Optimal Design of Multiplant Cogeneration Systems with Uncertain

Research Article pubs.acs.org/journal/ascecg

Optimal Design of Multiplant Cogeneration Systems with Uncertain Flaring and Venting Javier Tovar-Facio,† Fadwa Eljack,‡ José M. Ponce-Ortega,*,† and Mahmoud M. El-Halwagi§,∥

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†

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Edificio V1, Ciudad Universitaria, Morelia, Michoacán 58060, México ‡ Department of Chemical Engineering, Qatar University, P.O. Box 2713, Doha, Qatar § Chemical Engineering Department, Texas A&M University, 200 Jack E. Brown Engineering Building, College Station, Texas 77843-3122, United States ∥ Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia S Supporting Information *

ABSTRACT: This paper presents an optimization approach for designing cogeneration systems using flares and vents under abnormal conditions from different industrial plants. The aim of the proposed approach is to enhance resource conservation by utilizing waste flares and vents to produce power and heat while reducing the negative environmental impact associated with discharging these streams into the atmosphere. A nonlinear optimization model is proposed to determine the optimal design of the cogeneration system that maximizes the net profit of the system. The model addresses the inevitable uncertainties associated with the abnormal situations leading to venting and flaring. A random generations approach based on historical data and a computationally efficient algorithm are introduced to facilitate design under uncertainty and to enable the assessment of different scenarios and solutions with various levels of risk. A case study is presented to show the applicability of the proposed model and the feasibility of using cogeneration systems to mitigate flaring and venting and to reduce the environmental impact and operating costs. KEYWORDS: Flaring, Venting, Abnormal situations, Cogeneration, CO2 reduction

■

approximately 150 billion cubic meters of natural gas are flared each year leading to about 400 million metric tons of CO2 equivalent to the GHG emissions.11 Furthermore, flaring produces a number of harmful byproducts such as nitrogen oxides, sulfur oxides, and volatile organic compounds. In the energy and process industries, flaring and venting are standard practices to deal with deviations from the normal operation process (for example, during process upsets, plant start-up or shut-down, and process emergencies), which are known as abnormal situations. The flow rates, compositions, and frequency of flares from abnormal situations are uncertain. The flares can be categorized as emission events and variable continuous emissions. Emission events are frequently discrete episodes (such a plant emergency) in which a very large flow is flared. Variable continuous emissions can occur frequently and these are categorized into multiple modes of operation, depending on the scale of the variability.12 Several options have been implemented to minimize industrial flaring. The feasibility of implementing any of these

INTRODUCTION Current trends in using fossil fuels are not sustainable. In 2013, 91 million barrels of petroleum per day were consumed worldwide. Such usage also leads to a substantial carbon footprint. In 2013, 11 830.5 million metric tons of carbon dioxide were produced.1 The energy production sector is the main contributor to releasing greenhouse gases (GHG) as it accounts for about 70% of all anthropogenic GHG emissions.2 Notwithstanding of the various efforts to replace fossil fuels by sustainable energy forms and to optimize the energy use,3 there is a critical need to do more toward a sustainable energy future.4 Renewable energy sources, which include biomass, hydropower, geothermal, solar, wind, and marine energy, supply approximately 14% of the total world energy demand.5 The United Nations project that the global population will grow from about 7 billion today to 9.3 billion in 2050 and 10.1 billion in 2100.6 Nontraditional fossil fuels (e.g., shale gas) are expected to play an increasingly important role in meeting the growing demand for energy.7−9 In the fossil-based energy industry and chemical process industry, venting and flaring of flammable gases via combustion in open atmosphere flames is a common practice that leads to environmental concerns and economic losses.10 Globally, © 2016 American Chemical Society

Received: August 23, 2016 Revised: October 5, 2016 Published: October 26, 2016 675

DOI: 10.1021/acssuschemeng.6b02033 ACS Sustainable Chem. Eng. 2017, 5, 675−688

Research Article

ACS Sustainable Chemistry & Engineering

Figure 1. Proposed superstructure to manage flaring in oil complexes.

options depends on several factors including the flare composition and quantity, the processing technology, and the cost-benefit analysis. Gas recovery has been implemented to recompress and treat the gas for sales. Another option is the gas reinjection, where the gas is reinjected to the formation to promote an enhanced oil recovery or into the annulus of the well bore to facilitate gas lift. Power generation has also been considered, where the gas is burned to yield thermal energy that can be transformed into shaft work or electric energy. Finally, producing liquefied natural gas (LNG) or using gas-toliquid (GTL) technologies enable the chemical conversion of natural gas into clean diesel, naphtha, kerosene, and light oils.13 Flare minimization has been the focus of several works. Mourad et al.14 proposed the collection and compression of gases to send them to a plant where they are treated and valorized as a raw material for the petrochemical industry or compressed and reinjected into the reservoir to maintain the rate of oil production. However, this technique requires several compression stages that need large consumption of external energy and lead to CO2 emissions. Rahimpour et al.15 proposed three methods to recover gas to find the most suitable method for recovering flares. The proposed methods include production of liquid fuels, electricity generation, and compression and injection into pipelines. For a case study, gas compression was found to be the best choice due to the lower capital investment; however, abnormal operations were not considered. Jagannath et al.12 presented a multiperiod two-stage stochastic programming model to design and operate a fuel gas network considering fluctuating plant operation modes. They proposed to use waste gases to reduce the consumption of

costly fuels. Cogeneration systems can also be used to mitigate flaring. Bruno et al.16 presented a mixed-integer nonlinear programing model for performing structural and parametric optimization in utility plants to satisfy energy demands of industrial processes. Varbanov et al.17 presented new models for a better description of partial-load performance of steam and gas turbines. Al-Azri et al.18 introduced an algorithmic approach for the optimal design of cogeneration systems. The advantages of cogeneration systems for waste heat recovery were highlighted by Bamufleh et al.,19 Hipólito-Valencia et al.,20 Gutiérrez-Arriaga et al.,21 and Fuentes-Cortés et al.22 Kamrava et al.23 proposed a process integration approach to mitigate flaring for an ethylene plant with a known historical record of flaring. The results showed that cogeneration systems using flared gases can be used to yield environmental and economic benefits. Nonetheless, this work assumed constant flows for the flare streams. Furthermore, Kazi et al.24 developed an optimization framework for sizing a cogeneration system to integrate flares during abnormal operations minimizing the overall cost via the generation of Pareto fronts. The results of this work showed that cogeneration systems have the potential to reduce GHG emissions by utilizing flare streams. Nonetheless, this work did not consider price volatility of the fresh fuel or the time-based changes in the flare streams. Kazi et al.25 proposed an optimization framework to determine the optimum process configuration for simultaneous flare and wastewater management to minimize the total annual cost of the system where thermal membrane distillation and cogeneration were used to manage flare streams during abnormal situations. 676


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time period (t) and for each uncertain scenario that is randomly generated (s):

It should be noted that none of the above-mentioned works have considered the impact of uncertainty in flare characteristics and fossil fuel pricing on the optimal design of the cogeneration systems. Flare uncertainty includes flow rate, composition and frequency. Furthermore, none of the previous approaches have considered flares from multiple industrial processes that may be integrated via an eco-industrial park (e.g., Lovelady and El-Halwagi;26 Rubio-Castro et al.;27 Hipólitó et Valencia et al.;28 Boix et al.,29 Hortua et al.,30 López-Diaz al.31). Therefore, this paper presents an optimization approach to design a cogeneration system to manage flare streams from abnormal situations of multiple adjacent plants while considering the uncertainty associated with the frequency, duration, quantity, and quality of flaring. The approach also accounts for the economic and environmental aspects of the designed system.

Q tboiler = (Frt , sHFr + ,s

∑ FFi ,t ,sHFF)α boiler , ∀ t , ∀ s i

i

(2)

The energy balance in the boiler can be used to determine the mass flow rate in the steam Rankine cycle (ṁ s), which must consider the outlet enthalpy from the boiler (h1s) and the inlet enthalpy to the boiler (h4): Q tboiler = ṁ s(h1s − h4), ,s

∀ t, ∀ s

(3)

(Pturb t,s )

The power generated in the turbine is equal to the steam flow rate (ṁ s) multiplied by the difference between the inlet (h1s) and outlet enthalpy (h2) accounted for the involved efficiency (αturb):

■

turb Ptturb ṁ s(h1s − h2), ,s = α

PROBLEM STATEMENT The problem addressed in the paper is described as follow (see Figure 1). Given are several oil complexes sectioned in different plants with their corresponding flare streams. The uncertainty associated with the flares and vents in terms of frequency, quantity and composition is accounted for considering the historical data to randomly generate several scenarios (see Figure 2). Also, the uncertainty associated with the fuel price is

∀ t, ∀ s

(4)

(Qcond t,s )

The heat generated in the condenser is equal to the water flow rate in the cycle (ṁ s) times the difference between the inlet enthalpy (h3) and the outlet enthalpy (h2) while accounting for the condenser efficiency (αcond): Q tcond = αcondṁ s(h2 − h3), ,s

∀ t, ∀ s

(5)

The power required in the pump (Ppump t,s ) is equal to the water flow rate (ṁ s) times the difference between the inlet (h4) and (h3) outlet enthalpies accounting for the efficiency (αpump): Ptpump = α pumpṁs(h4 − h3), ,s

∀ t, ∀ s

(6)

The profit for the energy generated in the Rankine cycle (Salespower ) is calculated accounting for the power produced in s the turbine (Pt,sturb) and the power price in the market (pricepower): Salesspower =

power , ∑ Ptturb , s · price

Figure 2. Example of generated random scenarios.

∀s (7)

t

The water used in Rankine cycle to generate steam (ṁ s) is limited by a maximum allowed flow rate (ṁ max):

32

accounted for. The problem consists in determining the optimal integrated cogeneration system to produce power and trapping the flares from abnormal operations, whereas maximizing the overall profit and minimizing the greenhouse gas emissions.

ṁ s ≤ ṁ max ,

∀s

(8)

The flow rate in the steam Rankine cycle (ṁ s) is determined as a function of the power generated in the cycle (Pturb):

■

ṁ s = 0.000768(Pturb) + 1020.85,

MODEL FORMULATION The proposed mathematical formulation includes mass and energy balances to model the mixers and equipment considering the superstructure shown in Figure 1. The formulation also includes the cost function and the environmental considerations, as well as design and performance equations for the used units. In the next section is presented the proposed mathematical model. The first expression involves the total mass balance for the flare streams (Fi,t,s), which can be flared (Di,t,s), sent to the boiler of the cogeneration system (FFi,t,s), or both: Fi , t , s = Di , t , s + FFi , t , s , ∀ t , ∀ s (1)

∀s

(9)

Then, the operating costs for the needed units are determined as follows. First, the operating cost for the condenser (OpCostcond ) is determined as a function of the head load in s cw the condenser (Qcond t,s ) and the price for cooling water (price ): OpCost cond = s

·pricecw , ∑ Q tcond ,s

∀s (10)

t

The operating cost for the pump (OpCostpump ) is determined s as a function of the power needed (Ppump ) and the electric t,s power price (pricepower): OpCost s pump =

power , ∑ Ptpump , s · price

∀s

t

Then, it is needed a set of relationships for the cogeneration system. The heat produced in the boiler (Qboiler t,s ) is equal to the sum of the energy obtained from fresh fuels (Frt,sHFr) plus the flares sent to the boiler (FFi,t,sHFFi) times the involved efficiency (αboiler). It should be noted that this balance is required for any

(11)

(OpCostrep s )

The cost for the fresh fuel needed is determined considering the cost of fresh fuel (Frt,s) and the corresponding fuel price (pricerep) as well as the operating hours per period (HFr): 677


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ACS Sustainable Chemistry & Engineering OpCost s rep =

∑ (Frt ,sHFr)pricesrep,

And the capital cost for the pump (CapCostpump ) accounts for s the unit factors (C1pump, C2pump, Cpump) and the capacity (Ppump ): s

∀s (12)

t

The cost for combusting the flare streams as supplementary fuel is calculated using the method of Ulrich and Vasurdevan,33 as follows: First, the utility cost coefficients for combusting gas emissions as supplementary fuel are calculated using eqs 13 and 14. The low heating value and waste gas flows (Nm3/s) are parameters used to find the coefficients. Ai , t , s = (2.5 × 10−5LHVi 0.77)(qi , t , s)−0.23 ,

CapCost spump = C1pump + C2pump(Pspump)c

Bi = −6 × 10 LHV,i

∀ i, ∀ t , ∀ s

∀i

(14)

FFi , t , s PMi

,

∀ i, ∀ t , ∀ s

∀ i, ∀ t , ∀ s

∑ ∑ (2.592 × 106qi , t , sCSUi , t , s), t

∀s

i

(16)

≥

Q tboiler , ,s

Psturb ≥ Ptturb ,s ,

∀ t, ∀ s

Q scond ≥ Q tcond , ,s

∀ t, ∀ s

(20)

Pspump ≥ Ptpump , ,s

∀ t, ∀ s

(21)

,

∀s

turb

∀s

CapCost s

= CF

cond

+ CV

cond

(Q s

cond ccond

)

,

∀s

Card(s)

(28)

∀s

∀s

(30)

The associated greenhouse gas emissions (GHGCSs) for the cogeneration system are determined accounting for the emissions for combustion of fresh fuel (Frt,s) and the combustion for flares (FFi,t,s): ⎛ ⎛ 1000FFi , t , sXcYc , i ⎞⎞⎛ PM CO2 ⎞ GHGCSs = ⎜⎜∑ ∑ ∑ ⎜ ⎟⎟⎟⎜ ⎟ PMc ⎠⎠⎝ 1000 ⎠ ⎝ t i c ⎝ ⎛ ⎛ Frt , sXc FrYc Fr ⎞⎞ + ⎜⎜∑ ∑ ⎜ ⎟⎟⎟(PM CO2) ∀ s ⎝ t c Fr ⎝ PMc Fr ⎠⎠

(31)

Also, the emissions generated by flare streams when flare gases are not exploited (GHGFSs) are calculated by the following equation: ⎛ ⎛ 1000Di , t , sXcYc , i ⎞⎞⎛ PM CO2 ⎞ GHGFSs = ⎜⎜∑ ∑ ∑ ⎜ ⎟⎟⎟⎜ ⎟∀s PMc ⎠⎠⎝ 1000 ⎠ ⎝ t i c ⎝

(22)

(32)

Therefore, total emissions generated by the whole system (TGHGs) are the sum of the emissions for flares (GHGFS) and emissions from the cogeneration system (GHGCSs). TGHGs = GHGCSs + GHGFSs ∀ s

(23)

(33)

Then, the average annual greenhouse gas emissions (MGHG) for all the analyzed random scenarios (Card(s)) are determined as follows:

The capital cost for the condenser (CapCostcond ) involves the s corresponding unit factors (CFcond, CVcond, Ccond) and the capacity for the unit (Qcond ): s cond

∑s Profits

WProfit ≤ Profits,

In the same way, the capital cost for the turbine (CapCostturb s ) involves a fixed part (CFturb) and a part (CVturb) that is multiplied by the capacity (Pturb s ) elevated at the exponent (Cturb): CapCost s turb = CFturb + CV turb(Ps turb)c ,

(27)

The worst-case scenario for the profit (WProfit) is determined accounting for all the obtained profits for the different scenarios (Profits):

The equations for the capital costs for the used units were taken from Bruno et al.16 This way, the boiler cost (CapCostboiler ) s involves a fixed part (CFboiler) as well as a part that depends on the unit size (CVboiler) elevated at the exponent (cboiler) to account for the economies of scale: boiler

∀ t, ∀ s

(29) (17)

(19)

CapCost s boiler = CFboiler + CV boiler(Q sboiler)c

Pt , s turb ≤ EMAX,

boiler ⎧ + CapCostturb ⎫ ⎪ CapCost ⎪ ⎬, − KF⎨ ⎪ cond pump ⎪ + CapCost ⎭ ⎩+ CapCost

(18)

∀ t, ∀ s

(26)

Profits = Salesspower − OpCost cond − OpCost spump − OpCost rep s s

To determine the size needed for the units, the capacity must be greater than the one needed over any time period and for each random scenario, which is modeled as follows: Q sboiler

∀ t, ∀ s

The profit for each scenario (Profits) considers the sales (Salespower ) minus the operating and capital costs for the units s accounting for the annualization factor (KF):

Finally, eq 17 calculates the cost to use waste streams as supplementary fuel to feed the cogeneration system. Also, this equation uses a conversion factor to calculate this cost in $US per month. OpCost flow = s

(25)

Pt , s turb ≥ EREQ,

MProfit =

(15)

Then, the utility cost coefficients are used to calculate the price of the utility ($/Nm3) using this equation: CSUi , t , s = Ai , t , s CEPCI + Bi CSF ,

∀s

The objective of the model is to maximize the average annual profit for the system (MProfit) in all the considered random scenarios (Card(s)).

To solve eq 13, it is necessary to use eq 15 to convert units. qi , t , s = 0.008697

,

It should be noted that the power produced by the Rankine cycle (Pturb t,s ) must be lower than the demand (EREQ) and greater than the minimum required (EMAX), which is modeled as follows:

(13) −4

pump

MGHG =

(24) 678

∑s TGHGs Card(s)

(34) DOI: 10.1021/acssuschemeng.6b02033 ACS Sustainable Chem. Eng. 2017, 5, 675−688

Research Article


Figure 3. Cumulative probability to obtain a value of profit when the mean and worst profits are maximized.

0 ≤ SV4 ≤ 1

Furthermore, the worst-case scenario for the emissions (WGHG) should be greater that all the emissions for the random scenarios analyzed, which is determined as follows: WGHG ≥ TGHGs ∀ s

Then, the global objective function is formulated as follows: min FO = SV1 + SV2 + SV3 + SV4

(35)

In the proposed system, there are more than one objective, which must be maximized or minimized. The optimal solution must minimize the greenhouse gas emissions and maximize the profit accounting for the involved uncertainty. This way, first the objectives are normalized as follows: MProfit + ProfitMax = SV1 ProfitMax − ProfitMin

(36)

WProfit + ProfitMax = SV2 ProfitMax − ProfitMin

(37)

MGHG − GHGMin = SV3 GHGMax − GHGMin

(38)

WGHG + ProfitMin = SV4 ProfitMax − ProfitMin

(39)

(40)

0 ≤ SV2 ≤ 1

(41)

0 ≤ SV3 ≤ 1

(42)

(44)

It should be noted that the corresponding optimization formulation is a nonlinear programming (NLP) problem, which was coded in the GAMS software using the solver BARON.34 Furthermore, the boiler should be as big as necessary to satisfy the power demand of the plants; however, the power generated cannot be more that the maximum value that can handle the plants as modeled in eqs 26 and 27. According with the mass balance (eq 1), there are three possibilities for each waste stream: (1) All the flow of the waste stream can be burn in the flaring system; (2) All flow of the waste stream can be mixed with fresh fuel to feed the cogeneration system as supplementary fuel; (3) A fraction of the waste stream can be burn in the flaring system and the other part can be used as supplementary fuel in the cogeneration system. The objective of the optimization approach is to find the best option, it means to determine how much waste gas should be burn in the flaring system and how much should be used by the cogeneration system for every waste stream. It is worth noting that the cost of some units (for example the pump) may be not significantly; however, it is included to determine the targets for the involved units in the system and to consider these in the future detailed design.

It should be noted that the values for the normalization of profit, ProfitMax and ProfitMin, were obtained solving the problem for the scenario with the lowest and the highest costs for natural gas of all scenarios, respectively. On the other hand, the parameter GHGMin corresponds to the solution of the scenario where all flare streams are used in the cogeneration system, and consequently it has the maximum save of natural gas, and GHGMax is related to the scenario where all flare streams are burned in the traditional way, it means that waste gases are not used by the cogeneration system. This way, the normalized objectives are restricted as follows: 0 ≤ SV1 ≤ 1

(43)

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SOLUTION APPROACH The strategy to solve the addressed problem is described in the next subsections. Superstructure. The superstructure is constructed to show the available fuel waste streams from different petrochemical and natural gas plants, and the two ways that these streams can be disposed during abnormal situations. Furthermore, it is shown the possibility to use only fresh fuel or to mix fresh fuel with fuel waste gases in order to satisfy the demand and to analyze the economic and environmental benefits for taking advantage of abnormal situations. 679


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Figure 4. Cumulative probability to obtain a value of greenhouse gas emissions when the mean and worst profit is maximized.

Table 1. Composition and Flows for Fuel Waste Streams A−G flow

ton/y

190.59

171.12

171.12

124.61

120.74

21.87

46.5

component

name

A

B

C

D

E

F

G

H2 CH4 C2H2 C2H4 C2H6 C3H6 C4H6 C6H6 H20 C3H8 C4H10 C5H12 C9H12 C12H18

hydrogen methane acetylene ethylene ethane propene butadiene benzene water propane butane pentane cumene diisopropylbenzene

0.038 0.066 0.008 0.513 0.094 0.008 0.011 0.009 0.253 0 0 0 0 0

0.427 0.091 0.007 0.406 0.069 0 0 0 0 0 0 0 0 0

0.423 0.092 0 0.416 0.069 0 0 0 0 0 0 0 0 0

0 0.04 0 0.845 0.115 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0 0 0

Where x represents continuous variables like flow rates, operating and capital costs, and equipment size. Furthermore, y represents discrete variables generated randomly for each scenario, and these variables are the flow rate during abnormal situations and the prices of natural gas. In this paper, the goal programming method was applied to solve the multiobjective optimization problem. It should be noticed that all the involved variables of the model formulation affect the objective functions. Uncertainty Analysis. The problem is solved using the random parameters to obtain the cumulative probability graphs. When the economic and the environmental impacts are individually studied (Option 1 and Option 2), the problem does not include the eqs 36−43, and the graphs are generated as follows: For the economic analysis, the riskiest solution is solved. It means maximizing the average profit of all scenarios (maximizing eq 28), which allows obtaining the solution with the highest profit. Once the problem is solved, it is possible to plot the profit and the GHG emissions in each scenario versus their cumulative probability. For example, as it is shown in the blue lines of Figure 3 and Figure 4. After that, the problem is solved

Uncertain Parameters. When the superstructure is defined, it is necessary to select the parameters under uncertainty. In this case, uncertain parameters are the flow rates of fuel waste gases from abnormal situations and natural gas prices. Consequently, a sampling of one hundred random scenarios was done based on a normal distribution from historical data. Each scenario has the same probability to occur because the scenarios are completely random; there is not influence or preference for any scenario. Solution of Deterministic Multiobjective Problem. As mentioned before, the multiobjective problem was reformulated as a single objective problem. Thus, it is solved a deterministic optimization problem for all scenarios simultaneously and it can be expressed as follows: min FO = SV1 + SV2 + SV3 + SV4

Subject to h(x , y) = 0 ⎫ ⎪ ⎬ eqs 1−43 g (x , y ) ≤ 0 ⎪ ⎭ x ∈ R, y ∈ s 680


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ACS Sustainable Chemistry & Engineering Table 2. Composition and Flow for Fuel Waste Streams H−L flow

ton/y

566.332

169.89

283.166

651.28

component

name

H

I

J

K

L



0.0215 0.807 0 0 0.054 0 0 0 0 0.1 0.0116 0.005 0 0

0.0503 0.112 0 0 0.727 0 0 0 0 0.08 0.02 0.01 0 0

0.03 0.05 0 0 0.5 0 0 0 0 0.38 0.04 0 0 0

0 0 0 0 0 0 0 0 0 0.52 0.3 0.18 0 0

0.1 0.1 0 0 0.24 0 0 0 0 0.25 0.26 0 0 0

127.42

Table 3. Composition and Flow for Fuel Waste Streams M−Q flow

ton/y

46.20

1.40

44.80

20.85

0.65

formula

name

M

N

O

P

Q



0 0 0 0 0 0.0048 0 0.4945 0 0.0255 0 0 0.4605 0.0145

0 0 0 0 0 0.1597 0 0 0 0.8403 0 0 0 0

0 0 0 0 0 0 0 0.5101 0 0 0 0 0.4749 0.015

0 0 0 0 0 0 0 0 0 0 0 0 0.999 0.001

0 0 0 0 0 0 0 0 0 0 0 0 0 1

3. There are 17 streams that have three possibilities; the first one is to mix with fresh fuel and feed the cogeneration system, the second one is to burn in the flare system without being exploited, and the third is that a fraction of the waste stream can be burn in the flare system and the rest can be used as supplementary fuel in the cogeneration system. Furthermore, the amounts of waste fuel from the three plants are considered as uncertain parameters. Two options are considered for solving the addressed problem. The first option considers the economic objective maximizing the average profit and the worst case for the analyzed scenarios, which were randomly generated. The second option accounts for minimizing the average and worst case for the greenhouse gas emissions for the different analyzed random scenarios. As mentioned before the model was coded in the software GAMS, the model consists of 96 528 constraints and 109 926 continuous variables, where the solver BARON was used to solve it in a computer with and i7 processor with 16 GB of RAM, and the consumed CPU time was of 2.5 h. Option 1. This option focuses on analyzing the economic impact considering as objective function the maximization of the average profit for all the analyzed scenarios, and the maximization of the profit in the worst case. It means the maximum and the minimum risk solutions from the economic point of view. Figure 3 presents the cumulative probability

to obtain the solution with the lowest risk, which corresponds to maximize the worst profit (maximizing eq 30). Then, to solve the model for all the scenarios, the profit and the emissions versus their cumulative probability are plotted. For example, as it can be seen in the red lines of Figure 3 and Figure 4. The cumulative probability graphs for the environmental analysis are obtained in the same way; however, in this case the riskiest solution corresponds to minimize the average greenhouse gases generated in all scenarios (minimizing eq 34), which allows obtaining the solution with the lowest GHG emissions. Then, the lowest risk solution corresponds to minimize the worst GHG emissions (minimizing eq 35). Once the problem is solved using the goal programming method, the uncertainty of the problem is represented and analyzed using cumulative probability curves associated with each scenario. These curves are used to analyze the economic and environmental behavior under uncertainty when both objectives are taken into account simultaneously.

■

RESULTS AND DISCUSSION

A case study is presented to show the applicability of the proposed optimization approach. It includes three process plants and each plant has different flare streams. The average flow and composition for each flare are given in Tables 1, 2, and 681


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Figure 5. (a) Profit in different scenarios when the expected profit is maximized; (b) profit in different scenarios when the worst scenario is maximized.

Figure 6. Natural gas prices in different scenarios.

Figure 7. (a) Greenhouse gas emissions in different scenarios when the expected profit is maximized; (b) greenhouse gas emissions in different scenarios when the worst scenario is maximized.

and 3.2 × 107 $US/y; consequently, the probability to obtain at lease these values of profit for the three solutions with the highest risk are 97%, 44%, and 7%, respectively. On the other hand, the probability to have at least the mentioned values of profit are 96%, 40%, and 2%, respectively. It should be noted that both curves are similar, so there is almost the same

curves for the maximization of the expected profit solution (riskiest solution) and the maximization of the worst case solution (solution with the lowest risk). There are analyzed three possible values for the profit to show the probability to obtain each of them for the solutions with the highest and lowest risks. The profit values chosen are 5.0 × 106, 2.1 × 107, 682


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Figure 8. Greenhouse gas emissions generated in each solution for option 1.

Figure 9. Cumulative probability to obtain a value of profit when the mean and worst values for the greenhouse gas emissions are minimized.

Figure 10. Cumulative probability to obtain a value of greenhouse gas emissions when the mean and worst values are minimized.

minimum risk. In this case, the profit is nearly independent of the cumulative probability because in the cogeneration system the operational variables are almost the same for all scenarios. The blue curve is the solution for the greenhouse gas emissions generated in the case when the mean profit of all scenarios is maximized, which is the solution with the maximum risk. It should be noted that in this solution is possible to reach the

probability to have a high profit value with the maximum and the minimum risk solutions. Figure 4 shows the cumulative probability curves for the greenhouse gas emissions generated by the system when the expected profit is maximized and when the worst case for profit is maximized. The red curve is the solution for the greenhouse gas emissions related to maximize the worst case for profit, which is the solution with the 683


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Figure 11. Profit in different scenarios when expected greenhouse gas emissions are minimized; (b) profit in different scenarios when the worst scenario is minimized.

Figure 12. (a) Greenhouse gas emissions in different scenarios when the expected emissions are minimized; (b) greenhouse gas emissions in different scenarios when the worst scenario is minimized.

emissions are reduced; however, this behavior is originated by the objective function, which maximizes the profit. Finally, Figure 8 shows that the greenhouse gas emissions are mitigated when the cogeneration system is fed by waste streams. Also, most of the scenarios reduce the greenhouse gas emissions through the use of flare streams fed to the cogeneration system. Option 2. This option seeks to prioritize the environmental impact caused by the greenhouse gases. Figure 9 shows the cumulative probability curves for the maximum expected profit solution and the maximum worst case solution. However, Figure 9 does not give the opportunity to analyze different scenarios due to both curves are almost self-same because the objective function is the greenhouse gas emissions, so there is almost the same probability to have a high profit value with the maximum and minimum risks. Moreover, it implies that the proposed design is stable for this case. Figure 10 presents the cumulative probability curves for the minimum average and worst greenhouse gas emissions, where the points 348 600, 349 240, and 349 760 ton/y have the probability to have the average solutions of 98%, 77%, and 50%, respectively; whereas,

lowest value for the greenhouse gas emissions (348 830 ton/y). Nevertheless, a quantity of greenhouse gas emissions 1.3 times the lowest value is generated by the same solution (452 420 ton/y). Figure 5 presents the profit for the different scenarios. Figure 5a shows the profit for the riskiest solution and Figure 5b shows the profit for the solution with the lowest risk. In both cases, the scenarios with the highest and the lowest profits are scenarios sixty four and seventy seven, respectively. It should be noted in Figure 6 that the natural gas price has a strong relation with the profit because the mentioned scenarios correspond to the once with the highest and the lowest prices of natural gas. Furthermore, Figure 7 shows that natural gas price is closely related to the greenhouse gas emissions generated by the proposed system because when the natural gas prices fall, it is cheaper to flare some waste streams from the plants than to use them in the cogeneration system; consequently, the greenhouse gas emissions increase. On the other hand, when the natural gas price rises, the waste streams from the plants become an economically feasible option in the cogeneration system, and at the same time the profit increases and the greenhouse gas 684


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Figure 13. Greenhouse gas emissions generated in each scenario for option 2.

Figure 14. Greenhouse gas emissions difference between carbon dioxide generated when the cogeneration system is not used and emissions when the cogeneration system is used, and profit generated in each scenario for Option 3.

Figure 15. Cumulative probability to obtain a value of profit when the mean and worst values for the greenhouse gas emissions and profit are minimized at the same time.

the same points in the worst cases have the probability of 94%, 20%, and 1%, respectively. Figure 11 shows the profit for all scenarios for the solutions with the highest (Figure 11a) and lowest (Figure 11b) risks. The profit depends on the natural gas prices as was reported for the case 1; however, the results show that for all the scenarios all the flare streams from the plants are used in the cogeneration system because the objective function is to minimize the greenhouse gas emission. Therefore, the variation in greenhouse gas emissions depends only on the composition and magnitude of the abnormal situations in each scenario (see Figure 12); this is because natural gas is used to compensate the

needed fuel to produce the specific electric demand of the plants. Finally, Figure 13 shows that the greenhouse gas emissions are strongly reduced when the flares are used in the cogeneration system. Option 3. In this option, the four objective functions (previously presented in describing Option 1 and Option 2) are simultaneously considered for all scenarios under uncertainty for the abnormal situations using eq 44 as objective function. Figure 14 shows the profit in each scenario taking into account the uncertainty in the natural gas price. The blue points represent the profit in each scenario and the yellow bars in the figure represent the difference in carbon dioxide emissions as a 685


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CapCostboiler = Boiler capital cost ($/y) s CapCostcond = Condenser capital cost ($/y) s CapCostpump = Pump capital cost ($/y) s CapCostturb = Turbine capital cost ($/y) s CSF = Fuel price ($/GJ) CSUi,t,s = Utility price ($/Nm3) Di,t,s = Flare flow rate from different plants sent to the flaring system (ton/month) FFi,t,s = Flare flow rate from different plants sent to the cogeneration system (ton/month) Frt,s = Fresh fuel fed to the cogeneration system (ton/ month) GHGCSs = GHG generated by the cogeneration system in each scenario (ton/y) GHGFSs = GHG generated by the flaring system in each scenario (ton/y) h1s = Water enthalpy at the boiler outlet (GJ/ton) h2 = Water enthalpy at the turbine outlet (GJ/ton) h3 = Water enthalpy at the condenser outlet (GJ/ton) h4 = Water enthalpy at the pump outlet (GJ/ton) ṁ s = Water mass flow in cogeneration system (kg/s) MGHG = Average annual greenhouse gas emissions (ton/y) MProfit = Average annual profit ($/y) OpCostcond = Condenser operating cost ($/y) s OpCostflow = Flare streams as supplementary fuel operation s cost ($/y) OpCostpump = Pump operating cost ($/y) s OpCostrep s = Fresh fuel cost ($/y) Ppump = Energy consumed by the pumps in each scenario s (GJ/y) Pturb = Power generated by the turbine in each scenario (GJ/ s y) Ppump = Energy consumed by the pumps (GJ/y) t,s Pturb = Power generated by the turbine (GJ/y) t,s Profits = Profit in each scenario ($/y) qi,t,s = Total waste gases used as supplementary fuel (Nm3/s) Qboiler = Energy generated by the boiler in each scenario s (GJ/y) Qcond = Energy removed by the condenser in each scenario s (GJ/y) Qboiler = Energy generated by the boiler (GJ/y) t,s Qcond = Energy removed by the condenser (GJ/y) t,s Salespower = Profit by generated electricity ($/y) s TGHGs = Total GHG generated by the entire system in each scenario (ton/month) WProfit = Profit in the worst scenario ($/y)

result of using a cogeneration system. Carbon dioxide emissions are almost the same in each scenario. As long the cost of the waste streams is less than the purchased cost of the fresh fuel, the optimization objective function will endeavor to maximize the use of waste streams and the minimization of the carbon dioxide emission. Otherwise, the optimization approach will provide a trade-off between profit and GHG emissions. Figure 15 shows the cumulative probability for the profit for this solution and it can be seen that there are not scenarios with economic losses; furthermore, this figure is a useful tool for decision makers to analyze the probability to obtain at least the selected profit.

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CONCLUSIONS This paper has presented a multiobjective optimization approach for incorporating flare and vent streams from different industrial plants into a cogeneration system while accounting for the flare uncertainty and price volatility. The model was formulated as a nonlinear programming problem based on a new superstructure that enables the optimal design and operation of the system. A computationally efficient solution approach has been presented to show the optimal solutions that reconcile the involved objectives and allows determining low risk solutions for the desired objectives. A case study with several flares from different industries in a chemical−oil complex from Mexico was considered. The results show that there is potential economic and environmental merits for adopting the proposed approach in using flare streams to produce power and heat, integrating multiple plants, and accounting for uncertainty of the abnormal scenarios and fossil fuel prices. Finally, on the basis of the CPU time needed for the model, other formal stochastic programming approaches can be implemented to solve this problem to obtain additional information about the involved uncertainty.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.6b02033. All parameters used and additional results for the solutions obtained(PDF)

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AUTHOR INFORMATION

Parameters

Corresponding Author

*J. M. Ponce-Ortega. E-mail: [email protected]; Tel.: +52 443 3223500 ext. 1277; Fax: +52 443 3273584.

cboiler = Constants for the equation of boiler capital cost cturb = Constants for the equation of the turbine capital cost ccond = Constants for the equation of the condenser capital cost Card = Number of scenarios CEPCI = Chemical engineering plant cost index CFboiler = Unit boiler fixed cost CFcond = Unit condenser fixed cost CFturb = Unit turbine fixed cost CVboiler = Unit boiler variable cost CVcond = Unit condenser variable cost CVturb = Unit turbine variable cost C1pump, C2pump, C3pump = Constants for the equation of the pump capital cost EREQ = Energy required to satisfy the plant demands (GJ/ month)

Notes

The authors declare no competing financial interest.

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

Variables

Ai,t,s = Utility cost coefficient, which reflects inflationdependent cost elements Bi = Utility cost coefficient, which reflects energy-dependent cost elements 686


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EMAX = Energy to satisfy the requirements inside and outside the plants (GJ/month) Fi,t,s = Flare streams from different plants (ton/month) HFr = Calorific value for fresh fuel (GJ/ton) HFi = Calorific value for flare streams of the plants (GJ/ton) LHVi = Low heating value (MJ/Nm3) ṁ MAX = Maximum water flow in the cogeneration system (kg/s) pricepower = Power price ($/GJ) pricecw = Cooling water price ($/GJ) pricerep = Fresh fuel price ($/GJ) PMc = Molecular weight for each component (kg/kmol) PMi = Molecular weight (kg/kmol) PMcFr = Molecular weight for fresh fuel (kg/kmol) PMCO2 = Molecular weight for carbon dioxide (kg/kmol) Xc = Stoichiometric constant for each component (kgCO2/ kgC) XcFr = Stoichiometric constant for fresh fuel (kgCO2/kgC) Yc,i = Mole fraction of each component YcFr = Mole fraction of each component for fresh fuel Greek Symbols

αboiler = Boiler efficiency αturb = Turbine efficiency αcond = Condenser efficiency αpump = Pump efficiency Indices

c = Component i = Waste stream from plants t = Time period s = Scenario

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