Simultaneous synthesis of a biogas process and heat exchanger network

Simultaneous synthesis of a biogas process and heat exchanger network

Applied Thermal Engineering 43 (2012) 91e100 Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: www.el...

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Applied Thermal Engineering 43 (2012) 91e100

Contents lists available at SciVerse ScienceDirect

Applied Thermal Engineering journal homepage:

Simultaneous synthesis of a biogas process and heat exchanger network Rozalija Drobe z a, Zorka Novak Pintari c b, Bojan Pahor c, Zdravko Kravanja b, * a

Tanin Sevnica d.d., Hermanova cesta 1, SI-8290 Sevnica, Slovenia University of Maribor, Faculty of Chemistry and Chemical Engineering, Smetanova 17, SIe2000 Maribor, Slovenia c Perutnina Ptuj d.d, Potrceva 10, Ptuj SI-2250, Slovenia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 September 2011 Accepted 7 March 2012 Available online 15 March 2012

This paper presents an energy efficient synthesis of the biogas process, performed simultaneously with the synthesis of its heat exchanger network (HEN). Its overall superstructure is composed of i) the process and ii) the HEN superstructure, and linked with iii) a proposed process stream superstructure where streams could be mixed into a smaller number of hot and cold streams, in order to obtain simpler and, yet, energy efficient solutions. The combined synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem. The model consists of an MINLP model for the biogas process [1] and a modified MINLP model for the simultaneous synthesis of heat-integrated HEN [2]. It enables the selection of an optimal biogas process scheme with an optimal arrangement of its HEN. The synthesis, as applied to an existing large-scale meat company, yielded a complete energy self-sufficient solution for thermophilic biogas production, closed-loop water configuration, and simple HEN arrangement.  2012 Elsevier Ltd. All rights reserved.

keywords: Heat exchanger network Process synthesis Simultaneous synthesis Biogas MINLP Heat recovery

1. Introduction Over the last few years, waste minimization and pollution prevention have become everyday terms throughout the process industry. Rising energy costs, coupled with stringent environmental regulations regarding the accumulation of animal manure and organic matter, have forced the food industry [3e5] towards additional opportunities for the utilization of renewable resources and energy savings, by applying process integration [6,7]. A diversity of papers within the literature has dealt with heat exchanger networks that have become the subject of numerous investigations over the last 40 years. Three major approaches have been applied: the one based on thermo-dynamical insights known as ‘pinch technology’ (PT) [8], a mathematical programming approach [9,10], and a combined approach [11]. Many studies and methodologies have been proposed for making energy recovery possible within those industrial plants dealing with either the concept of heat and process integration, in general [12,13] or with the synthesis and retrofit of heat exchanger networks, in particular [14,15]. As the concept of process integration was initially applied to those plants isolated from their vicinities, it has now extended to enterprise-wide and total site integration [16], including the

* Corresponding author. Tel.: þ386 2 229 44 81; fax: þ386 2 252 77 74. E-mail address: [email protected] (Z. Kravanja). 1359-4311/$ e see front matter  2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.03.009

integration of renewables [17]. On the other hand, the scope of synthesis and the retrofit of HENs have been developed and expanded also, by considering more detailed heat exchanger designs, allowing for flexibility [18] and even simultaneously minimizing the total annual cost and the environmental impact [19]. Some recent papers have also used meta-heuristic techniques, such as genetic algorithms [20,21], and introduced global optimization techniques for the synthesis of HEN [22,23]. An excellent review with a complete timeline of HEN synthesis approaches is provided by Furman and Sahinidis [24] whilst for process integration and optimization by Friedler [25]. Mathematical optimization methods for the synthesis of HEN can be classified as sequential [26] or, as mentioned, simultaneous. The main advantages of the simultaneous approach are that the trade-offs between the capital and operating costs of the network can be handled explicitly, and that it enables the performing the simultaneous synthesis of overall systems, e.g. integrated water and HEN networks [27e30], when simultaneous models of HEN are merged with water network models, or a combined process with HEN schemes, when HEN models are included within the process models [14,31e33]. One of the better known simultaneous optimization models for the synthesis of HEN was developed by Yee & Grossmann [2]. It is based on a stage-wise superstructure and formulated as a mixed-integer nonlinear programming (MINLP) model, with the objective of simultaneously minimizing the utilities and capital costs of the network.


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It should be noted that the simultaneous process and HEN synthesis is regarded as a difficult task, not only because the size of the overall model is enlarged, but more importantly because the process streams heat capacity flow-rates, supply and target temperatures, which remain fixed during the synthesis of HEN, become synthesis optimization variables during the simultaneous process and HEN, thus making the model more nonlinear and nonconvex. The task becomes especially harder to solve when a large number of potential hot and cold process streams exist, as is the case during the synthesis of biogas production by anaerobic fermentation. However, superior solutions are expected to be obtained because appropriate trade-offs between raw materials and operating costs, products’ income, and the capital investment, can thus be achieved. Therefore, this paper introduces a mathematical approach for the simultaneous synthesis of an energy efficient biogas process from animal and organic wastes, and other substrates, including the selection of different auxiliary facilities. In order to achieve this task optimally and efficiently, a new superstructure is proposed and formulated for the simultaneous synthesis of the biogas process and HEN. A special superstructure for alternative process streams was introduced for the selection of the least number of process hot and cold streams in order to synthesise simple and yet efficient HENs. 2. Combined process and HEN superstructure As a basic formulation, the model recently developed by Drobe z et al. (2010) [1] was applied and extended using Yee and Grossman’s model [2], which was modified to enable a simultaneous process and HEN synthesis. This model is based on a single-stage superstructure, with temperature driving forces and heat capacity flow-rates as optimization variables, where each hot stream segment is potentially matched with each cold stream segment. The assumptions made are the following:  Heat capacities of the liquid process streams are the same values as for water, because all inlet substrates contain 70e90% of water. Similarly, since the produced biogas contains 50e80% of methane, its heat capacity is that of methane.  Only one hot and one cold utility is available, and  Only double-pipe heat exchangers are considered due to the heat exchangers’ operational characteristics, and relatively small transfer areas. In addition, the original HEN model [2] was also written for double-pipe exchangers. Note that, if we considered using different exchange types, the combinations and sizes of the extended model would drastically increase [34]. The general superstructure is schematically shown in Fig. 1 and consists of the biogas production superstructure (Fig. 2), extended for process stream superstructures (Fig. 3b) and the HEN superstructure (Fig. 4b). The superstructure of the biogas production is composed of three parts. The one on the left has various options for inlet substrates and water supplies, taken from the meat company, and the transport routes of industrial wastewater. Inlet substrates can be utilized by anaerobic fermentation under mesophilic or thermofilic conditions, and the animal offal can be alternatively processed by the rendering plant e part in the middle of Fig. 2. The part on the right represents the production and usages of biogas within a combined heat and power cogeneration plant, and the production of solid products within a rendering plant, distribution of the heat and electricity to the network, and an alternative wastewater treatment. The process streams superstructure is shown in detail in Fig. 3. Note that, in principle, each alternative inlet stream, as directed to

Fig. 1. General superstructure for simultaneous synthesis of biogas process and HEN.

each biogas process unit, can be regarded as an alternative cold stream (Fig. 3a). However, inlet streams with the same or similar temperature can be mixed and combined into a reduced number of streams (Fig. 3b), which would then enable the synthesis of less complex HEN arrangements with smaller numbers of heat exchanger units. Also note that, in mixers M1, M2 and M3, the process stream was defined as containing 8% of the overall dry matter. Mixer M1 is an exclusive or logical mixer for process water that can be supplied either as freshwater or as industrial wastewater, M2 animal wastes from a pig farm, and the water supply, and M3 animal wastes from a new potential poultry farm, wastes from a poultry farm, animal and other wastes from the meat company, and recycled purified water from the purification system. Note that the first superstructure (Fig. 3a) contains 20 cold and 5 hot process streams, whilst with the mixer units the number is reduced to 10 alternative streams (7 cold and 2 hot), which can be decreased even further during optimization, i.e. when streams occur with zero flows or with equal supply and target temperatures. In order to decrease the number of alternative heat exchanger matches in HEN superstructure further, the stage-wise superstructure by Yee and Grossmann with three stages (Fig. 4a) [2] has been reduced to a single-stage superstructure (Fig. 4b), where some process streams are partitioned into several segments. Note that in this case the number of alternative heat exchanger matches has been almost halved, which considerable improves the efficiency of simultaneous optimization. 3. Formulation of mathematical model A basic process synthesis model was taken from our earlier work [1] and linked to the modified Yee and Grossmann’s model [2], which was then applied and modified for the simultaneous process, and HEN synthesis. Different sets were used throughout the combined model and a detailed definition of these sets appears in Drobe z et al. [1]:  I ¼ fiji for the inlet substrates and water supplyg; I ¼ f1; .; 25g with different subsets I1 ; I2 ; .; I7 ,  J ¼ fjjj for the process for utilizing animal and other organic wastes; g; J ¼ f1; .; 4g with subsets J1,J2 and J3  K ¼ fkjk is the solid products from the rendering plantg; K ¼ f1; 2; 3g;  L ¼ fljl for the auxiliary facilities for the utilization of different wastesg; L ¼ f1; .; 8g with subsets L1 ; L2 ; .; L9  C ¼ fcjc is the cold streamg; C ¼ f1; .; 7g and  H ¼ fhjh is the hot streamg; H ¼ f1; 2g:

R. Drobez et al. / Applied Thermal Engineering 43 (2012) 91e100


Fig. 2. Superstructure for the simultaneous synthesis of biogas production.

3.1. Process synthesis model

2 qM mj ¼

The basic process synthesis model according to its representation in Fig. 3b (biogas superstructure with the merging of process streams), defines several mass balances, the heat capacity flowrates of cold and hot process streams, and logical constraints of the process synthesis model. Part of this model has been presented in previous works [1], therefore only a brief description of the applied extensions is presented. 3.1.1. Mass balances of the process synthesis model Overall mass balance regarding biogas production (j˛J1 ). The overall mass balances of biogas production for anaerobic fermentation units (j ¼ 1,2) relate inlet mass flow-rates from mixer unit M3 together with the sum of the mass flow-rates of substrate i in process j (only for the process which has a sterilization unit) to the sum of the out-flowing mass flow-rate of biogas and the residue from the process: 3 qM mj þ


BG qmi;j ¼ qBG þ qRmj vj $r

ðj ¼ 1 and j ¼ 2Þ



and the overall mass balance of biogas production by the mesophilic process without a sterilization unit, is similarly defined as: BG BG 3 qM þ qRmj mj ¼ qvj $r

ðj ¼ 3Þ


1 qmi;j þ qM mj

3 qM mj ¼


qmi;j þ



qmi;j þ




2 qRWW þ qM mj mj;l




M2 M3 1 where qM mj , qmj , and qmj /(kg/d) are the mass flow-rates for the mixer unit, respectively.

3.1.2. Cold inlet streams The heat capacity flow-rates. Heat capacity flow-rates of the mixer outlet streams (FcM/(kW/K)) for all mixer units (M1, M2, M3), are defined as follows:

FcM ¼


IS qM mj $cp $fd



3.1.3. Hot outlet streams Heat balances of the mixer units. The overall heat balance for the first mixer unit (M1) is given by Eq. (7), for the second (M2) by Eq. (8), and for the last one (M3) by Eq. (9): M1 FcM1 $TOUT ¼


S;IN FcSi;j $Ti;j þ

i˛I4 j˛J1


Note that the mass flow-rate from the mixer unit M3 is for the mesophilic process the only inlet stream.where qmi,j/(kg/d) denot3 ing the mass flow-rate of substrate i in process j, qBG vj /(m /d) denotes the volume flow-rate of the biogas produced during process j, rBG/ (kg/m3) is the density of the biogas, and qRmj /(kg/d) is the mass flowrate of the residue leaving process j.



M2 FcM2 $TOUT ¼



S;IN FcSi;j $Ti;j


i˛I5 j˛J1 S;IN M2 FcSi;j $Ti;j þ FcM1 $TIN


i˛I2 j˛J1 M3 FcM3 $TOUT ¼


S;IN FcSi;j $Ti;j þ

i˛I3 j˛J1




S;IN FcSi;j $Ti;j

i˛I7 j˛J1 S;IN M1 FcRWW $Tj;l þ FcM2 $TIN j;l


j˛J1 l˛L8 Mass balances of mixer units. The mixer units (M1, M2, M3), as shown in Fig. 3b, have multiple inlet streams and a single outlet stream. 1 qM mj ¼

X i˛I4

qmi;j þ

X i˛I5




M1 M2 M3 where TOUT , TOUT , and TOUT /(K) are the outlet temperatures for the M2 M3 , TIN /(K) are the inlet temperatures mixer units (M1, M2, M3), TIN S;IN for the mixer units (M2, M3), and Ti;j /(K) is the inlet temperature

of the inlet substrates to the mixer units.

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Fig. 3. (a) Superstructure of process streams without merging of process streams, (b) New process streams superstructure with merging of process streams. Sterilization of the slaughterhouse wastes. The heat needed for sterilization of the slaughterhouse wastes of III. category (FSW/kW), is calculated as:



  SW SW qmi;j $cIS p $fd $ TOUT  TIN




to simplify this task, these segments will be called ‘streams’. The other difference is that the inlet and outlet temperatures, and the heat capacity flow-rates are now optimization variables. Since the description of the original model and notation with the given constraints can be found elsewhere [2,35], only the notation of temperature differences is described alone.

SW , T SW /(K) are the inlet and outlet temperatures of the where TIN OUT sterilized slaughterhouse wastes of the III category, respectively.

3.2.1. Lower bounds regarding temperature differences

3.2. HEN model

LO DTh;c ¼ EMAT h˛H; c˛C





DTcuLO h ¼ EMAT h˛H


Two important modifications were implemented within the MINLP formulation of Yee and Grossmann [2]. The main difference between the original stage-wise formulation and the proposed one is the use of a single-stage HEN superstructure where process streams can be partitioned into several segments, e.g. cold stream ¼ TcIN C3 into C3 and C4, with TcOUT 3 4 , as shown in Fig. 4b. In order

where EMAT/(K) is the exchanger minimum approach temperature.

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Fig. 4. (a) The stage-wise superstructure by Yee and Grossmann [2], (b) single-stage HEN superstructure.

3.3. Linking the process synthesis and the HEN models Both, the process and the HEN models are linked through the appropriate mapping of streams heat capacity flow-rates, and their supply and target temperatures, as defined in the process synthesis ; ThOUT ; h˛HÞ and cold model, with the corresponding hot ðFhh ; ThIN h h OUT ; c˛CÞ in the HEN model. For hot streams, we ones ðFcc ; TcIN c ; Tcc relate the vectors of the heat capacity flow-rates by Eq. (14) and the supply and target temperatures by Eq. (15) and Eq. (16) and, in addition, we had to define:




¼ ðFhh ; h˛1; 2Þ ¼


IN ThIN 1 ; Th2




ThOUT ; ThOUT 1 2


where TjWW;IN /(K) is the inlet temperature of the process waste/(K) is the outlet temperature of the water for process j, ThWW;OUT j process wastewater for process j. In analogy, for the cold streams the following linking equations are used:

FcM ; FcAF j˛J j

¼ ðFcc ; c˛CÞ

0 @T Mm ;m OUT

¼ 1;2;3;


(17) 1

TjAD;IN $yPj A ¼

TcIN c ;c ¼ 1;2;3;5;6;7

TcOUT ¼ TcIN 3 4


Fc3 ¼ Fc4


3.4. Objective function To obtain an economic trade-off between the products’ incomes, cost of raw materials, operating cost, and the process and HEN investment, the objective function is written as a maximization of the net present value (NPV):

Fobj ¼ I þ ½ð1  rt Þ$ðR  EÞ þ rt $D$

0 @T Mm ;m ¼ 2;3; Tj¼1; IN



  TjAD;OUT $yPj A ¼ TcOUT ;c ¼ 1;2;4;5;6;7 c


(19) Mm whereTOUT /(K) Mm TIN /(K) is the

is the outlet temperature of the mixer units, and inlet temperature of the mixer unit. In addition, continuity relationships for cold stream segments C3 and C4 are given by Eq. (20) and Eq. (21):

rd ð1 þ rd ÞtD


where I/(EUR), represents the investment, rt the tax rate, R/(EUR/y) the revenues or incomes, E/(EUR/y) the expenditures on the raw materials and operating costs including the costs for hot and cold utilities, for the sterilization of slaughterhouse wastes category III., D/(EUR/y) depreciation, rd the discount rate, and tD/(y) the depreciation period. The investment comprises the term for the process (IBG), as defined by Eq. (23), and HEN (IHEN), as defined by Eq. (24). The investment of the process includes investment in the biogas process, the rendering plant, and the auxiliary facilities:



# " ð1 þ rd ÞtD 1

I BG ¼

X j˛J1

Ij0 $

qBG vj qBG;0 vj

!n þ

X j˛J2

IjR;0 $yPj þ


IlB $yBl



where Ij0 /(EUR) is the base capital investment for anaerobic /(m3/d) the daily production of biogas for conversion (j˛J1 ), qBG;0 vj the base-case biogas production in process j, n denotes the investment capacity exponent, IjR;0 /(EUR) is the base capital investment for the rendering plant (j˛J2 ), and IlB /(EUR) (l˛L) represents the capital investment for auxiliary facilities. The investment of HEN involves a combination of the fixed charges and area costs for heat exchangers, heaters, and coolers:

R. Drobez et al. / Applied Thermal Engineering 43 (2012) 91e100





Cc;h $zc;h þ

c˛C h˛H





Ch;CU $zcu h þ


c˛C h˛H



and substrates, and the costs of wastewater treatment, the transportation of industrial wastewater, and the sterilization of slaughterhouse wastes:


Cc;HU $zhu c


h˛H c;h v Cc;h $Ac;h þ


h;CU v Ch;CU $Ah;CU þ



C;HU v Cc;HU $Ac;HU (24)



f f f v , Cv where Cc;h , Ch;CU and Cc;HU /(EUR) are the fixed costs, Cc;h and h;CU


v /(EUR/m2) the area cost coefficient, and bc,h, bh,CU and bc,HU/(/) Cc;HU


the area exponent for the heat exchangers, coolers, and heaters. The corresponding areas Ac,h, Ah,CU and Ac,HU/(m2) and heat transfer coefficients, are given by the following standard relationships:

Ac;h ¼

qc;h 1 h˛H; c˛C   DTc;h;1 þ DTc;h;2 3 Uc;h $ DTc;h;1 $DTc;h;2 $ 2

Ah;CU ¼

Ac;HU ¼

1 Uh;CU 1 Uc;HU


1 1 þ hh hCU






  . BG E cES $qBG þ cTS $FSOLD fd1 vj $ej $h


XX j˛J2 k˛K


P qWW mj;l $cl þ

j˛J1 l˛L9


qcuh $cCU


qTmi;l $cTl

i˛I5 l˛L6



fd1 þ @



1, LP A FSW j $c







where cE/(EUR/kWh) is the price of the purchased electricity, p0j /(kWh/d) is the base-case electricity consumption of process j, cR;0 f

1 1 ¼ þ hc hHU


1 PP qmi; j B R;0 X P R;0 i˛I1 j˛J2 C þB yj þcv $ P R;0 C @cf $ A qmj j˛J2


qhuc $cHU þ


qhuc   IN  TcOUT !#13  DThuh þ THU  c IN  TcOUT $ Uc;HU $ DThuc $ THU c 2 "



qmi;j $cSi þ



where Uc,h, Uh,CU and Uc,HU/(kW/(m2K)) are the heat transfer coefficient for matches between hot and cold streams, hot process streams and the cold utility, and hot utility and cold process and TcOUT /(K) are the outlet temperstreams, respectively. ThOUT c h IN and T IN /(K) their inlet atures of the hot and cold streams, TCU HU temperatures. hh,hc,hHU, and hCU/(kW/(m2K)) are the stream individual heattransfer coefficients for hot and cold streams, and hot and cold utilities. The logarithmic mean difference in the objective function is approximated by the Chen approximation [36], in order to avoid singularities within the logarithmic term. Because the investment term of the biogas process is concave, (Eq. (23)), a piecewise linearization method [23,37,38] was thus applied to linearize the term. The term (RE) in Eq. (22) represents the surplus of income over expenses. Incomes R/(EUR/y) represent (Eq. (31)) the revenue from selling electricity, heat, solid products, and organic fertilizer:

R ¼



cE $p0j $ BG;0 qvj



qcuh   IN !#13  DTcuh þ ThOUT   TCU h IN $ Uh;CU $ DTcuh $ ThOUT  TCU h 2

h˛H; c˛C

qBG vj

i˛I6 j˛J1


1 1 1 ¼ þ Uc;h hh hc


SP cSP k $qmj;k þ


OF cOF l $qmj;l


j˛J1 l˛L8

where cES and cTS both in (EUR/kWh) are the selling prices of the produced electricity and heat, respectively, hE is the efficiency of /(EUR/kg) is the price of the solid the electricity generation, cSP k /(EUR/kg) is the price of product k for the rendering plant, and cOF l organic fertilizer from the wastewater treatment unit l. The expenses E/(EUR/y) for the process synthesis and HEN are further composed of the costs for purchasing electricity, utilities,

and cR;0 are the base-case fixed and variable operating cost coefv ficients for the rendering plant, qR;0 mj /(kg/d) is the base-case daily consumption of substrates in the rendering plant. cSi , cPl , and cTl /(EUR/kg) in the second line are the cost coefficients for the substrates (maize, freshwater), wastewater purification, and industrial wastewater transportation, respectively. The third line represents the heat consumption of process j, where cHU and cCU/

Table 1 Data of the model parameter for the simultaneous synthesis of a biogas process and heat exchanger network. Model parameters for synthesis of heat exchanger network Heat exchanger

Fixed cost coefficient (kEUR) Area cost coefficient (kEUR/m2) Exponent for area cost Stream heat transfer coefficient of cold stream (kW/(m2K) cc˛C Stream heat transfer coefficient of hot stream (kW/(m2K) ch˛H Heater Fixed cost coefficient (kEUR) Area cost coefficient (kEUR/m2) Exponent for area cost Cooler Fixed cost coefficient (kEUR) Area cost coefficient (kEUR/m2) Exponent for area cost Cold utility Inlet temperature ( C) Outlet temperature ( C) Stream heat transfer coefficient (kW/(m2K) Price (EUR/kWh) Hot utility Inlet temperature ( C) Outlet temperature ( C) Stream heat transfer coefficient (kW/(m2K) Price (EUR/kWh) Exchanger minimum approach temperature (K)

CAc,h ¼ 46 CAc,h ¼ 2.742 bc,h ¼ 1 hc ¼ 1 hh ¼ 1 CAc,h ¼ 46 CAc,h ¼ 2.742 bc,h ¼ 1 CAc,h ¼ 46 CAc,h ¼ 2.742 bc,h ¼ 1 IN ¼ 15 TCU OUT ¼ 25 TCU hCU ¼ 1 CCU ¼ 0.005 IN ¼ 157 THU OUT ¼ 147 THU hHU ¼ 5 CHU ¼ 0.05 EMAT ¼ 1

R. Drobez et al. / Applied Thermal Engineering 43 (2012) 91e100

(EUR/kWh) are the prices of the hot and cold utilities, FSW j /(kW) is the heat consumption for the sterilization of slaughterhouse wastes, and cLP/(EUR/kWh) is the price of low pressure steam. Finally, the depreciation is defined as a straight-line depreciation over a depreciation period. 4. Industrial case study A simultaneous approach, using the above concept, for the process and HEN synthesis was applied to an existing large-scale meat company, as shown in Fig. 2. For this problem a process stream superstructure was applied with 3 mixer units (M1, M2 and M3), depending on the inlet temperatures and compositions of the inlet substrates (Fig. 3b). Rather than applying a 3-stage superstructure of HEN, for 2 hot and 7 cold process streams, a single-

Table 2 Inlet and outlet temperature of inlet substrates, water supply, biogas and process wastewater. Temperature of inlet substrates, water supply biogas and process wastewater Mixer unit 1

Mixer unit 2 Mixer unit 3

Anaerobic fermentation

Cogeneration unit

Inlet temperature of water supply as freshwater (K) cj˛J Inlet temperature of water supply as industrial wastewater (K) cj˛J Inlet temperature of inlet substrates from pig farm (K) cj˛J Inlet temperature of inlet substrates from new potential poultry farm (K) cj˛J Inlet temperature of inlet substrates from poultry farm and other wastes (K) cj˛J Outlet temperature of biogas at thermophilic condition (j ¼ 1) Outlet temperature of biogas at mesophilic condition with sterilization unit (K) (j ¼ 2) Outlet temperature of biogas at mesophilic condition without sterilization unit (K) (j ¼ 3) Outlet temperature of process wastewater (j ¼ 1) Outlet temperature of process wastewater (j ¼ 2) Outlet temperature of process wastewater (j ¼ 3) Inlet temperature of heating requirements of anaerobic fermentation at thermophilic condition (K) (j ¼ 1) Inlet temperature of heating requirements of anaerobic fermentation at mesophilic condition with sterilization unit (K) (j ¼ 2) Inlet temperature of heating requirements of anaerobic fermentation at mesophilic condition without sterilization unit (K) (j ¼ 3) Outlet temperature of heating requirements of anaerobic fermentation at thermophilic condition (K) (j ¼ 1) Outlet temperature of heating requirements of anaerobic fermentation at mesophilic condition with sterilization unit (K) (j ¼ 2) Outlet temperature of heating requirements of anaerobic fermentation at mesophilic condition without sterilization unit (K) (j ¼ 3) Inlet temperatures of the hot water (K) Outlet temperatures of the hot water (K)

TjFW;IN ¼ 283 TjIW;IN ¼ 283 TjPF;IN ¼ 293 TjNPF;IN ¼ 293 TjOW;IN ¼ 293 T1BG;OUT ¼ 328


stage superstructure (Fig. 4b) was applied by splitting the third ¼ TcIN cold stream into two segments (C3 and C4), where TcOUT 3 4 . The company was interested in achieving an optimal process scheme for utilizing animal and other organic wastes simultaneously with its HEN. Data for inlet waste material and other substrates were collected and calculated as average values from the actual annual reports. Some other details were taken from the internal project documentation of the company. Data for the model parameters, as well as data for economical evaluation, were taken from actual industrial case studies. All investment data for reconstruction of the rendering plant, local farm, construction of a pressure sewage pipeline, and ultrafiltration and reverse osmosis, are estimated values. Also, average local market prices were used for product prices (i.e. meat meal, electric energy, etc.), and for the costs of wastewater treatment, maize, heat and electric energy etc. The model’s parameters are given in Table 1, whilst the inlet and outlet temperature of the inlet substrates, water supply, biogas, and process wastewater for the simultaneous synthesis of a biogas process and its HEN, are given in Table 2. The corresponding economic data are shown in Table 3. For further details regarding the data, please refer to Drobe z et al. [1]. The MINLP model with approximately 3,400 constraints, 6400 continuous variables, and 16 binary variables, was implemented in GAMS [39] and solved using DICOPT [40] on a PC machine (2.53G Hz, 2 GB RAM). The economical analysis of the optimal solution obtained by the applied optimization model is shown in Table 4 whilst Table 5 represents the optimal solution regarding the selection of process streams. The optimal process scheme with the selected process streams is shown in Fig. 5. According to the solution, the byproducts, animal offal, and animal manures from the meat company should be converted into biogas under thermophilic

T2BG;OUT ¼ 308 T3BG;OUT ¼ 308 T1WW;OUT ¼ 328 T2WW;OUT ¼ 308 T3WW;OUT ¼ 308 T1HR;IN ¼ 327 T2HR;IN ¼ 307

T3HR;IN ¼ 307

T1HR;OUT ¼ 328 T2HR;OUT ¼ 308

T3HR;OUT ¼ 308


¼ 333

Table 3 Economical date. Economic data Investment capacity exponent Depreciation period (y) Discount rate Tax rate Number of operating days per year (d/y) Investment of background alternatives (EUR)

Investment of anaerobic conversion (EUR) Investment of the rendering plant (EUR) Selling price of produced electricity (EUR/kWh) Prices of surplus heat (EUR/kWh) Selling price of solid product (EUR/kg) Price of organic fertilizer (EUR/kg) Cost coefficient of substrate (EUR/kg) Price of the purchased electricity (EUR/kWh) Price of cold utility - cooling water (EUR/kWh) Price of hot utility - steam (EUR/kWh) Cost coefficient of purification in wastewater treat. unit (EUR/kg) Cost coefficient of industrial wastewater transportation (EUR/kg)

n ¼ 0.6 tD ¼ 10 rd ¼ 0.1 rt ¼ 0.25 d ¼ 360 IlB IlB IlB IlB Ij0 Ij0 Ij0

¼ ¼ ¼ ¼ ¼ ¼ ¼

5$106 2:5$106 1$106 1:8$106 11:567$106 11:985$106 9:745$106

IjR;0 ¼ 2$106

l¼1 l¼2 l¼5 l¼7 j¼1 j¼2 j¼3 j¼4

cES ¼ 0.155 cTS ¼ 0.03 ¼ 0:270 cSP k cSP ¼ 0:355 k SP ck ¼ 0:084 ¼ 0:022 cOF l cSi ¼ 0:026 cSi ¼ 0:0005 cE ¼ 0.0833

k¼1 k¼2 k¼3 l¼7 i ¼ 23 i ¼ 16

cCU ¼ 0.005 cHU ¼ 0.05 cPl ¼ 0:0025


cTl ¼ 0:004 cTl ¼ 0:0

l¼4 l¼5

R. Drobez et al. / Applied Thermal Engineering 43 (2012) 91e100


Table 4 Resulting economic analysis and some process parameters. Selected process


Economic quantities WNP I BG MEUR MEUR 10.458 16.684 Some process quantities qBG v m3 =d 35,587

AHE m2 219

I HEN MEUR 0.740


AH m2 0.0

AC m2 0.0


EBG MEUR=y 0.772

EHEN MEUR=y 0.000

FC MEUR=y 4.538

rIRR %

tPB y











MW 4.1

MW 3.9

P CHP MW 3.5

Table 5 Results for hot and cold streams selection. Streams


H1 H2 C1 C2 C3 C4 C5 C6 C7

Selected Selected Rejected Rejected Selected Selected Selected Rejected Rejected

Fhh kWK1 20.255 3.920 0.657 0.657 21.378 21.378 98.010 0.000 0.000


ThIN h C




55 85 10 10 31 50 54 34 34

35 60 10 10 50 55 55 35 35

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

405.10 198.60 0.00 0.00 405.10 100.60 98.00 0.00 0.00

conditions, and subsequently, the biogas should be converted into electricity and heat within the CHP unit. The optimal scheme also includes a freshwater source from a local well and a closed water network using technologies for wastewater re-usage, and the production of organic fertilizer. The net present value (NPV) is 10.458 MEUR and the payback period 3.68 y. The disadvantage of this solution, from the sustainable development perspective, is that it utilizes freshwater. If freshwater was supplemented by wastewater, some additional quantities of biogas could be produced because it contains small amounts of manure. However, at the moment this solution is uneconomical due to additional investment and transportation costs. It should be noted that, by using the closed wastewater treatment network, the

Fig. 6. Optimal solution of single-stage HEN superstructure.

consumptions of freshwater, and the heating utility are significantly reduced. The latter is reduced because the purified water has a higher temperature than freshwater. As expected, biogas production under thermophilic conditions has the highest yield of biogas production compared to the mesophilc process, irrespective of the quality and quantity of the inlet’s wastes.

Fig. 5. Optimal process scheme with the selected process streams.

R. Drobez et al. / Applied Thermal Engineering 43 (2012) 91e100


Fig. 7. Optimal scheme for the simultaneous synthesis of biogas production and HEN.

According to the results in Table 5, from 2 hot and 7 cold alternative process streams, only 2 hot (H1, H2) and 3 cold (C3, C4, C5) streams were selected, resulting in HEN consisting of only three heat exchangers, with a corresponding total area of 219.2 m2 (Fig. 6). Cold streams C3, C4 represent the outlet stream of M3 and C5 relates to the heating requirements for anaerobic fermentation. Hot stream H1 represents the outlet stream from the thermophilic process and H2 corresponds to the hot stream from the cogeneration unit. For heating up the resulting three cold streams, the heat is supplied by heat recovery within the process (608.7 kW). The optimal scheme for the simultaneous synthesis of the biogas process and its HEN, is shown in Fig. 7. The capital cost for the process is 16.684 MEUR whilst the one for HEN 0.740 MEUR, and the annual operating cost for the process is 0.772 MEUR/y and for HEN is 0.000 MEUR/y (Table 4). The biogas is utilized by a cogeneration system for heat (4.1 MW) and electricity production (3.5 MW). The heat produced is partially used for heating up the C4 and C5 cold process streams (199 kW), whilst the surplus heat (3.9 MW) is sold to the distribution network. It should be noted that before the optimization the heating of biogas digester was carried out by the outlet stream using heat pump. The optimization indicates that the use of heat pump can be avoided and its electricity consumption compensated by better energy recovery within the process.

5. Conclusion In this study we attempted to further develop the concept of a superstructure based approach for a simultaneous process, and HEN synthesis, as applied to biogas processes. According to it, the variety of this process and its utilities and heat exchange alternatives can be considered within the simultaneous structure and parameter optimization of the overall system, yielding solutions that are, with respect to the consumption of raw materials, energy, water and investment, superior to the sequential ones. However, such an overall system synthesis is, in most cases a challenging combinatorial task, which is difficult to solve. Based on the experience gained during this study, we have concluded that it can be implemented and used successfully for solving real process energy problems. Two opposing directions regarding actions have to be pursued in order to expedite the task. The first one refers to the simplifications of individual subsystems, which have to be reduced to reasonable structural alternatives, and the other is an upgrade of an overall system with new structural alternatives and optimization

variables, in order to exploit interactions between the subsystems completely and properly. The proposed reduction in the HEN superstructure to a single-stage, is an example of the first direction, whilst defining alternative hot and cold process streams by mixing process streams, is in accordance with the second direction, both enabling obtainable solutions with simple HEN arrangements, and yet efficient heat recovery. The developed MINLP model enables the selection of an optimal biogas process scheme together with its HEN. It is a generic model and enables the synthesis of biogas process together with “background” alternatives (selection of water network type, HEN configuration, supply of raw materials, selection of other production plants, etc.). It can be easily modified and adapted to any specific situation. It can thus be used to test different options in order to support decision making for future investment in biogas production, including sustainable multi-objective optimization. It is interesting to note that in the case study the consumption of hot utility by applying the overall system synthesis was completely removed whilst in the original industrial flowsheet around 1.7 MW would be needed only for digesters. The study also indicates that selecting closed water system rather than existing open one would decrease the consumption of freshwater by at least two thirds and practically stop loading the central wastewater system whilst a valuable organic fertiliser could be produced at the same time. The research is under way to carry out the synthesis under uncertainty for most important input parameters, e.g. prices for electricity, some substrates and investment coefficients, in order to obtain optimal and robust solutions, and to perform LCA-based multi-criteria synthesis to identify economically efficient and yet environmentally benign biogas process flowsheet solutions [41]. Acknowledgements The authors would like to acknowledge the financial support from the Slovenian Research Agency (Program P2-0032, Project L20358, and PhD research fellowship contract No. 1000-06e310080).

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