2010, 101 (13), 4980−4991. (21) Sutherland, I. W. Bioplastic and Biopolymer Production; EOLSS Publishers: 2007; Vol. 5, pp 152−176. (22) Grossmann, I. E.; Santibanez, J. Applications of mixed-integer linear programming in process synthesis. Comput. Chem. Eng. 1980, 4 (4), 205−214. (23) Grossmann, I. E. Mixed-integer programming approach for the synthesis of integrated process flowsheets. Comput. Chem. Eng. 1985, 9 (5), 463−482. (24) Grossmann, I. E.; Daichendt, M. M. New trends in optimization-based approaches to process synthesis. Comput. Chem. Eng. 1996, 20 (6), 665−683. (25) Yeomans, H.; Grossmann, I. E. A systematic modeling framework of superstructure optimization in process synthesis. Comput. Chem. Eng. 1999, 23 (6), 709−731. (26) Kim, J.; Sen, S. M.; Maravelias, C. T. An optimization-based assessment framework for biomass-to-fuel conversion strategies. Energy Environ. Sci. 2013, 6 (4), 1093−1104. (27) Tan, R. R.; Ballacillo, J.-A. B.; Aviso, K. B.; Culaba, A. B. A fuzzy multiple-objective approach to the optimization of bioenergy system footprints. Chem. Eng. Res. Des. 2009, 87 (9), 1162−1170. (28) Murillo-Alvarado, P. E.; Ponce-Ortega, J. M.; Serna-González, M.; Castro-Montoya, A. J.; El-Halwagi, M. M. Optimization of Pathways for Biorefineries Involving the Selection of Feedstocks, Products, and Processing Steps. Ind. Eng. Chem. Res. 2013, 52 (14), 5177−5190. (29) Kelloway, A.; Daoutidis, P. Process Synthesis of Biorefineries: Optimization of Biomass Conversion to Fuels and Chemicals. Ind. Eng. Chem. Res. 2014, 53 (13), 5261−5273. (30) Ponce-Ortega, J. M.; Pham, V.; El-Halwagi, M. M.; El-Baz, A. A. A Disjunctive Programming Formulation for the Optimal Design of Biorefinery Configurations. Ind. Eng. Chem. Res. 2012, 51 (8), 3381− 3400. (31) Pham, V.; El-Halwagi, M. Process synthesis and optimization of biorefinery configurations. AIChE J. 2012, 58 (4), 1212−1221. (32) Tang, M.; Chin, M. S.; Lim, K.; Mun, Y.; Ng, R. L.; Tay, D. S.; Ng, D. S. Systematic approach for conceptual design of an integrated biorefinery with uncertainties. Clean Technol. Environ. Policy 2013, 15 (5), 783−799. (33) Andiappan, V.; Ko, A. S. Y.; Lau, V. W. S.; Ng, L. Y.; Ng, R. T. L.; Chemmangattuvalappil, N. G.; Ng, D. K. S. AIChE J. 2015, 61, 132. (34) Ulonska, K.; Voll, A.; Marquardt, W. Screening Pathways for the Production of Next Generation Biofuels. Energy Fuels 2016, 30 (1), 445−456. (35) Voll, A.; Marquardt, W. Reaction network flux analysis: Optimization-based evaluation of reaction pathways for biorenewables processing. AIChE J. 2012, 58 (6), 1788−1801. (36) Bao, B.; Ng, D. K. S.; Tay, D. H. S.; Jiménez-Gutiérrez, A.; ElHalwagi, M. M. A shortcut method for the preliminary synthesis of process-technology pathways: An optimization approach and application for the conceptual design of integrated biorefineries. Comput. Chem. Eng. 2011, 35 (8), 1374−1383. (37) Kong, Q.; Shah, N. An optimization-based framework for the conceptual design of reaction-separation processes. Chem. Eng. Res. Des. 2016, 113, 206−222. M


Article

Industrial & Engineering Chemistry Research and Oxygen-Containing Compounds. J. Phys. Chem. Ref. Data 2013, 42 (3), 033102. (60) Underwood, A. J. V. Fractional Distillation of Multicomponent Mixtures. Ind. Eng. Chem. 1949, 41 (12), 2844−2847.

N


Development of an Optimization-Based Framework ... - ACS Publications

Recommend Documents