linear mixed-integer models for biomass supply chains with
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Energy 35 (2010) 1338–1350
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Energy
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Linear mixed-integer models for biomass supply chains with transport, storageand processing
Silke van Dyken*, Bjorn H. Bakken, Hans I. SkjelbredSINTEF Energy Research, Sem Saelands vei 11, NO-7465 Trondheim, Norway
a r t i c l e i n f o
Article history:Received 23 February 2009Received in revised form17 November 2009Accepted 18 November 2009Available online 7 December 2009
Keywords:Energy supply systemsBiomassLong-term processesLinear mixed-integer models
* Corresponding author. Tel.: þ 47 73 55 04 47; faxE-mail address: [email protected] (S. van D
0360-5442/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.energy.2009.11.017
a b s t r a c t
This paper presents a linear mixed-integer modeling approach for basic components in a biomass supplychain including supply, processing, storage and demand of different types of biomass. The main focus inthe biomass models lies on the representation of the relationship between moisture and energy contentin a discretized framework and on handling of long-term processes like storage with passive dryingeffects in the optimization. The biomass models are formulated consistently with current models for gas,electricity and heat infrastructures in the optimization model ‘eTransport’, which is designed for plan-ning of energy systems with multiple energy carriers. To keep track of the varying moisture content inthe models and its impact on other biomass properties, the current node structure in eTransport hasbeen expanded with a special set of biomass nodes. The Node, Supply, Dryer and Storage models arepresented in detail as examples of the approach. A sample case study is included to illustrate thefunctionality implemented in the models.
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1. Introduction
Biomass can be defined as organic matter that has been directlyor indirectly derived from contemporary photosynthesis reactions,and hence can be considered a part of the present carbon cycle. It isconsidered a renewable resource when utilized in a sustainableway (harvesting equals re-growth). Many countries have largebiomass resources, and it is considered as one of the most prom-ising renewable energy sources in the near to mid-term perspec-tive. Forest biomass represents the largest energy resource, butbiomass can also be produced by dedicated cultivation, i.e. energyfarming. By-products from forestry and agriculture can also be usedfor energy purposes, referred to as biomass waste. Examples of suchwaste sources are maintenance work in parks and gardens, thin-ning wood from forestry and straw from wheat farming. There arealso general waste streams from household and industry, whichinclude biomass products like food, paper, demolition wood andsaw dust.
The generic term ‘biomass’ is used on a wide and diverse rangeof energy resources that can be used in solid or gasified form forheating applications or electricity production, or in liquid or gasi-fied form as transportation fuel. E.g. 5–8 assortments of forestspecies will diverge into 30–60 log types and 100–200 raw
: þ 47 73 59 72 50.yken).
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products. In the end of a general biomass supply chain, the numberof products may become many thousands. Thus, it is not sufficientto set up a techno-economic optimization model where flow ofgeneric ‘biomass’ is considered in the same way as flow of elec-tricity, heat or natural gas. Large international research programsare initiated to develop efficient technologies for increased utili-zation of biomass resources both for stationary and mobile use[1,2]. Compared to more traditional energy transport technologieslike electricity and gas, however, fewer efforts have so far beenapparent in techno-economic modeling and optimization ofbiomass supply chains. Most reports and studies [3–8] shownumerical assessments on specific biomass activities and technol-ogies necessary to meet energy demand. Although many have anenergy system approach, few actually use a model that accounts forthe many trade offs and the alternative handling options in thedesign of a general biomass supply chain.
A detailed dynamic simulation program for collection andtransportation of large quantities of biomass, the IBSAL model, ispresented in Ref. [3]. The model considers time-dependent avail-ability of biomass under the influence of weather conditions andpredicts the number and size of equipment needed to meeta certain demand. The delivered cost of biomass is calculated basedon the utilization rate of the machines and storage spaces. Themodel uses non-linear equations to describe the dependencies, e.g.a third-degree polynomial to represent the moisture content asa function of number of days since the start of harvest.
Nomenclature
Parametersasp
St binary parameter to determine storage type (passivedrying yes/no) for biomass product p
cdDr specific operating cost per m3 biomass fed to dryer
d [USD/m3]cs
St cost of biomass handling in storage s [USD/timestepand m3]
CbptBSup cost of biomass product p from biomass supply b in
timestep t [USD/m3]Csab
St biomass handling cost in storage s during the wholestorage time Tinsa
St �ToutsbSt [USD/m3]
dspSt moisture reduction in storage s for biomass product p
[%wt/timestep and m3]Dspab
St moisture reduction in storage s for biomass product pduring the whole storage time Tinsa
St �ToutsbSt , assuming
a decreasing drying rate with increasing storage time[decimal fraction mass/m3]
Dpref reference density of product p [kg/m3]
Dpzero density of product p, completely dry [kW h/m3]
3dpDr volume loss coefficient for product p in dryer
d [decimal fraction volume basis]3sp
St volume loss coefficient for biomass product p instorage s, average at storage starting point [decimalfraction volume basis/timestep]
emde emission coefficient for emission type e from dryerd [kg/MW h]
emse emission coefficient for emission type e from storage s[kg/MW h]
EspabSt volume loss for biomass product p in storage s during
the whole storage time TinsaSt �Toutsb
St , increasing withincreasing storage time [decimal fraction volumebasis/m3]
FsSt fuel use in storage s per m3 biomass input to run e.g.
wheel loaders [l/m3]HVp
ref reference heating value of product p [kW h/m3]HVindlp
Dr heating value of biomass product p for moisture pair lto dryer d in timestep t [kW h/m3]
HVoil heating value of oil to dryer d or storage s [MW h/l],global parameter
MCpref reference moisture content of product p [decimal
fraction mass]MCbp
BSup moisture content of biomass product p from biomasssupply b [decimal fraction mass]
MCidDr maximum input moisture content to dryer d [decimal
fraction mass]MCIdl
Dr input moisture in moisture pair l in dryerd (linearization) [decimal fraction mass]
MCmaxnpNo maximum moisture content of product p in biomass
node n [decimal fraction mass]MCminnp
No minimum moisture content of product p in biomassnode n [decimal fraction mass]
MCodDr lowest level of output moisture content achievable in
dryer d [decimal fraction mass]MCOdl
Dr output moisture in moisture pair l in dryerd (discretization) [decimal fraction mass]
MCstepdDr moisture reduction in dryer d per discretization step
[decimal fraction mass]NT total number of timestepsNlid
Dr number of discretization points in the dryer model(moisture)
NpairsdDr number of discretization pairs in the dryer model
(moisture)Nstepsd
Dr number of discretization steps in the dryer model(moisture)
NbvdDr number of discretization points in the dryer model
(biomass burned)Pende
Em emission penalty for emission type e from dryerd [USD/kg]
PenseEm emission penalty for emission type e from storage s
[USD/kg]qdp
Dr specific energy required in dryer d to evaporate 1 kgwater from biomass product p [kW h/kg]
QmaxdpDr rated capacity of dryer d for biomass product p [MW]
sdlpDr specific energy required to dry biomass product p in
dryer d for all moisture pairs l [MW h/kg]Tinsa
St input timestep to storage s in timestep aToutsb
St output timestep from storage s in timestep bVmaxbp
BSup maximum flow of biomass product p from biomasssupply b [m3/timestep]
VmaxdpDr maximum flow of biomass product p to dryer d [m3/
timestep]Vbmaxd
Dr maximum volume of biomass burned in dryer d [m3/timestep]
VBdvDr amount of biomass burned in dryer d at discretization
point v in Burn [m3/timestep]Vmaxs
St maximum flow of biomass to storage s [m3/timestep]Vminbp
BSup minimum flow of biomass product p from biomasssupply b [m3/timestep]
WevapdpDr amount of water evaporated in dryer d from biomass
product p per moisture step MCstepdDr [kg/m3]
VariablesBio_load_flowijpt biomass volume flow of product p from network
node i to load node j in timestep t [m3/timestep]Bio_local_flowijpt biomass volume flow of product p from supply
node i to load node j in timestep t [m3/timestep]Bio_net2net_flowijpt biomass volume flow of product p from
network node i to j in timestep t [m3/timestep]Bio_supply_flowijpt biomass volume flow from supply node i to
network node j in timestep t [m3/timestep]CZ operating cost for different technologies,
Z ˛ TechnologiesDnpt
No � 0 density of biomass product p in node n in timestep t[kg/m3]
Emitedt� 0 amount of emission type e from dryer d in timestep t[kg/timestep]
Emitest� 0 amount of emission type e from storage s in timestept [kg/timestep]
FdptDr � 0 fuel (oil) used by dryer d in timestep t to dry biomass
product p [l/timestep]HVnpt
No � 0 density of biomass product p in node n in timestep t[kg/m3]
Load_flowijt energy flow from network node i to load node j intimestep t [MW h/timestep]
Local_flowijt energy flow from supply node i to load node j intimestep t [MW h/timestep]
ldlvtDr binary variable for discretization of moisture pair l and
burned volume v in dryer d and timestep t, the value is1 if moisture pair l is chosen, 0 if not
lspabSt binary variable to determine how long (tinsa
St � toutsbSt)
a biomass product p has to be stored in storage s toreach a certain output moisture level, the value is 1 ifinput time is tinsa
St and output time is toutsbSt , 0 if not
S. van Dyken et al. / Energy 35 (2010) 1338–1350 1339
MCnptNo � 0 biomass moisture content of product p in biomass
node n in timestep t [decimal fraction mass]MCindpt
Dr � 0 biomass input moisture content of product p todryer d in timestep t [decimal fraction mass]
MCinsptSt � 0 biomass input moisture content of product p to
storage s in timestep t [decimal fraction mass]MCoutdpt
Dr � 0 biomass output moisture content of product pfrom dryer d in timestep t [decimal fraction mass]
MCoutsptSt � 0 biomass output moisture content of product p
from storage s in timestep t [decimal fraction mass]Net2net_flowijt energy flow from network node i to j in timestep
t [MW h/timestep]Pjit
N 2N power flow in timestep t from/to other networkmodels at node i [MW h/timestep]
PsitSup power flow in timestep t from local supply connected
at node i [MW h/timestep]Qdpt
Dr � 0 amount of energy required to dry biomass product p indryer d and timestep t [MW h/timestep]
QexdtDr� 0 external drying heat to dryer d in timestep t [MW h/
timestep]Supply_flowijt energy flow from supply node i to network node j
in timestep t [MW h/timestep]V bpt
BSup� 0 amount of biomass product p supplied in timestep tfrom supply b
VpnltLd biomass flow of product p in timestep t to load l
connected to node n [m3/timestep]Vpnjt
N 2N biomass flow of product p in timestep t from/to othernetwork models j at node n [m3/timestep]
VpsntSup biomass flow of product p in timestep t from biomass
supply s connected at node n [m3/timestep]Vbdpt
Dr � 0 amount of biomass product p burned in dryer d andtimestep t to supply drying heat [m3/timestep]
VindptDr � 0 input volume of biomass product p to dryer d in
timestep t [m3/timestep]Vinspt
St � 0 input volume of biomass product p to storage s intimestep t [m3/timestep]
VoutdptDr � 0 output volume of biomass product p from dryer d in
timestep t [m3/timestep]Voutspt
St � 0 output volume of biomass product p from storage s intimestep t [m3/timestep]
VtransspabSt � 0 transferred volume of biomass product p in
storage s between timestep a, b [m3/timestep]t, a, b index for timesteps within operational model, t, a,
b ˛ Time_steps
SetsBioSupplies set of biomass suppliesBioNodes set of biomass nodesBurn set of all values for linearization of the amount of
biomass burned in the dryer modelDryers set of biomass dryersEmissions set of (predefined) emission types;
Emissions¼ [CO2, CO, NOx, SOx]Index index set for calculation of specific drying energy in
dryer modelLoad_points set of load and market nodesNet2load set to define connections between network nodes
and load nodesNet2net set to define connections between two different
networks tNetwork_nodes set of network nodesPairs set of all discretization moisture pairs in the dryer
modelProducts set of all biomass productsStorages set of biomass storagesSupply_points set of energy sourcesSupply2load set to define direct connections between supply
nodes and load nodesSupply2net set to define connections between supply nodes
and network nodesTime_steps set of hours in the operational model (circular)
S. van Dyken et al. / Energy 35 (2010) 1338–13501340
A rather simple non-linear decision support model is given inRef. [4]. The problem considered is optimal exploitation of biomassresources with several harvesting sites and a few centralizedcombustion plants on a regional level. The aim is to find the optimalcapacity of heat and power generation as well as the optimalutilization of biomass resources and transport options. The timehorizon considered is one year so that the model is capable ofgiving long-term decision support.
Another modeling approach describes a methodology for opti-mization of agricultural supply chains by dynamic programming(DP) [5] to find the lowest cost from harvest to end use. The DPmodel works by defining a set of stages of the supply chain andstages for the biomass. The model explicitly deals with the productproperties, which are influenced by handling, processing, trans-portation and storage actions.
The work presented in Ref. [6] describes an environmentaldecision support system (EDDS) based on a geographic informationsystem (GIS). The optimization model used can be classified asa non-linear mixed-integer programming problem. The main focusis the optimal planning of forest biomass use for energy production.Different scenarios can be analyzed over a long-time period sup-ported by a user interface.
The model described in Ref. [7] focuses on biomass collectionand transportation systems and presents a multicriteriaassessment model. Economic, social, environmental and tech-nical factors are included in the ranking of the alternatives
investigated. Another mixed-integer linear optimization model isdemonstrated in Ref. [8]. The methodology allows for biomassmanagement for energy supply on a regional level. The model isbased on the dynamic evaluation of economic efficiency and theobjective is to find the most economical and ecological supplystructure.
Both Refs. [9] and [10] analyze logistic issues of biomass andpresent the application of the concepts developed in case studies.The work in Ref. [9] deals with the storage problem and theadvantages a multi-biomass supply chain might have on the logisticcost. The objective of Ref. [10] was the development of a forestbiomass supply logistics model.
In this paper, we present a linear mixed-integer modelingframework that can be applied to most relevant components ina biomass supply chain, including sources, handling/processing,storage and end use. Characteristic for our generic model is itsflexible structure which allows for the modeling of value chainswith multiple biomass types and technologies. The modelingframework is based on an approach with a network node systemapplied in Ref. [16] and [17]. The main objective of our approach isthe presentation of the new functionality. Minor focus has beengiven to an application with real case data.
The amount of energy flowing (and specific operating cost) atany point in the supply chain depends both on the volume and themoisture content in the biomass, and can be defined as a function oftwo main properties of the biomass product [5]:
S. van Dyken et al. / Energy 35 (2010) 1338–1350 1341
� Appearance; describing if the biomass is in chips, pellets, logs,etc.� Quality; primarily moisture content
The following types of actions can then be distinguished [5]:
� Handling; actions that intentionally alter or modify theappearance of a product, e.g. chipping or pelleting� Processing; actions which intentionally alter or modify the
quality of a product, e.g. drying� Transportation and storage; actions which unintentionally alter
the quality of a product, e.g. natural drying during long-termstorage
In the current framework, we do not distinguish betweenhandling and processing. The main issue during optimization is tokeep track of what kind of changes a specific action or module doesto the product, both in terms of quality and appearance.
Furthermore, the long-term effects of passive drying (change ofquality) during storage has to be considered together with forceddrying in a processing module. The typical hourly and seasonal loadprofiles used for optimization of heat and electricity supply thushave to be modified to allow the algorithm to choose betweencheap/free long-term passive drying and spending fuel for forcedand fast drying.
The paper is organized as follows: Section 2 gives a brief over-view of the eTransport optimization model and the basic networkstructure, Section 3 describes the new biomass model structurewith the biomass node system. The Supply, Dryer and Storagemodels are presented in detail as samples of the methodology.Section 4 contains a sample case study to demonstrate the prop-erties of the new biomass models. Section 5 contains aspects ofdiscussion and Section 6 an explanation of current and furtherwork.
2. The eTransport model
The optimization model eTransport is developed for expansionplanning in energy systems where several alternative energycarriers and technologies are considered simultaneously [11–14].The model uses a detailed network representation of technologiesand infrastructure to enable identification of single components,cables and pipelines. The current version optimizes investments ininfrastructure over a planning horizon of 10 to 30 years for mostrelevant energy carriers and conversion between these. It is notlimited to continuous transport like lines, cables and pipelines, butcan also include discrete transport by ship, road or rail.
The model is separated into an operational model (energy systemmodel) and an investment model where both economical andenvironmental aspects are handled by a superior modeling struc-ture [14]. In the operational model there are sub-models for eachenergy carrier and for conversion components. With the presentedbiomass module, several new sub-models have been added to theoperational model. The operational planning horizon is relativelyshort (1–3 days) with a typical timestep of 1 h. The operationalmodel finds the cost-minimizing diurnal operation for a giveninfrastructure and for given energy loads. Annual operating costsfor different energy system designs are calculated by solving theoperational model repeatedly for different seasons/segments (e.g.peak load, low load, intermediate, etc.), investment periods (e.g. 5year intervals) and relevant system designs. Annual operating andenvironmental costs for all different periods and energy systemdesigns are then used by the investment model to find the invest-ment plan that minimizes the present value of all costs over theplanning horizon.
Mathematically, the model uses a combination of linearprogramming (LP) and mixed-integer programming (MIP) for theoperational model, and dynamic programming (DP) for theinvestment model. The operational model is implemented inthe AMPL programming language with CPLEX as solver [15], whilethe investment model is implemented in Cþþ. A modular designensures that new technology modules developed in AMPL for theoperational model are automatically embedded in the investmentmodel. A full-graphical Windows interface is developed for themodel in MS Visio. All data for a given case are stored in a database.
The sub-models for different components are connected bygeneral energy flow variables that identify the flow betweenenergy sources (Supply_points), network components for transport,conversion and storage (Network_nodes) and energy sinks likeloads and markets (Load_points). The connections between supplypoints, network nodes and load points are case-specific, and theyare identified by sets of pairs where each pair shows a possible pathfor the energy flow between component types:
Supply2net
Set of pairs (i, j), where i ˛ Supply_points andj ˛ Network_nodesSupply2load
Set of pairs (i, j), where i ˛ Supply_points andj ˛ Load_pointsNet2net
Set of pairs (i, j), where i, j ˛ Network_nodes Net2load Set of pairs (i, j), where i ˛ Network_nodes andj ˛ Load_points
General energy flow variables are defined over the energysystem structure to account for the actual energy flow betweendifferent components (except for internal flow within each model).These general variables are included in and restricted by the variousmodels and they are the link between the different models:
Supply_flowijt
Energy flow from i to j at t, where (i, j) ˛ Sup-ply2net and t ˛ Time_stepsLocal_flowijt
Energy flow from i to j at t, where (i, j) ˛ Sup-ply2load and t ˛ Time_stepsNet2net_flowijt
Energy flow from i to j at t, where (i, j) ˛ Net2netand t ˛ Time_stepsLoad_flowijt
Energy flow from i to j at t, where (i, j) ˛ Net2-load and t ˛ Time_stepsIn the operational model, the different technology models areadded together to form a single linear mixed-integer optimizationproblem. The object function is the sum of the contributions fromthe different models and the restrictions of the problem include allthe restrictions defined in the models. Emissions are caused bya subset of components (power plants/CHP, boilers, road/shiptransport, etc.) that are defined as emitting CO2, NOx, CO and SOx.Further environmental consequences can be defined. Emissions arecalculated for each module and accounted for as separate results.When emission penalties PenEm are introduced by the user (e.g.a CO2 tax), the resulting costs are included in the objective functionand thus added to the operating costs.
The task for the investment model is to find the optimal set ofinvestments during the period of analysis, based on investmentcosts for different projects and the pre-calculated annual operatingcosts for different periods and states. The optimal investment planis defined as the plan that minimizes the discounted present valueof all costs in the planning period, i.e. operating costs plus invest-ment costs minus the rest value of investments. The optimal planwill therefore identify the optimal design of the energy system (i.e.the optimal state) in different periods.
Chipper
Biomass Node Demand
Storage Dryer
Supply
Combustion Pellets Plant
ChipperChipper
Electricity
Biomass
Fuel
Heat
Bio Oil
Fig. 1. Biomass models in eTransport – symbolic pictures.
S. van Dyken et al. / Energy 35 (2010) 1338–13501342
More details of the investment algorithm and the emissionhandling in eTransport are previously published in Ref. [14] andwill not be presented here.
3. Biomass in eTransport
When analyzing a biomass supply chain, it is of great importance toconsider the effects associated with the variation of moisture contentfor avast variety of materials. Ensuring that the moisture content of thebiomass entering or leaving a process is within a certain range isessential for the proper operation and efficiency of conversion tech-nologies, as for instance combustion or fast pyrolysis plants. Theoriginal version of eTransport only takes the flow of energy fromone node to another into account (node types: Supply_points,Network_nodes and Load_points). However, with biomass, the amountof energy flowing from one node to another depends both on thevolume flow and the moisture content. The biomass density andthe heating value are additional key parameters. Thus, in contrast tothe original LP structure of eTransport, more than one variable has tobe handled during the optimization. This leads to a non-linear problemwhich has to be discretized to be able to carry out the LP-optimization.To keep track of the variables of volume and moisture throughout thesystem a newset BioNodes hasbeen defined in addition tothe commonnetwork nodes. This set assures consistency between connectedcomponents of the biomass module. The same modeling approach isapplied in Refs. [16] and [17] to describe the technological character-istics of natural gas flows in pipelines in combination with optimiza-tion of gas markets. The approach is based on a network node systemwhich allows for the control of both the gas flow and the pressure. Thisnetwork structure has already been applied in the gas models ineTransport. However, since the control of both the gas flow and thesystem pressure is similar to the interdependent variables which haveto be handled in a biomass chain, the gas network modeling approachhas been transferred to the biomass module.
Aside from the interdependent variables, the modeling ofbiomass processes differs from the original design in eTransport bythe occurrence of long-term effects. Compared to the analysis ofelectricity networks, long-term processes and seasonal variation(harvest period, amount of biomass available, weather conditions,etc.) play a major role in a study of a biomass supply chains.Biomass properties will change in a long-term perspective, mainlydue to passive drying effects and degradation processes. The typicaltime resolution in the operational model in eTransport is 1 h [14],suitable for a detailed analysis of e.g. electricity networks, but it isnot appropriate when analyzing biomass processes. Furthermore,the current investment module does not allow for the optimizationof long-term processes since the information given/obtained aboutoperating conditions and material properties in one year orsegment cannot be transferred to another year or segment.
However, an approach to modeling the long-term effects can bemade by using the functionality existing in the short term structure.The default time resolution in the operational model is on an hourlybasis with 24 timesteps, but this can be changed freely. Thus, time-dependent variables are defined per timestep in the nomenclature.By choosing 52 timesteps and one single segment the model willoptimize the operation of the system for a whole year on a weeklybasis (input values¼weekly average values). With such a weeklytime resolution, the long-term functions implemented in thebiomass chains can be handled by the operational optimization.
With the BioNodes as a connecting basic structure, seven newtechnology models are implemented in eTransport:
1) Supply: different kinds of biomass supplied to the system withmoisture levels defined by the user, varying cost profile andrestricted volume.
2) Chipping: grinding/chipping of solid biomass to user-definedquality/appearance.
3) Pellets Plant: production of pellets with user-definedproperties.
4) Storage: storage of biomass with passive drying function(optional). Might cause emissions due to internal units (oil-fired) for biomass handling.
5) Dryer: active drying of biomass. Causes emissions when oil-fired.
6) Combustion: heat production in a large scale biomass boiler,co-fired with oil (optional), causes emissions.
7) Demand: biomass load point, demand of biomass volume ata certain moisture and quality level.
The symbolic technology models and the symbolic biomassnode are shown in Fig. 1. Some of the models originate fromRef. [18], but have been further developed and adjusted to the newnode structure. In the following sections, the basic structure of thebiomass module and the LP formulations for the BioNodes,the Supply, the Dryer and the Storage model are presented in detail.The model description is followed by a case study to illustrate thenew functionality and possible model applications.
3.1. Basic biomass module structure and biomass nodes
To be able to handle both the basic characteristics of differentkinds of biomass and the effects the variation in moisture contentmight have on these properties, a set of different Products iscreated. For each p ˛ Products, a reference point is specifieddefining the following reference parameters:
� the moisture content MCpref,
� the bulk density Dpref,
� and the heating value HVpref.
The common flow variables used to model the flow in theeTransport network are (as presented in Section 2): Supply_flowijt,Local_flowijt, Net2net_flowijt and Load_flowijt. These variables onlytake into account the flow of energy [MW h/h] between two pointsi and j in the network in different timesteps t. That is not sufficientin a biomass model, since information about the moisture contentat various steps in the chain is crucial for the optimization. For thatreason, each of the four common flow variables in eTransport hasbeen extended with a forth index p ˛ Products to be able to repre-sent the product properties. Thus, information about moisturecontent is given and transferred between the models and the
S. van Dyken et al. / Energy 35 (2010) 1338–1350 1343
BioNodes in the network. In contrast to the common flow variables,the flow between the biomass models in the network is a volumeflow [m3/h] and not a flow of energy. The extended flow variablesare only valid in the biomass module.
Bio_supply_flowijpt
Biomass volume flow of product p from ito j at t, where (i, j) ˛ Supply2net,p ˛ Products and t ˛ Time_stepsBio_local_flowijpt
Biomass volume flow of product p from ito j at t, where (i, j) ˛ Supply2load,p ˛ Products and t ˛ Time_stepsBio_net2net_flowijpt
Biomass volume flow of product p from ito j at t, where (i, j) ˛ Net2net, p ˛ Productsand t ˛ Time_stepsBio_load_flowijpt
Biomassvolume flow of product p from i toj at t, where (i, j) ˛ Net2load, p ˛ Productsand t ˛ Time_stepsFig. 2. Relation between moisture content and EHV [kW h/m3].
By means of the biomass node structure, the quality variablemoisture content MCnpt
No is controlled in addition to the biomassvolume flow. This requires the connection of each biomass model toa biomass node. In this way, it can be accounted for that changes inone part of the system might influence the performance of the restof the system. Extended passive storage keeping could for exampleshorten the residence time in a dryer which in turn influences theoperating cost of the whole system.
The moisture content is modeled as a free variable which can berestricted by different sets of parameters in the biomass nodes andin the technology models. The biomass density and the heatingvalue are not separately restricted since these values are directlylinked to the moisture content assuming linear dependencies. Thebiomass density in a node is linked to the moisture content byassuming a linear dependency:
DNonpt ¼ Dref
p1þMCNo
npt
1þMCrefp
; cn˛BioNodes; p˛Products; t˛Time steps:
(1)
The density of completely dry biomass (MCnptNo ¼ 0) is defined
asDpzero.
Dzerop ¼
Drefp
1þMCrefp
; cp˛Products: (2)
Applying the formulation of Dpzero to Eq. (1), the linear depen-
dency of biomass moisture content and density can be expressed by
DNonpt¼Dzero
p
�1þMCNo
npt
�;cn˛BioNodes; p˛Products; t˛Timesteps:
(3)
The dependency of the biomass heating value on the moisturecontent is modeled by linearization of the relation shown in Fig. 2.It is assumed that the correlation applies to all kinds of biomass.The curve shown for spruce is taken as a reference curve. It isdivided into three linear parts using four linearization points (morepoints possible for increased accuracy). The linearized curve forspruce is scaled up and down to represent other biomass typesp ˛ Products using the corresponding reference values MCp
ref andHVp
ref.Three different definitions are common for the heating value of
biomass:
– HHV (higher heating value) which is the gross heating value
– LHV (lower heating value) which is the net heating value. Incontrast to the HHV, the LHV does not include the heat whichoriginates from the water vapor formed during the combustion
– EHV (effective heating value) is the LHV subtracting the energyof evaporating the moisture content of the biomass
The relation shown in Fig. 2 is based on the EHV, but thereference heating values defined in the model do not necessarilyhave to be the EHV. Since the dependency found based on Fig. 2 isan approximation, it is also possible to use the LHV or HHV as longas this choice is consistent in the whole model. Furthermore, it hasto be considered that the heating values available for differentkinds of biomass often represent average values. This is caused bythe wide variation of biomass quality.
There are no operating costs associated with the biomass nodemodel
CNo ¼ 0: (4)
The biomass node model does not represent a physical technologymodel. It is implemented to enable the transfer of biomass propertyinformation between the network models and to keep track of thebiomass flow and the variation in moisture content. Thus, neitherthe biomass volume flow nor the three quality variables are modi-fied in the biomass node model. The amount of biomass that goesinto a biomass node equals the amount of biomass that leaves it. Themass balance equation for a biomass node n ˛ BioNodes is given by
Xi:ði;nÞ˛Supply2net
VSupinpt þ
Xj:ðj;nÞ˛Net2net
VN2Njnpt ¼
Xl:ðn;lÞ˛Net2load
VLdnlpt
þX
j:ðn;jÞ˛Net2net
VN2Nnjpt ; cn˛BioNodes;p˛Products; t˛Time steps:
(5)
Table 1Example: generation of moisture pairs for discretization in dryer model.
Parameter data
MCiDrd ¼ 0:6
MCoDrd ¼ 0:4
NliDrd ¼ 3
NstepsDrd ¼ 4
NpairsDrd ¼ 15
MCstepDrd ¼ ðMCiDr
d �MCoDrd Þ=NstepsDr
d ¼ 0:05
40 %60 %
point
step
DrdMCi Dr
dMCo
40 %60 %
point
step
DrdMCi DrdMCi Dr
dMCoDrdMCo
Generated moisture pairs
(0.60/0.60) (0.60/0.55) (0.60/0.50) (0.60/0.45) (0.60/0.40)(0.55/0.5) (0.55/0.50) (0.55/0.45) (0.55/0.40)
(0.50/0.50) (0.50/0.45) (0.50/0.40)(0.45/0.45) (0.45/0.40)
(0.40/0.40)
S. van Dyken et al. / Energy 35 (2010) 1338–13501344
3.2. Supply model
The biomass supply model is a generic source that accounts forcost and moisture content of any biomass product p. The outputvolume Vbpt
BSup cannot exceed the maximum output capacity. At thesame time, the minimum output conditions have to be kept.
VminBSupbp �VBSup
bpt �VmaxBSupbp ;
cbn˛BioSupplies;p˛Products; t˛Timesteps: (6)
The cost of using biomass is given by
CBSup ¼X
t˛Time steps
Xb˛BioSupplies
Xp˛Products
CBSupbpt VBSup
bpt : (7)
The biomass taken from a given supply point has to be fed toa biomass node. The special properties of the biomass node systemonly take effect when each model belonging to the biomass chain isconnected to a biomass node. Thus, the biomass balance for thebiomass supply point is
VBSupbpt ¼
Xi:ðb;iÞ˛Supply2net
VSupbipt ; cb˛BioSupplies; p˛Products;
t˛Time steps: (8)
Eq. (8) restricts the biomass volume flow from the biomass supplyto the network. In addition, information about the moisture contenthas to be transferred to the network. The moisture content in thebiomass supply is set equal to the moisture content in the biomassnode connected to the supply point. This is done applying thegeneral node structure and the set ‘‘Supply2net’’.
MCBSupbp ¼ if n˛BioNodes then MCNo
npt else MCBSupbp ;
cb˛BioSupplies; ðb;nÞ˛Supply2net; p˛Products; t˛Time steps:
(9)
3.3. Dryer model
The dryer model reduces the moisture content of a biomassproduct p. The heat required to run the drying process can either besupplied by an external heat source, by direct burning of biomass oroil, or a combination of these. The amount of biomass dried in themodel is restricted by the maximum biomass feed rate Vmaxdp
Dr tothe dryer [m3/h]. In addition, it is restricted by its rated capacityQmaxdp
Dr [MW] and the drying rate qdpDr [kW h/kg water evaporated].
The drying rate, which is defined by the user, is treated as anaverage rate. It is assumed that the energy required to evaporatethe biomass moisture slightly increases when the drying is carriedout on a low moisture level. Hence, reducing the moisture contentfrom 60% wt to 50% wt requires less energy than reducing it from20% wt to 10% wt. Volume losses during the drying process areaccounted for applying the volume loss coefficient 3dp
Dr (percentageof input volume). In addition to the energy costs calculated in theenergy supply models, a specific operating cost cd
Dr per m3 biomassfed to the dryer can be specified.
The optimization of the amount of biomass fed to the dryer andboth the variable input and output moisture level leads to a non-linear problem which has to be discretized. This is done using a setof predefined pairs of possible input and output moisture contentcombinations, MCIdl
Dr and MCOdlDr. The user defines the number of
discretization points between the maximum input moisture levelMCid
Dr and the lowest output moisture level achievable in the dryerMCod
Dr. The moisture pairs are generated automatically in the
model. A numerical example with the definition of MCstepdDr is
shown in Table 1. The optimal moisture pair is found by means ofthe binary variable ldlvt
Dr .The heat required in the drying process can be obtained by
burning a fraction of the biomass. The biomass volume required tocover the drying heat depends on the heating value of the biomass.Again, the heating value is linked to the moisture content which isnot known before the optimization is carried out. Thus, the amountof biomass burned for heating purposes Vbdpt
Dr has to be discretized,too. This is implemented by defining a certain number of dis-cretization points Nbvd
Dr. Applying this number and the upper boundVbmaxd
Dr, biomass volume values VBdvDr are calculated in the model.
Due to the linear dependency of biomass density on moisturecontent, the amount of water evaporated (equals the densitychange) does not decrease at low moisture levels. Thus, a moisturereduction corresponding to MCstepd
Dr always corresponds to thesame amount of water Wevapdp
Dr.
WevapDrdp ¼ Dzero
p
�1þMCiDr
d
�� Dzero
p
�1þMCiDr
d �MCstepDrd
�¼ Dzero
p MCstepDrd ; cd˛Dryers; p˛Products: (10)
To be able to consider a decreasing drying rate nevertheless,a modifying factor has been implemented in the calculation of thespecific drying energy sdlp
Dr given in Eq. (11). By means of this factor,the specific evaporation energy qdp
Dr linearly increases at low dryingmoisture levels.
sDrdlp ¼ WevapDr
dp
Xi in Index
qDrdp
�1þMCiDr
d ��
MCIDrdl � ði� 1Þ
MCstepDrd
��; cd˛Dryers; l˛Pairs; p˛Products: (11)
Table 2 gives a numerical example of the modification of qdpDr
implemented in the calculation of the specific drying energy sdlpDr .
To maintain a linear mixed-integer problem, both the input andoutput moisture content has to be further restricted. This is done byapplying the predefined discretization moisture pairs. The binaryvariable ldlvt
Dr is implemented to select the most suitable moisturepair. The values of ldlvt
Dr are set by the solver. The constraint given by
Xl˛Pairs;v˛Burn
lDrdlvt ¼ 1; cd˛Dryers; t˛Time steps (12)
Table 2Example: calculation of specific drying energy in dryer model.
MCidDr MCod
Dr qdpDr, const
0.6 0.2 2.0
MCIdlDr MCOdl
Dr qdpDr, mod
0.6 0.5 2.00.6 0.4 2.10.6 0.3 2.20.6 0.2 2.30.5 0.4 2.20.5 0.3 2.30.5 0.2 2.40.4 0.3 2.40.4 0.2 2.50.3 0.2 2.6
S. van Dyken et al. / Energy 35 (2010) 1338–1350 1345
assures that only one ldlvtDr is set to equal one. Thus, only one
moisture pair (the most appropriate one) is chosen. This choice istaken by the solver considering the other constraints and the costfunctions.
Eqs. (13) and (14) restrict the difference between input andoutput moisture (the level of moisture reduction in the dryer),applying the combinations given by the moisture discretizationpairs.
MCinDrdpt �
Xl˛Pairs;v˛Burn
MCIDrdl lDr
dlvt ; (13)
MCoutDrdpt �
Xl˛Pairs;v˛Burn
MCODrdl lDr
dlvt ; cd˛Dryers; l˛Pairs;
p˛Products; t˛Time steps: (14)
In the same way as the moisture level, the amount of biomassburned has to be restricted by applying the discretized values VBdv
Dr
and the binary variable ldlvtDr .
VbDrdpt ¼
Xl˛Pairs;v˛Burn
VBDrdvlDr
dlvt ; cd˛Dryers; p˛Products;
t˛Time steps: (15)
The energy required to reduce the biomass moisture in the dryeris calculated by means of the specific drying energy sdlp
Dr and givenby
QDrdpt � sDr
dlpVinDrdpt �
1�
Xv˛Burn
lDrdlvt
!sDr
dlpVmaxDrdp;
cd˛Dryers; l˛Pairs; p˛Products; t˛Time steps: (16)
The heat required to dry the biomass volume can either be suppliedby an external heat source or by burning biomass or oil. The heatingvalue HVindlp
Dr of the biomass input volume is calculated applyingthe dependency described in Section 3.2, subject to the moisturepairs given for discretization. The amount of drying heat cannotexceed the drying heat capacity of the dryer:
QDrdpt � QexDr
dt þ FDrdptHVoilþ
Xl˛Pairs;v˛Burn
VBDrdvHVinDr
dlpldlvt ; (17)
where
QDrdpt � QmaxDr
dp; cd˛Dryers; p˛Products; t˛Time steps: (18)
It is assumed that some of the biomass gets lost or becomesunusable during the drying process. This is modeled by defininga certain percentage of the input volume as loss volume (Eq. (19)).
Furthermore, the input volume cannot exceed the maximum inputcapacity (Eq. (20)):
VinDrdpt ¼ VoutDr
dpt
�1þ eDr
dp
�; (19)
where
VinDrdpt � VmaxDr
dp; cd˛Dryers;p˛Products; t˛Time steps:
(20)
The operating costs of the dryer model are energy costs whichare calculated in the supply models. Fuel costs due to oil use Fdpt
Dr ,external heat use Qexdt
Dr or the cost for the biomass burned in thedryer are accounted for in the oil supply, the external heat supplyand the biomass supply model object function, respectively. An oil-fired dryer causes emission, and the emission costs are calculatedas given in Eq. (21), provided that an emission penalty Pende
Em isdefined.
CDr ¼X
e˛Emissions
Xt˛Time steps
Xd˛Dryers
PenEmde Emitedt ; (21)
where
Emitedt ¼ emdeFDrdptHVoil; cp˛Products; d˛Dryers;
t˛Time steps; e˛Emissions: (22)
The amount of biomass flowing to the dryer is the sum of thebiomass volume dried and the (optional) biomass volume burnedto supply drying heat. The biomass is fed to the dryer from thebiomass node n connected to the dryer input point i. The input andoutput volume is linked by Eq. (19). The dried biomass is sent to thebiomass node n connected to the dryer output point j:
VinDrdpt þ VbDr
dpt ¼X
i:ðn;iÞ˛Net2net
VN2Nnipt ; (23)
VoutDrdpt ¼
Xj:ðj;nÞ˛Net2net
VN2Njnpt ; cd˛Dryers;n˛BioNodes;
p˛Products; t˛Time steps: (24)
The biomass moisture content at the dryer inlet (outlet) is setequal to the moisture content in the biomass node connected to thedryer inlet (outlet). This is done applying the general node structureand the set ‘‘Net2net’’.
MCinDrdpt ¼ if n˛BioNodes then MCNo
npt ; cd˛Dryers;
ðn; dÞ˛Net2net; p˛Products; t˛Time steps; (25)
MCoutDrdpt ¼ if n˛BioNodes then MCNo
npt ; cd˛Dryers;
ðd;nÞ˛Net2net; p˛Products; t˛Time steps: (26)
In addition to the heat obtained by burning biomass in the dryer,it is possible to reuse external waste heat or to produce drying heatfrom burning oil. The energy balance for the dryer heat input pointh and the dryer fuel input point f is
QexDrdt ¼
Xh:ði;hÞ˛Net2net
PN2Niht þ
Xh:ðs;hÞ˛Supply2net
PSupsht ; (27)
FDrdptHVoil ¼
Xf :ði;f Þ˛Net2net
PN2Nift þ
Xf :ðs;f Þ˛Supply2net
PSupsft ;
cd˛Dryers; t˛Time steps: (28)
Table 3Example: calculation of constants in storage model.
dspSt 3sp
St csSt
0.05 0.01 200
ToutsbSt � Tinsa
St DspabSt Espab
St CsabSt
1 0.0500 0.9900 2002 0.0488 0.9801 4003 0.0475 0.9703 6004 0.0464 0.9606 8005 0.0452 0.9510 1000
S. van Dyken et al. / Energy 35 (2010) 1338–13501346
Here, the common energy flow variables are used, since noinformation on biomass quality is required. The biomass chain thusinteracts directly with the other energy carriers in the system.
3.4. Storage model
Any biomass product can be sent to the storage model. Inaddition to the energy storage function, the model provides theopportunity to indicate passive drying effects as a function of thestorage time. The passive drying function is not appropriate for anhourly time resolution, but it becomes applicable when the analysisis carried out on a weekly basis as described in Section 3. However,the passive drying functionality is defined per timestep and is notlimited to a certain time resolution. To indicate internal fuel use dueto biomass handling in the storage, a fuel input point is also defined.
The drying rate dspSt is user-defined and describes the reduction of
biomass moisture (percentage) which can be achieved per time-step. In addition to the moisture reduction coefficient, the volumeloss coefficient 3sp
St and the storage cost coefficient csSt are also
defined per timestep.Similarly to the drying model, the moisture reduction coefficient
is treated as an average input value. However, in contrast to thedryer model, the decreasing drying rate at lower moisture levels isnot implemented. It is assumed that the moisture reduction ratedecreases with increasing storage time Toutsb
St � TinsaSt , expressed in
parameter DspabSt . The volume loss coefficient is dealt with in the
same way: The volume losses are increasing with increasingstorage time, expressed in the calculated parameter Espab
St . In thisway, volume and quality losses due to long-term storage can beindicated. The storage cost is defined per timestep, too, but the costis assumed as constant and summed up over the total storage timein the parameter Csab
St . That means that no cost increase due toincreasing storage time is implemented.
The binary variable lspabSt keeps track of how long (how many
timesteps) the biomass at least has to be stored to reach themoisture level required at the storage output. It is not possible totake out biomass with a moisture level higher than that onerequired at the storage output point.
It is assumed that increasing storage time has an impact on boththe moisture reduction coefficient dsp
St and the volume loss coeffi-cient 3sp
St . The storage costs are assumed to be stable, thus they donot change with increasing storage time and are constant in eachtimestep. The total storage costs are calculated by multiplying thecost coefficient by the number of timesteps spent between inputand output of biomass to/from storage (Toutsb
St � TinsbSt) given by
CStsab ¼ if TinSt
sa ¼ ToutStsb then 0 else cSt
s
�ToutSt
sb � TinStsb
�;
cs˛Storages; ab˛Time steps: (29)
Another assumption is that the longer the biomass is stored, themore volume gets lost (due to biomass handling). In addition tohandling losses, other negative effects may appear (quality loss dueto e.g. fungal decay). These effects are modeled by defininga volume loss parameter dependent on storage time:
EStspab ¼ if TinSt
sa ¼ ToutStsb then 1 else
�1� eSt
sb
�ðToutStsb�TinSt
sbÞ;
cs˛Storages; p˛Products; ab˛Time steps: (30)
An increasing time difference between biomass input andoutput of the same volume leads to growing volume losses. Theequation implemented to express a decreasing drying rate iscomparable to the volume loss calculation in Eq. (30). The mode ofcalculation of both factors is based on assumptions. It is assumedthat less moisture is evaporated when the biomass already has
been stored for a long time. This offers the possibility to display thedecelerated drying effect at lower moisture levels in the model.Contrary to the volume loss calculation, the decreasing drying rateis still defined per timestep, given by
DStspab ¼ if TinSt
sa ¼ ToutStsb then dSt
sp
else1�
�1� dSt
sp
�ðToutStsb�TinSt
saÞ
ToutStsb � TinSt
sa;
cs˛Storages; p˛Products; ab˛Time steps: (31)
Table 3 gives a numerical example of the calculation of both thetime-dependent parameters Dspab
St and EspabSt and the constant cost
parameter CsabSt in the storage model.
The user defines whether passive drying effects occur duringstorage or not. This is done by implementing the binary parameterasp
St . If aspSt is set to zero (no passive drying in storage), the storage time
is not restricted. That means that the optimization algorithmchooses freely (only restricted by the storage cost in the objectivefunction) for how many timesteps the biomass is stored and when itis sent to the next biomass model in the supply chain. However, if asp
St
is set to one (passive drying effects in storage), time-dependentrestrictions have to be met. In this case, the storage time is restrictedapplying the binary variable lspab
St . Considering the maximum andminimum values of moisture content given in the biomass node atthe storage output or the demand moisture level in the end of thesupply chain, a certain moisture range for the storage outputmoisture level is defined. Applying the binary variable lspab
St and thedrying rate Dspab
St , it is calculated how many timesteps the biomasshas to be stored to reach the output moisture level required:
2NT lStspab �
�ToutSt
sb � TinStsa
��
MCinStspt �MCoutSt
spt
DStspab
; (32)
2NT�
lStspab � 1
���
ToutStsb � TinSt
sa
��
MCinStspt �MCoutSt
spt
DStspab
;
cs˛Storages; p˛Products; ab˛Time steps: (33)
lspabSt is set to one if the output moisture level can be reached
during the time period TinsaSt � Toutsa
St , otherwise it is set to zero. It isassumed that some of the biomass gets lost or becomes unusableduring the storage process. This is modeled by defining a certainpercentage of the input volume as loss volume. The biomassvolume flow to and from storage is restricted by
VinStspt ¼
Xb˛Time steps
VtransStspab; (34)
VoutStspt ¼
Xa˛Time steps
VtransStspabESt
spab; (35)
S. van Dyken et al. / Energy 35 (2010) 1338–1350 1347
where
VtransStspab�lSt
spabVmaxSts ;cs˛Storages;p˛Products;ab˛Timesteps:
(36)
where the volume loss factor EspabSt is defined in Eq. (30).
The user-defined cost factor is multiplied by the biomassvolume Vtransspab
St handled in storage to determine the storage cost:
CSt ¼X
a;b˛Time steps
Xs˛Storages
Xp˛Products
CStsabVtransSt
spab
þX
e˛Emissions
PenEmse Emitest (37)
where
Emitest ¼ emseFSts HVoil$VinSt
spt ; cp˛Products; s˛Storages;
a; b˛Time steps; e˛Emissions: (38)
Storage keeping causes emissions only when an external fueldemand is defined, applying the parameter Fs
St. In this case, theemission costs are added to the operating costs, provided that anemission penalty Pense
Em is defined. Fuel costs are accounted for inthe oil supply model objective.
The biomass is fed to the storage from the biomass node nconnected to the storage input point i and sent from the storage tothe biomass node n connected to the storage output point j
VinStspt ¼
Xi:ðn;iÞ˛Net2net
VN2Nnipt ; (39)
VoutStspt ¼
Xj:ðj;nÞ˛Net2net
VN2Njnpt ; cs˛Storages;n˛BioNodes;
p˛Products; t˛Time steps; (40)
BIO_SUP_S
CHIP
STOR_IDRY
STOR_II
BIO_SUP_C
FUEL_SUP_I
0.5
0.5
Electricity
Biomass
Fuel
Heat
Bio Oil
0.5 Moisture
content
Fig. 3. Biomass case
applying the biomass flow variable VjnptN 2N (Bio_net2net_flowijpt).
The input and output volume is linked by Eq. (34) and (35). Simi-larly to the dryer model with Eq. (25) and (26), the biomassmoisture content at the storage inlet (outlet) is set equal to themoisture content in the biomass node connected to the storageinlet (outlet):
MCinStspt ¼ if n˛BioNodes then MCNo
npt ; cs˛Storages;
ðn; sÞ˛Net2net;p˛Products; t˛Time steps; (41)
MCoutStspt ¼ if n˛BioNodes then MCNo
npt ; cs˛Storages;
ðs;nÞ˛Net2net;p˛Products; t˛Time steps: (42)
The fuel needed by the storage to handle the biomass is fed fromthe network to the storage fuel input point f.
FSts HVoil$VinSt
spt ¼X
f :ði;f Þ˛Net2net
PN2Nift þ
Xf :ðs;f Þ˛Supply2net
PSupsft ;
cd˛Storages; t˛Time steps: (43)
According to Eq. (28) in the dryer model, the common energyflow variables are used, since no information on biomass qualityparameters is required.
4. Case study
To demonstrate the use of the new biomass models, especiallythe functionality of the active and passive drying processes in theDryer and Storage model, a simple case study is carried out. Themain intention is to point out the properties and functionality ofthe new models rather than to represent a detailed analysis of a realbiomass supply chain with several alternatives. Therefore, noinvestment analysis is carried out and the emissions caused by the
RELIOBSTELLEPHEAT LOAD
BIO_LOAD_C
EL_SUP
FUEL_SUP_II
HEAT_SUP
0.1
0.11
in eTransport.
Table 4Reference values of case products.
Parameter Unit Spruce Chips Pellets
MCpref %wt 0 18 8
Dpref kg/m3 405 340 700
HVpref kW h/m3 2155 1000 3200
S. van Dyken et al. / Energy 35 (2010) 1338–13501348
different processes applied in the case are not investigated. Onlylimited focus has been given to obtain realistic input data.
4.1. Case overview
The analysis is run over a time period of twelve weeks (twelvetimesteps t). This period is appropriate to describe the active dryingprocesses in the dryer and to allow for moisture decrease from oneweek to another in the storage model.
It is assumed that the amount of biomass products availablewithin a time period of twelve weeks varies. Thus, the biomasssupply profile is not constant, but the biomass demand profile isassumed to be constant. Hence, storage keeping is required to beable to cover the demand in all weeks. The combination of moisturecontent demanded at different points in the case is set in sucha way that both passive and active drying processes are possible.
The case setup is shown in Fig. 3. Three different biomassproducts are handled in the case: spruce, chips and pellets with thereference values given in Table 4. On the demand site, there isa biomass load point demanding chips at a constant level of100 m3/week (average 0.6 m3/h) and a heat load point witha demand of 20 MW h/week (average 119 kW h/h). To cover thedemand, two different biomass supplies with restricted capacitiesare available: a chip supply (45 USD/m3) and a spruce supply(35 USD/m3). As can be seen from Fig. 4, the chip supply volume isnot sufficient to cover the chip demand. Thus, chips have to beprocessed from spruce in the chipper before they are sent tostorage. This increases the price (spruce) due to the additionalenergy costs generated in the chipper.
The moisture content required in the different supply, conver-sion and load points is indicated in the case setup in Fig. 3. Both thechips and the spruce are supplied with a moisture content of 50%wt. The moisture content demanded by the biomass load (chips) is11% wt while the moisture content of the biomass burned in theboiler cannot exceed 10% wt. Thus, drying is required. This can becarried out either active in the dryer or passive in the storages. Inboth storage models, the drying option is enabled and it is assumedthat the moisture content of the biomass stored is reduced with 1%
0
20
40
60
80
100
120
140
160
180
1 2 3 4 5 6 7 8 9 10 11 12weeks
Vo
lu
me [m
3]
Spruce
Chips
Fig. 4. Maximum volume capacity spruce and chips supply.
wt during one week. The specific energy required in the dryer toevaporate one kg of water from biomass is set to 2 kW h/kg(average heat requirement for dryers [19]).
After having passed the dryer, the main fraction of chips is sentto the biomass demand point. The remaining chips are sent toa second storage which is followed by a combination of a pelletsproduction plant and a boiler to cover the heat demand. The dryingheat required in the dryer is supplied both by an external heatsource (restricted capacity) and by burning fuel. The option ofburning biomass is not used. The heat required in the pelletproduction plant is covered by an external heat source, too. Boththe pellet plant and the boiler demand electricity to run internalcontrol systems and other supplementary devices. The amount ofenergy required to handle the biomass inside storage is neglected.Similarly, no additional operating costs are defined.
Apart from the combustion model, the maximum capacity(volume and heat) in the conversion models is not restricted. In thecombustion model, the maximum volume capacity is limited sothat the integrated additional oil firing option has to be applied. Thevolume losses are set to 1% of the input volume in the storage andthe dryer model, while losses of 5% are assumed in the chipper andthe pellet plant. There is no cost associated with the use of externalheat. The fuel cost is set to 0.65 USD/liter, the electricity cost to84 USD/MW h.
4.2. System operation and results
The model chooses from the two supply sources available asshown in Fig. 5. The volume capacity of the spruce supply is utilizedfully while the chips supply only is used to cover lacking chipsproduction. With the cost combination defined in the model, it ismore profitable to process chips from spruce and to pay for the fuelrequired in the process than to purchase chips directly from supply.
Fig. 6 illustrates both the drying effect and the storage keepingin storage I. The moisture content is reduced from 50% wt at thestorage input to values in the range between 46.4% wt and 42.3% wt.The lowest output moisture content is reached in week four. Onehas to keep in mind that the set Time_steps is defined as circular.Thus, week twelve is followed by week one in the model. A certainamount of biomass sent to storage in week seven for instance mightbe sent out in week four. This leads to a storage time of nine weeksassociated with a fairly high moisture reduction. As can be seenfrom Fig. 6(a) and (c) the storage is filled to a high level to takeadvantage of the increasing moisture reduction with longer storagetime.
In storage II, the moisture content of the chips is reduced from11% wt (dryer output) to 10% wt (boiler input required). With the
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12weeks
Vo
lu
me [m
3]
Chips
Spruce
Fig. 5. Total output volume spruce and chips supply.
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11 12weeks
vo
lu
me [m
3]
input
output
0,38
0,40
0,42
0,44
0,46
0,48
0,50
0,52
1 2 3 4 5 6 7 8 9 10 11 12weeks
mo
is
tu
re
c
on
te
nt
input
output
0
50
100
150
200
250
300
350
1 2 3 4 5 6 7 8 9 10 11 12weeks
vo
lu
me [m
3]
a
b
c
Fig. 6. Storage I, (a) input and output volume, (b) moisture content, (c) volume stored.
Table 5Solving time and objective value for a range of gap tolerances in the solver.
MIPGAP [% of lower boundon objective value]
Solvingtime [s]
Objectivevalue [USD]
10 7.07 69,123.70039 7.83 69,123.70038 14.12 69,028.60767 37.86 68,910.70836 159.06 68,733.51175 747.70 68,733.51174 >1 h
S. van Dyken et al. / Energy 35 (2010) 1338–1350 1349
moisture reduction factor of 1% wt assumed in storage II, therequested moisture level can be reached during one week. Thus,chips sent to storage in one week are sent out with a moisture levelof 10% wt in the following week. Therefore, in contrast to storage I,no remarkable storage effects are to be observed in storage II.
The objective value represents the operating cost for the wholesystem. Over a time horizon of twelve weeks the operating costadds up to 68,733.51 USD. This value represents the fuel cost, thebiomass cost and the electricity cost.
5. Discussion
The objective of the present work is to develop a linearmodeling framework as a part of the eTransport optimization toolthat can be applied to most relevant components in a biomasssupply chain, including sources, handling/processing, storage and
end use. The moisture content has large influence on the efficiencyof various biomass conversion processes like combustion andpyrolysis [20]. Thus, the main focus of this work has been torepresent the relationship between moisture and energy content ofdifferent kinds of biomass and to handle long-term processes in theoptimization like passive drying effects.
With the modeling approach presented in this paper, a solid basisfor the linear modeling of general biomass supply chains has beendeveloped. Due to assumptions and simplifications made in the modelsas well as the fact that the biomass module is embedded in the alreadyexisting eTransport framework, there are some model limitations.
The modeling of long-term effects in the biomass module isa new approach which is partly limited by the time structure ineTransport. Long-term effects in the biomass models can bea challenge when combined with shorter time resolution e.g. inheat and electricity loads. In the case study presented this has beensolved by using weekly average values.
Another time aspect in the model is the solving time. It varieswith the complexity of the problem depending on system size, therange of products to be handled and the number of timestepschosen. One possibility to avoid prohibitive solving times is tolower the precision of the solver. This can be justified by the factthat uncertainty in the input dataset contributes significantly moreto the total uncertainty of the objective value than the gap betweenthe best feasible solution and its lower bound. To illustrate this, thecase presented has been solved with a range of allowed gaps in theCPLEX branch and bound algorithm. The resulting solving time andobjective values are given in Table 5. As seen from the table thesolution time is reduced by a factor of 100 by increasing the allowedgap from 5% to 10% of lower bound on the objective value.
The economic part of the biomass model application and theemission handling are not discussed in detail since the calculationfollows the main eTransport algorithms documented in [14]. Emis-sions can be accounted for both in biomass sources (due to harvesting,handling, etc.), energy use in biomass processing models and fromcombustion. These emissions are then considered by the investmentalgorithm in the same way as for other combustion models.
In the case study, only limited focus has been given to obtainrealistic input data. The main objective with the case study is todemonstrate the functionality of the new methodology presented.The assembly of models shown in the case study represents onepossibility out of an unlimited number of combinations. With thedata chosen, the functionality available in the biomass models isdemonstrated. A next step in the model development andimprovement would be to validate the results with workingconditions of a real system.
6. Summary
Both the eTransport model and the biomass module discussedin this paper are still under development. The biomass models arepartly an expansion of models from a master thesis [18]. The work
S. van Dyken et al. / Energy 35 (2010) 1338–13501350
presented in this paper has been carried out with financial supportfrom the Research Council of Norway and StatoilHydro. Require-ments from StatoilHydro have influenced the technologies to bemodeled. In addition to the seven biomass models presented inSection 3, two more models have been developed:
Transport: Truck transport. Discrete model, emissions due to fueluse.Pyrolysis: Bio oil production in a fast pyrolysis process. Link tobio fuel applications.
These two models are not discussed in detail, but they illustratethe many possibilities for further development of the biomassmodule. The transport model is a discrete model. The pyrolysismodel can be seen as a link to bio fuel applications. This link showsthe wide variety of biomass utilization. Other processing technol-ogies as for instance bundling and grinding could be implementedin future. Moisture dependent efficiency of biomass combustionmodels can also be implemented within the new framework. Thewhole biomass sector itself is under development and new andmore improved technologies frequently appear. With its flexiblestructure, the biomass module presented here is a solid basis forfurther development and improvement.
Acknowledgements
The authors gratefully acknowledge the support from theResearch Council of Norway and from StatoilHydro as a sponsor ofthe project.
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