Optimal Design of Distributed Algae-Based Biorefineries Using CO2

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Article

Optimal design of distributed algae-based biorefineries using CO emissions from multiple industrial plants 2

Oscar Martín Hernández-Calderón, José María Ponce-Ortega, Jesús Raúl Ortiz -del-Castillo, Maritza Elizabeth Cervantes-Gaxiola, Jorge Milán-Carrillo, Medardo Serna-González, and Eusiel Rubio-Castro Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b01684 • Publication Date (Web): 28 Jan 2016 Downloaded from http://pubs.acs.org on February 3, 2016

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Industrial & Engineering Chemistry Research

Optimal design of distributed algae-based biorefineries using CO2 emissions from multiple industrial plants Oscar Martín Hernández-Calderón1, José María Ponce-Ortega2, Jesús Raúl Ortiz-delCastillo1, Maritza E. Cervantes-Gaxiola1, Jorge Milán-Carrillo1, Medardo SernaGonzález2, Eusiel Rubio-Castro1*.

1

Chemical and Biological Sciences Department, Universidad Autónoma de Sinaloa, Culiacán, Sinaloa 80000, Mexico

2

Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México, 58060

*

Author for correspondence: E. Rubio-Castro

Email: [email protected]. Tel. +52 667 7137860 ext. 115.

ACS Paragon Plus Environment


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Abstract

This work proposes an optimization approach for capturing carbon dioxide from different industrial facilities to yield an algae-based biorefinery. The proposed approach is based on a distributed system to account for the economies of scale and it involves the site selection for the processing facilities. Additionally, the model considers the optimization for the technologies used in the process stages and different technologies to yield several products. The algae oil that is obtained from each facility can be sent to processing hubs located in the same plant and/or to a central processing unit. The objective function is to minimize the total annual cost for the treatment of flue gases, which includes the capital and operating costs for the different processing stages, the overall transportation costs associated to the system minus the sales of products plus the tax credit for reducing the CO2 emissions. The results show several economic benefits.

Keywords: CO2 sequestration, Distributed system, Bio-refinery, Optimization.


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1. Introduction The current economy, based on energy production by the combustion of fossil fuels, emits considerable quantities of greenhouse gases (GHG), especially CO2. Greenhouse gases are considered the most important factor contributing to the global warming problem. Since the beginning of the Industrial Revolution, the burning of fossil fuels and the extensive deforestation have contributed to increase around 40 % the atmospheric concentration of carbon dioxide1. In this regard, reducing the CO2 level in the atmosphere could be a good option to tackle the global warming problem. Therefore, recently there have been developed several methodologies for improving the energy efficiency2 as well as to increase the use of sustainable energy forms3-7 to overcome the dependence on fossil fuels (such as coal and oil) as well as to reduce the CO2 emissions to the atmosphere8. In this context, several works are focused on the mitigation of CO2 emissions from industrial sectors9-13. Besides, one of the most promising strategies to overcome the dependence on fossil fuels and to reduce the CO2 discharged to the environment is the use of biomass as renewable energy. Here, the microalgae-systems are the technologies with the highest interest for producing biofuels in the last decade. It is because the microalgae production offers some advantages over the conventional biomass production, for example: higher photosynthetic productivity, use of nonproductive land, reuse and recovery of nutrients in the wastewater streams, use of saline or brackish water, and reuse of CO2 from flue gases from power plants or similar sources14. It should be noted that alga-systems are particularly promising for the production of biodiesel, but today this is still too costly15. One of the main bottlenecks in the algae production is the great amount of energy used in the whole process and the associated investment costs16. Therefore, the investigation in the algae processing must be focused on minimizing the used energy17. Then, it is desirable to integrate liquid industrial effluents and the flue gases in the algae-systems18. This way, Pokoo-Aikins et al.19 presented a techno-economic analysis of an integrated system for an algae-based biorefinery using carbon dioxide from the flue gases from a power plant. Rizwan et al.20 developed a mathematical formulation to determine the optimal pathway for the biodiesel production from algae biomass. Martín and Grossmann21 addressed the optimal use of waste cooking and algae for the production of second-generation biodiesel. Murillo-Alvarado et al.22 presented a methodology to identify the optimal biorefinery



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pathway through the consideration of technological, environmental and economic objectives. de la Cruz et al.23 performed a rigorous simulation including energy integration for the production of substitutes of diesel from algae. Gong and You24 developed a mixed integer non-linear programming (MINLP) model for minimizing the unit carbon sequestration and utilization cost, this MINLP is based on a novel superstructure that considers the corresponding stages of an algae-based biorefinery. Besides, recent papers have reported MINLP models for the optimal algae-based biorefinery, where the CO2 mitigation is taking into account25-27. On the other hand, several works have addressed the sustainable biorefinery design (economic and environmental impacts are simultaneously evaluated) and planning of supply chains related to the biomass conversion as well as liquid transportation fuel production28, the hydrocarbon biofuels29 and obtaining of multiple products from algae biomass30. It is noteworthy that there is not a methodology that accounts for the optimization involving simultaneously water integration, CO2 sequestration, biorefinery allocation and the distribution of products. Therefore, in this work is developed a MINLP formulation to find the optimal design and allocation of an algae-based biorefinery where flue gases from different industrial facilities are used as raw material. The proposed model is based on a new superstructure that includes the selection of the used technologies in the different processing stages (growth, harvesting, extraction and processing) as well as to determine the allocation of processing facilities in a distributed system. The objective function is the minimization of the total annual cost formed by the capital and operating costs associated to each processing stage, the cost to transport the algae oil from the extraction stage to central processing facilities and the cost to transport the products from the hub and/or central processing facilities to consumers minus the savings owing to the sales of products and the tax credit for CO2 reduction. The developed MINLP model was implemented in the software GAMS31, and to demonstrate its applicability, a case study from Mexico is solved and the results show the advantages of considering the use of flue gases as raw materials for growing algae as well as the economic and environmental benefits of including water integration and a distributed system for an algae-based biorefinery design. The paper is organized as follows: a general description of the process is given in Section 2, Section 3 presents the proposed superstructure, Section 4 shows the model


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formulation, while Sections 5 and 6 present a case study and the results obtained respectively, whereas Sections 7, 8, 9 and 10 show the conclusions, appendices, nomenclature and references, respectively.

2. Description of the production system The overall system to obtain algae oil is constituted by three processing modules (algae growth, algae harvesting and algae oil separation) as it is shown in Figure 1a. In the first module, for the algae growth an open system (raceway pond) or a closed system (photobioreactor) can be used. Noticed that the algae growth requires water, sunlight, carbon dioxide and nutrients (phosphorous and nitrogen). Regarding to the carbon dioxide (see Figure 1b), the algae growth is an opportunity to capture CO2 from flue gases of industrial processes. It should be noted that this option reduces the CO2 emissions, which improves the air quality reducing the adverse effect of the global warming problem. Then, the algae must be separated, where several separation options are available for harvesting and the choice depends on parameters like the type of algae, cell density and process conditions. The most common separation processes are sedimentation, filtration and centrifugation. Here, it is important to mention that this stage represents the biggest energy consumption, which is used for filtration and/or centrifugation. However, independently of the used separation process, there are two outlet streams. This can be seen in the second module of Figure 1a, which shows a general representation for a separation process (e.g., sedimentation, filtration, centrifugation, etc.), where the upstream and downstream are poor and rich biomass (algae) streams, respectively. In other words, the rich stream has a high content of algae and a low content of water, therefore, this stream is used to obtain the algae oil. On the other hand, the poor stream presents a low content of algae and a high content of water. Regarding to it, there are two options to use it. The first option is to send this stream to the waste discharged to the environment, while the other one is to look for a reuse of this stream in another part of the process (for example in the module of algae growth). This is shown in Figure 1b. Once the algae biomass has been separated from the water, this is crushed to separate the solid algae membranes and other solids from the algae oil. Here, parameters like the capital and operating costs for each method, the feasibility, the extraction speed and others must be taken into account to choose the right extraction



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method for recovering the algal oil. In this stage, there are three outlet streams: the algae oil, water and the cell paste. The separation efficiency determines the quantity of the obtained algae oil. With respect to the water and the cell paste streams, these can be sent to the waste that is discharged to the environment or these can be reused in the algae growth stage (water stream) and the drying of cell paste could be done using excess flue gases. Finally, Figure 1a shows that the algae oil can be processed with different technologies and to obtain different products (biodiesel, methane, ethanol, etc.) and byproducts (heat, steam, fertilizers, etc.). But, a pretreatment is needed after the oil extraction. This pretreatment depends on the quality of the algae oil required for producing a specific product. In this regard, the production (biodiesel, ethanol, methane, etc.) depends on the specific customer demands, selling prices, processing costs and plant capacities. Hence, in this work is proposed an optimization model based on Figure 1b to determine the optimal pathway for yielding different products from algae oil via the sequestration of carbon dioxide of the flue gases coming from different industries. Then, a novel superstructure is developed to consider multiple technologies for each stage of the algae oil processing. These technologies have specific efficiencies and costs (operating and capital costs). The proposed superstructure is shown in Figure 2, which is an extended representation of Figure 1b. Notice in the proposed superstructure that water integration is considered. It is because the outlet water from the harvesting and extraction stages can be reused in the growth stage.

3. Superstructure description Figure 2 shows a new configuration to obtain several products from algae oil. These products are required by specific consumers and they have given demands Furthermore, this configuration is an opportunity to sequester flue gases, which helps to reduce the global warming problem. In the proposed superstructure, the optimal allocation of facilities for algae oil processing is considered. This is because the processing can be done in a central processing facility or in distributed processing facilities. The produced oil can be segregated to the different processing plants, and then the product can be distributed to the different markets (each one with specific demands). In each processing facility, the sequestered flue gases are segregated and sent to a set of photobioreactors, where the


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number, operation and configuration are optimized. The outlet flowrates from the photobioreactors are sent to a set of harvesting methods, which also are optimized. Then, the algae biomass is transported to a set of extraction methods to obtain the algae oil using optimized extraction methods, and the next step is the algae oil processing and the selling of products. Therefore, the optimal selection of the pathway depends on the optimal relationship between the capital and operating costs, the transportation cost as well as the profits owing to the product sales. Finally the targets of the proposed superstructure are given as follows: •

to optimize simultaneously each process stage for the algae oil processing,

•

to determine the feasibility of the used algae,

•

to find the optimal allocation of the processing facility and

•

to offer a new option to reduce the flue gas emissions.

4. Model Formulation In the equations that form the proposed model, the subscripts k, r, h, e, p, c and d are used to denote plants, photobioreactors, harvesting methods, extraction methods, technologies located in the hub processing facilities, technologies located in the central processing facilities and consumers, respectively. The superscript CO2 denotes the carbon dioxide, f the fresh sources, n the nutrients, hs the harvesting stage, gs the growing stage, es the extraction stage, ps the processing stage, in inlets, out outlets, pr the poor streams, ri the rich streams, t the total flowrates, l the electricity, and s the transportation. Mass balance in the growth stage Figure 3 is used for explaining the mass balance in the module of algae growth. Notice that for growing algae, fresh water ( Fwrf,k ), CO2 that is carried out by water ( Fwrco,k2 ), nutrients ( Demrn,k ) and sunlight are required. In addition, to reduce the use of fresh water, an aqueous stream coming from the harvesting ( Fhrhs,k, gs ) and oil separation ( Fwres,k, gs ) stages are recirculated to the photobioreactors. Then, the inlet flowrate to each photobioreactor ( Frrin,k ) is given as follows:



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Frrin,k = Fwrf, k + Fwrco,k2 + Fhrhs,k, gs + Fwres,k, gs ; r ∈ GT ; k ∈ K

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(1)

where Fhrhs,k, gs is composed by water and the algae that were not separated in the harvesting stage: Fhrhs, k, gs = Fwrhs, k, gs + Farhs,k, gs ;

r ∈ GT ; k ∈ K

(2)

Farhs, k, gs is the recirculated algae flowrate and Fwrhs,k, gs is the water flowrate recirculated from the harvesting stage to each photobioreactor. In this regard, the inlet flowrate to each photobioreactor includes water ( Fwrin,k ) as well as algae ( Farin,k ): Frrin,k = Fwrin,k + Farin,k ; r ∈ GT ; k ∈ K

(3)

The inlet water and algae flowrates to each photobioreactor are calculated as follows: Fwrin,k = Fwrf,k + Fwrco, k2 + Fwrhs,k, gs + Fwres, k, gs ; r ∈ GT ; k ∈ K

(4)

Farin,k = Farhs,k, gs ; r ∈ GT ; k ∈ K

(5)

It should be noticed in Figure 3 that the inlet flowrate to the photobioreactor is formed by Fwrf,k , Fwrco,k2 , Fhrhs,k, gs and Fwres, k, gs ; which are shown in Equation 1. Here, Fhrhs,k, gs is the recirculated flowrate coming from the harvesting stage and it is composed by water ( Fwrhs, k, gs ) and algae ( Farhs,k, gs ) like is indicated in Equation 2. Therefore, the inlet flowrate to the photobioreactor includes both water ( Fwrin,k ) as well as algae ( Farin,k ); which is represented in Equation 3. And Equations 4 and 5 defines that Fwrin,k considers Fwrf,k ,

Fwrco,k2 , Fwres, k, gs and Fwrhs, k, gs ; while Farin,k is represented just by Farhs,k, gs . Furthermore, the recirculated algae flowrate from the harvesting stage ( Farhs, k, gs ) depends on the algae concentration in the recirculated stream ( Cakhs , gs ):

Farhs,k,gs = Cakhs, gs Fhrhs,k, gs ; r ∈ GT ; k ∈ K


(6)

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In addition, the fresh water used in each plant ( Fwkf ), the water flowrate in each plant where is carried out the CO2 ( Fwkco2 ), the recirculated flowrate from the harvesting stage on each plant ( Fhkhs , gs ), and the recirculated water flowrate from the separation stage on each plant ( Fwkes , gs ) are determined as follow:

Fwkf =

∑ Fw

; k∈K

f r ,k

(7)

r∈GT

Fwkco2 =

∑ Fw

co2 r ,k

; k ∈K

(8)

r∈GT

Fhkhs , gs =

∑ Fh

hs , gs r ,k

; k∈K

(9)

; k∈K

(10)

r∈GT

Fwkes , gs =

∑ Fw

es , gs r ,k

r∈GT

It should be noted that the total recirculated flowrate from the harvesting stage to the growth stage is formed by water and algae:

Fhkhs , gs = Fwkhs , gs + Fakhs , gs ;

k∈K

(11)

Here Fakhs , gs and Fwkhs , gs are the total flowrate of recirculated algae and the total flowrate of recirculated water from the harvesting stage to the growth stage, respectively. The algae concentration in the recirculated stream from the harvesting stage is determined as follows:

Cakhs , gs =

Fakhs , gs ; k∈K Fhkhs , gs

(12)

Finally, the next mathematical expressions represent the mass balances for Fakhs , gs and Fwkhs , gs in the growth stage:

Fakhs , gs =

∑ Fa

hs , gs r ,k

; k∈K

(13)

; k∈K

(14)

r∈GT

Fwkhs , gs =

∑ Fw

hs , gs r ,k

r∈GT



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Notice that the water recirculation can be or cannot be considered. In the first option, the flowrates Fhkhs , gs and Fwkes , gs are optimization variables and these ones could be greater or equal to zero. But, for the second option, both above flowrates must be equal to zero; hence, the next mathematical expressions must be included to fix the recirculation flowrates ( Fhrhs,k, gs and Fwres,k, gs ) equal to zero: Fhkhs , gs = 0; k ∈ K

(15)

Fwkes , gs = 0; k ∈ K

(16)

Furthermore, in the photobioreactor there is the algae generation. Then, the outlet flowrate in the photobioreactors ( Frrout , k ) is equal to the sum of the inlet flowrate and the generated algae flowrate ( Farrx,k ): in rx Frrout , k = Frr , k + Far , k ; r ∈ GT ; k ∈ K

(17)

Like in the inlet flowrate to each photobioreactor, there is algal biomass that is recirculated from the harvesting stage, then the total algae flowrate in each photobioreactor ( Farout , k ) is equal to the sum of the recirculated algae flowrate and the generated algae flowrate: rx hs , gs Farout , k = Far , k + Far , k ; r ∈ GT ;k ∈ K

(18)

Farrx,k depends on the photobioreactor volume ( vrgs,k ), the specific growth rate ( µrgs,k ) and the algae concentration ( Car ,k ): Farrx,k = µ rgs,k vrgs,k Car , k ; r ∈ GT ; k ∈ K

Car ,k =

Farout ,k Frrout ,k

; r ∈ GT ; k ∈ K

(19)

(20)

The methodology given in the Appendix A is used to calculate µrgs,k . Besides, the


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outlet water flowrate from each photobioreactor ( Fwrout , k ) is the difference between the outlet total flowrate and the outlet algae flowrate, out out Fwrout , k = Frr , k − Far , k ; r ∈ GT ; k ∈ K

(21)

and this one is equal to the inlet water flowrate ( Fwrin,k ), in Fwrout , k = Fwr , k ; r ∈ GT ; k ∈ K

(22)

Finally, the total flowrate in the outlet of the growth stage ( Frkgs ,out ) is calculated as follows:

Frkgs ,out =

∑ Fr

out r ,k

; k∈K

(23)

r∈GT

which is formed by the total algae and water flowrates in the outlet of the growth stage ( Fakgs ,out , Fwkgs ,out , respectively).

Frkgs,out = Fakgs,out + Fwkgs,out

(24)

Fakgs ,out and Fwkgs ,out are determined as follows:

Fakgs ,out = ∑ Farout,k ; k ∈ K

(25)

Fwkgs ,out = ∑ Fwrout,k ; k ∈ K

(26)

r∈R

r∈R

Moreover, an important factor for the efficiency and cost of the algae harvesting process is the algae concentration in the fed flowrate in this stage. This factor is the ratio between the total outlet flowrate from the photobioreactor and the algae content, and it allows the calculation of the algae flowrate in the outlet of the growth stage: Ca

gs ,out k

Fakgs ,out = ; k ∈K Frkgs ,out


(27)


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Cakgs ,out is the algae concentration in the outlet of the growth stage.

Mass balance in the algae harvesting stage The flowrate coming from the growth stage ( Frkgs ,out ) is fed to the harvesting stage and it can be sent to each technology used to separate the algae from the broth:

Frkgs ,out =

∑ Fh

in h ,k

; k∈K

(28)

h∈HT

where Fhhin,k is the total flowrate in the inlet of each harvesting method. This flowrate is water and algae: Fhhin,k = Fahin,k + Fwhin,k ; h ∈ HT ; k ∈ K

(29)

Fahin,k and Fwhin,k are the algae and water flowrates segregated from the outlet of the growth stage to the inlet of the harvesting methods. The sum of the above flowrates must be equal to the algae and water coming from the growth stage:

Fakgs ,out =

∑ Fa

in h ,k

; k∈K

(30)

; k∈K

(31)

h∈HT

Fwkgs ,out =

∑ Fw

in h,k

h∈HT

The algae flowrate inlet to each harvesting method is determined by the next relationship: Fahin, k = Cahin,k Fhhin, k ; h ∈ HT ; k ∈ K

(32)

here Cahin,k is the algae concentration inlet to each harvesting method, which must be equal to the algae concentration outlet from the growth stage: Cahin,k = Cakgs ,out ; h ∈ HT ; k ∈ K

(33)

Notice in Figure 3 that any separation process has two outlet flowrates. These streams are rich and poor in solids (algae), respectively. Then, the inlet flowrate to each


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harvesting method is equal to the sum of the rich stream flowrate ( Fhhri,k,out ) and poor stream flowrate ( Fhhpr, k,out ): Fhhin, k = Fhhri, k,out + Fhhpr,k,out ; h ∈ HT ;k ∈ K

(34)

Besides, both the rich stream as well as the poor stream in the harvesting methods are composed by a portion of water and algae: Fhhri, k,out = Fwhri,,kout + Fahri,,kout ; h ∈ HT ; k ∈ K

(35)

Fhhpr, k,out = Fwhpr,k,out + Fahpr,k,out ; h ∈ HT ; k ∈ K

(36)

here Fwhpr,k,out is the water content in the poor stream or the removed water flowrate on each harvesting method, Fwhri,,kout is the flowrate of water in the rich stream, Fahri,,kout is the separated algae flowrate and Fahpr,k,out is the algae flowrate in the poor stream or the algae that was not separated. In addition, the inlet water and algae flowrate of each harvesting method is equal to the water and algae in the rich and poor streams: Fwhin,k = Fwhri,,kout + Fwhpr, k,out ; h ∈ HT ; k ∈ K

(37)

Fahin,k = Fahri,,kout + Fahpr, k,out ; h ∈ HT ; k ∈ K

(38)

It should be noted that the separated algae flowrate is the production of dry algae in the facility. Notice that the separated algae and removed water in this step depend on the efficiency to remove water and separate algae ( η h , k , η h , k ) in the separation process: w

a

Fahri,,kout = η ha,k Fahin, k ; h ∈ HT ; k ∈ K

(39)

Fwhpr,k,out = η hw,k Fwhin,k ; h ∈ HT ; k ∈ K

(40)



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Once the flowrate coming from the growth stage has been handled in the harvesting stage, both the rich stream as well as the poor stream are mixed, which determine the flowrates in the outlet of harvesting stage:

Fhkhs , ri ,out =

∑ Fh

; k∈K

(41)

∑ Fa

; k∈K

(42)

ri ,out h ,k

h∈HT

Fakhs ,ri ,out =

ri ,out h,k

h∈HT

Fwkhs ,ri ,out =

∑ Fw

ri ,out h ,k

; k∈K

(43)

∑ Fh

pr ,out h ,k

; k∈K

(44)

; k∈K

(45)

; k∈K

(46)

h∈HT

Fhkhs , pr ,out =

h∈HT

Fakhs , pr ,out =

∑ Fa

pr ,out h,k

h∈HT

Fwkhs , pr ,out =

∑ Fw

pr ,out h ,k

h∈HT

where Fhkhs ,ri ,out is the total flowrate of the rich stream in the outlet of the harvesting stage, Fakhs ,ri ,out is the algae flowrate in the rich stream in the outlet of the harvesting stage, Fwkhs ,ri ,out is the water flowrate in the rich stream in the outlet of the harvesting stage, Fhkhs , pr ,out is the total flowrate of the poor stream in the outlet of the harvesting stage, Fakhs , pr ,out is the algae flowrate in the poor stream in the outlet of the harvesting stage and Fwkhs , pr ,out is the water flowrate in the poor stream in the outlet of the harvesting stage. And the total flowrates are formed by water and algae: Fhkhs ,ri ,out = Fakhs , ri ,out + Fwkhs ,ri ,out ; k ∈ K

(47)

Fhkhs , pr ,out = Fakhs , pr ,out + Fwkhs , pr ,out ; k ∈ K

(48)

Here, the flowrate of the poor stream is divided and sent to the waste stream that is discharged to the environment ( Fhkev ) and/or to the growth stage ( Fhkhs , gs ):


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Fhkhs , pr ,out = Fhkev + Fhkhs , gs ; k ∈ K

(49)

On the other hand, the rich stream is sent to the extraction stage and it is divided for each used technology: Fhkhs ,ri ,out =

∑ Fe

in e ,k

; k∈K

(50)

e∈EX

where Feein,k is the inlet flowrate on each oil extraction method. Furthermore, the algae oil concentration in the outlet of the harvesting stage ( Cakhs ,ri ,out ) is determined as follow: Cakhs ,ri ,out =

Fakhs ,ri ,out ; Fhkhs ,ri ,out

k∈K

(51)

Mass balance in the extraction algae oil stage The inlet flowrate on each extraction method is composed by algae and water: Feein,k = Faein, k + Fwein,k ;

e ∈ EX ; k ∈ K

(52)

Faein, k and Fwein,k are the algae flowrate and water flowrate in the inlet of each oil extraction method, respectively. And the inlet algae flowrate on each extraction methods ( Faein, k ) is calculated as follows: Faein,k = Caein,k Feein,k ;

e ∈ EX ; k ∈ K

(53)

Caein, k is the algae concentration in the inlet flowrate of the oil extraction methods, and it is equal to the algae concentration in the outlet rich stream of the harvesting stage: Caein, k = Cakhs ,ri ,out ;

e ∈ EX ; k ∈ K

(54)

It should be noted that the dry algae contains both algae oil ( Foein,k ) and cell walls ( Fcwein,k ): Faein,k = Foein, k + Fcwein, k ;

e ∈ EX ; k ∈ K


(55)


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Page 16 of 44

In this regard, the oil content ( Foein,k ) is determined by a percentage of oil content in dry algae ( ε ein, k ): Foein, k = ε ein,k Faein,k ;

e ∈ EX ; k ∈ K

(56)

Independently of the extraction methods, the target is to extract the oil from the algae separated in the previous stage. Furthermore, the quantity of extracted oil ( Foeex,k,out ) is determined by the efficiency of the used device that can be bead mills, presses, solvent extraction or cavitation ( ηeex,k ): Foeex, k,out = η eex, k Foein, k ;

e ∈ EX ; k ∈ K

(57)

while the rest of alga oil ( Foels,k,out ) is segregated with the cell paste ( Fcpeout , k ), it is carried out out the outlet cell walls ( Fcweout , k ). In addition, in the cell paste there is a part of water ( Fcpwe , k )

that is separated and segregated: ls , out out Fcpeout + Fcweout , k = Foe , k , k + Fcpwe , k ;

e ∈ EX ; k ∈ K

(58)

Because the inlet and the outlet cell walls are the same, the next relationship is needed: in Fcweout , k = Fcwe , k ;

e ∈ EX ; k ∈ K

(59)

out Both the outlet cell paste ( Fcpeout , k ) as well as the outlet water ( Fwe , k ) in the

extraction oil stage could be used in other parts of the process. For example, the water can be recirculated to each photobioreactor and the cell paste could be used to the thermal pretreatment of CO2 before use it in the photobioreactor. From a mass balance in the oil extraction stage of Figure 3, the next mathematical relationships are obtained:

Foein,k = Foeex,k,out + Foels,k,out ;

e ∈ EX ; k ∈ K

out Feein,k = Foeex,k,out + Fcpeout , k + Fwe , k ;

e ∈ EX ; k ∈ K


(60) (61)

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Fcpeout , k is related to the dry weight of cell paste ( ωe , k ), which is the relationship between the cell walls and cell paste:

ωe , k =

Fcweout ,k Fcpeout ,k

e ∈ EX ; k ∈ K

;

(62)

Furthermore, the total flowrate of water and cell paste in the outlet of the extraction stage ( Fwkes ,out , Fcpkes ,out ) are determined by the following equations:

∑ Fw

Fwkes ,out =

out e, k

; k∈K

(63)

e∈EX

Fcpkes ,out =

∑ Fcp

out e,k

; k∈K

(64)

e∈EX

As it is shown in Figure 3, the water flowrate in the outlet of oil extraction stage can be segregated and sent to the environment ( Fwkes ,ev ) and/or recirculated to the growth stage ( Fwkes , gs ): Fwkes ,out = Fwkes ,ev + Fwkes , gs ;

k∈K

(65)

Finally, the total algae oil flowrate in the outlet of the extraction stage ( Fokes ,out ) is equal to the sum of the algae oil flowrate obtained in each extraction method:

Fokes ,out =

∑ Fo

ex ,out e, k

; k∈K

(66)

e∈EX

Mass balance for the discharge to the environment The total waste that is discharged to the environment from each plant ( Fwastekev ) is equal sum of the segregated flowrates from the harvesting and extraction stages: Fwastekev = Fhkev + Fwkes ,ev ;

k∈K


(67)


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Page 18 of 44

Mass balance in the algae oil processing stage Once the algae oil is obtained, this flowrate is segregated and sent to several processes in the algae oil processing stage to generate multiple products for satisfying the requirements of multiple consumers. Like it is shown in Figure 4, the processing can take place in a hub processing facility installed in the same plant and/or in a central processing facility; therefore, the flowrate for algae oil is equal to the algae oil sent from each plant to the processing technologies to obtain a specific product located in the same plant ( Fokps, g , p ,k ' ) and/or to the central processing facility ( Fokps, g , p ,c ):

Fokes ,out =

∑ ∑ ∑ Fo

ps k , g , p ,k '

p∈PC k ∈K g∈G k ' =k '

+

∑ ∑ ∑ Fo

ps k , g , p ,c

;

k ,∈ K

(68)

p∈PC c∈C g∈G

Therefore, the inlet algae oil flowrate of each processing technology of the different products, both in the hub processing facilities as well as in the central processing facility ( Fogin, p ,k , Fogin, p ,c ), is equal to the sum of portions of algae oil coming from each plant:

Fogin, p ,k =

∑ Fo

k ', g , p , k

;

g ∈ G; p ∈ PC ; k ∈ K

(69)

∑ Fo

k ', g , p , c

;

g ∈ G; p ∈ PC ; c ∈ C

(70)

k '∈K k' =k

Fogin, p ,c =

k '∈K

k ' is an alias for the index k used to model the algae oil flowrate that is sent to the hubs

and central processing facilities. Once the algae oil is fed to each processing technology, the outlet product flowrate of each technology in the hub and in the central processing facilities ( Fpgout, p ,k , Fpgout, p ,c ) depends on the efficiency for each technology used in this stage ( ηg , p,k , ηg , p,c ):

Fpgout, p ,k = η g , p , k Fogin, p , k ;

g ∈ G; p ∈ PC ; k ∈ K

(71)

Fpgout, p ,c = η g , p ,c Fogin, p ,c ;

g ∈ G; p ∈ PC ; c ∈ C

(72)


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Therefore, the total outlet flowrate from each product in the hub and the central t , out processing facilities ( Fp tp,,out k , Fp p , c ) is the sum of the flowrate of each product generated in

the technologies available for obtaining this one: out Fp tp,,out k = ∑ Fp g , p , k ;

p ∈ PC ; k ∈ K

(73)

out Fptp,,out c = ∑ Fp g , p , c ;

p ∈ PC ; c ∈ C

(74)

g∈G

g∈G

In addition, the flowrate of products generated in the hub and in the central processing facilities are sent to multiple consumers and/or to the storage tank:

Fp tp,,out k =

∑ Fp

$ p ,k ,d

;

p ∈ PC ; k ∈ K

(75)

∑ Fp

$ p ,c,d

;

p ∈ PC ; c ∈ C

(76)

d ∈Dm

Fp tp,,out c =

d ∈Dm

Then, the total flowrate of each product that is sold to the different consumers ( Fp tp,$,d ) is calculated as follows: Fp tp,$, d =

∑ Fp

k ∈K

$ p ,k ,d

+ ∑ Fp $p ,c , d ;

p ∈ PC ; d ∈ Dm

(77)

c∈C

Besides, like can be seen in Figure 4, the flowrate of algae oil between different plants is not allowed; then the next constraint is required: Fok , p ,k ' = 0;

k , k ' ∈ K ; k ≠ k ', p ∈ PC

(78)

It should be noted in previous equations that the energy balances were not included. It is because in the proposed methodology the selection of the optimal process equipment is made from a set of available technologies, which are designed and modeled prior to the optimization process; and the used data are efficiency, capacity (upper and lower limits for flowrate and volume) and the associated capital and operating costs. In other words, this work does not consider the detailed design for the process equipment simultaneously with the optimal selection of the biorefinery pathway.



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Objective Function The objective function is to minimize the total annual cost ( Pft ) owing to the capital ( Cap ) and operating ( Cop ) costs of the technologies used for the algae oil processing, the cost to transport the algae oil to the hub processing facility and/or to the central processing facility ( Cta ), the cost to transport the products to the consumers ( Ctp )

and the piping cost ( Csp ) minus the sales of products to consumers ( Spc ) and the tax credit for the reduction of CO2 emissions ( Gse ):

Pft = Cap + Cop + Cta + Ctp + Csp − Spc − Gse

(79)

Here, the savings by the sales of products and the tax credit for the reduction of CO2 emissions are calculated as follows:

Spc = H Y

∑ ∑ Fp

t ,$ p ,d

Psp p

(80)

p∈PC d ∈Dm

Gse = H Y ∑ Fg kco2 Tcrkco2

(81)

k∈K

H Y is the annual operating time, Psp p is the product price, Tcrkco2 is the tax credit for the

reduction of CO2 emissions and Fg kco2 is the flowrate of the sequestered CO2, which is used in the photobioreactor where the algae growth takes place. According to Lassing et al.32, 2.9 co2 2 ton of CO2/ton of dry algae ( R co is determined by the following a ) are required, hence Fg k

relationship: hs , ri , out 2 Fg kco2 = R co ; a Fak

k∈K

(82)

And from the value of Fg kco2 as well as the composition (see Table S1) and density ( ρ fg ) of the flue gas, the total flue gas ( Fg kt ) can be determined:

Fg kt =

1

ψ

co2 ftg

ρ fg

Fg kco2 ;

k∈K


(83)

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ψ coftg is the weight of CO2 in 1 kg of flue gas; which is equal to 0.06204 kg CO2/kg flue gas 2

and the flue gas density is equal to 1.27x10-3 ton/Nm3 . In addition, owing to the flue gas is at a high temperature (around 90°C), this must be cooled with water to have the right temperature for the algae growing; therefore, the water flowrate to cool the flue gas of each plant ( Fwkco2 ) is determined as follows: Fwkco2 = R fgw Fg kt ,

k ∈K

(84)

R fgw is the water absorbed per Nm3 of flue gas, and Lassing et al.32 reported a value of 2x105

ton of water/Nm3 of flue gas. On the other hand, when the CO2 disolved in water is used,

it is needed a relationship to know the ratio kg water/kg CO2. Furthremore, Carrol et al.33 reported a solubility of CO2 in water at different pressures, and at 90°C and 1 atm it is 0.000214 mole of CO2/mole of H2O. Therefore, there are required around 0.5 g of CO2/kg of H2O or 2000 kg of H2O/kg of CO2; which means a great water demand and this is the reason to prefer bubble up the flue gas prior to dissolve CO2 in water. With respect to the capital cost, this is generated by the sum of the capital costs demanded in the growth stage ( Cap gs ), in the harvesting stage ( Cap hs ), in the extraction oil stage ( Cap es ) and in the algae oil processing stage ( Cap ps ): Cap = Cap gs + Cap hs + Cap es + Cap ps

(85)

In consequence the capital cost for each stage is determined by the next general relationship34:

CapQ = K F Cf Q (Y Q )

α

(86)

here the index Q represents any process stage (growth stage, harvesting stage, extraction stage and processing stage), Y Q represents the variable used to evaluate the variable cost of any process equipment and it can be either flowrate or volume, K F is the factor used to annualize the inversion and Cf Q is the fixed capital cost associated to the technologies considered during the optimization problem. Particularly, in this work Cf Q is selected for the growth and processing stages as function of the reactor volume; while for the harvesting



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and extraction stages Cf Q is selected in terms of algae concentration and equipment efficiency (ηacQ ). Thus, the following general disjunction is required to select the optimal reactor for growth and processing stages:

   ¬Z Q  Z rvQ rv     max Q min Q  M YQ ≤ Y ≤ M YQ  ∀  Y = 0     Q  Q Data  Cf rv = M CfrvQ  Cf rv = =0  While the next disjunction is used to determine the capital cost for the harvesting and extraction stages: Q   Z ac=1   Q min max M YQ ≤ Y ≤ M YQ       ZQ'   ZQ'   ZQ'  ac=1,ef=1 ac=1,ef=2 ac=1,ef=NEF      Q   ∀... Q Data    ∀ η = M ...  η acQ = 0     η ac = M Data Q ac ηQ η ac ac       Q Q Q Data  Data     Cf ac = M Cf Q Cf ac = M Cf Q  Cf ac = 0    ac   ac      Q   Z ac=NAI   Q min max M YQ ≤ Y ≤ M YQ       ZQ'   ZQ'   ZQ'   ac=NAI,ef=1   ac=NAI,ef=2   ac=NAI,ef=NEF   ;  Q Data  ...  η Q = 0     η ac = M ηQ  ∀  η acQ = M ηData Q ac ac ac        Q Q Q Data Data  Cf ac = M Cf Q  Cf ac = M Cf Q   Cf ac = 0   ac  ac      

ac ∈ AC ; ef ∈ EF

In the above disjunctions, ZrvQ , ZacQ , ZQ' ac,ef are Boolean variables to select the optimal reactor volumes, the interval of algae concentration and the efficiency for the process equipment, respectively. Furthermore, M min and M max are the lower and upper limits for the variables included, M Data is the known data related to the above variables, AC is a set to define the number of algae concentration intervals, EF is set to define the number of efficiencies for process equipment, ac is used to denote an interval of algae concentration and rv denotes the reactor volume. Previsous disjunctions are reformulated as algebraic relationships through the convex hull reformulation35, which are presented for each process stage


Page 22 of 44

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( Cap gs , Cap hs , Cap es and Cap ps ) in the Appendix B. In addition, in this appendix is presented a strategy to find the fixed capital cost as function of the algae concentration. In the same way, the operating cost is the sum of the operating costs of the equipment installed in each stage of the system: Cop = Cop gs + Cop hs + Cop es + Cop ps

(87)

Cop gs , Cop hs , Cop es and Cop ps are the unit operating costs in the growth stage, in the

harvesting stage, in the extraction oil stage and in the algae oil processing stage, respectively. And these are calculated as follows: Cop gs = H Y Cu l Deml , gs + H Y Cu n Dem n , gs + H Y Cu w ∑ Fwkf + H Y Cu w ∑ Fwkco2

(88)

Cop hs = H Y Cu l Deml ,hs

(89)

Cop es = H Y Cu l Dem l ,es

(90)

Cop ps = H Y Cu l Deml , ps

(91)

k∈K

k∈K

C u is unit cost of the resource demanded in the equipment, either electricity or nutrients,

and Dem is the demand of the resource in the equipment. Notice that for the growth stage the operating cost includes both the demands of electricity and nutrients, while for the rest of stages the operating cost just includes the electricity cost. Finally, the cost for transporting the algae oil from the extraction oil stage to the hub and to the central processing facilities, the cost to transport the products to consumers, and the piping cost are estimated as follows:

Cta = Cu s

∑ ∑ ∑ Fo

ps k , g , p ,k '

s Dkes, p,out , k ' + Cu

p∈PC k ' ∈K g∈G k ' =k

Ctp = Cu s

∑ ∑ ∑ Fp

p∈PC k∈K d ∈Dm

∑ ∑ ∑ Fo

ps k , g , p ,c

Dkes, p,out ,c

(92)

p∈PC c∈C g∈G

$ p , k ,d

Dp$ , k ,d + Cu s

∑ ∑ ∑ Fp

p∈PC c∈C d ∈Dm


$ p ,c , d

D$p ,c , d

(93)


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co2 2  D fr,k Fwrf, k D co r,k Fwr , k f co 2 2 + ∑ ∑ D fr,k Cfp r,k +p∑ ∑ + ∑ ∑ D co p ∑ ∑ r,k Cfp r,k + 3600ρs 3600ρs r ∈ GT k ∈ K r ∈ GT k ∈ K r ∈ GT k ∈ K r ∈ GT k ∈ K  es , gs  D hs,gs Fwrhs, k, gs Des,gs r,k Fwr , k hs,gs es,gs  p ∑ ∑ r,k + ∑ ∑ D es,gs + ∑ ∑ D hs,gs r,k Cfp r,k + p ∑ ∑ r,k Cfp r,k + 3600ρs  r∈GT k∈K 3600ρs r∈GT k ∈K r∈GT k ∈K r∈GT k ∈K  out D out Dinh,k Fhhin, k r,k Fwr , k p out out + D Cfp +p + ∑ ∑ Dinh,k Cfp inh,k + ∑ ∑ ∑ ∑ ∑ ∑ r,k r,k  r∈GT k∈K 3600ρs r∈GT k∈K h∈HT k ∈K 3600ρs h∈HT k ∈K  ri , out ri,out pr,out  D Fhh , k D h,k Fhhpr, k, out ri,out pr,out + ∑ ∑ D ri,out Csp = K F  p ∑ ∑ h,k Cfp + p + ∑ ∑ D pr,out ∑ ∑ h,k h,k h,k Cfp h,k 3600ρs 3600ρs h∈HT k ∈K h∈HT k ∈K h∈HT k ∈K  h∈HT k ∈K in in hs,ev hs , ev  D Fe D Fhk p ∑ k + ∑ D khs,ev Cfp khs,ev + p ∑ ∑ e,k e , k + ∑ ∑ Dine,k Cfpine,k +  k∈K 3600ρs k ∈K e∈EX k ∈K 3600ρs x∈EX k ∈K  es,out es , out out out D Fo D e,k e, k e,k Fwe , k es,out es,out out p + D Cfp + p + ∑ ∑ D out ∑ 3600ρs x∑ ∑ e,k ∑∑ e,k e,k Cfp e,k +  e∑ ∈EX k ∈K ∈EX k ∈K e∈EX k ∈K 3600ρs x∈EX k ∈K  D es,ev Fwkes ,ev  es,ev es,ev k  p ∑ 3600ρs + ∑ D k Cfp k k ∈K k ∈K 

Page 24 of 44

           +  (94)           

D , Cfp , p , C u and s are the distance (for the considered pipe segments, the algae oil and

hub and processing facilities, hub and central processing facilities and consumers), the fixed cost of the considered pipe segments, a parameter for cross-plant pipeline capital cost, the unit cost for transporting either algae or products, and the stream velocity, respectively. Notice that the piping cost includes the fixed cost and the variable cost of the pipes, where the last one is multiplied by the flowrate in the pipes. It should be noted that the proposed model is nonconvex because it has twelve bilinear terms (these bilinear terms are in Equations 6, 12, 19, 20, 27, 39, 40, 51, 53, 57, 71 and 72) and nine exponential terms (these exponential terms are in Equations B.1, B.7, B.19, B.27, B.38, B.43, B.44). Hence, it is not possible to guarantee the global optimum solution using approaches for convex problems. In this sense, a spatial branch and bound approach can be used to guarantee the global optimal solution but at expenses of the computation time. In this sense, for upper bound can be used the reformulated MINLP model as a mixed integer linear programming (MILP) problem by discretizing either the flowrate or the algae concentration for the case of bilinear terms36-38 and the exponential terms can be handled by a piecewise linearization procedure37, and for lower bound can be used the convex reformulation38. However, it is important to mention that the linearization of the great number of bilinear and exponential terms aforementioned generates a lot of binary variables, which represents a great demand of CPU time. This way, in this paper the


Page 25 of 44

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global optimal solution is not guaranteed.

5. Case Study To show the application of the proposed model, it is applied to a case study from Mexico. In this case, there are considered two power plants located in the State of Sinaloa. These are located in the cities of Los Mochis Sinaloa (25°47′N 109°00′O) and Mazatlán Sinaloa (23°14′29″N 106°24′35″O), and biodiesel is considered the only product. However,

it should be noted that the model is an indexed representation for several products. It can be seen in Equations 68-78 that depending on the required products by the consumers, there are fixed the type and demand of products as well as the technologies considered to obtain them. It means that different products can be considered simultaneously. The above mentioned power plants generate around 1’912 GWh (Los Mochis) and 2’434 GWh (Mazatlán)39, which imply emissions by 170 tonCO2/h and 216 tonCO2/h, respectively. This represents approximately a potential production of 40-50 ton/h of biodiesel. On the other hand, Table S2 shows the States of Mexico with the highest diesel demand for the agricultural activity40. It must be noted that the total diesel demand is around 56 ton/h; therefore, there are economic and environmental opportunities for the biodiesel production from algae in the State of Sinaloa (25°00′10″N 107°30′10″O). In that sense, the aforementioned states are distributed into four groups (see Table S2) with the purpose of determining the optimal distribution for the biodiesel produced in the biorefineries located in the cities of Los Mochis and Mazatlán. Then, group 1 is composed just by the State of Sinaloa, where the main consumer is the City of Culiacán (24°48′00″N 107°23′00″O),

whose biodiesel demand is between 4 and 4.5 ton/h. While for the group 2, the main consumer is the city of Chihuahua (28°38′07″N 106°05′20″O) and it requires around 10-12 ton/h to satisfy the biodiesel consumed in the states of Sonora (29°38′46″N 110°52′08″O), Durango (24°56′05″N 104°54′43″O) and Chihuahua (28°48′51″N 106°26′22″O). And the

consumer of group 3 is the city of Ciudad Victoria Tamaulipas (23°44′00″N 99°08′00″O), and it demands between 15 ton/h and 20 ton/h. Finally, the consumer of group 4 is the city of Guadalajara Jalisco (20°39′58″N 103°21′07″O) with demands between 18 ton/h and 20 ton/h. In the Figure S1 is presented a map of México to give the allocation of biorefineries and consumers.



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From the above, the city of Guadalajara as a potential option to install a central processing facility. Besides, there are possibilities to install hub processing facilities in the

cities of Los Mochis and Mazatlán. In this regard, Table S3 shows the distances between these processing facilities and consumers. In addition, for designing the biorefineries, there are taken into account two technologies for the growth, harvesting and extraction stages. While in the processing stage, there are included five technologies. The economic data of these technologies are given in Table S4; and the efficiencies for each stage are: a) 85 % for sedimentation tanks, b) 100 % for oil extraction and c) 90 % for conversion in the transesterification reactors. Besides the unitary electricity and water costs correspond to the cost associated to the Mexican State of Sinaloa. Particularly, the values for parameters l n l,es,pump l,ps , R l,es,ctf , R l,ps are 0.13 US$/ton, 0.089 Cu w , Cu l , R r,k , Cu n , R r,k , R k k k , Rc

US$/kWh, 238 kWh/ton of dry algae, 0.400 US$/kg of nutrients, 271 kg of nutrients/ton of dry algae, 0.0655 kWh/ton, 1.3 kWh/ton, 32 kWh/ton and 32 kWh/ton, respectively. Finally, the biodiesel price is 3.69 US$/gal and R lh,k was not considered because it was included the harvesting method in the harvesting stage. In the Appendix B can be found the associated references of the above values. A list of the used technologies for each plant is the following: two photobioreactors (for the growth stage), two sedimentation tanks (for the harvesting stage), two ultrasounds and two sedimentation tanks (for the extraction stage), one unit for the oil pretreatment and five transesterification reactor (for the processing stage); and the detailed information for this technologies is presented in the supplementary material section (see Table S4).

6. Analysis of Results In order to identify the advantages of the distributed system, the case study is solved considering both configurations, the distributed system (Scenario A) as well as centralized system (Scenario B). It is important to mention that in the Scenario A the existence of hubs and central processing facilities is considered simultaneously; and in the Scenario B includes only the possibility to select the central processing facilities. Therefore, for the last case, all the binary variables associated to the reactors of the hub processing facilities are fixed as zero before to the optimization process.


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The obtained results are shown in Table 1, it should be noted that Scenario A represents a total annual cost 63% lower than the one of Scenario B; this saving is because the algae transportation cost is significantly reduced in Scenario A due to the existence of several processing facilities. Figure 5 shows the optimal configuration for Scenario A; where the flue gas coming from the thermoelectric plant is transported to four photobioreactors (two for each thermoelectric) whose volumes are optimized. In the harvesting stage one sedimentation tank for each plant is used, while the extraction stage is composed by one ultrasound equipment and sedimentation tanks. Specifically in the plant located in Los Mochis the reactors 1 and 5 were selected; and with respect to the plant of Mazatlán the reactors 3 and 5 are needed.

From the above analysis, it must be noted that the optimal processing stage does not include the central processing facilities. Therefore, the biodiesel is sent to consumers from each hub and it allows savings by US$18.9 million. But, the biodiesel transportation cost is increased by US$6.6 million with respect to the cases where the biodiesel is obtained and sent to the consumers from the central processing facilities. It happens because the simultaneous optimization of central and hub processing facilities allows to compensate those components related the total transport cost. For example, Figure 5 shows that the hub processing facility located in Los Mochis sends the biodiesel demanded by the consumers located in Culiacán, Chihuahua as well as part of the demand by the consumers located in Ciudad Victoria, whose remaining demand is sent from the hub facility located in Mazatlán. In addition, the last hub processing facility sends biodiesel to the consumer

located in Guadalajara. In addition, Figure 6 presents the optimal configuration for Scenario B, which is similar to Figure 5 in the part previous to the processing stage, where the selected central processing facility is located in Guadalajara. Here four reactors are used to process the algae oil coming from Los Mochis and Mazatlán (the biodiesel distribution for the Scenario B is given in Figure 7). Another important aspect to highlight in Figures 5 and 6 is that water integration allows reducing the fresh water used and the wastewater discharged to the environment. Specifically, in both configurations there is a reduction of about 83 % of fresh water.



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Finally, Figure 7a shows the distribution of costs for Scenario A, notice that the growing stage represents the biggest capital and operating costs. It should be noted that the remaining stages represent only around 17 % of the total annual cost; but this investment generates an income that represent 92 % of the total annual cost, while the tax credit is 2 % of the total annual cost (see Figure 7b). Even with these incomes, it is not possible to obtain positive profits. Therefore, the cost of algae-based biorefinery must be seen as a part of the processing cost associated to treat the flue gases.

7. Conclusions A mixed integer non-linear programming problem is proposed for determining the optimal design and allocation of algae-based biorefineries using CO2 from different facilities. The proposed model is based on a superstructure that includes several technologies in each process stage (algae growth, harvesting, extraction and processing), which are modeled accounting for efficiencies and capacities. Also, the economies of scale are considered because it is possible to have either a distributed or centralized processing system, and the water integration for the different process stages is also involved to reduce the fresh water demand, the wastewater discharged to the environment as well as its cost. The results show the importance to use flue gases as source of CO2 for the algae growing and the positive economic effects related to the biomass processing to reduce the cost associated to the growing stage, while these represent the greatest cost, and the investment and operating costs of the remaining stages are reduced almost 90%. Furthermore, the use of waste CO2 could represent an environmental benefit, but to confirm it, there must be considered a proper methodology to evaluate the environmental impact. Finally, one interesting result for the case study is that for the Scenario A, the central processing facility was not selected. The main reason is that the fixed location for this central processing facility is far from the considered power plants. It is noteworthy that this is not general for other cases. In addition, for Scenario B, the only central processing facility was selected.


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Supporting Information Section The supporting information section contains the Appendices and includes detailed information for the case study. This information is available free of charge via the Internet at http://pubs.acs.org/.

Nomenclature Ca

algae concentration, ton algae/ton or kg/m3

Cap

capital cost, US$/year

Cfp

fixed cost of the considered pipe segments, US$//m

Cop

operating cost, US$//year

Cta

cost to transport the algae oil, US$//year

Ctp

cost to transport the product, US$//year

Csp

piping cost, US$//year

Cu

unit cost of the resource demanded in the equipment, US$/kWh or US$/kg or US$/ton or US$/km ton.

Dem

utility demand, kW or kg/h

D

distance for the considered pipe segments, m

Fa

algae flowrate, ton/h

Fcp

cell paste flowrate, ton/h

Fcpw

water flowrate in the cell paste, ton/h

Fcw

cell walls flowrate, ton/h

Fe

flowrate associated to the extraction stage, ton/h

Fg

flue gas flowrate, ton/h

Fh

flowrate associated to the harvesting stage¸ ton/h

Fo

algae oil flowrate, ton/h



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Fp

product flowrate, ton/h

Fr

photobioreactor flowrate, ton/h

Fw

water flowrate, ton/h

Fwaste

flowrate in the environment discharge, ton/h

Gse

tax credit for the reduction of CO2 emissions

HY

annual operating time, h/year

KF

factor used to annualize the investment, year-1

M Data

known data

M max

upper limits

M min

lower limit

p

parameter for cross-plant pipeline capital cost,

Pft

total annual cost, US$//year

Pspp

product price, US$/gal

Spc

sales of products to consumers, US$/year

R

relationship, water/Nm3 or ton of CO2/ton of dry algae or

s

velocity, m/s

Tcrkco2

tax credit for the reduction of CO2 emissions,

v

photobioreactor volume, m3

YQ

variable used to evaluate the variable cost of any process equipment, ton/hr or m3

Boolean variables Z rvQ

Boolean variables to select the optimal reactor volumes, false or true

Z acQ

Boolean variables to select the optimal interval of algae concentration, false or true


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ZQ' ac,ef

Boolean variables to select the optimal efficiency for the process equipment, false or true are

Greek symbols µ

specific growth rate¸ h-1

η

efficiency, dimensionless

ε

percent of oil content in dry algae, dimensionless

ω

dry weight of cell paste, dimensionless

ψ

weight of CO2 in 1 kg of flue gas, kg CO2/kg flue gas

ρ

density, ton/Nm

3

Subscripts ac

algae interval

rv

rector volume

c

technologies located in the central processing facilities

d

consumer

e

extraction method

g

processing method

Superscripts CO2

carbon dioxide

f

fresh sources

n

nutrients

hs

harvesting stage

gs

growing stage



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

es

extraction stage

ps

processing stage

in

inlets

out

outlets

pr

poor streams

ri

rich streams

t

total flowrates

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27. Gong, J.; You, F., Value-added chemicals from microalgae: Greener, more economical, or both? ACS Sustain. Chem. Eng. 2014, 3, (1), 82-96. 28. You, F.; Wang, B., Life cycle optimization of biomass-to-liquid supply chains with distributed–centralized processing networks. Ind. Eng. Chem. Res. 2011, 50, (17), 1010210127. 29. Yue, D.; Kim, M. A.; You, F., Design of sustainable product systems and supply chains with life cycle optimization based on functional unit: general modeling framework, mixed-integer nonlinear programming algorithms and case study on hydrocarbon biofuels. ACS Sustain. Chem. Eng. 2013, 1, (8), 1003-1014. 30. Yue, D.; Gong, J.; You, F., Synergies between geological sequestration and microalgae biofixation for greenhouse gas abatement: Life cycle design of carbon capture, utilization, and storage supply chains. ACS Sustain. Chem. Eng. 2015, 3, (5), 841-861. 31. Brooke, A.; Kendrick, D.; Meeraus, A., GAMS - A user's guide. The Scientific Press: Redwood City, CA, 2014. 32. Lassing, M.; Martensson, P.; Olsson, E.; Svensson, M. Biodiesel Production from Microalgae-A Feasibility Study; Lund University: Oslo, Norway, 2008. 33. Carroll, J. J.; Slupsky, J. D.; Mather, A. E., The solubility of carbon dioxide in water at low pressure. J. Phys. Chem. Ref. Data 1991, 20, (6), 1201-1209. 34. Ulrich, G. D., A guide to chemical engineering process design and economics. Wiley New York, NY, 1984. 35. Vecchietti, A.; Lee, S.; Grossmann, I. E., Modeling of discrete/continuous optimization problems: characterization and formulation of disjunctions and their relaxations. Comput. Chem. Eng. 2003, 27, (3), 433-448. 36. Pham, V.; Laird, C.; El-Halwagi, M., Convex hull discretization approach to the global optimization of pooling problems. Ind. Eng. Chem. Res. 2009, 48, (4), 1973-1979. 37. Rubio-Castro, E.; Ponce-Ortega, J. M. a.; 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. 38. Rubio‐Castro, E.; Ponce‐Ortega, J. M.; Serna‐González, M.; El‐Halwagi, M. M.; Pham, V., Global optimization in property‐based interplant water integration. AIChE J. 2013, 59, (3), 813-833. 39. National Council of Electricity (CFE) in Mexico. http://app.cfe.gob.mx/Aplicaciones/CCFE/Tarifas/Tarifas/tarifas_industria.asp 40. Secretariat of Agriculture, Livestock, Rural Development, Fisheries and Food (SAGARPA) in México. http://www.sagarpa.gob.mx/Paginas/default.aspx


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Caption for Figures Figure 1. General production system to the algae oil processing Figure 2. Proposed superstructure for algae oil processing Figure 3. Mass balance in the growth, harvesting and extraction stages Figure 4. Mass balance in the algae oil processing and product distribution stages Figure 5. Optimal configuration for Scenario A Figure 6. Optimal configuration for Scenario B Figure 7. Costs for Scenario A



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Figure 1. General production system to the algae oil processing


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Figure 2. Proposed superstructure for algae oil processing



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PLANT k-1 Fwkf

GROWTH STAGE

Demkn co2 Fw1,1 Fw1,1f es , gs Fw1,1

HARVESTING STAGE

n Dem1,1

in 1,1

Fr

r-1

Fr1,1out

in Fh1,1

h-1

hs , gs Fh1,1

Fwkco2

co2 Fw2,1

f 2,1 es , gs 2,1 hs , gs 2,1

Fw Fw Fh

co2 GTN ,1

Fw

f FwGTN ,1

es , gs FwGTN ,1 hs , gs FhGTN ,1

EXTRACTION STAGE

ri ,out Fh1,1

in 1,1

Fo

Fe

Fh1,1pr ,out

e-1

n Dem2,1

in Fr2,1

PT-2 r-2

out Fr2,1

Fr1gs ,out

in Fh2,1

Fa1gs ,out

PT-2 h-2

gs , out 1

Fw n GTN ,1

Fh1hs , ri , out

ri ,out Fh2,1

pr ,out Fh2,1

ri ,out FhHTN ,1

in FhHTN ,1

r-N

h-N

pr ,out FhHTN ,1

Fo1es , out

out Fcp2,1 out Fw2,1

ex ,out FoEXN ,1

in FeEXN ,1

out FrGTN ,1

Fcp Fw

ex ,out Fo2,1

e-2

Fw1hs , ri , out

Dem

in FrGTN ,1

in Fe2,1

Fa1hs , ri , out

Fcp1es.out

ex ,out 1,1 out 1,1 out 1,1

e-N

out FcpEXN ,1 out FwEXN ,1

Fw1es.out

Fh1hs , pr , out

Fa1hs , pr , out Fw1hs , pr , out

Fw1es , ev

Fh1hs , gs

Fa1hs , gs Fw1hs , gs

Fh1hs , ev

Fw1es , gs

PLANT k-N

Figure 3. Mass balance in the growth, harvesting and extraction stages


Fw1ev

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Fo1,1,1

Fo1es ,out

Fo1, PCN ,1

in Fo1,1

in FoPCN ,1

Fp1,1

$ Fp1,1,1

FpPCN ,1

t ,$ Fp1,1

t ,$ FpPCN ,1

Fo1,1,1 in Fo1,1

Fp1,1

FoKN ,1,1

Fo1,CPN ,1 in FoCPN ,1

FpCPN ,2

FoKN ,CPN ,1 es , out FoKN

FoKN ,1, KN

FoKN , PCN , KN

Fo1,inKN

in FoPCN , KN

Fp1,KN

FpPCN , KN

Fp1,t ,$DMN

t ,$ FpPCN , DMN

Figure 4. Mass balance in the algae oil processing and product distribution stages



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Figure 5. Optimal configuration for Scenario A


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Figure 6. Optimal configuration for Scenario B



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a)

b)

Figure 7. Costs for Scenario A


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Caption for Tables Table 1. Results for the case study



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Table 1. Results for the case study

8.419 409.05 27.956 276.982 146.425

Scenario B: Centralized System 23.139 407.407 27.956 277.029 147.182

0

18.929

21.633

15.024

0.385 5,892 36,242 795 115 688 182.3

0.338 6,626 36,242 805 115 688 173.1

Scenario A: Distributed System Total annual cost (million US$/year) Sales of products (million US$/year) Tax credit (million US$/year) Capital cost (million US$/year) Operating cost (million US$/year) Cost to transport the algae oil (million US$/year) Cost to transport the biodiesel (million US$/year) Piping cost (million US$/year) Fresh water (ton/h) Nutrients (kg/h) Number of equations Binary variables Continuous variables CPU time (s)


Optimal Design of Distributed Algae-Based Biorefineries Using CO2

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