Development of an Integrated Technique for Energy and Property

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Development of an Integrated Technique for Energy and Property Integration in Batch Processes Wan Sieng Yeo, Yin Ling Tan, and Yudi Samyudia Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03803 • Publication Date (Web): 08 Jan 2018 Downloaded from http://pubs.acs.org on January 8, 2018

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Industrial & Engineering Chemistry Research

Development of an Integrated Technique for Energy and Property Integration in Batch Processes Wan Sieng Yeo,*, † Yin Ling Tan,† and Yudi Samyudia‡ †

Department of Chemical Engineering, Curtin Universitiy, Malaysia, CDT 250, 98009, Miri,

Sarawak Malaysia ‡

School of Applied Science, Technology, Engineering and Mathematics, Universitas Prasetiya

Mulya, Kavling Edutown I.1, Jl. BSD Raya Utama, BSD City Kabupaten Tangerang, 15339 Indonesia

ABSTRACT: This paper presented a new technique for targeting minimum total annual cost of property-based heat integrated resource conservation networks (HIRCNs) for batch processes. This new technique takes in consideration of simultaneously heat and property integration with an objective to minimize the usage of fresh resources and energy utilities prior to the detailed network design. It is formulated as a mixed integer nonlinear programming (MINLP) mathematical model for HIRCNs which consists of property-based resource conservation network (RCN) and heat exchanger network (HEN) models. The property-based RCN model is formulated based on super-targeting approach while HEN model is developed via automated targeting approach. Two case studies were used to demonstrate the proposed model’s applicability and advantages. Moreover, comparisons of the results for the proposed model for HIRCN with storage system and without storage system as well as sequential targeting approach are also addressed.

1. INTRODUCTION The current drive towards high-value, low tonnage products such as specialty chemicals, fine chemicals and pharmaceuticals have encouraged batch process industries to develop new methods to minimize energy and raw materials consumption as well as maximize materials and energy recovery. Process integration is recognized as a systematic strategy for resource conservation and waste minimization. In particular, mass integration techniques for material reuse and recycle are “chemo-centric” as this integration is only based on the composition of 1 ACS Paragon Plus Environment

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process streams without considering other properties or functionalities of the streams such as pH, colour, toxicity, Total organic carbon (TOC), biological oxygen demand (BOD), viscosity and solubility.1 Thus, property integration that considers all of these properties was introduced. Property integration is defined as a functionality-based, holistic approach to the allocation and manipulation of streams and processing units, which is based on the tracking, adjustment, assignment, and matching of functionalities throughout the process.2 Many methodologies have been developed for property-based resource conservation networks (RCNs). Shelley and ElHalwagi proposed the concept of property-based clustering technique to identify optimal strategies for the recovery and allocation of volatile organic compounds.1 Thereafter, El-Halwagi et al. enhanced the clustering method that were developed by Shelley and El-Halwagi.1,2 ElHalwagi et al. developed mathematical expression that incorporated with rigorous optimization rules to define the optimal blends, allocation strategies and tasks of property-modifying devices.2 However, these methods can only tackle three properties and is not suitable to handle large scale high-dimensional problems. Hence, Qin et al. solved the aforementioned limitations by using algebraic tools for the property integration via component-less design.3 Later, Kazantzi and El-Halwagi and Foo et al. incorporated the concept of property integration into property-based pinch analysis technique to allow material reuse/ recycle and process modification for a RCN with one key property.4,5 On the other hand, Ng et al. developed Automated Targeting Approach (ATM) for propertybased RCN.6 The authors also extended the developed ATM approach for single impurity RCN, RCN with water interception placement as well as total RCN.7-9 Besides, Foo introduced ATM for batch HEN, mass exchange network and property-based water network to determine the minimum resource, energy and waste targets with the presence of storage system.10 The above research methodologies on property integration are useful but those methods only focus on steady-state system and yet unsteady-state system is not considered. Hence, Grooms et al. formulated a MINLP mathematical model to synthesize and schedule a hybrid of steady-state and dynamic for property-interception and allocation network based on the defined properties.11 Besides, Ng et al. developed an optimization mathematical programming approach to synthesize a cost-effective batch WN with incorporating property interceptors to optimize the reuse/ recycle of process streams and minimize the usage of external fresh resources.12 Furthermore, Chen et al.

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addressed a generic mathematical model for property-based RCN employed in batch and continuous processes with the consideration of waste treatment.13 Notice that the abovementioned research works have neglected the relationships between properties and the effect of one process variable. Thus, Sandate-Trejo et al. introduced models for these considerations to minimise the usage of fresh resources and waste discharged.14 In their study, models are developed within a property operator framework for the chemical process operation to stabilise its property balance and incorporated environmental constraints in the models. Besides considering property integration only, there are some works on mass and property integration.15-17 Ponce-Ortega et al. demonstrated a MINLP model to optimize the direct recycle networks together with waste water treatment in order to minimize the total annual cost (TAC) of the system that involves the cost for fresh sources, the piping cost for process integration and the waste water treatment cost.15 Nevertheless, the aforementioned studies did not involve property interceptor in their networks which may enhance the direct recycle and reuse strategy. Thereafter, Ponce-Ortega et al. presented a mathematical programming model for the direct recycle and reuse of mass and property integration networks that includes property interceptors while satisfying process and environmental constraints in order to minimize the TAC which includes the cost of fresh resources and the annualized capital cost for property interceptors.16 Later, Nápoles-Rivera et al. presented a mathematical programming model for the recycle and reuse of mass and property integration networks that considers both process and environmental constraints as well as consists of in-plant property interceptors within the structure of the network to optimize the design of the network.17 Later on, Kheireddine et al. extended the area of mass and property integrations with temperature effect to generate a cost-effective direct-recycle network.18 However, Kheireddine et al. did not include any temperature adjustment through temperature interceptors (e.g. heat exchangers, heaters or coolers) in the designed network.18 Hence, Rojas-Torres et al. introduced a systematic method that considers mixing operators for environmental properties, temperature dependence of the properties and the effects of heat, mass, and property to synthesize the regeneration recycling water networks.19 On the other hand, Kheireddine et al. only considered direct mixing without heat integration in their direct reuse/ recycle network.18 Therefore, Tan et al. presented a technique that 3 ACS Paragon Plus Environment


incorporated heat integration in the concentration- and property-based direct-recycle network to form HIRCNs with the consideration of varying process parameters to minimize the total operating cost of fresh resources and energy utilities.20 Tan et al. proposed the insight-based approach to achieve the optimization while the environmental regulations had been ignored. 20 Later, Tan et al. developed a MINLP model for HIRCN of the fixed flow rate problem that fulfils both process and environmental constraints.21 In their work, floating pinch method for HEN that had been established by Tan et al. is used to solve cases with different process parameters.22 However, the possible penalty costs on the piping and heat exchangers were not carried out in this work. In addition, Jiménez-Gutiérrez et al. developed an MINLP model for heat integrated water networks with considerations of contaminants and properties interceptor units.23 The objective function is to minimize the total annual cost fulfilling energy, mass and property constraints. A staged superstructure is presented, in which a first HEN before mixing streams, then mass and property integration network, and lastly a second HEN is included after mixing. Ghazouani et al. presented a mixed integer linear programming (MILP) model for heat integrated resource allocation network that considers non-isothermal heat recovery.24 The objective function is to minimize the consumption of fresh resources, waste discharge and energy utilities. The methodology is a sequential approach which first utilizes composite curves method to determine optimal flow rate of fresh resource, follow by a new linear approach based on transhipment model to achieve maximum heat recovery via non-isothermal mixing. Later, Ghazouani et al. extended their previous work to synthesis mass allocation and heat exchange networks simultaneously.25 A superstructure which allows non-isothermal mixing to occur before and after heat exchanger network is presented to show the interconnection between mass allocation and heat exchange networks. A MILP model is formulated to minimise the TAC of both networks which includes the annual operating costs for mass and energy utilities as well as the capital cost of the HEN. In order to keep the model linear, a discrete values of temperatures is used. However, this may have restricted the search space of the optimal solution. Notice that most of the abovementioned research works in the area of heat and property integrations have been studied separately. In many property-based RCNs cases, temperature is an important parameter. For example, solvent that is used for stripping purpose needs to be heated or cooled to the desired temperature before entering the stripping unit. This shows that both of 4 ACS Paragon Plus Environment

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the temperature and quality of fresh resources are equally important. Thus, it is necessary to consider both heat and property integrations simultaneously. To date, limited works have been conducted in this area and yet those works are only applicable to continuous processes. Therefore, there is a need to develop a systematic approach to synthesize property-based HIRCNs for batch processes. In this work, a MINLP model which is used for targeting total annual cost of property-based HIRCNs for batch processes is proposed. This model consists of property-based RCN model that is formulated based on super-targeting approach and HEN model which is developed via automated targeting approach. Two case studies are employed to show the effectiveness of the developed model.

2. PROBLEM STATEMENT Given is a batch process with τ batch cycle and a set of time intervals, INTERVALS = {t|t = 1,...,NINTERVALS}. The batch process is associated with a set of process sources, SOURCES = {i|i = 1,...,NSOURCES} and a set of process sinks, SINKS = {j|j = 1,..., NSINKS}. Sources may be used for reuse/ recycle to sinks or be discharged as waste. Each source i has a fixed flow rate (Fi), property operator (ψi ), temperature (Ti) as well as a start time (ti,ST), and end time (ti,ET). Sinks are process units that can accept sources. Each sink j requires a flow rate (Fj), temperature (Tj), property operator (ψ j ) and has a start time (tj,ST) and end time (tj,ET). The allowable property constraint for each sink j is stated as:

ψ min ≤ ψ j ≤ ψ max j j where ψ j

min

(1)

and ψ j

max

are the lower and upper limits of the acceptable property operator of sink j.

Moreover, there is a set of external fresh resources, FRESH = {m|m = 1,...,NFRESHS} that may be purchased to supplement the sinks. Each fresh resource has a given temperature (Tm) and property operator (ψm). The flow rate of fresh resource m is to be determined as part of the solution. Furthermore, a set of storage tanks, STORAGES = {s|s = 1,...,NSTORAGES} is available to store each individual sources from one time interval to another. It is assumed that the properties and temperature of process streams remain unchanged in the storage tanks. When various process streams are mixed, a general mixing rule is required to specify all the potential mixing patterns among these individual properties and it is expressed as below.1 5 ACS Paragon Plus Environment


ψ ( p ) = ∑ xlψ l

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(2)

l

where

ψ (p) and ψl are the operators on mixture property p and property of stream l

respectively; while xl is the fractional distribution of stream l of the total mixture flow rate. In the HIRCNs, all streams are intended for the HEN. These streams are to be heated (cold streams) or cooled (hot streams) before entering sinks. The classification of hot and cold streams is predefined as the supply and target temperatures of these streams are directly extracted from the given source and sink temperature limiting data. The flow rate and temperatures of these streams are to be obtained simultaneously within the HIRCN. Heat is exchanged between the hot streams and cold streams. Besides, external hot (QH) and cold (QC) utilities are available to fulfil the heating and cooling requirements after maximum energy recovery. Note that after passed through HEN, the properties and flow rate of process streams remain the same. Figure 1 shows the superstructure of source-HEN-sink for this problem. As shown in this figure, source i and stored source in storage tank s are sent to sink j for reuse or discharged as waste. Fresh resources are only sent to sink j whenever it is needed. Storage tanks are added to the superstructure to enhance the energy recovery. Besides, a HEN is placed in the superstructure to allow heat exchange among all the hot and cold streams in order to obtain the energy recovery. The objective is to minimise the total annualised cost of the property-based HIRCNs for batch processes. It takes into consideration of the operating costs for the fresh resources, energy utility as well as the capital cost of storage tanks. To synthesize property-based HIRCNs for batch processes, the following assumptions are made: (i) Counter-current heat exchange mode is assumed for heat recovery to achieve high efficiency.26 (ii) Only single impurity or property is considered in the synthesis of HIRCNs problems. (iii) Each storage tank is assumed to maintain to be isothermal with external heating or cooling system. (iv) Storage tanks are restricted to store sources of the same quality.


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3. MODEL FORMULATION The models for property-based RCN and HEN of the HIRCN are formulated as following. Firstly, data conversion equations which are needed for both property-based RCN and HEN models are presented. 3.1. Data Conversion The raw data of batch processes are given in total amount in each batch cycle as well as the start time and end time for each sinks and sources. However, the desired limiting data for the RCN and HEN models developed in this work are the fractional amount of each sinks and sources in each time interval. Thus, data conversion for sinks and sources is needed. The fractional amounts of source i and sink j in time interval t can be achieved via eqs 3 and 4 respectively.

 Fi  Fi ,t =  ∆tt ∀i ∈ I , t ∈T ti ,ET − ti,ST 

(3)

  Fj Fj ,t =  ∆tt ∀j ∈ J , t ∈T  t j ,ET − t j ,ST 

(4)

where Fi and Fj are the total amounts of source i and sink j in each batch cycle respectively, while

ti ,ET , ti ,ST , t j,ET and t j ,ST are the end and start times of the source i and sink j respectively; ∆tt is the duration of time interval t and can be achieved via eq 5. ∆ t t = t t − t t −1 ∀ t ∈ T

where

(5)

tt−1 and tt represent the start and end times of time interval t.

In order to define

tt−1 and tt , the time interval of the sinks and sources are arranged in

ascending order, from the lowest time interval t = 0 to the highest time interval t = T. For example, the first time interval starts at t0 and ends at t1. Thus, t0 and t1 are the start and end times of time interval 1 respectively. For the second time interval, t1 and t2 are the start and end times respectively. The same definition is repeated for the rest of the time intervals.



3.2. Property-based Resource Conservation Network The following sub-sections present the models for stream parameterisation and property-based RCN. In stream parameterisation model, binary variables are used to parameterise the existence of sinks and sources in each time interval. The model for property-based RCN is derived based on the source-HEN-sink superstructure in Figure 1 and mainly consists of mass balances for various sources, sinks and storage tanks.

Figure 1. Superstructure of source-HEN-sink for property-based HIRCNs for batch processes Stream parameterisation Stream parameterisation models are introduced to allocate sources and sinks in their respective time intervals respectively. The binary variables used to parameterise the source i in each time interval are given by the constraints in eqs 6 - 8.


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Z i ,t

 1, if t t > t i , ST = ∀i ∈ I , t ∈ T 0, if t t ≤ t i , ST 

(6)

X i ,t

 1, if t i , ET > t t -1 = ∀i ∈ I , t ∈ T 0, if t i , ET ≤ t t −1 

(7)

Y i , t= X i , t Z i , t ∀ i ∈ I , t ∈ T

(8)

where Z i , t , X i ,t and Yi,t are binary variables for source i in time interval t. The values of Z i , t and X i ,t are determined by eqs 6 and 7 respectively. When Z i , t and X i ,t are equal to 1, Yi,t in eq 8 becomes 1 indicates that source i presences in time interval t. Based on eq 8, if either Z i , t or X i ,t is equal to zero, Yi,t = 0 which indicates that source i does not presence in time interval t. Additionally, eqs 9 to 11 are used to define the existence of sink j in each time intervals. 1, if t > t t j , ST Z j ,t =  ∀j ∈ J , t ∈ T 0, if t ≤ t t j , ST 

(9)

1, if t j , ET > tt −1 X j ,t =  ∀j ∈ J , t ∈T 0, if t j , ET ≤ tt −1

(10)

Y j ,t = X

(11)

j ,t

Z j ,t ∀ j ∈ J , t ∈ T

where Z j ,t , X j,t ,and Y j , t are binary variables for sink j in time interval t. Eqs 9 and 10 are used to determine the values of Z j ,t and X j,t . Y j , t in eq 11 equals to 1 only when Z j ,t and X j,t are 1. Thus, this indicates that sink j exists in time interval t. If either Z j ,t or

X j,t is zero, then Y j ,t = 0 which reflects sink j does not presence in time interval t. Note that these stream parameterisation models for source i and sink j shown are developed for each time interval in the HIRCN. Process source i may be segregated and sent to sink j, the respective storage tank s and/or be discharged as waste. Eq 12 describes the flow balance on the splitting of source i in time interval t. 9 ACS Paragon Plus Environment


Fi ,tYi ,t = ∑ Fi, j ,tYj ,t + Fi, s,t + Fi,waste ∀i ∈ I , t ∈T , s = i t

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(12)

j∈J

waste where Fi, j,t , Fi,s,t , and Fi ,t are the fractional amounts of source i that are sent to sink j, the

respective storage tank s and waste storage in time interval t respectively. Process sink j may accept flow from source i, storage tank s and/or fresh resource m. Eq 13 presents the flow balance at the mixing point before sink j in time interval t.

Fj,tYj,t = ∑Fi, j,tYi,t + ∑Fs, j,t + ∑Fm, j,t ∀j ∈ J , t ∈T i∈I

s∈S

(13)

m∈M

where Fs, j,t and Fm, j ,t are the amounts from storage tank s and fresh resource m that are sent to sink j in time interval t respectively. In addition to flow balance, property operator balance has to be considered for each sink j. Eq 14 shows the property operator balance for sink j in time interval t.

Fj,tYj,tψ j = ∑Fi, j,tYi,tψ i + ∑ Fs, j,tψ s + ∑Fm, j,tψ m ∀j ∈ J , t ∈T i∈I

where

s∈S

ψi , ψm, and ψs

(14)

m∈M

are the property operators of source i, fresh resource m and the stored

source, respectively. Note that each source i has its own designated storage tank s. Thus, the property operator of source i in the respective storage tank s remains unchanged and is represented by eq 15. ψ 1  ψ 1  ψ  ψ   2  =  2  ∀i ∈ I  M   M      ψ s  ψ i 

(15)

Fresh resource m is sent to sink j if it is needed but not to waste. The total amount of fresh resource m which is required for each batch cycle can be obtained via eq 16.

Fm = ∑∑ Fm, j ,t ∀m ∈ M

(16)

t∈T j∈J

Waste is flow from source i and storage tank s which are unable to reuse/recycle to sink j. The total amount of waste in each batch cycle can be determined by eq 17.

F waste = ∑∑ Fi ,waste + ∑∑ Fswaste ,t t t∈T i∈I

(17)

t∈T s∈S


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waste where Fs,t is the amount from storage tank s that is sent to waste storage in time interval t.

Figure 2 shows the schematic representation for storage tank s. The input stream consists of the respective source i from previous time interval t-1 while the output streams may be sent to sink j or be discharged as waste in time interval t. Furthermore, some mass may be accumulated from the previous time interval as well as in the current time interval. The material balance for storage tank s is defined by eq 18.

Fi,s,t −1 + CSTs,t −1 = ∑ Fs, j,t + Fswaste + CSTs,t ∀s ∈ S , t ∈T , i ∈ I , s = i ,t

(18)

j∈J

Fi,s,t −1 represents the amount of source i which is sent to the respective storage tank s in time interval t-1 while CSTs,t−1 and CSTs,t are the cumulative mass in storage tank s in time interval t-1 and t respectively. Note that for single batch process, the first cumulative mass in storage tank s will always take a value of zero as no stored source in storage tank s at the beginning stage.

Time interval t-1 Process source i

Time interval t

Fs , j , t −1

F s , j ,t Storage tank s

CSTs,t−1

Process sink j

Fswaste ,t

CSTs,t

Cumulative mass

Waste Cumulative mass

Figure 2. Schematic representation for storage tank s 3.3. Heat Exchanger Network In this study, the ATM that was developed by Foo is used to model the targeting for HEN.10 Note that the targeting task of HEN is performed in every time intervals to ensure the overall targets for the given problem. Firstly, sources i and sinks j are allocated in their respective time intervals to allow the performance of the HEN targeting task in every time interval. In each time interval, all possible streams that are connected from sources and sinks to fresh resources, storage tanks and waste are identified based on the source-HEN-sink superstructure. 11 ACS Paragon Plus Environment


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These streams are either hot or cold streams. Hot streams are to be cooled and cold streams are to be heated. In this study, these hot and cold streams are pre-defined directly based on the supply and target temperatures of the given source, sink, fresh resource and waste temperature limiting data. For example, a stream that is segregated from a source with a given temperature of 50oC to a sink which has a given temperature of 80oC is categorized as a cold stream with supply and target temperatures of 50oC and 80oC respectively. The heat capacity for each hot and cold stream is assumed to be constant. In additional, external hot and cold utilities are available to fulfil the process requirement after maximising the energy recovery between the hot and cold streams. To conduct ATM, cascade diagram for HEN as illustrated in Figure 3 is first generated for each time interval to determine the minimum external hot and cold utilities. As shown, a total of n temperatures is arranged vertically in descending order, from the highest temperature (q0) to the lowest temperature (qn). These temperatures are the shifted supply and target temperatures of all the hot and cold streams which are obtained by shifting the supply and target temperatures with a minimum temperature different ( ∆ T min ). This is important to ensure feasible heat transfer between the hot and cold streams. For hot streams, the supply and target temperatures are shifted by subtracting

∆Tmin as shown 2

in eqs 19 and 20. ST ST q Hot = THot −

∆ Tmin 2

(19)

TT TT q Hot = THot −

∆ Tmin 2

(20)

ST

TT

where THot and THot are the supply and target temperatures for the hot stream respectively. For cold streams, the supply and target temperatures are shifted by adding

∆Tmin as shown by 2

the following equations, ST ST q Cold = T Cold +

∆ T min 2

(21)

TT TT q Cold = T Cold +

∆ T min 2

(22)

ST

TT

where TCold and TCold are the supply and target temperatures for the cold stream respectively. 12 ACS Paragon Plus Environment

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Heat cascade H0,t = QH,t

q0 Hi,j,1,t Hm,j,1,t H Hs,j,1,t + Hwastes,1,t q1 q2 q3

waste

i,1,t +

k=1 H1,t = H0,t + Hi,j,1,t + Hm,j,1,t Hwastei,1,t + Hs,j,1,t +Hwastes,1,t

Hi,j,2,t Hm,j,2,t Hwastei,2,t + Hs,j,2,t + Hwastes,2,t

k=2


k=3


k=4

Hi,j,k,t Hm,j,k,t Hwastei,k,t + Hs,j,k,t + Hwastes,k,t

k=n

H2,t = H1,t + Hi,j,2,t + Hm,j,2,t Hwastei,2,t + Hs,j,2,t +Hwastes,2,t H3,t = H2,t + Hi,j,3,t + Hm,j,3,t Hwastei,3,t + Hs,j,3,t +Hwastes,3,t H4,t = H3,t + Hi,j,4,t + Hm,j,4,t Hwastei,4,t + Hs,j,4,t +Hwastes,4,t

q4 qn-1

Hn,t = Hk-1,t + Hi,j,k,t +Hm,j,k,t Hwastei,k,t + Hs,j,k,t + Hwastes,k,t = QC,t

qn

Figure 3. Generic cascade diagram for each time internal in a batch heat exchange network

Next, a heat cascade is carried out across all temperature intervals (qk – qk-1) in all time intervals. To performed heat cascade, the heat balance equations within each temperature interval k are developed to determine the interval heat flows of the streams based on the ratio of the

duration of the time interval to that of the stream. Generally, the overall heat balance equation for each temperature interval k in time interval t can be expressed as: H k ,t = H k −1,t + ∑∑ H i , j , k ,t + i∈I j∈J

∑∑ H

m∈M j∈J

m , j , k ,t

waste + ∑ H iwaste , k ,t + ∑∑ H s , j , k ,t + ∑ H s , k , t i∈I

s∈S j∈J

∀k ∈ K , t ∈ T

(23)

s∈S

where Hk ,t and Hk −1,t are the residual heat loads within temperature interval k and k-1 in time waste interval t; H i , j , k , t and Hi, k,t are the heat loads for the streams from source i that are sent to sink

j and waste within temperature interval k in time interval t; Hm, j , k ,t is the heat load for the

streams from fresh resource m that is sent to sink j within temperature interval k in time interval 13 ACS Paragon Plus Environment


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waste t; H s , j , k ,t and Hs,k,t are the heat loads for the streams from storage tank s that are sent to sink j

and waste within temperature interval k in time interval t. All of the above heat loads for the streams within temperature interval k in time interval t are determined from the product of the mass flow and the specific heat capacity of the streams as well as the temperature different of temperature interval k and are shown in eqs 24 – 29. Eq 24 presents the heat balance for the streams from source i that are sent to sink j within temperature interval k in time interval t.

Hi, j ,k ,t = ∑∑ Fi, j ,t Cpi ∆qk ∀k ∈ K , t ∈T

(24)

i∈I j∈J

where Cpi is the specific heat capacity of source i. The heat balance for the streams from fresh resource m that are sent to sink j within temperature interval k in time interval t can be determined by eq 25.

Hm, j ,k ,t =

∑ ∑F

m, j ,t

Cpm∆qk ∀k ∈ K, t ∈T

(25)

m∈M j∈J

where Cpm is the specific heat capacity of fresh resource m. Eq 26 describes the heat balance for the streams from source i that are sent to waste storage within temperature interval k in time interval t. waste Hiwaste Cpi ∆qk ∀k ∈ K , t ∈T , k ,t = ∑ Fi , t

(26)

i∈I

The heat balance for the streams from stored source in storage tank s that are sent to sink j within temperature interval k in time interval t can be defined as follows.

Hs, j ,k ,t = ∑∑ Fs, j ,t Cps ∆qk ∀k ∈ K , t ∈T

(27)

s∈S j∈J

where Cps is the specific heat capacity of the stored source. As mentioned earlier, each source i has its own respective storage tank s. Thus, the specific heat capacity of the source i, Cps remains the same and it can be represented by the following equation.


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 Cp1   Cp1  Cp  Cp   2 =  2  M   M      Cp s   Cpi 

∀i ∈ I

(28)

The heat balance for the streams from stored source in storage tank s that are sent to waste storage within temperature interval k in time interval t can be achieved via eq 29. waste H swaste Cps ∆qk ∀k ∈ K , t ∈T , k ,t = ∑ Fs ,t

(29)

s∈S

Since the temperature range for each temperature interval k is difference, hence eq 30 is used to determine the temperature different for each temperature interval k, ∆qk .

∆ q k = q k − q k −1

∀k ∈ K

(30)

According to Foo, the heat flow has to be a positive value to ensure the feasible of heat transfer.14 Therefore, eq 31 is added to ensure the residual heat load is a non-negative value. H k ,t ≥ 0

∀k ∈ K , t ∈ T

(31)

In the heat cascade diagram (Figure 3), the external hot utility will be placed at the first temperature level. On the other hand, the external cold utility will be allocated at the lowest temperature level in the heat cascade diagram. Thus, the minimum hot and cold utilities for each time intervals are defined as follow,

QH,t = H 0,t

∀t ∈T

(32)

QC,t = H n,t ∀t ∈T

(33)

where H0,t and Hn,t are the heat loads at the first and final temperature levels in time interval t. Eqs 34 and 35 are included to determine the total required external hot (QH) and cold (QC) utilities for all time intervals in each batch cycle.

QH = ∑QH,t

(34)

QC = ∑QC,t

(35)

t∈T

t∈T



3.4

Page 16 of 34

Objective Function

This section presents the objective function of the proposed model which is to minimize the total annual cost (TAC) of HIRCNs. The TAC includes the total annual operating cost for fresh resources, hot and cold utilities as well as the annualised capital cost for storage tanks. It is expressed as follow,

minTAC = Nb (Cm Fm + CHUQH + CCUQC + CHUQloss ) + ∑ Cs s∈S

where

(36)

Cm, CHU, and CCU are the costs for fresh resources, hot and cold utilities. Cs is the

annualised capital cost for storage tank s, Nb is the number of batches per year, and Qloss is the total heat losses from storage tanks to the surrounding. The annualised capital cost for storage tanks, Cs is given as,27

Cs =

I [A0 (A1CSTs )d ] AF ∀s ∈ S Ib

(37)

where A0, A1, and d are the cost parameters for storage tank s based on the chemical engineering plant cost index of 394. I and Ib are the chemical engineering plant cost index in the present time and base cost index. 10% of freeboard is assumed for storage tank s.28 It is also assumed that the cone-roofed, well insulated and covered carbon steel storage tanks are utilized. Therefore, A0, A1, and d are taken as 210, 1.10 and 0.51 respectively.

CSTs is the capacity of storage tank s and

AF is the annualizing factor. The annualisation factor can be calculated by the following

equation.

As (1 + As ) yr AF = (1 + As ) yr − 1

(38)

where As is the annual fractional interest rate and yr is the time life of the storage tanks. The capacity of storage tank s can be determined based on the input flow rate balance equation of the storage tank in time interval t-1 or the output flow rate balance of the storage tank in time interval t (refer to Figure 2). In this model, the output of storage tank is used to identify the capacity of storage tank s and is represented by eq 39.

CSTs ≥ ∑ Fs, j ,t + Fswaste + CSTs ,t ,t

∀s ∈ S , t ∈ T

(39)

j∈J


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Moreover, a positive value is taking into consideration for the capacity of each storage tank s,10, 29 as shown in eq 40.

CST s ≥ 0

∀s ∈ S

(40)

Total heat loss from storage tanks to the surrounding, Qloss is calculated by eqs 41 to 44.30

T s − T∞ s∈S R tot , s

Q loss = ∑

R tot , s =

1 h1 A1, s

∀s ∈ S

(41)

r  r  In  2 , s  In  3 , s  r1, s  r2 , s  1 +  +  + 2π L s k ves 2π L s k ins h 3 A3 , s

∀s ∈ S

(42)

A1, s = 2π r1 . s L s

∀s ∈ S

(43)

A3 , s = 2π r3 . s L s

∀s ∈ S

(44)

v s = π r12,S L s

∀s ∈ S

(45)

where Ts , T∞ , and Rtot , s are storage tank s temperature, steady state ambient temperature and thermal resistance for heat storage s. A1,s , A3, s , r1.s , r2,s , r3.s , Ls and V s are the internal area for heat loss by convection from the heat transfer medium in storage tank s, the area for convection heat transfer losses from storage tank s to the environment, inside radius of storage tank s, outside radius of storage tank s, outside radius of insulation, height of the storage tank s and the volume of storage tank s respectively. Meanwhile, h1 , h3 , kves and k ins are convective heat transfer coefficient for free convection of liquids, convective heat transfer coefficient for free convection of gases, thermal conductivity of heat storage tank and thermal conductivity of insulation respectively. The values of h1 , h3 , kves and k ins are taken as 0.525 kW/(m2. oC), 0.002 kW/(m2. oC), 0.0605 kW/(m. oC), and 0.00005 kW/(m. oC) respectively.31 Moreover, the ratio of height of the storage tank s, Ls to diameter is taken as 4:1.32

4. CASE STUDIES In this section, the developed property-based HIRCNs mathematical model for batch processes described in Section 3 is applied to two case studies. Each case study is solved using three 17 ACS Paragon Plus Environment


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different scenarios. In Scenario 1, the developed HIRCN model is solved without the consideration of storage system to minimize the total annual operating cost (TOC) for fresh resources, external hot and cold utilities. For Scenario 2, the developed HIRCN model is solved with the consideration of storage system to minimize the TAC which includes the cost of fresh resources, external hot and cold utilities as well as the cost of storage tanks. In Scenario 3, the developed HIRCN model is solved with the consideration of storage system using sequential targeting approach. The objective functions are first to minimise the TOC of fresh resource for property-based HIRCNs (eq 46), follow by minimizing the cost of hot and cold utilities (eq 47).

min TOC = N bCm Fm

(46)

min TOC = N b (C H U QH + C CUQC )

(47)

Since storage system is not present in Scenario 1, process source will not be sent to any storage tank. Thus, additional constraint is added as follow:

Fi , s,t = 0 ∀i ∈ I , s ∈ S , s = i, t ∈ T

(48)

The results of all these three scenarios are compared and analyzed. Besides, the HIRCNs involving the RCN and HEN design for each case study are also presented. All these case studies are solved using Extended LINGO version 11.0 with Global Solver. The following costing and stream parameters are used to solve the case studies, a. The capital cost of storage tank s is annualized with 10 % of annual fractional interest rate over 6 years. Therefore, the annualizing factor, AF which is calculated by eq 38 gives a value of 0.229. b. The chemical engineering plant cost index of 572.7 is used. c. The costs of fresh resource, Cm, hot utility, CHU, and cold utility, CCU are taken as $0.001/kg13, $0.017/kW.hr and $0.006/kW.hr respectively.33 d. The minimum temperature difference (∆Tmin) and the specific heat capacities of all streams (Cpi, Cps and Cpm) are assumed as 10oC and 4.2 kJ/kg.oC respectively. e. The density of process streams is assumed as 1000 kg/m3 as majority is water. f. The steady state ambient temperature, T∞ is assumed as 30 oC. g. Storage tank wall thickness and insulation thickness are assumed as 0.02m and 0.13m.31 18 ACS Paragon Plus Environment

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4.1 Case study 1 Case Study 1 is a modified case study which is adopted from Bagajewiz et al.34 In this case study, there are three sources and three sinks, with the limiting data shown in Table 1. The concentration and supply temperature of fresh resource is 0 ppm and 20°C respectively. The waste must be released at 30°C. A batch cycle of 4 hours and the annual operating days of 330 days are assumed. Thus, the number of batches per year, Nb is 1,980.

Table 1. Limiting data for Case Study 1

Sink

Amount (t)

Concentration (ppm)

Temperature (oC)

SK1

360

50

SK2

144

SK3

600.12

Source

Amount (t)

Time (h) Start

End

100

1

3

50

75

0

4

800

100

1

3

Concentration (ppm)

Temperature (oC)

Time (h) Start

End

SR1

360

100

100

0

2

SR2

144

800

75

2

4

SR3

600.12

1100

100

1

3

Based on the limiting data in Table 1, the time intervals for sources and sinks are arranged in ascending order (t0 = 0 h, t1 = 1 h, t2= 2 h, t3 = 3 h and t4 = 4 h). Four time intervals which are time intervals 1, 2, 3 and 4 are found. The stream parameterisation model is first solved to determine the existence of sources and sinks in their corresponding time interval. Then, possible source-HEN-sink superstructure in each time interval is found. In each time interval, the process streams in the superstructure are categorized as hot or cold streams according to the supply and target temperature of the given fresh resource, waste, sources and sinks. Next, these streams are used to establish the HEN cascade diagram for each time interval. The TOC of fresh resource as well as hot and cold utilities in the property-based HIRCNs without storage system are minimized in Scenario 1. The optimization objective in eq 36 is solved subject to constraints given by eqs 3 to 18, 23 to 26, 30 to 35 and 48, yields the minimum 19 ACS Paragon Plus Environment


TOC of $1,714,563/year. The required fresh resource, hot and cold utilities are determined as 444.5 ton/batch, 19,676 kWh/batch and 14,490 kWh/batch respectively. The optimal network configurations of property-based HIRCNs and HENs for Scenario 1 of Case Study 1 are shown in Figures 4 and 5 respectively.

Figure 4. Property-based HIRCNs for Scenario 1 of Case Study 1 (All flow terms appeared in HEN are given in tons)

Figure 5. HENs for Scenario 1 of Case Study 1 (All heat terms under heat exchangers are given in kilowatts of heat (kWh); values shown in parentheses represent F*Cp (kWh/oC))


Page 20 of 34

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The optimization objective for Scenario 2 is set to minimize the TAC for property-based HIRCNs with storage system. The TAC involves the TOC of fresh resource, hot and cold utilities as well as the annualised capital cost for storage tanks. Hence, eq 36 is solved subject to constraints in eqs 3 to 18, 23 to 35 and 37 to 45, yields the TAC of $724,613/year. The requirements of fresh resource, hot utility, cold utility and storage tanks for Scenario 2 are 293.2 ton/batch, 3,421 kWh/batch, 0 kWh/batch, 175.6 tons and 67.6 tons respectively. Figures 6 and 7 show the optimal network configurations of property-based HIRCNs and HENs for Scenario 2 in Case Study 1.

HEN SR1 F = 180 ton T = 100 oC ψ = 100 ppm Fresh F = 25 ton T = 20oC ψ = 0 ppm Storage S2 F = 67.56 ton T = 75oC ψ = 800 Ppm

10

HEN

HEN

HEN

SK2 F = 36 ton T = 75oC ψ = 50 ppm

SR1 F = 180 ton T = 100 oC ψ = 100 ppm

SK1 F = 180 ton T = 100 oC ψ = 50 ppm

SR2 F =72 ton T = 75oC ψ = 800 ppm

SK1 F = 180 ton T = 100 oC ψ = 50 ppm

SR2 F = 72 ton T = 75oC ψ = 800 ppm

SK2 F = 36 ton T = 75oC ψ = 50 ppm

Waste F = 25 ton T = 30oC

SR3 F = 300.06 ton T = 100 oC ψ = 1100 ppm

SK2 F = 36 ton T = 75oC ψ = 50 ppm

SR3 F = 300.06 ton T = 100 oC ψ = 1100 ppm

SK2 F = 36 ton T = 75oC ψ = 50 ppm

Fresh F = 25 ton T = 20oC ψ = 0 ppm

Waste F = 25 ton T = 30oC

Fresh F = 119.45 ton T = 20oC ψ = 0 ppm Storage S1 F = 170 ton T = 100 oC ψ = 100 Ppm Storage S2 F = 41.56 ton T = 75oC ψ = 800 ppm

SK3 Fresh F = 300.06 ton F = 123.75 ton T = 100 oC T = 20oC ψ = 800 ppm ψ = 0 ppm

SK3 F = 300.06 ton T = 100 oC ψ = 800 ppm

Waste F = 119.45 ton T = 30oC Storage S1 F =175.56 ton T = 100 oC ψ = 100 ppm

Storage S2 F = 67.56 ton T = 75oC ψ = 800 ppm

Waste F = 123.75 ton T = 30oC

10

Storage S1 F =10 ton T = 100 oC ψ = 100 ppm Storage S2 F = 21.56 ton T = 75oC ψ = 800 ppm

t0 = 0 hr

t1 = 1 hr

t2 = 2 hr

t3 = 3 hr

t4 = 4 hr


The optimization objective of Scenario 3 is initially set to minimize the TOC of fresh resource for property-based HIRCNs in order to achieve the first stage optimization. Therefore, eq 46 is solved subject to constraints in eqs 3 to 18, yields the minimum required fresh resource of 278.2 ton/batch. The obtained fresh resource target is then embedded as an additional constraint (eq 49). Fm = 278.2

(49)

In second stage optimization, the objective function is set to minimize the TOC of hot and cold utilities. Thus, eq 47 is solved subject to constraints in eqs 3 to 18, 23 to 35, 37 to 45 and 49, yields 4,636 kWh/batch of hot utility and 1,391 kWh/batch of cold utility. Besides that, 182.9 21 ACS Paragon Plus Environment


tons, 72.0 tons and 19.4 tons of storage tanks are needed. The optimal network configurations of property-based HIRCNs and HENs for Scenario 3 in Case Study 1 are shown in Figures 8 and 9. Table 2 presents the results for Scenarios 1, 2 and 3 of Case Study 1. As shown, the presence of storage system in Scenarios 2 and 3 resulted in significant reduction in fresh resource as well as hot and cold utilities. Even though storage tanks capital cost is needed in these scenarios, but it still required less total annual cost as compared to Scenario 1. Comparing Scenarios 2 and 3, less storage tank, less heat loss and less total operating cost is needed for Scenario 2. Therefore, it can be concluded that it is more beneficial to simultaneously consider the total operating cost and the capital cost of storage tanks in the targeting of property-based HIRCNs.

Figure 7. HENs for Scenario 2 of Case Study 1 (All heat terms under heat exchangers are given in kilowatts of heat (kWh); values shown in parentheses represent F*Cp (kWh/oC))

4.2 Case Study 2 Case Study 2 is a case study modified from Case Study in Kheireddine et al. with the limiting data shown in Table 3.18 There are three sources and three sinks. The fresh resource 1 (FR1) and 2 (FR2) with the vapour pressures of 3 kpa and 6 kpa are available to fulfil the requirements of sinks. FR1 and FR2 have temperatures of 25oC and 35oC, respectively. In this case study, the 22 ACS Paragon Plus Environment

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unit costs for FR1 and FR2 are $0.00132/kg and $0.00088/kg. The waste is discharged at 30oC. It is assumed that the cycle time for a batch cycle is 4 hours and the annual operating days is 330 days. Hence, the number of batches per year, Nb is 1,980.


Figure 9. HENs for Scenario 3 of Case Study 1 (All heat terms under heat exchangers are given in kilowatts of heat (kWh); values shown in parentheses represent F*Cp (kWh/oC)) 23 ACS Paragon Plus Environment


Page 24 of 34

Table 2. Summary of results for Scenarios 1, 2 and 3 of Case Study 1 Concept

Scenario 1

Scenario 2

Scenario 3

Fresh resource, Fm (t/batch)

444.5

293.2

278.2

Hot utility, QH (kWh/batch)

19,676

3,421

4,636

Cold utility, QC (kWh/batch)

14,490

0

1,391

Capacity for storage tank S1, CSTS1 (t)

-

175.6

182.9


-

67.6

72.0


-

0

19.4

Total heat losses from storage tanks (kwh/batch)

-

16.2

35.2

Annual capital cost of storage tanks ($/ year)

-

28,410

34,860

Total operating cost, TOC ($/year)

1,714,563

696,203

724,628

Total annualized cost, TAC ($/ year)

1,714,563

724,613

759,488

Table 3. Limiting data for Case Study 2

Sink

Amount (kg)

Vapour pressure (kpa)

Time (h)

Temperature (oC)

Start

End

SK1

5,436

15 - 35

85

1

3

SK2

3,986

10 - 25

50

0

2

SK3

3,381

13 - 40

65

1

4

Vapour pressure (kpa)

Temperature (oC)

Source

Amount (kg)

Time (h) Start

End

SR1

10,983

38

75

0

3

SR2

1,766

25

65

1

2

SR3

5,940

7

40

0

4

Based on the data displayed in Table 3, four time intervals which are t0 = 0 hr, t1 = 1 hr, t2 = 2 hr, t3 = 3 hr and t4 = 4 hr are found for this case study. Similar to earlier case studies, stream parameterisation model is solved for Case Study 2 first to determine the existence of sources and 24 ACS Paragon Plus Environment

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sinks in each time interval. Then, the sources and sinks are arranged in the respective time intervals. A revised source-HEN-sink superstructure for each time interval in Case Study 2 is constructed. Based on the superstructure, all the hot and cold streams in each time interval are pre-defined. Then, the HEN cascade diagram for each time interval is established. In Scenario 1, the TOC of fresh resource as well as hot and cold utilities in the property-based HIRCNs without storage system are minimized. Similar to the previous case studies, the objective function in eq 36 is solved subject to constraints given by eqs 3 to 18, 23 to 26, 30 to 35 and 48, yields the minimum TOC of $6,306/year. In this case study, only hot and cold utilities are required. The hot and cold utilities for this case study are obtained as 102.4 kWh/batch and 240.6 kWh/batch respectively. The optimal network configurations of property-based HIRCNs and HENs for Scenario 1 of Case Study 2 are displayed in Figures 10 and 11 respectively.

Figure 10. Property-based HIRCNs for Scenario 1 of Case Study 2 (All flow terms appeared in HEN are given in kg)

The objective function for Scenario 2 is fixed to minimize the TAC for property-based HIRCNs with storage system. In this scenario, the TOC of fresh resources, hot and cold utilities as well as the annualised capital cost for storage tanks are minimized simultaneously. Thus, eq 36 is solved subject to constraints in eqs 3 to 18, 23 to 35 and 37 to 45 yields the TAC of $5,949/year. The requirements of fresh resources (FR1 and FR2), hot utility, cold utility and storage tank for Scenario 2 are 0 kg/batch, 0 kg/batch, 69.6 kWh/batch, 207.7 kWh/batch and 805 kg respectively. Figures 12 and 13 show the optimal network configurations of propertybased HIRCNs and HENs for Scenario 2 in Case Study 2. 25 ACS Paragon Plus Environment


Figure 11. HENs for Scenario 1 of Case Study 2 (All heat terms under heat exchangers are given in kilowatts of heat, kWh; values shown in parentheses represent F*Cp, kWh/oC)

Figure 12. Property-based HIRCNs for Scenario 2 of Case Study 2 (All flow terms appeared in HEN are given in kg)


Page 26 of 34

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Figure 13. HENs for Scenario 2 of Case Study 2 (All heat terms under heat exchangers are given in kilowatts of heat, kWh); values shown in parentheses represent F*Cp, kWh/oC) Firstly, the optimization objective for Scenario 3 is set to minimize the TOC of fresh resources for property-based HIRCNs in order to achieve the first stage optimization. Hence, eq 46 is solved subject to constraints in eqs 3 to 18, yields 0 kg/batch of FR1 and FR2. The obtained fresh resources of FR1 and FR2 target are then embedded as additional constraints (eqs 50 and 51).

FFR1 = 0

(50)

FFR2 = 0

(51)

For second stage optimization, the objective function is set to minimize the TOC of hot and cold utilities. Therefore, eq 47 is solved subject to constraints in eqs 3 to 18, 23 to 35, 37 to 45, 50 and 51, yields 69.6 kWh/batch of hot utility and 207.7 kWh/batch of cold utility. Moreover, 3,199.8 kg, 600.3 kg and 523.5 kg of storage tanks are needed. The optimal network configurations of property-based HIRCNs and HENs for Scenario 3 in Case Study 2 are shown in Figures 14 and 15. Table 4 presents the summarized results for Scenarios 1, 2 and 3 of Case Study 2. Scenarios 2 and 3 required less total operating cost as compared to Scenario 1. However, the need for huge storage tanks in Scenario 3 has resulted in higher total annual cost as compared to Scenario 1. Meanwhile, notice that heat loss in Scenario 3 is higher than Scenario 2. Comparing Scenarios 1 and 2, the presence of storage tank has reduced the total operating cost which results in lower 27 ACS Paragon Plus Environment


Page 28 of 34

total annual cost. Similar to Case Study 1, it is cheaper to simultaneously consider the total operating cost and the capital cost of storage tanks in the targeting of property-based HIRCNs.

Figure 14. Property-based HIRCNs for Scenario 3 of Case Study 2 (All flow terms appeared in HEN are given in kg) Table 4. Summary of results for Scenarios 1, 2 and 3 of Case Study 2 Concept

Scenario 1

Scenario 2

Scenario 3

Fresh resource, FFR1 (kg/batch)

0

0

0

Fresh resource, FFR2 (kg/batch)

0

0

0

Hot utility, QH (kWh/batch)

102.4

69.6

69.6

Cold utility, QC (kWh/batch)

240.6

207.7

207.7

Capacity for storage tank S1, CSTS1 (kg)

-

805

3,199.8


-

0

600.3


-

0

523.5

Total heat losses from storage tanks (kwh/batch)

-

0.31

29.9

Annual capital cost of storage tanks ($/year)

-

1,129

4,161

Total operating cost, TOC ($/year)

6,306

4,820

5,816

Total annualized cost, TAC ($/year)

6,306

5,949

9,977


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Figure 15. HENs for Scenario 3 of Case Study 2 (All heat terms under heat exchangers are given in kilowatts of heat, kWh; values shown in parentheses represent F*Cp, kWh/oC)

5. CONCLUSIONS In this work, a novel methodology has been developed for the synthesis of HIRCNs for batch processes. The model formulation is a hybrid of super-targeting approach for RCN model with automated targeting method for HEN model. It is used to determine the minimum TAC of a HIRCN which simultaneously optimise the fresh resources, hot and cold utilities as well as the size of the storage system. Besides, comparison of the proposed model with HIRCN without storage system as well as sequential targeting approach has been addressed and applied into two case studies. In those case studies, it has been concluded that the proposed model (Scenario 2) achieved the lowest TAC. Moreover, the results from these case studies showed that this model has the ability to reduce the number of required storage tanks for HIRCNs. Future study can include the synthesis of HEN design along with the capital costs of heat exchangers and piping system to determine an optimal HIRCN.



AUTHOR INFORMATION Corresponding Author Address: CDT 250, 98009 Miri, Sarawak, Malaysia. Tel: +6085 443939 Ext. 2471. ∗E-mail: [email protected]

ABBREVIATION ATM = Automated targeting method BOD = Biological oxygen demand HEN = Heat exchanger network HIRCNs = Heat integrated resource conservation networks MILP = Mixed integer linear programming MINLP = Mixed integer nonlinear programming RCN = Recourse conservation network TAC = Total annual cost TOC = Total organic carbon WN = Water network WAHEN = Water allocation and heat exchange network WAN = Water allocation network

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Development of an Integrated Technique for Energy and Property

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