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Applied Energy 90 (2012) 154–160

Contents lists available at ScienceDirect

Applied Energy

jou r n a l hom ep ag e : www . e l sev i e r . co m / l ocat e / a p e n e r g y

A fuzzy multi-regional input–output optimization model for biomass production and trade under resource and footprint constraints

Raymond R. Tan a,b,⇑, Kathleen B. Aviso a,b, Ivan U. Barilea a, Alvin B. Culaba b,c, Jose B. Cruz Jr. d

a Chemical Engineering Department, De La Salle University, Manila, Philippinesb Center for Engineering and Sustainable Development Research, De La Salle University, Manila, Philippinesc Mechanical Engineering Department, De La Salle University, Manila, Philippinesd Department of Electrical and Computer Engineering, The Ohio State University, USA

a r t i c l e i n f o

Article history:Received 16 September 2010Received in revised form 11 January 2011Accepted 13 January 2011Available online 12 February 2011

Keywords: Biomass Input–output model Fuzzy optimization Footprint

a b s t r a c t

Interest in bioenergy in recent years has been stimulated by both energy security and climate change concerns. Fuels derived from agricultural crops offer the promise of reducing energy dependence for countries that have traditionally been dependent on imported energy. Nevertheless, it is evident that the potential for biomass production is heavily dependent on the availability of land and water resources. Furthermore, capacity expansion through land conversion is now known to incur a significant carbon debt that may offset any benefits in greenhouse gas reductions arising from the biofuel life cycle. Because of such constraints, there is increasing use of non-local biomass through regional trading. The main chal- lenge in the analysis of such arrangements is that individual geographic regions have their own respec- tive goals. This work presents a multi-region, fuzzy input–output optimization model that reflects production and consumption of bioenergy under land, water and carbon footprint constraints. To offset any local production deficits or surpluses, the model allows for trade to occur among different regions within a defined system; furthermore, importation of additional biofuel from external sources is also allowed. Two illustrative case studies are given to demonstrate the key features of the model.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Global interest in bioenergy has grown in recent years due to a number of factors. Historically, demand for biofuels has always grown in response to upward trends in the prices of conventional fossil fuels, particularly petroleum. More recently, concerns about climate change have also driven growth in biofuel production, since bioenergy fuel cycles can, in principle, approach carbon neu- trality at steady-state production levels. Under such conditions, upstream carbon fixation by energy crops during photosynthesis offsets the corresponding downstream carbon emissions from bio- mass combustion. In addition, the production and use of biofuels can yield some important economic benefits, such as enhancing energy security in countries that are otherwise heavily dependent on petroleum imports. Increased utilization of crops can also stim- ulate economic growth in underdeveloped rural areas by creating employment opportunities and by developing alternative markets for crops. Thus, in recent years there has been a dramatic increase

⇑ Corresponding author at: Chemical Engineering Department, De La SalleUniversity, Manila, Philippines. Tel.: +63 2 536 0260.

E-mail addresses: raymond.tan@dlsu.edu.ph (R.R. Tan), kathleen.aviso@dlsu. edu.ph (K.B. Aviso), idbarilea@yahoo.com (I.U. Barilea), alvin.culaba@dlsu.edu.ph (A.B. Culaba), jbcruz@ieee.org (J.B. Cruz).

in the global production and use of liquid biofuels for motor vehi- cles. In many countries, policies have been implemented that encourage, or even mandate, the commercial use of biodiesel or bioethanol at prescribed blending rates [1–7].

Although environmental and economic benefits may arise from the large-scale production and use of biofuels, there may also be significant disadvantages to this global trend. Firstly, because mostfirst-generation biofuels are derived from traditional food crops, the limited availability of agricultural land imposes constraints on the production of biofuels [8–10]. This remains a key issue in both developed economies (which are often characterized by high energy intensity levels) as well as in the developing world (where low agricultural productivity often accompanies rapid growth in population and energy demand). Similarly, the availability of water is also expected to be a major constraint to biofuel production [11,12]. The problem is now exacerbated by the risk of shifts in rainfall patterns across the world as a result of climate change. It has also been shown that the increase of biofuel production levels results in a ‘‘carbon debt’’ due to land use changes whenever pris- tine ecosystems are converted into plantations for the cultivation of energy crops [13]. This initial surge of carbon emissions may thus offset the greenhouse gas reductions that arise from biofuel use. Furthermore, there is a tradeoff between carbon emissions and land or water footprints, as more energy-intensive (and thus

0306-2619/$ - see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.01.032

q

q

r

r

v

w

y

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R.R. Tan et al. / Applied Energy 90 (2012) 154–160 155

carbon-intensive) agricultural inputs are required in order to improve crop yields. It is evident from all of these considerations that the potential benefits of large-scale bioenergy production need to be weighed against the possible strain placed on agricul- tural resources that are also essential for food production.

Different methodologies have been proposed to aid in planning bioenergy production under such resource and footprint con- straints. Graphical or numerical pinch analysis approaches have been proposed to account for carbon [14–16], land [16] and water footprint [17] constraints. The techniques are able to identify opti- mal levels, or ‘‘targets,’’ of bioenergy production, and provide guidelines or heuristics for optimal allocation across economic sec- tors. Related modeling techniques such as input–output analysis (IOA) [18,19], system perturbation analysis (SPA) [20], life cycle assessment (LCA) [21,22] may also be used to analyze bioenergy production systems. Recent variants of LCA have been proposed to account for uncertainties in data using fuzzy numbers [23] as well as the dynamics of production growth [24]. Furthermore, graphical approaches based on pinch analysis have also been developed to aid in planning while taking into account the season- ality of biomass production [25,26].

LCA-based fuzzy optimization models have been proposed for generic life cycle systems [27] and for bioenergy systems in particu- lar [28]. The latter made use of a ‘‘triple footprint’’ profile that simul- taneously accounts for carbon emission, land use and water consumption goals of a given system. However, these models as- sumed a single unified system wherein all the biomass production and consumption takes place. On the other hand, recent trends have shown increased biomass trade from regions with surplus produc- tion capacities to regions with deficits [29–33]. For example, Walter et al. [31] concluded that, without significant breakthroughs in cel- lulosic ethanol production technologies, 10% displacement of the2030 gasoline demand in major oil-consuming economies can only be achieved through bioethanol trade; they also reported that about one-tenth of current global bioethanol production is traded. Further-

production, are then solved to illustrate the use of the model. Finally, conclusions and prospects for future work are given.

2. Problem statement

The problem addressed by the model is as follows. The system has Nk regions, NR feedstocks and NP final bioenergy products. Each region has a specified fuzzy final demand for a set of bioenergy products, a fuzzy limit on relevant environmental (i.e., carbon, land and water) footprints, and fixed agricultural and process yields as defined in the form of technological coefficients. Linear fuzzy membership functions are used here since, in practice, sparse data often makes it difficult to determine the exact shape of non-linear membership functions; furthermore, the assumption of linearity minimizes computational difficulties in determining a globally optimal solution. Each region may produce feedstocks internally in order to satisfy its final biofuel demand. It may also select to im- port or export biomass, depending on the internally specified pro- duction-based footprint limits. In addition to biomass trade among the regions within the system, importation of biomass from out- side of the system boundary is also considered in the model. The problem is to determine the optimal production and trade levels to satisfy the fuel demand and resource constraints of the regions that comprise the system. A schematic diagram of such a system with two regions is shown in Fig. 1.

3. Parameters and indexes

Ak Technology matrix for region kBk Environmental matrix for region k k Index for regionsNk Number of regionsNP Number of biofuel productsNR Number of feedstocks

more, there still remains significant potential for growth in total bio-energy trade, given that the current trade global level, which is about

Uexp;k

Upper bound vector for the export of bioenergy from region k to all other regions

1 EJ/a, is still well under the total bioenergy production of roughly50 EJ/a [33]. In some cases, there have also been demonstrable envi-

Dqexp,k Tolerance vector for the export of bioenergy from region k to all other regions

ronmental benefits in the non-local production of biofuels [34]. Suchcases require the cooperation of the importing and exporting parties,

Uimp;k

Upper bound vector for the import of bioenergy by region k from all other regions

who both need to take into account their respective bioenergy de-mands, as well as their carbon, land and water footprint limitations.

Dqimp,k Tolerance vector for the import of bioenergy by region k from all other regions

One approach for such systems makes use of graphical displays toidentify opportunities for biomass trade across adjacent geographi-

Uexp;k

Upper bound vector for the export of biomass from region k to all other regions

cal regions [35,36]. Likewise, mathematical programming basedmethods have been proposed to systematically plan biofuel produc-

Drexp,k Tolerance vector for the export of biomass from region k to all other regions

tion across multiple regions [37,38] or with recourse to importationin case of deficit [39].

Uimp;k

Upper bound vector for the import of biomass by region k from all other regions

This paper describes a multi-region extension of the modelsdeveloped by Tan et al. [27,28] that takes into account trade effects that have been integrated into standard IOA models [40]. There is a significant volume of global bioenergy trade that has emerged in re- sponse to imbalances between local energy demand and resource availability in various geographic regions; hence, the model devel- oped here is intended to provide a rigorous basis for determining the optimal production and trade patterns, given each region’s fuzzy energy demand and fuzzy resource or environmental limitations. The model is based on Bellman and Zadeh’s concept of seeking a

Drimp,k Tolerance vector for the import of biomass by regionk from all other regions

U Upper bound vector for biomass import by region kk

from beyond system boundaryDvk Tolerance vector for biomass imported by region k

from beyond system boundaryU Upper bound vector for final bioenergy import byk

region k from beyond system boundaryDwk Tolerance vector for final bioenergy imported by

region k from beyond system boundary‘‘confluence’’ of fuzzy goals and constraints in a complex decision Lmaking problem [41], which was later integrated into fuzzy mathe- k Lower bound vector of final bioenergy demand in

region kmatical programming using max–min aggregation [42]. The rest ofthis paper is organized as follows. A formal problem statement is gi-

Dyk Tolerance vector of final bioenergy demand in regionk

ven in the next section. This is followed by a description of the opti- Umization itself. Two case studies, the first involving generation of k

Upper bound vector of footprint limit in region k

electricity from biomass, and the second involving bioethanol Dzk Tolerance vector of footprint limit in region k

U

k

L

k

k

Reg

ion

1R

egio

n 2

156 R.R. Tan et al. / Applied Energy 90 (2012) 154–160

BiomassImports

BioenergyImports

Resources Biomass Bioenergy Demand

1 1 1 1

I R P J

NI NR NP N

J

Interregional Trade

1 1 1 1

I R P J

NI NR

NP

NJ

BiomassImports

BioenergyImports

Fig. 1. Schematic diagram of a multi-regional bioenergy supply chain (Nk = 2).

4. Variables

k Overall level of satisfaction of fuzzy constraintsqk0 k Final bioenergy import vector from region k0 to region krk0 k Biomass import vector from region k0 to region ksk Internal biomass production vector in region kvk Biomass import vector to region k from beyond system

boundarywk Final bionergy import vector to region k from beyond

system boundaryxk Internal biomass requirement vector in region k

5. Optimization model

corresponding to various modes of shipment, which is the ap- proach used even in conventional input–output models. In addi- tion, for the case of carbon footprints, the contribution of greenhouse gas emissions from transportation may also be re-flected in the coefficients of Bk. Each region k meets its biomass requirement (xk) through internal production (sk), import of biomass from a source external to the system (vk), and import of biomass (rk0 k) from every other region k0 within the system:

Nk

xk ¼ sk þ v k þ X

rk0 k 8k ð5Þ

k0

The import of final bioenergy by a region k from sources outside of the system boundary is restricted to within the correspondingfuzzy limit wU

The objective function is to maximize the overall level of satisfac- wk 6 wU

k - kðDwk Þ):

tion, k, of fuzzy goals or constraints within the entire model:

max k ð1Þk - kðDwk Þ 8k ð6Þ

Likewise, importation of biomass by a region k from external sources is also restricted to within the corresponding fuzzy limit v U

)

The variable k is bounded within the interval:

k 2 ½0; 1] ð2Þ

k - kðDvk Þ :

vk 6 v k - kðDv k Þ 8k

ð7Þ

Upon conversion, the total biomass requirement (xk) within a given region k, combined with imports of final bioenergy from be- yond the system (wk) and from every other region k0 within the system (qk0 k) must be sufficient to meet the corresponding fuzzy fi- nal demand for bioenergy (yL + k(Dyk)):

Nk

Ak xk þ wk þ X

qk0 k P yk þ kðDyk Þ 8k ð3Þk0

Total internal production of biomass (sk) within a given region k

This formulation implies the decision-makers within the re- gions of the system are not concerned with the environmental or natural resource burdens of the biomass imported from beyond the system itself. However, a limit on importation of either final bioenergy or raw biomass from this external source is imposed using Eqs. (6) and (7), respectively, as it defeats the energy security benefits of utilizing biofuels in the first place. Inter-regional trade of final both bioenergy and biomass feedstock is then subject to the following constraints. By definition, each region does not trade with itself:

is subject to corresponding fuzzy environmental constraints that reflect flexible limits on resources and emissions (zU - k(Dzk)):

qk0 k ¼ 0 8k ¼ k0 ð8Þ

Bk sk 6 zU - kðDzk Þ 8k ð4Þ

Matrices Ak and Bk signify the processing and agricultural yields, respectively, in a given region k. These yields may be deter- mined from first principles (i.e., theoretical material and energy balances) or empirically (i.e., from historical field data). It can also be seen that the yields may or may not be the same across the dif- ferent regions. Note that, if necessary, transportation may be incor-

porated in the model simply by inserting additional columns

rk0 k ¼ 0 8k ¼ k0 ð9Þ

Trade flows for any two regions are reflexive, such that the im- port of either final bioenergy or raw biomass region k from k0 is equivalent to the export of region k0 to k:

qk0 k ¼ -qkk0 8k–k0 ð10Þ

rk0 k ¼ -rkk0 8k–k0 ð11Þ

Region Electricity demand lower

Electricity demand

Electricity export upper

Electricity export

limit (106 GJ/a) tolerance(106 GJ/a)

limit (106 GJ/a) tolerance(106 GJ/a)

BiomassA

I II

I 5 5 20 20 Biomass III 15 15 10 10 B II

U

exp;k

exp;k

U

k

R.R. Tan et al. / Applied Energy 90 (2012) 154–160 157

Fuzzy limits are also imposed on the total inter-regional export or import of final bioenergy within each region k:

Nk

it is no longer necessary to define their corresponding import lim- its, as these are already implied by the export constraints, and in this instance Eq. (12b) is no longer necessary. Furthermore, importX

qkk0 6 q ;k - kðDqexp;k Þ 8k–k0 ð12aÞ of electricity from sources outside of the two regions is not consid-exp

k0 ered (thus, we impose the constraintwk = 0 in place of Eq. (6)). It is

NkX qk0 k 6 qimp;k - kðDqimp;k Þ 8k–k0 ð12bÞ

k0

Likewise, fuzzy limits are also imposed on the total inter-regio- nal export or import of raw biomass within each region k:

Nk

assumed that there are two biomass resources, denoted here asBiomass A and Biomass B, which can be used as fuel for generating electricity in thermal power plants in either region. Biomass A can be cultivated only in Region I, while Biomass B can be grown in both regions. Table 2 gives the land and water footprint data of the two types of biomass, which serve as coefficients for Bk, as well as their respective heating values. The latter data, combined withthe assumption of 30% thermal efficiency for all power plants with-X

rkk0 6 rk0

Uexp;k - kðDrexp;k Þ 8k–k0 ð13aÞ in the system, give the parameters of Ak. Table 3 gives the upper

limits (zU ) and fuzzy tolerances (Dz ) on land and water resourcesk k

in Regions I and II that are available for biomass production. Fur-Nk

U thermore, it is assumed that the raw biomass can be traded be-X rk0 k 6 rimp;k - kðDrimp;k Þ 8k–k0 ð13bÞ

k0 tween the two regions, or even imported from external sources.The fuzzy limits for biomass inter-regional exports (rU , Drexp,k)

Total biomass production (sk), requirement (xk) and externalimport (vk and wk) levels within each region k are non-negative:

sk P 0 8k ð14Þ

are given in the third and fourth columns of Table 4, respectively. With only two regions in the system, Eq. (13b) also becomes redundant since one region’s export immediately defines the other’s import. The fuzzy limits for import of biomass from exter-

xk P 0 8k ð15Þ nal sources (v U

Table 4.and Dvk) are also found in the last two columns of

v k P 0 8k ð16Þ

wk P 0 8k ð17Þ

The variable k occurs in Eqs. (3), (4), (6), and (7), which define the fuzzy goals for final energy demand, resource consumption, fi- nal energy imports and biomass imports, respectively. Note that the most desirable values for these goals (i.e., maximum energy output and minimum resource use and minimum imports) occur when k = 1. Hence, maximizing k is equivalent to seeking a solution which simultaneously approaches the most desirable limits of all fuzzy goals. Since the fuzzy goals may be mutually conflicting, the resulting optimal value of k will typically fall within the fuzzy tolerance; thus, such a solution represents a compromise among the various fuzzy goals specified for the system. It can also be seen

Table 5 gives the biomass production and trade levels of the two regions upon solving for the objective function (Eq. (1)) subject to Eqs. (2)–(5) and Eqs. (7)–(11), (12a), (12b), (13a), (13b), (14)–(17). Similarly, Table 6 gives the production and trade levels of the elec- tricity generated. It can be seen that Region I produces 0.6 x 106

t/a of Biomass A and 2.9 x 106 t/a of Biomass B; however, all of the for- mer is exported to Region II, while all of the latter is consumed internally. Furthermore, nearly half of the electricity generated by Region I using Biomass B (i.e., 6.3 x 106 GJ/a out of a total of13.2 x 106 GJ/a) is also exported to Region II, whose energy de-mand of 20.8 x 106 GJ/a is disproportionately large in comparison

Table 2Land and water footprint and heating value data of feedstocks (Case 1).

that this formulation is a linear programming (LP) model, and hence finding the global optimum presents no significant compu- tational difficulties, if such a solution exists. In the case studies that follow, the solutions are determined using the optimization soft- ware Lingo 11.0.

6. Case study 1

Feedstock Land use (ha a/t) Water use (t/t) Heating value (GJ/t)

Biomass A 0.10 600 20Biomass B 0.07 450 15

Table 3Regional land and water availability limits (Case 1).This case study presents a representative scenario that involves

the production of biomass for electricity generation in two regions Region Upper limit Tolerance

(denoted simply as Regions I and II). Its primary purpose is to illus- Land (ha) Water (106 t/a) Land (ha) Water (106 t/a)trate the main features of the model described in the previous sec- I 100,000 2000 50,000 800tion. Table 1 gives the lower limits (yL ) and tolerances (Dyk) fork II 22,500 450 15,000 300electricity demand in the two regions. There are also correspond-ing fuzzy limits (qU and Dqexp,k) for the export of electricity fromone region to the other; since there are only two regions involved,

Table 1

Table 4Interregional feedstock trade limits and limitations of imports from external sources in 106 t/a (Case 1).

Regional electricity demand and inter-regional trade limits (Case 1). Feedstock Region Feedstock export upper limit

Feedstock export tolerance

Feedstock import upper limit

Feedstock import tolerance

2 2 0 02 2 2 2

0 0 0 00 0 0 0

158

Table 5

R.R. Tan et al. / Applied Energy 90 (2012) 154–160

scenarios in the Republic of the Philippines [16,17,44], where leg-F inal regional

feedstock pro uction and trade levels

6in 10 t/a (Case 1)

. islation mandating ethanol blending (at levels of to up to 10% ofInternal Import from regiona Import from Total gasoline demand starting in 2011) has recently been enacted. Inproduction

I IIexternal source

demand our previous work using input–output methods, we noted signifi-

Biomass Acant problems in establishing the desired production levels of bio-

Region I 0.6 – -0.6 0 0 fuels [24]. In this section, we demonstrate the application of theRegion II 0.0 0.6 – 1.2 1.8 model previously described to a static energy planning problemBiomass B constrained by land and water resources. For energy planning pur-Region I 2.9 – 0 0 2.9 poses, there are three main geographic regions in the Philippines,Region II 0.7 0 – 0 0.7 namely, the northern major island of Luzon, the central cluster of

Region Internal Import from regiona Import from Totalproduction

I IIexternal source demand

I 13.2 – -6.3 0 6.9II 14.5 6.3 – 0 20.8

k

k

k

d

a Negative values denote exports.

Table 6Final regional electricity production and trade levels in 106 GJ/a (Case 1).

islands known as the Visayas, and the southern island of Minda- nao; in this case study, these are simply referred to as Regions I, II and III, respectively. Table 8 shows the regional lower limits (yL ) and fuzzy tolerances (Dyk) of annual ethanol demands, as well as the upper limits (wU ) and tolerances (Dwk) of imports from external sources (outside of the system defined by the three re- gions). In the case of the ethanol demand data, both the lower lim- its and tolerances correspond to the displacement of 5% of gasoline demand, hence resulting in upper limits that correspond to the de-

sired 10% ethanol substitution rates. Note that the demand in Re-a Negative values denote exports.

Table 7Final regional electricity production and trade levels in 106 GJ/a (Case 1).

gion I is disproportionately large; the imbalance results from differences in the levels of population density and economic devel- opment across the country. The limitations on importation of eth- anol from external sources are assumed values.

The feedstocks being considered here for ethanol production areRegion Internal Import from regiona Import from Total sugarcane and corn, whose production levels are given by xk. These

productionI II

external source demand are currently staple crops in the Philippines, and are thus available

I 18.8 – -13.1 0 5.7II 4.1 13.1 – 0 17.2

a Negative values denote exports.

to its available land and water resources. Thus, in addition to cul- tivating 0.7 x 106 t/a of Biomass B internally, Region II also imports1.8 x 106 t/a of Biomass A (comprised of 0.6 x 106 t/a from Region Iand 1.2 x 106 t/a from external sources). Furthermore, it meets about 30% of its energy demand from 6.3 x 106 GJ/a of direct elec- tricity imports from Region I. The maximum value of the objective function is k = 0.384.

It is possible to see the effects of eliminating energy imports or exports on the system by modifying the constraints. For example, if trade of both types of biomass and electricity is forbidden (i.e., qk0 k, rk0 k and vk = 0), there will be no feasible solution at all, since the re- sources available within Region II are not sufficient to supply bio- mass for its internal energy demand. Alternatively, if only import or export of electricity between the two regions is allowed (i.e., rk0 k = 0), the resulting optimal production and trade levels areshown in Table 7. In this case, Region I produces 18.8 x 106 GJ/aof electricity (from 3.1 x 106 t/a of Biomass A), while Region II pro- duces 4.1 x 106 GJ/a of electricity (from 0.9 x 106 t/a of Biomass B).

in sufficient quantities to minimize the sort of difficulties that arisein nascent bioenergy supply chains [24]. The land and water foot- prints of these two crops, which form Bk, are given in Table 9. Thesefigures are similar to those found in previous papers [16,17,44]. Asthe values given are already in terms of final ethanol equivalent, each of the coefficients of Ak is equal to 1. Table 10 shows the land and water resources available in the three regions (zU and Dzk). The land resources are the same as those used by Foo et al. [16], while the water resources have been adjusted relative to the original val- ues [17,44] to account for regional differences in rainfall. Finally, since only bioethanol is traded, we also impose rk0 k = 0 and vk = 0 for all regions k.

Using these data to optimize Eq. (1) subject to Eqs. (2)–(6), (8), (10), (12a), (12b), (14)–(16), (and) (17) gives the final regional pro- duction and trade values shown in Table 11. In the optimal solu- tion, k = 0.565, and all of the ethanol produced across the three regions, which amounts to 434.7 x 106 l/a, is derived solely from sugarcane, which requires less land and water inputs per unit of ethanol equivalent than does corn. It can also be seen that Region

Table 8Regional ethanol demand and limitations of imports from external sources (Case 2).

While both regions consume all of their biomass production inter- nally, Region I also exports about 70% of its electricity output (13.1 x 106 GJ/a) to Region II. The optimal value of the objective function is k = 0.145.

Region Ethanol demand lower

limit (106 l/a)

Ethanol demand tolerance(106 l/a)

Ethanol import upper limit

(106 l/a)

Ethanol import tolerance(106 l/a)

7. Case study 2

There has been significant growth in the international trade of biofuels for motor vehicles in recent years [29–34]. In the case of biodiesel, much of the trade has been of vegetable oil feedstocks, such as palm and rapeseed oil; on the other hand, in the case ofethanol, it is the finished product that is traded [43]. In either of

I 211 211 100 100II 52.5 52.5 60 60III 58.8 58.8 0 0

Table 9Land and water footprint data for feedstocks (Case 2).

a 6 a 6 6

these situations, the optimization model described in the previous section can be readily used, using either only the terms for final bioenergy imports, or, alternatively, just the terms for raw biomass imports. This case study is adapted from ethanol production

Feedstock Land use (ha a/10 l) Water use (10 t/10 l)

Sugarcane 238 2.43Corn 1429 3.29

a Per liter of ethanol equivalent.

R.R. Tan et al. / Applied Energy 90 (2012) 154–160 159

Table 10Regional land and water availability limits (Case 2).

Region Upper limit Tolerance

Land (ha) Water (106 t/a) Land (ha) Water (106 t/a)

I 75,000 1200 50,000 800II 22,500 450 15,000 300III 60,700 607 30,350 303.5

Table 11Final regional production and trade levels in 106 l/a of sugarcane ethanol (Case 2).

seen that Regions I and II are net importers of biomass from Region III, with only about 70% (216.8 x 106 l/a) and 84% (65 x 106 l/a) of their ethanol demands (309.8 x 106 l/a and 77.1 x 106 l/a, respec- tively) being supplied from local production. On the other hand, Region III utilizes only 45% of its total production (86.3 x 106 l/a out of 191.3 x 106 l/a), with the balance being exported to the other two regions (93 x 106 l/a and 12 x 106 l/a, respectively). Fur- thermore, comparing these results with those in Table 11 shows that the total ethanol available for use in the three regions is re- duced by about 6%, from 504.3 x 106 l/a to 473.2 x 106 l/a, when the option to import externally-sourced ethanol is removed. This

Region Internal production Import from regiona Import from

external sourceTotal demand

reduction in fuel availability is also accompanied by increasedstrain on internal resources within the three regions, as indicated

I II III

I 196.5 – 2.9 87.3 43.5 330.2II 58.9 -2.9 – 0 26.1 82.1III 179.3 -87.3 0 – 0 92.0

a Negative values denote exports.

I is a net importer of biomass from the other two regions as well as from the external source, with only about 60% of the ethanol de- mands (196.5 x 106 l/a out of 330.2 x 106 l/a) being supplied from local production. On the other hand, Region II meets close to 70% of its ethanol requirement from local production (56 x 106 l/a out of82.1 x 106 l/a), exports a small portion of its output (2.9 x 106 l/a) to Region I, and sources the rest of its demand from the external ethanol imports amounting to 26.1 x 106 l/a. In this case, Region II exports some of its local production of ethanol to Region I despite the fact that Region II’s local production is insufficient in meeting its own fuel demand and Region I in effect reduces its imports from external sources by relying more on inter-regional trade. This oc- curs due to the fact that a limit is imposed on importation from external sources and no limit is placed on inter-regional trade. Fi- nally, Region III is entirely self-sufficient, and exports almost half of its production (87.3 x 106 l/a out of 179.3 x 106 l/a) to Region I. This result arises from the imbalances between energy demand (which are largely a function of population size and economic affluence) and resource availability (which is determined by geo- graphic and climatic factors such as landmass and precipitation levels) across the three regions. Note that such imbalances also may occur on much larger geographic scales, for example across different countries or continents [29–33]. It is also worth noting that optimization problems of this type can be degenerate, such that there may be multiple possible allocation schemes that achieve the same optimal value, k = 0.565. In such cases, the degen- erate solutions can be interpreted as being equally good, as in every solution each of the fuzzy goals will be satisfied to at least the degree k.

It is interesting to see the effect of solving the model while for- bidding imports from external sources (i.e., requiring that the sys- tem comprised of the three regions be self-sufficient by setting all wk = 0). Solving the case with this additional assumption gives thefinal regional production and trade values shown in Table 12. Inthe optimal solution, k = 0.468, and all of the ethanol across the three regions is still derived solely from sugarcane. It can also be

Table 12Final regional production and trade levels without external ethanol source in 106 l/a of sugarcane ethanol (Case 2).

Region Internal production Import from regiona Total demand

I II III

I 216.8 – 0 93.0 309.8II 65.0 0 – 12.0 77.1III 191.3 -93.0 -12.0 – 86.3

a Negative values denote exports.

by the reduction in the optimal value of k.

8. Conclusion

A multi-regional fuzzy input–output model has been developed to optimize biomass production and trade under resource avail- ability and environmental footprint constraints. This model was developed in response to the clear trend in increased biomass trade reported in the literature, which results from regional imbalances between bioenergy production capacity and demand. The ap- proach makes use of scale-invariant technological coefficients, and max–min aggregation is used so that a compromise solution can be found by maximizing an overall index of fuzzy goal satisfac- tion, k. The result is a linear programming model for which a global optimum may be easily determined. Case studies based on electric- ity generation from biomass and ethanol production were presented to illustrate how the model determines optimal produc- tion levels of feedstocks within each region, as well as optimal levels of trade between regions and imports from external sources.

Future work on extending the model should focus primarily on developing a dynamic, multi-period variant. Such an extension can also integrate time-dependent technical parameters to account for technological learning curves and yield improvements, as well as incorporate game theoretic principles to accurately reflect the mul- ti-agent nature of the problem. Also, the use of non-linear fuzzy membership functions may be explored in the future. Significant non-convexities may result from such extensions, so it will also be necessary to develop solution algorithms to ensure that globally optimal, or near-optimal, solutions can be found.

Acknowledgments

The authors would like to acknowledge partial financial support through the Graduate Fellowship Program of De La Salle Univer- sity, and the ERDT Scholarship Program of the Philippine Depart- ment of Science and Technology.

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