Analysis of Carbon Policies in the Optimal Integration of Power Plants

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Analysis of Carbon Policies in the Optimal Integration of Power Plants Involving Chemical Looping Combustion with Algal Cultivation Systems Aurora del Carmen Munguía-López, Vicente Rico-Ramírez, and José María Ponce-Ortega ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.7b04903 • Publication Date (Web): 16 Feb 2018 Downloaded from http://pubs.acs.org on February 18, 2018

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ACS Sustainable Chemistry & Engineering

Analysis of Carbon Policies in the Optimal Integration of Power Plants Involving Chemical Looping Combustion with Algal Cultivation Systems

Aurora del Carmen Munguía-López,a Vicente Rico-Ramírez b and José María Ponce-Ortega a*

a

Universidad Michoacana de San Nicolás de Hidalgo, Departamento de Ingeniería Química, Francisco J. Mujica S/N, Ciudad Universitaria, Morelia, Michoacán, México, 58060 b

Instituto Tecnológico de Celaya, Departamento de Ingeniería Química, Av. Tecnológico y García Cubas S/N, Celaya, Guanajuato, México, 38010

* Corresponding author: Prof. José María Ponce-Ortega E-mail: [email protected] Phone: +52 443 3223500 ext. 1277 Fax: +52 443 3273584

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Abstract Presently, reducing the CO2 emissions produced by electric energy generation is one of the most relevant challenges. This paper aims to address such problem by means of proposing an integrated system including: i) chemical looping combustion systems, ii) power generation cycles and iii) algae-to-biodiesel subsystems to utilize the carbon dioxide. The developed approach consists in a mixed-integer linear programming model that represents the global system at a macroscopic level and allows finding the optimal design for the integrated system that involves the selection of the optimum fuel and technology for the power generation (for both the combustion system and the power cycle) as well as for the biodiesel production in all the stages of the algae cultivation system. In addition, the impact of different values for economic penalizations and compensations associated with carbon dioxide emissions on the optimum configuration is evaluated. The results show important economic benefits and reductions in the emissions, especially when considering the carbon bonus. Furthermore, the optimal tradeoffs between multiple objectives (economic and environmental) are discussed through different Pareto sets.

Keywords: Carbon policies, Carbon sequestration, Power plants, Algae systems, Optimization.


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Introduction Nowadays, the global temperature rise is a growing concern. The heat-trapping nature of carbon dioxide and other gases was already demonstrated in the mid-19th century. Therefore, the increased levels of greenhouse gases are considered to contribute to the warming of the climate system. According to the Intergovernmental Panel on Climate Change, the human influence on the current warming trend is clear.1 Since the beginning of the Industrial Revolution, the atmospheric CO2 concentration has increased by more than a third.2 Currently, over 80% of the energy consumption is originated from fossil fuel combustion.3 As a consequence, the energy sector is the largest source of carbon dioxide emissions, representing about 58% of global emissions.4 In order to tackle this problem, strategies to keep satisfying the increasing demand of electricity and simultaneously reducing the CO2 emissions must be developed. An innovative technique to capture the carbon dioxide in electric power plants is the chemical looping combustion (CLC). This process is classified as a variety of post-combustion, oxycombustion and pre-combustion, including the CO2 capture to enhance the thermodynamic performance of the power plant.5 CLC is an indirect fuel combustion system with the particular characteristic of allowing the inherent separation of the CO2 from the other flue gas components. Besides no additional processes to separate the CO2 are required, the penalty in thermal efficiency is small and the production of nitrogen oxides is avoided. Unlike conventional combustion, in the CLC technology there is no direct contact between fuel and combustion air. In addition to this, the combustion occurs in two distinct reactors (oxidation and reduction reactors), where a metal working as an oxygen carrier allows the transference of the oxygen from combustion air to fuel. Hence, there is no contact between nitrogen and CO2 either, obtaining a separate stream of exhaust air and other of CO2. Alternative CLC configurations include the extended chemical looping



combustion (exCLC), the three-reactor chemical looping combustion (CLC3) and the calcium looping process (CLP). In the exCLC technology a third reactor is added (calcination reactor) along with a carbon carrier. The CLC3 system has also three reactors (one reduction and two oxidation reactors). The CLP configuration consists of two reactors (the carbonator and the calciner) and uses a regenerable sorbent of CO2. The basic principles of the CLC systems, other reactor configurations and their possible use in power generation cycles have been widely reported.6-9 Some simulation studies address the technical and economic feasibility along with sensitivity analysis of several parameters (fuels, oxygen carriers, CLC configurations and power cycles). For instance, PetrizPrieto et al.10 considered fifteen configurations involving three combustion systems (CLC, exCLC and CLC3) and three power generation cycles: a steam cycle (SC), a humid air turbine cycle (HAT) and a combined cycle with steam injected gas turbines (STIG); their results include plant efficiencies and an economic evaluation. Similarly, Zhu et al.11 reported the differences in energy and exergy efficiency, as well as the economics between two indirect combustion systems (CLC and CLP) using the integrated gasification combined cycle for power generation. After the capture of the CO2, its utilization is desirable. There are various methods to mitigate and harness this gas; however, the use by means of an algal system has gained attention recently because of its numerous benefits.12-14 The algae cultivation system is intrinsically efficient and sustainable since it only requires carbon, nutrients, room temperature and sunlight. The main product of the cultivation is biomass, which can be processed to produce biofuels and other valuable byproducts such as glycerol, ethanol and proteins.15,16 Other bioproducts (hydrogen, propylene glycol, glycerol-tert-butyl ether, and poly-3-hydroxybutyrate) can be generated by modifying the design and synthesis of the manufacturing algal processes.17-19 The microalgae systems have a high CO2 capture potential, the gas can be delivered from a flue gas stream or from a pure CO2 stream.


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The variation between these two streams is the harnessing.20 Some advantages of generating biodiesel from algae are: high growth rates, any kind of soil can be used and it is more efficient than generating biodiesel from other sources. For instance, while soy typically produces 450 liters of biodiesel per hectare per year, canola produces 1,200 liters and palm oil 6,000 liters; researchers predict that algae could produce 90,000 liters or even more.21,22 In this context, Gutiérrez-Arriaga et al.23 reported an optimization approach to obtain tradeoff solutions, considering economic and environmental objectives, for the integration of a steam power plant with an algae system to produce biodiesel. The analysis includes energy integration, a conventional power plant (without modifying combustion systems) and a single-process evaluation for each stage of the algae cultivation system. In a similar way, Lira-Barragán et al.24 studied the biological capture of CO2 emissions in the electric power generation through microalgae, adding cogeneration systems and addressing technical, economic and environmental objectives. Alternatively, Hernández-Calderón et al.25 presented an optimization approach for distributed algaebased biorefineries, proposing a mathematical model that considers the election of the optimal technologies for the process stages of the cultivation system. The results show the environmental impact and the economic benefits too. In addition, previous works reported the optimization of only one stage of the algal system, for instance the production stage including several paths and alternatives to reduce the energy and water consumption.26-28 On the other hand, in order to reduce the emissions, certain economic instruments29 have been developed by several governments, including penalties and compensations.30,31 One of these metrics is the carbon tax, which is a penalization for generated emissions that is defined as a monetary cost per tonne of produced CO2.32 Another important and opposite parameter consists in taking into account the avoided emissions and based on the amount of reduction, a carbon bonus (institutional,



public or private) is given. The reductions occur after a change in technologies or in the production process.33 From an economic point of view, the aforementioned instruments have been discussed in relation to the “polluter pays principle” and the “provider gets principle”; where those affecting or improving environmental qualities should pay or be compensated, respectively.29 Both strategies have been criticized for several reasons such as: the tax is standardized without accounting for the economic sectors, industrial development and regional conditions; also, another issue is the arbitrary economic value of the compensations.34--36 Whether the final decision is investing in order to reduce emissions or paying taxes, there is always a cost associated.37 Therefore, it is important to analyze the effect of certain economic instruments such as the carbon tax and bonus. In this regard, previous studies have addressed different approaches including the trade-off between economic and environmental objectives in the monetization of the carbon externalities,38,39 as well as the impact of carbon policies to promote the generation of clean energy40,41 and comparative scenarios with penalties or compensations to monetize the externalities related to the CO2 emissions in combined heat and power systems.42,43 Furthermore, a multi-objective approach for the minimization of the emissions at a global scale through changes in the economic sectors has been developed by PascualGonzález et al.44 Recently, Galán-Martín et al.45 proposed another alternative based on the study of the effect of interregional cooperation in meeting the emissions targets with cost-effective solutions. However, a macroscopic analysis, including the optimal selection of the processes for each stage of the algae cultivation system as well as the optimum operation conditions, combustion systems and power cycles for the power generation plant has not been considered; in this context, the harnessing of the generated CO2 via biodiesel production with microalgae and simultaneously involving the carbon externalities has not been studied either. Therefore, the aim of the present work is to propose a multi-objective optimization approach through a general mixed-integer linear programming


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(MILP) model contemplating the economic and environmental aspects of sustainability for the integrated system (see Figure 1).

System description The proposed integrated system involves the generation of electricity by means of a power plant that uses a novel combustion system (CLC), along with the utilization of the captured CO2 in an algae cultivation system considering diverse stages to obtain: biodiesel, glycerol, ethanol and proteins. This approach includes different processes that can be studied separately: i) combustion systems, ii) power cycles and iii) algae-to-biodiesel subsystems. Therefore, the basic idea is to study the global system at a macroscopic level using an optimization model. The diagram with the main processing operations and flowrates is shown in Figure 2. Various fuels, combustion systems (CLC, CLP, conventional) and power cycles are considered for the power plant, in addition to the possibility of delivering all, or only a part, of the produced carbon dioxide to the algal system according to its specific demand. The potential fuels for this power generation plant are coal and natural gas. Regarding the combustion systems, the traditional chemical looping combustion is evaluated, as well the calcium sorbent-based looping process (CLP), the extended three-reactor versions of the CLC (exCLC and CLC3) and the conventional combustion. Each system has different outlet streams, including exhausted air (mainly N2), the combustion products (CO2 with H2O or only a CO2 rich stream) and flue gas (from the conventional combustion). The election of the optimum oxygen carrier, carbon carrier and sorbent for the CLC configurations is not included since several studies in the literature have reported the suitable materials (for instance, metal oxides such as nickel, copper, cobalt, iron and manganese). For the CLC and exCLC configurations, nickel is used as carrier, while for the CLC3 system iron is



selected. The carbon carrier required in the exCLC and the sorbent for the CLP is calcium oxide.10,11The considered power generation cycles involve typical cycles as the steam cycle and the natural gas combined cycle (NGCC), likewise a humid air turbine cycle, a combined cycle with steam injected gas turbines and an integrated gasification combined cycle are taken into account. The algae-to-biodiesel process is formed by four stages (cultivation, harvesting, oil extraction and production). In the cultivation stage, two technologies can be used: open (raceway pond) and closed (photobioreactor). For any of these processes, the algal cultivation requires nutrients (phosphorus and nitrogen), water, sunlight, carbon dioxide and the culture inoculum (Chlorella vulgaris). The election of the optimal process is subject to certain restrictions, some of the parameters needed are shown in Table 1. Similarly, for the next stages several options are considered, each one with particular costs, efficiencies and specifications. The second stage is the harvesting, where the algal biomass is recovered from the culture medium by removing part of the water. It is assumed that some technologies (centrifugation, gravity sedimentation and dissolved air flotation) require two steps in which the first step needed is flocculation.24 The others single step processes include magnetic separation and tangential flow filtration. To continue with the transformation procedure of the algal biomass to biodiesel, the oil extraction is required. If a dried-based extraction process is chosen, the thermal drying of the algal slurry is included. The advantages of choosing it involve a rise in the level of solids and a greater efficiency, although the power demand is greater too. In order to extract the lipid molecules from the biomass, the solvent and supercritical CO2 extraction methods are considered.


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Finally, in the biodiesel production stage the alternatives include the alkali based and the enzymatic processes. Both streams obtained from the oil extraction stage (residual biomass and lipids) are used in this production step. The lipid-depleted biomass is converted to ethanol and proteins, while the extracted triglycerides are transformed into biodiesel and glycerol. It is assumed that the electricity demand for each particular step of the algae-to-biodiesel subsystem is provided by the power plant.23 The electric energy requirements for all the stages depend on different variables, such as the biomass or the removed water flow (see Table 2). The whole parameters for the power generation plant and the algae cultivation system can be found in the Supporting Information section.

Problem statement The addressed problem consists in designing the optimal integrated power plant with an algae cultivation system simultaneously accounting for economic and environmental objectives. Furthermore, the effect of different values for the carbon tax and for the carbon bonus is evaluated. The optimal configuration must include finding the following: •

The optimal selection of fuel and its flowrate.

•

The optimal technologies or processes for the combustion systems, power cycles and for each stage of the algae system.

•

The amount of CO2 that is delivered to the algae-to-biodiesel process.

•

Specific conditions, for instance the required nutrients and water, the area for the cultivation stage and the biomass flowrate from one stage to another.

•

The tradeoffs between the economic and environmental functions.



•

The profitability and the environmental impact.

The aforementioned problem is addressed through a mathematical programming model formulation, which, in general, involves mass balances for the inlet and outlet flowrates, discrete decisions for the selection of the distinct processes and relationships to represent the costs, as well as the revenues and the overall requirements.

Mathematical model formulation We propose a MILP model to evaluate the integrated global system, which is based on the superstructure shown in Figure 3. The sets of the present model are indicated with the uppercase I, J, K, M, H, O and B that represent fuels, combustion systems, outlet streams, power cycles, technologies for the harvesting stage, technologies for the oil extraction stage and technologies for the production stage, respectively. Specifying the elements of each set (indexes), the general process can be described as follows, firstly, the fuel i is used in the power generation cycle m with a combustion system j. Then, the energy in the outlet stream k is recovered and such stream is delivered to the atmosphere or to the cultivation stage of the algae system. Next, the produced biomass is sent to the technology h of the harvesting stage, after that, to the technology o of the extraction stage and finally to the technology b of the last stage (production). Power generation system Equation (1) represents the disjunction for the election of the fuel i used in the combustion system j and power generation cycle m. If the Boolean variable Zi , j ,m is true, the inlet flowrate of fuel lies between a lower value

( FMIN ) i , j ,m

and an upper bound ( FMAX i , j , m ) , and also the fixed cost is


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activated. On the other hand, if Zi , j ,m is false, the fuel flowrate ( FCi , j ,m ) is equal to zero as well as the costs. Besides, in Equation (2) a logic restriction is included to specify that only one fuel, system combustion and power cycle must be chosen. Z i , j ,m     FC   ¬Z i , j , m FMIN ≥   i , j ,m i , j ,m   ∨  FCi , j , m = 0   FCi , j , m ≤ FMAX i , j , m    CCLCi , j , m = 0  CCLCi , j , m = PCLi , j , m  

∑∑ ∑ Z

i , j ,m

∀i ∈ I , j ∈ J , m ∈ M

=1

(1)

(2)

i∈I j∈J m∈M

The previous disjunction is reformulated in order to obtain logical relationships using the Big-M reformulation.55

FCi, j ,m ≥ FMINi, j,m zi, j ,m

∀i ∈ I , j ∈ J , m ∈ M

(3)

FCi, j ,m ≤ FMAX i, j,m zi, j,m

∀i ∈ I , j ∈ J , m ∈ M

(4)

CCLCi, j,m = PCLi, j ,m zi, j,m

∀i ∈ I , j ∈ J , m ∈ M

(5)

Electricity generated, outlet streams and variable costs Once the inlet flowrate of fuel is obtained, the electric energy produced ( FEi , j ,m ) and the outlet streams

( FO

i , j ,m ,k

)

can be computed as shown in Equations (6) and (7). The parameter Ei, j ,m

symbolizes the net efficiency of the scheme i, j, m, and CTi , j , m , k refers to a technical coefficient that allows to attain the outlet flowrate of the distinct configurations. In Equations (8) and (9), the relationships for the variable costs of the scheme i, j, m are presented, where the variable CCi , j ,m is



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the cost due to the fuel consumption. While the terms PCALi , PCi and PMi represent the heating power, the unitary cost and the molecular weight of the fuel i, respectively. Figure 4 shows the superstructure for the flowrates and fixed costs involved in the combination i, j, m.

FEi, j,m = Ei, j ,m PCALi PMi FCi, j ,m

∀i ∈ I , j ∈ J , m ∈ M

(6)

FOi, j,m,k = CTi, j ,m,k FCi, j,m

∀i ∈ I , j ∈ J , m ∈ M , k ∈ K

(7)

COPi, j,m = CV1i, j,m FEi, j,m

∀i ∈ I , j ∈ J , m ∈ M

(8)

CCi, j,m = PCALi PCi PMi α FCi, j,m

∀i ∈ I , j ∈ J , m ∈ M

(9)

Global effluents The values of the outlet streams ( FOi , j , m , k ) are assigned to new variables so as to distinguish among the various global effluents: carbon dioxide ( FCO) , carbon dioxide with water ( FCA) , exhausted air ( FGC ) , hydrogen sulfide ( FHS ) and flue gas ( FCOM ) .

∑∑ ∑ FO

= FCO

(10)

∑∑ ∑ FO

= FCA

(11)

∑∑ ∑ FO

= FGC

(12)

∑∑ ∑ FO

= FHS

(13)

i , j , m,k =1

i∈I j∈J m∈M

i , j ,m, k = 2

i∈I j∈J m∈M

i , j ,m,k =3

i∈I j∈J m∈M

i , j , m,k =4

i∈I j∈J m∈M


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∑∑ ∑ FO

i , j , m , k =5

= FCOM

(14)

i∈I j∈J m∈M

Algae cultivation system Determination of the source of CO2 Equation (15) indicates a mass balance to determine the source of carbon dioxide (outlet stream) to be sent to the first stage of the algae cultivation system. The utilization of the CO2 varies depending on the source where it comes from, the parameters ECO , ECA and ECOM symbolize this difference. ECO refers to the efficiency of the pure CO2 stream, while ECA to the efficiency of the CO2 with water stream and ECOM to the efficiency of the flue gas stream. F CO2 R and F CO2 P represent the CO2 that is delivered to either cultivation technologies (raceway pond or photobioreactor), F CO2 L is the flowrate of CO2 that is released to the atmosphere and M FCO is the molecular weight of the gas.

M FCO ( FCO ECO + FCA ECA + FCOM ECOM ) = F CO 2 R + F CO 2 P + F CO 2 L

(15)

Selection of the optimal technology in the cultivation stage The following disjunction is used to determine the technology employed and the biomass produced in this first stage. As shown in Equation (16), if the Boolean variable W is true, the raceway pond is selected and the flowrate of biomass for this process is calculated ( FBR ) . In contrast, if W is false, the photobioreactor is chosen and the produced biomass is also calculated technology has a distinct efficiency

βR and βP. While the common terms are

( FBP ) .

Each

τ D T and δ CO

2

representing the fraction of hours per day that the gas is sent to the cultivation step and the CO2



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demand, respectively. By the Big-M reformulation, the relationships shown in Equations (17), (18), (19) and (20) are obtained.

W ¬W         DT β R CO2R  ∨  τ DT β P CO2P   FBR = τ F FBP = F   δ CO2 δ CO2  

(16)

τ DT β R CO2R FBR = F δ

(17)

τ DT β P CO 2 P FBP = F δ

(18)

FBR ≤ M B w

(19)

FBP ≤ M

(20)

CO2

CO2

B

(1 − w )

Costs and water and power requirements in the cultivation stage The fixed costs as well as the variable costs and the required electric energy for this stage are function of the biomass flowrate. Equations (21) and (22) correspond to the investment costs, which likewise depend on the operating hours ( HY ) , since the capacity of each technology changes with this value and the biomass flowrate. PRR and PRP symbolize the unitary fixed cost of the raceway pond and the photobioreactor. CCR = PR R HY FBR

(21)

CCP = PR P HY FBP

(22)

The total variable costs are estimated considering the variable cost of the selected system for the cultivation stage and the cost because of the urea, phosphate and water consumption. For


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calculating the flowrate of nutrients required (urea and phosphate), it is necessary to consider the biomass flowrate going to the next stage as shown in Equations (23) and (24). The efficiencies for the technologies in the harvesting stage are also taken into consideration ( βh

FLOC

and

γ h ). From

these values, some typical factors and the specific requirements of each urea and phosphate ( RU and RP ) can be obtained. Equations (25) and (26) represent the urea flowrate for the different technologies: F U

R

referring to the raceway pond and F U P to the photobioreactor. Similarly,

Equations (27) and (28) determine the phosphate flowrate required.

FBR = ∑ FhFLOC1

(23)

FBP = ∑ FhFLOC 2

(24)

  FU R =  ∑ ( FhFLOC1 β hFLOC γ h )  RU α N  h∈H 

(25)

  FU P =  ∑ ( FhFLOC 2 β hFLOC γ h )  RU α N  h∈H 

(26)

  FP R =  ∑ ( FhFLOC1 β hFLOC γ h )  RP α N  h∈H 

(27)

  FP P =  ∑ ( FhFLOC 2 βhFLOC γ h ) RP α N  h∈H 

(28)

h∈H

h∈H

The water flowrate needed for the raceway pond and the photobioreactor depends on the particular demand of each technology, which considers only the makeup water required since it is assumed that the harvested water is recycled (Grima et al.48) and it is obtained as follows:



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FW

R

= DW

R

FBR

(29)

FW

P

= DW

P

FBP

(30)

As already mentioned, once the requirements of water and nutrients are attained, the total variable costs can be computed. The terms C V

R

and C V

P

symbolize the unitary variable costs of the

raceway pond and the photobioreactor. CU , CP and CW are the unitary costs of urea, phosphate and water, respectively. COP R = ( CV R FBR + CU FU R + CP FP R + CW FW R )

(31)

COP P = ( CV P FBP + CU FU P + CP FP P + CW FW P )

(32)

The power demand changes according to the process and the biomass flowrate ( FBR, FBP ) as shown in Equation (33) that indicates the electric energy requirement for the raceway pond and equally for the photobioreactor in Equation (34). EC R = ENC R FBR

(33)

EC P = ENC P FBP

(34)

Required area for the cultivation stage The area is function of the selected technology. Typically, the raceway ponds need great areas

( A ) , while the photobioreactors require smaller areas ( A ) . In order to calculate it, the hours of R

P

operation in the cultivation stage ( HD) and the productivity must be given. The number of needed raceway ponds and photobioreactors ( NUM R and NUM P ) is estimated considering their calculated area and specific measurements (for the photobioreactor the number and measurements of its tubes are taken into account).


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AR =

HD FBR PR

(35)

AP =

HD FBP PP

(36)

NUM

R

=

L AR I W

(37)

NUM

P

=

LT D T AP UT

(38)

Election of the optimal technology in the harvesting stage The next step in the algae-to-biodiesel system is the harvesting stage. Equation (39) represents the total biomass flowrate that enters to this stage. Equations (23), (24) and (39) give the relationship expressed in Equation (40).

∑F

FLOC h

= FBR + FBP

(39)

h∈H

FhFLOC = FhFLOC1 + FhFLOC 2

∀h ∈ H

(40)

The selection of the employed process h is modeled using the disjunction shown in Equation (41). If the Boolean variable

Yh

is true, the inlet flowrate to this process exists, and its costs and electric

energy required too. On the other hand, if Yh    ¬Yh   FLOC1    = FBR  ∨  FhFLOC1 = 0   Fh  FLOC 2 = FBP   F FLOC 2 = 0   Fh   h 

Yh

is false the inlet flowrate is equal to zero.

∀h ∈ H

(41)

Via the Big-M reformulation, the following relationships for the previous disjunction are obtained:



∀h ∈ H

FhFLOC1 ≤ M B yh

(42)

∀h ∈ H

FhFLOC 2 ≤ M B yh

Page 18 of 68

(43)

Certain processes h require two steps, the outlet flowrate of the first step is presented in Equation (44) , where βh

FLOC

symbolizes the fraction of biomass recovered. For the technologies h that do not

require this step, βh

FLOC

is equal to 1. Similarly, Equation (45) shows the outlet flowrate for the

second step of the process h.

FhFLOCS = βhFLOC FhFLOC FhCOS = γ h FhFLOCS

∀h ∈ H

(44)

∀h ∈ H

(45)

Costs and power requirements in the harvesting stage The total variable and fixed costs are determined by the following relationships. Equation (46) FLOC

represents the fixed cost of the first step for the harvesting stage, where the inlet flowrate is Fh

.

While the variable cost of this first step ( C V hAL ) depends on the alum coagulant flowrate ( FhAL ) , and to calculate such flowrate the concentration at the beginning of the harvesting stage ( CONCh ) AL

is needed. The terms T RES , PROF , Ch

and P AL refer to the residence time, the depth of the

raceway pond, the concentration and cost of the coagulant, respectively.

CThFLOC = CTUh FhFLOC

CONCh =

1 T RES

∀h ∈ H

(46)

 DEPHT FhFLOC1 DT FhFLOC2  +   PR PP  

∀h ∈ H


(47)

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∀h ∈ H

FhAL = ChAL CONCh CVhAL = P AL FhAL

(48)

∀h ∈ H

(49)

The amount of withdrawn water is expressed using Equation (50), where

ρ FB and

C FB symbolize

the density of the biomass slurry and the concentration of algal biomass leaving the harvesting stage.

COS h

FW

 ρ FB  COS =  FB −1 Fh C 

∀h ∈ H

(50)

The overall fixed costs vary for each process h, so they are computed separately according to the characteristics of each process. CT C , CT S , CT SM , CT TF and CT DAF refer to the unitary fixed costs. Whereas,

ρ W is the density of liquid water.

C FLOC CThCOS + CThFLOC =1 = CT Fh=1 =1

(51)

S FLOC CThCOS + CThFLOC =2 = CT Fh=2 =2

(52)

SM CThCOS HY FhCOS =3 = CT =3

COS h=4

CT

=

CT TF

ρ

W

(53)

FWhCOS =4

(54)

DAF CThCOS HY FhFLOC + CThFLOC =5 = CT =5 =5

(55)



Page 20 of 68

Likewise, Equations (56), (57), (58), (59) and (60) represent the unit variable costs. Equations (61) and (62) refer to the electric energy consumption of all the processes, including the power demand FLOC

for the first and for the second step of this stage ( ECh

COS

and ECh ).

AL CVhCOS =1 = CVh=1

(56)

AL CVhCOS =2 = CVh=2

(57)

SM CVhCOS FhCOS =3 = CV =3

(58)

CVhCOS =4 =

CV TF

ρ

W

FWhCOS =4

(59)

DAF CVhCOS FhFLOC + CVhAL =5 = CV =5 =5

(60)

EChFLOC = ENChFLOC FhFLOC

∀h ∈ H

(61)

ENChCOS

∀h ∈ H

(62)

COS h

EC

=

ρ

W

FWhCOS

Election of the optimal technology in the extraction stage The total biomass flowrate leaving the harvesting stage enters to the extraction stage, this is represented in Equation (63). As the costs in this stage depend on the amount of biomass leaving the cultivation stage, it is also included the hypothetical balance shown in Equation (64).

∑F

COS h

h

∑F

= ∑FoEXT

BIOF o

(63)

o

= FBR + FBP

(64)

o


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The disjunction used to determine the technology o for the extraction stage is presented in Equation (65). If X o is true, the inlet flowrate to that process ( FoEXT ) exists and the flowrate that activates the costs of the process o ( FoBIO F ) exists too. On the contrary, if the Boolean variable is false, both flowrates are equal to zero. Xo    ¬X o   EXT   EXT  COS  Fo = Fh  ∨  Fo = 0   F BIOF = FBR + FBP   F BIOF = 0   o   o 

∀o ∈ O

(65)

Reformulating the prior disjunction using the Big-M reformulation, the following equations are attained for each alternative:

FoEXT ≤ M B xo

∀o ∈ O

(66)

FoBIOF ≤ M B xo

∀o ∈O

(67)

The flowrate of oil extracted ( FoOIL ) and the lipid-depleted biomass ( FoLD ) are calculated from the recovery fraction of oil for each process (σ o ) and the lipid content in algal biomass (W OIL ) .

FoOIL = σo W OIL FoEXT

∀o ∈O

FoLD = FoEXT (1 − σ o W OIL )

(68)

∀o ∈ O

Costs and power requirements in the extraction stage


(69)


Page 22 of 68

The fixed costs are expressed in Equation (72) and include the cost of the dryer that some processes o require

(C ) and the specific cost of each process (C ) . C SEC o

E o

SE o

TE

and Co symbolize the unitary

investment costs.

CoSEC = CoSE FoBIOF CoE = CoTE FoBIOF

∀o ∈O

(70)

∀o ∈O

CToEXT = CoSEC + CoE

(71)

∀o ∈O

(72)

Equation (74) shows the variable costs that involve only the hexane consumption

( F ) , which HEX o

is obtained from the feed mass ratio, the loss fraction and the biomass flowrate entering to the stage. The electric energy demand

( EC ) is computed by the Equation (75). EXT o

FoHEX = MRH HEXoLO FoEXT CoHEX = PHEX FoHEX ECoEXT = ENCoEXT FoEXT

∀o ∈O

∀o ∈O

(73)

(74)

∀o ∈ O

(75)

Selection of the optimal technology in the production stage The last stage in the system is the production of biodiesel. Equations (76) and (77) include the balances for the outlet streams of the extraction stage and the inlet streams of the production stage.

∑F

OIL o

o

= ∑FbPROD

(76)

b


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∑F

LD o

o

= ∑FbSTARCH

(77)

b

As described above, the oil stream

( F ) is utilized to produce biodiesel and glycerol. In the PROD b

same way, the lipid-depleted biomass stream

( F ) is used to produce ethanol and proteins. In STARCH b

Equation (78), the disjunction that allows selecting the optimal technology b is presented. Similar to the other disjunctions proposed, the Boolean variable Qb controls the value of the inlet flowrate. The logical relationships obtained by the Big-M reformulation for this disjunction are shown in Equations (79) and (80).

Qb    ¬Qb   F PROD = F OIL  ∨  F PROD = 0  o  b   b  STARCH LD  Fb = Fo   FbSTARCH = 0

FbPROD ≤ M B qb FbSTARCH ≤ M B qb

∀b ∈ B

(78)

∀b ∈ B

(79)

∀b ∈ B

(80)

The products of this stage: biodiesel, glycerol, ethanol and proteins, are represented in Equations RB

(81), (82), (83) and (84). The terms Wb

RG

, Wb

RE

, Wb

RP

and Wb

make reference to the recovery

fraction of the distinct products.

FbBD = WbRB FbPROD

∀b ∈ B

(81)

FbGLI = WbRG FbPROD

∀b ∈ B

(82)

FbET = WbRE FbSTARCH

∀b ∈ B

(83)



FbPROT = WbRP FbSTARCH

Page 24 of 68

∀b ∈ B

(84)

Part of the generated ethanol is required in the process b for the biodiesel production, so in order to attain the ethanol flowrate available for sale, Equation (86) is employed.

FbETREQ = MRbET FbPROD FbETS = FbET − FbETREQ

∀b ∈ B

(85)

∀b ∈ B

(86)

Costs and power requirements in the production stage PROD

The fixed and variable costs are computed as shown in Equations (87) and (88). The terms Cb PROD

and Pb

catalyst

symbolize the unitary costs and

ρBD the density of biodiesel. The necessary flowrates of

( F ) and lipase ( F ) are estimated too.

CTbPROD =

CVbPROD =

CAT b

CbPROD

ρ

BD

PbPROD

ρ

BD

LIP b

∀b ∈ B

FbBD

HY FbBD

FbCAT = WbCAT FbPROD FbLIP = WbLIP FbPROD

(87)

∀b ∈ B

(88)

∀b ∈ B

(89)

∀b ∈ B

(90)

Finally, Equations (91) and (92) represent the water and power consumption. The unitary BD

requirements of water and electric energy are expressed with the parameters DWb


PROD

and ENCb

.

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PROD b

FW

PROD b

EC

=

DWbBD

=

ENCbPROD

ρ

BD

ρ

BD

∀b ∈ B

FbBD

(91)

∀b ∈ B

FbBD

(92)

Electric energy produced and water consumption for the whole system In Equation (93), the annual net electric power is attained by subtracting the power demanded in each stage of the algae cultivation system from the electric energy produced by the scheme i, j, m in the power plant. The total water consumption involves the demand of the raceway pond

of the photobioreactor

( FW ) , R

( FW ) and of the production stage ( FW ) . Equation (94) represents P

PROD b

the overall water requirement.  EC R + EC P + ∑ EChFLOC + ∑ EChCOS    h∈H h∈H EP = ∑ ∑ ∑ FEi , j , m −   EXT PROD i∈I j∈J m∈M  + ∑ ECo + ∑ ECb  b∈B  o∈O 

(93)

CONSW = FW R + FW P + ∑ FWbPROD

(94)

b∈B

Carbon dioxide emissions To obtain the total emissions ( EM ) , the CO2 mitigated must be subtracted from the CO2 generated, as shown in Equation (97). The produced CO2 is computed from its fraction present in the outlet streams ( FCO , FCA and FCOM ). While the amount of gas mitigated is calculated from the CO2 flowrate that is delivered to the cultivation system. prod CO 2 = M FCO

( FCO + FCA

FCACO 2 + FCOM FCOM CO 2 )


(95)


fixed CO 2 = τ DT

(F

CO 2 R

+ F CO 2 P

)

Page 26 of 68

(96)

EM = prod CO2 − fixed CO2

(97)

Combining Equations (15), (96), and (97), the following relationship for the CO2 emissions is obtained:

(

EM = M FCO FCO + FCA FCACO2 + FCOM FCOM CO2

)

−τ DT M FCO ( FCO ECO + FCA ECA + FCOM ECOM ) − F CO2L 

(98)

Note that the variable EM includes: the CO2 that was not used in the raceway pond or photobioreactor

(F

CO 2 L

),

the carbon dioxide that cannot be utilized due to the stream which

contains it and the amount of CO2 that is not possible to mitigate for the restriction of the fraction of hours per day that the gas is sent to the cultivation step. The variable F CO2L can be zero or not depending on the objectives considered for the optimal design (maximizing the profit or minimizing the emissions). Nevertheless, the emissions generated for the CO2 that is not utilized due to the stream and the emissions for the restriction of supply hours to the system are unavoidable.

Costs The total fixed and variable costs ( CAP and COPER ), which include the costs related to the power generation system as well as the algae cultivation system, are shown in Equations (99) and (100). K F

represents the capital recovery factor according to a specific interest rate and

investment time horizon (see Table S10 from the Supporting Information section).

CAP = K

F

 ∑∑ ∑ CCLCi , j ,m + CCR + CCP   i∈I j∈J m∈M   COS EXT PROD   + ∑ CTh + ∑ CTo + ∑ CTb  o∈O b∈B  h∈H 


(99)

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 ∑∑ ∑ COPi , j ,m + ∑∑ ∑ CCi , j ,m   i∈I j∈J m∈M  i∈I j∈J m∈M COPER = HY   + HD COS HEX PROD + CV + C + CV ∑ o ∑ b  ∑ h  o∈O b∈B  h∈H 

 COP R    P   +COP 

(100)

Revenues The overall revenues ( IN ) account for the sale of electricity and the products (biodiesel, glycerol, ethanol and proteins).  EP SP E + ∑ FbBD SP BD + ∑ FbGLI SP GLI    b∈B b∈B IN = HY   ETS ET PROT PROT SP  + ∑ Fb SP + ∑ Fb  b∈B  b∈B 

(101)

Carbon tax and bonus An economic penalty (carbon tax) for the generation of CO2 emissions is considered, which is defined by Equation (102). In contrast, an economic compensation is also included, with the purpose of comparing the effects on the objective function. This carbon bonus for avoiding emissions is represented in Equation (104). The avoided emissions are given by the difference between the emissions generated in a conventional system and the emissions in the proposed integrated system. In order to calculate the emissions for the conventional system, the unit greenhouse gas emissions for the fuel i (U iGHGE ) is used as shown in Equation (103).

CCTAX = EM HY CTAX

(102)

EMCONVi , j ,m = UiGHGE PCALi PM i FCi , j ,m

∀i ∈ I , j ∈ J , m ∈ M

  CCOMP =  ∑∑∑ EMCONVi, j ,m − EM  HY COMP  i∈I j∈J m∈M  ACS Paragon Plus Environment

(103)

(104)


Page 28 of 68

Objective functions The economic objective function is to maximize the annual profit and the environmental objective function is to minimize the CO2 emissions. Although these objectives are opposite, the solution strategy for this multi-objective optimization problem is explained further. F .O = max

PROFIT ;

min

EM

(105)

The emissions are estimated as stated above in Equation (97)Error! Reference source not found., while the profit can be estimated by Equation (106) if the carbon tax is taken into account, or by Equation (107) if the carbon bonus is considered.

PROFIT = IN − CAP − COPER − CCTAX PROFIT = IN − CAP − COPER + CCOMP

(106) (107)

Solution procedure The constraint method56 is employed to generate the set of optimal solutions (Pareto front). The procedure starts considering the formulation exclusively for the environmental objective function, in other words, the proposed model is solved for the minimization of the emissions without involving the maximization of the profit. With this first step, the solution with the minimum EM and likewise with the minimum PROFIT is achieved. Then, the formulation is applied for the maximization of the profit while the minimization of the emissions is not considered. By means of the economic objective maximization, as expected, the solution with the maximum PROFIT and also with the maximum EM is accomplished. Now, the multi-objective optimization problem is changed to a single-objective one that consists in maximizing the profit and simultaneously setting several constraints for the emissions between the previous minimum and maximum values obtained


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for EM . Each restriction gives a point of the Pareto curve, which represents the tradeoffs between the economic and environmental functions.

Results and discussion The optimization results were attained based on the considerations mentioned above and the parameters presented in the Supporting Information section. This section is divided in three parts. The first one refers to the solutions for the carbon tax, the next one contains the results for the carbon bonus and finally the impact of the penalizations and compensations is discussed.

Carbon tax analysis The Pareto curves for the case that involves a carbon tax for the generation of emissions are shown in Figure 5. The first two values (10 and 15 $/tonne CO2) are taken into account since they are likely to be considered in future regulations in Mexico.31 The next values (25, 32, 41 and 52 $/tonne CO2) are those used for monetizing the externalities in the USA.57 As no further reduction of the emissions was found with these carbon taxes, the required tax that allows this change was estimated. With a hypothetical value of 84 $/tonne CO2, the emissions are reduced to 788,829 tonne CO2/year (maximum PROFIT ). While with the other carbon prices, when maximizing the PROFIT the emissions are equal to 1,408,578 tonne CO2/year. Even though a higher carbon tax of 84 $/tonne CO2 is considered, the process is still viable since it continues being profitable and the PROFIT decreases only in a 16.4% (comparing to the solution of a carbon tax equal to 10 $/tonne CO2 that gives the maximum PROFIT of the Pareto set). Note that, the greater the carbon tax is and the lower the emissions are, the less the profit is. Despite this, the profit for all the set of solutions is positive.



Each solution of the Pareto set makes reference to a different optimal configuration in terms of the selection of energy sources and technologies, including their required specific conditions. As shown in Figure 5, points A and B correspond to the extreme solutions. While point A represents the best economic and the highest environmental impact solutions, point B symbolizes the opposite. Also, it is important to notice that with carbon taxes lower than 84 $/tonne CO2 there is no change in the emissions (for instance, point A), this occurs since these economic penalizations are not enough to promote the use of processes that help in a further reduction of emissions. Nonetheless, this behavior changes for other intermediate solutions between points A and B. Some of the variations between solutions A and B for a carbon tax equal to 10 $/tonne CO2, which provides the maximum PROFIT of the Pareto set (635 MM$/year), are analyzed. For this specific penalization, the solution with the maximum PROFIT (point A) uses coal as fuel, CLP as combustion system and IGCC as power cycle whereas; the solution with the minimum EM (point B) uses natural gas, exCLC and STIG, respectively. For solution A, the selection of coal is expected due to its low cost and for solution B, the natural gas because of its lower environmental effect. The involved flowrates of fuel, CO2, water and products are shown in Table 3. The optimal technologies in the algae cultivation system are equivalent for both solutions: raceway pond for the cultivation stage, gravity sedimentation for the harvesting stage, solvent extraction for the extraction stage and enzymatic process for the production stage. Other important results for the analyzed tax are presented in Table 4. Notice that solution B symbolizes the highest possible mitigation (44%) since, as aforementioned, a 100% is not achievable due to the particular implicated restrictions. There are significant differences in the produced and demanded electric energy for these extreme solutions. It is worth mentioning that the increase of power demanded by the algae cultivation system in solution B is proportional to the rise of biodiesel production.


Page 30 of 68

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The destination of the produced CO2 (raceway pond, photobioreactor or atmosphere) throughout the solutions of the Pareto set is represented in Figure 6. Note that, the maximum fraction of mitigated CO2 is attained when no CO2 is released to the atmosphere. Nevertheless, high mitigation values can be obtained too with solutions where some of the generated CO2 is released but the major part is delivered to the cultivation system. An example of this is the solution with profit equal to 600 MM$/year and mitigation fraction equal to 0.34. For the entire Pareto front, no carbon dioxide is sent to the photobioreactor mainly due to its high cost and power requirements, however, if a greater amount of biodiesel is needed, the photobioreactor would be elected. As it can be observed in Figure 6, there are optimal solutions with different profits but similar amount of CO2 released to the atmosphere, this occurs because the optimization model always tries to give the optimal solution that satisfies both objective functions (economic and environmental). So, depending on the amount of CO2 produced and the optimal technologies, the profit can increase without releasing more CO2. Nevertheless, as the profit reaches its highest values, the CO2 released tends to go up too.

Carbon bonus analysis Similarly, several economic compensations for avoiding emissions are taken into consideration. Carbon bonuses vary from 0.3 to 130 $/tonne CO2 avoided. Since the average carbon price for these compensations has changed in the last years from 4 to 7 $/tonne CO2 and most of the world emissions are priced as 10 $/tonne CO2, such intermediate values are included in the analysis, as well as the price 80-120 $/tonne CO2 that has been estimated by economic models.58 The Pareto curves representing the optimal solutions for each carbon bonus are presented in Figure 7. Note that with the values of 120 and 130 $/tonne CO2, an important reduction of the emissions is achieved, specifically to 788,829 tonne CO2/year when the profit is the maximum. As expected, if the greatest compensation is considered, the maximum PROFIT of the Pareto set is attained (843 MM$/year).



Notice that with carbon bonuses lower than 120 $/tonne CO2, there are some points such as the extreme solutions where there is no change in the emissions (just as it occurs with the lowest values of the carbon tax). Still, this trend does not apply for all the Pareto front. In Figure 7, the opposite points A and B represent the best economic (maximum PROFIT ) and environmental (minimum

EM ) solutions, respectively. The main outcomes for these points, with a carbon bonus equal to 130 $/tonne CO2, are further discussed. For both solutions, the optimum fuel and technologies for the power plant as well as for the algae cultivation system are the same as the optimal ones with the carbon tax of 10 $/tonne CO2 (previously analyzed). However, as shown in Table 5, the flowrates vary, mainly for the solution A where the amount of produced biodiesel increases significantly since the flowrate of carbon dioxide sent to the cultivation stage is greater too. Such configuration leads to obtaining the maximum PROFIT but with low EM . As no CO2 is released to the atmosphere, the highest mitigation is achieved. Despite the net electric power for the solution A with a COMP of 130 $/tonne CO2 is lower (see Table 6) than the one with a CTAX of 10 $/tonne CO2 (see Table 4), the consideration of the bonus along with the rise of biodiesel production allow to achieve a higher PROFIT . The annual net electric energy throughout the Pareto front is presented in Figure 8. The electric power increases with the PROFIT , although there is no a linear relationship between these variables due to the effect of the power demanded by the algae cultivation system. The optimum fuel, combustion system and power cycle for different solutions of the Pareto set are included too. In order to obtain greater values for the PROFIT , the use of coal is required, whereas the selection of the optimal combustion system and power cycle changes with the produced electric energy.

Impact of the carbon tax and bonus


Page 32 of 68

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A comparison among the generated CO2 considering a carbon bonus, a carbon tax and a conventional system without any compensation or penalization is shown in Figure 9. The conventional scheme also involves the emission of all the produced CO2 since no cultivation system exists in this case. The three presented solutions are suitable to compare because their optimal configuration for the technologies in the power plant is equal and thus, the net electric power too. The optimum fuel is coal with a flowrate of 1,049,874 tonne/year, while the combustion system is CLP and the power cycle is IGCC. The annual net electric energy is 326 MW. Notice that, to generate this amount of electric power without a mitigation process, the emissions are equal to 2,680,594 tonne CO2/year. When the algae cultivation system is included and a carbon bonus of 130 $/tonne is considered, the CO2 emissions are reduced in a 71%. This corresponds to the solution of maximum PROFIT (843 MM$/year). On the other hand, if the algae system is involved but now considering a carbon tax of 10 $/tonne, the emissions are reduced 70%. Such optimal solution corresponds to a PROFIT of 591 MM$/year. Note that the highest compensation and the lowest penalization were considered in order to find the best economic and environmental solution (as described above, no further reduction of the emissions was found with greater penalizations). Despite the difference in the reduction of emissions is only of one percent, the profit is higher considering the carbon compensations. Therefore, it can be concluded that the use of carbon bonus based on the avoided emissions allows finding better tradeoffs for the objective functions.

Conclusions This paper has proposed an optimization approach for the integration of power plants using chemical looping combustion with algae-to-biodiesel systems, and evaluating different carbon policies. Economic and environmental objectives are considered. The first objective function refers to the maximization of the annual profit, while the other objective function consists in the



minimization of the CO2 emissions. The proposed mathematical model is based on a superstructure that includes different technologies for each process step (combustion system, power cycle; cultivation, harvesting, extraction and production stage). The optimal technologies vary according to the value of the objectives and the carbon bonus or tax involved, although some trends can be observed. The selection of the optimum fuel and amount of CO2 sent to the cultivation system is included too. Results show the Pareto sets for several economic penalizations and compensations, likewise the variation of the profit with some variables (annual net electric power, CO2 destination and mitigation). The benefits of considering the carbon taxes and bonuses as a strategy to reduce the emissions and simultaneously to attain a profitable system of power generation and biofuels production are identified. When the economic compensations are involved, better values for the profit and for the emissions are obtained, particularly with a carbon bonus of 130 $/tonne. The current carbon policies for the carbon tax are not sufficient to reduce the emissions as much as when considering the carbon bonus, therefore, the required tax to reduce the environmental impact was estimated as 84 $/tonne CO2. However, important reductions in the emissions and promising profits can be achievable with the other values of carbon tax and bonus.

Nomenclature Acronyms CLC

Chemical Looping Combustion

CLC3

Three-reactor Chemical Looping Combustion

CLP

Calcium Looping Process


Page 34 of 68

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exCLC

Extended Chemical Looping Combustion

HAT

Humid Air Turbine Cycle

IGCC

Integrated Gasification Combined Cycle

NGCC

Natural Gas Combined Cycle

SC

Steam Cycle

STIG

Combined Cycle with Steam Injected Gas Turbines

Sets = 1, 2, 3, …

technologies for the production stage

= 1, 2, 3, …

technologies for the harvesting stage

= 1, 2, 3, …

fuels

= 1, 2, 3, …

combustion systems

= 1, 2, 3, …

outlet streams

= 1, 2, 3, …

power cycles

= 1, 2, 3, …

technologies for the extraction stage

Indexes

represents the elements of set

ℎ



represents the elements of set ACS Paragon Plus Environment


represents the elements of set represents the elements of set

!


Binary variables

qb

ONE if the process b of the production stage exists

w

ONE if the raceway pond exists and ZERO if the photobioreactor exists

xo

ONE if the process o of the extraction stage exists

yh

ONE if the process h of the harvesting stage exists

zi , j ,m

ONE if the inlet flowrate of the fuel i used in the combustion system j and power generation cycle m exists

Variables AP

required area for the photobioreactor

AR

required area for the raceway pond

CoE

specific cost for the process o in the extraction stage

CoHEX

variable cost for the process o in the extraction stage

CoSEC

cost of the dryer for the process o in the extraction stage

CAP

total annualized fixed costs


Page 36 of 68

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CCi, j ,m

variable cost due to the consumption of the fuel i in the combustion system j and power generation cycle m

CCLCi, j ,m

fixed cost of the scheme i, j, m

CCOMP annualized compensation for avoiding CO2 emissions CCP

fixed cost for the photobioreactor

CCR

fixed cost for the raceway pond

CCTAX annualized penalization for generating CO2 emissions

CONCh concentration of algal biomass in the technology h at the beginning of the harvesting stage CONS W total water consumption

COPi, j ,m variable cost of the scheme i, j, m COPP

variable cost of the photobioreactor

COPR

variable cost of the raceway pond

COPER total annualized variable costs

CThCOS

fixed cost for the technology h in the harvesting stage

CToEXT

fixed cost for the process o in the extraction stage

CThFLOC

fixed cost for the first step of technology h in the harvesting stage

CTbPROD

fixed cost for the process b in the production stage



CVhAL

variable cost for the first step of technology h in the harvesting stage

CVhCOS

variable cost for the technology h in the harvesting stage

CVbPROD variable cost for the process b in the production stage EChCOS

power demand for the second step of technology h in the harvesting stage

ECoEXT

power demand for the process o in the extraction stage

EChFLOC power demand for the first step of technology h in the harvesting stage EC R

power demand for the raceway pond

EC P

power demand for the photobioreactor

ECbPROD power demand for the process b in the production stage

EM

CO2 emissions

EMCONVi, j ,m emissions generated in a conventional system i, j, m without mitigation

EP

annual net electric power

FhAL

alum coagulant flowrate for the technology h in the harvesting stage

FbBD

flowrate of biodiesel produced by the process b in the production stage

FoBIOF

flowrate used to activate the cost of the process o in the extraction stage

FbCAT

catalyst flowrate for the process b in the production stage

F CO2R

flowrate of CO2 sent to the raceway pond ACS Paragon Plus Environment

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F CO2P

flowrate of CO2 sent to the photobioreactor

F CO2L

flowrate of CO2 released to the atmosphere

FhCOS

flowrate leaving the second step of technology h in the harvesting stage

FbET

flowrate of ethanol produced by the process b in the production stage

FbETREQ

flowrate of ethanol required by the process b

FbETS

flowrate of ethanol available for sale

FoEXT

biomass flowrate entering to the process o of the extraction stage

FhFLOC

biomass flowrate entering to the process h of the harvesting stage

FhFLOC1

flowrate of biomass produced in the raceway pond and sent to the process h of the harvesting stage

FhFLOC 2

flowrate of biomass produced in the photobioreactor and sent to the process h of the harvesting stage

FhFLOCS

flowrate leaving the first step of technology h in the harvesting stage

FbGLI

flowrate of glycerol produced by the process b in the production stage

FoHEX

hexane consumption for the process o in the extraction stage

FoLD

lipid-depleted biomass flowrate for the process o in the extraction stage

FbLIP

lipase flowrate for the process b in the production stage



FoOIL

oil extracted flowrate for the process o in the extraction stage

FbPROD

oil flowrate entering to the process b of the production stage

FbPROT

flowrate of proteins produced by the process b in the production stage

FbSTARCH lipid-depleted biomass flowrate entering to the process b of the production stage

FBP

flowrate of biomass produced in the photobioreactor

FBR

flowrate of biomass produced in the raceway pond

FCi, j ,m

inlet flowrate of the fuel i used in the combustion system j and power generation cycle m

FCA

carbon dioxide with water effluent

FCO

carbon dioxide effluent

FCOM flue gas effluent

FEi , j ,m

electric energy produced by the scheme i, j, m

FGC

exhausted air effluent

FHS

hydrogen sulfide effluent

fixedCO2 CO2 mitigated by the algal system FOi , j ,m,k outlet stream k of the scheme i, j, m FP P

phosphate flowrate for the photobioreactor

FP R

phosphate flowrate for the raceway pond


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FU P

urea flowrate for the photobioreactor

FU R

urea flowrate for the raceway pond

FWhCOS

withdrawn water in the technology h of the harvesting stage

FW P

water flowrate needed for the photobioreactor

FWbPROD water consumption for the process b in the production stage FW R

water flowrate needed for the raceway pond

IN

total annualized revenues

NUM P

number of required photobioreactors

NUM R

number of required raceway ponds

prod CO2 CO2 produced by the power plant PROFIT annual profit Parameters

ChAL

coagulant concentration for the technology h in the harvesting stage

CoTE

unitary fixed cost for the process o in the extraction stage

C FB

concentration of algal biomass leaving the harvesting stage

CbPROD

unitary fixed cost for the process b in the production stage

CoSE

unitary fixed cost of the dryer for the process o in the extraction stage



COMP

carbon bonus

CP

unitary cost of phosphate

CTi, j,m,k

technical coefficient to obtain the outlet stream k of the scheme i, j, m

CT C

unitary fixed cost of the centrifugation process

CT DAF

unitary fixed cost of the dissolved air flotation process

CT

S

unitary fixed cost of the gravity sedimentation process

CT SM

unitary fixed cost of the magnetic separation process

CT TF

unitary fixed cost of the tangential flow filtration process

CTAX

carbon tax

CTUh

unitary fixed cost for the first step of technology h in the harvesting stage

CU

unitary cost of urea

CV 1i , j ,m

unitary variable cost of the scheme i, j, m

CV DAF

unitary variable cost of the dissolved air flotation process

CV P

unitary variable cost of the photobioreactor

CV R

unitary variable cost of the raceway pond

CV SM

unitary variable cost of the magnetic separation process

CV TF

unitary variable cost of the tangential flow filtration process

CW

unitary cost of water


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DT

diameter of the tubes in the photobioreactor

DEPTH

depth of the raceway pond

DWbBD

unitary requirement of water for the process b in the production stage

DW P

specific water demand for the photobioreactor

DW R

specific water demand for the raceway pond

Ei, j,m

net efficiency the scheme i, j, m

ECA

efficiency of the CO2 with water stream

ECO

efficiency of the pure CO2 stream

ECOM

efficiency of the flue gas stream

ENChCOS

specific power demand for the second step of technology h in the harvesting stage

ENCoEXT

specific power demand for the process o in the extraction stage

ENChFLOC

specific power demand for the first step of technology h in the harvesting stage

ENC P

specific power demand for the photobioreactor

ENCbPROD

specific power demand for the process b in the production stage

ENC R

specific power demand for the raceway pond

F C ACO 2

carbon dioxide fraction in FCA

FCOM

CO 2

carbon dioxide fraction in F COM



FMAX i , j ,m

maximum inlet flowrate of the fuel i used in the combustion system j and power generation cycle m

FMINi, j ,m

minimum inlet flowrate of the fuel i used in the combustion system j and power generation cycle m

HD

hours of operation for the cultivation stage

HEX oLO

hexane loss fraction for the process o in the extraction stage

HY

hours of operation for the plant

KF

capital recovery factor

L

length of the raceway pond

LT

length of the tubes in the photobioreactor

MB

positive number greater than one used for modeling

M FCO

molecular weight of the CO2

MRbET

feed mass ratio of ethanol for the process b in the production stage

MR H

feed mass ratio of hexane

P AL

unitary cost of coagulant

P HEX

unitary cost of hexane

PP

algal culture productivity in the photobioreactor

PbPROD

unitary variable cost for the process b in the production stage


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PR

algal culture productivity in the raceway pond

PCi

unitary cost of fuel i

PCALi

heating power of fuel i

PCLi , j ,m

cost of the scheme i, j, m

PM i

molecular weight of fuel i

PR P

unitary fixed cost of the photobioreactor

PR R

unitary fixed cost of the raceway pond

RP

unitary requirement of phosphate

RU

unitary requirement of urea

SP BD

unitary selling price of biodiesel

SP E

unitary selling price of electricity

SP ET

unitary selling price of ethanol

SP GLI

unitary selling price of glycerol

SP PROT

unitary selling price of proteins

T

RES

U iGHGE U

T

residence time unit greenhouse gas emissions for the fuel i number of tubes in the photobioreactor



WbCAT I

W

unitary requirement of catalyst for the process b in the production stage wide of the raceway pond

WbLIP

unitary requirement of lipase for the process b in the production stage

WOIL

lipid content in algal biomass

WbRB

recovery fraction of biodiesel for the process b in the production stage

WbRE

recovery fraction of ethanol for the process b in the production stage

WbRG

recovery fraction of glycerol for the process b in the production stage

WbRP

recovery fraction of proteins for the process b in the production stage

α

conversion factor

α

N

βhFLOC

conversion factor for the nutrients recovery fraction of algal biomass for the first step of technology h in the harvesting stage

βP

efficiency of the photobioreactor

βR

efficiency of the raceway pond

δ

CO2 demand

CO2

γh

recovery fraction of algal biomass for the second step of technology h in the harvesting stage


Page 46 of 68

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ρBD

density of biodiesel

ρ FB

density of the biomass slurry

ρW

density of liquid water

σo

recovery fraction of oil for the process o in the extraction stage

τ DT

fraction of hours per day that the gas is sent to the cultivation stage

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Detailed information for the case study can be found in this section. Parameters for the fuels are presented in

Table S1. Table S2 and Table S3 show efficiencies, costs and technical coefficients for the different combustion systems and power cycles. The data for the harvesting, extraction and production stage are presented in Table S4, Table S5 and Table S6, respectively. Table S7 shows the water demand. The minimum and maximum inlet flowrate of fuel is shown in Table S8 and

Table S9. Other general parameters are presented in Table S10.

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.

Acknowledgements The authors appreciate the financial support provided by the Mexican National Council for Science and Technology (CONACYT).



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Page 56 of 68

Table 1. Main parameters for the cultivation stage technologies Efficiency Unitary fixed cost ($/kg) Unitary variable cost ($/kg) Productivity (g/m2 d) System geometry

Raceway pond 0.35 0.227 0.421 15 10 m wide, 100 m long, 0.30 m deep

Photobioreactor 0.75 9.54 4 30 132 parallel tubes/unit; 80 m long tubes; 0.06 m tube diameter

Reference Slade and Bauen46 Jorquera et al.47 Slade and Bauen46 Grima et al.48 Menetrez49

Table 2. Specific electricity demands for the distinct technologies considered in each stage Process Cultivation stage Raceway pond

Power demands

Reference

426.9 kWh/t

Grima et al.48

Photobioreactor

9432 kWh/t

Grima et al.48

Harvesting stage Flocculation

167 kWh/t

Lira-Barragán et al.24

Centrifugation

8 kWh/m3

Singh et al.50

Gravity sedimentation

0.1 kWh/m3

Singh et al.50

Magnetic separation

4.5 kWh/ m3

Wang et al.51

Tangential flow filtration

2.06 kWh/ m3

Danquah et al.52

Dissolved air flotation Extraction stage Solvent extraction

15 kWh/ m3

Uduman et al.53

1.13 kWh/kg

Yuan et al.54

Supercritical CO2 extraction

1.74 kWh/kg

Yuan et al.54

Solvent extraction with previous drying

5.11 kWh/kg

Yuan et al.54

Supercritical CO2 extraction with previous drying Biodiesel production stage Alkali based process

5.41 kWh/kg

Yuan et al.54

1.86 kWh/gal

Martín and Grossmann27

Enzymatic process

1.11 kWh/gal

Martín and Grossmann27


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Table 3. Flowrates for Points A and B with a CTAX of 10 $/tonne CO2 Material/fuel Fuel

( prod CO sent to the photobioreactor ( F CO sent to the raceway pond ( F CO released to the atmosphere ( F CO2 generated

CO 2

CO 2 P

2

CO 2 R

2

CO 2 L

2

) ) ) )

Solution A (tonne/y) 1,049,874

Solution B (tonne/y) 122, 946

1,408,623

322,616

0

0

90

283,901

1,239,499

0

1,408,578

180,665

5141

16,292,084

Produced biodiesel

1

3852

Produced glycerol

0.12

403

Produced proteins

1

4687

Produced ethanol

0.6

1928

CO2 emissions Consumption of water

Table 4. Main results for Points A and B with a CTAX of 10 $/tonne CO2 Variable Profit (MM$) CO2 mitigation (%)

Net electric power (MW) Electric power demanded by the algae system (MW)

Solution A (annual)

Solution B (annual)

635

127

0.0032

44

346

94

0.0014

5



Page 58 of 68

Table 5. Flowrates for Points A and B with a COMP of 130 $/tonne CO2 Material/fuel Fuel

( prod CO sent to the photobioreactor ( F CO sent to the raceway pond ( F CO released to the atmosphere ( F CO2 generated

CO 2

CO 2 P

2

CO 2 R

2

CO 2 L

2

) ) ) )

CO2 emissions

Solution A (tonne/y) 1,049,874

Solution B (tonne/y) 122, 946

1,408,623

322,616

0

0

1,239,588

283,901

0

0

788,829

180,665

71,135,397

16,292,084

Produced biodiesel

16,817

3852

Produced glycerol

1755

403

Produced proteins

20449

4687

Produced ethanol

8418

1928

Consumption of water

Table 6. Main results for Points A and B with a COMP of 130 $/tonne CO2 Variable

Solution A (annual)

Solution B (annual)

Profit (MM$)

843

CO2 mitigation (%)

44

44

Net electric power (MW)

326

94

Electric power demanded by the algae system (MW)

20

5


149

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Figures

Figure 1. Schematic representation for the integrated system



Figure 2. System proposed for the CO2 mitigation in a power plant using chemical looping combustion and microalgae cultivation for biodiesel production.


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POWER CYCLE PC-1 COMBUSTION SYSTEM

CS-1 CS-2 . . .

CS-J ALGAE SYSTEM FUEL F-1 F-2

. . . F-I

PC-2 COMBUSTION SYSTEM

OUTLET STREAM

CS-1

OS-1

CS-2

OS-2

. . .

CS-J

. . .

OS-K

CULTIVATION STAGE

C-1 C-2 Atmosphere

HARVESTING STAGE

EXTRACTION STAGE

PRODUCTION STAGE

HS-1

ES-1

PS-1

HS-2

ES-2

PS-2

. . .

. . .

ES-O

PS-B

. . .

HS-H

Products

. . . PC-M COMBUSTION SYSTEM

CS-1 CS-2 . . .

CS-J

Figure 3. Superstructure proposed to represent the possibilities in the global system.



Z1,1,1 Z1,1,m

Z1,1,M −1

Z I −1, j ,m

Z1,J ,m

. . .

FMIN1, j ,m ≤ FC1, j ,m ≤ FMAX1, j ,m

Z1, J −1,m

. . .

Z1, j ,m

FMIN I −1, j ,m ≤ FCI −1, j ,m ≤ FMAX I −1, j ,m

Z1,1,M

Z I ,1,1

. . .

Z I ,1,m ZI ,1,M −1

FMIN I , j ,m ≤ FCI , j , m ≤ FMAX I , j ,m

Z I , J −1,m Z I , J ,m

. . .

Z I , j ,m

. . .

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

Page 62 of 68

ZI ,1,M

Figure 4. Superstructure for the election of the fuel i used in the combustion system j and power generation cycle m


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Figure 5. Pareto curves for the integrated system with distinct penalties for the generation of CO2 emissions



Figure 6. Amount of CO2 sent to the cultivation stage or atmosphere considering a CTAX of 10 $/tonne CO2


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Figure 7. Pareto curves for the integrated system with different compensations for the avoided CO2 emissions



Figure 8. Annual net electric power including the optimal fuel and technologies with a COMP of 130 $/tonne CO2


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Figure 9. Variation of the emissions according to different cases



For Table of Contents Use Only

Synopsis: This paper proposes an optimization approach for the integration of power plants using

chemical looping combustion with algae-to-biodiesel systems evaluating different carbon policies.


Page 68 of 68

Analysis of Carbon Policies in the Optimal Integration of Power Plants

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