Optimal Design of Multiplant Cogeneration Systems with Uncertain

Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)

Article

Optimal Design of Multi-Plant Cogeneration Systems with Uncertain Flaring and Venting Javier Tovar-Facio, Fadwa Eljack, José María Ponce-Ortega, and Mahmoud M El-Halwagi ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.6b02033 • Publication Date (Web): 26 Oct 2016 Downloaded from http://pubs.acs.org on November 7, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Sustainable Chemistry & Engineering is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 46

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

ACS Sustainable Chemistry & Engineering

Optimal Design of Multi-Plant Cogeneration Systems with Uncertain Flaring and Venting Javier Tovar-Facio,a Fadwa Eljack,b José M. Ponce-Ortega,a* Mahmoud M. ElHalwagic,d

a

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Edificio V1, Ciudad Universitaria, Morelia, Mich., 58060, México b

Department of Chemical Engineering, Qatar University, P.O. Box 2713, Doha, Qatar. c

Chemical Engineering Department, Texas A&M University, 200 Jack E. Brown Engineering Building, College Station TX, 77843-3122, 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; Fax. +52 443 3273584

ACS Paragon Plus Environment


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

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.


Page 2 of 46

Page 3 of 46

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


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 produced1. The energy production sector is the main contributor to releasing greenhouse gases (GHG) as it accounts for about 70% of all anthropogenic GHG emissions2. 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 towards a sustainable energy future4. Renewable energy sources, which include biomass, hydropower, geothermal, solar, wind, and marine energy, supply approximately 14% of the total world energy demand5. 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 21006. Non-traditional fossil fuels (e.g., shale gas) are expected to play an increasingly important role in meeting the growing demand for energy.7,8,9 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, 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 by-products 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 flowrates, 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



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

Several options have been implemented to minimize industrial flaring. The feasibility of implementing any of these 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-to-liquid (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 multi-period 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


Page 4 of 46

Page 5 of 46

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


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. 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 flowrate, 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-Halwagi26; Rubio-Castro et al.27; Hipólito-Valencia et al.28; Boix et al.29, Hortua et al.30, López-Díaz et 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.

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 accounted



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 6 of 46

for.32 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.

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)

Then, it is needed a set of relationships for the cogeneration system. The heat produced in the boiler ( Qtboiler ) is equal to the sum of the energy obtained from fresh fuels ,s ( Frt , s H Fr ) plus the flares sent to the boiler ( FFi ,t , s H FFi ) times the involved efficiency ( α boiler ). It should be noted that this balance is required for any time period ( T ) and for each uncertain scenario that is randomly generated ( S ):   Qtboiler =  Frt , s H Fr + ∑ FFi ,t , s H FFi  α boiler , ∀T , ∀S ,s i  

(2)

The energy balance in the boiler can be used to determine the mass flowrate in the steam Rankine cycle ( m& s ), which must consider the outlet enthalpy from the boiler ( h1 s ) and the inlet enthalpy to the boiler ( h 4 ):

Qtboiler = m& s (h1 s − h 4 ), ∀T , ∀S ,s


(3)

Page 7 of 46

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


The power generated in the turbine ( Pt , s turb ) is equal to the steam flowrate ( m& s ) multiplied by the difference between the inlet ( h1s ) and outlet enthalpy ( h 2 ) accounted for the involved efficiency ( α turb ):

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

(4)

The heat generated in the condenser ( Qtcond , s ) is equal to the water flowrate in the cycle ( m& s ) times the difference between the inlet enthalpy ( h 3 ) and the outlet enthalpy (

h 2 ) while accounting for the condenser efficiency ( αcond ): Qtcond = α cond m& s (h 2 − h 3 ), ∀T , ∀S ,s

(5)

The power required in the pump ( Pt ,pump ) is equal to the water flowrate ( m& s ) times s the difference between the inlet ( h 4 ) and ( h 3 ) outlet enthalpies accounting for the efficiency ( α pump ):

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

(6)

The profit for the energy generated in the Rankine cycle ( Saless power ) is calculated accounting for the power produced in the turbine ( Pt turb , s ) and the power price in the market (

pricepower ): power Saless power = ∑ Pt turb , ∀S , s ⋅ price

(7)

t

& s ) is limited by a maximum allowed The water used in Rankine cycle to generate steam ( m flowrate ( m& max ): m& s ≤ m& max , ∀ S

(8)

& s ) is determined as a function of the power The flowrate in the steam Rankine cycle ( m generated in the cycle ( P

turb

):

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


(9)


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 8 of 46

Then, the operating costs for the needed units are determined as follows. First, the operating cost for the condenser ( OpCosts

cond

) is determined as function of the head load in the condenser

cond

( Qt , s ) and the price for cooling water ( price

cw

):

cw OpCostscond = ∑Qtcond , s ⋅ price , ∀S

(10)

t

The operating cost for the pump ( OpCosts pump ) is determined as a function of the power needed ( Pt ,pump ) and the electric power price ( pricepower ): s

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

(11)

t

The cost for the fresh fuel needed ( OpCosts rep ) is determined considering the cost of fresh fuel ( Frt , s ) and the corresponding fuel price ( pricerep ) as well as the operating hours per period ( H Fr ): OpCost s rep = ∑ ( Frt , s H Fr ) pricesrep , ∀S

(12)

t

The cost for combusting the flare streams as supplementary fuel is calculated using the method of Ulrich and Vasurdevan33, as follows: First, the utility cost coefficients for combusting gas emissions as supplementary fuel are calculated using equations (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 × 10−5 LHVi 0.77 ) ( qi , t , s )

−0.23

, ∀I , ∀T , ∀S

Bi = −6 ×10−4 LHV,i ∀I

(13) (14)

To solve equation (13), it is necessary to use equation (15) to convert units.

qi,t , s = 0.008697

FFi,t , s PMi

, ∀I , ∀T , ∀S

(15)

Then, the utility cost coefficients are used to calculate the price of the utility ($/Nm3) using this equation:


Page 9 of 46

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


CSU i , t , s = Ai , t , s CEPCI + Bi CSF , ∀ I , ∀ T , ∀ S

(16)

Finally, equation (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. O pC ost sF low =

∑ ∑ ( 2.592 × 10 t

6

q i , t , s C SU i , t , s ) , ∀ S

(17)

i

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: boiler

Qs

turb

≥ Qtboiler , s , ∀T , ∀S

(18)

≥ Pt turb ∀T , ∀S ,s ,

(19)

Qs ≥ Qtcond , s , ∀T , ∀S

(20)

Pspump ≥ Pt,pump s , ∀T , ∀S

(21)

Ps

cond

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

CapCostsboiler = CFboiler + CV boiler (Qsboiler )c , ∀S

(22)

In the same way, the capital cost for the turbine ( CapCosts turb ) involves a fixed part ( CF turb ) and a part ( CV turb ) that is multiplied by the capacity ( Ps turb ) elevated at the exponent ( Cturb ): turb

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

(23)

The capital cost for the condenser ( CapCosts cond ) involves the corresponding unit factors ( CFcond , CV cond , C cond ) and the capacity for the unit ( Qs cond ):



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 10 of 46

cond

CapCostscond = CFcond + CV cond (Qscond )c , ∀S

(24) pump

And the capital cost for the pump ( CapCosts

) accounts for the unit factors (

C1pump , C2 pump , C pump ) and the capacity ( Ps pump ): pump

= C1pump + C2pump ( Ps pump )c

CapCosts

pump

, ∀S

(25)

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

Pt , s turb ≥ EREQ, ∀T , ∀S

(26)

Pt , s turb ≤ EMAX, ∀T , ∀S

(27)

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

MProfit =

∑ Profit

s

s

(28)

Card ( s )

The profit for each scenario ( Profits ) considers the sales ( Saless power ) minus the operating and capital costs for the units accounting for the annualization factor ( K F ):

Profits = Saless power − OpCostscond − OpCosts pump − OpCosts rep CapCost boiler + CapCost  − KF  , ∀S cond pump  +CapCost + CapCost  turb

(29)

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

WProfit ≤ Profit s , ∀S

(30)


Page 11 of 46

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


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 ):

  1000 FFi ,t , s Xc Yc,i    PMCO2    Fr X Y   GHGCSs =  ∑∑∑ +  ∑∑  t , s cFr cFr   PMCO2      t i c    PMc     1000   t cFr  PMcFr  

(

)

∀S

(31) Also the emissions generated by flare streams when flare gases are not exploited ( GHGFSs ) are calculated by the following equation.

  1000 Di ,t , s Xc Yc,i    PMCO2  GHGFSs =  ∑∑∑       t i c PM c      1000 

∀S

(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

(33)

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

∑TGHG

s

MGHG =

s

(34)

Card ( s )

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

(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 + Profit Max = SV1 Profit Max − Profit Min

(36)



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 12 of 46

WProfit + Profit Max = SV2 Profit Max − Profit Min

(37)

MGHG − GHG Min = SV3 GHG Max − GHG Min

(38)

WGHG + Profit Min = SV4 Profit Max − Profit Min

(39)

It should be noticed that the values for the normalization of profit, Profit Max and

Profit Min , 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 GHG Min 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 GHG Max 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

(40)

0 ≤ SV2 ≤ 1

(41)

0 ≤ SV3 ≤ 1

(42)

0 ≤ SV4 ≤ 1

(43)

Then, the global objective function is formulated as follows:

min FO = SV1 + SV2 + SV3 + SV4

(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 Equations 26 and 27. According with the mass balance (Equation 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


Page 13 of 46

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


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.

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. Uncertain parameters When the superstructure is defined, it is necessary to select the parameters under uncertainty. In this case, uncertain parameters are the flowrates 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 multi-objective problem As mentioned before, the multi-objective 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:



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

min FO = SV1 + SV2 + SV3 + SV4 Subject to

h( x, y ) = 0   Equations (1) − (43) g ( x, y ) ≤ 0  x ∈ R, y ∈ S Where x represents continues 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 flowrate 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 equations (36) to (43), and the graphs are generated as follows: For the economic analysis it is solved the riskiest solution. It means maximizing the average profit of all scenarios (maximizing equation (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 to obtain the solution with the lowest risk, which corresponds to maximize the worst profit (maximizing equation (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 equation (34)), which allows


Page 14 of 46

Page 15 of 46

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


obtaining the solution with the lowest GHG emissions. Then, the lowest risk solution corresponds to minimize the worst GHG emissions (minimizing equation (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 3. There are seventeen 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 equations 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 hours. 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 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



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

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 5.0x106, 2.1x107 and 3.2x107 $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 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 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 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 emissions are reduced; however, this behavior is originated by the objective function, which maximizes


Page 16 of 46

Page 17 of 46

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


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, this Figure 9 does not give the opportunity to analyze different scenarios due to both curves are almost selfsame 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, 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 options 1 and 2) are simultaneously considered for all scenarios under uncertainty for the abnormal situations using equation (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



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

represent the profit in each scenario and the yellow bars in the figure represent the difference in carbon dioxide emissions as a 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 tradeoff 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.

CONCLUSIONS This paper has presented a multi-objective 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, based on the CPU time needed the model, other formal stochastic programming approaches can be implemented to solve this problem to obtain additional information about the involved uncertainty.

ASSOCIATED CONTENT Supporting Information


Page 18 of 46

Page 19 of 46

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


The Supporting Information is available free of charge on the ACS Publications website. All parameter used in the paper were included in the supporting information in Tables S1 to S6. Also, additional results for the solutions obtained are presented in Table S7.

AUTHOR INFORMATION Corresponding Author *Ponce-Ortega José M. Tel. +52 443 3223500. Ext. 1277. Fax. +52 443 3273584. E-mail: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENT 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 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)

Di , t ,s

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



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

FFi , t , s

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

F rt , 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)

h1 s

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)

m& s

Water mass flow in cogeneration system (kg/s)

MGHG

Average annual greenhouse gas emissions (ton/y)

MProfit

Average annual profit ($/y).

OpCost s cond

Condenser operating cost ($/y)

OpCost s pump

Pump operating cost ($/y)

OpCost s rep

Fresh fuel cost ($/y)

OpCost s Flow

Flare streams as supplementary fuel operation cost ($/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)


Page 20 of 46

Page 21 of 46

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


Profits

Profit in each scenario ($/y)

qi,t , s

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

Q s b o ile r

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

Q s cond

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

Qtboiler ,s

Energy generated by the boiler (GJ/y)

Qtcond ,s

Energy removed by the condenser (GJ/y)

Sales s power

Profit by generated electricity ($/y)

TGHGs

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

WProfit

Profit in the worst scenario ($/y)

Parameters c boiler

Constants for the equation of boiler capital cost

c turb

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

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



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

EREQ

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

EMAX

(GJ/month)

Fi,t,s

Flare streams from different plants (ton/month)

H Fr

Calorific value for fresh fuel (GJ/ton)

HFFi

Calorific value for flare streams of the plants (GJ/ton)

LHVi

Low heating value (MJ/Nm3)

& MAX m

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

price power

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)

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

Greek symbols

α boiler

Boiler efficiency


Page 22 of 46

Page 23 of 46

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


α turb

Turbine efficiency

α cond

Condenser efficiency

α pump

Pump efficiency

Indices c

Component

i

Waste stream from plants

t

Time period

s

Scenario

REFERENCES (1)

U.S. Energy Information Administration. https://www.eia.gov/ (Accessed April, 2016).

(2)

Höök, M.; Tang, X. Depletion of fossil fuels and anthropogenic climate change—A review. Energy Policy 2013, 52, 797-809.

(3)

Banos, R.; Manzano-Agugliaro, F.; Montoya, F.; Gil, C.; Alcayde, A.; Gómez, J. Optimization methods applied to renewable and sustainable energy: A review. Renewable Sustainable Energy Rev. 2011, 15 (4), 1753-1766.

(4)

Connolly, D.; Lund, H.; Mathiesen, B. V.; Leahy, M. A review of computer tools for analysing the integration of renewable energy into various energy systems. Appl. Energy 2010, 87 (4), 1059-1082.

(5)

Panwar, N. L.; Kaushik, S. C.; Kothari, S. Role of renewable energy sources in environmental protection: A review. Renewable Sustainable Energy Rev. 2011, 15 (3), 1513-1524.

(6)

Lee, R. The Outlook for Population Growth. Science (New York, N.Y.) 2011, 333 (6042), 569-573.

(7)

Kinnaman, T. C. The economic impact of shale gas extraction: A review of existing studies. Ecol. Econ. 2011, 70 (7), 1243-1249.

(8)

Arogundade, O.; Sohrabi, M. A Review of recent developments and challenges in shale gas recovery. Soc. Pet. Eng. 2012, Paper 160869.



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

(9)

Arredondo-Ramírez, K.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Optimal planning and infrastructure development for shale gas production. Energy Convers. Manage. 2016, 119, 91-100.

(10)

Davoudi, M.; Rahimpour, M. R.; Jokar, S. M.; 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.

(11)

Farina M.F. Flare Gas Reduction. Recent global trends and policy considerations. General Electric Company 2010, GE Energy, Washington, D.C., USA.

(12)

Jagannath, A.; Hasan, M. M. F.; Al-Fadhli, F. M.; Karimi, I. A.; Allen, D. T. Minimize flaring through integration with fuel gas networks. Ind. Eng. Chem. Res. 2012, 51 (39), 12630-12641.

(13)

Onwukwe Stanley, I. Gas-to-liquid technology: Prospect for natural gas utilization in Nigeria. J. Nat. Gas Sci. Eng. 2009, 1 (6), 190-194.

(14)

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. 2010, 26 (6), 1706-1716.

(15)

Rahimpour, M. R.; Jamshidnejad, Z.; Jokar, S. M.; Karimi, G.; Ghorbani, A.; Mohammadi, A. H. A comparative study of three different methods for flare gas recovery of Asalooye Gas Refinery. J. Nat. Gas Sci. Eng. 2012, 4, 17-28.

(16)

Bruno, J. C.; Fernandez, F.; Castells, F.; Grossmann, I. E. A Rigorous MINLP model for the optimal synthesis and operation of utility plants. Chem. Eng. Res. Des. 1998, 76 (3), 246-258.

(17)

Varbanov, P. S.; Doyle, S.; Smith, R. Modelling and optimization of utility systems. Chem. Eng. Res. Des. 2004, 82 (5), 561-578.

(18)

Al-Azri, N.; Al-Thubaiti, M.; El-Halwagi, M. An algorithmic approach to the optimization of process cogeneration. Clean Technol. Environ. Policy 2008, 11 (3), 329-338.

(19)

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. Environ. Policy 2012, 15 (1), 185-197.


Page 24 of 46

Page 25 of 46

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


(20)

Hipólito-Valencia, B. J.; Rubio-Castro, E.; Ponce-Ortega, J. M.; Serna-González, M.; Nápoles-Rivera, F.; El-Halwagi, M. M. Optimal design of inter-plant waste energy integration. Appl. Therm. Eng. 2014, 62 (2), 633-652.

(21)

Gutiérrez-Arriaga, C. G.; Abdelhady, F.; Bamufleh, H. S.; Serna-González, M.; ElHalwagi, M. M.; Ponce-Ortega, J. M. Industrial waste heat recovery and cogeneration involving organic Rankine cycles. Clean Technol. Environ. Policy 2014, 17 (3), 767-779.

(22)

Fuentes-Cortés, L. F.; Martinez-Gomez, J.; Ponce-Ortega, J. M., Optimal design of inherently safer domestic combined heat and power systems. ACS Sustainable Chem. Eng. 2016, 4 (1), 188-201.

(23)

Kamrava, S.; Gabriel, K. J.; El-Halwagi, M. M.; Eljack, F. T. Managing abnormal operation through process integration and cogeneration systems. Clean Technol. Environ. Policy 2015, 17 (1), 119-128.

(24)

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.

(25)

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 (7), 2020-2034.

(26)

Lovelady, E. M.; El-Halwagi, M. M. Design and integration of eco-industrial parks for managing water resources. Environ. Prog. Sustainable Energy 2009, 28 (2), 265-272.

(27)

Rubio-Castro, E.; Ponce-Ortega, J. M.; Nápoles-Rivera, F.; El-Halwagi, M. M.; Serna-González, M.; Jiménez-Gutiérrez, A. Water integration of eco-industrial parks using a global optimization approach. Ind. Eng. Chem. Res. 2010, 49 (20), 9945-9960.

(28)

Hipólito-Valencia, B. J.; Lira-Barragán, L. F.; Ponce-Ortega, J. M.; SernaGonzález, M.; El-Halwagi, M. M. Multiobjective design of interplant trigeneration systems. AIChE J. 2014, 60 (1), 213-236.



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

(29)

Page 26 of 46

Boix, M.; Montastruc, L.; Azzaro-Pantel, C.; Domenech, S. Optimization methods applied to the design of eco-industrial parks: a literature review. J. Cleaner Prod. 2015, 87, 303-317.

(30)

Hortua, A. C.; El-Halwagi, M. M.; Ng, D. K. S.; Foo, D. C. Y. Integrated approach for simultaneous mass and property integration for resource conservation. ACS Sustainable Chem. Eng. 2013, 1 (1), 29-38.

(31)

López-Díaz, D. C.; Lira-Barragán, L. F.; Rubio-Castro, E.; Ponce-Ortega, J. M.; ElHalwagi, M. M., Synthesis of eco-industrial parks interacting with a surrounding watershed. ACS Sustainable Chem. Eng. 2015, 3 (7), 1564-1578.

(32)

Mexican Secretary of Economyhttp://portalweb.sgm.gob.mx/economia/es/energeticos/precios/701seguimiento-precio-gas-natural-datos.html (Accessed July, 2016).

(33)

Ulrich, G. D.; Vasudevan, P. T. How to estimate utility costs. Chem. Eng. 2006, 113 (4), 66.

(34)

Brooke, D. Kendrick, A. Meeraus, R. Raman. GAMS user’s guide. GAMS Development

Corporation,

Washington,


D.C.,

USA,

2016.

Page 27 of 46

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


Tables:

Table 1. Composition and flows for fuel waste streams A-G. Flow ton/y Component Name H2 Hydrogen CH4 Methane C 2 H2 Acetylene C 2 H4 Ethylene C 2 H6 Ethane C 3 H6 Propene C 4 H6 Butadiene C 6 H6 Benzene H2 0 Water C 3 H8 Propane C4H10 Butane C5H12 Pentane C9H12 Cumene C12H18 Diisopropylbenzene

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

171.12 171.12 124.61 120.74 B C D E 0.427 0.423 0 0 0.091 0.092 0.04 0 0.007 0 0 0 0.406 0.416 0.845 1 0.069 0.069 0.115 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

21.87 F 0 0 0 0 1 0 0 0 0 0 0 0 0 0

46.5 G 0 1 0 0 0 0 0 0 0 0 0 0 0 0

Table 2. Composition and flow for fuel waste streams H-L. Flow Component

H2 CH4 C 2 H2 C 2 H4 C 2 H6 C 3 H6 C 4 H6 C 6 H6 H2 0 C 3 H8 C4H10 C5H12 C9H12 C12H18

ton/y Name Hydrogen Methane Acetylene Ethylene Ethane Propene Butadiene Benzene Water Propane Butane Pentane Cumene Diisopropylbenzene

566.332 H 0.0215 0.807 0 0 0.054 0 0 0 0 0.1 0.0116 0.005 0 0

169.89 I 0.0503 0.112 0 0 0.727 0 0 0 0 0.08 0.02 0.01 0 0

283.166 J 0.03 0.05 0 0 0.5 0 0 0 0 0.38 0.04 0 0 0


651.28 K 0 0 0 0 0 0 0 0 0 0.52 0.3 0.18 0 0

127.42 L 0.1 0.1 0 0 0.24 0 0 0 0 0.25 0.26 0 0 0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 46

Table 3. Composition and flow for fuel waste streams M-Q. Flow Formula

H2 CH4 C 2 H2 C 2 H4 C 2 H6 C 3 H6 C 4 H6 C 6 H6 H2 0 C 3 H8 C4H10 C5H12 C9H12 C12H18

Ton/y Name Hydrogen Methane Acetylene Ethylene Ethane Propene Butadiene Benzene Water Propane Butane Pentane Cumene Diisopropylbenzene

46.20 M 0 0 0 0 0 0.0048 0 0.4945 0 0.0255 0 0 0.4605 0.0145

1.40 N 0 0 0 0 0 0.1597 0 0 0 0.8403 0 0 0 0


44.80 O 0 0 0 0 0 0 0 0.5101 0 0 0 0 0.4749 0.015

20.85 P 0 0 0 0 0 0 0 0 0 0 0 0 0.999 0.001

0.65 Q 0 0 0 0 0 0 0 0 0 0 0 0 0 1

Page 29 of 46

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


Caption for Figures:

Figure 1. Proposed superstructure to manage flaring in oil complexes. Figure 2. Example of generated random scenarios. Figure 3. Cumulative probability to obtain a value of profit when the mean and worst profits are maximized. Figure 4. Cumulative probability to obtain a value of greenhouse gas emissions when the mean and worst profit is maximized. 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. 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. 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. Figure 13. Greenhouse gas emissions generated in each solution for option 2.



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

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.


Page 30 of 46

Page 31 of 46

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


P = Plant

P=1

Boiler

P=2 Pump

. . .

Turbine

Condenser

P=n

Fresh Fuel

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



260

Flow (Ton/month)

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 32 of 46

240 220 200 180 160 140 120 1

2

3

4

5

6

7

8

9

10

Month (From January = 1 to December = 12)

Figure 2. Example of generated random scenarios.


11

12

Page 33 of 46

1 0.9 0.8

Cumulative 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


0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

3.0E+07

3.5E+07

4.0E+07

Profit ($US/y)

Maximization Expected Profit

Maximization Worst Case for Profit

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



1 0.9 0.8


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 34 of 46

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 3.4E+05

3.6E+05

3.8E+05

4.0E+05

4.2E+05

4.4E+05

4.6E+05

GHG Emissions (Ton/y)

Maximization Expected Profit

Maximization Worst Case for Profit

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


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

10

20

30

40

50

60

70

80

90

100

60

70

80

90

100

Scenarios (s)

a) Profit ($US/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


Profit ($US/y)

Page 35 of 46

$35,000,000 $30,000,000 $25,000,000 $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 0

10

20

30

40

50

Scenarios (s)

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



$10.0

Price ($US/GJ)

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 46

$8.0 $6.0 $4.0 $2.0 $0.0 0

10

20

30

40

50

60

70

Scenarios (s)

Figure 6. Natural gas prices in different scenarios.


80

90

100

Page 37 of 46

CO2 Emissions (Ton/y)

460,000 440,000 420,000 400,000 380,000 360,000 340,000 0

10

20

30

40

50

60

70

80

90

100

60

70

80

90

100

Scenarios (s)

a) 354,000

CO2 Emissions (Ton/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


353,000 352,000 351,000 350,000 349,000 348,000 0

10

20

30

40

50

Scenarios (s)

b) 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.


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 46

460,000 440,000 420,000 400,000 380,000 360,000 340,000 0

10

20

30

40

50

60

70

80

90

Scenarios (s) Solution without using proposed system

Max(MProfit)

Max(WProfit)

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


100

Page 39 of 46

1 0.9


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


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

3.0E+07

3.5E+07

Profit ($US/y) Minimization of Expected GHG emissions

Minimization of Worst Case for GHG Emissions

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



1 0.9 0.8


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 46

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 348200

348400

348600

348800

349000

349200

349400

349600

349800

350000

GHG Emissions (Ton/y) Minimization of Expected GHG Emissions

Minimization of Worst Case for GHG Emissions

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


$35,000,000 $30,000,000 $25,000,000 $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 0

10

20

30

40

50

60

70

80

90

100

60

70

80

90

100

Scenarios (s)

a) Profit ($US/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


Profit ($US/y)

Page 41 of 46

$35,000,000 $30,000,000 $25,000,000 $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 0

10

20

30

40

50

Scenarios (s)

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


Page 42 of 46

350,000 349,500 349,000 348,500 0

10

20

30

40

50

60

70

80

90

100

60

70

80

90

100

Scenarios (s)

a) GHG Emissions (Ton/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



350,000 349,500 349,000 348,500 348,000 0

10

20

30

40

50

Scenarios (s)

b) 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.


Page 43 of 46

460,000


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


440,000 420,000 400,000 380,000 360,000 340,000 0

10

20

30

40

50

60

70

80

90

Scenario (s) Solution without using proposed system

Min(MGHG)

Min(WGHG)

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


100


100,000

$25,000,000

80,000

$20,000,000 60,000 $15,000,000 40,000 $10,000,000 20,000

$5,000,000 $0

0

10

20

30

40

50

60

70

80

90

100

∆GHG Emissions (Ton/y)

$30,000,000

Profit ($US/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 44 of 46

0

Scenarios (s)

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.


Page 45 of 46

1 0.9

Cumulative 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


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 $0

$5,000,000

$10,000,000 $15,000,000 $20,000,000 $25,000,000 $30,000,000 $35,000,000

Profit ($US/y)

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.



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 46 of 46

For Table of Content Use Only

P = Plant

P=1

Boiler

P=2 Pump

. . .

Turbine

Condenser

P=n

Fresh Fuel

Optimal Design of Multi-Plant Cogeneration Systems with Uncertain Flaring and Venting

Javier Tovar-Facio,a Fadwa Eljack,b José M. Ponce-Ortega,a* Mahmoud M. ElHalwagic,d

Synopsis: This paper presents an optimization approach to design cogeneration systems to reduce the environmental and economic impacts caused by the flaring and venting of fuel gases during abnormal situations in different industrial plants.


Optimal Design of Multiplant Cogeneration Systems with Uncertain

Recommend Documents