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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. el sevi er .com /l ocate / a p e n er gy

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, Philippines

b Center for Engineering and Sustainable Development Research, De La Salle University, Manila, Philippines

c Mechanical Engineering Department, De La Salle University, Manila, Philippines

d 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 2010

Received in revised form 11 January 2011

Accepted 13 January 2011

Available 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.

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 Salle

University, Manila, Philippines. Tel.: +63 2 536 0260.

E-mail addresses: (R.R. Tan), kathleen.aviso@dlsu. edu.ph (K.B. Aviso), (I.U. Barilea), (A.B. Culaba), (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 most

ﬁrst-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

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 the

2030 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 k

Bk Environmental matrix for region k k Index for regions

Nk Number of regions

NP Number of biofuel products

NR 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

exp;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 roughly

50 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]. Such

cases require the cooperation of the importing and exporting parties,

imp;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 to

identify opportunities for biomass trade across adjacent geographi-

exp;k

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

cal regions [35,36]. Likewise, mathematical programming based

methods 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 importation

in case of deﬁcit [39].

imp;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 models

developed 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 region

k from all other regions

U Upper bound vector for biomass import by region k

from beyond system boundary

Dvk Tolerance vector for biomass imported by region k

from beyond system boundary

U Upper bound vector for ﬁnal bioenergy import by

region k from beyond system boundary

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

‘‘conﬂuence’’ of fuzzy goals and constraints in a complex decision L

making problem [41], which was later integrated into fuzzy mathe- k

Lower bound vector of ﬁnal bioenergy demand in region k

matical programming using max–min aggregation [42]. The rest of

this paper is organized as follows. A formal problem statement is gi-

Dyk Tolerance vector of ﬁnal bioenergy demand in region

ven in the next section. This is followed by a description of the opti- U

mization 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

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

Biomass

Imports

Bioenergy

Imports

Resources Biomass Bioenergy Demand

1 1 1 1

I R P J

NI NR NP NJ

Interregional Trade

1 1 1 1

I R P J

NI NR NP NJ

Biomass

Imports

Bioenergy

Imports

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

4. Variables

k Overall level of satisfaction of fuzzy constraints

qk0 k Final bioenergy import vector from region k0 to region k

rk0 k Biomass import vector from region k0 to region k

sk Internal biomass production vector in region k

vk Biomass import vector to region k from beyond system boundary

wk Final bionergy import vector to region k from beyond system boundary

xk Internal biomass requirement vector in region k