Involving the WaterâEnergyâFood Nexus in Integrating Low-Income

Research Article pubs.acs.org/journal/ascecg

Cite This: ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Involving the Water−Energy−Food Nexus in Integrating Low-Income and Isolated Communities Brenda Cansino-Loeza† and Jose ́ María Ponce-Ortega*,† †

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Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Francisco J. Múgica S/N, Ciudad Universitaria, Morelia, Michoacán 58060, México ABSTRACT: This work presents a general mathematical programming model for satisfying water, energy, and food needs in isolated and low-income communities involving different process integration approaches. The problem consists in determining the optimal and sustainable configuration to satisfy the energy, water, and food demands of the inhabitants. Also, the use of waste-to-energy technologies is proposed to handle the municipal solid waste correctly and obtain valuated products from wastes to reduce the environmental impact. A multiobjective analysis is presented considering the consumption of fresh water, the greenhouse gas emissions, and the cost of the integrated system as objective functions. As a case study, the community with the lowest index of poverty and marginalization from the State of Guerrero in Mexico is presented. The results show that it is possible to satisfy the water, energy, and food needs in isolated communities accounting for integrated processes. Besides, it is possible to obtain trade-off solutions considering contradicting objectives. KEYWORDS: Water−energy−food nexus, Isolated community, Polygeneration, Optimization, Multistakeholder approach, Process integration

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INTRODUCTION Water, energy, and food are critical resources for meeting the social demands and socioeconomic development of communities and societies around the world.1 Nevertheless, there are communities that do not have access to energy, and consequently, there is a lack of access to water and food.2 Many rural communities or small towns still do not have access to these resources mainly due to their geographic location that makes difficult the interconnection with the electrical grid.3 Moreover, the provision of water from the public network is a big problem. Satisfying the basic needs of inhabitants in isolated communities is a problem that is closely related to the water−energy−food nexus because the inhabitants consume considerable amounts of resources to meet their demands.4 Water, energy, and food are inextricably interrelated, and each of them depends on others.5 Interactions between these resources are presented in Figure 1. Water is required for the extraction and processing of fuels as well as for energy production,6 and it is also needed to provide cooling utilities; energy is required for the extraction, treatment, and distribution of water. In addition, water and energy are necessary resources for food production; agriculture is the activity with major consumption of water accounting for 80−90% of fresh water use;7 and energy is required in food production for processing, storage, and harvesting.8 The water−energy−food nexus is considered to achieve a sustainable development that allows maintaining the security of these resources and promote economic growth without affecting the environment considerably.9 © XXXX American Chemical Society

Figure 1. Interactions of resources in the water−energy−food nexus.

In recent years, many studies have focused on studying the water−energy−food nexus to manage more sustainable production, consumption, and distribution processes in the nexus.10 In this context, Biggs et al.11 presented a study related to Received: October 5, 2018 Revised: November 9, 2018 Published: November 14, 2018 A

DOI: 10.1021/acssuschemeng.8b05134 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering

and environmental objectives. Diaz-Barriga-Fernandez et al.36 proposed a multiobjective optimization approach for the planning of a municipal solid waste management system considering recycle, reuse, transportation, separation, and distribution of solid wastes. The management of municipal solid waste has been identified as one of the global challenges that must be carefully faced in order to achieve sustainable goals, and recent studies have focused on proposing processes that convert waste-toenergy or valuated products. Fernández-González et al.37 evaluated economic and environmental aspects of waste-toenergy systems in small municipalities studying the Life Cycle Assessment, which presents environmental benefits when this type of technologies is used. Matsakas et al.38 investigated the conversion of municipal solid waste to energy and chemicals by biological and thermochemical treatments that are among the most used technologies. Anaerobic digestion is one of the most used biological treatments because approximately 90% of the energy available from biomass is converted to methane.39 Thermochemical treatments involve incineration40 and other recent technologies such as pyrolysis41 and gasification42 that present greater efficiencies and a reduction of greenhouse gas emissions.43 However, none of the previous research has focused on studying different types of solid waste treatments in a lowincome municipality to be a community in which their needs can be met through the proper management of their resources and recycled wastes. In addition, no research has been conducted to address the integration of water−energy−food nexus and the management of solid wastes in isolated communities, which can help to reduce the environmental impact and improve the living conditions of the inhabitants. Faced with this problem, it is needed to implement a system capable of integrating the water−energy−food nexus so that the needs of the inhabitants of the isolated community can be met. In this context, a polygeneration system is an attractive option to provide electricity, heating, and cooling to the community, satisfying the energy demands making proper management of water and the resources which in turn will facilitate the food production and consequently the access to food.

sustainable development considering the water−energy−food nexus on livelihoods, analyzing the environmental security and looking for a balance between natural resources supply and the basic demands of inhabitants. Rasul12 developed strategies to manage the water−energy−food nexus in South Asian countries because there has been a rapidly growing population which in turn has caused overexploitation of natural resources. Hang et al.13 introduced an optimal design of local production systems for satisfying the demands in an eco-town located in ́ et al.14 proposed an optimization model England. López-Diaz for producing biofuels involving the water−energy−food nexus. Wa’el et al.15 presented an integrated model that considers the interactions between the water−energy−food nexus at an enduse level at a household scale contemplating the seasonal variability on the resources and the behavior and characteristics of the inhabitants. Zhang and Vesselinov5 proposed a model to integrate the interactions of the water−energy−food nexus for its security. Karan et al.16 studied the influences between water, energy, and food in a sustainable system that allows to satisfy the demands for a family. However, the inadequate management of these resources may also produce significant environmental impacts. Currently, alternative energy sources such as geothermal,17 solar,18 and wind19 have been used to decrease the environmental impact.20 Also, there have been reported several studies related to the use of renewable energies implemented in isolated communities to generate electric energy.21 Furthermore, other works have focused on distributed generation22 to produce electricity in remote places by isolated systems because the generation units are close to the consumers and the transmission energy losses are negligible;23 examples of this type of generation are polygeneration systems, which can be defined as the simultaneous production of two or more energy utilities and products, seeking to take advantage of the maximum potential of the consumed resources. Recently, polygeneration systems have been introduced to achieve systems that are increasingly efficient and sustainable. In this context, Karschin and Geldermann24 presented an optimization model for the location of a biorefinery considering a cogeneration system. Kabalina et al.25 developed a polygeneration system including a gasification process to produce syngas, char, hydrogen, and natural gas and they made an exergoeconomic analysis of the system. It has been demonstrated that polygeneration systems reduce fuel consumption,26 operational costs,27 and consequently reduce the environmental impact,28 which is associated with the greenhouse gas emissions.29 There are many studies that propose the use of different schemes of distributed generation30 to meet the energy demands at a household level.31 Other studies have been focused on integrating different processes32 to take advantage of the available resources in residential complexes.33 Nevertheless, none of the previous mentioned works has considered the water−energy−food nexus involving a polygeneration system that allows to decrease the use of fresh resources and the environmental impact in an isolated community. Another important challenge to decrease the environmental impact is to plan a sustainable waste management system. Recycling is considered as one of the best options in the solid waste management to reduce the environmental impact;34 thus, it is important to manage the municipal solid waste correctly. In this context, Santibañez-Aguilar et al.35 proposed a multiobjective optimization for the planning of a biorefinery optimizing the biomass conversion and considering economic

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PROBLEM STATEMENT This work presents a mathematical programming model for the design of a residential polygeneration system in an isolated community considering the water−energy−food nexus (Figure 2).

Figure 2. Problem statement representation in the isolated community. B


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Figure 3. Proposed superstructure.

this problem, in this paper is proposed the superstructure shown in Figure 3 to satisfy the water and electricity demands of the community.

The problem consists in determining the optimal and sustainable configuration to satisfy the water, energy, and food demands of the inhabitants. To meet energy demands, the existence of different cogeneration units and the use of renewable energies such as solar collectors, aerogenerators, and solar panels were considered. Water demand was satisfied by rainwater collection systems and wells. Wastewater generated in the community was sent to blackwater and greywater treatment plants. Pollutant balances as well as the mixed of different types of wastewater is not included in the model in order to avoid numerical and environmental complications, but it has been considered the adequate treatment for each use of water with their corresponding costs. Therefore, the treated greywater was used in gardening, cattle, and agriculture. Different types of crops and animal production were considered to satisfy the food demands of the inhabitants. The generated municipal solid wastes are separated in plastic, metal, paper, glass, and nonrecyclables, and the latter can be treated in process plants such as pelletization, incineration, gasification, pyrolysis, and anaerobic digestion to obtain pellets, steam, natural gas, and pyrolysis oil that can be used as an energy source. The economic objective function considers the minimization of the total annual cost associated with satisfy the needs of the community, which includes operating and capital costs for each needed unit and the sales associated with animals, crops, pyrolysis oil, natural gas, biogas, pellets, and recyclable products. Additionally, the environmental objective function involves the minimization of fresh water consumption and the minimization of greenhouse gas emissions produced by the cogeneration units and the process plants for nonrecyclable wastes. To solve

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MODEL FORMULATION The propose model formulation is based on the superstructure shown in Figure 3, and it is described as follows. Cogeneration Units. The proposed cogeneration units (CHP) are constituted by the Internal Combustion Engine, Fuel Cell, Microturbine and Stirling Engine. Electric (ηQu, t) and the thermal efficiency (ηEu, t) indicates the relation between products, electricity (Eu, t) or heat (Wu, t), and the fuel requirements (Fu, t): Eu , t = ηuE ·Fu , t , ∀ t , ∀ u

(1)

Wu , t = ηuQ ·Fu , t , ∀ t , ∀ u

(2)

The capacity of the CHP units is determined by the greater capacity allowed in the market (CapCHP‑MAX ), and the binary u variables (yu) indicate the existence of the CHP unit; if the binary variable is equal to one the CHP unit exists, and if it is equal to zero, then the CHP unit does not exist: CapCHP ≥ Eu , t , ∀ u , ∀ t u

(3)

‐ MAX CapCHP ≤ CapCHP ·yu , ∀ u u u

(4)

(CapCHP ) u

In this model, the lower limit for is equal to zero. In the case where the capacity is equal to zero, this indicates that the cogeneration technology is not producing energy, and its existence is not necessary in such a period. Because Eu, t C


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determined multiplying each of the streams of hot water that enter to the tank by a factor. In this way, it is possible to reach a temperature of 80 °C in the tank:

represents the demand of energy that has to be met in any period, the model focuses on selecting the units with which it is optimal to satisfy that demand and to define the remaining technologies as zero, indicating they are not necessary for its existence. Absorption Refrigeration System. An absorption refrigeration system is considered to provide the needed cooling in the community, and the produced refrigeration (WCL t ) is calculated by the refrigeration factor (αAC) and the inlet hot water: W tCL = α AC·W tST‐AC , ∀ t

WtFresh‐T =

u

(15)

In addition, the water sent to the community must have a suitable temperature for sanitary use, which is determined by the amount of fresh water that is supplied to reach a temperature of 40 °C:

(5) AC

The capacity of the absorption refrigeration system (Cap ) must be greater than the maximum refrigeration required in a given time period, and it must be lower than the greatest refrigeration needed (CapAC‑MAX) multiplied by their associated binary variable: Cap AC ≥ W tCL , ∀ t

Cap

AC

≤ Cap

·y

AC

W tSC = Q tSC/Cp·ΔT , ∀ t

(9)

A

SC‐MAX

≤A

·y

SC

ρ

(V tST

−

V tST − 1)

EtRE = EtSP + EtAG , ∀ t

(10)

=

∑ Wu ,t +

W tSC

+

ASP ≤ ASP‐MAX ·y SP

Cap

≤ Cap

E AG = CP max ·ρair ·Arotor · Speedt 3, ∀ t

Arotor ≤ Arotor ‐ MAX ·y AG

(24)

Electricity Produced in the Cogeneration Units. The total electricity produced in the cogeneration units (ECHP ) is t equal to the sum of the electricity produced by each of the units of the cogeneration system and, it is used to satisfy the demands of the community, cattle (ECHP‑cattle ) and agriculture t (ECHP‑agriculture ): t

(13)

Supply of Hot Water to the Community. The steam generated in the incineration plant (Stt) is utilized to heat water that will be sent to the thermal storage tank (WFresh‑St ): t WtFresh‐St = τ HW ·St t , ∀ t

(23)

The installation of the aerogenerator is limited by the maximum area available for installation (Arotor‑MAX):

(12)

·y

(22)

The energy generated by the aerogenerator is a function of the wind speed, and it is determined by the following equation, where CPmax is the maximum power coefficient, and Arotor is the rotor area of the aerogenerator.

The water storage level in the period of time t is equal to the addition of the water stored in the time period t − 1 plus the water sent to the tank coming from the cogeneration units minus the water sent to the community and the water sent to the absorption refrigeration system. The size of the tank (CapST) is determined by the maximum level of stored water (VST t ) and for the maximum capacity available in the market.

ST

(21)

The size of the solar panel is limited by its available installation area (ASP‑MAX): (11)

ST‐MAX

(20)

EtSP = ASP ·ηSP ·ht ·PR, ∀ t

WtFresh‐St

+ WtFresh‐T − W tST‐AC − W tST , ∀ t

ST

(19)

The electricity produced by the solar panel is calculated as the product of the area (ASP) times its efficiency (ηSP), times the solar radiation factor (ht), and times the performance coefficient (PR):

u

CapST ≥ V tST , ∀ t

(18)

Electricity Generated by the Renewable Energies. The use of renewable energies such as solar panels and aerogenerators to produce electricity is proposed:

Thermal Storage Tank. A thermal storage tank is considered to synchronize the electricity and hot water demands of the cogeneration units. The mass balance in the thermal storage tank is modeled as follows: w

(17)

WtTotal‐IC = WtIC + WtRWSS‐IC , ∀ t

The dimensioning of the solar collector is limited by the available area for its installation: SC

WtIC = WtFresh‐IC + W tST , ∀ t

Water Balance in the Isolated Community. To satisfy the water demands in the community (WTotal‑IC ), both water t coming from the thermal storage tank (WIC t ) plus the water provided by the rainwater collector system (WRWSS‑IC ) are t used:

Solar Collector. A solar collector can help to satisfy the thermal energy demands. The heat provided by the solar collector is function of the solar radiation factor (αt) and the area of the solar collector (ASC): (8)

(16)

WtTFresh‐IC = WtFresh‐T + WtFresh‐IC , ∀ t

(7)

Q tSC = αt ·ASC , ∀ t

WtFresh‐IC = λ Fresh‐IC ·W tST , ∀ t

Therefore, the flow of water used to regulate the supply temperature to the community, as well as to the tank, is calculated as follows:

(6)

AC‐MAX

∑ λu ·Wu ,t + λSC·W tSC + λSt ·WtFresh‐St , ∀ t

(14)

EtCHP =

(WFresh‑T ) t

The inlet fresh water of the thermal storage tank has the function of set the temperature of the tank, which is

∑ Eu ,t , ∀ t u

D

(25) DOI: 10.1021/acssuschemeng.8b05134 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

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ACS Sustainable Chemistry & Engineering EtCHP = EtCHP‐RE + EtCHP‐cattle + EtCHP‐agriculture , ∀ t

Fresh-Water Balance. The fresh water consumed (WFresh ) t is determined by adding the water sent to the thermal storage tank, the solar collector, the community, the absorption refrigeration system, the water sent to each cogeneration unit, and the water extracted by the wind and photovoltaic pumping systems:

(26)

Electricity Supplied to the Community. The electricity supplied to the community is equal to the sum of the electricity generated by renewable energies (ERE t ) plus the electricity produced in the cogeneration units (ECHP‑RE ): t EtTotal ‐ IC = EtRE + EtCHP‐RE , ∀ t

WtFresh = WtFresh‐St + W tSC + WtTFresh‐IC +

(27)

u

Rainwater Collecting Systems. To determine the amount of harvested rainwater in the community in a time period (WRW‑IC ), the collecting area (ARW‑IC) is multiplied by t the precipitation in that period (Pcpt): WtRW‐IC = ARW‐IC ·Pcpt , ∀ t

+

RW

=A

A

RW ‐ IC ‐ MAX

≤A

·y

ARW ≤ ARW ‐ MAX ·y RW

W tGWT = αGWT·WtIC‐GW , ∀ t

Cap

RWSS

≥

WtRW ,

The outlet greywater is distributed to satisfy the water demands in agriculture, gardening and cattle:

(31)

W tGWT = W tGW‐cattle + W tGW‐agriculture + W tGW‐garden , ∀ t (42)

The capacity of the treatment plant must be greater than the inlet water to the treatment plant:

(32)

∀t

CapGW ≥ WtIC‐GW , ∀ t

(33)

Cap

RWSS

≤ Cap

RWSS‐MAX

·y

CapGW ≤ CapGW‐MAX ·yGW

(34)

RWSS

Balance in the Rainwater Storage System. The stored water in the rainwater storage system over the period of time t (WRWSS−IC ) is equal to the stored water at the end of previous t time period (WRWSS‑IC ) plus the inlet water to the storage t−1 system (WRW‑IC ): t

WtIC‐BW = α BW ·WtTotal‐IC , ∀ t

=

WtRWSS −1

+

WtRW

−

WtRW‐cattle

WtBWT = α BWT·WtIC‐BW , ∀ t

(36)

−

− WtRW‐garden , ∀ t

(46)

The capacity of the blackwater treatment plant must be lower than the maximum capacity of water that can be treated multiplied by the associated binary variable:

WtRW‐agriculture

CapBW ≥ WtIC‐BW , ∀ t

(47)

CapBW ≤ CapBW‐MAX ·y BW

(48)

Photovoltaic Pumping. The amount of water pumped through the photovoltaic pumping system (WPPump pw, t ) can be distributed either to agriculture or to cattle where the wells are adequate for installing the photovoltaic pumping system:

(37)

Water Balance in Gardening. To satisfy the water ), both the water provided by demands in gardening (Wgarden t the rainwater system (WRW‑garden ) and by the greywater treatt ment plant (WGW‑garden ) are used: t W tgarden = WtRW‐garden + W tGW‐garden , ∀ t

(45)

The treated wastewater is equal to the inlet water into the blackwater treatment plant (WtIC‑BW) multiplied by the blackwater factor (αBWT):

The stored water in the rainwater storage system over the period of time t (WRWSS ) is equal to the stored water at the end t of previous time period (WRWSS t − 1 ), plus the inlet water to the storage system (WRW ), minus the outlet water from the storage t system that is sent to cattle (WRW‑cattle ), agriculture (WRW‑agriculture ) t t RW‑garden and gardening (Wt ): WtRWSS

(44)

Blackwater Treatment Plant. The blackwater generated in the isolated community (WIC‑BW ) is equal to the inlet water t to the community times the blackwater factor (αBW):

(35)

‐IC WtRWSS‐IC = WtRWSS + WtRW‐IC , ∀ t −1

(43)

The capacity of the greywater treatment plant must be lower than the maximum capacity of water that can be treated multiplied by the associated binary variable:

To determine the existence of the thermal storage tank, binary variables and the maximum capacity available are used as follows: CapRWSS‐IC ≤ CapRWSS‐IC‐MAX ·y RWSS‐IC

(41)

(30)

Rainwater Storage Tank. The capacity of the rainwater storage system should be greater than the water stored over the considered periods: CapRWSS‐IC ≥ WtRW‐IC , ∀ t

(40)

The greywater treated is equal to the inlet water to the treatment plant (WIC‑GW ) multiplied by the greywater factor t (αGWT):

(29)

RW‐IC

∀t (39)

ww

WtIC‐GW = αGW ·WtTotal‐IC , ∀ t

The existence of the rainwater collector is function of the collection area and it is determined by its binary variable and the maximum area available to install the collector: RW‐IC

∑

+

WPump Www, , t

Greywater Treatment Plant. The greywater generated in the isolated community (WIC‑GW ) is modeled using a greywater t conversion factor (αGW) multiplied by the amount of water that enters to the community:

(28)

·Pcpt , ∀ t

∑

PPump Wpw, t

pw

In the same way, the amount of water harvested for cattle, agriculture, and gardening (WRW t ) is determined as follows: WtRW

∑ Wu ,t

PPump PPump‐agriculture Ppump‐cattle ∑ Wpw, = ∑ Wpw, + ∑ Wpw, ,∀ t t t pw

pw

t , ∀ pw

(38) E

pw


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ACS Sustainable Chemistry & Engineering CapPP pw

PP

PPump ≥ Wpw, t , ∀ t , ∀ pw

(50)

PP CapPP ≤ CapPP‐MAX ·ypw , ∀ pw pw

(51)

Where the production of animals is determined by the amount of food needed (foodaa, t) multiplied by the growth factor (ϕgrowth ). a The amount of food needed for each type of animal is limited by the minimum and maximum needed food.

Wind Pumping. The amount of water pumped through the wind pumping system (WWPump pw, t ) can be sent to agriculture or to cattle where the wells are adequate for installing the wind pumping system:

∑

WPump Www, t

ww

=

∑

WPump‐agriculture Www, t

+

ww

∑

WPump‐cattle Www, , t

MAX fooda aMIN , t ≤ foodaa , t ≤ fooda a , t

Municipal Solid Waste Balance. The total of solid wastes Total generated per type (MSWr,t ) is equal to the sum of the solid waste generated in the community, cattle, agriculture, and gardening, which is modeled as follows:

∀ t , ∀ ww

ww

(52) WP WPump Cap ww ≥ Www, , ∀ t , ∀ ww t

WP Cap ww

≤ Cap

WP‐MAX

WP ·yww ,

MSWrTotal = MSWrIC, t + MSW cattle + MSW agriculture ,t r ,t r ,t

(53)

∀ ww

+ MSW rgarden , ∀ r, ∀ t ,t

(54)

y WPump‐agriculture z zz = + ∑ Www, zz t z ww {

∑

PPump‐agriculture ∑ Wpw, t

PEL MSWrTotal + MSW GAS + MSW tPYR + MSWtIN = 1, t = MSW t t

pw

W ccrop ,t ,

+ MSWtAD, ∀ t

c

(55)

Water required for each crop is calculated multiplying the crops produced per area (cropc, t) times the production crop factor (φc):

PtPEL = δ PEL·MSW tPEL , ∀ t

The crop production (cropc, t) is calculated as the product of the type of crop produced per area (cc, t) times the area of each crop (Ac): (57)

a

yz WPump‐cattlez zz ∑ Www, zz t z ww {

=

∀ a, ∀ t

(59)

(68)

CapGAS ≥ MSW GAS ,∀t t

(69)

CapGAS ≤ CapGAS‐MAX ·yGAS

(70)

Ftpyrolysis‐oil = δ PYR ·MSW tPYR , ∀ t

(71)

The capacity of the pyrolysis unit must to be greater than the inlet solid wastes and must be lower than the maximum capacity of treated solid wastes.

(60)

The produced animals (aa, t) are determined using the following equation: aa , t = foodaa , t · ϕagrowth , ∀ a , ∀ t

(67)

Pyrolysis Plant. The produced pyrolysis oil is calculated as the pyrolysis oil conversion factor multiplied by the nonrecyclable wastes treated in the pyrolysis plant:

The water needed in cattle is calculated as the product of the factor that represents the water required by each type of animal (ϕwreq a ) times the type of animals: aa , t · ϕawreq ,

CapPEL ≤ CapPEL‐MAX ·y PEL

The capacity of the gasification unit must be greater than the inlet solid wastes and lower than the maximum capacity for treating solid wastes:

(Wcattle‑req ) a, t

‐req W acattle ,t

(66)

Ftgasification = δ GAS·MSW GAS ,∀t t

(58)

Water Required in Cattle. The water required in cattle (Wcattle‑req ) is constituted by the water provided by the a, t greywater treatment plant, rainwater collector, photovoltaic, and wind pumps: ij jj GW‐cattle PPump‐cattle jjW t + WtRW‐cattle + ∑ Wpw, + t jj pw k ‐req = ∑ W acattle , ∀ a, ∀ t ,t

CapPEL ≥ MSW tPEL , ∀ t

Gasification Plant. The produced natural gas is calculated as the gas conversion factor multiplied by the nonrecyclable wastes treated in the gasification plant:

Where the production of each crop is limited by the minimum (θC‑MIN ) and maximum production (θC‑MAX ), which depend on c, t c, t the crop demands. C‐MAX θcC, t‐MIN ≤ cc , t ≤ θc,t , ∀ c, ∀ t

(65)

The capacity of the pelletization unit must to be greater than the inlet solid wastes and must to be lower than the maximum capacity for treating solid wastes:

(56)

cropc , t = cc , t · Ac , ∀ c , ∀ t

(64)

Pelletization Plant. The produced pellets are calculated as the pelletization conversion factor (δPEL) multiplied by the nonrecyclable wastes treated in the pelletization plant (MSWPEL t ):

∀t

W ccrop , t = cropc , t · φc , ∀ c , ∀ t

(63)

Distribution for Solid Wastes. Solid wastes are classified according to their types in nonrecyclable, metals, glass, plastic and paper, where the nonrecyclables are sent to different processes such as pelletization, gasification, pyrolysis, incineration and anaerobic digestion to obtain valuated products:

Water Required in the Agriculture. The water required in agriculture is determined by the water required for each crop (Wcrop c, t ): jij GW‐agriculture jjW + WtRW‐agriculture + jj t j k

(62)

(61) F

CapPYR ≥ MSW tPYR , ∀ t

(72)

CapPYR ≤ CapPYR‐MAX ·y PYR

(73)


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ACS Sustainable Chemistry & Engineering Incineration Plant. The steam produced is calculated as the steam conversion factor multiplied by the nonrecyclable wastes treated in the incineration plant: St t = δ IN·MSWtIN , ∀ t

Capital costs of solar collector CapCostSC = FCostSC·y SC + VCostSC ·ASC

Capital costs of solar panel

(74)

CapCostSP = FCostSP·y SP + VCostSP ·ASP

The capacity of the incineration unit must be greater than the inlet solid wastes and must be lower than the maximum available capacity of solid waste treatment unit. Cap

IN

≥

MSWtIN

CapCostAG = FCostAG·y AG + VCostAG ·Arotor

(76)

CapCostGW = FCostGW ·yGW + VCostGW · CapGW (90)

Capital costs of blackwater treatment plant

(77)

CapCostBW = FCostBW ·y BW + VCostBW · CapBW

The capacity of the anaerobic digestion unit must be greater than the inlet solid wastes and must be lower than the maximum capacity to treat solid wastes. Cap

AD

≥

MSWtAD,

∀t

Cap AD ≤ Cap AD‐MAX ·y AD

(91)

Capital costs of rainwater harvesting systems

(78)

CapCostRW = FCostRW ‐ IC· y RW‐IC + VCostRW‐IC · ARW‐IC

(79)

+ CapRWSS‐IC · VCostRWSS ‐ IC + FCostRW · y RW + VCostRW · ARW

Pellet Stoves. The produced pellets are sent to meet the demands of the community, which are equal to the sum of the pellets used by each pellet stove over a given time period (PIC t ): PtPEL = PtIC , ∀ t

+ CapRWSS · VCostRWSS

Cap

≥

PtIC ,

∀t

CapCostGAS = FCostGAS·yGAS + VCostGAS · CapGAS (93)

Capital costs of pelletization plant CapCostPEL = FCostPEL ·y PEL + VCostPEL · CapPEL

(81)

CapPS ≤ CapMAX ·y PS

(94)

(82)

Capital costs of pyrolysis plant

Produced Biofuels. The biofuel production is represented by the natural gas produced in the gasification plant and the anaerobic digestion plant: FtBF

=

Ftgasification

+

Ftad ,

∀t

CapCostPYR = FCostPYR ·y PYR + VCostPYR · CapPYR (95)

(83)

Capital costs of incineration plant

Fuel Balance. The fuel supplied to the cogeneration units (Fu, t) is equal to the sum of the amount of biofuel produced NG (FBF t ) plus the amount of natural gas consumed (Ft ):

∑ Fu ,t = FtBF + FtNG , ∀ t u

CapCostIN = FCostIN·y IN + VCostIN · CapIN

(96)

Capital costs of anaerobic digestion plant CapCostAD = FCostAD·y AD + VCostAD· Cap AD

(84)

(97)

Capital Costs. Capital costs are constituted by the fixed cost of each of the units (FCost) multiplied by their binary variables plus the variable cost for each unit (VCost) multiplied by its capacity. This way, for each unit, the corresponding capital cost is determined as follows: Capital costs of CHP Units CapCostCHP =

(92)

Capital costs of gasification plant

(80)

In addition, the capacity of the pellet stove must be greater than the pellets that can be supplied for its operation and must be lower than the maximum available capacity of the pellets: PS

(89)

Capital costs of greywater treatment plant

Anaerobic Digestion Plant. The biogas produced is calculated as the biogas conversion factor multiplied by the nonrecyclable wastes treated in the anaerobic digestion plant: Ftad = δ AD·MSWtAD, ∀ t

(88)

Capital costs of aerogenerator

(75)

CapIN ≤ CapIN‐MAX ·y IN

(87)

Capital costs of wind pumping CapCostWP =

WP WP + VCostWP · Cap ww ) ∑ (FCostWP·yww ww

(98)

Capital costs of photovoltaic pumping

) ∑ (FCostu·yu + VCost u ·CapCHP u

CapCostPP =

u

(85)

PP + VCostPP · CapPP ) ∑ (FCostPP·ypw pw pw

(99)

Capital costs of absorption refrigeration system Capital costs of thermal storage tank

CapCostAC = FCostAC·y AC + VCostAC · Cap AC

CapCostST = FCostST·y ST + VCostST · CapST

(86) G

(100)


Research Article


OMCostPEL = UCOMPEL ∑ MSW tPEL

Capital cost of pellets stoves CapCostPS =

) ∑ (FCostPS·ysPS + VCostPS·CapPS s s

OMCostPYR = UCOMPYR ∑ MSW tPYR

Total Capital Cost. The total capital cost is the sum of all the capital costs and it is determined as follows: CHP

TCapCost = CapCost

AC

+ CapCost + CapCost BW

+ CapCost

+ CapCost

+ CapCost

ST

+ CapCost

OMCostAD = UCOMAD ∑ MSWtAD

GAS

+ CapCost

PYR

+ CapCost

AD

+ CapCost

+ CapCost

+ CapCost

OMCostWP =

(102)

OMCostPP =

(103)

ij

ij

u

{

t

t

OMCost

AC

= UCOM

∑

W tCL

t

+ OMCostIN + OMCostAD

OMCost

BWT

= UCOM

∑

WtIC‐BW

t

(105)

t

(106)

SalesC =

∑ USCc ·∑ cc ,t c

(107)

(119)

t

Animal sales SalesA =

∑ USCa ·aa

(120)

a

Pellets sales

(108)

SalesPellets = USCPEL ·∑ PtPEL t

SalesOil = USCPYR‐OIL ·∑ Ftpyrolysis‐oil

(109)

t

OMCost

= UCOM

GAS

∑ t

MSW GAS t

(121)

Pyrolysis oil sales

Operation and maintenance costs of municipal solid waste processing plants GAS

(117)

Sales. The profit obtained for the sale of the products is equal to the quantity of sold products multiplied by their unitary costs. This way, the different sales are stated as follows: Crop sales

Operation and maintenance costs of greywater treatment plant OMCostGWT = UCOMGWT ∑ WtIC‐GW

(116)

Total Annual Cost. The total annual cost (TAC) is equal to the total operating cost (TOCost) plus the total capital cost (TCostCap): TAC = TCapCost + TOCost (118)

Operation and maintenance costs of blackwater treatment plant BWT

{

+ OMCostGAS + OMCostPEL + OMCostPYR

Operation and maintenance costs of absorption refrigeration system AC

t

+ OMCostGWT + OMCostWP + OMCostPP

Operation and maintenance costs of solar collector OMCostSC = UCOMSC·∑ W tSC

k

+ OMCostSC + OMCostAC + OMCostBWT

yz

k

yz

TOCost = OCostFreshW + OCostNG + OMCostCHP

(104)

∑ jjjjjUCOMu·∑ Eu ,t zzzzz

(115)

Total Operating Cost. The total operating cost is constituted by the operation cost of fresh water, natural gas, and the operation and maintenance costs of all the process:

Operation and Maintenance Costs. Operation and maintenance costs of all the process are calculated on the basis of their production as follows: Operation and maintenance costs of CHP units OMCostCHP =

{

t

PP z z ∑ jjjjjUCOM PP pw · ∑ Wpw, t z zz pw

Natural Gas. The natural gas cost (OCost ) is equal to the natural gas unitary cost (UCNG) multiplied by the natural gas used in each of the CHP units: t

k

Operation and maintenance cost of photovoltaic pumping

NG

OCostNG = UCNG · ∑ FtNG

yz

WP WP z z ·∑ Www, ∑ jjjjjUCOM ww tz zz ww

• Operating Costs Fresh Water. The fresh water cost (OCostFreshW) is equal to the fresh water unitary cost (UCFreshW) multiplied by the water extracted from the wells: t

ij

Operation and maintenance cost of wind pumping

+ CapCostWP

OCostFreshW = UCFreshW ·∑ WtFresh

(114)

t

IN

+ CapCostPP + CapCostPS

(113)

t

GW

RW

PEL

OMCostIN = UCOMIN ∑ MSWtIN

+ CapCost

AG

(112)

t

SC

+ CapCost

SP

(111)

t

(101)

(122)

Biofuel sales SalesGas = USCGAS ·∑ Ftgasification

(110)

t

H

(123)


Research Article


Figure 4. Case study representation.

SalesAd = USCAD·∑ FtAD t

Table 1. Main Parameters for the Proposed Process (124)

parameter

Recyclable products sales 5

SalesRP =

∑ ∑ USCr ·MSWrTotal ,t t

r=2

(125)

Greenhouse Gas Emissions. The greenhouse gas emissions are calculated through multiplying the emission factor (γ) associated with each of the CHP units by the natural gas flow supplied to the unit: • CHP units GHGECHP = γ CHP· ∑ Fu , t t

(126)

The greenhouse gas emissions of the process plants are calculated through multiplying the emission factor associated with each of the process plant times the quantity of treated solid wastes: • Pelletization plant GHGEPEL = γ PEL· ∑ MSW tPEL t

(127)

• Gasification plant GHGEGAS = γ GAS· ∑ MSW GAS t t

(128)

GHGE

=γ

reference Al-Jayyousi46 Núñez-López et al.33 Al-Jayyousi46 Núñez-López et al.33 Núñez-López et al.33 Fuentes-Cortés Fuentes-Cortés Fuentes-Cortés Fuentes-Cortés

et et et et

al.32 al.32 al.32 al.32

Fuentes-Cortés Fuentes-Cortés Fuentes-Cortés Fuentes-Cortés

et et et et

al.32 al.32 al.32 al.32

Fuentes-Cortés et al.32 Fuentes-Cortés et al.32 Fuentes-Cortés et al.32 Fuentes-Cortés et al.32 MSW) Czajczynska et al.47 Núñez-López et al.33 Irving et al.48 Weiland et al.49

• Incineration plant

• Pyrolysis plant PYR

value

blackwater generated factor 0.2 conversion factor of the blackwater 0.85 treatment plant greywater generated factor 0.8 conversion factor of the greywater 0.93 treatment plant refrigeration factor 0.85 Electrical Efficiency internal combustion engine 37.25 microturbine 26 fuel cell 38 stirling engine 30 Thermal Efficiency internal combustion engine 47.5 microturbine 47.5 fuel cell 50 stirling engine 60 Maximum Capacity internal combustion engine 15 800 microturbine 12 500 fuel cell 2000 stirling engine 1500 Processing Factor (kg Product/kg pyrolysis 0.581 gasification 0.15 incineration 5.5 anaerobic digestion 0.25

PYR

·∑

MSW tPYR

t

GHGEIN = γ IN· ∑ MSWtIN

(129)

t

Profit. The total profit of the system (Profit) is constituted by the sum of the product sales like crops, animals, pellets, pyrolysis oil, natural gas, biogas, and recyclable products minus the total annual cost.

• Anaerobic digestion plant GHGEAD = γ AD· ∑ MSWtAD t

(131)

(130) I


Research Article


Figure 5. Representation of feasible solutions and individual objectives for the addressed case study.

Table 2. Results Obtained for the Different Scenarios Evaluated concept

min water

min GHGE

max profit

cost ($/year) fresh water (m3/year) GHGE (ton CO2/year) TAC ($) Sales ($) MSWAD (kg msw/year) MSWGAS (kg msw/year) MSWIN (kg msw/year) MSWPEL (kg msw/year) MSWPYR (kg msw/year) Eu (kWh/year) ICE MT FC SE ESP (kWh/year) FBF (m3/year) FNG (m3/year) WIC (m3/year) WBWT (m3/year) WGWT (m3/year) WGW‑agriculture (m3/year) WGW‑cattle (m3/year) WGW‑garden (m3/year) WPPump (m3/year) WPPump‑agriculture (m3/year) WPPump‑cattle (m3/year) WWPump (m3/year) WWPump‑agriculture (m3/year) WWPump‑cattle (m3/year) WRW (m3/year) WRWSS (m3/year) WRW‑agriculture (m3/year) WRW‑cattle (m3/year) WRW‑garden (m3/year) WSC (m3/year)

161 000 000 3 060 000 147 400 000 183 940 000 22 924 414 0 0 6,762 4275 115 531

161 000 000 3 088 500 12 790 000 183 920 000 22 924 532 0 0 0 4275 122 293

−27 903 000 3 178 700 900 200 000 7 086 900 34 990 209 0 84 633 37 660 4275 0

0 2140 1305 306 6048 0 12 757 85 383 23 367 102 266 82 537 18 382 1348 1 467 800 1 465 990 0 1 500 000 1 500 000 0 52 072 75 422 18 015 1470 36 152 243

0 0 3778 0 6048 0 9943 113 496 23 367 102 266 92 853 0 4000 1 500 000 1 500 000 0 1 467 790 1 451 530 16 242 23 959 28 372 22 136 0 33 500 243

0 3778 0 0 6048 12 695 1837 70 195 23 367 102 266 72 170 29 515 581 1 493 620 1 493 620 0 1 500 000 1 500 000 0 0 633 735 3158 36 919 0

Objective Functions. The considered objective functions are stated as follows. Cost. The cost is equal to the negative value of the profit:

Profit = SalesC + SalesA + SalesPel + SalesOil + SalesPyr + SalesGas + SalesAd + SalesRP − TAC

(132)

Cost = − Profit J


Research Article


Figure 6. Scenario for the minimum consumption of fresh water.

Consumption of Fresh Water. The total consumed fresh water (TotWFresh) is equal to the water extracted in the community: TotWFresh =

∑ WtFresh t

hand, the upper bounds (UB) of the individual objectives correspond to the Nadir Point, which is the worst solution of the problem. In the proposed solution approach, first, we generated the scenarios for the minimum consumption of fresh water, the minimum greenhouse emissions, and the minimum cost. Then, from the results obtained in these three scenarios, we selected the minimum value of water consumption between the three scenarios, and this value represents the lower bound for the water objective. In the same way, the lower bounds for the greenhouse gas emissions and cost objectives were selected. Similarly, from these solutions, the upper bounds for the objective functions are obtained. Because the Utopian Point represents an infeasible solution, it is necessary to obtain the compromise solution, which is the closer solution to the Utopian Point, and it is possible to obtain it by minimizing simultaneously the three objective functions evaluated in this problem through eq 137 with the target to approach their lower bounds.

(134)

Greenhouse Gas Emissions. The greenhouse gas emissions correspond to the emissions of the CHP units and the process plants of solid wastes: GHGE = GHGECHP + GHGEPEL + GHGEGAS + GHGEPYR + GHGEAD + GHGEIN

(135)

The proposed model corresponds to a multiobjective optimization problem, where there is proposed the minimization of each objective function simultaneously.

■

OF = {min Cost; min TotWFresh; min GHGE}

(136)

UB TotWFreshUB − TotWFresh ji Cost − Cost + minjjj UB LB j Cost − Cost TotWFreshUB − TotWFreshLB k GHGEUB − GHGE yzz + zz GHGEUB − GHGELB z{

MULTISTAKEHOLDER APPROACH The proposed model corresponds to a multiobjective problem that seeks to minimize simultaneously three objective functions (consumption of fresh water, greenhouse gas emissions, and total annual cost of the system). Because the evaluated objectives are in conflict, in this study, we considered using an optimization strategy that allows obtaining a solution in which the individual objectives approach simultaneously to their lower bounds (LB), and these lower bounds constitute the optimal solution that is called the Utopian Point. On the other

(137)

In addition, by eq 138, it is possible to evaluate different feasible solutions assigning priorities to the objectives (ω), and this allows evaluating how the objectives influence on the others. K


Research Article


Figure 7. Scenario for the minimum generation of greenhouse gas emissions.

ij CostUB − Cost TotWFreshUB − TotWFresh +ω minjjjω j CostUB − CostLB TotWFreshUB − TotWFreshLB k GHGEUB − GHGE yzz +ω zz GHGEUB − GHGELB z{ (138)

location which coincides with a mountainous zone called “Sierra Madre del Sur”. The difficult access to the community as well as the irregular distribution of their localities cause that the water supply of the public network represents a severe problem, and consequently, agricultural and livestock activities are affected. Therefore, there is difficult access to food. Likewise, there is a lack of electric power, affecting the provision of services that are essential for human, social, and economic development. In addition, the community development has been affected by the absence of resources and technology to meet these needs, which represents a problem for the government which has sought to provide and give incentives to programs in which better management of resources is carried out and the quality of life of the inhabitants is improved even when the implementation of this type of technology involves high costs. Faced with this problem, there is proposed a polygeneration system capable of integrate water, energy, and food demands of this isolated community (Figure 4). The community consists of 18 778 habitants and approximately 3350 households.

To compare the feasible solutions with the Nadir Point and the Utopian Point, we considered the percentage of dissatisfaction, which is calculated by the following equation: ij yz Cost − CostLB jj zz + jj zz UB LB jj zz Cost − Cost jj zz jj zz LB zz i 1 zy jjj TotWFresh − TotWFresh j zz %Dissatisfaction = jj zz·jj + z k 3 { jjj TotWFreshUB − TotWFreshLB zzz jj zz jj zz LB jj zz GHGE − GHGE jj zz j z UB LB GHGE − GHGE k {

(139)

Previous equation indicates that if the percentage of dissatisfaction is 100%, the solution corresponds to the Nadir Point, otherwise the dissatisfaction of 0% corresponds to the Utopian Point. Therefore, the lower the value of dissatisfaction, the closer the utopian point.

■

RESULTS The proposed model corresponds to a Mixed-Integer Linear Programming problem, and it was implemented in the software GAMS.45 The model represents a multiobjective optimization formulation, in which the objective is to minimize the cost, consumption of fresh water, and greenhouse gas emissions. The mathematical model consists of 3138 continuous variables, 21 binary variables, and 1561 equations. In order to avoid nonconvex problems, the involved processes in the superstructure are modeled by linear relationships,

■

CASE STUDY As a case study, we considered the community of “Cochoapa el Grande”, located in the State of Guerrero in Mexico with coordinates 17° 12′ N 98° 27′ O. This community has been listed as the municipality with the highest index of poverty and marginalization in the country,44 mainly because of its geographical L


Research Article


Figure 8. Scenario for minimum cost.

system consumes around 3 060 000 m3 of water per year, while in comparison with the water consumption of the minimum cost scenario, it only increases by approximately 4%. The use of rainwater collection systems helps to reduce the use of fresh water from wells, which is demonstrated in the obtained results, since it provides around 127 494 m3 of water per year through rainwater collectors. However, for the scenarios of minimum generation of emissions and minimum cost, 52 331 m3 and 632 m3 of water are provided per year, respectively; therefore, there is greater use of fresh water from wells. This can be attributed to the fact that in the case of minimizing costs, the capital costs of the rainwater collectors are avoided. The selected cogeneration technologies for the case of minimizing the consumption of fresh water are represented by a Microturbine, a Fuel Cell, and a Stirling Engine; in the case of minimizing emissions, a Fuel Cell is proposed; and in the case of minimizing costs, the selected technology was the Microturbine. The case for minimizing the emissions selects the Fuel Cell for power generation. In the case of minimum consumption of fresh water, fuel requirements increase by 28%. On the other hand, in the case of minimizing costs, 46% more fuel is required than in the case of minimizing emissions, which causes a greater generation of greenhouse gases. For solid waste management, the processing plants selected in the scenario of minimizing emissions are the pelletization and pyrolysis plants. In the case of minimum consumption of fresh water, the pelletization, pyrolysis, and incineration plants are selected, which represent an increase of 1152% in the GHGE and, in the case of minimizing costs, gasification, incineration, and pelletization plants are selected, which increase the generation of emissions by 7038%.

which are simplified on the basis of efficiency factors related to each of them. It should be noticed that the used factors are obtained from experimental reports. It means that these factors are exact enough. In the proposed model, the optimization implies that the use of a given technology and the associated size to yield a general configuration was determined; the operating conditions for the used technologies are not optimized; and the nominal values for using such technologies were considered, which are according to the considered conversion factors. Table 1 shows the main parameters used in the mathematical model. The points obtained from the functions to minimize water consumption, greenhouse gas emissions, and cost are shown in Figure 5. The values of the most important variables are reported in Table 2. The configuration obtained for the scenario of minimum consumption of fresh water is presented in Figure 6, the scenario of minimum generation of greenhouse gas emissions is shown in Figure 7, and the case of minimum cost is presented in Figure 8. None of the proposed scenarios selects the anaerobic digestion plant used for solid waste management, and no aerogenerator is selected for electric power generation. The selection of technologies depends on the studied scenario. In the case of these processes, the model does not select them because it was possible to use other processes that are more economically viable and that generate emissions in a smaller proportion compared with others, and also the benefits to use other technologies are better because they represent higher profits for the system. For the evaluated scenarios, water consumption does not vary significantly between the different solutions (Figure 9). In the scenario of minimum consumption of fresh water, the M


Research Article


Figure 9. Comparison for the different identified scenarios.

proposed feasible solutions. The dissatisfaction of each of the objective functions, as well as the total dissatisfaction for each of the scenarios is presented in Table 4. There were randomly generated weights (ω) in the software Matlab through the Latin hypercube function, and there were 10 weights generated for each objective. The function was solved with the multistakeholder approach, and the percentage of dissatisfaction was calculated. The results obtained show that the maximum percentage of dissatisfaction was Case 6 with 24% of dissatisfaction, in which the greater weight was given to the GHGE. Additionally, more cases were generated assigning different weights for the objectives from 0 to 10 with the purpose to obtain a response surface and to show the behavior of the objective functions when there are assigned randomly priorities regardless of the magnitude of these priorities. A value of 10 was assigned to one of the objectives, and 0 was assigned for the others; these cases correspond to the cases 11, 12, and 13 of Table 4. The results of dissatisfaction show that the greatest percentage of dissatisfaction corresponds to Case 1, in which there was assigned the weight of 10 for the cost objective. Nevertheless, the results for the rest of the cases in general show that in cases where the objective has a greater weight in the GHGE objective, they present a greater percentage of dissatisfaction. Moreover, it is possible to obtain better results in cases in which the weights are distributed between the three objectives, as Cases 4, 5, and 6 with 4.5% of dissatisfaction, which is the lowest percentage of dissatisfaction of all the evaluated feasible solutions.

Due to the conditions of the community and because of the lack of processes to generate energy and manage the resources, very high costs are presented, which leads to an exponential increase in greenhouse gas emissions, as well as an increase in the use of water. This can be attributed to the fact that in the case of minimizing costs, we sought to obtain the maximum production of animals and crops for sale (Table 3). In the same Table 3. Valuated Products Generated in the Different Scenarios product

min water

min GHGE

pellets (kg/year) 855 855 0 0 Fgasification (m3/year) Fpyrolysis‑oil (m3/year) 67 123 71 052 t Animal Production (Animals/Year) bovine 75 75 porcine 79 79 ovine 85 85 goat 384 384 bird 1368 1368 Crops (kg/Year) peanut 360 360 jicama 1020 1020 corn 580 580 lemon 1680 1680 mango 1020 1020 papaya 3460 3460 sorghum 6387 6387

max profit 855 12 695 0 115 119 128 576 2052 2340 6630 3775 10 920 6630 22 495 41 519

■

CONCLUSIONS This paper has presented a multiobjective optimization approach for the optimal design of a polygeneration system applied in a low-income and isolated community. The proposed model is capable to determine the optimal configuration of technologies that meet the demands of water, energy and food of the community accounting for economic and environmental objectives. There were evaluated different scenarios for the minimum cost of the integrated system, the minimum fresh water consumption and the minimum greenhouse gas emissions generated. To trade-off the proposed objectives, it is presented a multistakeholder approach which is capable to find the compromise solution which is the point where the

way, the gasification and pyrolysis plants are selected to make use of the natural gas generated in the gasification plant and thereby reduce the cost associated with the purchase of natural gas and obtain profits from the sale of pyrolysis oil. Because the objectives (minimization of cost, minimization of water consumption and minimization of GHGE) are in conflict, the methodology of Multistakeholder Optimization is used in this work with the purpose of finding a balance between the objective functions and giving feasible solutions to the problem. For properly solving this problem, the multiobjective formulation was reformulated as a single objective to obtain a feasible solution close to the utopian point. In addition, a dissatisfaction analysis is included in each of the N


0.2646 0.3213 0.4375 0.4030 0.7135 0.1542 0.2647 0.4164 0.4056 0.0446 10 0 0 4 3 3 2 1 7 6 2 2 8 1 1 5 3 2

Utopia Nadir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

cost

($U.S./year)

case

0.4427 0.5278 0.1831 0.2640 0.2089 0.0017 0.2529 0.3591 0.3629 0.6002 0 10 0 3 4 3 7 2 1 2 6 2 1 8 1 3 2 5

0.2927 0.1509 0.3794 0.3330 0.0776 0.8441 0.4825 0.2245 0.2315 0.3552 0 0 10 3 3 4 1 7 2 2 2 6 1 1 8 2 5 3

GHGE (ton CO2/year)

water

(m3/year)

stakeholder weights

Table 4. Results for the Multistakeholder Analysis

3 060 000 3 178 700 3 060 600 3 060 300 3 063 700 3 063 700 3 063 800 3 148 200 3 063 700 3 063 700 3 063 700 3 060 000 3 178 700 3 060 000 3 141 200 3 063 700 3 063 700 3 063 700 3 060 000 3 084 100 3 070 400 3 063 800 3 060 000 3 087 800 3 070 400 3 060 000 3 094 200 3 063 700 3 087 800 3 060 000

−27 903 000 161 000 000 −16 770 000 −15 760 000 −24 650 000 −24 660 000 −24 830 000 −27 110 000 −24 770 000 −24 500 000 −24 500 000 −14 950 000 −27 800 000 136 160 000 135 950 000 −24 770 000 −24 770 000 −24 770 000 −15 080 000 −14 950 000 −26 990 000 −24 820 000 −15 080 000 −24 770 000 −26 990 000 −15 080 000 −24 660 000 −24 770 000 −24 770 000 −15 080 000

water (m3/year)

($U.S./year)

cost

objectives GHGE 12 790 000 900 200 000 96 820 000 96 820 000 96 820 000 96 820 000 96 820 000 12 790 000 96 820 000 97 410 000 97 410 000 96 670 000 757 600 000 275 200 000 12 800 000 96 820 000 96 820 000 96 820 000 96 820 000 21 580 000 96 820 000 96 820 000 96 820 000 21 580 000 96 820 000 96 820 000 12 790 000 96 820 000 21 580 000 96 820 000

(ton CO2/year)

0.9411 0.9357 0.9828 0.9828 0.9837 0.9958 0.9834 0.9820 0.9820 0.9314 0.9995 0.1315 0.1326 0.9834 0.9834 0.9834 0.9321 0.9314 0.9952 0.9837 0.9321 0.9834 0.9952 0.9321 0.9828 0.9834 0.9834 0.9321

cost

0.9949 0.9975 0.9688 0.9688 0.9680 0.2570 0.9688 0.9688 0.9688 1.0000 0.0000 1.0000 0.3159 0.9688 0.9688 0.9688 1.0000 0.7970 0.9124 0.9680 1.0000 0.7658 0.9124 1.0000 0.7119 0.9688 0.7658 1.0000

water

0.9053 0.9053 0.9053 0.9053 0.9053 1.0000 0.9053 0.9046 0.9046 0.9055 0.1607 0.7043 1.0000 0.9053 0.9053 0.9053 0.9053 0.9901 0.9053 0.9053 0.9053 0.9901 0.9053 0.9053 1.0000 0.9053 0.9901 0.9053

GHGE

stakeholder contribution

0.9471 0.9462 0.9523 0.9523 0.9523 0.7509 0.9525 0.9518 0.9518 0.9456 0.3867 0.6119 0.4828 0.9525 0.9525 0.9525 0.9458 0.9062 0.9376 0.9523 0.9458 0.9131 0.9376 0.9458 0.8982 0.9525 0.9131 0.9458

FS 0.00 1.00 0.06 0.06 0.02 0.02 0.02 0.00 0.02 0.02 0.02 0.07 0.00 0.87 0.87 0.02 0.02 0.02 0.07 0.07 0.00 0.02 0.07 0.02 0.00 0.07 0.02 0.02 0.02 0.07

cost 0.00 1.00 0.01 0.00 0.03 0.03 0.03 0.74 0.03 0.03 0.03 0.00 1.00 0.00 0.68 0.03 0.03 0.03 0.00 0.20 0.09 0.03 0.00 0.23 0.09 0.00 0.29 0.03 0.23 0.00

water 0.00 1.00 0.09 0.09 0.09 0.09 0.09 0.00 0.09 0.10 0.10 0.09 0.84 0.30 0.00 0.09 0.09 0.09 0.09 0.01 0.09 0.09 0.09 0.01 0.09 0.09 0.00 0.09 0.01 0.09

GHGE

% Dis % Dis 0.00 100.00 5.29 5.38 4.77 4.77 4.77 24.91 4.75 4.82 4.82 5.44 61.33 38.81 51.72 4.75 4.75 4.75 5.42 9.38 6.24 4.77 5.42 8.69 6.24 5.42 10.18 4.75 8.69 5.42

ACS Sustainable Chemistry & Engineering Research Article

O


Research Article

ACS Sustainable Chemistry & Engineering φc, t ϕwreq a ϕgrowth a γAD

objectives are minimized simultaneously. As case study, it was considered the community of Cochoapa el Grande, which is the community with the lowest human development index of Mexico. There were generated different feasible solutions and it was evaluated the dissatisfaction percentage of each one. The results show that the compromise solution is very close of the Utopian Point, which indicates that is possible to obtain a solution that satisfies almost entirely the minimum of the objectives. It should be noticed that in the generated feasible solutions the dissatisfaction increases when it is assigned a major priority to the GHGE objective. On the other hand, the lowest percentage of dissatisfaction corresponds to the cases in which the priorities are distributed between the three objectives.

■

γCHP γGAS γIN γPEL γPYR λu

AUTHOR INFORMATION

λFreshIC λSC

Corresponding Author

*E-mail: [email protected]. Phone: +52 443 3223500 ext. 1277 Fax: +52 443 3273584. ORCID

λSt

José María Ponce-Ortega: 0000-0002-3375-0284

ASC‑MAX

Notes

The authors declare no competing financial interest.

ASP‑MAX

ACKNOWLEDGMENTS The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT).

Arotor‑MAX

■ ■

ARW‑IC‑MAX ARW‑MAX

NOMENCLATURE

Sets

a c pw r t u ww

CapAC‑MAX

Set for different types of animals Set for different types of crops Set referent to the available wells to photovoltaic pumping Set for different types of solid wastes Set referent to time Set referent to cogeneration units Set referent to the available wells to wind pumping

CapAD‑MAX CapCHP‑MAX u CapBW‑MAX CapGAS‑MAX

Parameters

αt αAC αBW αBWT

αGW αGWT ΔT δAD δIN δGAS δPEL δPYROIL ηEu, t ηQu, t ηSP τHW θC‑MAX c, t θC‑MIN c, t ρair ρw

Solar radiation factor Refrigeration factor Blackwater generated factor Conversion factor of the blackwater treatment plant Greywater generated factor Conversion factor of the greywater treatment plant Delta for temperature Production factor of the anaerobic digestion plant Production factor of the incineration plant Production factor of the gasification plant Production factor of the palletization plant Production factor of the pyrolysis plant Electric efficiency of the cogeneration units Thermal efficiency of the cogeneration units Solar panel efficiency Fresh water heating factor by steam Maximum production of crops Minimum production of crops Air density Water density

CapGW‑MAX CapIN‑MAX CapPP−MAX pw CapPS‑MAX s CapPEL‑MAX CapPYR‑MAX CapRWSS‑IC‑MAX CapRWSS‑MAX CapST‑MAX CapwwWP‑MAX CPmax Cp P

Factor production Factor of water required per animal Growth factor of animals Emission factor associated with anaerobic digestion plant Emission factor associated with the cogeneration units Emission factor associated with gasification plant Emission factor associated with incineration plant Emission factor associated with palletization plant Emission factor associated with pyrolysis plant Fraction of water coming from the cogeneration units sent to the thermal storage tank Fraction of fresh water sent to the community Fraction of water from the solar collector sent to the thermal storage tank Fraction of fresh water sent to the thermal storage tank Maximum area available for the installation of the solar collector Maximum area available for the installation of the solar panel Maximum area available for the installation of aerogenerators Maximum area available for the community rainwater collector Maximum area available for the rainwater collector of cattle, agriculture and gardening Maximum available capacity of the absorption refrigeration system Maximum available capacity of the anaerobic digestion plant Maximum available capacity of the cogeneration units Maximum available capacity of the blackwater treatment plant Maximum available capacity of the gasification plant Maximum available capacity of the greywater plant Maximum available capacity of the incineration plant Maximum available capacity of the photovoltaic pumping Maximum available capacity of the pellets stove Maximum available capacity of the pelletization plant Maximum available capacity of the pyrolysis plant Maximum available capacity of the community rainwater storage system Maximum available capacity of the rainwater storage system Maximum available capacity of the storage tank Maximum available capacity of the wind pumping Maximum power coefficient Water heat capacity DOI: 10.1021/acssuschemeng.8b05134 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering ECHP‑agriculture t ECHP‑cattle t ETotal‑IC t FCostu FCostAC FCostAD FCostAG FCostBW FCostIN FCostGAS FCostGW FCostPP FCostPS FCostPEL FCostPYR FCostSC FCostSP FCostST FCostRW FCostRW‑IC FCostWP MSWagriculture r, t MSWcattle r, t MSWIC r, t MSWgarden r, t MSWTotal r, t MSWrTotal = 1, t PR Speedt UCFreshW UCNG UCOMu UCOMAC UCOMAD UCOMGAS UCOMIN UCOMPP pw UCOMPEL UCOMPYR UCOMSC UCOMWP ww USCAa USCCc USCMSW r USCAD USCGAS PEL

USC USCPYR‑OIL

VCostu

Demand for electricity in agriculture Demand for electricity in cattle Total electricity supplied to the community Fixed cost of each of the cogeneration units Fixed cost of the absorption refrigeration system Fixed cost of the anaerobic digestion plant Fixed cost of the aerogenerators Fixed cost of the blackwater treatment plant Fixed cost of the incineration plant Fixed cost of the gasification plant Fixed cost of the greywater plant Fixed cost of the photovoltaic pumping Fixed cost of the pellets stove Fixed cost of the pelletization plant Fixed cost of the pyrolysis plant Fixed cost of the solar collector Fixed cost of the solar panel Fixed cost of the storage tank Fixed cost of the rainwater collection system for livestock, agriculture and gardening Fixed cost of the community rainwater storage system Fixed cost of the wind pumping system Solid waste generated in agriculture Solid waste generated in cattle Solid waste generated in the community Solid waste generated in gardening Total solid waste generated in agriculture Nonrecyclable solid waste Performance coefficient Wind speed Fresh water unitary cost Natural gas unitary cost Operation and maintenance cost of each of the cogeneration unit Operation and maintenance cost of the absorption refrigeration system Operation and maintenance cost of the anaerobic digestion plant Operation and maintenance cost of the gasification plant Operation and maintenance cost of the incineration plant Operation and maintenance cost of the photovoltaic pump Operation and maintenance cost of the pelletization plant Operation and maintenance cost of the pyrolysis plant Operation and maintenance cost of the solar collector Operation and maintenance cost of wind pumping Unitary sale cost of animals Unitary sale cost of crops Unitary sale cost of municipal solid wastes Unitary sale cost of biogas produced in the anaerobic digester Unitary sale cost of natural gas produced in the gasification plant Unitary sale cost of pellets Unitary sale cost of pyrolysis oil

VCostAC VCostAD VCostAG VCostBW VCostGAS VCostGW VCostIN VCOSTPP pw VCostPS VCostPEL VCostPYR VCostRWSS‑IC VCostRWSS VCostRW VCostRW‑IC VCostSC VCostSP VCostST VCOSTWP ww W CL t W garden t WTotal‑IC t

Variable cost of cogeneration units Variable cost of the absorption refrigeration system Variable cost of the anaerobic digestion plant Variable cost of the aerogenerators Variable cost of the blackwater treatment plant Variable cost of the gasification plant Variable cost of the greywater plant Variable cost of the incineration plant Variable cost of the photovoltaic pumping Variable cost of the pellets stove Variable cost of the pelletization plant Variable cost of the pyrolysis plant Variable cost of the community rainwater storage system Variable cost of the rainwater storage system Variable cost of the community rainwater collector system Variable cost of the rainwater collector system Variable cost of the solar collector Variable cost of the solar panel Variable cost of the storage tank Variable cost of the wind pumping Demand for air conditioning for the community Water demand in gardening Water demand in the community

Variables

aa, t Ac AAG Arotor ARW‑IC ARW ASC ASP cc, t CapAC CapAD CapBW CapCHP u CapGAS CapGW CapIN CapPP pw CapPS s CapPEL CapPYR CapRWSS−IC CapRWSS CapST CapWP ww CapCostu CapCostAC CapCostAD CapCostAG CapCostBW Q

Animals produced in cattle Available area for crops Available area for aerogenerator installation Rotor area for aerogenerators Rainwater area for the community Rainwater area for the cattle, agriculture and gardening Solar collector area Solar panel area Crops produced in agriculture Capacity of the absorption refrigeration system Capacity of the anaerobic digestion plant Capacity of the black water treatment plant Capacity of the cogeneration units Capacity of the gasification plant Capacity of the greywater plant Capacity of the incineration plant Capacity of the photovoltaic pumping Capacity of the pellets stove Capacity of the palletization plant Capacity of the pyrolysis plant Capacity of the community rainwater storage system Capacity of the rainwater storage system Capacity of the storage tank Capacity of the wind pumping Capital cost of the cogeneration units Capital cost of the absorption refrigeration system Capital cost of the anaerobic digestion plant Capital cost of aerogenerators Capital cost of the blackwater treatment plant DOI: 10.1021/acssuschemeng.8b05134 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering CapCostGAS CapCostGW CapCostIN CapCostSC CapCostSP CapCostPP CapCostPS CapCostPEL CapCostPYR CapCostRW CapCostST CapCostWP Eu, t EAG t ECHP t ECHP‑RE t ERE t ESP t Fu, t Fad t FBF t Fgasification t FNG t Fpyrolysis−oil t foodaa, t GHGEAD GHGECHP GHGEGAS GHGEIN PEL

GHGE

GHGEPYR ht MSWAD t MSWGAS t MSWIN t MSWPEL t MSWPYR t OCostFreshW OCostNG OMCostu OMCostAC OMCostAD OMCostBWT OMCostGAS OMCostGWT

OMCostIN

Capital cost of the gasification plant Capital cost of the greywater plant Capital cost of the incineration plant Capital cost of the solar collector Capital cost of the solar panel Capital cost of the photovoltaic pumping Capital cost of the pellets stove Capital cost of the palletization plant Capital cost of the pyrolysis plant Capital cost of the rainwater system Capital cost of the storage tank Capital cost of the wind pumping Electricity generated by the cogeneration units Electricity produced in the aerogenerators Electricity produced by the cogeneration units Electricity generated by the cogeneration units sent to the community Electricity produced by renewable energies Electricity produced in solar panels Fuel required for each cogeneration unit Biogas flow from the anaerobic digestion plant Total biofuel generated Flow of natural gas from the gasification plant Natural gas flow Pyrolysis oil flow Food needed for animals Greenhouse gas emissions associated with the anaerobic digestion plant Greenhouse gas emissions associated with the cogeneration units Greenhouse gas emissions associated with the gasification plant Greenhouse gas emissions associated with the incineration plant Greenhouse gas emissions associated with the pelletization plant Greenhouse gas emissions associated with the pyrolysis plant Solar panel radiation factor Nonrecyclable solid waste sent to the anaerobic digestion plant Nonrecyclable solid waste sent to the gasification plant Nonrecyclable solid waste sent to the incineration plant Nonrecyclable solid waste sent to the pelletization plant Nonrecyclable solid waste sent to the pyrolysis plant Operation cost of fresh water Operation cost of natural gas Operation and maintenance cost of the cogeneration units Operation and maintenance cost of the absorption refrigeration system Operation and maintenance cost of the anaerobic digestion plant Operation and maintenance cost of the blackwater treatment plant Operation and maintenance cost of the gasification plant Operation and maintenance cost of the greywater treatment plant

OMCostPP OMCostPEL OMCostPYR OMCostSC OMCostWP PPEL t PIC s, t Q SC t SalesA SalesAd SalesC SalesGas SalesOil SalesPellets SalesRP Stt VST t Wu, t WSC t Wcattle‑req a, t WFresh t WFresh‑IC t WFresh‑St t WFresh‑T t WIC t WIC‑BW t WIC‑GW t WGW‑agriculture t WGW‑cattle t WGW‑garden t WGWT t WPPump pw, t WPPump‑agriculture pw, t WPPump‑cattle pw, t WWPump‑agriculture ww, t WWPump‑cattle ww, t WRW‑agriculture t WRW t WRW‑IC t WSC t WST‑AC t R

Operation and maintenance cost of the incineration plant Operation and maintenance cost of the photovoltaic pump Operation and maintenance cost of the pelletization plant Operation and maintenance cost of the pyrolysis plant Operation and maintenance cost of the solar collector Operation and maintenance cost of the wind pumping Pellets generated in the palletization plant Pellets send to the pellet stoves Heat transferred in the solar collector Sales of animals Sales of biogas Sales of crops Sales of natural gas Sales of pyrolysis oil Sales of pellets Sales of recyclable wastes Flow of steam sent to the internal combustion engine Water stored in the thermal storage tank Water flow from each of the cogeneration units sent to the thermal storage tank Hot water coming out of the solar collector Flow water required in agriculture Total fresh water flow Flow of fresh water sent to the community Flow of fresh water heated with steam from the incineration plant Flow of fresh water sent to the thermal storage tank Flow of water supplied to the community Black water flow generated in the community sent to the black water treatment plant Greywater flow generated in the community sent to the gray water treatment plant Flow of treated greywater sent to agriculture Flow of treated greywater sent to cattle Flow of treated greywater sent to gardening Flow of treated greywater leaving the gray water treatment plant Flow of water pumped by the photovoltaic pumping system Water flow from the photovoltaic pumping system to agriculture Water flow from the photovoltaic pumping system to livestock Water flow from the wind pumping system to agriculture Water flow from the wind pumping system to cattle Water flow from the rainwater collection system sent to agriculture Flow of water collected in the rainwater collector Water flow sent from the rainwater collection system to the community Flow of water sent to the solar collector Flow of water sent from the thermal storage tank to the absorption cooling system DOI: 10.1021/acssuschemeng.8b05134 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering WTFresh‑IC t WCropc, t

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Flow of fresh water sent to the community Water needed for each crop

Binary Variables

yAD yAC yAG yBW yGW yGAS yIN yPP pw yPEL yPES s yPYR yRW‑IC yRW yRWSS‑IC yRWSS ySC ySP yST yu yWP ww

■

Binary variable for the existence of the anaerobic digester Binary variable for the existence of the refrigeration absorption system Binary variable for the existence of the aerogenerator Binary variable for the existence of the black water treatment plant Binary variable for the existence of the greywater treatment plant Binary variable for the existence of the gasification plant Binary variable for the existence of the incineration plant Binary variable for the existence of the photovoltaic pumping Binary variable for the existence of the pelletization plant Binary variable for the existence of the pellet stoves Binary variable for the existence of the pyrolysis plant Binary variable for the existence of the community rainwater collector Binary variable for the existence of the rainwater collector for the agriculture, cattle and gardening Binary variable for the existence of community rainwater storage system Binary variable for the existence of the rainwater storage system for the agriculture, cattle and gardening Binary variable for the existence of the solar collector Binary variable for the existence of the solar panel Binary variable for the existence of the storage tank Binary variable for the existence of the cogeneration units Binary variable for the existence of the wind pumping

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