<figure><img src="image_1.png" /></figure>

HAL
open science

# A Sequential Fast Pyrolysis Facility Location-Allocation Model

Yihua Li, Guiping Hu

► To cite this version:

Yihua Li, Guiping Hu. A Sequential Fast Pyrolysis Facility Location-Allocation Model. 20th Advances in Production Management Systems (APMS), Sep 2013, State College, PA, United States. pp.409-415, 10.1007/978-3-642-41266-0_49 . hal-01452140

HAL Id: hal-01452140

https://inria.hal.science/hal-01452140

Submitted on 1 Feb 2017

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A sequential fast pyrolysis facility location-allocation model

Yihua Li¹ and Guiping Hu¹, *

¹ Industrial and Manufacturing Systems Engineering, Iowa State University
Ames, IA, 50011, USA

**Abstract.** The revised Renewable Fuel Standard (RFS2) mandates the U.S. consume16 billion gallons per year (BGY) of biofuels from cellulosic sources by the year 2022. Fast Pyrolysis of biomass is a renewable conversion process developed for producing liquid transportation fuels, such as gasoline and diesel. The pathway investigated in this study is fast pyrolysis and hydroprocessing to produce transportation fuels from corn stover. A mathematical model is formulated to study the supply chain design problem. The objective is to optimize an orderly fast pyrolysis facility locations and capacities that maximize the net present value (NPV) of the total profit for the next 10 years (2013-2022). Numerical examples for Iowa are also presented.

**Keywords:** cellulosic biofuels, fast pyrolysis, sequential location

## 1 Introduction

Biofuels has been recognized as important sources of renewable energy for their potential benefit on the environment, rural development, and reducing dependency on petroleum import. With the stimulation of enactment of Renewable Fuel Standard (RFS2) (1) in 2007, cellulosic based biofuels are gaining more attention. Biofuel industry can help improve the rural economics and job creation. Cellulosic biofuel production technologies are still mainly on the experimenting stage (2, 3). Studies on biomass logistics and biofuel supply chain management are also emerging. Stephen et al. show technology selection strategy based on biomass moisture content, energy density and load capacity of different transportation mode (4). Kocoloski et al. develop a mathematical model to optimize facility placement, and examine the impact of location and sizing selection (5). Ekşioğlu et al. propose a mixed integer programming model to design supply chain and manage logistics con-

* Corresponding author: Guiping Hu
Email address: gphu@iastate.edu
sidering biomass transportation, inventory and process ability (6). And
intermodal transportation is taken into consideration in the following
work (7). In this paper, a sequential location allocation model for the
fast pyrolysis facilities is investigated. Formulations are presented in
Section 2, and case study based on Iowa is included in Section 3. Paper
concludes in Section 4 with major findings and future research direc-
tions.

## 2 Methodology

### 2.1 Problem description

This study considers lignocellulosic biomass as the feedstock for fast
pyrolysis facility to produce bio-oil, and the bio-oil will be used as
feedstock of biorefinery, where it is converted to liquid transportation
fuels. Fig. 1 illustrates the supply network setting.

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Supply chain structure for cellulosic biomass pyrolysis – hydroprocessing – refining process</figcaption></figure>

Major assumptions used in modeling are listed as follows:

1. Facility construction time is one-year and the facility life is 20-year.

2. A biorefinery with enough capacity exists in Iowa, and the location of the biorefinery is the county centroid that minimizes the total annual cost if all facilities are at optimal locations and capacities.
3. The facility location and material (feed and products) allocation decisions are made to maximize total profit of all facilities as a system.

4. The requirement for Iowa biofuel consumption in transportation increase linearly from 2013 to 2022, with demand in 2013 set at 0, and in 2022 set as the total gasoline demand within Iowa.

5. Fast pyrolysis and hydroprocessing for the cellulosic biomass are performed at distributed fast pyrolysis facility, while the hydroprocessed bio-oil are refining to gasoline/diesel range fuels in a centralized biorefinery.

6. Annual budget is set for construction of the distributed fast pyrolysis facilities.

## 2.2 Model formulation

Notations:

i Index for biomass supply locations

j Index for candidate fast pyrolysis facility locations

k Index for gasoline demand locations

l Index for fast pyrolysis facility capacity level

t Index for time period (decision making time)

GP<sub>t</sub> Projected gasoline price (8)

BCC<sub>i</sub> Unit biomass collecting cost (9)

BSC<sub>ij</sub> Unit biomass shipping cost (10, 11), BSC<sub>ij</sub> = FSC + VSC × D<sub>ij</sub>, which is a combination of fixed shipping cost and variable shipping cost (related to shipping distance)

HSC<sub>j</sub> Unit hydroprocessed bio-oil shipping cost (11, 12)

GSC<sub>k</sub> Unit gasoline shipping cost (12)

FOC<sub>l</sub> Fixed facility operating cost (3)

GCC Gasoline conversion cost, derived from variable facility operating cost, related to facility operating level (proportional to gasoline production amount) (3)

FFC<sub>l</sub> Fast pyrolysis facility capital cost, using scaling factor of 0.6 (3)

AFC<sub>l</sub> Amortized fast pyrolysis facility capital cost, derived from facility capital cost, with facility life of 20-year (3)

SPP<sub>it</sub> Maximum biomass supply amount, total corn stover available amount (13, 14) times maximum removal proportion (15)

loss Biomass loss during transportation, assumed to be 5 wt%

θ<sub>1</sub> Conversion ratio from cellulosic biomass to hydroprocessed bio-oil (3)
$\theta_2$ Conversion ratio from hydroprocessed bio-oil to gasoline diesel fuel (3)

$\overline{Dmn}_k$ Total gasoline demand level (16)

$Dmn_t$ Gasoline demand, $Dmn_{kt} = \sum_k \overline{Dmn}_k \times pr_t$, $pr_t$ is the mandate proportion of total demand to be satisfied during the $t^{th}$ year

$F_t$ Fund raised from government or company

$r$ Annual interest rate, assumed to be 10%

$x_{ijt}$ Cellulosic biomass shipping amount (decision variable)

$y_{jt}$ Hydroprocessed bio-oil shipping amount (decision variable)

$z_{kt}$ Gasoline shipping amount (decision variable)

$A_t$ Total available fund (decision variable)

$\delta_{jlt}$ Indicator of fast pyrolysis facility construction state (decision variable)

Mixed integer linear programming method is used to formulate the sequential location and allocation problem. The objective is to maximize the net present value (NPV) of the total profit of the next 10 years (2013-2022). Total profit calculation considers revenue from selling products, feedstock costs (collecting and shipping costs), intermediate product (hydroprocessed bio-oil) shipping costs, final products shipping costs, facility capital cost, and operating costs (reflected by fixed operating costs and conversion cost).

Objective function is presented below:

$$ \max \sum_{t=1}^{T} (1+r)^{-t} \left( \sum_{k=1}^{K} z_{kt} (GP_t - GCC) - \sum_{i=1}^{N} \sum_{j=1}^{M} (BSC_{ij} + BCC_i) x_{ijt} - \sum_{j=1}^{M} HSC_j y_{jt} - \sum_{k=1}^{K} GSC_k z_{kt} - \sum_{j=1}^{M} \sum_{l=1}^{L} FOC_l \delta_{jlt} \right) - \sum_{t=1}^{T} (1+r)^{-t} \sum_{j=1}^{M} \sum_{l=1}^{L} AFC_l \delta_{jlt} \quad (1) $$

Major constraints include: biomass supply availability due to total grown amount and sustainability factor (2), biofuel conversion balance with conversion ratios from pathway techno-economic analysis (3,6), fast pyrolysis facility existence and capacity limit (4), a maximum of one facility per candidate facility construction location (5), no destruction of facility (9), minimum demand requirement and demand upper bound with linearly increase demand each year (7,8), limited available construction budget (10-12), and initialization of current situation of fast pyrolysis facility, which is none of such facilities exist at current stage (13).
$$ \sum_{j=1}^{M} x_{ijt} \leq Spp_{it}, \forall i, t \quad (2) $$

$$ y_{jt} = (1 - loss) \theta_1 \sum_{i=1}^{N} x_{ijt}, \forall j, t \quad (3) $$

$$ (1 - loss) \sum_{i=1}^{N} x_{ijt} \leq \sum_{l=1}^{L} \delta_{jlt} C_l, \forall j, t \quad (4) $$

$$ \sum_{l=1}^{L} \delta_{jlt} \leq 1, \forall j, t \quad (5) $$

$$ \theta_2 \sum_{j=1}^{M} y_{jt} = \sum_{k=1}^{K} z_{kt}, \quad \forall t \quad (6) $$

$$ \sum_{k=1}^{K} z_{kt} \geq \sum_{k=1}^{K} Dmn_{kt}, \quad \forall t \quad (7) $$

$$ Dmn_{kt} \geq z_{kt}, \quad \forall k, t \quad (8) $$

$$ \delta_{j,l,t} \geq \delta_{j,l,t-1}, \quad \forall j, l, t \geq 2 \quad (9) $$

$$ \sum_{j=1}^{M} \sum_{l=1}^{L} FFC_l \delta_{j,l,2} \leq F_1 \quad (10) $$

$$ \sum_{j=1}^{M} \sum_{l=1}^{L} FFC_l (\delta_{j,l,t+1} - \delta_{j,l,t}) \leq A_{t-1}(1+r) + F_t, \quad (11) $$

$$ \forall T - 1 \geq t \geq 2 $$

$$ A_t = A_{t-1}(1+r) + F_t - \sum_{j=1}^{M} \sum_{l=1}^{L} FFC_l (\delta_{j,l,t+1} - \delta_{j,l,t}), \quad (12) $$

$$ \forall T - 1 \geq t \geq 2 $$

$$ \delta_{j,l,1} = 0, \quad \forall j, l \quad (13) $$

$$ x_{ijt}, y_{jt}, z_{kt} \geq 0, \delta_{jlt} \in \{0,1\}, \forall i, j, k, l, t \quad (14) $$

# 3 Results and discussion

In this section, the results of a case study in Iowa are illustrated. Candidate fast pyrolysis facility locations are the county centroids in Iowa, and four facility capacities are allowed: 400, 1000, 1500, and 2000 metric ton of dry basis biomass per day, respectively.

To satisfy the minimum demand requirement, available fund per year needs to be at least enough to construct two 2000 metric ton/day facilities. The results under this minimum budget scenario are shown in Fig. 2. The county that is assumed to locate the existing biorefinery is represented using cross-shaded lines. Stars represent the fuel demand locations (centroids of MSAs), and star sizes illustrate the magnitude of fuel demand from the MSAs. From the results, all facilities built are of

Fig. 2. The county that is assumed to locate the existing biorefinery is represented using cross-shaded lines. Stars represent the fuel demand locations (centroids of MSAs), and star sizes illustrate the magnitude of fuel demand from the MSAs. From the results, all facilities built are of
the highest allowed capacity, and in the figure, different color circles
are used to represent the difference in construction order. The labeled
year is the first year the corresponding facility starts to operate (con-
struction finished). Facility locations are listed in legend, using FIPS
codes of facility-located counties. The optimal NPV in the scenario is
$5.28 billion.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Sequential facility construction under annual fund of twice the capital cost of 2000 metric ton/day facility</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Sequential facility construction under annual fund of 2.5 times capital cost of 2000 metric ton/day facility</figcaption></figure>

If annual available fund increases to 2.5 times capital cost of 2000 met-
ric ton/day facility, the results are shown in **Fig. 3**. It could be seen in
the figure, that with more available fund, it takes fewer years to finish
constructing all facilities needed for the demand goal in 2022. The op-
timal NPV in the scenario is $6.03 billion.

Comparing the results under different budget limitations, several obser-
vations are summarized as follows:

* All facilities are built with the highest allowed capacity level. This is due to the scaling factor in capital cost estimation, which makes larger capacity facilities more cost-effective.

* Facility locations are very much affected by the centralized biorefinery location. From the yearly allocation results, most biomass supply could be satisfied within the facility-located county; therefore, hydroprocessed bio-oil shipping costs become a major concern in facility location decisions. To minimize the transportation costs, locating fast pyrolysis facilities close to biorefinery is the optimal option.

* With the increase in annual available fund, the overall sequence of fast pyrolysis facility construction does not change much. It's noticed that with higher available fund, facilities tend to build earlier to achieve a higher NPV.

# 4 Conclusion

Biofuels have become increasingly attractive to replace petroleum
fuels. In this study, the pathway of fast pyrolysis, hydroprocessing and
refining is considered to produce gasoline-diesel ranged fuels from cel-
lulosic biomass. Mixed integer linear programming models are formu-
lated to investigate the supply network design and the sequence of the
facility construction. The objective is to maximize the NPV of the total
profit till 2022, which is the target year of RFS2. A case study in Iowa
is conducted to illustrate the modeling approach. Numerical results
show the preference for high capacity facilities, facility locations that
are close to existing biorefinery, and earlier construction time as long as
the budget allows. It is also concluded that the increase in annual avail-
able fund level does not have much impact on the construction se-
quence.

It should be noted that this sequential facility location problem is an
ongoing research work that can be further investigated. Better data or
modeling information, including the annual requirement of bio-based
fuels, annual budget, and uncertainties in the feedstock availability and
logistic cost, are to be investigated for more realistic decision making.
In addition, facility capacity expansion could also be taken into consid-
eration in the modeling framework.

References

1. Coyle WT. Next-Generation Biofuels: Near-Term Challenges and Implications for Agriculture: DIANE Publishing Company; 2010.

2. Brown TR, Zhang Y, Hu G, Brown RC. Techno-economic analysis of biobased chemicals production via integrated catalytic processing. Biofuels, Bioproducts and Biorefining. 2012;6(1):73-87.

3. Wright MM, Daugaard DE, Satrio JA, Brown RC. Techno-economic analysis of biomass fast pyrolysis to transportation fuels. Fuel. 2010;89, Supplement 1(0):S2-S10.

4. Stephen JD, Mabee WE, Saddler JN. Biomass logistics as a determinant of second-generation biofuel facility scale, location and technology selection. Biofuels, Bioproducts and Biorefining. 2010;4(5):503-18.

5. Kocoloski M, Michael Griffin W, Scott Matthews H. Impacts of facility size and location decisions on ethanol production cost. Energy Policy. 2011;39(1):47-56.

6. Ekşioğlu SD, Acharya A, Leightley LE, Arora S. Analyzing the design and management of biomass-to-biorefinery supply chain. Computers & Industrial Engineering. 2009;57(4):1342-52.

7. Ekşioğlu S, Li S, Zhang S, Sokhansanj S, Petrolia D. Analyzing Impact of Intermodal Facilities on Design and Management of Biofuel Supply Chain. Transportation Research Record: Journal of the Transportation Research Board. 2010;2191(-1):144-51.

8. Petroleum product prices, U.S. Energy Information Administration.

9. Graham RL, Nelson R, Sheehan J, Perlack RD, Wright LL. Current And Potential U.s. Corn Stover Supplies. Agron. J. 2007;99(1):1-11.

10. Searcy E, Flynn P, Ghafoori E, Kumar A. The relative cost of biomass energy transport. Applied Biochemistry and Biotechnology. 2007;137-140(1):639-52.

11. CBO. Energy use in freight transportation. Congressional Budget Office (CBO); 1982.

12. BTS. Average Freight Revenue per Ton-mile. Bureau of Transportation Statistics, http://www.bts.gov/publications/national_transportation_statistics/html/table_03_21.html (accessed November, 2012).

13. USDA/NASS Quickstats.

14. Heid WG. Turning Great Plains crop residues and other products into energy / Walter G. Heid, Jr. Washington, D.C. :: U.S. Dept. of Agriculture, Economic Research Service; 1984.

15. Papendick RI, Moldenhauer WC. Crop Residue Management to Reduce Erosion and Improve Soil Quality: Northwest. U.S. Department of Agriculture Conservation Research Report; 1995:10-6.

16. DOE/EIA. Annual Energy Review 2010. 2011.