Estimation of renewable-based steam costs

Supporting Information

Salvador I. Pérez-Urestia, Mariano Martínb*, Arturo Jiménez-Gutiérreza

a Departamento de Ingeniería Química, Instituto Tecnológico de Celaya, Celaya, Gto. 38010, México

b Department of Chemical Engineering. University of Salamanca. Plz. Caídos 1-5, 37008, Spain

*Author for correspondence: Mariano Martín

Email: mariano.m3@usal.es

Phone: +34-923-294-479. Fax: +34-923-294-574

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S1. Modelling description

In this section we provide a description of the model, and the main assumptions taken.

S1.1.1 Biomass processing

Selection of technologies to process biomass: The biomass that is used to produce utilities (B) can be processed by selecting at most one technology, a biomass boiler (Bc) or a gasifier reactor (Bq). Equation (2) is a big-M constraint used to limit the use of biomass.

B=∑q∈Q

Bq+Bc (1)

B ≤ BMAX ybiomass (2)

ybiomass−(∑q∈Qyq+ yc )=0 (3)

∑q∈Q

yq+ yc ≤ 1 (4)

Bq ≤ BMAX yq (5)

Bc ≤ BMAX y c (6)

Equation (3) indicates that the selection of any technology is conditioned to the selection of

biomass. Equation (4) indicates the possible technologies to process biomass, while

Equations (5)-(6) are constraints used to restrict the flowrate of biomass processed by each

technology.

Biomass boiler: If a biomass boiler is selected, then it could generate as many as four types of steam, s, and it could carry out the steam reheating as well. This fact is modeled by Equations (7)-(10).

yc−∑s∈ S

ycs ≤0 (7)

yc− ∑reheat n∈ REHEAT

yreheat n

s , C ≤0 (8)

∑s∈ S

ycs ≥ 0 (9)

∑reheatn∈REHEAT

yreheatn

s , C ≥ 0(10)

where production or non-production of steam, s, by biomass boiler, c, is represented by the binary variableyc

s, while the variable yreheatn

s , C is used to select the steam reheating, reheat n.

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Steam production and reheating are restricted by the existence of the biomass boiler, according to Equations (7) and (8).

Flowrate of the steam, s, produced in the biomass boiler, F cs, is computed by Equations

(11)-(12).

Qcs=F c

s [ H (T s ,P s )−H (T v1 , Pv 1)]⩝ s (11)

F cs ≤ F MAX yc

s⩝ s (12)

The heat required for the steam reheating is calculated as follows:

QreheatC = ∑

reheat n∈ REHEATQreheatn

C (13)

Qreheat n

C =F reheatn

s , C *∆ H reheat n⩝reheat n

(14)

F reheat n

s ,C ≤ F MAX yreheat n

s , C ⩝ reheatn(15)

where F reheat n

s ,C is the flowrate of steam to be reheated in the biomass boiler and Qreheat n

C is the heat required to carry out the steam reheating, reheat n, selected.

Finally, a total heat balance for a biomass boiler is determined by Equations (16) and (17).

QTc=∑s∈S

Q cs+Qreheat

C(16)

QTc=B c LHV c (17)

where LHV c is the Lower Heating Value of Biomass, Qcs is the heat required to produce

steam, while QreheatC is the heat required to reheat steam.

S1.1.2 Syngas processing modelling approach

The gasification stage was modeled as a surrogate model which consists of four steps. a) determination of the syngas composition, which is obtained in each gasifier, b) simulation of the reforming stage in Aspen plus, c) simulation of the syngas turbine in Aspen plus, d) Development of an optimization sub-routine to design the HRSG system. The syngas composition data via Indirect gasification (IG) and Direct gasification (DG) were taken from [1] and [2], respectively, and they were used to simulate the reforming stage in Aspen Plus. In the following section, the main assumptions for the development of the surrogate model are shown.

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Reforming stage: POX reactions (18)-(19) were simulated in Aspen Plus as an Rstoic reactor. It was considered that the oxygen is fed in stoichiometric proportions. The conversions were taken the same as the ones reported by [3].

Cn Hm +n2

O2→ nCO+ m2

H2 (18)

NH3→ 12

N2+32

H2 (19)

On the other hand, steam reforming (SR) was simulated as an RGibbs reactor in Aspen plus. Steam is fed to the reactor in stoichiometric proportions. Furthermore, the conversions reported in [3] were assumed. The reactor conditions were determined by carrying out a sensitivity analysis of conversion in reactor against pressure and temperature.

Gas Turbine: There is a trade-off between power produced and the turbine outlet temperature (TOT). The higher the power produced the lower the TOT. Additionally, the net power produced is directly related to the compression ratio. Therefore, in order to evaluate such effects, a sensitivity analysis of the turbine outlet temperature with respect to the compression ratio was carried out in Aspen plus. The next considerations were taken:

1. Syngas is compressed to 10, 20 and 50 bar (represented as units GT-10, GT-20, GT-50 in Figure S2).

2. The excess air fed to the combustion chamber must be such that the turbine inlet temperature does not exceed 1400 ° C.

3. Combustion chamber is simulated as an Rstoic reactor. The combustion efficiency was considered to be 98%.

It worth pointing out that, for the purposes of this work, knowing the value of TOT is important since it determines the capability of the exhausted gas to produce heat in the HRSG system.

Heat Recovery Steam Generator: In this work, the single-pressure or multi-pressure performance of the HRSG was determined by carrying out an optimization problem. In this sense, a set of sub-problems, SP-1 (see Table S1), is evaluated in order to compute the optimal value 𝞓Tpinch that minimizes the total annual cost of each HRSG. For each sub-problem, n, it is assumed that as many as two types of steam, s, can be generated in a single HRSG unit. The kind of the steam generated depends on the turbine exhaust gas temperature calculated from simulations. For instance, because of its temperature, the exhaust gas from unit GT-10 can generate VHP while the exhausted gas from unit GT-20 cannot generate it. The set of steams that each turbine exhausted gas can generate are shown in Table S1. The sub-problems SP-1 are optimized in Matlab by using fmincon function. Additionally, the followings assumptions were considered:

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1. The approach temperature, 𝞓Tapproach, was set to 20 °C. 2. Operating cost of each steam were estimated by taking assumptions from [4].3. To calculate the heat exchangers cost, the correlations proposed in [5] were used.

Table S1. Definition of sub-problems, SP-1

Type of HRSG, n Exhaust gas fed to HRSG Steam

generated

N=1 GT-10/Dq (Flue gas from combustor chamber at 995 °C) VHP

2 GT-10/ Dq VHP+HP

3 GT-10/ Dq VHP+MP

4 GT-10/ Dq /GT-20 HP

5 GT-10/ Dq /GT-20 HP+MP

6 GT-10/ Dq GT-20/GT-50 MP

7 GT-10/ Dq /GT-20/GT-50 MP+LP

8 GT-20/GT-50 LP

The sub-problem, SP-1, is represented by the set of Equations (20)-(29) and it consists of computing the optimal value of 𝞓Tpinch, defined by Equation (27), that minimizes the total annual cost of each HRSG. Then, under the optimal conditions, the steam flowrate produced per unit per unit of exhausted gas fed to the HRSG, Rq , j , k

n , s , is computed. It worth pointing out that the sub-index of variables in equations, are referred for the HRSG flowsheet shown in Figure S2.

minx

{TACn (x ) }⩝n

(SP-1) s.t. Eqs. 20 to 29

(SP-1)

Determining Rq , j , kn , s in HRSG, n

Rq , j , kn , s ¿ Fm

n , s/Fmn , g⩝n , s , q , j , k ,m (20)

Heat balance of steam S in Heat exchanger m

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Qmn , s¿ Fm

n , s [H (T ms , Pm

s )−H (Tm+1s ,Pm+1

s )]⩝m,s ,n (21)

Heat balance of steam exhaust gas, Gq , j , ki ,n , in Heat exchanger m

T m=1n , g =TOT q , j ,k⩝n ,q , j , k (22)

Gq , j , kn =Fm

n ,g⩝n , q , j , k ,m (23)

Qmn , g=Fm

n , gC p (T m−1n ,g −T m

n ,g ) ⩝m,n (24)

Qmn , g=Qm

n , s⩝m ,s ,n (25)

Area of Heat exchanger m

Qms =Um Am ∆ Tm⩝m, s (26)

Pinch temperature difference of HRSG n

∆ T Pinchn ¿T m=2

n , g −T m=2s ⩝n (27)

Cost of Heat exchanger m

Cm=K H Amα⩝m (28)

Total annualized cost of HRSG, n

TACn=K F ∑m∈ NHeat

Cm−H y∑s∈ S

3600∗(F¿¿mn ,s∗Cops ¿)⩝n¿¿ (29)

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In a second step, the data obtained from simulations and optimization sub-routines are used to formulate a set of disjunctions to select the optimal syngas processing route. Each disjunction is described in detailed below.

Gasification and reforming stage: When gasification is selected to process biomass, then, there are two options. Direct and indirect gasification. This fact is stated by Equation (30).

∑q∈Q

yq≤ 1 (30)

The requirements of steam and oxygen for the gasification stage are computed as follows:

STq=KST qBq⩝q (31)

OX q=KOX qBq⩝q (32)

Flue gas from combustor chamber: Additional heat is recovered from IG process by feeding the leaving flue gas from combustor chamber at 995 °C to a HRSG system. The flowrate of flue gas combustor chamber, Dq, is calculated using Equation (33).

Dq=KD qBq⩝q (33)

where K Dq is defined as ratio of kg of flue gas produced in combustor chamber per kg of biomass fed to gasifier reactor and its value is shown in Table S2. It is calculated by mass balances and taking assumptions shown in [1]. It is worth pointing out that when direct gasification is selected, the value of K Dq is zero.

The existence of the flue gas from the combustor chamber, Dq, is restricted to the selection of the gasification process (Equation 34). This flue gas is fed to a HRSG to produce one or two kinds of steam as Equations (35)-(37) state.

∑q∈Q

yq− ∑n∈ NHRSG

y Dqn =0 (34)

∑n∈NHRSG

yDqn ≤ 1 (35)

Dq= ∑n∈NHRSG

D qn⩝q (36)

Dqn ≤ DMAX y Dq

n ⩝q ,n (37)

where y Dqn represents the selection of HRSG, n, which uses flue gas Dq

n to produce steam and DMAX is the maximum capacity of the HRSG.

FDq

n ,s=RD q

n , s∗Dqn⩝q ,n , s (38)

Equation (38) is used to calculate the flowrate of the steam generated in the HRSG, FDq

n ,s .

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where RDq

n , s is defined as the ratio of kg of steam, s, generated in HRSG, n, per kg of the flue

gas fed,Dqn, to HRSG and their values are shown in Table S3.

Reforming stage: To increase the hydrogen production, the syngas exiting from gasification stage is sent to the reformer reactor. The biomass flowrate that is processed via gasification, q, and reforming, j, is determined as follows:

where yq , j is a binary variable used to represent the selection of the biomass processing via q gasification and j reforming technologies. When binary variable yq , j is equal to one, Equations (41)-(43) are activated

Water q , j=KW q , jBq , j⩝q , j (41)

Oxygenq , j=KO q , j Bq , j⩝q , j (42)

SY q , j=K SYq , jBq , j⩝q , j (43)

where parameters KOX q, K ST q

,KW q, j,K oq , jand KSY q , j are calculated from simulations in Aspen plus and their values are shown in Table S2. Whereas SY q , j is the syngas flowrate obtained by the gasification, q, and the reforming j.

Options for syngas processing

Once syngas is obtained, it can be sent to gas turbine, SY q , j ,k, or the syngas boiler SY q , j ,sb. This fact is stated by the following set of equations:

SY q , j= ∑k∈TURBINE

SY q , j ,k+SY q , j , sb⩝q , j (44)

SY q , j ,k ≤ SY MAX yq , j ,k⩝q , j , k (45)

SY q , j ,sb ≤ SY MAX yq , j , sb⩝q , j , sb (46)

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Bq=∑j∈J

Bq , j⩝q (39)

∑q∈Q

yq−∑q∈Q

∑j∈J

yq , j=0 (40)

yq , j−( ∑k∈TURBINE

yq , j ,k+ yq , j , sb)=0⩝q , j (47)

∑k∈TURBINE

yq, j , k+ yq , j ,sb ≤1⩝q , j , sb (48)

∑k∈TURBINE

yq , j , k ≤ 1 (49)

Equations (44) and (45) limit the flowrate of syngas that can be sent to the syngas boiler and syngas turbine, respectively. Whereas, yq , j , sb is the binary variable that indicates the selection or non-selection of the syngas boiler. In the same way, yq , j , k indicates the selection of gas turbine k. According to Equation (47), the selection of either gas turbine or syngas boiler is restricted by the type of gasification and reforming selected. In this way, the selection of at most one can be made (Equation 48). If the gas turbine is selected, then its selection is restricted to be at most one (Equation 49).

Syngas boiler: The flowrate of syngas that is sent to the boiler of syngas is represented by SY q , j ,sb. The boiler of syngas can generate as many as four kinds of steam and it can also carry out the reheating of the steam. This is represented by set of Equations (50)-(53) as follows:

yq , j , sb−∑s∈ S

yq , j , sbs ≤ 0⩝q , j , sb (50)

yq , j , sb− ∑reheat n∈REHEAT

yreheat n

s , q , j ≤ 0⩝q , j , sb (51)

∑s∈s

yq , j ,sbs ≥0 (52)

∑reheatn∈REHEAT

yreheatn

s , q , j ≥ 0⩝q , j (53)

where the binary variable, yq , j , sbs , indicates the production of steam, s, by using syngas

boiler, sb while the variable yreheat n

s , q , j is used to select the steam reheating, reheat n, which is carried out by the syngas boiler which uses SY q , j ,sb. Note that either the steam production or reheating are restricted by the existence of the biomass boiler, according to Equation (50) and (51).

The flowrate of steam produced by the syngas boiler, FSBq , j

s , is calculated by using the following Equations

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QSBq , j

s =FSBq , j

s [ H (T s ,P s )−H (T v 1 , Pv1)]⩝q , j , sb , s (54)

FSBq , j

s ≤ F MAX yq , j ,sbs ⩝q , j , sb (55)

The heat required for the steam reheating is calculated as follows:

Qreheatq , j = ∑

reheatn∈ REHEATQreheatn

q , j(56)

Qreheatn

q , j =F reheat n

s , q , j *∆ H reheatn⩝q , j , reheat n

(57)

F reheat n

s ,q , j ≤ F MAX yreheat n

s , q , j ⩝q , j , reheatn

(58)

where F reheatn

s ,q , j is the flowrate of steam to be reheated in the syngas boiler which uses syngas, SY q , j ,sb and Qreheat n

q , j is the heat required to carry out the steam reheating, reheat n, selected.

Finally, the total heat in the syngas boiler is calculated by summing up the heat required to produce steam and steam reheating as Equation (59) sets. Furthermore, the flowrate of syngas, that is used in the syngas boiler, is calculated by the heat balance represented by Equation (60).

QTSBq , j=∑

s∈ SQSBq , j

s +Qreheatq , j ⩝q , j (59)

QTSBq , j=SY q , j , sb∗LHV q , j⩝q , j (60)

where LHV q , j is the lower heating value of syngas, SY q , j while QSBq , j

s is the heat required to

produce steam , Qreheatq , j is the heat required to reheat .

Syngas Turbine: The syngas can be compressed to different pressures. Therefore, gas turbine, k, is classified depending on its compression pressure. In this sense, when turbine k is selected, then the value of yq , j , k is one and the Equations (61)-(65) are activated.

Airq , j , k=K Aq , j, kSY q , j ,k⩝q , j , k (61)

Pcoq , j , k=(K SCoq , j,k+K ACoq , j,k ) SY q , j , k⩝q , j , k (62)

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Pq , j , k=K Pq, j ,kSY q , j , k−Pcoq , j , k⩝q , j , k

(63)

Gq , j , k=KGq , j,kSY q , j ,k⩝q , j , k (64)

CDq, j ,k=KCDq, j, kSY q , j ,k⩝q , j , k (65)

where Gq , j , k is the flue gas produced in the turbine k due to the combustion of syngas SY q , j ,k, while K Pq, j ,k, KGq , j, k ,KCDq , j ,k,K A q, j ,k, K SCo q, j ,k

∧K ACoq , j, k are parameters computed from simulations and their values are shown in Table S4.

HRSG: The flue gas produced in the gas turbine, Gq , j , k, is used to produce steam in an HRSG system. The possible HRSG configurations were stated according to the criteria explained above in Table S1 and they are limited by the existence of turbine k as follows:

yq , j , k− ∑n∈NHRSG

yq , j ,kn =0⩝q , j ,k (66)

where yq , j , kn indicates the selection of configuration, n, of HRSG which are restricted to be

at most one as Equations (67) -(69) show:

Gq , j , k= ∑n∈NHRSG

Gq , j ,kn ⩝q , j , k (67)

∑n∈NHRSG

yq , j ,kn ≤ 1⩝q , j , k (68)

Gq , j , kn ≤ Gmax yq , j , k

n ⩝q , j , k , n (69)

where Gq , j , kn is the flowrate of exhaust gas that is sent to HRSG, n. Finally, the steam

generated from HRSG, n, is calculated as follows:

Fq , j ,kn ,s =G q , j ,k

n ∗Rq , j ,kn ,s ⩝q , j , k ,n , s (70)

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where Rq , j , kn , s is computed by the optimization of SB-1 and it is defined as the ratio of kg of

steam, s, produced in HRSG, n, per kg the exhaust gas, Gq , j , k. Their values are shown in Table S5.

Total production of biomass-based steam: total production of the biomass-based steam, s, is calculated by the summation of the steam produced in the biomass boiler, F c

s, plus

steam produced in the HRSG system, Fq , j ,kn ,s , FDq

n ,s and the syngas boiler, FSBq , j

s , as follows:

Power produced in the syngas turbine: Power produced in the syngas turbine is calculated by Equation (72). It consists of the summation of the power produced by each syngas turbine, k, Pq , j , k. In the same way, the total cooling required by the gas turbine is determined by Equation (73).

Powe rbiomass=∑q∈Q

∑j∈J

∑k∈Turbine

Pq , j ,k (72)

CDbiomass=∑q∈Q

∑j∈ j

∑k∈Turbine

CDq , j ,k (73)

Equipment cost

The equipment cost were calculated by using correlations proposed in literature [4-8]. Then, depending on case study, these correlations were linearized in a specific operation range. Constant of the linearized functions are shown in Table S9. In this sense, the equipment cost was calculated as follows:

Biomass boiler cost

Cost cs=Ac (Qc

s )+B c ycs ⩝ s (74)

Cost creheatn=A c (Qreheatn

C )+Bc yreheatn

s ,C ⩝ reheatn (75)

BBCOST=∑s

Costcs + ∑

reheat n

Costcreheat n (76)

Syngas boiler cost

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FBs =∑

q∈Q∑j∈ J

∑k∈Turbine

∑n∈ NHRSG

Fq , j ,k , tn ,s +F ct

s +∑q∈Q

∑j∈J

FSBq, j , t

s +∑q∈Q

∑n∈ NHRSG

FDq ,t

n ,s ⩝ s∈S (71)

Cost SBq, j

s =A sb (QSBq , j

s )+Bsb yq , j ,sbs ⩝q , j , s (77)

Cost SBq, j

reheat n=A sb (Qreheatn

q , j )+B sb yreheat n

s , q , j ⩝q , j , reheat n (78)

SBCOST=∑q∑

j∑

sCost SBq, j

s +∑q∑

j∑

reheatn

Cost SBq , j

reheatn (79)

Gas turbine and compressor cost

CostT q , j ,k=AT (Pq , j ,k )+BT yq , j , k⩝q , j , k (80)

CostCOMP q, j ,k=ACOMP ( Pcoq , j ,k )+BCOMP yq , j , k⩝q , j , k (81)

Heat recovery steam Generator cost

Cost HRSGq, j ,k

n =AHRSG (∑sFq , j , k

n , s )+BHRSG yq , j , kn ⩝q , j , k , n (82)

Cost DHRSGq

n =AHRSG (∑sFDq

n , s)+BHRSG y D, qn ⩝q ,n (83)

Gasification-Reforming investment and operating costs

CostGasq , j=A gas (SY q , j )+Bgas yq , j⩝q , j (84)

OpCostGasq, j=AOpgas ( SY q , j )+BOpgas yq , j⩝q , j (85)

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The costs of the biomass processing section (Cost BIOMASS) and the biogas processing section

is calculated by Equation (86).

Cost BIOMASS=BBCOST +SBCOST+∑q∑

j∑

kCost Tq , j,k

+∑q∑

j∑

kCostCOMP q, j, k

+∑q∑

j∑

k∑

nCost HRSGq, j ,k

n +∑q∑

jCostGasq , j

+∑q∑

nCost DHRSGq

n(86)

The operating cost of biomass processing is computed as follows,

Opcostbiomass=∑q∑

jOpCostGasq , j

+B∗Cbio (87)

where B is the biomass used in the process in kg/s and Cbio is the cost of biomass in $USD/ton.

S1.2 Concentrated solar power

The production of any type of steam is related to the selection of CSP technology. This is expressed by Equation (88)-(90).

yCSP -∑s

yCSPs ≤0 (88)

∑s

yCSPs ≥ 0 (89)

FCSPs ≤ Fmax yCSP

s ⩝ s (90)

where yCSP is a binary variable to indicate the selection or non-selection of CSP, whereas yCSP

s is a binary variable used to indicate the production or non-production of the steam, s, by CSP, while Fmax is the maximum steam flowrate allowable in the heat exchangers.

Area of the solar field: The heliostat performance and its efficiency are influenced by several factors such as cosine losses (20%), shading and blocking (2%), heliostat reflectivity (0.9-0.0.95) and transmission losses through the atmosphere (5%) [9]. In this work, a value of 55% was taken as global efficiency of heliostat field. The typical size of a heliostat range between 40- 150 m2. In this work, a value of 120 m2 was considered. The total energy received by the heliostat field, E, is computed by Equation (91).

where rad, is the average annual solar radiation in kWh/m2day. On the other hand, the heat transferred by the collector to molten salt is given by Equation (92)

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E=rad* Asolar field * ηfield∗N days (91)

Qcollector =Ehsun

(92)

where hsun is the sun hours per day.

The total area needed to meet heating requirements is restricted by the followings constraints:

where Amin is equal to 120 m2 corresponding to the area of one heliostat, while Amax is equal

to 1, 500, 000 m2 corresponding to the area of the largest CSP plant [10]. In this sense,

when its value is one, CSP technology is selected and constraints (94)-(95) are activated.

Calculating Molten salts flowrate: The flowrate of molten salts is computed by the

following equation:

Qcollector =FTsalt * Cpsalt * ( Tsalt1 - Tsalt11 ) (96)

The total flowrate of molten salts, FTsalt, is divided. A portion is sent to the steam generation section, Fsalt, while the rest is sent to the reheating section, F reheat

salt . This fact is stated by the following equation,

FTsalt =Fsalt + F reheatsalt

(97)

In the same way, the total heat required to produce both steam generation and reheating is given for the following equation:

Qcollector=QsteamCSP +Q reheat

CSP (98)

Global mass and heat balance for steam production:The total heat needed to produce steam required is determined by Equation (99) and the mass balance given by Equation (100)

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Number of heliostats=A solar field

A heliostat(93)

Asolarfield ≤ Amax yCSP (94)

Asolarfield ≥ Aheliostat yCSP (95)

QsteamCSP = QEC1

+ QEV1+QEC2

+QEV2+ QEC3

+QEV 2+QSC3

+ QEC4+QEV 4

+QSC4(99)

FTCSP= FCSP

LP +FCSPMP +FCSP

HP +FCSPVHP (100)

Temperature profile of molten salts in the steam generation section: The temperature profile of the molten salts depends on the kind of steam produced. Therefore, temperatures are determined from the energy balances shown above. Additionally, the temperature profile is restricted by the following set of constraints:

Tsalt1 ≥ Tsalt(SC4, EV4) (101)

Tsalt(SC4, EV4) ≥ T salt(EV4, EC4) (102)

Tsalt(EV4, EC4) ≥ Tsalt(EC4, SC3) (103)

Tsalt(EC4, SC3) ≥ Tsalt(SC3, EV3) (104)

Tsalt(SC3, EV3)≥ T salt(EV3, EC3) (105)

Tsalt(EV3, EC3) ≥ Tsalt(EC3, EV2) (106)

Tsalt(EC3, EV2) ≥ Tsalt(EV2, EC2) (107)

Tsalt(EV2, EC2) ≥ Tsalt(EC2, EV1) (108)

Tsalt(EC2, EV1) ≥ Tsalt(EV1, EC1) (109)

Tsalt(EV1, EC1) ≥ Tsalt11 (110)

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Steam generation section

Heat balance for LP steam production: To produce LP steam, water (FT) at Tv1is sent to EC1 to be heated to the boiling temperature, Tv2,at 2.07 bar. Then, the leaving stream is sent to the evaporator EV1. The heat required to produce it is provided by the molten salts whose inlet and outlet temperatures are Tsalt (EC2, EV1) and Tsalt11, respectively, and it is determined by Equations (111)-(116).

FT = FCSPLP +FA

(111)

QEC1= Fsalt Cpsalt [T salt(EV1, EC1) -Tsalt11 ] (112)

QEC1= Fsalt Cpsalt [T salt(EV1, EC1) -Tsalt11 ] (113)

QEC1= FTCpwater ( Tv2- Tv1) (114)

QEV 1=Fsalt Cpsalt [T salt(EC2, EV1) -T salt(EV1, EC1) ] (115)

QEV 1= FCSP

LP λ( Tv2 ,2.07 bar)(116)

LP steam production implies that the value of binary variable yCSPLP is equal to one.

Therefore, the cost functions (Equation 118 and 119) are activated and Equation (117) is used to calculate the area of heat exchanger.

QEC1=UEC1

AEC1∆ TEC1

(117)

CEC1=K∗AEC1

∝ (118)

CEV1=B∗AEV1

+C∗yCSPLP (119)

17

∆ TEC1=0.67* [ (T salt11- Tv1 ) ( Tsalt(EV1, EC1) -Tv2 ) ]0.5

+0.33*( Tsalt11- Tv1 )+ ( Tsalt(EV1, EC1) - Tv2 )2

(120)

where ∆ TEC1 in Equation (120) is the logarithmic mean difference temperature of heat exchanger EC1 and it is calculated as follows:

Finally, the area of evaporator EV1 is calculated as AEC1.

Heat balance for MP steam production: MP steam is produced by heating FA in EC2 to the saturation temperature, Tv3 at 27.6 bar. The leaving stream, FMP, is sent to EV2 to be evaporated. The heat required to produce it is provided by the molten salts whose inlet and outlet temperatures are Tsalt (EC3, EV2) and Tsalt (EC2, EV1), respectively, and it is determined by Equations (121)-(125).

As the previous case, MP steam production implies that the value of binary variable yCSPMP is

equal to one which adds more cost to the total investment. The costs and areas of both heat exchangers are calculated as the previous case.

Heat balance for HP production: HP steam is produced by heating FB in EC3 to the saturation temperature, Tv4 at 42.5bar. The leaving stream, FHP, is sent to EV3 to be evaporated. Then it is superheated at Tv5 in SC3. The inlet and outlet temperatures of the molten salt are Tsalt(EC4, SC3) and Tsalt(EC3, EV2), respectively, and it is determined by Equations (126)-(132).

FB =FCSPHP + FCSP

VHP (126)

18

FA =FCSPMP + FB

(121)

QEC2= Fsalt Cpsalt [T salt(EV2, EC2)−Tsalt(EC2, EV1) ] (122)

QEC2=FT Cpwater (Tv3- Tv2 ) (123)

QEV 2=Fsalt Cpsalt [T salt(EC3, EV2) -T salt(EV2, EC2) ] (124)

QEV 2= FCSP

MP λ( Tv3 .27.6 bar)(125)

QEC3=Fsalt Cpsalt [T salt(EV3, EC3)−Tsalt(EC3, EV2) ] (127)

QEC3= FB Cpwater (Tv4 - Tv3 ) (128)

QEV 3= Fsalt Cpsalt [T salt(SC3, EV3)- Tsalt(EV3, EC3) ] (129)

QEV 3= FCSP

HP λ( Tv4 , 42.5 bar)(130)

QSC3=F salt Cpsalt [ Tsalt(EC4, SC3)−Tsalt(SC3, EV3) ] (131)

QSC3= FCSP

HP ∗(HT v5 ,42.5 bar -HT v4 , 42.5 bar) (132)

Similarly to the previous cases, HP steam production implies that the value of binary variable yCSP

HP is equal to one. Therefore, cost functions (Equations 133-135) are activated where heat transfer areas of the heat exchangers are calculated as in LP steam production.

CEC3=K∗AEC3

∝ (133)

CEV3=B∗AEV3

+C∗yCSPHP (134)

CSC3=B∗ASC3+C∗yCSP

HP (135)

Heat balance for VHP steam production: VHP steam is produced by heating up FVHP_CSP in EC4 to the saturation temperature, Tv6 at 165 bar. Then, it is sent to EV4 to be evaporated and finally to SC4 where is superheated at Tv7. The heat required to produce it is provided by the molten salts whose inlet and outlet temperatures are Tsalt1 and Tsalt(EC4, SC3), respectively, and it is determined by Equations (136)-(141).

QEC4= F salt Cpsalt [ Tsalt(EV4, EC4)−Tsalt(EC4, SC3) ] (136)

QEC4= FCSP

VHPCpwater ( Tv6- Tv4 ) (137)

19

QEV 4=F salt Cpsalt [ Tsalt(SC4, EV4)- Tsalt(EV4, EC4) ] (138)

QEV 4= FCSP

VHPλ ( Tv6 , 165 bar)(139)

QSC4= Fsalt Cpsalt [Tsalt1−T salt(SC4, EV4) ] (140)

QSC4=FCSP

VHP∗(HT v7 ,42.5 bar- HT v6 , 42.5 bar) (141)

VHP steam production implies that the value of binary variable yCSPVHPis equal to one.

Therefore, cost functions (Equations 142-144) are activated where the areas of the heat exchangers are calculated as in LP steam production.

CEC4=B∗AEC 4

+C∗yCSPVHP (142)

CEV4=B∗AEV4

+C∗ yCSPVHP (143)

CSC4=B* ASC4+C* yCSP

VHP (144)

Steam Reheating Section

A portion of molten salt, F reheatsalt , can be used to reheat steam leaving from the steam turbine.

The flowrate is calculated as follows:

F reheatsalt = ∑

reheat n

Freheat n

salt (145)

While the total heat needed to reheat steam is given by Equation (146)

QreheatCSP = ∑

reheat n

Qreheat n

CSP (146)

20

Heat Balance of the Steam Reheating Section: The set of Equations (147)-(150) are the energy balance used to calculate the flowrate of the molten salts used in each reheating.

Qreheat n

CSP = F reheat n

s ,CSP *∆ H reheatn⩝ reheat n , s (147)

Qreheat n

CSP = F reheat n

salt *Cpsalt * (T salt1 -T salt11)⩝ reheatn(148)

Qreheat n

CSP = Ureheat Areheat_n ∆ T reheat_n⩝reheat n(149)

C reheat n

CSP =B∗Areheat_n+C∗yreheat n

s ,CSP ⩝ reheatn(150)

Cost of CSP plant section: In this work, a heliostat cost of 120 $/m2 was taken [11], [12]. Cost data of towers and receivers were taken from [12] and [13] while molten cost price was set as 0.67 $ USD /kg [14].

Csolar field=Ctower yCSP+Creceiver yCSP+FTsalt CMsalt+Asolarfield∗CHeliostat (151)

The cost of the CSP plant section, CostCSP, was obtained from the summation of the cost of the steam generation section (C steam

CSP ), reheating cost (C reheatCSP ) and the cost of the solar field (

Csolar field):

C steamCSP =CEC4

+CEV4+CSC4

+CEC3+CEV3

+CSC3+CEC2

+CEV2+CEC1

+CEV1

(152)

C reheatCSP =∑

nC reheat n

CSP (153)

CostCSP=Csolar field+C steamCSP +C reheat

CSP (154)

S1.3 Biogas processing

21

Feedstock selection: In this work, we have considered two possible kinds of waste as feedstock to produce biogas. Namely, municipal solid waste (MSW) and cattle manure (CM). In this way, to make a decision on the selection of the feedstock to be used, the following disjunction is formulated:

where y z is a binary variable used to select the feedstock to produce biogas while MaxWaste z is the maximum availability of waste, z, in the zone in kg/s. The biogas produced for each feedstock is based on yield data for each compound from literature and it is calculated as follows:

CH 4z=Waste z KCH 4z ⩝ z (157)

CO 2z=Waste z K CO2z ⩝ z (158)

WATER z=Waste z K wz ⩝ z (159)

NH 3z=Waste z K Ammoiaz ⩝ z (160)

where KCH 4z , KCO 2

z , Kwz , and K Ammoia

z are the ratio of kg of methane, carbon dioxide, water , and ammonia per kg of waste fed to the digestor, respectively. These parameters were adjusted from data by [15]. The model is flexible to consider other residues too. Once biogas is obtained, carbon monoxide and the other components are separated from biogas. In this way, the total methane produced by the process is calculated as follows:

CH 4=∑z

CH 4z(161)

CH 4=∑k

CH 4k+CH 4BGB(162)

∑z

yz−(∑kyk

biogas+ yBGB )≤ 0 (163)

∑k

ykbiogas+ y BGB≤ 1 (164)

∑k

ykbiogas≤ 1 (165)

22

∑z

yz ≤1 (155)

Waste z≤ MaxWaste z ¿ yz⩝ z (156)

Biogas processing selection: Biogas can be sent to a biogas turbine, CH 4k, or a biogas boiler, CH 4BGB, to produce electricity and heat. This condition is stated by the following disjunction,

where ykbiogas is a binary variable to select gas turbine k while yBGB indicates the selection of

biogas boiler. In this sense, Equation (163) is a disjunction used to restrict any selection of biogas turbine or biogas boiler to the existence of feedstock z, while Equation (164) restricts this selection to be one. Equation (165) indicates that at most one gas turbine can be selected.

Biogas Boiler: The biogas boiler is used to generate as many as four types of steam and carry out the steam reheating, as well. This is stated by the following disjunctions:

yBGB−∑s

yBGBs ≤ 0⩝ z (166)

∑s

yBGBs ≥ 0 (167)

yBGB−∑n

yreheatn

s , BGB≤ 0 (168)

∑reheat n

yreheat n

s , BGB ≥0 (169)

where the production or non-production of steam, s, by the biogas boiler is represented by the binary variable yBGB

s while yreheat n

s , BGB is the binary variable used to select the steam reheating, reheat_n, which is carried out by the biogas boiler. Note that because of Equations (166) and (168), both steam production and steam reheating are restricted to the existence of the biogas boiler. In this sense, the flowrate of steam, s, produced by the biogas boiler, FBGB

s , is computed as follows:

QBGBs =FBGB

s [ H (T s ,P s )−H (T v1 ,Pv 1)]⩝ s (170)

23

FBGBs ≤ FMAX y BGB

s ⩝ s (171)

The heat required for the steam reheating is calculated as follows:

QreheatBGB = ∑

reheatn

Qreheatn

BGB(172)

Qreheat n

BGB =F reheatn

s , BGB*∆ H reheat n⩝reheat n

(173)

F reheatn

s , BGB≤ FMAX yreheatn

s , BGB⩝reheat n

(174)

where F reheat n

s , BGB is the flowrate of steam to be reheated in the biogas boiler and Qreheat n

BGB is the heat required to carry out the steam reheating, reheat n, selected.

The total heat in the biogas boiler is calculated by the heat balance shown below:

QTBGB=∑s

QBGBs +Qreheat

BGB(175)

QTBGB=CH 4BGB LHV CH 4 (176)

where LHV CH 4 is the Lower Heating Value of methane, QBGBs is the heat required to

produce steam , QreheatBGB is the heat required to reheat steam It is considered that the biogas

boiler can be used to reheat the steam coming from steam headers in the steam network.

Biogas Turbine: Similarly to the syngas case, the biogas can be compressed to different pressures. Once compressed, biogas is burned and is expanded in the turbine to produce electricity. In this sense, when the gas turbine, k, is selected, then the value of yk

biogas is one and the Equations (177)-(181) are activated:

Airkbiogas=K A k

biogas CH 4k⩝k (177)

24

Pcokbiogas=( KSCo k

biogas+K ACok

biogas )CH 4k⩝k(178)

Pkbiogas=K p k

biogasCH 4k−Pcokbiogas⩝ k (179)

Gkbiogas=KG k

biogasCH 4k⩝k (180)

CDkbiogas=KCDk

biogas CH 4k⩝k (181)

where Gkbiogas is the exhaust gas produced in the turbine k due to the combustion of methane

while K pk

biogas, K A k

biogas, K SCo k

biogas , K ACok

biogas KGk

biogas, and KCDk

biogas are parameters computed from gas turbine simulations. Their values are shown in Table S7.

The exhaust gas exiting the gas turbine is used to produce steam in an HRSG. The possible configurations of HRSG are stated by using the same criteria explained in syngas processing section (see Table S1) and they are restricted by the existence of the gas turbine, k, as follows:

ykbiogas−∑

nyk ,n

biogas=0⩝k (182)

where yk , nbiogasindicates the selection of configuration, n, of HRG which are restricted to be at

most one as Equations (183) and (185) show:

Gkbiogas=∑

nG k ,n

biogas⩝k (183)

∑n

yk ,nbiogas≤ 1⩝ k (184)

Gk , nbiogas≤ GMAX yk ,n

biogas⩝k , n(185)

25

where Gk , nbiogasis the flowrate of exhaust gas that is sent to HRSG, n. Finally, the steam

generated from HRSG, n, is calculated as follows:

F k ,ns ,biogas=G k ,n

biogas∗Rk , ns , biogas⩝k , n , s (186)

where Rk , ns ,biogas is computed by the optimization of SB-1 and it is defined as the ratio of kg of

steam, s, produced in HRSG, n, per kg the exhaust gas, Gkbiogas. Their values are shown in

Table S8.

Total production of biogas-based steam: the total production of steam is calculated by adding the amount of steam produced in the biogas boiler, FBGB

s , plus that produced in the HRSG system, F k ,n

s ,biogas,

Fbiogass =∑

k∑

nFk ,n

s ,biogas+FBGBs ⩝ s (187)

Total production of biogas-based power: Total power produced by the biogas turbine is calculated from Equation (188). It consists of the summation of the power produced by each biogas turbine, k. In the same way, total cooling required by the gas turbine is determined by Equation (189).

Powe rbiogas=∑k

Pkbiogas

(188)

CDbiogas=∑k

CDkbiogas

(189)

Equipment cost

Equipment costs were calculated by using correlations proposed in the literature [6-10]. Then, depending on the case study, these correlations were linearized with a specific operation range. Constant of the linearized functions are shown in Table S9. In this sense, the costs of equipment are calculated as follows:

Biogas processing

Cost biogasz=ABiogas ( Wastez )+Bbiogas yz⩝ z (190)

26

OpCostbiogasz=AOpbiogas (Waste z )+BOpbiogas y z⩝ z (191)

Biogas boiler cost

Cost BGBs =ABGB (QBGB

s )+BBGB yBGBs ⩝ s (192)

Cost BGBreheat n=ABGB (Qreheat n

BGB )+BBGB yreheatn

s , BGB⩝ reheatn (193)

BGBCOST=∑s

Cost BGBs + ∑

reheatn

Cost BGBreheatn (194)

Biogas Turbine/compressor

Cost Biogas Turbinek=ABiogasT (Pk

biogas)+BBiogasT ykbiogas⩝k (195)

Cost Biogas Compk=ABiogasCOMP (Pcok

biogas)+BBiogasCOMP ykbiogas⩝k (196)

HRSG

Cost BIO−HRSGk

n =ABIO−HRSG (∑sFk ,n

s ,biogas)+BBIO−HRSG yk ,nbiogas⩝k , n (197)

The total cost of the biogas processing section was calculated as the summation of each equipment unit needed to process biogas:

Cost BIOGAS=BGBCOST+∑z

Costbiogasz+∑

kCost BiogasTurbinek

+∑k

Cost Biogas Compk+∑

k∑

nCost BIO−HRSGk

n(198)

S1.4 Steam Network

This section shows the mass and energy balances corresponding to the steam generation section.

27

Steam Headers: Equations 199-202 represent the mass balance of each steam header. Where, FT 1

s is the flowrate of the steam produced by the renewable sources that was not reheated.

Mass balance in VHP steam header, SVHP

FBiomassVHP +FCSP

VHP+FbiogasVHP =F( S VHP ,V 1)

VHP +F ( S VHP , ST )VHP (199)

Mass balance in HP steam header, SHP

FBiomassHP +FCSP

HP +FbiogasHP =FT 1

HP+F reheat 2

HP +F (S HP , V 5)HP (200)

Mass balance in MP steam header, SMP

FBiomassMP +FCSP

MP +FbiogasMP =FT 1

MP+F reheat3

MP (201)

Mass balance in LP steam header, SLP

FBiomassLP +FCSP

LP +FbiogasLP =FT 1

LP+Freheat4

LP (202)

In order to enhance the power production, a portion of the steam produced by the renewables resources can be reheated to be fed to the steam turbine (F reheatn

s ). Therefore, the inlet steam turbine flowrate is given by the summation of steam flowrate that has not been extracted, F(EXn , ST)

s , plus the flowrate of the steam reheated, as it is stated in Equations (203)-(208).

Second feed to steam turbine, FSTHP

FSTHP=F reheat1

HP +Freheat2

HP (203)

28

FSTHP ≥ F ( S VHP ,ST )

VHP ∗R (204)

Third feed to steam turbine, FSTMP

FSTMP=F reheat 3

MP +F(EX 2 ,ST )MP (205)

FSTMP ≥ FST

HP∗R (206)

Fourth feed to steam turbine, FSTLP

FSTLP=F reheat 4

LP +F (EX 3 , ST )LP (207)

FSTLP ≥ FST

MP∗R (208)

Where Equations (204), (206), and (208) are used to ensure an inlet flowrate in each feeding of the steam turbine.

Steam Reheating: The steam reheating can be carried out by either a biomass boiler, syngas boiler, biogas boiler or the molten salts of CSP plant. The heat required and source selection to reheating is calculated as follows:

Reheating of F(EX 1 ,reheat 1)HP

Qreaheat 1=F(EX 1 ,reheat 1)HP ∆ H reaheat 1 (209)

F(EX 1 ,reheat1)HP =F reheat 1

HP (210)

F reheat1

HP =Freheat1

HP ,CSP+F reheat1

HP,BGB+F reheat1

HP, C +∑q∑

jFreheat1

HP,q , j (211)

29

yreheat 1

HP ,CSP+ yreheat 1

HP , BGB+ yreheat1

HP , C +∑q∑

jyreheat1

HP , q , j≤ 1 (212)

Reheating of F reheat2

HP

Qreaheat 2=F reheat2

HP ∆ H reaheat 2 (213)

F reheat2

HP =Freheat2

HP ,CSP+F reheat2

HP,BGB+F reheat2

HP ,C +∑q∑

jF reheat2

HP, q , j(214)

yreheat 2

HP,CSP+ yreheat 2

HP , BGB+ yreheat 2

HP , C +∑q∑

jyreheat2

HP, q , j≤ 1 (215)

Reheating of F reheat3

MP

Qreaheat 3=F reheat3

MP ∆ H reaheat 3 (216)

F reheat3

MP =Freheat 3

MP ,CSP+F reheat 3

MP , BGB+F reheat 3

MP ,C +∑q∑

jF reheat3

MP , q , j(217)

yreheat3

MP ,CSP+ yreheat 3

MP , BGB+ yreheat 3

MP , C +∑q∑

jyreheat3

MP ,q , j ≤1 (218)

Reheating of F reheat 4

LP

Qreaheat 4=F reheat 4

LP ∆ H reaheat 4 (219)

F reheat 4

LP =F reheat4

LP ,CSP+F reheat 4

LP , BGB+F reheat4

LP,C +∑q∑

jF reheat 4

LP ,q , j (220)

30

yreheat 4

LP,CSP+ yreheat4

LP , BGB+ y reheat4

LP ,C +∑q∑

jyreheat 4

LP ,q , j ≤1 (221)

where yreheat n

s , i is the binary variable to select the kind of reheat, reheat n, carried out by the

resources, i while F reheat n

s is the steam flowrate to be reheated. When the steam produced by cooling down a steam turbine extraction cannot be reheated.

Multiple extractions: The multiple extractions were considered as alternatives pathways to produce LP, MP, and HP steams. They are assumed to be isentropic expansions. Each steam pathway and extractions characteristics are explained in detail below.

Production of HP steam

a) Expanding the VHP steam through a valve without electricity production

A portion of the VHP steam produced by the renewable resources can be isentropically expanded through the valve V1 to produce HP steam. However, an additional cooling, unit CU1, is needed in order to reach the operating conditions of HP steam. Mass and heat balance are given by set of Equations (222)-(225).

Balance in valve V1 and unit CU_1

F(S VHP , V 1)VHP =F(V 1 , CU1)

HP (222)

Heat balance in CU_1

Qcu1=F(V 1 ,CU1)

HP ∆ HCU 1(223)

Qcu1=Acu1

U cu1∆ T cu1 (224)

F(V 1 ,CU 1)HP =F(CU1 , SHP 2)

HP (225)

b) Cooling down the first steam turbine extraction

31

The first steam turbine extraction, EX1, was set to be the same as the HP steam pressure while the temperature was calculated by using Mollier diagram. Therefore, it needs to be cooled down, by using unit CU2, to reach the operating conditions of HP steam. Mass and heat balance are given by Equations (226)-(230).

Balance in the first steam turbine expansion, EX1

F(S VHP , ST)VHP =F(ST , EX 1)

HP (226)

F(ST , EX 1)HP =F (EX 1 ,reheat 1)

HP +F( EX 1 ,CU 2)HP +F(EX 1 ,V 2)

HP (227)

Heat balance in unit CU_2

Qcu2=F (EX 1 , CU2)HP ∆ HCU2

(228)

Qcu2=Acu2

U cu2∆ T cu2 (229)

F(EX 1 ,CU2 )HP =F(CU2 , SHP 2)

HP (230)

Production of MP steam

a) Expansion of the first steam turbine extraction, EX1, without electricity production

A fraction of the first steam turbine extraction flowrate can be isentropically expanded through the valve, V2, where an additional cooling, unit CU3, is needed in order to reach the operating conditions of MP steam.

F(EX 1 ,CU2 )HP =F(CU2 , SHP 2)

HP (231)

Balance in valve V2 and unit CU_3

F(EX 1 ,V 2)HP =F(V 2 ,CU3 )

MP (232)

32

Heat balance in CU_3

Qcu3=F(V 2 ,CU3 )

MP ∆ HCU 3(233)

Qcu3=Acu3

U cu3∆ T cu3 (234)

F(V 2 ,CU 3)MP =F(CU3 , SMP 2)

MP (235)

b) Cooling down the second steam turbine extraction

Similarly to the previous case, the pressure of the second steam turbine extraction was assumed to be same as the MP steam pressure. Where it is eventually cooled down by unit CU4.

Balance in the second steam turbine expansion, EX2

FSTHP=F (ST , EX 2 )

MP (236)

F(ST , EX 2)MP =F (EX 2 , ST)

MP +F( EX 2 ,CU 4)MP +F( EX 2 ,V 3 )

MP (237)

Heat balance in unit CU_4

Qcu 4=F( EX 2 ,CU 4)MP ∆ HCU4

(238)

Qcu 4=Acu 4

U cu4∆ T cu4 (239)

F(EX 2 ,CU 4)MP =F (CU 4 ,SMP 2)

MP (240)

c) Cooling down the HP steam produced by the renewable resources

Because of the superheating conditions of the HP steam produced by the renewable sources, it is possible to expand it through valve, V5, at the pressure of MP steam. After being expanded, it is cooled down in unit CU8 to reach the operating conditions of MP steam.

33

Balance in valve V5 and unit CU_8

F(S HP,V 5 )HP =F(V 5 ,CU 8)

MP (241)

Heat balance in CU_8

Qcu8=F(V 5 ,CU8 )

MP ∆ HCU8(242)

Qcu8=Acu8

U cu 8∆T cu8 (243)

F(V 5 ,CU 8)MP =F (CU 8 ,SMP 2)

MP (244)

Production of LP steam

a) Expansion of the second steam turbine extraction, EX2, without electricity production

The second steam turbine extraction can be expanded through valve, V3 to produce LP steam. The unit CU5 is used to cool down the steam to reach the operating conditions of LP steam.

Balance in valve V3 and unit CU_5

F(EX 2 ,V 3 )MP =F(V 3 ,CU 5)

LP (245)

Heat balance in CU_5

Qcu5=F(V 3 ,CU5 )

LP ∆ H CU5(246)

Qcu5=Acu5

U cu5∆ T cu5 (247)

34

F(V 3 ,CU 5)LP =F (CU5 , SLP2)

LP (248)

b) Cooling down the third steam turbine extraction, EX3.

The pressure of the third steam turbine extraction was assumed to be the same as the pressure LP steam. Similarly to the previous cases, the temperature was calculated by using Mollier diagram and assuming an isentropic expansion. The cooling down is carried out by unit CU6.

Balance in the third steam turbine expansion, EX3

FSTMP=F (ST , EX 3 )

LP (249)

F(ST , EX 3)LP =F (EX 3 , ST)

LP +F (EX 3 , CU6)LP +F( EX 3 ,V 4)

LP (250)

Heat balance in unit CU_6

Qcu6=F(EX 3 ,CU6 )

LP ∆ H CU 6(251)

Qcu6=Acu6

U cu 6∆T cu 6 (252)

F(EX 3 ,CU 6)LP =F(CU6 , SLP2)

LP (253)

Exhausting and Cooling : After being reheated and expanded, the steam is cooled down in the condenser, CON, which uses cooling water supplied by the cooling tower shown in Figure 6. Mass and heat balance are represented by Equations (254)-(257).

Balance in exhausting

FSTLP=F(ST , COND)

EXT (254)

Heat balance for condenser

FEXT=F (ST ,COND )EXT +F (V 4 ,COND )

EXT (255)

35

QCOND=FEXT ∆ HCOND (256)

QCOND=ACONDUCOND ∆ T COND (257)

Cooling Tower: The cooling required by the process is provided by a cooling tower. The energy balance of cooling tower takes into account the required by the steam network, QCOND, the biomass processing section, CDbiomass, and biogas processing section, CDbiogas. This fact is stated by the following equation,

Qcooling=QCOND+∑cu n

Qcun+CDbiomass+CDbiogas (258)

Qcooling=mwater Cpw ∆ TW (259)

On the other hand, the water lost in cooling tower due to evaporation was calculated by using the following correlation [16].

mevap=0.00085∗mwater ∆ TW∗( 95 ) (260)

Equipment cost: The equipment cost of the steam network was calculated by carrying out a piecewise linear approximation of the non- linear correlations cost for each equipment in the steam network. In this sense, the piecewise linearization was developed for a pre-specified capacity of the equipment. The values of the constants of the linearized functions are shown in Table S10. They are represented by Equations (261)-(279).

Heat exchangers, CUn

ACU n=∑

fACU n

f ⩝CU n (261)

CostCU n

f =BCU∗ACUn

f +DCU∗yCUn

f ⩝CU n , f (262)

CostCU n=∑

fCost CUn

f ⩝CU n(263)

∑f

yA CUn

f ≤ 1⩝CU n(264)

36

ACU n

f ≤ A MAXCU n

f yCU n

f ⩝CU n , f (265)

ACU n

f ≥ A MINCU n

f yCU n

f ⩝CU n, f (266)

Steam turbine

Power ST=∑p

Power p⩝ p (267)

Cost STP =BST∗Power p+ DST∗yST

P ⩝ p (268)

Cost ST=∑p

Cost STP (269)

∑p

ySTP ≤1 (270)

Power p ≤ Power MAXp yST

P (271)

Power p ≥ PowerMINp yST

P (272)

Cooling tower

Qcooling=∑r

Qcoolingr ⩝ r (273)

CostCTr =BCT∗Qcooling

r +DCT∗yCTr ⩝ r (274)

CostCT =∑r

CostCTr (275)

∑r

yCTr ≤1 (276)

37

Qcoolingr ≤QMAX cooling

r yCTr (277)

Qcoolingr ≥QMIN cooling

r yCTr (278)

The cost of the steam network section, Cost SN, was calculated as the summation of the heat exchanger cost plus the cost of the steam turbine and the cooling tower.

Cost SN=∑CUn

Cost CUn+Cost ST+CostCT (279)

S2. Figures and additional information

Optimal cogeneration scheme of renewable-based HP steam

VHP steam is generated in the biomass boiler and sent to the steam turbine, where it is

expanded at 42.5 bar. The exit steam is cooled to 320 ºC to reach the operating conditions

of the HP steam.

Figure S1. Optimal topology for the cogeneration scheme of the renewable-based HP steam.

Optimal cogeneration scheme of renewable-based MP steam

38

The cogeneration scheme of the biomass-based MP steam begins with the production of

VHP steam in the biomass boiler that is sent to the steam turbine. The steam is expanded to

42.5 bar and sent to an expansion valve where it is expanded again to 27.5 bar. Finally, the

exhausted steam is cooled to 230°C to reach the operating conditions of the MP steam (see

Figure S2).

Figure S2. Optimal topology for the cogeneration scheme of the renewable-based MP steam.

Optimal cogeneration scheme of renewable-based LP steam

For this case, the biomass-based LP steam produced via a cogeneration scheme is obtained

by cooling the steam exiting from the third extraction of the steam turbine at 2.07 bar.

39

Figure S3. Optimal topology for the cogeneration scheme of the renewable-based LP steam.

Figure S4. Comparative analysis for the cost of the biomass-based steam with respect to the current price of

steam based on natural gas.

40

Figure S5. Comparative analysis for the cost of the biomass-based steam with respect to the current price of

steam based on natural gas when steam is obtained via cogeneration scheme

41

Figure S6. Comparative analysis for the cost of the solar-based steam with respect to the current price of

steam based on natural gas.

42

Figure S7. Comparative analysis for the cost of the solar-based steam with respect to the current price of

steam based on natural gas when solar radiation is increased.

43

Figure S8. Comparative analysis for the cost of the solar-based steam with respect to the current price of steam based on natural gas when steam is obtained via cogeneration scheme.

44

Figure S9. Comparative analysis for the cost of the solar-based steam with respect to the current price of steam based on natural gas when steam is obtained via cogeneration scheme.

Figure S10. Sensitivity analysis of cost of the biomass-based a) HP, b) MP and c) LP steam without electricity production against biomass price.

45

Figure S11. Sensitivity analysis of cost of the solar-based a) HP, b) MP and c) LP steam without electricity production against heliostat price

46

Figure S12. Sensitivity analysis of cost of the solar-based a) HP, b) MP and c) LP steam at current price of heliostats, 120 $/m2, and different values of solar radiation

47

Figure S13. Cost of the biogas-based a) HP, b) MP and c) LP steam.

Table S2. Value of parameters for gasification and Reforming stages

Gasifier, q=

Reforming, j=

KST qKOX q

K DqKW q , j

KOq , j KSY q , j

IGPOX 0.4 0 2.71298966 0 0.2024838 0.7408

SR 0.4 0 2.71298966 0.29778393 0 0.5776

DGPOX 0.2 0.23 0 0 0.31630262 0.28137611

SR 0.2 0.23 0 0.24843591 0 0.34214056

Table S3. Value of RDq

n , s

S=

VHP HP MP LP

48

HRSG, n=1 0.33896679 0 0 0

2 0.24431734 0.0897417 0 0

3 0.24619926 0 0.10664207 0

4 0 0.38571956 0 0

5 0 0.34136531 0.00140221 0

6 0 0 0.41948339 0

7 0 0 0.41354244 0.00199262

Table S4. Value of parameters for syngas turbine

Turbine, k=

Gasifier, q=

Reforming, j=

K Pq, j ,kKCDq ,j ,k

KGq , j, kK A q, j ,k

K ACoq , j,kKSCo q, j , k

GT-10

IG

POX 5301.83585 1480.76404 11.3687095 10.3671706 2944.9244

1174.94600

4

SR 7111.49584 1991.96676 14.9385388 13.9369806 3963.9889

2249.30747

9

DG

POX 6328.55431 1766.51457 13.3677874 12.3828538 3505.6280

9222.10840

8

SR 6078.55446 1707.42693 12.9541519 11.9545856 3388.0812

5126.52354

6

GT-20

IG

POX 6055.07559 2660.23218 11.3687095 10.3671706 3717.6025

9320.73434

1

SR 8017.72853 3734.61738 14.9385388 13.9369806 5048.4764

5446.26038

8

DG

POX 7203.17013 3155.59838 13.3677874 12.3828538 4375.6379

9 409.41642

SR 6973.97593 3099.92482 12.9541519 11.9545856 4305.5989 227.27501

5

GT-50 IG POX 6609.07127

3732.07343 11.3687095 10.3671706 5102.59179

194.384449

49

SR 8709.55679 5092.72853 14.9385388 13.9369806 6936.9806

1 809.00277

DG

POX 7855.67755 4523.69604 13.3677874 12.3828538 6141.2463 716.47873

4

SR 7575.83384 4372.09204 12.9541519 11.9545856 5934.4031

8694.45143

6

Table S5. Value of Rq , j , kn , s for syngas HRSG, system

S=

Turbine, k=

Gasifier, q=

Reforming, j=

HRSG, n= VHP HP MP LP

GT-10

IG

POX

1 0.220437 0 0 0

2 0.18573804 0.04232276 0 0

3 0.22033013 0 0.00168626 0

4 0 0.26256977 0 0

5 0 0.28553616 0.00073625 0

6 0 0 0.28906306 0

7 0 0 0.30465503 0.00483316

SR

1 0.2394438 0 0 0

2 0.22906141 0.00118192 0 0

3 0.23791425 0 0.00147161 0

4 0 0.28267671 0 0

5 0 0.26310545 0.00069525 0

6 0 0 0.31057937 0

7 0 0 0.32713789 0.0036153

DG POX 1 0.25422872 0 0 0

2 0.18954787 0.06465426 0 0

3 0.23776596 0 0.00273936 0

50

4 0 0.29726064 0 0

5 0 0.26345745 0.00119681 0

6 0 0 0.32569149 0

7 0 0 0.32765957 0.00385638

SR

1 0.25959368 0 0 0

2 0.2369526 0.00180587 0 0

3 0.24598194 0 0.00232506 0

4 0 0.30404063 0 0

5 0 0.27232506 0.00106095 0

6 0 0 0.33329571 0

7 0 0 0.33860045 0.00388262

GT-20

IG

POX

4 0 0.18982306 0 0

5 0 0.17736611 0.00085501 0

6 0 0 0.21178007 0

7 0 0 0.21155445 0.02910581

8 0 0 0 0.23157582

SR

4 0 0.21275782 0 0

5 0 0.19928158 0.00082271 0

6 0 0 0.23652375 0

7 0 0 0.24003476 0.02560834

8 0 0 0 0.25644264

DG

POX

4 0 0.23417553 0 0

5 0 0.20635638 0.00135638 0

6 0 0 0.25885638 0

7 0 0 0.24848404 0.02507979

8 0 0 0 0.27925532

SR 4 0 0.23322799 0 0

5 0 0.20819413 0.00124153 0

6 0 0 0.25844244 0

51

7 0 0 0.25022573 0.02702032

8 0 0 0 0.27837472

GT-50

IG

POX

6 0 0 0.14467403 0

7 0 0 0.13892649 0.04227526

8 0 0 0 0.16791355

SR

6 0 0 0.17235226 0

7 0 0 0.16893395 0.04154114

8 0 0 0 0.19599073

DG

POX

6 0 0 0.18760638 0

7 0 0 0.17042553 0.04255319

8 0 0 0 0.21074468

SR

6 0 0 0.19069977 0

7 0 0 0.17616253 0.04345372

8 0 0 0 0.21467269

Table S6. Value of parameters for digestor

Z= KCH 4z KCO 2

z Kwz K Ammonia

z

CM 0.008 0.0098 0.0025 1.1346E-06

MW 0.0387 0.0473 0.012 5.4811E-06

Table S7. Value of parameters for biogas turbine

Turbine, k= K pk

biogas K A k

biogas KGk

biogas KCD k

biogas K ACok

biogas KSCo k

biogas

GT-10 15007.50 32.5 33.62 4641.25 9243 184.5

52

GT-20 17302.50 32.5 33.62 8015 11610 337.5

GT-50 18810.00 32.5 33.62 11083.75 16200 540

Table S8. Value of Rq , j , kn , s for biogas HRSG, system

Turbine, k= HRSG, n= VHP HP MP LP

GT-10

1 0.2471 0 0 0

2 0.1127 0.1525 0 0

3 0.1191 0 0.1651 0

4 0 0.2879 0 0

5 0 0.1376 0.1558 0

6 0 0 0.3152 0

7 0 0 0.2924 0.0152

GT-20

4 0 0.2194 0 0

5 0 0.0786 0.1544 0

6 0 0 0.2433 0

7 0 0 0.2082 0.0387

8 0 0 0 0.262

GT-50

6 0 0 0.1767 0

7 0 0 0.1408 0.0514

8 0 0 0 0.2009

Table S9. Constants of linearized cost functions

($MM USD)

53

Ac 2.37E-4

Bc 2

A sb 2.37E-4

Bsb 2

AT 3.18E-4

BT 4.028E-1

AHRSG 2

BHRSG 6.636

Agas 2.2968

Bgas 183.42

AOpgas 0.0622

BOpgas 0

ACOMP 7.71E-4

BCOMP 1.74E-1

ABiogas 0.4935

Bbiogas 28.301

AOpbiogas 3.7409E-6

BOpbiogas 2.2929E-4

ABGB 2.132E-3

BBGB 1.0267E-2

ABiogasT 1.018E-3

BBiogasT 3.553E-3

ABiogasCOMP 7.82E-4

BBiogasCOMP 1.4656E-2

ABIO−HRSG 9

54

BBIO−HRSG 1.5445E-2

Table S10. Constants for linear piecewise cost function

Acun= 0 1 25 140 1000

BCU($MMUSD) 0 2.94E-4 1.499E-3 1.593E-3 3.94E-2

DCU

($MMUSD)0

-1.5E-5 -3.508E-3 2.583E-3 1.86E-1

PowerST= 0 1 10 60 700

BST ($MMUSD) 0 5.03e-1 1.02E-1 3.22E-2 1.56E-2

DST ($MMUSD) 0 1.64E-1 6.19E-1 1 2

Qcooling 0 10000 15000 25000 50000

BCT($MMUSD) 0 0.74592 0.947 1.2818 1.9307

DCT($MMUSD) 0 0 0 0 0

Nomenclature

Parameters

Rq , j , ki , n ,s : kg of steam, s, produced in HRSG, n, per kg of exhaust gas Gq , j , k

. n

ABGB: Constant of the linearized biogas boiler cost function

ABiogas: Constant of the linearized digestor and separation stage cost function

ABiogasCOMP: Constant of the linearized compressor cost function

ABiogasT: Constant of the linearized biogas turbine cost function

ABIO−HRSG: Constant of the linearized HRSG cost function

Ac: Constant of the linearized biomass boiler cost function

ACOMP: Constant of the linearized compressor cost function

55

Agas: Constant of the linearized gasification and reforming cost function

Aheliostat: Heliostat area (m2)

AHRSG: Constant of the linearized HRSG cost function

AOpbiogas: Constant of the linearized digestor and separation stage operation cost function

AOpgas: Constant of the linearized gasification and reforming operation cost function

A sb: Constant of the linearized syngas boiler cost function

AT : Constant of the linearized gas turbine cost function

BBGB: Independent term of the linearized biogas boiler cost function

Bbiogas: Independent term of the linearized digestor and separation stage cost function

BBiogasCOMP: Independent term of the linearized compressor cost function

BBiogasT : Independent term of the linearized biogas turbine cost function

BBIO−HRSG: Independent term of the linearized HRSG cost function

Bc: Independent term of the linearized biomass boiler cost function

BcMAX: Maximum biomass flowrate that biomass boiler can process (kg/s)

BCOMP: Independent term of the linearized compressor cost function

Bgas: Independent term of the linearized gasification and reforming cost function

BHRSG: Independent term of the linearized HRSG cost function

BOpbiogas: Independent term of the linearized digestor and separation stage operation cost function

BOpgas: Independent term of the linearized gasification and reforming operation cost function

BqMAX: Maximum biomass flowrate that gasifier can process (kg/s)

Bsb: Independent term of the linearized syngas boiler cost function

BT: Independent term of the linearized gas turbine cost function

Cbio: Biomass cost ($/kg)

CHeliostat: Cost of heliostat ($ USD/m2)

CMsalt: cost of molten salt ($ USD/kg)

56

COpCSP: Operating cost of CSP plat ($USD/kWh)

Cops : Operation cost of steam, s ($USD/s)

Cpsalt: Molten salt heat capacity (kJ/Kg °C)

DMAX: Maximum capacity of HRSG (kg/s)

FMAX: Maximum steam flowrate in biomass boiler (kg/s)

hsun: Insolation hours per day (h/day)

HT,P: enthalpy of steam at temperature T and Pressure P (kJ/kg)

H y: Hours per year

K A k

biogas: kg of Air required in the gas turbine, k, per kg of methane fed

K A q, j ,k: kg of Air required in the gas turbine, k, per kg of syngas, SY q , j

KCD k

biogas: kW of cooling required in the gas turbine k per kg of methane fed

KCDq , j ,k: kW of cooling required in the gas turbine k per kg of syngas SY q , j

K Dq: kg of Flue gas, Dq, per kg of biomass processed in gasification, q

KGk

biogas: kg of exhaust gas in the gas turbine, k, k per kg of methane fed

KGq , j, k: kg of exhaust gas in the gas turbine, k, per kg of syngas, SY q , j

KOq , j: kg of oxygen required in reforming q,j per kg of biomass processed

KOX q: kg of oxygen required in gasification q per kg of biomass processed

K pk

biogas: kW produced in the gas turbine k per kg of methane fed

K Pq, j ,k: kW produced in the gas turbine k per kg of syngas SY q , j

KST q: kg of steam required in gasification q per kg of biomass processed

KSY q , j: kg of SY q , j per kg of biomass processed by gasification q and reforming j

KW q , j: kg of steam required in reforming q,j per kg of biomass processed

K Ammoiaz : kg of ammonia produced per kg of waste z fed to digestor

KCH 4z : kg of methane produced per kg of waste z fed to digestor

KCO 2z : kg of carbon dioxide produced per kg of waste z fed to digestor

57

K F: constant to annualize investment cost

K H: constant of cost function

Kwz : kg of water produced per kg of waste z fed to digestor

LHV c: Lower heating value of biomass (kJ/kg)

LHV CH 4: Lower Heating Value of methane (kJ/kg)

LHV q , j: Lower heating Value of SY q , j (kJ/kg)

Pms : Steam pressure in unit m (bar)

Ps: Pressure of steam, s (bar)

RDq

n , s: kg of steam, s, produced per kg of flue gas, Dq,in HRSG, n.

Rk , ns ,biogas: kg of steam, s, generated in HRSG ,n, per kg of exhaust gas,Gk , n

biogas.

Rq , j , kn , s : kg of steam, s, generated in HRSG ,n, per kg of exhaust gas, Gq , j , k

n .

SY MAX: Maximum syngas flowrate allowed in gas turbine and syngas boiler (kg/s)

T ms : Steam temperature in unit m (°C)

TOT q , j ,k: Gas turbine temperature outlet

T s: Temperature of steam, s (°C)

Tsalt1: Temperature of molten salt at storage tank 1 (°C)

Tsalt11: Temperature of molten salt at storage tank 2 (°C)

Tv: Steam temperature (°C)

UEC: Global coefficient heat transfer of unit EC (kW/m2 °C)

Um: Global coefficient heat of unit m (kW/m2°C)

ηfield: Efficiency of solar field

λ (T, P): Latent heat of steam at temperature T and pressure P (kJ/kg)

ηeff : Turbine efficiency

∆ T W: Temperature difference in Cooling tower (°C)

∝: Exponent of cost function

58

B: Constant of linearized cost function

C: independent term of linearized cost function

H (T s , P s ): Steam enthalpy at temperature T s and pressure Ps(kJ/kg)

rad: average annual solar radiation (kWh/m2day)

K : Constant of cost function

Variables

∆ T Pinchn : Pinch point temperature of HRSG, n (°C)

Acu n: Area of Heat exchanger CUn (m2)

AEC: Area of heat exchanger EC (m2)

Airkbiogas: Air required in the gas turbine, k, which uses biogas to produce power (kg/s)

Airq , j , k: Air required in the gas turbine, k, which uses syngas, SY q , j, to produce power (kg/s)

Am: Heat transfer area of unit m (m2)

Amax: Maximum area of solar field allowed (m2)

Asolar field: Area of solar field (m2)

BBCOST: Total cost of the biomass boiler ($USD)

Bc: Biomass flowrate processed in biomass boiler (kg/s)

BGBCOST: biogas boiler cost ($USD)

Bq , j: Biomass processed by gasification q and reforming j (kg/s)

Bq: Biomass flowrate processed by gasification q (kg/s)

CDbiogas: Total cooling requirements of biogas processing (kW)

CDbiomass: Total cooling requirements of biomass processing (kW)

CDkbiogas: Cooling required in gas turbine, k, which uses biogas to produce power (kJ/s)

59

CDq , j ,k: Cooling required in gas turbine, k, which uses syngas, SY q , j, to produce power (kJ/s)

CEC :Cost of unit EC ($ USD)

CH 4BGB: Methane flowrate sent to biogas boiler (kg/s)

CH 4k: Methane flowrate sent to gas turbine, k (kg/s)

CH 4z: methane flowrate produced by waste z (kg/s)

Cm: Cost of unit m ($USD)

CO2z: carbon monoxide flowrate produced by waste z (kg/s)

Cost biogasz: cost of digestor and separation stage ($USD)

Cost BIO−HRSGk

n : Cost of HRSG, n, which uses the exhaust gas, Gk , nbiogas ($ USD)

CostCOMP q, j ,k: Compressor cost used to compress the syngas, SY q , j ,k($USD)

CostCU n: Cost of unit CUn ($USD)

Cost DHRSGq

n : Cost of HRSG, n, which uses the flue gas, Dqn ($ USD)

CostGasq , j: Reforming and gasification cost ($ USD)

Cost HRSGq, j ,k

n : Cost of HRSG, n, which uses the exhaust gas, Gq , j , kn ($ USD)

Cost SBq, j

reheatn: Cost of steam reheating, reheat_n, in the syngas boiler ($USD)

Cost SBq, j

s : Syngas boiler cost which uses syngas, SY q , j to produce steam, s ($ USD)

CostT q , j ,k: Gas turbine cost which uses syngas, SY q , j ($ USD)

Cost BGBreheatn: Cost of steam reheating, reheat_n, in the biogas boiler ($USD)

Cost BGBs : Biogas boiler cost to produce steam, s ($ USD)

Cost Biogas Compk: cost of compressor used in biogas turbine, k ($USD)

Cost Biogas Turbinek: cost of the biogas turbine, k ($USD)

Cost creheatn¨: cost of steam reheating, reheat_n, in the biomass boiler ($USD)

Cost cs: Biomass boiler cost to produce steam, s ($ USD)

C reheatCSP : cost of reheating steam using molten salts ($ USD)

60

C steamCSP : cost of steam generation section ($ USD)

Dq: Flue gas flowrate leaving combustor chamber in IG (kg/s)

Dqn: Flue gas flowrate used in HRSG, n, to produce steam (kg/s)

FDq

n ,s: Steam, s, flowrate generated in HRSG, n by recovery heat from flue gas, Dq (kg/s)

FSBq , j

s : Flowrate of steam, s, produced by a syngas boiler which uses syngas, SY q , j (kg/s)

F (unit1 , unit2 )s : Flowrate of steam, s, from unit1 to unit2 (kg/s)

FA: Flowrate of stream A (kg/s)

FB: Flowrate of stream B (kg/s)

FBGBs : Flowrate of steam, s generated in biogas boiler (kg/s)

Fbiogass : Total of steam, s, flowrate produced by biogas processing (kg/s)

Fbiomasss : Total of steam, s, flowrate produced by biomass processing (kg/s)

F cs: Flowrate of steam, s generated in biomass boiler (kg/s)

FCSPMP : MP steam produced by CSP technology (kg/s)

FCSPs : Production of the steam ,s , by the CSP technology (kg/s)

FCSPT : Water flowrate in CSP technology (kg/s)

F k ,ns ,biogas: Flowrate of steam, s, produced in HRSG, n, by using exhaust gas, Gk , n

biogas.

Fmax: Maximum steam flowrate allowable in the steam turbine (kg/s)

Fmn ,g: Flowrate of exhaust gas in unit m of HRSG, n (kg/s)

Fmn ,s: Steam flowrate in unit, m, of HRSG, n (kg/s)

Fq , j ,kn ,s : Flowrate of steam, s, produced in HRSG, n, by using exhaust gas,Gq , j , k

n .

F reheat1

HP, CSP: HP steam flowrate in reheating_1 (kg/s)

F reheat n

s , BGB: steam flowrate to be reheated in the biogas boiler (kg/s)

F reheat n

s ,C : steam flowrate to be reheated in the biomass boiler (kg/s)

F reheat n

s ,q , j : steam flowrate to be reheated in the syngas boiler (kg/s)

61

F reheat n

s : Flowrate of steam, s, sent to reheat n (kg/s)

F reheatsalt : Flowrate of molten salt to reheat steam (kg/s)

F salt: Flowrate of molten salt to produce steam (kg/s)

FTsalt: Total flowrate of molten salts (kg/s)

Gk , nbiogas: Flowrate of exhaust gas, Gk , n

biogas, which is used in HRSG, n (kg/s)

Gkbiogas: exhaust gas from the gas turbine, k, which uses biogas to produce power (kg/s)

Gq , j , k: exhaust gas from the gas turbine, k, which uses syngas, SY q , j, to produce power (kg/s)

Gq , j , ki ,n : Exhaust gas flowrate from turbine, q, j, k, in HRSG, n (kg/s)

Gq , j , kn : Flowrate of exhaust gas, Gq , j , k, which is used in HRSG, n (kg/s)

INV BIOGAS: Total investment for biogas processing ($USD)

mwater: Water cooling Flowrate (kg/s)

NH 3z: Ammonia flowrate produced by waste z (kg/s)

OpCostbiogasz: Operation cost of digestor and separation stage ( $USD/S)

OpCostGasq, j: operation cost of gasification and reforming ( $USD/S)

OX q: Oxygen required in gasification, q,(kg/s)

Oxygenq , j: Oxygen required in reforming, j, to process the syngas obtained from gasification, q, (kg/s)

Pcoq , j , k: Power required to compress air and syngas, SY q , j(kW)

Pkbiogas: Power produced in the gas turbine, k, by using biogas (kW)

Power ST: Power produced by the steam turbine (kW)

Pq , j , k: Power produced in the gas turbine, k, by using syngas, SY q , j(kW)

QSBq , j

s : Heat required to produce steam, s, in a syngas boiler which uses syngas, SY q , j (kJ/s)

QTSBq , j: Total heat of the syngas boiler which uses syngas, SY q , j (kJ/s)

QBGBs : Heat required to produce steam, s, in biogas boiler (kJ/s)

Qcollector: Heat transferred to molten salt (kJ/s)

62

Qcs: Heat required to produce steam, s, in biomass boiler (kJ/s)

QE: Heat in unit E (kJ/s)

Qmn , s: Steam heat in unit m of HRSG, n (kJ/s)

Qreheatn

BGB : Heat required to carry out the steam reheating, reheat_n, in the biogas boiler (kJ/s)

Qreheatn

C : Heat required to carry out the steam reheating, reheat_n, in the biomass boiler (kJ/s)

Qreheatn

q , j : Heat required to carry out the steam reheating, reheat_n, in the syngas boiler (kJ/s)

QreheatBGB : Heat required to carry out the steam reheating in the biogas boiler (kJ/s)

QreheatC : Total heat required to carry out the steam reheating in the biomass boiler (kJ/s)

QreheatCSP : Heat required to reheat steam (kJ/s)

Qreheatq , j : Total heat required to carry out the steam reheating in the syngas boiler (kJ/s)

QsteamCSP : Heat required to produce steam (kJ/s)

QTBGB: Total heat required to produce steam in biogas boiler (kJ/s)

QTc: Total heat in biomass boiler (kJ/s)

Qunit 1: Heat in unit1 (kJ/s)

SBCOST: Total cost of the syngas boiler ($USD)

STq: : steam required in gasification, q,(kg/s)

SY q , j ,k: Syngas flowrate SY q , j sent to gas turbine k (kg/s)

SY q , j ,sb: Syngas flowrate SY q , j sent to syngas boiler (kg/s)

SY q , j: Syngas flowrate generated by gasification q and reforming j (kg/s)

TACn: Total annualized cost of HRSG, n ($USD/year)

T mn , g: Temperature of exhaust gas in unit m of HRSG, n (°C)

Tsalt(unit1, unit2): Temperature of molten salt from unit1 to unit2 (°C)

Waste z: Flowrate of was, z, used in to produce biogas (kg/s)

Water q , j: steam required in reforming, j, to process the syngas obtained from gasification, q, (kg/s)

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WATER z: water flowrate produced by waste z (kg/s)

CostCSPTotal cost of CSP plat ($USD)

T MAX : Maximum value of temperature that the molten salt can reach (°C)

∆ TEC: Logarithmic mean temperature difference at unit EC (°C)

∆ T m: Logarithmic Mean temperature difference (°C)

B: Biomass flowrate to processed (kg/s)

CH 4: Methane flowrate produced (kg/s)

Cost BIOMASS: Total cost of biomass processing ($USD)

E: energy received by the heliostat field (kWh)

Max Wastez: maximum availability of waste, z (kg/s)

Opcost: Total Operation cost of biomass processing ($ USD/s)

OpCSP: Annualized operating cost ($ USD/year)

Powe rbiogas: Total power produced by biogas processing (kW)

Powe rbiomass: Total power produced by biomass processing (kW)

Binary variables

y ACU n

f : Binary variable to select capacity, f, of unit Cun in terms of its area

yreheatn

s , q , j : Binary variable to indicate selection of syngas boiler, which uses SYq,j , to carry out steam reheating, reheat_n

yBGB: Binary variable to select biogas boiler

yBGBs : Binary variable to indicate the production steam, s in biogas boiler

yc: Binary variable to select biomass boiler

ycs: Binary variable to indicate the production steam, s in biomass boiler

yCSP: Binary variable to select CSP plant

yCSPs : Binary variable to select the production of the steam, s, by a CSP plant

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yCTr : Binary variable to select Cooling Tower capacity, r, in terms of the total cooling

require

y Dqn : Binary variable to select HRSG, n that uses flue gas, Dq

n, to produce steam

yk , nbiogas: Binary variable to select HRSG, n, which uses exhaust gas, Gk , n

biogasto produce steam

ykbiogas: Binary variable to select gas turbine, k

yq , j , k: Binary variable to select gas turbine, k, to which syngas, SY q , j, is sent

yq , j , kn : Binary variable to select HRSG, n, which uses exhaust gas, Gq , j , k

n to produce steam

yq , j , sb: Binary variable to select syngas boiler

yq , j , sbs : Binary variable to select production of steam, s in a syngas boiler which uses

syngas, SY q , j

yq , j: Binary variable to select gasification q and reforming j

yq: Binary variabale to select gasification q

yreheatn

s , BGB: Binary variable to indicate selection of biomass boiler to carry out steam reheating, reheat_n

yreheatn

s , C : Binary variable to indicate selection of biomass boiler to carry out steam reheating, reheat_n

yreheatn

s , CSP : Binary variable to select steam reheating, reheat n , by molten salt

ySTP : Binary variable to select Steam turbine capacity, p, in terms of its Power produced

y z: binary variable to select waste, z

Sets

Cun: set for cooling units in Steam network ¿

F: sets for capacities of heat exchanger in terms of its Area ( { f|f =1 ,.. , F })

GASIFICCATION: set for gasification stage ( {q|q=IG , DG } )

NHeat: set for Heat exchanger used in HRSG ( {m|m=1 , .. ,NHeat } )

NHRSG: set for possible HRSG configuration to produce steam ( {n|n=1 , .. , NHRSG } )

P: sets for capacities of Steam turbine in terms of Power produced¿)

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R: sets for capacities of the cooling tower in terms of cooling required¿)

Reaheat_n: Set for reheats in the steam network ¿)

REFORMING: set for reforming stage ( { j| j=Pox , SR } )

STEAM: set for types of steams produced ( {s|s=LP , MP ,HP ,VHP } )

TURBINE: set for gas turbine ( {k|k=¿−10 ,>−20 ,>−50 } )

Z: set for waste used to produce biogas ( {z|z=MW ,CM } )

References

[1] Phillips, S., Aden, A., Jechura, J., Dayton, D., & Eggeman, T. (2007). Thermochemical ethanol via indirect gasification and mixed alcohol synthesis of lignocellulosic biomass (No. NREL/TP-510-41168). National Renewable Energy Lab.(NREL), Golden, CO (United States). Accessed in March 2018: http://neotericsint.com/pubs/Mixed%20Alcohols.pdf.

[2] Dutta, A., & Phillips, S. D. (2009). Thermochemical ethanol via direct gasification and mixed alcohol synthesis of lignocellulosic biomass (No. NREL/TP-510-45913). National Renewable Energy Lab.(NREL), Golden, CO (United States). Accessed in March 2018 : https://www.nrel.gov/docs/fy09osti/45913.pdf.

[3] Spath, P., Aden, A., Eggeman, T., Ringer, M., Wallace, B., & Jechura, J. (2005). Biomass to hydrogen production detailed design and economics utilizing the Battelle Columbus laboratory indirectly-heated gasifier (No. NREL/TP-510-37408). National Renewable Energy Lab., Golden, CO (US).

[4] Ulrich, G. D., & Vasudevan, P. T. (2006). How to estimate utility costs. Chem. Eng, 113(4), 66-69.

[5] Almena, A., & Martín, M. (2015). Technoeconomic analysis of the production of epichlorohydrin from glycerol. Ind. Eng. Chem. Res., 55(12), 3226-3238.

[6] Kumar, R., Sharma, A. K., & Tewari, P. C. (2015). Cost analysis of a coal-fired power plant using the NPV method. J. Ind. Eng. Int. l, 11(4), 495-504.

[7] Caputo, A. C., Palumbo, M., Pelagagge, P. M., & Scacchia, F. (2005). Economics of biomass energy utilization in combustion and gasification plants: effects of logistic variables. Biomass Bioenerg., 28(1), 35-51.

[8] Martín, M., & Grossmann, I. E. (2018). Optimal integration of renewable based processes for fuels and power production: Spain case study. Appl. Energ., 213, 595-610

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[9] Martín, L., & Martín, M. (2013). Optimal year-round operation of a concentrated solar energy plant in the south of Europe. Appl. Therm. Eng., 59(1-2), 627-633.

[10] National Renewable Energy Laboratory (NREL). (2017). Accessed in April 2018: https://www.nrel.gov/csp/solarpaces/ .

[11] Mehos, M., Turchi, C., Vidal, J., Wagner, M., Ma, Z., Ho, C., ... & Kruizenga, A. (2017). Concentrating solar power Gen3 demonstration roadmap (No. NREL/TP-5500-67464). NREL (National Renewable Energy Laboratory (NREL), Golden, CO (United States)). Accessed in March 2018: https://www.nrel.gov/docs/fy17osti/67464.pdf.

[12] International Renewable Energy Agency (IRENA). (2016). The power to Change: Solar and Wind Cost Reduction Potential to 2025. Accessed in April 2018: http://www.irena.org/publications/2016/Jun/The-Power-to-Change-Solar-and-Wind-Cost-Reduction-Potential-to-2025.

[13] International Renewable Energy Agency. (IRENA.) (2012). Renewable Energy Technologies Cost Analysis Series: Concentrating Solar Power. Comprehensive Renewable Energy, 3(2), 595–636. Available at: https://www.irena.org/documentdownloads/publications/re_technologies_cost_analysis-csp.pdf.

[14] Glatzmaier, G. (2011). Developing a cost model and methodology to estimate capital costs for thermal energy storage(No. NREL/TP-5500-53066). National Renewable Energy Laboratory (NREL), Golden, CO. Accessed in March 2018: https://www.nrel.gov/docs/fy12osti/53066.pdf.Hernández, B., León, E., & Martín, M. (2017). Bio-waste selection and blending for the optimal production of power and fuels via anaerobic digestion. Chem. Eng. Res. Des., 121, 163-172.

[14] Glatzmaier, G. (2011). Developing a cost model and methodology to estimate capital costs for thermal energy storage(No. NREL/TP-5500-53066). National Renewable Energy Laboratory (NREL), Golden, CO. Accessed in March 2018: https://www.nrel.gov/docs/fy12osti/53066.pdf.Hernández, B., León, E., & Martín, M. (2017). Bio-waste selection and blending for the optimal production of power and fuels via anaerobic digestion. Chem. Eng. Res. Des., 121, 163-172.

[15] Martín-Hernández, E., Sampat, A. M., Zavala, V. M., & Martín, M. (2018). Optimal integrated facility for waste processing. Chem. Eng. Res. Des., 131, 160-182.

[16] Perry, R.H.; Green, D.W. Perry’s Chemical Engineer’s Handbook (1997) McGraw-Hill: New York. U.S.A.

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