Supply Chain MILP Model Integrating Biorefining Technology

Subscriber access provided by Kaohsiung Medical University

Process Systems Engineering

Supply chain MILP model integrating biorefining technology superstructure Anna Panteli, Sara Giarola, and Nilay Shah Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05228 • Publication Date (Web): 31 May 2018 Downloaded from http://pubs.acs.org on May 31, 2018

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

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

Page 1 of 56 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

Industrial & Engineering Chemistry Research

Supply Chain MILP Model Integrating Biorefining Technology Superstructure Anna Panteli,† Sara Giarola,‡ and Nilay Shah∗,† †Centre for Process Systems Engineering, Chemical Engineering Department, Imperial College London, South Kensington Campus, London SW7 2AZ, UK ‡Earth Science & Engineering Department, Imperial College London, South Kensington Campus, London SW7 2AZ, UK E-mail: [email protected] Abstract A crucial element of the quest of curbing carbon dioxide emissions is deemed to rely on a biobased economy, which will rely on the development of financially sustainable biorefining systems enabling a full exploitation of lignocellulosic biomass (and its macrocomponents, i.e. cellulose, hemicellulose and lignin) for the co-production of biofuels and bioderived platform chemicals. In this work, a general modelling framework conceived to steer decision-making regarding the strategic design and systematic planning of advanced biorefining supply networks is presented. The design task is formulated as a mixed integer linear program (MILP) which accounts for the maximisation of the supply chain profit, considering multi-echelon, multi-period, multi-feedstock and multiproduct aspects as well as spatially explicit features. The applicability of the proposed model, along with the use of a bi-level decomposition approach, are demonstrated with a case study of lignocellulose-based biorefining production systems in the South-West of Hungary. Results show the effectiveness of the tool in the decision-making regarding the systematic design of advanced biorefining SC networks. An economic analysis

1

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 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

of different design configurations (i.e. centralised and distributed scenarios) through a holistic evaluation of the entire biobased SC, integrating technology superstructure, shows that both instances generate profitable investment decisions that could be equally trusted by the decision-maker unless regional restrictions are applied.

1

Introduction

1.1

Background

In the last few years, dependence on limited fossil resources, energy security as well as environmental health, have become major societal concerns, leading to a growing interest into renewable-based alternatives. Reports of the Intergovernmental Panel on Climate Change (IPCC) 1 have driven governments across the world to set mandatory renewable energy and greenhouse gas (GHG) emissions reduction targets for promoting and increasing the share of renewable materials and energy. The European Commission (EC), accordingly, has established several ambitious targets by 2020, such as 20% share of energy from renewable resources, 20% improvement in energy efficiency, 10% share of renewables in the transport sector, as well as GHG emissions reductions reaching a minimum threshold of 35% from 2009, 50% from 2017 and 60% from 2018 onwards. 2 Biomass is considered as a viable renewable source option, gaining great interest during recent years, due to its capability of generating electric and thermal energy, as well as producing liquid biofuels (e.g. bioethanol) for automotive purposes, in a near carbon-neutral manner, along with several platform chemicals. 3 In addition to improving energy security and GHG emissions, the development of biorenewable value chains can support the development of a thriving rural economy. 4 Athough the current production of biofuels is based on first generation technologies, the use of food crops has raised serious social concerns. Hence, the primary research focus has been on the development of second generation technologies that use non-food energy crops as well as biomass waste. 3,5 Advanced biorefining systems

2


Page 2 of 56

Page 3 of 56 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


use such technologies to treat lignocellulosic biomass for the co-production of biofuels along with bioderived chemical products 6 . However, certain challenges need to be addressed before such novel production systems can reach commercialisation. In this perspective, the temporal availability of lignocellulosic biomass requires the consideration of storage-related issues, such as storage location and its role in dictating supply chain (SC) structure, in order to ensure a continuous biomass supply. Local availability is considered to be an additional lignocellulosic biomass characteristic that should be properly taken into account as it affects the design of the biobased SC in terms of capacity output, location and transport modes. Another key issue related to lignocellulosic biomass is the complexity of the biobased product portfolios deriving from its treatment, imposing the need of a potentially full exploitation of the biomass value. This could be achieved through the examination of biomass pretreatment, which deals with the fractionation of biomass into its three macrocomponents, i.e. cellulose, hemicellulose and lignin, and usually represents the highest cost part of the entire biorefining network. It is apparent that the feasibility study of advanced biorefineries requires a comprehensive modelling of a full SC, which includes all the steps from biomass availability to the market of final products, as well as all the constraints in the biomass transformation (the so-called technology superstructure). Process Systems Engineering (PSE) tools and optimisation methods, based on mathematical programming, could boost the efficiency of decision-making in such advanced biorefining systems. In this framework, a suitable decision-making technique often proposed for such complex modelling and optimisation tasks of undetermined infrastructures, is Mixed Integer Linear Programming (MILP). 8,9

3


Upstream

Downstream

. . .

. . .

Biomass storage

Biomass pretreatment

Intermediates storage

. . .

. . .

. . .

. . . Biomass cultivation

Final product production

Demand centres

Transportation modes Figure 1: Biobased supply chain network. 7

1.2

Literature review

Research in the area of biobased SC optimisation was initiated by the consideration of first generation technologies. In this context, Zamboni et al. (2009) generated an MILP model for the cost-optimal spatially explicit design of bioethanol SC networks under steady state conditions. The model was applied to an Italian corn-based ethanol production system. 10 Akgul et al. (2011) developed MILP models for the optimal design of bioethanol SCs, applied to a case study of corn-based bioethanol production in Northern Italy with the aim to minimise the total SC cost. 11 Another MILP modelling framework, was presented by Bowling et al. (2011), for the maximum profit-based optimal production planning and facility establishment of oil seed biorefinery and was applied to two case studies, of distributed and centralised superstructure configurations, respectively. 12 Later, Corsano et al. (2014) proposed a multi-echelon MILP model for the identification of the maximum net profit-based design of sugar-cane-to-ethanol SC. 13 4

Page 5 of 56 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


However, the ethical dilemmas resulting from the use of first generation technologies has led to a research focus on second generation SCs to boost the development and operation of relating facilitites. In this perspective, Dunnett et al. (2008) proposed an MILP modelling framework for the economic assessment of different spatial infrastructures of lignocellulosic bioethanol SCs under steady-state conditions. 14 A multi-period MILP model, considering also inventory aspects, was formulated by Ekşioğlu et al. (2009) for the optimal design of lignocellulosic biomass-to-ethanol SC and management of logistics by minimising the total annual cost. The proposed model was applied to a case study regarding the use of corn stover and woody biomass for the production of ethanol in the State of Mississippi. 15 An et al. (2011) developed a model to design a multi-period lignocellulosic biomass-to-biofuel SC in Central Texas, considering strategic and planning decisions in both upstream and downstream echelons. 16 A general MILP model was formulated by Kim et al. (2011) to enable decision-making in the infrastructure of biofuel conversion processing in the SouthEast of the United States (US). In particular, the model involves the production of biogasoline and biodiesel from forestry biomass maximising the SC profit, considering both a distributed and a centralised conversion system. 17 Marvin et al. (2011) applied a spatially explicit MILP model to optimise the net present value of a lignocellulosic biomass-to-ethanol SC in a 9-state region in the Midewestern US. 18 Kim et al. (2013) generated an MILP model for the SC optimisation of ethanol production from hard woody biomass, integrating a biomass utilisation superstructure with multiple conversion technologies. 19 Lin et al. (2014) developed an MILP model to investigate the optimisation of a multi-echelon miscanthusto-ethanol SC in Illinois, focusing on the minimisation of the annual production costs. 20 Cambero et al. (2016) addressed a bi-objective, multi-period MILP modelling framework for the investigation of a Canadian forest-based biorefinery SC for bioenergy and biofuel production. 21 Ng et al. (2017) proposed a multi-period MILP model for larger-scale cellulosic biofuel SCs. 22 Finally, Gargalo et al. (2017) formulated a multi-period and multi-product MILP model to investigate a glycerol-based biorefining SC. 23

5



Some works have investigated both first and second generation technologies, simultaneously. Čuček et al. (2010) developed an MILP model for the regional economic optimisation of first and second generation biomass-based bioproducts, such as bioethanol, digestate, distillers dried grains with solubles (DDGS) and boards, and bioenergy SC superstructure. 24 Akgul et al. (2012) introduced a steady-state MILP optimisation framework for a UK-based hybrid first/second generation bioethanol SC, minimising total costs and considering generic sustainability issues into the modelling formulation 5 . Marvin et al. (2013) formulated an MILP model for determining economically optimal locations of first and second generation biofuel production facilities and their optimal capacities, assessing the biofuel SC network of a 12-state region in the Midewestern US. 9 Čuček et al. (2014) addressed the multi-period synthesis of an optimally integrated regional biomass-to-bioenergy SC network through an MILP approach to consider first, second and third generation technologies, targeting the maximisation of the economic performance of the entire network. 3 A multi-objective, multiperiod MILP modelling framework was proposed by Santibañez-Aguilar et al. (2014) to design and plan sustainable multi-product first and second generation biorefinery SCs considering economic, environmental and social criteria, and was applied to an ethanol and biodiesel production case study in Mexico. 25 Amore et al. (2016) presented a spatially explicit, multi-echelon and multi-period MILP model for the evaluation of the economic and environmental performance of first and second generation bioethanol and biopower SC production systems. 26 Finally, Miret et al. (2016) presented an MILP model for the examination of the trade-off between economic, environmental and social objectives, regarding a first and second generation bioethanol SC case study in France. 27 To the best of our knowledge no study has so far analysed a full (upstream and downstream) SC of advanced biorefining systems, incorporating temporal, spatial and storagerelated issues, while integrating a technology superstructure that can handle the complexity of such biobased production networks. Basically, technology superstructure models consist of synthesis blocks that for given objective functions (e.g. profit maximisation, cost, GHG

6


Page 6 of 56

Page 7 of 56 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


emissions or energy requirement minimisation, etc.) can lead to a holistic approach. In particular, such models explore the available and feasible combination of biomass and biobased products types as well as processing options, and provide, according to various criteria (e.g. economic, environmental, social, etc.), the optimal configurations for the design of the examined production system. In this paper, a deterministic, spatially explicit, multi-period, multi-feedstock and multiproduct MILP modelling framework is introduced to assist maximum profit-based optimal strategic and operational decisions on a multi-echelon lignocellulosic biorefining SC network. Hence, this article expands our previous research work, presented by Panteli et al. (2016), 28 by extending the technology superstructure examined with multiple biomass feedstocks, bioproducts and processing portfolios, while considering two different plant installation scenarios, i.e. centralised and distributed. The applicability of the model is demonstrated using a Hungarian biorefining case study for the production of five different biobased products, i.e. ethanol, power, xylitol, polyurethane (PU) elastomers and phenol formaldehyde (PF) resins, from the utilisation of three different types of lignocellulosic biomass through different types and scales of pretreatment and final conversion plants. The decoupling of pretreatment and final conversion facilities is examined through a distributed scenario, while a centralised scenario is used to compare results when deciding to group them in a single facility. A bi-level spatial decomposition approach is adopted to explore the dimensionality reduction of the discussed mathematical framework and the resulting effect on the computational time of the solution procedure. The remainder of this paper is organised as follows. The problem statement is presented in section 2, where the examined biorefining SC network along with its design issue, is described. The translation of that network into a SC optimisation mathematical formulation is explained in section 3. A Hungarian case study with defined parameters and modelling assumptions for each SC echelon is illustrated in section 4. A solution strategy using a bilevel spatial decomposition method is explained in section 5. The computational results of

7



the SC optimisation considering two different scenarios, a distributed and a centralised one accordingly, are discussed in section 6. Finally, concluding remarks on the model capabilities and challenges to be investigated in future works, are depicted in section 7.

2

Problem statement

The aim of this work is the development of a generic modelling framework to support decisionmaking in the strategic design and operation of lignocellulose-based SCs under economic criteria. As depicted in Figure 1, the biobased SC network addressed in this study includes the following collaborating upstream and downstream nodes: biomass cultivation sites, biomass storage sites, biomass pretreatment plants, intermediate product storage sites, final product production plants, and demand centres. Raw materials, intermediate and final products are transported between these nodes. The geographical representation of the system consists of a grid discretisation into equallysized cells. Hence, the biobased SC model introduced in this work adopts a "neighbourhood" flow approach with 4N configuration, also known, in two-dimensional cellular automaton spatial modelling studies, as von Neumann neighbourhoods. In particular, material flow directions from cell (region) is only allowed to the four orthogonally adjacent cells (regions), as depicted in Figure 2. Subsequently, the material is transported to its final destination by concatenating such flows one after another. 11 This reduces the model size. A planning horizon of 1 year is used for the SC design and is temporally discretised into 12 months, enabling the development of the SC model under multi-period conditions, despite the computational complexity that can be imposed. The design optimisation problem introduced in this paper is formulated based on the following inputs: • Biomass feedstock types and their seasonal and geographical availability. • Biobased intermediate and final product types. 8


Page 8 of 56

Page 9 of 56 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


1 4

2 3

Material flow Figure 2: "Neighbourhood" flow approach with 4N configuration. 11 • Biobased market characteristics and demand over a fixed time horizon. • Geographical distribution of demand centres in terms of grid discretisation. • Pretreatment and final production facilities of different scales. • Technical and economic values as a function of commodities and plants. • Transport logistics characteristics. Biomass-related economic and technical factors are defined on a wet basis assuming that each of the examined types of lignocellulosic biomass has a moisture content of 15%. Lignocellulosic biomass availability is considered to follow the seasonality of crops, assuming these to be harvested only during four months in summer and autumn, i.e. July, August, September and October. Competitive uses of biomass are also taken into account, reducing its local availability for biorefining purposes. The task of this problem is the identification of the profitably optimal SC system configuration, in terms of long-term planning and operational decisions, which can be stated as follows: • Number, locations, sizes and technology selections of biorefining plants. • Number and locations of cultivation and storage sites. 9



• Transport logistics. • Cultivation, storage, consumption and production rates. At this point, it is worth mentioning that product demands are assumed to be flexible, allowing investment decisions based on potential financial profitability and not on demand satisfaction restrictions. This approach is also closer to an investor’s perspective, rather to a social planner’s attitude and seeks to identify the most profitable system.

3

Mathematical formulation

Extending our earlier work, 28 the optimisation problem discussed in the previous section of this paper is mathematically formulated as an MILP model. In particular, based on previous research works 10,14 on the systematic design of SCs, we propose a modelling framework that represents a multi-period, multi-feedstock and multi-echelon lignocellulosic biomassto-biobased product SC network, integrating a superstructure of technology and product portfolios. Spatially explicit features are also embodied to address the high geographical dependence of such systems. The model describing a full biobased SC is structured as follows. First the objective function (i.e. profit) will be defined by expressing the included economic terms. Then, the overall mass balance will be presented along with the implementation of logical constraints that must be satisfied across the entire SC, ensuring sensible solutions. The detailed nomenclature is displayed at the end of the paper .

3.1

Objective function

To evaluate the overall performance of our biorefining SC, we use as the objective function the total annualised profit, T P (eM/y), which includes, as illustrated in Eq.(2), the following terms:

10


Page 10 of 56

Page 11 of 56 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


• Revenues, Rt (eM/month), obtained from selling the desired biobased products. • Total annualised capital cost, T CC (eM/y), relating to the annual payments of the capital cost due to the new facilities installed. • Total operating cost, T OCt (eM/month).

max T P

TP =

X

Rt − T CC −

(1)

X

T OCt

(2)

Out Pc Fc,k,g,t , ∀t ∈ T

(3)

t∈T

t∈T

The revenues term, Rt , is calculated as follows:

Rt =

XXX c∈C k∈K g∈G

Out where Pc (eM/kt or GWh) stands for the selling price of final biobased products c and Fc,k,g,t

(kt or GWh/month) is the production rate of products c from technology type k in region g at time t. Indices c and c0 are used as a notation for all the commodities, i.e. types of feedstocks, intermediates as well as final products. The total capital cost, T CC, is given by:

T CC =

XX

af CIk Xk,g

(4)

k∈K g∈G

where af is a scalar representing the annualisation factor under the assumption of 20 operational years and a discount rate of 8%, CIk (eM) refers to the investment expenditure for a plant of size and technology k, and Xk,g is the binary variable for the establishment of a plant of type and scale k in region g. As stated in Eq.(5), the definition of the total operating cost, T OCt , encompasses the 11



Page 12 of 56

following terms, respectively: (i) the cultivation cost, CCt (eM/kt), (ii) the storage cost, SCt (eM/kt), (iii) the transport cost, T Ct (eM/kt), and (iv) the processing cost, P Ct (eM/kt).

T OCt = CCt + SCt + T Ct + P Ct , ∀t ∈ T

(5)

As a consequence, the cultivation cost, CCt , is evaluated as follows:

CCt =

XX

U CCc BPc,g,t , ∀t ∈ T

(6)

c∈C g∈G

where U CCc (eM/kt) is the unit cultivation cost of biomass type c and BPc,g,t (kt/month) accounts for the cultivation rate of biomass type c in region g at time t. The storage cost, SCt , is expressed by the following equation:

SCt =

XX

U SCc StCc,g,t , ∀t ∈ T

(7)

c∈C g∈G

where U SCc (eM/kt) is the unit storage cost of commodity type c and StCc,g,t (kt/month) is the storage rate of commodity type c in region g at time t. The transport cost, T Ct , is described in Eq.(8):

T Ct =

X X X c∈C

g,g 0 ∈G

U T Cc,l LDg,g0 τg,l,g0 Qc,g,l,g0 ,t , ∀t ∈ T

(8)

l∈L

where U T Cc,l (eM/kt) is the unit transportation cost of commodity type c via mode l, LDg,g0 (km) is the linear delivery distance between cells g and g 0 , resulting from the measurement of the straight route between the centre of each network element g, τg,l,g0 is the tortuosity factor depending on the transport mode l and accounting for the non-linearity of the actual travel distance between two cells, and Qc,g,l,g0 ,t (kt/month) stands for the transport flow rate of commodity type c via mode l between regions g and g 0 at time t.

12


Page 13 of 56 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


Finally, the process cost, P Ct , is shown in Eq.(9):

P Ct =

XXX

In U P Cc,k Fc,k,g,t , ∀t ∈ T

(9)

c∈C k∈K g∈G

where U P Cc,k (eM/kt) is the unit process cost of commodity type c at a plant of technology In type and scale k and Fc,k,g,t (kt/month) indicates the consumption rate of commodity type

c at a plant of technology type and size k in region g at time t.

3.2

Logical constraints and mass balances

The entire SC network behavior is subsequently subjected to mass balances as well as logical constraints in each of the SC nodes.

3.2.1

Demand constraints

The following equality constraint indicates that the amount of product type c produced at Out a plant k in region g at time t, Fc,k,g,t (kt or GWh/month), is related to the amount of In commodity type c consumed by that plant in that region and at that time period, Fc,k,g,t

(kt/month), by the conversion factors γc0 ,c,k : Out Fc,k,g,t =

X

γc0 ,c,k FcIn 0 ,k,g,t , ∀c ∈ C, k ∈ K, g ∈ G, t ∈ T

(10)

c0 ∈C

where index c0 indicates the input commodity in a plant, i.e. biomass feedstock in a pretreatment facility or intermediate in a final conversion facility, whereas index c stands for the output commodity from that plant, i.e. intermediate product from a pretreatment facility or final product from a final conversion facility. The demand of commodity type c in region g at time t is upper-bounded, as shown in Eq.(11), allowing the decision-maker to invest up to the most profitable level without having

13



Page 14 of 56

to meet all of the demand.

Dc,g,t ≤ M Dc,g,t , ∀c ∈ C, g ∈ G, t ∈ T

(11)

where M Dc,g,t represents the market demand of the biobased products c in region g at time t. The calculation of these values can be based on the maximum biomass availability of the entire examined region as well as the conversion factors γc0 ,c,k , and the demands of the substituted materials.

3.2.2

Production constraints

The mass balance for each commodity type c in region g at time t is defined as:

BPc,g,t +

X

Out Fc,k,g,t +

XX

Qc,g0 ,l,g,t = Sc,g,t +

l∈L g 0 ∈G

k∈K

+Dc,g,t +

XX

X

In Fc,k,g,t

k∈K

Qc,g,l,g0 ,t , ∀c ∈ C, g ∈ G, t ∈ T

(12)

l∈L g 0 ∈G

In particular, Eq.(12) states that in region g and at time t the cultivation flow of biomass type c plus the production flow of product type c plus the incoming transport flows of commodity type c to that region must be equal to the storage flow of commodity type c plus the consumption flow of commodity type c plus the demand of commodity type c plus the outgoing transport flows of commodity type c from that region. The biomass cultivation rate is upper-bounded by the regional biomass availability, depending on agronomical factors and geographical characteristics, as follows:

BPc,g,t ≤ ALg GSg BCc BCYc,g,t , ∀c ∈ C, g ∈ G, t ∈ T

(13)

where ALg (km2 of arable land/km2 of grid surface) stands for the fraction of the arable land area in region g, GSg (km2 ) is the surface of square region g, BCc (km2 allocated to crop

14


Page 15 of 56 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


c/km2 of cereals) refers to the fraction of the cultivation area devoted to biomass type c and BCYc,g,t (kt/month/km2 ) is the cultivation yield of biomass type c in region g at time t. The capacity F Capk (kt/month) sets an upper bound on the overall consumption of biomass processed at a pretreatment facility or of an intermediate processed at a final conversion facility: X

In ≤ F Capk Xk,g , ∀k ∈ K, g ∈ G, t ∈ T Fc,k,g,t

(14)

c∈C

In addition, according to Eq.(14), operation can only take place if a conversion facility is established in that region, i.e. if the binary variable Xk,g takes a value of one. For a better view of the discussed mathematical formulation, an example of a pretreatment and a final conversion facility with the corresponding input and output commodities could be: wheat straw (i.e. biomass) processed in an Organosolv plant (i.e. pretreatment facility) resulting in the production of cellulose (i.e. intermediate), which is, subsequently, processed in an SSF (Simultaneous Saccharification and Fermentation) plant (i.e. final conversion facility) producing ethanol (i.e. biobased product). Two different configurations regarding the establishment of the plants are assessed, by differently formulating the related constraints, as it will be subsequently described in more detail. In particular, to reduce the computational complexity as well as benefit from economies of scale (i.e. a single large plant represents a less costly option than more smaller plants adding up to the same overall size), it is assumed, as shown in Eq.(15), that at most one conversion facility can be installed within region g. This statement indicates the distributed scenario where the pretreatment and processing plants are at separate locations. In this case the intermediate products of pretreatment can be transported to processing plants. X

Xk,g ≤ 1, ∀g ∈ G

k∈K

15


(15)


Page 16 of 56

However, when dealing with advanced biorefining systems, it is also important to investigate the centralised case where pretreatment and processing plants are in the same facility. In particular, this is achieved through the modification of Eq.(15) into Eq.(16), ensuring that at most all the examined scales and types of facilities of both pretreatment and final conversion processes can be established within a region g. X

Xk,g ≤ |K|, ∀g ∈ G

(16)

k∈K

3.2.3

Transportation constraints

The variables responsible for the transport logistics of the SC network also need to be constrained. In particular, the transport flow rate of commodities c between regions should be upper-bounded, as illustrated in Eq.(17).

Qc,g,l,g0 ,t ≤ QCapc,l , ∀c ∈ C, g, g 0 ∈ G, l ∈ L, t ∈ T

(17)

where QCapc,l (kt/month) represents the maximum monthly transport flow rate of commodity type c via mode l between regions. Furthermore, as previously mentioned, the direct flows from a cell are constrained to be only allowed to neighbouring cells; this is enforced via a "cut-off" distance LDlimit (km). This distance limit represents the longest linear distance between the centres of a cell and its neighbouring cells. For the 4N configuration, employed in this work, the distance between a cell and its neighbours is the same in all directions, as shown in Figure 2. Hence, for a square cell of dimensions 15 × 15 km, as used in the case study described in section 4, LDlimit is calculated as 15 km, for 4N representations.

Qc,g,l,g0 ,t = 0, ∀c ∈ C, g, g 0 ∈ G, l ∈ L, t ∈ T : LDg,g0 > LDlimit

(18)

Finally, it must be ensured that the transport flow rate of commodities c does not go through 16


Page 17 of 56 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


internal loop trips:

Qc,g,l,g0 ,t = 0, ∀c ∈ C, g, g 0 ∈ G, l ∈ L, t ∈ T : g = g 0

3.2.4

(19)

Storage constraints

Storage Sc,g,t (kt/month) is a free variable representing a commodity being stored when positive, and a commodity being released from the storage when negative. The description refers to the storage with shortages and is justified by lower storage costs compared to the rest of the chain. Subsequently, StCc,g,t (kt/month) is an upper bound to storage that is used as a capacity proxy for the definition of costs. A further set of constraints is devoted to these variables. First of all, according to Eq.(19), the entire amount of stored commodities should be used over the whole planning horizon. X

Sc,g,t = 0, ∀c ∈ C, g ∈ G

(20)

t∈T

The following constraint is based on the fact that Sc,g,t shows both the inflows (i.e. positive value) and outflows (i.e. negative value) of a storage site, as illustrated in Figure 3, while StCc,g,t shows only the inflows (i.e. positive value) of the actual storage activity.

StCc,g,t ≥ Sc,g,t , ∀c ∈ C, g ∈ G, t ∈ T

(21)

Finally, the inflow storage rate of a commodity type c in each region at time t should not exceed the maximum capacity of that storage site.

StCc,g,t ≤ SCapc , ∀c ∈ C, g ∈ G, t ∈ T

17


(22)


4

Wheat straw Barley straw Corn stover

2 Biomass surplus (kt/m)

0 2 4 6 8

Au

g Se p Oc t No v De c Jan Fe b Ma r Ap r Ma y Jun

10

Jul

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 18 of 56

Months

Figure 3: Storage inflows and outflows of biomass types for a selected storage site. 3.2.5

Non-negativity constraints

The following constraints are set for the key design variables of the SC network in order to maintain their physical meaning by being non-negative.

BPc,g,t ≥ 0, ∀c ∈ C, g ∈ G, t ∈ T

(23)

Dc,g,t ≥ 0, ∀c ∈ C, g ∈ G, t ∈ T

(24)

In Fc,k,g,t ≥ 0, ∀c ∈ C, k ∈ K, g ∈ G, t ∈ T

(25)

18


Page 19 of 56 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


4

Out Fc,k,g,t ≥ 0, ∀c ∈ C, k ∈ K, g ∈ G, t ∈ T

(26)

Qc,g,l,g0 ,t ≥ 0, ∀c ∈ C, g, g 0 ∈ G, l ∈ L, t ∈ T

(27)

StCc,g,t ≥ 0, ∀c ∈ C, g ∈ G, t ∈ T

(28)

Case study

The South-West of Hungary was chosen as a targeted area to assess the scale-up of advanced biorefining systems within the BIOCORE project, 6,29 from which all the agricultural and costing values are obtained. This is the area considered as the case study to highlight the applicability of the model as well as demonstrate its potential capabilities in driving decision-making in the systematic design of such novel infrastructures (including centralised vs decentralised systems). The regional soil conditions, cultivation yields and farming practices make the examined area suitable for lignocellulosic biomass production.

4.1

Spatially explicit features

The region under investigation comprises four counties, i.e.

Zala, Somogy, Tolna and

Baranya, including more than 2,000,000 ha, with arable, heterogeneous, agricultural lands and forests. To balance geographical data accuracy and computational burden, the area of interest, as schematically presented in Figure 4, is discretised into a grid of 102 square regions (cells) of equal size, i.e. 15 km of length. Each of these regions represents a territorial element identified by g and the x,y coordinates of their centroids are represented in Table S1. Based on that geographical configuration of the region, the area, GSg , of each square region g, is 225 km2 .

19



7

13

20

3

8

14

21

28

1

4

9

15

22

29

2

5

10

16

23

6

11

17

12

Page 20 of 56

62 44

53

63

36

45

54

64

72

81

89

98

30

37

46

55

65

73

82

90

99

24

31

38

47

56

66

74

83

91

100

18

25

32

39

48

57

67

75

84

92 101

19

26

33

40

49

58

68

76

85

93

27

34

41

50

59

69

77

86

94

35

42

51

60

70

78

87

95

43

52

61

71

79

88

96

97

102

80

Figure 4: South-West of Hungary.

4.2

Biomass cultivation

This study focuses on the arable land of the examined area and its agronomical factors. Three different types of lignocellulosic biomass, i.e. wheat straw, barley straw and corn stover, based on the BIOCORE project, 6 would be suitable for the Hungarian biobased production system. The geographical data regarding the regional biomass availability, i.e. cultivation yields BCYc,g,t as well as fractions ALg and BCc , resulting in a total availability of 136 kt/month wheat straw, 28 kt/month barley straw and 538 kt/month corn stover. Biomass seasonality was also taken into account for the configuration of this part of the SC network. In particular, biomass is considered to be cultivated and harvested during July, August, September and 20


Page 21 of 56 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


October (i.e. the first 4 months of the examined 12-month planning horizon). The fraction of cultivation area devoted to each biomass type, BCc , along with the unit cultivation cost of each biomass type, U CCc , are shown in Table 1. However, due to the large number of cells g, the geographical input parameters regarding the arable land density as well as the biomass cultivation yields, are illustrated in Table S2 and Table S3, respectively, in the Supporting Information. Table 1: Biomass cultivation input parameters. 6 Commodity type c wheat straw barley straw corn stover

4.3

BCc (km2 allocated to crop c/km2 of cereals) 0.319 0.064 0.579

U CCc (eM/kt) 0.034 0.034 0.037

Biomass pretreatment

Among the many pretreatment process types, although Organosolv is a rather expensive one, it is considered to be able to better preserve biomass macrocomponents 29,30 and hence, favour the development of a full biobased SC from biomass to biobased products. Three different sizes of Organosolv pretreatment facilities were considered for the fractionation of wheat straw, barley straw and corn stover, into cellulose, hemicellulose and lignin, also mentioned as intermediate products: (i) 176 kt/y (small), (ii) 382 kt/y (medium), and (iii) 588 kt/y (large). 29 The related economic and technical parameters are presented in Table 2 and Table 3. The process capital and operating costs, according to Table 2, are sensitive to plant capacity. Table 2: Biomass pretreatment input parameters. 29 Plant k Organosolv small Organosolv medium Organosolv large

CIk (eM) 230 386 460

21

U P Cc,k (eM/kt) 0.124 0.094 0.085


F Capk (kt/month) 31 48 74


Page 22 of 56

Table 3: Biomass-to-intermediates conversion factors. 29 γc0 ,c,k (kt of input commodity c0 /kt of output commodity c) Process type k Organosolv Organosolv Organosolv Commodities c0 , c small medium large wheat straw-to-cellulose 0.4293 0.4293 0.4293 wheat straw-to-hemicellulose 0.1938 0.1938 0.1938 wheat straw-to-lignin 0.227 0.227 0.227

4.4

barley straw-to-cellulose barley straw-to-hemicellulose barley straw-to-lignin

0.4378 0.1938 0.2185

0.4378 0.1938 0.2185

0.4378 0.1938 0.2185

corn stover-to-cellulose corn stover-to-hemicellulose corn stover-to-lignin

0.4335 0.1955 0.221

0.4335 0.1955 0.221

0.4335 0.1955 0.221

Biobased products production

In this work, the biorefining processes considered to be taking place after the biomass pretreatment process, involve the following: • Simultaneous Saccharification and Fermentation (SSF) process for the production of ethanol from cellulose and hemicellulose, as well as the production of power from lignin. • Catalytic process for the production of xylitol from hemicellulose. • Biochemical process for the production of xylitol from hemicellulose. • Lignin-based Polyurethane (PU) elastomer production process. • Lignin-based Phenol-Formaldehyde (PF) resin production process. The overall biorefining technology superstructure is illustrated in Figure 5. Subsequently, three different scales of SSF plants, along with a single scale of Catalytic process, Biochemical process, lignin-based PU process and lignin-based PF process plants were examined in this work, respectively: (i) 110 kt/y (SSF small), (ii) 220 kt/y (SSF medium), (iii) 330 kt/y (SSF large), (iv) 35 kt/y (Catalytic), (v) 35 kt/y (Biochemical), (vi) 44 kt/y (PU production process), and (vii) 44 kt/y (PF production process). The scale

22


Page 23 of 56 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


Wheat straw

Cellulose

SSF

Catalytic

Barley straw

Organosolv

Ethanol

Xylitol Xylitol

Hemicellulose Biochemical

SSF

PU process

Corn stover

Power PU elastomers

Lignin PF process

PF resins

Figure 5: Biorefining process technology superstructure. selection for the SSF plants is based on the previous relating work of Giarola et al. (2012) 31 to exploit the economies of scale. In addition, the scale of xylose production plants (i.e. Catalytic and Biochemical) is derived from the work of Mountraki et al. (2017) 30 and that of PU and PF production processes is assumed based on research works of the BIOCORE project. 29 Hence, the related economic and technical parameters are presented in Table 4 and Table 5. Production costs, as shown in Table 4, are highly dependent on the capacity of the plant because there is an economy of scale effect on capital and operating costs.

4.5

Transport system

Although our model is general, in this case the distribution infrastructure includes only trucks, as this mode is considered the most suitable transport mode for this region, accord-

23



Page 24 of 56

Table 4: Biobased products production input parameters. 29–31 CIk (eM) 273 434 570 4.27 20.97 10.3 96.9

Process type k SSF small 31 SSF medium 31 SSF large 31 Catalytic 30 Biochemical 30 PU process 29 PF process 29

U P Cc,k (eM/kt) 0.165 0.16 0.154 1.714 2.012 0.215 2.019

F Capk (kt/month) 9 18 28 3 3 4 4

Table 5: Intermediates-to-final products conversion factors. 29–31 γc0 ,c,k (kt of input commodity c0 /kt of output commodity c or GWh of power) Process type k Commodities SSF SSF SSF Catalytic Biochemical PU process PF process c0 , c small medium large cellulose-to-ethanol 31 0.2329 0.2329 0.2329 hemicellulose-to-ethanol 31 0.228 0.228 0.228 lignin-to-ethanol 31 cellulose-to-power 31 hemicellulose-to-power 31 lignin-to-power 31

0.7705

0.7705

0.7705

-

-

-

-

cellulose-to-xylitol 30 hemicellulose-to-xylitol 30 lignin-to-xylitol 30

-

-

-

0.85 -

0.73 -

-

-

cellulose-to-PU 29 hemicellulose-to-PU 29 lignin-to-PU 29

-

-

-

-

-

3.5

-

cellulose-to-PF 29 hemicellulose-to-PF 29 lignin-to-PF 29

-

-

-

-

-

-

14.176

ing to the CORINE Land Cover 2012 dataset. 32 Transport costs and other transport-related parameters used to characterise the delivery of commodities by truck are reported in Table 6. 10 Delivery distances, LDg,g0 (km), were calculated by measuring the linear route, if allowed by the road network in the geographical context, that links the centres of each square cell. The longest linear distance, LDlimit (km), between the centroids of a cell and its adjacent cells, is set equal to 15 km due to the dimensions, 15 × 15 km, of the examined square regions. As shown in Eq.(8), a tortuosity factor, τg,l,g0 , depending on the transport mode l and varying from 1 to 2.6, was introduced as a multiplier to the linear delivery distances, LDg,g0 ,

24


Page 25 of 56 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


taking into account that the actual transport route of the commodities is not linear. In particular, square cells connected through highways are assumed to have tortuosity factors closer to 1, indicating an almost linear connectivity between them. Table 6: Transport system input parameters. 10 Transport mode l Commodity type c wheat straw barley straw corn stover cellulose hemicellulose lignin ethanol power xylitol PU PF

4.6

truck U T Cc,l QCapc,l (eM/kt/km) (kt/month) 0.54 10-3 5000 0.54 10-3 5000 0.54 10-3 5000 0.5 10-3 3000 0.5 10-3 3000 0.5 10-3 3000 0.5 10-3 3000 0.5 10-3 3000 0.5 10-3 3000 0.5 10-3 3000

Storage

Storage is assumed to be located on-fields, not only for the agricultural residues, but also for the rest of the examined commodities (which are assumed to be in drums). Costs and other parameters defining the storage nodes of the examined biobased SC network are shown in Table 7. In particular, these values were calculated assuming large open storage capacity of 20 km3 with 5 e/m3 unit cost, 120 kg/m3 biomass density, 1500 kg/m3 intermediates density, 789 kg/m3 ethanol density, 1520 kg/m3 xylitol density, 1100 kg/m3 PU density and 1185 kg/m3 PF density. 6 This assumes that ethanol, xylitol, PU and PF are stored in drums, which form part of the production cost.

4.7

Demand centres

Two demand centres are considered in this work, located in cells, g = 69 and g = 89, respectively. This assumption is based on the fact that two real-life plants, using biomass for 25



Table 7: Storage input parameters. 6 Commodity type c wheat straw barley straw corn stover cellulose hemicellulose lignin ethanol power xylitol PU PF

U SCc (eM/kt) 41.67 10-3 41.67 10-3 41.67 10-3 3.333 10-3 3.333 10-3 3.333 10-3 6.337 10-3 3.29 10-3 4.546 10-3 4.219 10-3

SCapc,g (kt) 2.4 2.4 2.4 30 30 30 15.78 30.4 22 23.7

the production of power, already exist in these two cells. 6 The market demand values of the final biobased products in these terminals, as presented in Table 8, are set to a maximum level, by calculations based upon the conversion factors γc0 ,c,k and the maximum biomass availability of the entire examined region. In addition, the selling prices of intermediates and final products are illustrated in Table 9. The prices of the intermediates along with PU elastomers and PF resins are assumed based on the BIOCORE project, 6,29 while ethanol, power and xylitol prices are derived from the literature. 10,30 The products are assumed to be consumed at the demand centres. Table 8: Market demand of final products. Commodity c ethanol power xylitol PU PF

5

M Dc,g,t (kt of product/month or GWh of power/month) 14 17 16 77 312

Spatial decomposition approach

The proposed MILP model applied to the aforementioned case study is computationally intensive due to the large number of combinations of feedstocks, technologies, scales and product forms as well as relating fluxes, that need to be evaluated in each of the 102 territorial 26


Page 26 of 56

Page 27 of 56 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


Table 9: Selling prices of intermediates and final products. 6,10,29,30 Commodity c cellulose 6 hemicellulose 6 lignin 6 ethanol 10 power 10 xylitol 30 PU 29 PF 29

Pc (eM/kt of product or eM/GWh of power) 0.35 0.35 0.75 0.71 0.18 2.5 0.8 1.9

elements over the 12-month planning horizon. In particular, the model consists of 1020 binary variables, 1,478,474 continuous variables and 2,790,854 constraints. This will be referred to throughout the paper as full space optimisation problem. With the advances in current computational machines and MILP solvers, the full space optimisation problem can be solved in reasonable computational times, i.e. in less than 20 minutes with an optimality gap of 1%. However, bi-level decomposition methods 33–36 could enable the reduction of the required CPU time without significantly affecting the accuracy of the results, through a systematic identification and elimination of redundant criteria from the mathematical formulation. This could also support an extension to optimisation under uncertainty. Subsequently, the potential dimensionality reduction of the original full space MILP model, studied in this paper, is investigated through its spatial decomposition into two hierarchical sub-problems, a master and a slave problem, based on the approach of Vaskan et al. (2013). 34 In particular, the master MILP problem encompasses most of the equations of the original MILP, apart from constraints regarding the number of plants to be built (in both investigated scenarios) (i.e. Eq.(15) and Eq.(16)) as well as the transportation feasibility condition (i.e. Eq.(18)), but for a smaller number of (aggregated) cells, in order to provide an upper bound on the profit (or equivalently a lower bound on the cost). The k-means clustering method is used at the master level to aggregate the examined square regions into well-separated clusters, according to the x,y coordinates of their centroid locations.

27



The analytical master MILP modelling formulation is illustrated at the end of the paper, through Eq.(29) to Eq.(60), along with the related nomenclature. In particular, Eq.(29) to Eq.(35) describe the calculations of the required aggregated parameters to be used in the mathematical formulation of the master MILP model, subsequently analysed from Eq.(36) to Eq.(60). The slave MILP problem is, then, identically structured as the original full space one, by including exactly the same equations and disaggregating the relating aggregated spatial parameters of the master level. However, the number of variables and constraints in the slave level are reduced, as it is solved only for the cells belonging to the clusters that were selected to be active by the master MILP (i.e. the cells discarded by the master level are not considered in the slave level). The mathematical framework of the slave level is also demonstrated at the end of the paper, through Eq.(61) to Eq.(88), using the relative nomenclature. Hence, the slave subproblem provides a lower bound on the profit and after it is solved, integer cut is applied to the master level to exclude the solutions selected in previous iterations. Then both subproblems are solved iteratively until a termination criterion, regarding the difference between the upper and lower bounds, is satisfied. The features of the employed bilevel algorithm are illustrated in Figure 6.

6

Computational results

The discussed full space MILP optimisation problem, along with the decomposition method, including both the master and the slave hierarchical levels, were coded in GAMS 24.8.3 37 and solved with the solver CPLEX 12.7.0.0, to explore the potential lignocellulose-based Hungarian biorefining system. The optimality gaps were all set to 1%. Due to the computational burden of the model and in order to achieve a fast convergence between the upper and lower bounds, the bi-level approach was executed considering a high relative error of 5% 35 .

28


Page 28 of 56

Page 29 of 56 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


Initialisation 𝑖𝑡 = 0; 𝑈𝐵 = +∞; 𝐿𝐵 = −∞; 𝑒𝑟𝑟𝑜𝑟 = 𝑡𝑜𝑙 Set 𝑖𝑡 = 𝑖𝑡 + 1 Solve master MILP

Feasible?

Add integer cuts

No

Stop

Yes Update 𝑈𝐵 = 𝑈𝐵 01 67 Fix 𝑋3,5 Solve slave MILP

Update 𝐿𝐵 = 𝐿𝐵 01

No

𝑈𝐵 − 𝐿𝐵 < 𝑡𝑜𝑙? 𝑈𝐵

Yes End

Figure 6: Flowchart for the bilevel decomposition algorithm. 34,35 The k-means clustering method for the bi-level decomposition approach was implemented in MATLAB R2015b. 38 Targeting the maximisation of the annualised profit of the entire biorefining SC network, a deterministic optimisation under a centralised and a distributed scenario was performed for the full space model as well as the decomposed one. The aim of these two different cases, was to investigate the changes in the optimal configuration of the system in respect of different spatial installation decisions (i.e. either decoupling plants or grouping them within same regional cells, respectively) along with different solution procedures. The computational 29



Page 30 of 56

results regarding the full space optimisation are discussed in section 6.1, focusing on the main differences between the two examined scenarios. In section 6.2 a sensitivity analysis based on different numbers of clusters is briefly examined and subsequently, in section 6.3, the results of the spatial decomposition methodology are presented, emphasising on the major differences in comparison to the full space optimisation results for the equivalent scenarios. Model statistics of solving both scenarios by using the full space model as well as the decomposition approach, discussed in section 5, are summarised in Table 10. In all of the cases, the relative error of 5% between the lower and the upper bounds regarding the bilevel decomposition methodology is reached in four iterations, with 1% optimality gap each. Therefore, the CPU time of the master and the slave MILP models, identified in Table 10, accounts for all four iterations, indicating that the complete decomposition method is not helpful in terms of computational time reduction. Table 10: Summary of computational statistics of the full space and the decomposition optimisation for the distributed and the centralised scenario. Distributed Scenario MILP model statistics Number of binary variables Number of continuous variables Number of constraints Optimality gap (%) CPU time (s) Objective function (eM/y)

6.1

Full space 1020 1478474 2790854 1 1186 13380

Master 200 73486 73266 1 35 13545

Slave 730 778704 1439030 1 1317 12887

Centralised Scenario Full space 1020 1478474 2790854 1 464 13407

Master 200 73486 73266 1 41 13545

Slave 730 778704 1439030 1 1136 12902

Full space optimisation: centralised vs distributed scenario

Solving the full space SC model with the flexibility of grouping biorefining facilities within same territorial elements (i.e. centralised scenario), resulted in SC configuration decisions with a total profit of 13407 eM/y. According to Figure 7, the strategic decisions involve the installment of 5 Organosolv plants of large size, 4 SSF plants of large size, 14 Catalytic plants, 3 PU production process plants and finally, 13 PF production process plants, occupying approximately the 21% of the whole region. Economies of scale are largely exploited as the optimal configuration does not involve the installation of small and medium Organosolv and 30


Page 31 of 56 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


SSF plants. In addition, Biochemical plants of xylitol production are not part of the optimal solution either.

Organosolv large SSF large Catalytic PU process PF process

Figure 7: Optimal plant types and locations of centralised scenario using the full space optimisation.

Biomass is cultivated in most of the cells (i.e. 1-61 and 63-102), resulting in 542 kt/y wheat straw, 112 kt/y barley straw and 2152 kt/y corn stover, which has the highest yield per territorial element. Storage is located on-field and refers not only to biomass and intermediates, but also to xylitol. By the end of the examined horizon, the entire cultivated biomass is exploited by the Organosolv plants. In particular, the highest part of the optimal biomass feedstock mix in Organosolv plants is corn stover with 77%, followed by wheat straw with 19% and finally, by barley straw with 4%. Moreover, the optimal intermediates feedstock mix in SSF plants consists of 93% cellulose, 7% hemicellulose and 0% lignin, due to the absence of power production. Lignin was used as a feedstock for the PU and PF production process plants. Furthermore, the low contribution of hemicellulose in the SSF 31



Page 32 of 56

plants was expected due to the existence of Catalytic plants that also use hemicellulose for the production of xylitol. The distributed scenario resulted in being only 0.2% less profitable (i.e. 13380 eM/y) than the centralised one, with the installment of two fewer plants, Organosolv and SSF of large size, respectively. The detailed plant allocation decisions are depicted in Figure 8. The decoupling of the biorefining plants, considered in that case, increased the plant coverage of the examined area by 15% in comparison to the centralised case. However, the total biomass cultivation and usage were not affected.

Organosolv large SSF large Catalytic PU process PF process

Figure 8: Optimal plant types and locations of distributed scenario using the full space optimisation. According to the cost breakdown of the two investigated scenarios, presented in Table 11, the distributed case is approximately 8% cheaper than the centralised one in terms of investment costs, due to the establishment of a smaller number of biorefining plants. On the other hand, in terms of operational costs, the distributed instance is almost 3% more expensive 32


Page 33 of 56 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


based on the increase of the transport cost, caused by the installation of only one plant within each selected regional grid. Table 11: Cost breakdown for the distributed and centralised scenario of the full space model optimisation. Distributed Scenario Centralised Scenario Cost item Value (eM/y) Value (eM/y) Total operating cost 2816 2741 Annualised investment cost 558 605 Breakdown of operating costs Cultivation 4% 4% Processing 82% 84% Transport 12% 10% Storage 2% 2%

6.2

Sensitivity analysis on the number of clusters

Before deciding upon the number of clusters to be used to aggregate the original 102 regional cells for the formulation of the master sub-problem, a sensitivity analysis, described in Table 12 and Figure 9, was performed for different such numbers regarding the distributed scenario to investigate the trade-off between the computational time and the changes in the results regarding the distributed scenario, while comparing them with the ones of the full space model. In particular, the results depicted in Table 12 refer to the slave level, apart from the CPU time that stands for both hierarchical levels, while the economic analysis shown in Figure 9 refers only to the slave sub-problem. The application of integer cuts is not included in the discussed sensitivity analysis. It is firstly important to examine the performance of the slave sub-problem for different numbers of clusters (i.e. single iteration), in order to decide upon them, before completing the decomposition methodology by applying integer cuts. Our sensitivity analysis showed that 1o clusters are the best balance of performance and result accuracy as the output resembles the full space optimisation solution. The paper discusses the broader sensitivity analysis performed, including the cases where a greater number of clusters is used, to show the effects on computational speed as well as the relative impact on the decision variables. 33



Subsequently, this analysis showed that small numbers of clusters (e.g. 20), including a large number of cells, cause a significant increase in the production of final products, resulting in the installation of excessively many plants, mainly due to the interplay between highly flattened local biomass availability and reduced transport-related values. However, after using 20 clusters, the objective function of the slave level seems to have a value closer to the one derived from the full space model (i.e. 13380 eM/y), indicating that fewer iterations will be needed to reach the tolerance error between upper and lower bounds. In addition, the number of plants chosen to be built is close to the full space model result. On the contrary, a very large number of clusters (e.g. 80), has the exact opposite effect, causing a significant reduction of the SC network, and as a result both master and slave sub-problems require significantly more time to solve in order to reach the desired tolerance error between them. However, the case of using an almost mid-number of clusters (e.g. 60), has similar results to the ones of larger number of clusters (e.g. 80), while requiring a much lower computational time, but still greater than the one of smaller numbers of clusters. Based on the previously described sensitivity analysis, moving from the lowest to the largest number of clusters, apart from the increase in the computational time, the trade-off between the agricultural and transport costs changes, resulting into the reduction of the entire SC network, by selecting fewer plants, lower amounts of biobased products production and consequently lower costs and profits. The results particularly showed that 20 clusters seem to achieve a similar trade-off between cultivation and transport costs as the one resulting from the full space optimisation. Hence, it was decided that the use of 20 clusters could be the most appropriate option when solving the proposed MILP optimisation problem using the discussed spatial decomposition approach to examine a possible reduction of computational time along with the relating accuracy of the results.

34


Page 34 of 56

Page 35 of 56

Table 12: Summary of results of the full space model and of the different number of clusters. Full space Results Number of plants Objective function (eM/y) Final products production (kt/y) CPU time (s)

37 13380 8509 1186

20 33 12104 7467 302

40 21 8200 5052 137

Clusters 50 60 23 15 8666 4969 5362 3071 411 574

80 16 4787 2968 2070

2500

CAPEX OPEX 2000

Value (C M/y)

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


1500

1000

500

0

20

40

50 Number of clusters

60

80

Figure 9: Annual capital (CAPEX) and operating (OPEX) expenditures for different number of clusters.

6.3

Spatial decomposition approach: centralised vs distributed scenario

The application of the spatial decomposition approach in the centralised instance, using 20 clusters as decided from the sensitivity analysis in the previous section, resulted in a 4%

35



Page 36 of 56

less profitable SC configuration (i.e. 12902 eM/y) compared to the full space one, involving the establishment of three fewer plants. In particular, as depicted in Figure 10, the main differences compared to the full space optimisation in terms of the strategic decisions are the contribution of one SSF plant of medium size, the absence of lignin-based PU process plants as well as the installation of one fewer SSF plant of large size, one fewer Catalytic plant and one fewer lignin-based PF process plant, resulting in a 2% less regional coverage. Although no Organosolv and SSF plants of small size are part of the optimal solution, the existence of an SSF plant of medium size, indicates that the economies of scale are not largely exploited in this case.

Organosolv large SSF medium SSF large Catalytic PF process

Figure 10: Optimal plant types and locations of centralised scenario using the decomposition approach.

Similarly, the distributed scenario of the decomposition method is 4% less profitable (i.e. 12887 eM/y) than the one of the full space optimisation with plant allocation decisions referring to the establishment of four fewer facilities, involving a PF process plant and the 36


Page 37 of 56 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


entire absence of PU process plants, as illustrated in Figure 11. Hence, the area used for the plant allocation, in this case, is decreased by 4%.

Organosolv large SSF large Catalytic PF process

Figure 11: Optimal plant types and locations of distributed scenario using the decomposition approach. Interestingly, in both the explored scenarios of the decomposition approach, 24% less land usage seems to be devoted to biomass cultivation, in comparison to the equivalent cases of the full space optimisation, resulting, subsequently, in 17% smaller biomass quantity, i.e. 456 kt/y wheat straw, 94 kt/y barley straw and 1788 kt/y corn stover. Another key difference in contrast to the full space cases is observed in the optimal feedstock mix of the SSF plants, where there is almost no contribution of hemicellulose (i.e. 0.4%). According to the cost breakdown presented in Table 13, the installation of a smaller number of plants in both instances caused an 8% decrease in the annualised investment cost compared to the equivalent instances of the full space optimisation. In addition, both scenarios in the decomposition method seem to be cheaper in terms of operating costs, 37



mainly because of the significant reduction in the amount of the cultivated biomass, which subsequently results into lower storage capacities and transportation flows as well as feedstock to be processed. Table 13: Cost breakdown of distributed and centralised scenario using the decomposition approach. Distributed Scenario Centralised Scenario Cost item Value (eM/y) Value (eM/y) Total operating cost 2577 2528 Annualised investment cost 545 578 Breakdown of operating costs Cultivation 3% 3% Processing 85% 86% Transport 10% 9% Storage 2% 2%

7

Concluding remarks

A deterministic, spatially explicit and multi-period MILP modelling framework for the strategic design and tactical planning of multi-echelon, multi-feedstock and multi-product lignocellulose-based biorefining supply chain networks, considering both upstream and downstream aspects, has been developed. The aim of the study has been to build a generic decision-making tool to assess the development of economically sustainable advanced biorefining systems for the co-production of biofuels and bioderived platform chemicals, enhancing the promotion of a biobased economy. The maximum profit-based lignocellulosic biorefining production system of southwestern Hungary has been chosen as a case study to illustrate the proposed model applicability and capabilities. Two different scenarios in terms of plant installation decisions have been explored: (i) a distributed scenario, where conversion facilities are spatially decoupled, and (ii) a centralised scenario, where conversion facilities are grouped. In addition, a spatial decomposition approach, as a potential model reduction technique, has been investigated. Results showed that the examined lignocellulose-based biorefining network for both sce-

38


Page 38 of 56

Page 39 of 56 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


narios produce an interesting business case for investments in such novel infrastructures. In particular, the centralised scenario seems to be only 0.2% more profitable than the distributed scenario, due to the significant decrease of transport costs, despite a minor increase of the capital expenditures, caused by the installation of a few more plants. Regional restrictions could impose the dominance of the centralised configuration compared to the other. For instance, in the case that the examined region offers limited number of cells appropriate for facility installation, due to large agricultural areas, it would be more preferable to design the SC system considering grouping the relating processing facilities (i.e. centralised scenario). Similar results are obtained from the application of the proposed spatial decomposition methodology (i.e. the centralised scenario is 0.1% more profitable than the distributed one), without, though, improved computational time. Moreover, the economies of scale are not largely exploited in the centralised scenario, when using the discussed decomposition approach. Overall, although the spatial decomposition approach used as a potential solution procedure of the discussed biorefining SC problem, preserved accuracy of the results, it did not add benefit regarding the reduction of computational time. In the future, the model could account for different modes of transportation and distribution of commodities, along with different feedstocks, process technologies and product types, enhancing the integrated technology superstructure. Furthermore, a temporal decomposition approach, other regional case studies as well as the effects of uncertainties will be examined. In addition, environmental impacts will be evaluated along with economic criteria.

Acknowledgement The EC (Reneseng-607415 FP7-PEOPLE-2013-ITN) is gratefully acknowledged for supporting this work. Prof. Kohlheb Norbert and the Szent Istvan University (Hungary) are thanked for providing support in the agronomical and economic characterisation of the region studied.

39



Supporting Information Available Tables showing the regional input parameters of the Hungarian case study, such as the x,y coordinates of the cells centroids, the arable land density and the biomass cultivation yields, along with the relating references (Appendix I). This material is available free of charge via the Internet at http://pubs.acs.org/.

Nomenclature Sets/Indices C

set of all commodities (i.e. biomass, intermediates and final products) indexed by c, c0

G

set of square cells (regions) indexed by g, g 0

K

set of type and scale of conversion technologies indexed by k

L

set of transport modes indexed by l

T

set of time periods indexed by t

J

set of aggregated clusters indexed by j, j 0

GJ

subset of square cells g contained in the aggregated cluster j

GAJ

subset of square cells g contained in the aggregated clusters j that are ML active in the solution of the master MILP (those for which Xk,j takes

a value of one)

Scalars af

annualization factor

LDlimit

minimum distance between neighbour cells (km)

Parameters

40


Page 40 of 56

Page 41 of 56 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


ALg

arable land density in region g (km2 of arable land/km2 of grid surface)

BCc

fraction of cultivation area devoted to biomass type c (crop share) (km2 allocated to crop c/km2 of cereals)

BCYc,g,t

cultivation yield of biomass c in region g at time t (kt/month/km2 )

CIk

capital investment of technology k (eM)

F Capk

maximum input flow rate capacity of technology k (kt/month)

γc0 ,c,k

conversion factor of commodity c to commodity c0 in technology k (kt of input commodity c0 /kt or GWh of output commodity c)

GSg

surface of square region g (km2 )

LDg,g0

straight delivery distance between regions g and g 0 (km)

M Dc,g,t

market demand of product c in region g at time t (kt or GWh of product/month)

Pc

selling price of product type c (eM/kt or GWh of product)

QCapc,l

maximum transport flow of commodity c via mode l (kt/month)

SCapc

maximum storage capacity of commodity c in each region (kt)

τg,l,g0

tortuosity factor of transport mode l between regions g and g 0

U CCc

unit cultivation cost of biomass type c (eM/kt)

U P Cc,k

unit process cost of commodity c in technology k (eM/kt)

U SCc

unit storage cost for commodity c (eM/kt)

U T Cc,l

unit transportation cost for commodity c via mode l (eM/kt/km)

L ALM j

fraction of arable land area in cluster j (%) (master level)

ML BCYc,j,t

cultivation yield of biomass c in cluster j at time t (kt/month/km2 ) (master level)

GSjM L

surface of cluster j (km2 ) (master level)

ML LDj,j 0

straight delivery distance between clusters j and j 0 (km) (master level)

41



ML M Dc,j,t

market demand of product c in cluster j at time t (kt or GWh of product/month) (master level)

L SCapM c,j

maximum storage capacity of commodity c in cluster j (kt) (master level)

ML τj,l,j 0

tortuosity factor of transport model l between clusters j and j 0 (master level)

Binary variables Xk,g

1 if a production facility of technology k is installed in region g, 0 otherwise

ML Xk,j

1 if a production facility of technology k is installed in cluster j, 0 otherwise (master level)

Continuous variables BPc,g,t

cultivation flow rate of biomass type c in region g at time t (kt/month)

CCt

biomass cultivation cost at time t (eM/month)

Dc,g,t

demand of commodity type c in region g at time t (kt/month)

In Fc,k,g,t

consumtion (inflow) flow rate of commodities c in technology k in region g at time t (kt/month)

Out Fc,k,g,t

production (outflow) flow rate of commodities c from technology k in region g at time t (kt or GWh/month)

P Ct

process cost at time t (eM/month)

Qc,g,l,g0 ,t

transport flow rate of commodity c via mode l between regions g and g 0 at time t (kt/month)

Rt

revenues at time t (eM/month)

42


Page 42 of 56

Page 43 of 56 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


Sc,g,t

storage rate of commodities c in region g at time t (kt/month)

SCt

storage cost of commodities c at time t (eM/month)

StCc,g,t

physical meaning of storage rate of commodities c in region g at time t (kt/month)

T Ct

transport cost of commodities at time t (eM/month)

T CC

total (annualised) capital cost (eM/y)

T OCt

total operating cost at time t (eM/month)

TP

total (annualised) profit (eM/y)

ML BPc,j,t

cultivation flow rate of biomass type c in cluster j at time t (kt/month) (master level)

CCtM L

biomass cultivation cost at time t (eM/month) (master level)

ML Dc,j,t

demand of commodity type c in cluster j at time t (kt/month) (master level)

In,M L Fc,k,j,t

consumtion (inflow) flow rate of commodities c in technology k in cluster j at time t (kt/month) (master level)

Out,M L Fc,k,j,t

production (outflow) flow rate of commodities c from technology k in cluster j at time t (kt or GWh/month) (master level)

P CtM L

process cost at time t (eM/month) (master level)

L QM c,j,l,j 0 ,t

transport flow rate of commodity c via mode l between clusters j and j 0 at time t (kt/month) (master level)

RtM L

revenues at time t (eM/month) (master level)

ML Sc,j,t

storage rate of commodities c in cluster j at time t (kt/month) (master level)

SCtM L

storage cost of commodities c at time t (eM/month) (master level)

ML StCc,j,t

physical meaning of storage rate of commodities c in cluster j at time t (kt/month) (master level)

T CtM L

transport cost of commodities at time t (eM/month) (master level) 43



T CC M L

total (annualised) capital cost (eM/y) (master level)

T OCtM L

total operating cost at time t (eM/month) (master level)

T P ML

total (annualised) profit (eM/y) (master level)

Page 44 of 56

Master MILP model

L ALM = j

X

ALg , ∀j ∈ J

(29)

g⊂GJ

ML BCYc,j,t =

X

BCYc,g,t , ∀c ∈ C, j ∈ J, t ∈ T

(30)

g⊂GJ

GSjM L =

X

GSg , ∀j ∈ J

(31)

M Dc,g,t , ∀c ∈ C, j ∈ J, t ∈ T

(32)

X

(33)

g⊂GJ

ML M Dc,j,t =

X g⊂GJ

L SCapM c,j =

SCapc , ∀c ∈ C, j ∈ J

g⊂GJ

ML LDj,j min LDg,g0 , ∀j, j 0 ∈ J 0 = 0 g,g ⊂GJ

44


(34)

Page 45 of 56 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


ML τj,l,j min τg,l,g0 , ∀j, j 0 ∈ J, l ∈ L 0 = 0

(35)

max T P M L

(36)

g,g ⊂GJ

T P ML =

X

RtM L − T CC M L −

T OCtM L

(37)

t∈T

t∈T

RtM L =

X

XXX

Out,M L PcM L Fc,k,j,t , ∀t ∈ T

(38)

c∈C k∈K j∈J

T CC M L =

XX

ML af CIk Xk,j

(39)

k∈K j∈J

T OCtM L = CCtM L + SCtM L + T CtM L + P CtM L , ∀t ∈ T

CCtM L =

XX

(40)

ML U CCc BPc,j,t , ∀t ∈ T

(41)

ML U SCc StCc,j,t , ∀t ∈ T

(42)

c∈C j∈J

SCtM L =

XX c∈C j∈J

T CtM L =

X X X

ML ML ML U T Cc,l LDj,j 0 τj,l,j 0 Qc,j,l,j 0 ,t , ∀t ∈ T

c∈C j,j 0 ∈J l∈L

45


(43)


P CtM L =

XXX

Page 46 of 56

In,M L , ∀t ∈ T U P Cc,k Fc,k,j,t

(44)

c∈C k∈K j∈J

Out,M L Fc,k,j,t =

X

L γc0 ,c,k FcIn,M 0 ,k,j,t , ∀c ∈ C, k ∈ K, j ∈ J, t ∈ T

(45)

c0 ∈C

ML ML , ∀c ∈ C, j ∈ J, t ∈ T ≤ M Dc,j,t Dc,j,t

ML BPc,j,t +

X

Out,M L Fc,k,j,t +

XX

L ML QM c,j 0 ,l,j,t = Sc,j,t +

l∈L j 0 ∈J

k∈K ML +Dc,j,t +

XX

(46)

X

In,M L Fc,k,j,t

k∈K L QM c,j,l,j 0 ,t , ∀c ∈ C, j ∈ J, t ∈ T

(47)

l∈L j 0 ∈J

ML L ML ML BPc,j,t ≤ ALM BCc BCYc,j,t , ∀c ∈ C, j ∈ J, t ∈ T j GSj

X

In,M L L ML Fc,k,j,t ≤ F CapM k Xk,j , ∀k ∈ K, j ∈ J, t ∈ T

(48)

(49)

c∈C

L 0 QM c,j,l,j 0 ,t ≤ QCapc,l , ∀c ∈ C, j, j ∈ J, l ∈ L, t ∈ T

(50)

0 0 L QM c,j,l,j 0 ,t = 0, ∀c ∈ C, j, j ∈ J, l ∈ L, t ∈ T : j = j

(51)

X

ML Sc,j,t = 0, ∀c ∈ C, j ∈ J

t∈T

46


(52)

Page 47 of 56 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


ML ML StCc,j,t ≥ Sc,j,t , ∀c ∈ C, j ∈ J, t ∈ T

(53)

ML L StCc,j,t ≤ SCapM c,j , ∀c ∈ C, j ∈ J, t ∈ T

(54)

ML BPc,j,t ≥ 0, ∀c ∈ C, j ∈ J, t ∈ T

(55)

ML Dc,j,t ≥ 0, ∀c ∈ C, j ∈ J, t ∈ T

(56)

In,M L Fc,k,j,t ≥ 0, ∀c ∈ C, k ∈ K, j ∈ J, t ∈ T

(57)

Out,M L Fc,k,j,t ≥ 0, ∀c ∈ C, k ∈ K, j ∈ J, t ∈ T

(58)

L 0 QM c,j,l,j 0 ,t ≥ 0, ∀c ∈ C, j, j ∈ J, l ∈ L, t ∈ T

(59)

ML StCc,j,t ≥ 0, ∀c ∈ C, j ∈ J, t ∈ T

(60)

max T P

(61)

Slave MILP model

TP =

X

Rt − T CC −

t∈T

X

T OCt

t∈T

47


(62)


Rt =

XX X

Out Pc Fc,k,g,t , ∀t ∈ T

Page 48 of 56

(63)

c∈C k∈K g⊂GAJ

T CC =

X X

af CIk Xk,g

(64)

k∈K g⊂GAJ

T OCt = CCt + SCt + T Ct + P Ct , ∀t ∈ T

X X

CCt =

(65)

U CCc BPc,g,t , ∀t ∈ T

(66)

U SCc StCc,g,t , ∀t ∈ T

(67)

c∈C g⊂GAJ

SCt =

X X c∈C g⊂GAJ

T Ct =

X

X

X

U T Cc,l LDg,g0 τg,l,g0 Qc,g,l,g0 ,t , ∀t ∈ T

(68)

c∈C g,g 0 ⊂GAJ l∈L

P Ct =

XX X

In U P Cc,k Fc,k,g,t , ∀t ∈ T

(69)

c∈C k∈K g⊂GAJ

Out = Fc,k,g,t

X

γc0 ,c,k FcIn 0 ,k,g,t , ∀c ∈ C, k ∈ K, g ⊂ GAJ, t ∈ T

(70)

c0 ∈C

Dc,g,t ≤ M Dc,g,t , ∀c ∈ C, g ⊂ GAJ, t ∈ T

48


(71)

Page 49 of 56 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


BPc,g,t +

X

Out Fc,k,g,t +

X X

Qc,g0 ,l,g,t = Sc,g,t +

l∈L g 0 ⊂GAJ

k∈K

+Dc,g,t +

X X l∈L

X

In Fc,k,g,t

k∈K

Qc,g,l,g0 ,t , ∀c ∈ C, g ⊂ GAJ, t ∈ T

BPc,g,t ≤ ALg GSg BCc BCYc,g,t , ∀c ∈ C, g ⊂ GAJ, t ∈ T

X

(72)

g 0 ⊂GAJ

In Fc,k,g,t ≤ F Capk Xk,g , ∀k ∈ K, g ⊂ GAJ, t ∈ T

(73)

(74)

c∈C

X

Xk,g ≤ 1, ∀g ⊂ GAJ (distributed scenario)

(75)

Xk,g ≤ |K|, ∀g ⊂ GAJ (centralised scenario)

(76)

k∈K

X k∈K

Qc,g,l,g0 ,t ≤ QCapc,l , ∀c ∈ C, g, g 0 ⊂ GAJ, l ∈ L, t ∈ T

(77)

Qc,g,l,g0 ,t = 0, ∀c ∈ C, g, g 0 ⊂ GAJ, l ∈ L, t ∈ T : LDg,g0 > LDlimit

(78)

Qc,g,l,g0 ,t = 0, ∀c ∈ C, g, g 0 ⊂ GAJ, l ∈ L, t ∈ T : g = g 0

(79)

X

Sc,g,t = 0, ∀c ∈ C, g ⊂ GAJ

t∈T

49


(80)


Page 50 of 56

StCc,g,t ≥ Sc,g,t , ∀c ∈ C, g ⊂ GAJ, t ∈ T

(81)

StCc,g,t ≤ SCapc,g , ∀c ∈ C, g ⊂ GAJ, t ∈ T

(82)

BPc,g,t ≥ 0, ∀c ∈ C, g ⊂ GAJ, t ∈ T

(83)

Dc,g,t ≥ 0, ∀c ∈ C, g ⊂ GAJ, t ∈ T

(84)

In Fc,k,g,t ≥ 0, ∀c ∈ C, k ∈ K, g ⊂ GAJ, t ∈ T

(85)

Out Fc,k,g,t ≥ 0, ∀c ∈ C, k ∈ K, g ⊂ GAJ, t ∈ T

(86)

Qc,g,l,g0 ,t ≥ 0, ∀c ∈ C, g, g 0 ⊂ GAJ, l ∈ L, t ∈ T

(87)

StCc,g,t ≥ 0, ∀c ∈ C, g ⊂ GAJ, t ∈ T

(88)

References (1) Intergovernmental Panel on Climate Change (IPCC), Intergovernmental Panel on Climate Change (IPCC). Available from: http://www.ipcc.ch/ 2017, [last accessed May 2017]. (2) European Commission (EC) Directive 2009/28/EC of the European Parliament and

50


Page 51 of 56 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


of the Council of 23 April 2009 on the promotion of the use of energy from renewable sources and amending and subsequently repealing Directives 2001/77/EC and 2003/30/EC, European Commission (EC), Directive 2009/28/EC of the European Parliament and of the Council of 23 April 2009 on the promotion of the use of energy from renewable sources and amending and subsequently repealing Directives 2001/77/EC and 2003/30/EC. Official Journal of the European Parliament, 2009, Brussels, Belgium. (3) Čuček, L.; Martín, M.; Grossmann, I. E.; Kravanja, Z. Multi-period synthesis of optimally integrated biomass and bioenergy supply network. Computers and Chemical Engineering 2014, 66, 57–70. (4) You, F.; Tao, L.; Graziano, D. J.; Snyder, S. W. Optimal Design of Sustainable Cellulosic Biofuel Supply Chains: Multiobjective Optimization Coupled with Life Cycle Assessment and Input-Output Analysis. AIChE Journal 2012, 58, 1157–1180. (5) Akgul, O.; Shah, N.; Papageorgiou, L. G. Economic optimisation of a UK advanced biofuel supply chain. Biomass and Bioenergy 2012, 41, 57–72. (6) BIOCORE - FINAL REPORT, BIOCORE-FINAL REPORT [online]. Available from: http://www.biocore-europe.org/file/BIOCORE%20final%20report(1).pdf 2014, [last accessed May 2017]. (7) Panteli, A.; Giarola, S.; Shah, N. Biobased Supply Chain Optimisation Model under Uncertainties. Computer Aided Chemical Engineering 2017, 40, 961–966. (8) Giarola, S.; Zamboni, A.; Bezzo, F. Spatially explicit multi-objective optimisation for design and planning of hybrid first and second generation biorefineries. Computers and Chemical Engineering 2011, 35, 1782–1797. (9) Marvin, W. A.; Schmidt, L. D.; Daoutidis, P. Biorefinery location and technology

51



selection through supply chain optimization. Ind. Eng. Chem. Res. 2013, 52, 3192– 3208. (10) Zamboni, A.; Shah, N.; Bezzo, F. Spatially explicit static model for the startegic design of future bioethanol production systems. 1. Cost minimization. Energy Fuels 2009, 23, 5121–5133. (11) Akgul, O.; Zamboni, A.; Bezzo, F.; Shah, N.; Papageorgiou, L. G. Optimization-based approaches for bioethanol supply chains. Ind. Eng. Chem. Res. 2011, 50, 4927–4938. (12) Bowling, I. M.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Facility Location and Supply Chain Optimization for a Biorefinery. Ind. Eng. Chem. Res. 2011, 50, 6276–6286. (13) Corsano, G.; Fumero, Y.; Montagna, J. M. Integrated decision making for the optimal bioethanol supply chain. Energy Conversion and Management 2014, 88, 1127–1142. (14) Dunnett, A. J.; Adjiman, C. S.; Shah, N. A spatially explicit whole-system model of the lignocellulosic bioethanol supply chain: an assessment of decentralised processing potential. Biotechnology for Biofuels 2008, 1, 1–17. (15) Ekşioğlu, S. D.; Acharya, A.; Leightley, L. E.; Arora, S. Analyzing the design and management of biomass-to-biorefinery supply chain. Computers & Industrial Engineering 2009, 57, 1342–1352. (16) An, H.; Wilhelm, W. E.; Searcy, S. W. A mathematical model to design a lignocellulosic biofuel supply chain system with a case study based on a region in Central Texas. Bioresource Technology 2011, 102, 7860–7870. (17) Kim, J.; Realff, M. J.; Lee, J. H.; Whittaker, C.; Furtner, L. Design of biomass processing network for biofuel production using an MILP model. Biomass and Bioenergy 2011, 35, 853–871.

52


Page 52 of 56

Page 53 of 56 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


(18) Marvin, W. A.; Schmidt, L. D.; Benjaafar, S.; Tiffany, D. G.; Daoutidis, P. Economic optimization of a lignocellulosic biomass-to-ethanol supply chain. Chemical Engineering Science 2011, 67, 68–79. (19) Kim, J.; Sen, S. M.; Maravelias, C. T. An optimization-based assessment framework for biomass-to-fuel conversion strategies. Energy Environ. Sci. 2013, 6, 1093–1104. (20) Lin, T.; Rodríguez, L. F.; Shastri, Y. N.; Hansen, A. C.; Ting, K. C. Integrated strategic and tactical biomass-biofuel supply chain optimization. Bioresource Technology 2014, 156, 256–266. (21) Cambero, C.; Sowlati, T.; Pavel, M. Economic and life cycle environmental optimization of forest-based biorefinery supply chains for bioenergy and biofuel production. Chemical Engineering Research and Design 2016, 107, 218–235. (22) Ng, R. T. L.; Maravelias, C. T. Design of biofuel supply chains with variable regional depot and biorefinery locations. Renewable Energy 2017, 100, 90–102. (23) Gargalo, C. L.; Carvalho, A.; Gernaey, K. V.; Sin, G. Supply Chain Optimization of Integrated Glycerol Biorefinery: GlyThink Model Development and Application. Industrial & Engineering Chemistry Research 2017, 56, 6711–6727. (24) Čuček, L.; Lam, H. L.; Klemeš, J. J.; Varbanov, P. S.; Kravanja, Z. Synthesis of regional networks for the production and supply of renewable energy and bioproducts. Clean Techn. Environ. Policy 2010, 12, 635–645. (25) Santibanez-Aguilar, J. E.; González-Campos, J. B.; Ponce-Ortega, J. M.; SernaGonzález, M.; El-Halwagi, M. M. Optimal planning and site selection for distributed multiproduct biorefineries involving economic, environmental and social objectives. Journal of Cleaner Production 2014, 65, 270–294.

53



(26) D’Amore, F.; Bezzo, F. Strategic optimisation of biomass-based energy supply chains for sustainable mobility. Computers and Chemical Engineering 2016, 87, 68–81. (27) Miret, C.; Chazara, P.; Montastruc, L.; Negny, S.; Domenech, S. Design of bioethanol green supply chain: Comparison between first and second generation biomass concerning economic, environmental and social criteria. Computers and Chemical Engineering 2016, 85, 16–35. (28) Panteli, A.; Giarola, S.; Shah, N. Lignocellulosic supply chain MILP model: A Hungarian case study. Computer Aided Chemical Engineering 2016, 38, 253–258. (29) Mountraki, A.; Pyrgakis, K.; Nikolakopoulos, A.; Benjelloun-Mlayah, B.; Kokossis, A. Deliverable D5.5: Process designs and flowsheet models: CIMV and the BIOCORE pilots (Dissemination level: Restricted), u.o.: u.n. 2010-2014, (30) Mountraki, A. D.; Koutsospyros, K. R.; Mlayah, B. B.; Kokossis, A. C. Selection of Biorefinery Routes: The Case of Xylitol and its Integration with an Organosolv Process. Waste and Biomass Valorization 2017, 1–18. (31) Giarola, S.; Shah, N.; Bezzo, F. A comprehensive approach to the design of ethanol supply chain including carbon trading effects. Bioresource Technology 2012, 107, 175– 185. (32) CORINE Land Cover (CLC), CORINE Land Cover (CLC) 2012 [online]. Available from: http://land.copernicus.eu/pan-european/corine-land-cover/clc-2012 2012, [last accessed May 2017]. (33) Copado-Méndez, P. J.; Guillén-Gosálbez, G.; Jiménez, L. MILP-based decomposition algorithm for dimensionality reduction in multi-objective optimization: Application to environmental and systems biology problems. Computers and Chemical Engineering 2014, 67, 137–147.

54


Page 54 of 56

Page 55 of 56 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


(34) Vaskan, P.; Guillén-Gosálbez, G.; Kostin, A.; Jiménez, L. Decomposition algorithm for geographic information system based mixed-integer linear programming models: Application to sewage sludge amendment. Ind. Eng. Chem. Res. 2013, 52, 17640– 17647. (35) Guillén-Gosálbez, G.; Mele, F. D.; Grossmann, I. E. A bi-criterion optimization approach for the design and planning of hydrogen supply chains for vehicle use. AIChE Journal 2010, 56, 650–667. (36) Bok, J. K.; Grossmann, I. E.; Park, S. Supply chain optimization in continuous flexible process networks. Ind. Eng. Chem. Res. 2000, 39, 1279–1290. (37) GAMS - A user’s guide,

GAMS-A user’s guide [online]. Available from:

http://www.gams.com/latest/docs/userguides/ GAMSUsersGuide.pdf 2017, [last accessed May 2017]. (38) MATLAB, Available from: http://uk.mathworks.com/ 2017, [last accessed May 2017].

55


Graphical TOC Entry Biobased Supply Chain Network

Planning & Operating Decisions

MILP Optimisation 𝑚𝑎𝑥$,&𝑓 𝑥, 𝑦 𝑠. 𝑡. ℎ 𝑥, 𝑦 = 0 𝑔 𝑥, 𝑦 ≤ 0 𝑥 ⊂ ℛ, 𝑦 ⊂ {0,1}

OPEX 300

VALUE (M€)

250 8

downstream

6

Z

200 150 100

4

50

2

0 1

0

2

3

4

5

6

7

8

9

10

11

12

MONTHS

-2

Cultivation Cost

-4

Processing Cost

Transport Cost

Storage Cost

-6

REVENUES

-8 25 20

25 15

20 15

10

10

5

Y

5 0

0

X

VALUE (M€)

upstream

1440 1430 1420 1410 1400 1390 1380 1370 1360 1350 1340 1330 1

2

3

4

5

6

7

MONTHS

56

8

9

10

11

12

Supply Chain MILP Model Integrating Biorefining Technology

Recommend Documents