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Optimal Design of Sustainable Agricultural Water Networks Jesus Manuel Nuñez Lopez, Oscar Martín Hernández-Calderón, José María Ponce-Ortega, Maritza Elizabeth Cervantes-Gaxiola, and Eusiel Rubio-Castro ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.8b03901 • Publication Date (Web): 08 Nov 2018 Downloaded from http://pubs.acs.org on November 13, 2018

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ACS Sustainable Chemistry & Engineering

Optimal Design of Sustainable Agricultural Water Networks Jesús M. Núñez-López†, Oscar M. Hernández-Calderón†, José M. Ponce-Ortega‡, Maritza E. Cervantes-Gaxiola†, Eusiel Rubio-Castro†* †

‡

Chemical and Biological Sciences Department, Universidad Autónoma de Sinaloa, Blvd. De la Américas y Josefa Ortiz de Domínguez S/N, Ciudad Universitaria, Culiacán de Rosales, Sinaloa, 80013, México

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N, Ciudad Universitaria, Morelia, Michoacán, 58060, México

* Author for correspondence. Email: [email protected] Tel. +52 667 7137860 ext. 115.

1 ACS Paragon Plus Environment

ACS Sustainable Chemistry & Engineering 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT This work proposes a multi-period mixed integer non-linear programming model for the optimal design of agricultural water networks, which involves the optimal reuse of resources such as water, fertilizers and pesticides. This model is based on a new superstructure that includes attractive options for the use, reuse, recycle, regeneration and storage for the considered resources. The proposed model incorporates simultaneously the maximization of the net annual profit and the minimization of the environmental impact. The profit is formed by the economic incomes due to the sale of crops minus the corresponding capital and operating costs associated to the fresh water, fertilizer, storage, piping, pumping and water treatment. Whereas the environmental impact is determined through the Eco-indicator 95 and the water footprint to evaluate the effect over the global warming, acidification, eutrophication, green water footprint, gray water footprint and blue water footprint. Two case studies from the Mexican state of Sinaloa were solved with the proposed model. The operating, economic and design parameters are representative for the State of Sinaloa in Mexico; and the results are presented in three dimensional Pareto diagrams. From these diagrams is possible to find the optimal relationship between profit, eco-indicator and water footprint.

Keywords: Agriculture, water integration, environmental impact, fertilizer reuse, ecoindicator.


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INTRODUCTION Currently, some of the main problems that humanity faces are the reduction of hunger, the reduction of socioeconomic lag and the mitigation of environmental pollution.1 In this regard, agriculture is one of the viable options that allows solving the first two mentioned problems; however, this activity demands large amounts of water2 and influences the pollution of the same resource due to the excessive use of fertilizers, which are sources of CO2 emissions and nitrogen compounds (see Figure 1) that contribute to global warming, acidification of soils and eutrophication of aquifers.3 Thus, it is necessary to develop systematic strategies that allow to increase the agricultural production, but with the least environmental impact.4 In this sense, intensive agriculture, despite being a strategy used to reduce hunger, requires nitrogen fertilizers that exert a negative impact on the environment, such as ammonia volatilization, nitrous oxide or nitrate leaching;5 however, the total environmental burden associated with the agricultural production systems is broad, and the introduction of quantifiable indicators that consider all the possible adverse effects generated in the environment is required. This way, Eco-indicators have been developed to detect improvement options and compare or monitor the environmental impact associated to the agricultural activity.6-8 On the other hand, mitigation strategies around negative environmental effects can yield large uses of water, which, due to the current problem of water scarcity, cannot be considered as a viable option. Therefore, it is also necessary to consider the water footprint, since it allows evaluating the direct and indirect water consumption of an individual, community or business, and it is defined as the total volume of water that it needs to yield the products and needed services.9 Thus, the management of 3 ACS Paragon Plus Environment


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water in agricultural activities from a sustainable point of view consists in establishing a scenario that uses the least amount of water, under the least possible environmental impact, and the maximum possible economic gain from the sale of agricultural products.10 Regarding water management, recently some works have focused on applying the criteria of integration of chemical processes to agricultural activity. This, particularly to the reduction of the use of water for the irrigation of crops through the optimal design of water networks.11, 12 In this sense, a water exchange network is a scheme in which the reuse and recycling of water is implemented in some processes and/or activities in order to reduce the fresh water consumption.13 For this, it is necessary to install treatment units that allow reducing both, the demand for fresh water and the wastewater stream, as well as the installation of storage units and a pumping system and pipes, which allow the collection and distribution of treated wastewater for its later use, within the framework of compliance with an irrigation schedule established for a set of selected crops. Although such facilities must be justified by a better economic and environmental scenario than the original process without recycling and reuse of water.14 The advantages of water exchange networks have been exploited by industrial activity through the reuse and recycling of wastewater.15-18 However, in the agricultural activity there is not a systematic methodology to find scenarios that reduce water consumption and improve the use of fertilizers without affecting considerably the production, due to the conflict of interests that exists between the cost/benefit ratio;19 and even more, there is not a methodology that considers the importance and advantages of including the environmental impact, which allows to constitute agriculture as a sustainable activity, as well as to establish the degree of influence exerted by the eco-indicators and the water footprint on their economic profitability. Therefore, in this paper is presented a formal mathematical programming approach to 4 ACS Paragon Plus Environment

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synthesize agricultural water networks that considers the trade-offs between the economic and environmental points of view. It should be noted that the proposed optimization approach includes as decision variables determining the size and configuration of the involved units such as storage tanks, treatment units, pipes and pumps, in addition the proposed model optimizes the operating variables simultaneously. The objective functions are to maximize the profit (incomes due to the sales of crops) and minimize the environmental impact (consumption of fresh water and fertilizer). The decision variables to be considered for solving problem are the use of fresh water and fertilizer, the mass flowrates between the process components (crops, storage tanks, treatment units and environmental discharge), the existence and costs of pipes, storage tanks and treatment units. While the restrictions considered in the problem are the capacity of process units, the permissible limits of fertilizer concentration, the upper limits of the Eco-indicator 95 and water footprint. CO2 NO2 Fertilizer NH3 NO3-N

Global warming Acidification Eutrophication

Figure 1. Emissions and environmental effects by fertilizers’ application

MODEL FORMULATION The proposed model considers a multi-objective function, which consists in maximizing the profit ( Proffit ) associated to the crop sells as well as the minimization of environmental



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impact ( EnvImp ). This last takes into account the use of fertilizers as well as irrigation water for irrigating the crops.

Objective  max Proffit, min EnvImp

(1)

With regard to the objective function, in the next sections are given explanations over the estimation of environmental and economic impacts. Environmental impact. The environmental impact was evaluated using the Life Cycle Analysis (LCA) through the Eco-indicator 95,20 quantifying the damage contributed to global warming, acidification of soils and eutrophication of aquifers, whose different stages are described below. It should be noted that the Eco-95 was used because it has the necessary tools to analyze the effects in the environment for the use of fertilizers, such as climate change, acidification of soils, and eutrophication of aquifers, while Eco-99 generalizes into three broad categories (damage to resources, damage to human health, and damage to the ecosystem quality), which would require more data and would become an even more complex problem. Emissions inventory. The emissions of carbon dioxide (CO2), nitrogen oxide (N2O) and ammonia (NH3) are calculated through the multiplication of the fertilizer flowrate that is applied to the crop (Ffl,c) times an emission factor associated to each emission (EFl), and this result is divided by the crop yield (CYc) in order to obtain the emission by tonne of crop.21

 CO2 l ,c

emis



EFl CO2 Ffl ,c CYc

, l  L; c  C

(2)


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emis l ,c

N 2O



EFl N2O Ffl ,c

 NH 3 l ,c  emis

CYc

, l  L; c  C

EFl NH3 Ffl ,c CYc

(3)

, l  L; c  C

(4)

With regard to the above equations, in Table 1 are given the emission factors; while to determine the lixiviated nitrates, ( NO3  N )l ,c , there was used the balance of nitrogen emis

proposed by Brentrup, et al.

20

which is given in equation (6). Here, the inlets that were

considered are: mineral nitrogen fertilizer (Ffl,c), organic nitrogen fertilizer (Ofc), biological nitrogen fixation (Bfc), atmospheric nitrogen deposition (ADc) and nitrogen mineralization (NMc). Whereas, the outlets are: nitrogen removal with harvested crops (RNSc), nitrogen emis

emis

immobilization (Ifc), NH3-N emissions ( NH 3l ,c ), N2O-N emissions ( N 2Ol ,c ), and the obtained valor is multiplied by the frequency of water change (Efc). This is given in equation (5). It should be noted that that the lixiviated nitrates depend on filtered water into the soil. Then, for calculating the filtered water, it is employed the change frequency of water (Efc), which is determined through the field capacity in the effective rooting zone ( FCcRZe ) and drainage water (Wcdrain). It is given in equation (7), where the field capacity in the effective rooting zone is determined by the available field capacity (FCac) and the effective rooting zone (RZec). In addition, the rate of drainage water is obtained using the relationship developed by Liebscher and Keller,22 which is presented in equation (8). Here, Wcprecip_year is the annual precipitation rate, Wcprecip_summer is the summer precipitation rate and Wcprecip_winter is the winter precipitation rate.



 NO3  N l ,c

  NO3  N l ,c

 NO3  N l ,c

 Ffl ,c  Of c  Bf c  ADc  NM c 

emis

in soil in autum

emis

emis l ,c

N 2O

Wcdrain Ef c  , FCcRZe

 NH 3

emis l ,c

Ef c , l  L; c  C

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(5)

 RNSc  If c ,

l  L; c  C

c C

(6)

(7)

The values for FCac and RZec were taken from Tables S1 and S2 of the Supporting Information, respectively; and these ones depend on the soil type (a clayey sandly of soil type was used for the considered case study because it is the predominant soil in the considered region).

Wcdrain  0.86Wc precip _ year  11.6 FCcRZe  FCac RZec ,

Wc precip _ summer  241.4, Wc precip _winter

c C

(8)

c C

(9) Table 1. Emission Factors Fertilizer

Compound (Nx)

CAN (kg Nx/kg N)

UAN (kg Nx/kg N)

N2O

0.03

0.0218

UREA (kg Nx/kg N) 0.0125

NH3

0.01

0.08

0.15

CO2

0.2

0.2

0.2

Characterization. The emissions are related to the environmental impacts, including the following categories: global warming (Gwl,c), acidification (Acil,c) and eutrophication (Eutrol,c). These ones are affected by the emissions like is shown in Figure S1 of the Supporting Information, and these emissions are multiplied by an equivalence factor (see


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Table 2). It should be noted that the contribution of the emission in terms of environmental degradation depends directly on the value for the aforementioned equivalence factor. N 2O emis Gwleff,c  (CO2 )lemis , , c  ( N 2 O )l , c EfGw

NH 3 Acileff,c  ( NH 3 )lemis , , c EfAci

l  L; c  C

(10)

l  L; c  C

(11)

NH 3 NO3  N Eutroleff,c  ( NH 3 )lemis  ( NO3  N )lemis , , c EfEutro , c EfEutro

l  L; c  C

(12)

NH 3 N 2O where Ef Gw is the equivalence factor of N2O for global warming, Ef Aci is the equivalence NH 3 factor of NH3 for acidification, Ef Eutro is the equivalence factor of NH3 for eutrophication NO3  N and Ef Eutro is the equivalence factor of NO3-N for eutrophication.

Table 2. Equivalence factors for environmental effects Environmental Listing of Effect Interventions Global Warming

Eutrophication

Acidification

Equivalence Factor (Ef)

CO2

1.00

N2O CH4

310.00 21.00

NO3-

0.42

NTOT

0.42

PTOT

3.06

NH3

0.33

NOX

0.13

NH3

1.88

NOX

0.70

SO2

1.00

Normalization. Even after the characterization, it is not possible to conclude the importance of these values. It is because a big value of indicator can represent a small contribution with respect to the total environmental impact, while a small value can represent a great 9 ACS Paragon Plus Environment


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contribution about the environmental impact. In this regard, the goal of normalization is to have a better understanding related to the value of indicators. Therefore, the values obtained in the characterization stage were divided by a normalization value (see Table 3), which is associated to each environmental impact in order to know its contribution in the total environmental impact. It is given in equations 13, 14 and 15. NGwl ,c 

NAcil ,c 

Gwleff,c NvGw Acileff,c NvAci

NEutrol,c 

,

l  L; c  C

(13)

,

l  L; c  C

(14)

Eutroleff,c NvEutro

,

l  L; c  C

(15)

Table 3. Normalization values Environmental Effect

Unit

Normalization Value

Global Warming (NvGw)

Kg CO2 Eq.

13100.0

Acidification (NvAci)

Kg SO2 Eq.

113.0

Eutrophication (NvEutro)

Kg PO4- Eq.

38.2

Weighing. In order to consider the different levels of severity of environmental effects, there is required the weighing stage. According with the Eco-Indicator 95, this is obtained by multiplying each normalized effect by a weight factor (see Table 4), these factors are arbitrary to obtain a representative behavior for the different considered objectives. It should be noted that when there is assigned higher weight values for the environmental effects, the environmental impact has a higher penalty and this way the solutions tend to


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use lower amounts of fresh water and fertilizer even that the cost is higher. The next equations represent the weighed objectives: WGwl ,c  NGwl ,cWfGw,

l  L; c  C

(16)

WAcil ,c  NAcil ,cWfAci,

l  L; c  C

(17)

WEutrol,c  NEutrol,cWfEutro,

(18)

l  L; c  C

Table 4. Weighting factors for environmental effects Environmental Effect

Weighting Factor

Global Warming (WfGw)

2.5

Acidification (WfAci)

10.0

Eutrophication (WfEutro)

5.0

Heavy Metals

5.0

Carcinogens

10.0

Winter Smog

5.0

Summer Smog

2.5

Pesticides

25.0

Eco-indicator. From the weighing, there is obtained a value for the Eco-Indicator for each category of effect. Then, as these values are dimensionless, they can be added together and thus represent the total environmental impact like is given in equation (19).

Eco  indicatorl .c  WGwl ,c  WAcil ,c  WEutrol ,c ,

l  L;c  C

(19)

Water Footprint. The global water footprint of a process is determined by the addition of the blue water footprint (WFcazul), the green water footprint (WFcverde) and the gray water footprint (WFcgris) as follows: WFc proc  WFcazul  WFcverde  WFcgris

(20)



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In this regard, the blue water footprint is related to fresh water ( Fwfs ) and the crop yield ( CYc ), while the green water footprint is determined by the rainwater ( Fwp ) and the crop

yield.

azul c

WF



verde c

WF



wW ;tT

Fwfsw,c ,t

(21)

CYc



 Fwp

c ,t

tT

(22)

CYc

Finally, to calculate the graywater footprint, there is taken into account the fraction of contaminated water ( 1  Cleanwasher ), the total fresh fertilizer per hectare ( Fff ), the lower ( Cmin ) and upper ( Cmax ) permissible fertilizer concentrations as well as the crop yield.

WFcgris 

(1  Cleanwasherl ,c ) ( tT

Fffl ,c ,t máx min ) / (Cl,c  Cl,c ) Ac

CYc

(23)

Profit. The economic aspects are considered in terms of the obtained profit. This is generated by the incomes for the sale of crops ( Sr ) and the outcomes by capital ( Capc ) and operating costs ( Copc ). Proffit  Sr - Copc - Capc

(24)

where Sr , Capc and Copc are calculated as follows: Sr   Cucsl Pc Acc

(25)

Copc  Fwc  Flc  Pump op  Pip op  Swc op  Tuc op

(26)

Capc  Pump cap  Pip cap  Swc cap  Tuc cap

(27)

cC


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In the above equations, Cucsl is the unitary sale price of crops, Acc are the cultivated hectares, Fwc is the fresh water cost, Flc is the fertilizer cost, Pump op is the pumping operating cost, Pip op is the pipeline operating cost, Swc op is the operating cost of storage tanks, Tuc op is the operating cost of treatment units, Pump cap is the pumping capital cost, cap cap Pip cap is the piping capital cost, Swc is the capital cost of storage tanks and Tuc is the

capital cost of treatment units. Here, it must be noted that the cost for the crop harvesting in the proposed model is not included. This is because the harvesting cost is fixed per hectare and it can be calculated prior to the optimization process and added to final value of the economic objective function; which does not change the behavior of the results and conclusions. In addition, the consideration of the aforementioned cost has an effect on the performance of the results when the allocation of crops in croplands is a variable. And the mathematical relationships for calculating the above listed economical terms are given in the Supporting Information. Water network: reuse, recycle and regeneration. The design of the water network is based on the proposed superstructure by Rubio-Castro, et al.

12

whose configurations are

given in Figure 2. Where is possible to see that all configurations of interest for the use, reuse and regenerations of water are included.



Rainwater

Rainwater

Crop Land 1 Storage Tank 1 Crop Land 2

Discharge

Damn

Treatment Unit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Crop Land 3 Storage Tank 3 Crop Land 4 Storage Tank 4

Storage Tank 2

Natural Resorvoir

Figure 2. Proposed superstructure for agriculture water use optimization Required water of crops. The required water by crops for each period ( Fwccin,t ) is determined by the water depth ( Lic ,t ), the crop area ( Acc ) and the irrigation efficiency (cir ), Fwccin,t 

Lic ,t Acc

cir

,

(28)

c  C; t  T

and the water depth depends of the field capacity (  fc ), the root depth ( Drc ,t ) and the irrigation criterion ( Crc ): Lic ,t   fc Drc ,t Crc ,

c  C; t  T

(29)

In Table S3 of the Supporting Information are given values for  fc in terms of the type of soils. Besides, the water demand determines the irrigation time for each period ( Tic ,t ):


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Tic ,t 

Fwccin,t Qwccin,t

, c  C; t  T

(30)

where Qwccin,t is the volumetric flow. Mass balance for fresh water. The total fresh water flowrate for each period ( Fwf wtot,t ) is equal to the fresh water demanded by each crop ( Fwfsw,c ,t ):

Fwf wtot,t   Fwfsw,c ,t ,

w W ; t  T

(31)

cC

Here, there is needed an upper limit (  max w,t ) because the use of fresh water is related to the availability. (32)

Fwf wtot,t   max w W , t  T w,t ,

It should be noted that there are considered several types of fresh water. This because in some cases there are available different sources for fresh water. Crop yield. The crop yield ( Pc ) is a function of fertilizers and water: Pc  f  water , fertilizer  , c  C

In this sense, Martínez, et al.

23

(33)

developed a set of relationships to determine the yield of

corn, alfalfa, sunflower, rice, wheat and barley (see Table 5). While, Hinojosa-Velasco

24

reported a relationship to calculate the yield of bean in terms of nitrogen and sulfur (see Table 5). Table 5. Correlations to calculate the crop yield. Crop Corn

Flood Irrigation Y=0.506+0.113·10-2X-0.119·106X2+0.226·10-1 N-0.382·104N2+0.161·10-5XN

Sprinkling Irrigation Y=0.506+0.154·10-2X-0.141·106X2+0.210·10-1 N-0.361·104N2+0.140·10-5XN

R2aj=0.918

R2aj=0.995 15 ACS Paragon Plus Environment


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Wheat

Y=0.871+0.951·10-3X-0.145·106X2+0.172·10-1 N-0.336·104N2+0.249·10-5XN

Y=0.762+0.888·10-3X-0.114·106X2+0.185·10-1 N-0.538·104N2+0.272·10-5XN

Barley

R2aj=0.971 Y=0.936+0.845·10-3X-0.217·106X2+0.176·10-1 N-0.439·104N2+0.453·10-5XN

R2aj=0.983 Y=0.891+0.815·10-3X-0.196·106X2+0.168·10-1 N-0.499·104N2+0.48823·10-5XN

Alfalfa

R2aj=0.969 Y=4.522+0.295·10-2X-0.196·106X2+0.296·10-1 N-0.254·103N2+0.163·10-5XN

R2aj=0.982 Y=4.266+0.291·10-2X-0.196·106X2+0.279·10-1 N-0.274·103N2+0.282·10-5XN

R2aj=0.972 Y=0.325+0.573·10-3X-0.128·106X2+0.200·10-1 N-0.656·10Sunflower 4N2+0.127·10-5XN

R2aj=0.976 Y=0.521+0.502·10-3X-0.920·107X2+0.189·10-1 N-0.649·104N2+0.174·10-5XN

R2aj=0.982 Y=1.324+0.444·10-3X-0.210·107X2+0.172·10-1 N-0.930·104N2+0.104·10-5XN

Rice

R2aj=0.980

R2aj=0.975

Y=867.24+1.8822X1 -1.415X 2 +0.013X12 Bean

+0.0008X 22 +0.0068X1X 2 Note: Y is the crop yield in ton/ha, X is the used water in m3/ha, N is the employed nitrogen in kg/ha

Mass balance in the inlet of each crop. The total inlet flowrate on each crop ( Fcctot,t ,in ) is determined by water and fertilizer ( Fwccin,t , Ffclin,c ,t ),

Fcctot,t ,in  Fwccin,t   Ffclin,c ,t ,

c  C, t  T

(34)

lL

where the water flowrate is composed by fresh water ( Fwfsw,c ,t ), precipitated water ( Fwpcc ,t ), capillary rise of phreatic level ( Fwrcc ,t ), the water reused coming from other

crops ( Fwccc ,c ,t ) and the recirculated water from storage tanks ( Fwsts ,c ,t ). This is shown in 1

Figure S1 of the Supporting Information.

Fwccin,t 

 Fwfs

wW

w , c ,t

 Fwpcc ,t  Fwrcc ,t   Fwccc1 ,c ,t   Fwsts ,c ,t , c1C

c  C, t  T

(35)

sS


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In the same way, the fertilizer flowrate is formed by fresh fertilizer ( Fff l ,c ,t ), the reused fertilizer ( Ffccl ,c1 ,c ,t ), the fertilizer coming from the storage tanks ( Ffrtl , s ,c ,t ), atmospheric deposition ( ADc ), available organic fertilizer ( Of c ) and the mineralized nitrogen ( MN c ).

Ffclin,c ,t  Fffl ,c ,t   Ffccl ,c1 ,c ,t   Ffstl , s ,c ,t  ADc  Of c  MN c , c1C

l  L; c  C , t  T

(36)

sS

Therefore, the reused water and fertilizers of each period ( Fwrtc ,t , Ffrcl ,c ,t ) as well as the inlet fertilizer concentration ( Cfclin,c ,t ) are estimated as follows: Ffrcl ,c ,t   Ffstl , s ,c ,t   Ffccl ,c1 ,c ,t , sS

Fwrtc ,t   Fwsts ,c ,t   Fwccc1 ,c ,t , sS

in l , c ,t

Cfc



Ffclin,c ,t Fcctot,t ,in

l  L; c  C , t  T

(37)

c1C

c  C, t  T

(38)

c1C

l  L; c  C ; t  T

,

(39)

Mass balance in the outlet of each crop. The outlet flowrate (see Figure S2 of the Supporting Information) of each crop ( Fcctot,t ,out ) is formed by water and fertilizers that could not be used for the crops ( Fwccout,t , Ffclout , c ,t ).

Fcctot,t ,out  Fwccout,t   Ffclout , c ,t ,

c  C, t  T

(40)

lL

Here, the outlet water is equal to the inlet water minus the absorbed water ( Fwccab,t ) and the loss water due to evapotranspiration ( Fwccev,t ): in ab ev Fwccout ,t  Fwcc ,t  Fwcc ,t  Fwcc ,t ,

c  C; t  T

(41)

With respect to the absorbed and lost water, these are related to the efficiencies of soil storage and consuming use (cst ,ccu ): 17 ACS Paragon Plus Environment


Page 18 of 53

Fwccab,t  cst Lic ,t Ac ,

c  C; t  T

(42)

Fwccev,t  ccu Lic ,t Ac ,

c  C; t  T

(43)

In the above equations, the term Lic ,t Ac is the water depth times the total crop area. Besides, the fertilizer outlet is the difference between the inlet fertilizer and the absorbed fertilizer by crops ( Ffclab,c ,t ): in ab Ffclout , c ,t  Ffcl , c ,t  Ffcl , c ,t ,

l  L; c  C ; t  T

(44)

In this regard, the absorbed fertilizer is determined by absorption efficiency for each crop (

lab,c ): Ffclab,c ,t  lab,c Ffclin,c ,t ,

l  L; c  C ; t  T

(45)

Finally, the outlet flowrate of each crop can be sent to the environment ( Fcec ,t ), to other crops ( Fccc ,c ,t ), to the treatment units ( Fctuc ,u ,t ) and/or to the storage tanks ( Fcstc , s ,t ): 1

Fcctot,t ,out  Fcec ,t   Fccc ,c1 ,t   Fcstc , s ,t   Fctuc ,u ,t , c1C

sS

c  C, t  T

(46)

uU

Also, it is necessary to know the fertilizer concentration in the outlet of each crop ( Cfclout , c ,t ): out l , c ,t

Cfc



Ffclout , c ,t Fcctot,t ,out

,

l  L; c  C ; t  T

(47)

This concentration is required to determine the fertilizer that is exchanged between crops: Ffccl ,c ,c1 ,t  Cfclout , c ,t Fccc , c1 ,t

(48)

From the above flowrate, it is calculated the exchanged water between crops ( Fwccc ,c1 ,t ):

Fccc ,c1 ,t  Fwccc ,c1 ,t   Ffccl ,c1 ,c ,t , c1C

c  C ; c1  C ; t  T

(49)


Page 19 of 53 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mass balance in the storage tanks. The next mathematical relationship represents the mass balance in the storage tanks:

Fststot,t  Fststot,t 1   Fcstc , s ,t   Frscs ,c ,t , s  S ; t  T cC

(50)

cC

here Fststot,t is the total inlet flowrate of each period t, Fststot,t 1 is the total inlet flowrate in the period t-1, Fcstc , s ,t is the flowrate from crops to storage tanks and Frscs ,c ,t is the flowrate from the storage tanks to crops. In addition, the next constraint is used to fix that the storage tanks are empty before the first period. Fststot,t 0  0, s  S

(51)

With regard to determine the quantity of fertilizers in the storage tanks, it is required the next component mass balance: Cfsl , s ,t Fststot,t  Cfsl , s ,t 1 Fststot,t 1   Cfclout , c ,t Fcstc , s ,t   Cfsl , s ,t Frscs , c ,t , s  S ; t  T ; l  L cC

(52)

cC

In the above equation, Cfsl , s ,t is fertilizer concentration in the storage tanks during each time period. Hence, to determine the water in the storage tanks is necessary the next mass balance:

  Fststot,t   Cfsl , s ,t Fststot,t   Fststot,t 1   Cfsl , s ,t 1 Fststot,t 1   lL lL     out   Fcstc , s ,t   Cfcl ,c ,t Fcstc , s ,t   cC lL  cC      Frscs ,c ,t   Cfsl , s ,t Frscs ,c ,t  , s  S ; t  T cC lL  cC 

(53)

Notice that the left sides of equations 52 y 53 represent the fertilizer and water in the storage tanks in the period t, the first term of the right side represents the raw material in the period t-1, the second term of the right hand side represents the fertilizer ( Ffstl , s ,c ,t ) and 19 ACS Paragon Plus Environment


Page 20 of 53

water ( Fwstc , s ,t ) that are sent from the crops to the storage tank in the period t; while the last term of the right hand side includes the recirculated fertilizer ( Ffrtl , s ,c ,t ) and water ( Fwst s ,c ,t ) from the storage tanks to crops in the period t. In this sense, the aforementioned

variables are calculated as follows: Ffstl , s ,c ,t  Cfsl , s ,t Frscs ,c ,t ,

l  L; s  S ; c  C ; t  T

Fwsts ,c ,t  Frscs ,c ,t   Cfsl , s ,t Frscs ,c ,t ,

s  S ; c  C; t  T

(54) (55)

lL

Ffstl ,c , s ,t  Cfclout , c ,t Fcstc , s ,t ,

l  L; c  C ; s  S ; t  T

Fwctc , s ,t  Fcstc , s ,t   Cfclout , c ,t Fcstc , s ,t ,

c  C; s  S ; t  T

(56) (57)

lL

From the above equations is possible to determine the total flowrate from storage tanks to crops ( Frscs ,c ,t ) and from crops to storage tanks ( Fcstc , s ,t ):

Frscs ,c ,t  Fwsts ,c ,t   Ffstl , s ,c ,t , s  S ; c  C ; t  T

(58)

Fcstc , s ,t  Fwctc , s ,t   Ffctl ,c , s ,t ,

(59)

lL

c  C; s  S , t  T

lL

Mass balance in the treatment units. To meet the environmental constraints, the installation of treatment units is required (see Figure 2). The inlet flowrate in the treatment units ( Ftuutot,t ) is equal to the flowrate segregated from crops to these ones ( Fctuc ,u ,t ); while the

outlet flowrate is sent to the environment discharge ( Ftueu ,t ). Therefore, the mass balance is represented as follows:

Ftuutot,t   Fctuc ,u ,t  Ftueu ,t ,

u U ; t  T

(60)

cC

And a component balance is given in the next mathematical expression:


Page 21 of 53 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


out Cftlin,u ,t Ftuu ,t   Cfclout , c ,t Fctuc ,u ,t  Cftl ,u ,t Ftueu ,t ,

l  L; u  U ; t  T

(61)

cC

  Ftuu ,t  Cftlin,u ,t Ftuu ,t    Fctuc ,u ,t   Cfclout , c ,t Fctuc ,u ,t   cC  cC 

 Ftue

u ,t

 Cft

out l ,u ,t

Ftueu ,t  ,

(62)

l  L; u  U ; t  T

Similarly to equations 52 and 53, using the terms of equations 61 and 62 is possible to determine the flowrates of fertilizer and water ( Ffctul ,c ,u ,t , Fwctuc ,u ,t ) that are sent from the crops to the treatment units; and the fertilizer and water that are sent from treatment units to the environmental discharge ( Fftuel ,u ,t , Fwtueu ,t ). Ffctul ,c ,u ,t  Cfclout , c ,t Fctuc ,u ,t ,

l  L; c  C ; u  U ; t  T

Fwctuc ,u ,t  Fctuc ,u ,t   Cfclout , c ,t Fctuc ,u ,t ,

c  C; u U ; t  T

(63) (64)

lL

Fftuel ,u ,t  Cftlout ,u ,t Ftueu ,t ,

l  L; u  U ; t  T

Fwtueu ,t  Ftueu ,t   Cftlout ,u ,t Ftueu ,t ,

u U ; t  T

(65) (66)

lL

The total flowrate coming from the crops to the treatment units ( Fctuc ,u ,t ) and from treatment units to the environmental discharge ( Ftueu ,t ) are calculated with the next expressions: Fctuc ,u ,t   Ffctul ,c ,u ,t  Fwctuc ,u ,t ,

c  C; u U ; t  T

(67)

lL

Ftueu ,t   Fftuel ,u ,t  Fwtueu ,t ,

u U ; t  T

(68)

lL

Finally, the fertilizer concentration in the outlet of treatment units is determined by the efficiency of treatment units for removing each fertilizer (lrem ). ,u in rem Cftlout ,u ,t  Cftl ,u ,t 1  l ,u  , l  L; u  U ; t  T

(69) 21

ACS Paragon Plus Environment


Page 22 of 53

Mass balance in the environmental discharge. The wastewater discharged to the environment during each time period ( Fet ) is composed by the flowrate segregated form the crops ( Fcec ,t ) and the flowrate that is sent from the treatment units ( Ftueu ,t ): Fet   Fcec ,t   Ftueu ,t , cC

t T

(70)

uU

Hence, the component balance is represented as follows: out Cfel ,t Fet   Cfclout , c ,t Fcec ,t   Cftl ,u ,t Ftueu ,t , cC

l  L; t  T

(71)

uU

and to meet with the environmental constraints, there is used the next constraint: max Cfel ,t   Cfe , l,t

(72)

l  L; t  T

max Where Cfe is an upper limit for the concentration of fertilizers in the environmental l,t

discharge. RESULTS AND DISCUSSION To demonstrate the application of the proposed model and to show the implications of water integration in agriculture, two case studies were analyzed. The conditions are representative of the agricultural activity in the state of Sinaloa in Mexico. In the first case, four corn crops are considered, whose distribution is presented in Figure 3. In each distribution, five irrigations are considered (time periods), which are commonly known as: prior to planting, first, second, third and fourth auxiliary irrigation. The corn crop yield expressions for flood irrigation systems were taken from Table 5.23


200 m

Crop land 250 m

600 m

250 m

50 m

600 m 250 m

Corn

550 m

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Corn

50 m

100 m 100 m

Corn

250 m

250 m

550 m

Page 23 of 53

Corn

Figure 3. Crop distribution for case 1 Also, Table S4, of the Supporting Information, shows the values of both economic and operational parameters used for solving the first case. The minimum production for this farmland was of 150 tonnes, this to meet the market demands. In addition, an average precipitation for each irrigation period was considered (see Table S5 of the Supporting Information) and a water lost by evapotranspiration of 2.5 % of the water depth are considered. With regard to the water availability value in each period, it is assumed to have fresh water to meet with the required water by crops (traditional irrigation system). This assumption allows determining the effect over the traditional irrigation system when there is considered the environmental impact (Eco-indicator 95 and water footprint). While the second case study includes twelve crops, which are constituted by four corn crops, four bean crops, two wheat crops and two alfalfa crops, whose distribution is presented in Figure 4. For this case, 17 irrigation periods are considered; Table 6 presents the irrigation scheduling for each crop. Also, the yield expressions of each crop used in this work are presented in Table 5, which are yield expressions for flood irrigation systems.23,

24

Although the nitrogen and 23



Page 24 of 53

phosphorus are macronutrients, nitrogen requirements are higher than those of phosphorus, since nitrogen is a cellular structural component as well as being necessary for the formation of amino acids, proteins, and enzymes; while phosphorus participates in metabolic processes, such as photosynthesis, energy transfer and the synthesis and degradation of carbohydrates. In this sense, nitrogen is usually the limiting nutrient in crops, and its only consideration is enough to establish crop yields. In this regard, the used fertilizer in the considered cultivation site is Urea, which has an NPK composition of 46-00 (46% nitrogen, 0% phosphorous, 0% potassium). However, the proposed model is general, and this can consider any different fertilizer. To solve the proposed multi-objective optimization model for the addressed case studies, the Epsilon constraint method was implemented. This way, first the lower bound of fresh water consumption is obtained, minimizing this objective function, in this way the upper bound for the environmental objective was obtained at the same time, because they are contradictory objectives. Subsequently, the environmental objective is minimized and the lower bound is obtained, which in turn gives the upper bound of water consumption. Then, intermediate points of the environmental objective function were set and the consumption of fresh water in each of these points was minimized, with these points the Pareto curve was constructed. The addressed problem is a mixed-integer nonlinear problem, the model formulation for the case of study 2 consists of 3,1571 continuous variables, 3,9437 equations, and 499 binary variables. While the case study 1 consists of 1,925 continuous variables, 2,275 equations, and 52 binary variables. The model formulation was coded in the software GAMS and the solvers DICOPT, CONOPT and CPLEX, and a computer with an intel 7 processor and 8 GB of RAM were used to solve this model. The analysis of the obtained results is presented in the following sections. Table 6. Irrigation periods for Case 2.

Period 1 2 3

1 X

Corn 2 3 X X

4 X

5 X

Crop Bean 6 7 8 X X X

Wheat 9 10

Alfalfa 11 12 X X

X X 24


Page 25 of 53 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4 5 6 7 8 9 10 11 12 13 14 15 16 17

X X X X

X X

X X

X

X

X

X X X

X

X

X

X

X

X

X

X

X

X

X X X X X X X

X X X X X X X

X

X X

X

X

X

Analysis for the first case study. Figure 5 shows the economic benefit as a function of the water footprint and the Eco-indicator. To obtain a better analysis for the surface plot, Figure 5 has been divided into three zones: blue zone, yellow zone and red zone. Therefore, it is observed the following: in blue zone the lower the Eco-indicator value and the greater the water footprint value, the lower the economic benefits; in yellow zone, mean benefit values are obtained at mean values of both water footprint and Eco-indicator; and finally, in red zone, the highest gains are observed, all related to high Eco-indicators values, and it is also observed that at a lower water footprint value, the economic benefit is greater. The latter is because when the lower volume of water is used, the nitrogen needed for crops is higher, therefore the yield in corn production increases and the economic benefit increases.



Fresh Water

Page 26 of 53

Fresh Fertilizer

Corn

Bean

Alfalfa

Alfalfa

Bean

Bean

Corn

Corn

Wheat

Wheat

Corn

Bean

Figure 4. Distribution of crops for case 2 In Figures 6a and 6b, it is possible to identify the maximum value of the economic benefit at the corresponding values of the water footprint, as well as the Eco-indicator. These figures are respectively left and right sides perspective views of Figure 5. Particularly, in these figures, it can be seen that the maximum value of the economic benefit is obtained at a water footprint value of 1500 m3/ha and an Eco-indicator value equal to 11.00. Thus, this case was solved by establishing fixed values for the Eco-indicator and optimizing both the economic benefit and the water footprint, and the results are presented in Figures 7a and 7b. In fact, in Figure 7a is observed a decrease in the water footprint at higher Eco-


Page 27 of 53

indicator values, with a minimum value of 1475 m3/ha at an Eco-indicator value equal to 10.50. This minimum value is the amount of water required to meet the minimum crop production demand. While in Figure 7b, it is possible to observe that at higher Ecoindicator values, higher economic benefit, because the greater the Eco-indicator value, greater the amount of nitrogen applied to the crop is, which results in higher corn production and therefore a higher economic benefit. Besides, the behavior of economic benefit and Eco-indicator respect to fixed values for the water footprint are given in the Figures 8a and 8b. Here, it can be observed that both economic benefits as well as Ecoindicator are directly proportional to the value of water footprint. This because high fertilizer values are required for high water values in order to have an optimal concentration of nutrients; therefore, the performance of crops is increased.

4

x 10 7.3 7.2 7.1 7 6.9

Profit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6.8 6.7 6.6 6.5 6.4

6.3 1700 1680 1660

13

1640

12

1620

11

1600

Water Footprint

10

1580

9

1560

8

1540

7

1520 1500

6

Eco-Indicator

Figure 5. Profit Behavior ($) as function of the Water Footprint (m3/Ha) and the EcoIndicator for case 1



4

7.3

x 10

7.2

7.1

7

Profit

6.9

6.8

6.7

6.6

6.5

6.4

6.3

1500

1520

1540

1560

1580

1600

1620

1640

1660

1680

1700

Water Footprint

a) 4

7.3

x 10

7.2

7.1

7

6.9

Profit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 53

6.8

6.7

6.6

6.5

6.4

6.3

6

7

8

9

10

11

12

13

Eco-Indicator

b) Figure 6. Value of the Water Footprint (a) and Eco-Indicator (b) for the maximum profit for case 1 28 ACS Paragon Plus Environment

Page 29 of 53

1700

Water Footprint

1650

1600

1550

1500

1450

5

6

7

8

9

10

11

12

Eco-Indicator

a) 10 4

7.4

7.2

7

Profit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6.8

6.6

6.4

6.2

5

6

7

8

9

10

11

12

Eco-Indicator

b) Figure 7. Water Footprint (a) and Profit optimization (b) as function of the Eco-Indicator for case 1 29 ACS Paragon Plus Environment


11.3

11.2

Eco-Indicator

11.1

11

10.9

10.8

10.7

10.6 1470

1475

1480

1485

1490

1495

1500

1505

1510

1515

1520

Water Footprint

a) 7.283

10 4

7.282 7.281 7.28 7.279

Profit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 53

7.278 7.277 7.276 7.275 7.274 7.273 1470

1475

1480

1485

1490

1495

1500

1505

1510

1515

1520

Water Footprint

b) Figure 8. Eco-Indicator (a) and Profit (b) behavior as function of the Water Footprint for case 1 30 ACS Paragon Plus Environment

Page 31 of 53 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Irrigation Time 129.63 h Rainwater 13,590 m3

Fresh Water 108 m3

Crop 1

27 m3

246 Kg

246 Kg

Crop 2

27 m3

27 m3

246 Kg

246 Kg

Treatment Unit

6,617 m3 125 Kg

Environmental Discharge3 26,468 m 50 Kg N

Crop 1

Crop 4

2,932 m3

2,932 m3

121 Kg

121 Kg

2,932 m3

121 Kg

121 Kg

3,782 m3 132 Kg

Treatment Unit

0 m3 0 Kg

Rainwater 250 m3

Crop 1 3,782 m3 132 Kg

Crop 2 3,782 m3 132 Kg

3,532 m3

3,532 m3

121 Kg

121 Kg

0 m3 0 Kg

3,532 m3

121 Kg

121 Kg

Treatment Unit Environmental Discharge 0 m3 0 Kg N

Crop 1

3,782 m 132 Kg

Crop 2 3,782 m3 132 Kg

3,782 m3 132 Kg

2,692 m3

2,692 m3

121 Kg

121 Kg

3,782 m3 132 Kg

2,692 m3

121 Kg

121 Kg

0 m3 0 Kg


Fertilizer on the ground 125 Kg

Crop 3

0 m3 0 Kg

2,692 m3

3,782 m3 132 Kg

Crop 4 0 m3 0 Kg

3,782 m3 132 Kg

d) Period 4

c) Period 3 Irrigation Time 70.03 h Rainwater 60 m3

Fresh Water 14,888 m3

Crop 1 3,782 m3 132 Kg

0 m3 0 Kg


Fresh Fertilizer 484 Kg

3,722 m3

3,722 m3

121 Kg

121 Kg

Crop 3

0 m3 0 Kg

0 m3 0 Kg

Crop 2 3,782 m3 132 Kg


0 m3 0 Kg

3,782 m3 132 Kg

3

Crop 4 0 m3 0 Kg


Rainwater 1,090 m3

Crop 3

0 m3 0 Kg

3,532 m3

Irrigation Time 70.03 h



0 m3 0 Kg

Crop 4

b) Period 2

Irrigation Time 70.03 h Fresh Water 14,128 m3

3,782 m3 132 Kg

0 m3 0 Kg

Environmental Discharge 0 m3 0 Kg N

a) Period 1


Crop 3

0 m3 0 Kg

2,932 m3

Crop 2

383 m3 7.25 Kg


0 m3 0 Kg

3,782 m3 132 Kg

383 m3 7.25 Kg

6,617 m3 125 Kg


Rainwater 850 m3

Crop 3

6,617 m3 125 Kg

6,617 m3 125 Kg

383 m3 7.25 Kg

383 m3 7.25 Kg

27 m3

Irrigation Time 70.03 h

Fertiizer on the ground 125 Kg


3,722 m3

3,722 m3

121 Kg

121 Kg


3,782 m3 132 Kg

Crop 4 0 m3 0 Kg

3,782 m3 132 Kg

e) Period 5

Figure 9. Optimal configuration for Case 1 (Best economic benefits) for case 1 31 ACS Paragon Plus Environment


Page 32 of 53

Table 7. Results for case study 1.

Configuration Maximum Intermediate Minimum

Profit $ $ $

72,817.48 68,346.63 63,914.37

Water Footprint (m3/ha)

Eco-Indicator

Corn Production (Tonne)

1500 1645.00 1700.00

11.00 8.00 5.50

193.16 180.56 168.18

It is important to mention that the three configurations studied require: the feed of both fresh water and fresh fertilizer in each of the five irrigation periods, the reuse of water and fertilizer in crops 2 and 4 obtained from crops 1 and 3, respectively. Also, the water and fertilizer recirculation from crops 2 and 4 to crops 1 and 3 through the pipeline and pumping system. Also, notice the implementation of a treatment unit in the first irrigation period of each of the configurations, which works with an efficiency of 90 % to reduce the fertilizer concentration in the discharge to the environment of water outlet, and thus to comply with the maximum permissible limit of nitrogen (50 ppm) in the water discharges by the agricultural activity according to NOM-001-SEMARNAT-1996 25 For the configuration with the minimum economic benefit, it is possible to observe that the water and nitrogen inflows to the treatment unit are of 27.332 m3 and 366.80 kg respectively, while the water outflow remains constant (27.332 m3) and the nitrogen outflow is of 36.8 kg. Whereas, for the configuration with the maximum economic benefit (see Figure 9), the inlets to the treatment unit are 26,468 m3 and 500 kg for water and nitrogen, respectively. While at the treatment unit outlet, the water outflow is remaining constant (26,468 m3) and the nitrogen outflow is 50 kg.


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Finally, for the configuration at intermediate values of the economic benefit and the environmental impact, the water and nitrogen inflows to the treatment unit are 28,000 m3 and 444 kg, respectively. The water outflow is remaining constant (28,000 m3) and the nitrogen outflow is 44.40 kg. As can be seen in the previous analysis, the implementation of the treatment unit allows to comply with the aforementioned norm at the permissible nitrogen concentration in the water discharge to the environment. It is also worth mentioning that each of the configurations reported in Table 7 meets the corn demand of 150 tonnes. In addition, the Eco-indicator reported in that table (11, 8 and 5) corresponds to one crop, therefore to obtain the total Eco-indicator each value must be multiplied by four. Analysis for the second case. Based on the results obtained, in Figure 10 it is possible to observe that the economic benefit increases as the eco-indicator does as well, exhibiting a maximum value when the Eco-indicator is equal to 225. Also, it is found that the economic benefit begins to decrease slightly after this point. In Figures 11a and 11b, which are respectively left and right-side views of Figure 10, it can be seen with greater clarity that the maximum economic benefit is at an Eco-indicator value of 225, as well as it can be observed that the economic benefit remains practically constant when the water footprint is varied, keeping the Eco-indicator value constant. Therefore, in this case study, it is possible to establish that the economic benefit is more sensitive to the Eco-indicator, rather than to the water footprint. In addition to the above, several configurations representing the maximum, intermediate and minimum economic benefit were analyzed (see Figures S3-S18 in the Supporting



Page 34 of 53

Information). In these figures, the environmental impact associated with each crop can be observed in Figures 12a, 12b and 12c, and it is found that for the configuration with the maximum economic benefit the majority of the crops have an Eco-indicator greater than 20, by which we can conclude that all crops with exception of crops 11 and 12 (alfalfa crops) have a significant contribution to the environmental impact. This is because the alfalfa crop yield is significantly higher than the yield of other crops in relation to the amount of fresh fertilizer. With regard to the configuration with the intermediate benefit, in Figure 12a is possible to observe that crops 5 and 7 (bean crops) are the crops that most impact the environment. It is because the Eco-indicator is calculated from the amount of fresh fertilizer applied to the crop and the crop yield. Therefore, in Table 8, it is found that these crops as well as crops 11 and 12 demand more fresh fertilizer; however, crops 5 and 7 have a yield of 2.18 tonne per hectare, while yields for crops 11 and 12 are 125 tonnes per hectare, thus crops 5 and 7 have a much larger Eco-indicator. Further, it is observed in Figure 12c that the Ecoindicator value for crop 5 is approximately double with respect to the other crops; it is because of the great amount of nitrogen demanded by the crop and the low crop yield; compared with other crops. Finally, in terms of the configurations reported in Figures S3-S18 in the Supporting Information, it is possible to observe the mass exchange (water and fertilizer) between crops that demand water in the same irrigation periods (see Table 6); for example in 34 ACS Paragon Plus Environment

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Figure 13 is presented the global configuration for the best economic scenario. Particularly, the flows given in Figure 13 correspond to the irrigation period 1; therefore, only in the crops 1-8 there are fed and outlet of water and fertilizer. It is due to these crops are irrigated in the period 1, while the remaining interconnections are given in the Supporting Information.

5

x 10 2.75 2.7 2.65 2.6 2.55

Profit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.5 2.45 2.4 2.35 2.3 2.25 4.5

4

4

x 10

Water Footprint

3.5

3

140

150

160

170

180

190

200

210

220

230

240

Eco-Indicator

Figure 10. Profit behavior as function of the Water Footprint and the Eco-Indicator for case 2


250


5

x 10 2.7

2.65

2.6

2.55

Profit

2.5

2.45

2.4

2.35

2.3

2.25 140

150

160

170

180

190

200

210

220

230

240

250

Eco-Indicator

a) 5

x 10 2.7

2.65

2.6

2.55

Profit

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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 53

2.5

2.45

2.4

2.35

2.3

2.25

3

3.5

4

Water Footprint

4.5 4

x 10

b) Figure 11. Variation of the de Eco-Indicator (a) and of the Water Footprint (b) for case 2


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a)

b)

c) Figure 12. Eco-Indicators by crop for the maximum (a), intermediate (b) and minimum (c) profit for case 2



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Table 8. Eco-Indicators, fresh fertilizer and yield values for each crop for case 2. Profit MAXIMUM $270,137.97

INTERMEDIATE $248,571.05

MINIMUM $226,142.71 Profit MAXIMUM $270,137.97

INTERMEDIATE $248,571.05

MINIMUM $226,142.71

Variable

Crop 1

Crop 2

Crop 3

Crop 4

Crop 5

Crop 6

Eco-Indicator

25.26

23.00

24.92

15.31

26.07

28.98

Fresh Fertilizer

1218.03

1067.69

1195.52

555.46

906.25

1015.49

Yield

9.93

9.93

9.93

9.92

2.18

2.18

Eco-Indicator

12.86

16.30

12.80

12.58

29.17

14.95

Fresh Fertilizer

362.42

592.21

364.32

352.25

1022.97

327.83

Yield

8.53

8.83

8.77

8.89

2.18

1.25

Eco-Indicator

12.32

13.25

12.32

11.55

31.89

16.66

Fresh Fertilizer

316.64

378.60

316.64

267.66

1125.00

373.34

Yield

8.00

8.13

8.00

Variable

Crop 7

Crop 8

Crop 9

8.00 Crop 10

2.18 Crop 11

1.25 Crop 12

Eco-Indicator

26.64

22.60

15.50

15.50

0.62

0.62

Fresh Fertilizer

927.76

775.50

843.75

843.75

2393.39

2385.57

Yield

2.18

2.18

8.40

8.40

125.16

124.92

Eco-Indicator

27.65

14.95

11.26

11.26

0.62

0.62

Fresh Fertilizer

965.70

327.83

507.14

507.14

2394.41

2390.13

Yield

2.18

1.25

6.81

6.81

125.20

125.07

Eco-Indicator

14.95

14.95

5.47

5.47

0.62

0.58

Fresh Fertilizer

327.83

327.83

72.42

72.42

2388.51

2035.15

Yield

1.25

1.25

3.68

3.68

125.01

114.05


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4,221 Kg N

83,381 m3

Fresh Water

Fresh Fertilizer 434 Kg N 160.19 h

201.85 h

Corn

Bean

625 Kg N

10,377 m3 208 Kg N

10,924 m3 16,801 m3

Alfalfa

Alfalfa

9,174 m3 184 Kg N

1,727 m3 35 Kg N

625 Kg N 8,650 m3 152 Kg N

201.85 h

201.85 h

625 Kg N

Bean

Bean 3

4,385 m 88 Kg N

10,586 m3 212 Kg N

10,924 m3

7,477 m3

Corn

414 Kg N

160.19 h

160.19 h 414 Kg N

Corn

16,801 m3

6,215 m3

Wheat

Wheat

8,650 m3 145 Kg N 8,650 m3 145 Kg N

458 Kg N

6,515 m3 131 Kg N

625 Kg N

160.19 h

201.85 h

Corn

Bean

8,151 m3

5,823 m3

314 m3 6 Kg N Environmental Discharge 9,173 m3 170 Kg N

Figure 13. Optimal configuration for Case 2 (Period 1, Best economic benefits)



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To show the overall merit of the proposed method, a comparison of the results obtained above with the conventional method, in which no integration is considered and only fresh water and fresh fertilizer is used is presented. In Table 9 are shown the Eco-indicator values, the water footprint and the associated costs for the proposed method and the conventional method, respectively. It should be noted that there is a reduction of approximately 52 % and 33 % in the fresh water and fertilizer consumption of the proposed method with respect to the conventional method. In the same way, there is a great reduction of the Eco-indicator by 33 % for the proposed method in comparison with the conventional method and the profit has an increment of 18 % in the proposed method with respect to the conventional one. Table 9. Results for the proposed and conventional methods for case study 2. Proposed Method

Conventional Method

270,861

229,500

225

339

Water footprint

44,500

170,821

Crops sell ($)

289,649

255,958

Fresh water ($)

5,747

12,179

Fresh fertilizer ($)

9,555

14,279

Pumps ($)

3,022

0

Piping ($)

464

0

Results Profit ($) Eco-indicator

CONCLUSIONS A mixed-integer nonlinear model was proposed for the optimization of the water and fertilizer use in agriculture considering simultaneously the environmental and economic aspects. Therefore, a multi-objective problem was formulated considering the environmental impact by the Eco-indicator 95 and the water footprint, while the economic impact is defined by the economic benefit associated with crop production. This model is 40 ACS Paragon Plus Environment

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based on a superstructure where all configurations of interest are considered, in terms of use, reuse, and recycle of water and fertilizer. The proposed model was applied to two case studies using operational, economic, and design data representative of the agricultural activity in the state of Sinaloa in Mexico with the purpose of demonstrating its applicability. The obtained results were presented and analyzed by 3D Pareto diagrams; which exhibit the advantages and importance of considering the environmental impact on agricultural activity to yield a sustainable process. Specifically, it is possible to indicate that the Eco-indicator 95 exerts the greatest impact on the economic objective function, this with respect to the water footprint.

AUTHOR INFORMATION Corresponding Author: *E-mail: [email protected] ORCID Jesús M. Núñez-López: 0000-0003-1543-9676. Oscar M. Hernández-Calderón: 0000-0002-4216-2409 José M. Ponce-Ortega: 0000-0002-3375-0284 Maritza E. Cervantes-Gaxiola: 0000-0002-5915-0703 Eusiel Rubio-Castro: 0000-0002-4790-5806 ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at Supporting_Information.docx. Detailed information for the case study, data parameters and mathematical relationships to estimate the capital and operating costs for the proposed model as well as its nomenclature.



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ACKNOWLEDGMENTS The authors acknowledge the financial support by SEP-CONACYT (2013-2014).

NOMENCLATURE Parameters Acc

crop area, Ha

ADc

atmospheric nitrogen deposition, kg/ha

Bf c

biological nitrogen fixation, kg/ha

Clmáx ,c

upper limit for fertilizer concentration in crops, kg/m3

Cl,cmin

lower limit for fertilizer concentration in crops, kg/m3

Crc

irrigation criteria

Drc ,t

root depth, cm

Ef c

exchange frequency of water

Ef l CO2

emission factor for carbon dioxide (CO2)

Ef l N 2O

emission factor for nitrogen dioxide (N2O)

Ef l NH 3

emission factor for ammonia (NH3)

N 2O Ef Gw

equivalence factor of N2O for global warming

NH 3 Ef Aci

equivalence factor of NH3 for acidification

NH 3 Ef Eutro

equivalence factor of NH3 for eutrophication


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NO3  N Ef Eutro

equivalence factor of NO3-N for eutrophication

FCac

available field capacity, mm/dm

FCcRZE

field capacity in the effective rooting zone, mm

Fwpcc ,t

precipitated water, mm

Fwrcc ,t

capillary rise of water table, mm

g

acceleration due to the gravity, m2/s

gc

conversion factor for the acceleration due to the gravity, kg m/ N s2

If c

nitrogen immobilization, kg/ha

n

number of years of operation, year

NM c

nitrogen mineralization, kg/ha

NvGw

normalization value for global warming, kg CO2 eq.

NvAci

normalization value for acidification, kg SO2 eq.

NvEutro

normalization value for eutrophication, kg PO4 eq.

Of c

organic nitrogen fertilizer, kg/ha

Pipcap

capital cost of pipelines, US$

Pump cap

capital cost of pumps, US$

Qwccin,t

volumetric flowrate, m3/h

RNSc

nitrogen removal with harvested crops, kg/ha



RZec

effective rooting zone, dm

Swccap

capital cost of storage tanks, US$

Tuccap

capital cost of treatment units, US$

Wcdrain

rate of drainage water, mm

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Wc precip _ year annual precipitation rate, mm Wc precip _ summer

summer precipitation rate, mm

Wc precip_winter

winter precipitation rate, mm

WfGw

weighting factor for global warming

WfAci

weighting factor for acidification

WfEutro

weighting factor for eutrophication

Greek symbols

ccu

efficiency of consumptive use, dimensionless

cir

irrigation efficiency, dimensionless

cst

storage efficiency, dimensionless

lab,c

efficiency of absorption of fertilizers by the crop, dimensionless

lrem ,u

efficiency in each treatment unit to remove each fertilizer, dimensionless

 fc

field capacity, cm3 of water cm-3 of soil

 pwp

permanent wilting point, cm3 of water cm-3 of soil 44 ACS Paragon Plus Environment

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max  Cfe l,t

upper limit of concentration for each fertilizer in the environmental discharge, ppm

 max Fcc

upper limit of the pump capacity to handle the flowrate between crops, m3/h

 max Fcst

upper limit of the pump capacity to handle the flowrate from the crops to storage tanks, m3/h

 max Fstc

upper limit of pump capacity to handle the flowrate between crops, m3/h

 max Fst

upper limit of capacity for treatment units, m3/h

max  ctu

upper limit of the pump capacity to handle the flowrate from the crops to treatment units, m3/h

 max Ftu

upper limit of capacity for treatment units, m3/h

 max w,t

upper limit for each type of fresh water in the periods, m3

Variables Acileff,c

acidification effect, kg SO2 eq.

Capc

capital cost, US$

Cfclout , c ,t

outlet fertilizer concentration in the crops, ppm

Cfclin,c ,t

inlet fertilizer concentration in the crops, ppm

Cfel ,t

fertilizer concentration in the environmental discharge, ppm

Cfsl , s ,t

fertilizer concentration in the storage tanks, ppm

Copc

operating cost, US$ 45 ACS Paragon Plus Environment


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Cleanwasher fraction of clean washer water

CO2 emissions, kg/ha (CO2 )lemis ,c Cu slc

unitary price of the sale of crops, US$ton-1

Eco  indicadorl ,c

eco-indicator value, dimensionless

Eutroleff,c

eutrophication effect, kg de PO4 eq.

Fcctot,t ,in

total inlet flowrate in the crops, kg/h

Fcctot,t ,out

total outlet flowrate in the crops, kg/h

Fccc ,c1 ,t

flowrate between crops, kg/h

Fcec ,t

flowrate from crops to environment discharge, kg/h

Fcstc , s ,t

flowrate from crops to the storage tanks, kg/h

Fcstccapc ,s

pump capacity to handle the flowrate from crops to the storage tanks, m3

Fctuc ,u ,t

flowrate from crops to treatment units, kg/h

Fet

flowrate in the environmental discharge, kg/h

Ffclab,c ,t

fertilizer absorbed by the crop, kg/h

Ffclin,c ,t

inlet fertilizer flowrate in the crops, kg/h

Ffclout , c ,t

outlet fertilizer flowrate in the crops, kg/h

Ffccl ,c1 ,c ,t

fertilizer flowrate between crops, kg/h

Ffctul ,c ,u ,t

fertilizer flowrate from crops to treatment units, kg/h


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Fff l ,c ,t

fresh fertilizer flowrate, kg/h

Ffrtl , s ,c ,t

fertilizer flowrate from the storage tanks to crops, kg/h

Fftuel ,u ,t

fertilizer flowrate from treatment units to environment discharge, kg/h

Flc

fertilizer cost, US$/year

Frscs ,c ,t

flowrate from storage tanks to each crop kg/h

Ftueu ,t

flowrate from treatment units to the environmental discharge, kg/h

Fwc

fresh water cost, US$/year

Fwccab,t

absorbed water flowrate by the crops (soil and plants), m3/h

Fwccev,t

lost water flowrate by evapotranspiration in the crops, m3/h

Fwccin,t

inlet water on each crop, m3/h

Fwccout ,t

outlet water on each crop, m3/h

Fwccc1 ,c ,t

water flowrate between crops, m3/h

Fwctuc ,u ,t

water flowrate from crops to treatment units, m3/h

Fwfsw,c ,t

fresh water flowrate on each crop, m3/h

Fwrtc ,t

reused water flowrate, m3/h

Fwst s ,c ,t

water flowrate from crops to storage tanks, m3/h

Fwtueu ,t

water flowrate from the treatment units to the environment discharge, m3/h

Gwleff,c

global warming effect, kg CO2 eq. 47 ACS Paragon Plus Environment


Lic ,t

depth water, m3/ha

NAcil ,c

normalized value for acidification effect

NEutrol ,c

normalized value for eutrophication effect

NGwl ,c

normalized value for global warming effect

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NH3 emissions, kg/ha ( NH 3 )lemis ,c NO3-N emissions, kg/ha ( NO3  N )lemis ,c ( N 2O)lemis ,c

N2O emissions, kg/ha

Pc

crop yield, ton/ha

Pip op

piping cost, US$/year

Proffit

annual profit, US$/year

Pumpop

pumping cost, US$/year

Sr

sales, US$/year

Swcop

storage tank cost, US$/year

Tic ,t

irrigation time, h

Tucop

treatment cost, US$/year

WAcil ,c

weighting value for acidification effect

WEutrol ,c

weighting value for eutrophication effect

WFc proc

total water footprint, m3/ha 48 ACS Paragon Plus Environment

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WFcazul

blue water footprint, m3/ha

WFcverde

green water footprint, m3/ha

WFcgris

grey water footprint, m3/ha

WGwl ,c

weighting value for global warming effect

Binary variables z

binary variable to determine the existence or not of accessories and equipment processes, 0 or 1

Subscript c

crop

l

fertilizer

s

storage tanks

t

period

u

treatment units

w

fresh water type

Superscript ab

absorbed

cap

capital

ev

evapotranspiration

in

inlet



max

upper limit

op

operating

out

outlet

pip

piping

pump

pump

rem

removal fertilizer

sl

sell

tot

total

tu

treatment unit

Page 50 of 53

Scalars NUMPT number of periods

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For Table of Contents Use Only

Fertilizer

Dam

Rainwater

Corn Crop

Sustainable Agriculture

Bean Crop

Storage Tank Treatment Unit

Water

Ecosystem Fertilizer

Water + Fertilizer

Synopsis This paper presents a mixed integer nonlinear programming model for the optimal design of agricultural water networks that simultaneously considers economic and environmental aspects.


Optimal Design of Sustainable Agricultural Water Networks - ACS

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