Optimal Design of Cogeneration Systems To Use Uncertain Flare

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Optimal Design of Cogeneration Systems to Use Uncertain Flare Streams Javier Tovar-Facio, Fadwa T. Eljack, José María Ponce-Ortega, and Mahmoud M El-Halwagi Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 24 May 2017 Downloaded from http://pubs.acs.org on May 28, 2017

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Industrial & Engineering Chemistry Research

Optimal Design of Cogeneration Systems to Use Uncertain Flare Streams Javier Tovar-Facio,a Fadwa Eljack,b José María PonceOrtega,a* Mahmoud M. El-Halwagic,d

a

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mich., 58060, México b c

Department of Chemical Engineering, Qatar University, Doha, Qatar.

Chemical Engineering Department, Texas A&M University, College Station TX, 77843, USA d

Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Saudi Arabia

* Corresponding author: J.M. Ponce-Ortega E-mail: [email protected];

Tel. +52 443 3223500 ext. 1277

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ABSTRACT

An optimization approach is proposed for managing flares from multiple plants. The aim of the proposed approach is to utilize flared gas during abnormal situation to produce combined heat and power while reducing the environmental impact associated with emitting greenhouse gases (GHGs) into the atmosphere. A mixed-integer nonlinear programming model is proposed to determine the optimal size of equipment for the cogeneration system. The model takes into account the uncertainty associated with the price volatility of external fuels and the characteristics of flare streams including the Wobbe Index. Starting from historical data, several scenarios are randomly generated to emulate variations in the uncertain variables with several levels of risk. A case study is presented to show the applicability of the proposed system. The results show economic and environmental benefits emanating from reductions in operating cost and GHGs emissions.

Keywords: Flare management; Cogeneration; Uncertainty; Abnormal Situations; Greenhouse gases.


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1. Introduction Flaring is an oxidation process used to burn gas mixtures, mainly hydrocarbons, when their recuperation is not economically feasible. In the fossil fuel industry, flaring is one of the most challenging energy and environmental concerns.1 Recent studies indicate that 150 billion cubic meters of natural gas are flared in the world every year, which is equivalent to 5% of global natural gas production and contribute to the climate change with 400 million tonnes of CO2 per year.2 Moreover, flaring can produce a number of harmful byproducts such as carbon monoxide, nitrogen oxide, sulfur oxides, and volatile organic compounds. Flares are mainly used to manage abnormal situations; for example: process upsets, equipment failure, off specification products, start-up, and shutdown plants because they are crucial for disposing waste and purge gases in a safe way.3 The flared gases from multiple plants can be integrated along with other streams to provide feedstocks for chemicals and/or energy through an eco-industrial park or industrial symbiosis.4-5 Hence, utilization of waste resources to produce value-added products is an opportunity for process engineers interested in designing new energy conversion schemes to enhance the economic benefits of the system and to reduce its negative environmental impact.6 Previous research efforts have pointed to the potential suitability of flared gases in supplementing fossil fuels used in fuel networks and cogeneration systems. Jagannath et al.,3 Rahimpour et al.,7 and Mourad et al.8 identified strategies for integrating flared gases with fuel networks. The use of flared gases in producing heat and power is also an attractive prospect. Cogeneration systems have been extensively studied, and different models have been developed to analyze, design and optimize cogeneration systems.9-12 The integration of cogeneration systems with flared streams has been addressed in literature. For example, Kamrava et al.13 presented a comparison between three options to show the benefits of using cogeneration and flare streams as supplementary fuel in an ethylene plant. In the first option, heat and power are generated separately using fresh fuel. In the second one, heat and power are generated simultaneously using cogeneration with fresh fuel as feed. In the third one, heat and power are generated with cogeneration and flare streams, which are mixed with fresh fuel to use them as supplementary fuel. The results showed that carbon dioxide emissions and operating costs can be diminished using the third option. Kazi et al.14 took the case of the ethylene plant presented by Kamrava et al.13 to develop a multi-objective optimization 3 ACS Paragon Plus Environment


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for sizing a cogeneration unit to manage flares during abnormal situations using genetic algorithms, and the results are presented in Pareto fronts which show the relationship between decision variables and their economic, technical and environmental impacts. Kazi et al.15 extended the above mentioned optimization framework to study the benefits of integrating a flare mitigation tool (cogeneration) with a wastewater treatment facility to mitigate flaring and increase the process efficiency. Previous works have demonstrated the advantages of using flared streams to supplement the fuel fed to the cogeneration systems. Nevertheless, the previous works have assumed that all the flared streams are fully and continuously available for use in the cogeneration system and that their characteristics are acceptable for blending with external fuels. The main contribution of this work falls in considering the random nature of abnormal situation. As mentioned before, abnormal situations occur during process upsets, equipment failure, off specification products, startup, and shutdown plants; therefore, the flow, composition, temperature and/or pressure of flare streams can change constantly. The novelty in this work is to take in to account these changes using random scenarios of flow and the Wobbe index to represent uncertainty. Wobbe index is defined by the next equation: WI =

HV

( SG )

1/ 2

Where Wi is the Wobbe index, HV the Calorific Value, and SGcthe Specific gravity. WI indicates the interchangeability of fuel gases. WI is used to compare the combustion energy output with different compositions of fuel gases. This helps to indicate that two gases with same WI will deliver the same amount of energy. In this paper, WI is used to know if waste fuel gases can substitute part of the main fuel (natural gas) in the proposed system. Additionally, previous efforts did not account for the price volatility of the fresh fuels. Natural gas price has been subjected to important increases and decreases in recent years, and the proposed formulation accounts for these economic phenomena. It should be noticed that a lot of uncertainty is associated to the abnormal situations. Fuentes-Cortés et al.16 have considered uncertainty in sizing residential cogeneration systems while accounting for uncertainty in ambient conditions, energy demands and prices


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of the produced power, and this strategy can be applied to abnormal situation in industrial complexes. In this work, an optimization framework is developed for utilizing flared gases in cogeneration systems. The framework accounts for the uncertainty in flared gas flowrates and characteristics resulting from abnormal situations. The framework also addresses the uncertainties in price volatility of a fossil fuel (e.g., natural gas) used to drive the cogeneration system. The characteristics of the flared gases including the Wobbe Index are included in the analysis. The proposed approach also handles flared gases from multiple plants/sources to promote industrial symbiosis which has traditionally focused on steady streams not abnormal flares. The uncertainty is represented by random scenarios based on historical data and considering a normal distribution behavior. The maximization of profit by electricity production and the minimization of carbon dioxide emissions are considered as objective functions to optimize the design by simultaneously considering economic and environmental factors.

2. Problem statement Consider a set of industrial plants that generate a number of flared gases (gaseous wastes) through steady operation and abnormal situation management. Each of the mentioned waste streams has an uncertain flow and quality with temporal changes. The gaseous wastes are considered for potential mixing with fresh feed (e.g., natural gas) to provide a blended feed to a cogeneration system to satisfy a certain energy demand. In a conventional system, these streams are burned during normal an abnormal operation in a flare stack, and the produced heat is dissipated into the atmosphere. In the proposed system, the streams can have different paths depending on economic and environmental objectives subject to technical feasibility. Each stream can be mixed with fresh fuel to feed the cogeneration system. This means that the entire stream or just a fraction may be reused. If the characteristics of the fuel waste streams do not satisfy the restrictions or if using it is not economically attractive, the streams will be burned in a flare stack without heat utilization. The price of the fresh feed is uncertain subject to market volatility. The aim is to design the cogeneration system so as to optimize the usage of the waste streams and the fresh fuels while accounting for uncertainties in flows, qualities, and prices and while addressing 5 ACS Paragon Plus Environment


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economic and environmental objectives. Figure 1 is a schematic representation of the problem statement.

3. Model formulation Starting from historical data (average values), fifty different scenarios were randomly generated to consider an increase or decrease in the quantity and quality of waste gas from the plants each period of time considering a normal distribution of the historical data. The mean fuel price, in this case natural gas, has had high variations over time. Hence, the historical data for natural gas prices were considered to represent the behavior of this variable in each scenario. Based on the superstructure, an optimization model was developed using mass and energy balances, cost functions, technical restrictions, and environmental considerations. This model uses elements from the previous work by TovarFacio et al.17 Nonetheless, new aspects were introduced to take into account the uncertainties in prices, flows, and qualities, the multi-plant nature of the system, and the flared gas quality using the Wobbe index as a decision factor to determine the technical feasibility of using waste gases of the plants as supplementary fuel. A disjunctive model is used in the mass balance of the waste streams for the plants ( Fi,t,s ). These streams can be burned without utilization ( Di , t , s ), used as supplementary fuel to generate electricity ( FFi , t , s ), or split to use a part and burn the rest ( FFi , t , s + Di , t , s ). The technical feasibility of

the extent of usage depends on the Wobbe index. This property must be within a suitable range to ensure a good performance and adequate combustion in the boiler. This disjunction is modeled through the following expression:  YiWIC      YiWIA YiWIB ,t , s ,t , s ,t , s       MAX MAX MIN   WIi,t,s ≥ WI   WI i,t,s ≤ WI   WIi,t,s ≤ WI   ∨ ∨ MIN   Di ,t , s = Fi,t,s   Di , t , s = Fi,t,s   WI i , t , s ≥ WI  FF = 0   FF = 0   D = F − FF  i,t , s i,t , s i,t,s i ,t , s       i,t , s

In the previous disjunction, the optimization variables are the flow that is not used and the flow which is fed to the cogeneration system. This disjunction is reformulated in terms of algebraic equations to be included in an optimization formulation which includes three Boolean variables associated with binary variables as follows: Only one option can be 6 ACS Paragon Plus Environment

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selected in each period of each scenario for every stream, so the binary variables yiWIA ,t , s , WIC yiWIB , t , s , and yi , t , s are needed for the different terms of the disjunction, where the optimal

selection of this options is modeled as follows: WIB WIC y iWIA , t , s + y i , t , s + y i , t , s = 1, ∀ I , ∀ T , ∀ S

(1)

If the Wobbe index is greater than the desired range, the binary variable yiWIA , t , s is activated:

WIi,t,s ≥ WIMAX − M WI (1 − yiWIA , t , s ) , ∀I , ∀T , ∀S

(2)

When the binary variable yiWIA , t , s is activated (i.e., it takes the value of one), the entire waste stream is burned without being exploited for cogeneration and the variable FFi , t , s is equal to zero.

Di,t , s ≤ Fi,t,s + MD (1 − yWIA )

(3)

Di,t , s ≥ Fi,t,s − MD (1 − yWIA )

(4)

FFi,t , s ≤ MFF (1 − yWIA )

(5)

FFi,t,s ≥ −MFF (1− yWIA )

(6)

If the Wobbe index is lower than the established range, the binary variable yiWIB , t , s is activated as follows:

WIi,t,s ≤ WIMIN + M WI (1 − yWIB )

(7)

Similarly, when the binary variable yiWIB , t , s is activated, the waste stream cannot be used in the cogeneration system because the combustion quality is not adequate and FFi , t , s is equal to zero:

Di,t , s ≤ Fi,t,s + MD (1 − yWIB )

(8) 7

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Di,t , s ≥ Fi,t,s − MD (1 − yWIB )

(9)

FFi,t , s ≤ MFF (1 − yWIB )

(10)

FFi,t,s ≥ −MFF (1− yWIB )

(11)

When the Wobbe index is between the desired ranges for the cogeneration system, the binary variable yWIC is activated and it is possible to use a fraction or the entire combustible waste stream as supplementary fuel to feed the cogeneration system when this is economically feasible:

WIi,t,s ≤ WIMAX +M WI (1 − yWIC )

(12)

WIi,t,s ≥ WIMIN − M WI (1 − yWIC )

(13)

Di,t , s ≤ Fi,t,s − FFi,t , s + MD (1 − yWIC )

(14)

Di,t , s ≥ Fi,t,s − FFi,t , s − MD (1 − yWIC )

(15)

The previous relationships are relaxed through the big M parameters. The next set of relationships describes the energy balances for the cogeneration system. These equations track the heat produced in the boiler and subsequently the heat and power produced or consumed by other equipment. The heat produced by fresh fuel ( Frt , s LHV Fr ) plus combusted waste streams (

FFi , t , s LHV FFi ) multiplied by boiler efficient represent the heat produced in the boiler: FFi  boil  Fr Qtboil ,s = η  Frt , s LHV + ∑ FFi ,t , s LHV  , ∀T , ∀S i  

(16)

An energy balance around the boiler is used to determine the water mass flow in the Rankine cycle ( m& s ) using the outlet and inlet boiler enthalpies. boil Qtboil m& s (h1 s − h 4 ), ∀T , ∀S ,s = η

(17) 8


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Similarly, the power produced in the turbine ( Pt turb , s ) is equal to the difference for the enthalpies between inlet and outlet streams multiplied by the water flow ( m& s ) and turbine efficiency ( η turb ):

Pt , s turb = ηturb m& s (h1s − h 2 ), ∀T , ∀S

(18)

The heat removed in the condenser from the exhausted steam after the turbine and the power required by the pump are calculated using the enthalpy differences, mass flow, and equipment efficiency as follows:

Qtcond = ηcond m& s (h 2 − h 3 ), ∀T , ∀S ,s

(19)

Pt ,pump = ηpump m& s (h 4 − h 3 ), ∀T , ∀S s

(20)

The profit related to the electricity produced in the Rankine cycle is calculated for elect each scenario as function of the turbine power ( Pt turb ) and , s ), electricity price ( price

generator efficiency ( η gene ):

  elect Saless elect = ηgene  ∑ Pt turb , ∀S , s  price  t 

(21)

Equation (22) indicates that the water flowing in the Rankine cycle (water that flows in the boiler, turbine, condenser and pumps) must be lower or equal that a maximum value that the commercially available equipment can handle. Equation (23) let calculate the water mass flow that Rankine cycle (water that flows in the boiler, turbine, condenser and pumps) to supply the energy demand. & max , ∀ S m& s ≤ m

(22)

m& s = 0.000768( P turb ) + 1020.85, ∀ S

(23)

This model takes into account capital and operating costs. The operating cost includes external utilities, required electricity, fresh fuel, and supplementary fuel. This way, the condenser operating cost is obtained as function of the removed head ( Qtcond , s ) for the exhaust steam and cooling utility price ( price cw ): 9 ACS Paragon Plus Environment


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cw OpCosts cond = ∑ Qtcond , s ⋅ price , ∀S

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(24)

t

The pumping cost can be calculated multiplying the power required by pumps ( Pt ,pump ) times its unit cost ( price power ). s

OpCosts pump = ∑ Pt ,pump ⋅ pricepower , ∀S s

(25)

t

Fresh fuel is needed to ensure a continuous operation for the boiler, the cost related to this input is calculated considering the boiler efficiency, fresh fuel flow (tonne/month) and its heat content (GJ/tonne), in addition to its unit price ($/GJ):

OpCost s

rep

 Frt , s LHV Fr = ∑  ηboil t 

 rep  prices , ∀S 

(26)

The cost of using flared streams to supplement the fresh fuel is calculated according to the approach proposed by Ulrich and Vasurdevan.18 In this method, it is necessary to calculate two utility cost coefficients ( Ai , t , s and Bi ) to evaluate the cost of using the flared streams as supplementary fuel instead of burning them. These coefficients are functions of the gas net calorific value or low heating values ( LHVi ) and volumetric flow ( qi , t , s ):

Ai ,t , s = ( 2.5*10−5 LHVi 0.77 ) ( qi ,t , s )

−0.23

, ∀I , ∀T , ∀S

Bi = − 6 *10 −4 LHVi , ∀ I

(27) (28)

To find the utility cost coefficient Ai , t , s , it is necessary to convert the mass flow of the streams to normal cubic meters per second as follows:

qi,t , s = (8.697*10−3 )

FFi,t , s PMi

, ∀I , ∀T , ∀S

(29)

Once the coefficients were calculated, they were used to calculate the cost of using the flared streams as supplementary fuel. The Chemical Engineering Plant Cost Index and the fresh fuel cost are used to obtain the updated unitary cost ($/Nm3): CSU i , t , s = Ai , t , s CEPCI + Bi CSF, ∀I , ∀T , ∀S

(30) 10


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Using the values obtained by Equations (27), (28), and (29), the operating total cost of using flare streams as supplementary fuel in the boiler to replace fresh fuel is determined as follows:

OpCostsFlow = ∑∑ ( 2.592 × 106 qi , t , s CSU i , t ,s ) , ∀S t

(31)

i

The following restrictions were established to determine the equipment size in the cogeneration system. In every scenario, the equipment size of the proposed system has to be greater than the solution in each time period to use flare streams as much as possible: Qsboil ≥ Qtboil ∀ T , ∀S ,s , turb

Ps

cond

Qs

≥ Pt turb ,s ,

(32)

∀T , ∀S

(33)

≥ Qtcond ∀T , ∀S ,s ,

(34)

Ps pump ≥ Pt ,pump , ∀T , ∀S s

(35)

The capital costs for the equipment were calculated using equations and parameters taken from Bruno et al.9 These results are updated using the Chemical Engineering Plant Cost Index. The capital cost equation for the boiler includes a fixed term ( CFboil ) and a variable part ( CV turb ) which depends on the unit size ( Q sboil ) raised to an exponent ( cboil ) to take into account the economy of scale: boil

CapCosts boil = CFboil + CV boil (Qsboil )c , ∀S

(36)

The capital costs of the turbine, condenser and pump ( CapCost s turb , CapCost s cond , CapCost s pump ) also include a fixed ( CF

turb

, CFcond , CFpump ) and a variable ( CVturb , CVcond ,

CVpump ) part multiplied by the unit size ( Ps turb , Q s cond , Ps pump ) raised to an exponent ( C turb , Ccond , Cpump ) as follows: turb

CapCoststurb = CFturb + CV turb ( Ps turb )c , ∀S

(37)

cond

CapCosts cond = CFcond + CV cond (Qs cond )c , ∀S

(38) 11



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pump

CapCosts

= C1pump + C2pump ( Ps pump )c

pump

, ∀S

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(39)

As mentioned before, the proposed system must satisfy a specific electricity demand of the plants ( EREQ ); however, it is possible to produce more electricity than the one needed to satisfy, at the same time, the plant requirements and an external market demand (for example, a building complex): Pt turb ,s ηgene Pt turb ,s ηgene

≥ EREQ, ∀T , ∀S

(40) ≤ EMAX, ∀T , ∀S

(41)

One of the objectives of the proposed model is to maximize the average annual profit of all scenarios, this is a way to obligate that every scenario has the best average. The mentioned average results of dividing the sum of the profit for all the scenarios ( ∑ Profits s

) between the number of considered scenarios ( Card ):

max MProfit =

∑ Profit

s

s

Card

(42)

The Profit in each scenario, Profit s takes into account the obtained earnings by the produced electricity Salesselect minus the operating and capital costs of the system that was presented in the superstructure:

Profits = Salesselect − OpCostscond − OpCostspump − OpCostsFlow − OpCostsrep CapCost boil + CapCost turb  − kF  , ∀S cond pump  +CapCost + CapCost 

(43)

Another way to solve the problem is to maximize the worst economic scenario, which means the scenario with the lowest profit.

max WProfit ≤ Profit s , ∀S

(44)


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To determine the carbon dioxide emissions produced by the cogeneration system (

GHGCS s ), the following expression is used:    FFi , t , s X c Yc,i    Frt , s X cFr YcFr   GHGCSs =  ∑∑∑    PM CO2 +  ∑∑    PM CO2 ∀S  t i c PM c PM cFr      t cFr  (45)

(

)

(

)

Equation (45) considers the emissions generated from the fresh fuel ( Frt , s ) plus the emissions from the utilized flared streams ( FFi , t , s ). To consider the carbon dioxide emissions, it is necessary to calculate the quantity produced by the flared streams that cannot be used in the cogeneration system and are consequently burned in a conventional flaring system (because of technical or economic hurdles):

  D X Y  GHGFSs =  ∑∑∑  i ,t , s c c,i   PMCO2  t i c  PMc   

(

)

∀S (46)

The total emissions ( TGHGs ) generated by the system result from sum of produced emissions by the cogeneration system ( GHGCS s ) plus the produced emissions by the flaring system ( GHGFS s ) as follows:

TGHGs = GHGCS s + GHGFS s

∀S

(47)

Using the previous equation, it is possible to generate a new objective function to minimize the environmental impact of the system. Hence, the objective function is aimed at minimizing the total average emissions of the whole system:

∑ TGHG

s

min MGHG =

s

Card

(48)

Similar to the profit maximization, it is possible to minimize the worst case scenario, which corresponds to the highest quantity of carbon dioxide emissions.

min WGHG ≥ TGHGs ∀S

(49)



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The proposed model seeks to minimize and maximize more than one objective. It is desired to minimize the carbon dioxide emissions and at the same time to maximize the profit. In order to address the multi-objective problem, a new version of the goal programming method is used. The application of this method requires the normalization of the objective variables to create a new objective function. The average profit and the worst profit of all scenarios are variables that must be maximized. On the other hand, the average quantity of carbon dioxide emissions and the quantity of carbon dioxide emissions in the worst scenario are variables that have to be minimized. Since the units of these variables are different, it is necessary to normalize these variables to combine them in only one objective function as follows: MProfit − Profit Min + SV1 = 1 Profit Max − Profit Min

(50)

WProfit − Profit Min + SV2 = 1 Profit Max − Profit Min

(51)

GHG Max − MGHG + SV3 = 1 GHG Max − GHG Min

(52)

GHG Max − WGHG + SV4 = 1 GHG Max − GHG Min

(53)

The normalized variables are restricted by the next group of equations because the values for the variables MProfit , WProfit , MGHG and WGHG cannot be out of their maximum and minimum limits:

0 ≤ SV1 ≤ 1

(54)

0 ≤ SV2 ≤ 1

(55)

0 ≤ SV3 ≤ 1

(56)

0 ≤ SV4 ≤ 1

(57)

Finally, these new dimensionless variables are used to create only one multiobjective function: 14 ACS Paragon Plus Environment

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min FO = SV1 + SV2 + SV3 + SV4

(58)

The model was coded in the software GAMS19 and run on a computer with an Intel Core i7-4710 at 2.50 GHz processor with 16 GB of RAM. The model was solved using the solver BARON. The multiobjective problem has 170,076 constraints, 75,974 continuous variables, and 27,000 binary variables. The computation time was 12,659.7 seconds.

4. Case study A case study is presented, which considers 3 process plants of an industrial complex with different waste streams. Originally, these streams were burned during normal operation or when an abnormal situation occurs, and the produced heat is dissipated into the atmosphere. In the proposed system, the streams may be assigned to different options depending on economic and environmental objectives subject to technical feasibility. Each stream can be mixed with fresh fuel to feed the cogeneration system. This means that the entire stream or just a fraction may be reused. If the characteristics of the fuel waste streams do not satisfy the restrictions or if using it is not economically attractive, the streams will be burned in a flaring system without heat utilization. Tables 1 and 2 show the flows and compositions for the streams that were used in the case study. Flows and compositions have been adapted from literature13,17,20 and the WI was calculated from this information. The uncertain variables are the flow of fuel waste streams from the plants, the Wobbe index of these streams and the fresh fuel price. The uncertainties associated with these variables are accounted for allowing them to take different values in fifty different scenarios, and each scenario has the same probability to occur. The values for the flows and Wobbe indexes for the different scenarios are randomly generated starting from the average values of these variables and considering a normal distribution. For the price volatility of natural gas, data from the Mexican Secretary of Economy21 were used to generate the random economic scenarios. To account for the uncertainty in the characteristics of the flared gases, random values of the Wobbe index were generated for each stream from the historical data shown in Table 3. It should be noted that changes in temperature, pressure and/or composition of



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the flared streams every time during an abnormal situation have an associated variation in the Wobbe index. Therefore, the flared streams must have a cost lower than the fresh fuel to be economically attractive for reusing, and at the same time their Wobbe index must be within the proper range to avoid low efficiencies or unacceptable changes in the performance of the cogeneration system.

5. Results and discussion This section presents the results of applying the proposed approach to the case study. Three perspectives were adopted in analyzing the case study. First, the results considering the economic objective function are presented. This involves maximizing the average profit for all scenarios and for the worst profit scenario. Then, the environmental aspects were used as objective function. This case corresponds to minimizing the average carbon dioxide emissions of all scenarios and of the worst scenario. Finally, the results for the multi-objective optimization approach are presented. In this case, a new objective function was utilized to maximize the profit while simultaneously minimizing the emissions. 5.1 Case 1. Economic analysis This case focuses on analyzing the economic feasibility of using the flare streams as supplementary fuel considering uncertainty in the flow, WI and main fuel price. The problem is solved two times. First, the average profit of all scenario is maximized (equation 42). It represents the maximum risk solution (the most optimistic solution). The second one uses as objective function the maximization of the worst profit case (equation 44), and it represents the minimum risk solution. In other words, the maximum risk solution shows a higher probability to earn the same quantity of money than the minimum risk solution. Figure 2 shows a cumulative probability curve when the profit is maximized. For example, if it is desired to determine the probability to earn at least 10, 30 and 42 million dollars per year. Figure 2 indicates that for the riskiest solution the probabilities are 90%, 66% and 46%, respectively; and for the solution with minimum risk the probabilities are 86%, 46% and 2%, respectively. The minimum risk solution lets make decisions with caution because it tries to maximize the unfavorable scenarios, and the maximum risk solution allows to obtain the maximum benefit under the best conditions. The results give to decision makers 16 ACS Paragon Plus Environment

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a useful tool to be conscious of the probability of having at least a desired profit. Using the appropriate data, the model can be applied to other cases to generate valuable insights. Figure 3 presents the results for the profit in the fifty solved scenarios. Figure 3a shows the profit for the riskiest solution, Figure 3b presents the profit in all the scenarios for the minimum risk solution, and the natural gas prices utilized by the model are shown in Figure 4. The three figures let see that profit is inversely proportional to natural gas price. Also, in this economic analysis carbon dioxide emissions are not considered in decisionmaking. Nonetheless, it is observed that in all the scenarios with a price higher than $10/GJ, there is a notable reduction in the greenhouse gases generated by the system as shown by Figure 5. Although the natural gas price is a very important variable that affects the profit, Figure 5 also shows that the emission are affected by two other factors: the availability of flared streams and their characteristics in each scenario. For example, scenario 36 has a natural gas price higher than $10/GJ, so emissions would be expected to decrease. However, this scenario has a low availability of the flared streams with the required characteristics to be fed to the cogeneration system (only 46.11% of the flared streams are in de desired Wobbe index range). Consequently, the greenhouse gas emissions increase. This is a confirmation of the importance of accounting for the uncertainty of the variables involved in the abnormal situations. Figure 6 shows the carbon dioxide emissions that are being mitigated when a cogeneration system is utilized. The yellow points represent the emissions when the flared streams are not used as supplementary fuel and the profit is maximized (conventional system), while the blue and red bars stand for emission when the average profit of all scenarios and the worst profit scenario are maximized (proposed system). It can be seen that in every scenario, there is a reduction in the carbon dioxide emissions generated by the system with a maximum reduction of 22.31%. The riskiest solutions (maximization of average profit) represented by the blue bars have an average decrease in carbon dioxide emission of 8.54%, and the minimum risk solutions (maximization of the worst profit scenario) represented by the red bars have a mean reduction of 11.03%. 5.2 Case 2. Environmental analysis



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This analysis seeks to find the system that minimizes the carbon dioxide emissions generated by the whole system without optimizing the profit function. Figure 7 presents the cumulative probability curves for the profit when the minimization of carbon dioxide emissions is the objective function. Similarly as with the economic analysis presented in the previous case, the problem is solved using two different approaches. First, the average carbon dioxide emissions for all scenarios are minimized (equation 48). This corresponds to the riskiest solution (blue curve). Then, the worst scenario of emissions (scenario with the highest value of carbon dioxide generated) is minimized (equation 49) to yield the minimum risk solution (red curve). It should be noticed in Figure 7 that it is not possible to analyze different scenarios as in the previous case because both curves are almost identical. Therefore, the probability to obtain a selected profit with the riskiest solution and the minimum risk solution is basically the same. The solutions for these scenarios are robust to uncertain variables. Figure 8 presents the results of profit in the different scenarios for the environmental analysis. Figure 8a shows the profit for the riskiest solution, and Figure 8b presents the profit in the fifty scenarios for the minimum risk solution. If they are compared with Figure 4, it can be seen that there is a strong relation between profit and natural gas price as it was presented in the economic analysis. Each scenario with high profit corresponds to a low price, and vice versa. The scenarios in this case (Figure 8) are less profitable than in economic analysis. This behavior is attributed to the aim of the objective function minimizes the emissions regardless of the cost involved. Therefore, as expected, carbon dioxide emissions in these scenarios are lower than those presented in Figures 3 and 5. Figure 9 shows the emissions generated by the system when the average emissions of all scenarios (equation 48) and the worst scenario (equation 49) are minimized. In the first solution (Figure 9a), all the flared streams are used when the Wobbe index is in the appropriate range. A maximum mitigation of 25.90% and an average decrement of 22.72% in carbon dioxide emissions can be achieved as shown by Figure 10. On the other hand, for the solution presented in Figure 9b (minimization of the worst scenario), some scenarios do not fully use the flared streams. The reduction of carbon dioxide emissions remains almost constant as illustrated by Figure 9b, with an average decrease of 21.22%compared 18 ACS Paragon Plus Environment

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to the solutions that do not use the proposed cogeneration system as can be seen in Figure 10. 5.3 Case 3. Multi-objective analysis In this case, both the economic and environmental objective functions are combined using the proposed goal programming method to create a new objective function that simultaneously considers the economic and environmental aspects (equation 58). Figure 11 shows the probability to obtain a certain profit when the model is formulated as a multiobjective problem. Although in this case the carbon dioxide emissions decrease up to levels like those showed in the environmental analysis, there are no scenarios that lead to economic losses. The profit levels are lower than the ones presented in the economic analysis. However, the economic benefits may improve substantially if carbon taxes or

credits are incorporated in future works. It should be noticed that the profit follows the tendency of natural gas price (see Figures 4 and 12a). The carbon dioxide emissions present a variation in each scenario (see Figure 12b), but they maintain an average value because the objective function seeks to utilize most of the flared streams of the different plants to feed the cogeneration system. A high price of natural gas promotes the use of the flared streams. Hence, the scenarios with an increase in the natural gas prices lead to a reduction in the carbon dioxide emissions.

6. Conclusions This paper has presented a multi-objective optimization approach for utilizing flared streams from different industrial sources as supplementary feed in a cogeneration system. The approach accounts for the uncertainties in the price of the main fuel as well as the quality and magnitude of the abnormal situations and the resulting flared streams. An optimization approach was developed based on a superstructure to determine the optimal size of the cogeneration system while accounting for uncertainty with respect to three important variables: flows of flare streams from plants, Wobbe index of industrial flares, and the natural gas price. The proposed model seeks to maximize the profit, minimize the greenhouse gas emissions, or simultaneously reconciling both objectives. A case study was presented to show the advantages of reusing flared streams as supplementary fuel. The results always show a positive balance between profit and costs. No matter if the objective 19 ACS Paragon Plus Environment


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function is economic, environmental, or multiobjective there is a decrease in carbon dioxide emissions having a maximum decrease of 25.9% in the environmental analysis. Furthermore, it was presented that the most important uncertain variable is the main fuel price. This formulation gives to decision makers a useful tool to study the economic and environmental feasibility of flaring mitigation using cogeneration systems.

7. Nomenclature 7.1 Variables Ai , t , s

Utility cost coefficient, which reflects inflation-dependent cost elements

Bi

Utility cost coefficient, which reflects energy-dependent cost elements

CapCost s boiler Boiler capital cost ($/y) CapCost s turb

Turbine capital cost ($/y)

CapCost s cond Condenser capital cost ($/y) CapCost s pump Pump capital cost ($/y) CSF

Fuel price ($/GJ)

CSU i , t , s

Utility price ($/Nm3)

D i , t ,s

Flare flowrate from different plants sent to the flaring system (tonne/month)

FFi , t , s

Flare flowrate from different plants sent to the cogeneration system (tonne/month)

FO

Objective function in the multiobjective optimization

F rt , s

Fresh fuel fed to the cogeneration system (tonne/month)

GHGCSs

GHG generated by the cogeneration system in each scenario (tonne/y)

GHGFSs

GHG generated by the flaring system in each scenario (tonne/y)

h1 s

Water enthalpy at the boiler outlet (GJ/tonne) 20 ACS Paragon Plus Environment

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m& s

Water mass flow in cogeneration system (kg/s)

MGHG

Average annual greenhouse gas emissions (tonne/y)

MProfit

Average annual profit ($/y).

O pCost s cond

Condenser operating cost ($/y)

OpCost s pump

Pump operating cost ($/y)

OpCost s rep

Fresh fuel cost ($/y)

O pC ost s Flow

Operating cost for flare streams as supplementary fuel ($/y)

Ps pump

Energy consumed by the pumps in each scenario (GJ/y)

Ps turb

Power generated by the turbine in each scenario (GJ/y)

Pt ,pump s

Energy consumed by the pumps (GJ/y)

Pt turb ,s

Power generated by the turbine (GJ/y)

Profit s

Profit in each scenario ($/y)

q i,t , s

Total waste gases used as supplementary fuel (Nm3/s)

Qs boil

Energy generated by the boiler in each scenario (GJ/y)

Qs cond

Energy removed by the condenser in each scenario (GJ/y)

Qtboil ,s

Energy generated by the boiler (GJ/y)

Qtcond ,s

Energy removed by the condenser (GJ/y)

Sales s elect

Profit by generated electricity ($/y)

SV1

Normalized variable 1

SV2




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SV3


SV4


TGHGs

Total GHG generated by the entire system in each scenario (tonne/month)

WIi,t,s

Wobbe index (MJ/Nm3)

WGHG

Carbon dioxide emissions in the worst scenario (tonne/y)

WProfit

Profit in the worst scenario ($/y)

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7.2 Parameters c boiler

Constant for the equation of boiler capital cost

c turb

Constant for the equation of the turbine capital cost

c cond

Constants for the equation of the condenser capital cost

C ard

Number of scenarios

CEPCI

Chemical engineering plant cost index

CFboiler

Unit boiler fixed cost

CF turb

Unit turbine fixed cost

CFcond

Unit condenser fixed cost

CV boiler

Unit boiler variable cost

CV turb

Unit turbine variable cost

CV cond

Unit condenser variable cost

C1pump , C2 pump , C3pump Constants for the equation of the pump capital cost CSF

Fresh fuel cost ($/Nm3)

EREQ

Energy required to satisfy the plant demands (GJ/month)

EMAX

Energy to satisfy the requirements inside and outside the plants (GJ/month)


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Fi,t,s

Flare streams from different plants (tonne/month)

GHG Max

Maximum quantity of carbon dioxide that the system can generate (tonne/y)

GHG Min

Minimum quantity of carbon dioxide that the system can generate (tonne/y)

h2

Water enthalpy at the turbine outlet (GJ/tonne)

h3

Water enthalpy at the condenser outlet (GJ/tonne)

h4

Water enthalpy at the pump outlet (GJ/tonne)

LHVFr Low heating value for fresh fuel (GJ/tonne) LHVFFi

Low heating value for flare streams of the plants (GJ/tonne)

LHVi

Low heating value (GJ/Nm3)

& MAX m

Maximum water flow in the cogeneration system (kg/s)

M WI

Big M parameter for Wobbe index

MD

Big M parameter for flare streams burned without be exploited

M FF

Big M parameter for flare streams fed to the cogeneration system

price elect

Electricity price ($/GJ)

pricecw

Cooling water price ($/GJ)

price power

Power price ($/GJ)

pricerep

Fresh fuel price ($/GJ)

Profit Max

Maximum profit that the system can generate ($/y)

Profit Min

Minimum profit that the system can generate ($/y)

PM c

Molecular weight for each component (kg/kmol)

PM i

Molecular weight (kg/kmol)



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PM cFr

Molecular weight for fresh fuel (kg/kmol)

PM CO2

Molecular weight for carbon dioxide (kg/kmol)

WIMAX

Maximum Wobbe index allowed by the system (MJ/Nm3)

WIMIN

Minimum Wobbe index allowed by the system (MJ/Nm3)

Xc

Stoichiometric constant for each component (kgCO2/kgC)

X cFr

Stoichiometric constant for fresh fuel (kgCO2/kgC)

Yc,i

Mole fraction of each component

YcFr

Mole fraction of each component for fresh fuel

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7.3 Boolean Variables

YiWIA ,t , s

Logic variable for case A of Wobbe index restriction

YiWIB ,t , s

Logic variable for case B of Wobbe index restriction

YiWIC ,t , s

Logic variable for case C of Wobbe index restriction

7.4 Greek symbols

η boil

Boiler efficiency

ηcond

Condenser efficiency

η gene

Generator efficiency

η pump

Pump efficiency

η turb

Turbine efficiency

7.5 Indices c

Component

i

Waste stream from plants

t

Time period 24 ACS Paragon Plus Environment

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s

Scenario

8. Acknowledgement The authors acknowledge the financial support from the Mexican Council for Science and Technology (CONACyT) and the Scientific Research Council of the Universidad Michoacana de San Nicolás de Hidalgo.

9. References (1) Davoudi, M.; Rahimpour, M.; Jokar, S.; Nikbakht, F.; Abbasfard, H. The major sources of gas flaring and air contamination in the natural gas processing plants: A case study. J. Nat. Gas. Sci. Eng. 2013, 13, 7-19.

(2) Farina, M. F. Flare Gas Reduction: Recent global trends and policy considerations. General

Electric

Company.

2011.

(Available

spark.com/spark/resources/whitepapers/Flare_Gas_Reduction.pdf)

at

http://www.ge-

(Accessed

February

2017). (3) Jagannath, A.; Hasan, M. F.; Al-Fadhli, F. M.; Karimi, I.; Allen, D. T. Minimize flaring through integration with fuel gas networks. Ind. Eng. Chem. Res. 2012, 51, 12630-12641. (4) Noureldin, M.; El-Halwagi, M. M. Synthesis of C-H-O Symbiosis Networks. AIChE J. 2015, 61, 1242-1262. (5) El-Halwagi, M. M. A shortcut approach to the multi-scale atomic targeting and design of C-H-O symbiosis networks. Process Integration and Optimization for Sustainability. 2017, 1-11. (6) Adams, T. A. Future opportunities and challenges in the design of new energy conversion systems. Comput. Chem. Eng. 2015, 81, 94-103. (7) Rahimpour, M.; Jamshidnejad, Z.; Jokar, S.; Karimi, G.; Ghorbani, A.; Mohammadi, A. A comparative study of three different methods for flare gas recovery of Asalooye Gas Refinery. J. Nat. Gas. Sci. Eng. 2012, 4, 17-28. (8) Mourad, D.; Ghazi, O.; Noureddine, B. Recovery of flared gas through crude oil stabilization by a multi-staged separation with intermediate feeds: A case study. Korean J. Chem. Eng. 2009, 26, 1706-1716. 25 ACS Paragon Plus Environment


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(9) Bruno, J.; Fernandez, F.; Castells, F.; Grossmann, I. A rigorous MINLP model for the optimal synthesis and operation of utility plants. Chem. Eng. Res. Des. 1998, 76, 246-258. (10) Varbanov, P.; Doyle, S.; Smith, R. Modelling and optimization of utility systems. Chem. Eng. Res. Des. 2004, 82, 561-578.

(11) Bamufleh, H. S.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Multi-objective optimization of process cogeneration systems with economic, environmental, and social tradeoffs. Clean Technol. Envir. 2013, 15, 185-197. (12) Fuentes-Cortés, L. F.; Ponce-Ortega, J. M.; Nápoles-Rivera, F.; Serna-González, M.; El-Halwagi, M. M. Optimal design of integrated CHP systems for housing complexes. Energ. Convers. Manage. 2015, 99, 252-263.

(13) Kamrava, S.; Gabriel, K. J.; El-Halwagi, M. M.; Eljack, F. T. Managing abnormal operation through process integration and cogeneration systems. Clean Technol. Envir. 2015, 17, 119-128. (14) Kazi, M.-K.; Mohammed, F.; AlNouss, A. M. N.; Eljack, F. Multi-objective optimization methodology to size cogeneration systems for managing flares from uncertain sources during abnormal process operations. Comput. Chem. Eng. 2015, 76 76-86. (15) Kazi, M.-K.; Eljack, F.; Elsayed, N. A.; El-Halwagi, M. M. Integration of energy and wastewater treatment alternatives with process facilities to manage industrial flares during normal and abnormal operations: Multiobjective extendible optimization framework. Ind. Eng. Chem. Res. 2016, 55, 2020-2034.

(16) Fuentes-Cortés, L. F.; Santibañez-Aguilar, J. E.; Ponce-Ortega, J. M. Optimal design of residential cogeneration systems under uncertainty. Comput. Chem. Eng. 2016, 88 86102. (17) Tovar-Facio, J.; Eljack, F.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Optimal design of multiplant cogeneration systems with uncertain flaring and venting. ACS Sustain. Chem. Eng. 2017, 5, 675-688.

(18) Ulrich, G. D.; Vasudevan, P. T. How to estimate utility costs. Chem. Eng. 2006, 113, 66.


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(19) Brooke A.; Kendrick D.; Meeraus A.; Raman R. GAMS User’s Guide, The Scientific Press, Washington, DC, 2017. (20) Heidari, M.; Ataei, A.; Rahdar, M. H. Development and analysis of two novel methods for power generation from flare gas. Appl. Therm. Eng. 2016, 104, 687-696. (21)Mexican_Secretary_of_Economy._http://portalweb.sgm.gob.mx/economia/es/energetic os/precios/701-seguimiento-precio-gasnatural-datos.html (Accessed January 2017).



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Tables Table 1. Flare stream flows and composition (mole fraction). Streams A to H.

Streams Flow (tonne/y) Component Methane Acetylene Ethylene Ethane Propene Butadiene Water Propane Butane Pentane

A 191.25

B 170.34

0.066 0.008 0.513 0.132 0.017 0.011 0.253 0 0 0

0.091 0.220 0.406 0.283 0 0 0 0 0 0

Plant 1 C D E 170.97 124.46 121.39 Mole fraction 0.304 0.040 0 0 0 0 0.416 0.845 1.000 0.281 0.115 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

F 46.76

G 565.49

0 0 0 1.000 0 0 0 0 0 0

1.000 0 0 0 0 0 0 0 0 0

Table 2. Flare stream flows and composition (mole fraction). Streams I to O.

Streams Flow (tonne/y) Component Methane Acetylene Ethylene Ethane Propene Butadiene Water Propane Butane Pentane

H 169.87

Plant 2 I J 284.47 652.79

0.807 0 0 0.076 0 0 0 0.100 0.012 0.005

0.112 0 0 0.727 0 0 0 0.131 0.020 0.010

0.050 0 0 0.530 0 0 0 0.380 0.040 0

K L 127.15 45.85 Mole fraction 0 0.100 0 0 0 0 0 0.240 0 0 0 0 0 0 0.520 0.250 0.300 0.410 0.180 0

M 44.82

Plant 3 N 21.93

O 20.80

0 0 0 0 0.005 0 0 0.026 0.356 0.613

0 0 0 0 0.160 0 0 0.840 0 0

0 0 0 0 0 0 0 0 1.000 0


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Table 3. Average Wobbe index of the flared streams. Plant

Plant 1

Plant 2

Plant 3

Stream A B C D E F G H I J K L M N O

Average Wobbe index 43.261 51.653 52.007 50.332 50.631 47.888 52.892 46.600 46.815 52.901 56.746 48.454 47.980 51.632 54.289



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Caption for Figures: Figure 1. Proposed superstructure to use flare streams as supplementary fuel. Figure 2. Cumulative probability to obtain a value of profit when the mean and worst profit scenarios are maximized. Figure 3. a) Profit in different scenarios when the average profit is maximized; b) Profit in different scenarios when the worst profit scenario is maximized. Figure 4. Natural gas prices used in proposed scenarios (Mexican Secretary of Economy). Figure 5. a) Carbon dioxide emissions in different scenarios when the average profit is maximized; b) Carbon dioxide emissions in different scenarios when the worst economic scenario is maximized. Figure 6. Carbon dioxide emissions generated in each solution for the economic analysis. Figure 7. Cumulative probability to obtain a value of profit when the mean and worst values of carbon dioxide emissions are minimized. Figure 8. a) Profit in different scenarios when the average carbon dioxide emission are minimized; b) Profit in different scenarios when the scenario for the worst emissions is minimized. Figure 9. a) Carbon dioxide emissions in different scenarios when the average carbon dioxide emissions are maximized; b) Carbon dioxide emissions in different scenarios when the worst emissions scenario is minimized. Figure 10. Carbon dioxide emissions generated in each solution for the environmental analysis.

Figure 11. Cumulative probability to obtain a value of profit when a multi-objective approach is considered. Figure 12. a) Profit in different scenarios when the goal programming method is used; b) Carbon dioxide emission when the goal programming method is implemented.


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Figure 1. Proposed superstructure to use flare streams as supplementary fuel.



1.00 0.90 0.80 Probability

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0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 $-

$15,000,000

$30,000,000

$45,000,000

$60,000,000

Profit ($/y) max(MProfit)

max(WProfit)

Figure 2. Cumulative probability to obtain a value of profit when the mean and worst profit scenarios are maximized.


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$60,000,000

Profit ($/y)

$50,000,000 $40,000,000 $30,000,000 $20,000,000 $10,000,000 $0

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Scenario (s)

a) $60,000,000 $50,000,000 Profit ($/y)

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


$40,000,000 $30,000,000 $20,000,000 $10,000,000 $0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Scenario (s)

b)

Figure 3. a) Profit in different scenarios when the average profit is maximized; b) Profit in different scenarios when the worst profit scenario is maximized.



$12.0

Natural Gas Price ($/GJ)

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$10.0 $8.0 $6.0 $4.0 $2.0 $0.0 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

Figure 4. Natural gas prices used in proposed scenarios (Mexican_Secretary_of_Economy).


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550,000

CO2 Emissions (tonne/y)

525,000 500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

a) 550,000 525,000


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


500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

b)

Figure 5. a) Carbon dioxide emissions in different scenarios when the average profit is maximized; b) Carbon dioxide emissions in different scenarios when the worst economic scenario is maximized.



550,000 525,000


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 43

500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s) max(MProfit)

max(WProfit)

Solution without using proposed system

Figure 6. Carbon dioxide emissions generated in each solution for the economic analysis.


Page 37 of 43

1.00 0.90 0.80

Probability

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


0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 $-

$10,000,000

$20,000,000

$30,000,000

$40,000,000

Profit ($/y) min(MGHG)

min(WGHG)

Figure 7. Cumulative probability to obtain a value of profit when the mean and worst values of carbon dioxide emissions are minimized.



$60,000,000

Profit ($/y)

$50,000,000 $40,000,000 $30,000,000 $20,000,000 $10,000,000 $0 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

a) $60,000,000 $50,000,000

Profit ($/y)

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 38 of 43

$40,000,000 $30,000,000 $20,000,000 $10,000,000 $0 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

b)

Figure 8. a) Profit in different scenarios when the average carbon dioxide emission are minimized; b) Profit in different scenarios when the scenario for the worst emissions is minimized.


Page 39 of 43


550,000 525,000 500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

a) 550,000 525,000


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


500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

b)

Figure 9. a) Carbon dioxide emissions in different scenarios when the average carbon dioxide emissions are maximized; b) Carbon dioxide emissions in different scenarios when the worst emissions scenario is minimized.



550,000 525,000


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 40 of 43

500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s) min(MGHG)

min(WGHG)

Solution without using the proposed system

Figure 10. Carbon dioxide emissions generated in each solution for the environmental analysis.


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


Probability

Page 41 of 43

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 $0

$10,000,000

$20,000,000

$30,000,000

$40,000,000

Profit ($/y)

Figure 11. Cumulative probability to obtain a value of profit when a multi-objective approach is considered.



$60,000,000

Profit ($/y)

$50,000,000 $40,000,000 $30,000,000 $20,000,000 $10,000,000 $0 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s)

a) 550,000 525,000


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 42 of 43

500,000 475,000 450,000 425,000 400,000 375,000 350,000 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Scenarios (s) Multiobjective

Solution without using proposed system

b)

Figure 12. a) Profit in different scenarios when the goal programming method is used; b) Carbon dioxide emission when the goal programming method is implemented.


Page 43 of 43

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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