Location Model for biogas facilities

Transcription

1 Location Model for biogas facilities Ruth Delzeit, Institut für Lebensmittel- und Ressourcenökonomik, Rheinische Friedrich-Wilhelms-Universität Bonn, Introduction Bioenergy is said to have a big potential in contributing to an energy-mix with regard to a sustainable energy concept. With an increasing use of bioenergy questions about the logistic of biomass to respective plants and effects on the environment arise. In the agricultural sector transport costs make up an important share of overall productions costs, and are expected to rise in the future due to rising crude oil price, tolls and environmental regulations (BOYSEN et al. 2006, p. 152). Hence, in order to maximize profits and to assess environmental effects (emissions) an optimal location and size of bioenergy plants has to be determined. The regional agricultural environmental information system (RAUMIS) has modelled the area and yields for energy crops, assuming a total marketability of all produced biomass at given producer prices and opportunity costs. This assumption is incorrect, if plants do not emerge all-over, and thus, the results of RAUMIS need to be revised by a location model, incorporating transportation costs. By using the location model it is assumed that, if raw material becomes scarce, only those bioenergy facilities persist, that produce cost effectively. Thus, identifying optimal location gives important information on where facilities will be located in the long run. An optimal location is defined as the combination of location and size that minimizes total costs, consisting of production and transportation costs. Ceteris paribus, this is equivalent to income or a profit maximisation. In this study profit maximisation is applied. Before describing the methods for developing the location model, basic assumptions and data availability are illustrated. 2 Description of the system and evolving assumptions The location and sizes of bioenergy facilities depend on a variety of factors which show interferences: legislation, the availability of raw materials (yields and share of land), production costs, the possibilities to use the produced energy, and resulting transportation costs. The first calculation is done for biogas from maize. This comprises the most significant part of the biomass production for which transportation costs are of crucial importance. 1

2 Relevant legislation The production of bioenergy highly depends on legislation which has important impacts on the choice of location, and the amount of bioenergy production. The production of biomass in Germany depends on incentives, set by the German government and the European Union. In the case of biogas from maize, the most important legislation is the Renewable Energy Source Act (EEG), which guarantees a feed-in tariff differentiated for different sizes of facilities. Additionally, surcharges are granted for the exclusive use of renewable primary products (RPP), the use of combined heat and power generation, and the use of new technologies. In the location model, the different tariffs are implemented for respective capacities and usages. Availability of raw material Biogas facilities can be divided into those, which are operated with 90% RPP and 10% of liquid manure and facilities which run with 90% of liquid manure and 10% RPP (see e.g. IN- STITUT FÜR ENERGETIK UND UMWELT 2005, p. 136). New facilities are able to be operated with RPP only, which makes modelling easier in a first step. Thus, it is assumed that biogas facilities are run solely with energy maize, which is in practice the most used crop for input. Data on the production of energy-maize per county and yields can be gained from RAUMIS. Differences of land use and yield of energy-maize determine number and size of facilities if borders of counties are defined as limit of raw material supply. The availability of raw material in one county determines the potential number of facilities there. It is assumed that the smallest capacity (100 kw) demands for 2388 tonnes by which the produced amount of maize is divided. Transportation costs Maize needs to be cut on the field and be transported to the biogas facility. After the fermentation process residues are brought back to the field. In the current version of the model, transport of residues as well as transports for fertilizers and chemicals are neglected, but are planned to be included in an improved version. When harvesting, a chaffing machine cuts maize while a transportation unit drives alongside. When the transportation unit is filled up, maize is transported to the facility. In order to save costs, several transport units are needed to avoid a standstill of the chaffing machine. In the model it is assumed that chaffing machines and transport units are rented, and costs are collected from regional machinery ring associations. Transport costs are calculated from labour costs and rental rate per transportation unit times the number of transportation units. The 2

3 latter depends on the speed of the chaffing machine, the time for filling and unloading the transportation units, and the distance to the facility. The filling time depends on the speed, width, and size of the chaffing machine, as well as on yields. The distance depends on the transported amount of maize, yields, and share of maize on the land-use. Production costs Production costs of biogas are divided into variable costs, which consist of costs for raw material, costs for maintenance and repair, labour, insurance, operating staff, and parasitic energy, and fixed costs (fixed capital), which include total investment costs, a discount rate of 6%, and a useful live expectancy of 16 years. Data on production costs were collected from literature and expert interviews for four capacity classes, which are oriented towards the availability of data and thresholds for subsidies. Capacity classes are 100kW, 500kW, 1000kW and 2000kW. Multi-use options for biogas Production of electricity and Combined Heat Generation (CHG) CHG is the simultaneous production of power (e.g. electricity) and heat (FACHAGENTUR NACHWACHSENDE ROHSTOFFE 2006, p.19). In Germany, the major technology is block heat power plants (BHPP) with combustion engines, combined with a generator. Currently, the produced biogas is almost entirely used for a direct production of electricity in motor-bhpp (INSTITUT FÜR ENERGETIK UND UMWELT 2005, p. 75). Additionally, the BHPP modules contain a heat exchanging device, for recovering heat from exhaust gas, cooling water and lubricating oil cycle, hydraulic advices for heat-distribution and electrical switchgear and controlling units for electricity distribution and regulation of the BHPP (FACHAGENTUR NACH- WACHSENDE ROHSTOFFE 2006, p. 101). A 500 kwh biogas facility produces kwh of electricity and kwh/a heat at 8000 operating hours (FACHAGENTUR NACH- WACHSENDE ROHSTOFFE 2005). Electric efficiency is the sum of thermal and electrical energy, and usually is 80-90% (FACHAGENTUR NACHWACHSENDE ROHSTOFFE 2006, p. 104). It is assumed that with rising prices for raw materials only those biogas facilities persist which use combined heat power generation. For the produced heat, suitable heat sinks (demand for heat) need to be found. When using CHC additional subsidies can be acquired, and additional investment costs for the BHPP have to be included. 3

4 Transportation of biogas to location with CHG Biogas can be conducted through a pipeline to a location with sufficient head demand. Biogas has to be processed to the same gas quality as for direct power generation. Additional costs occur for the construction of the pipeline. Additionally to costs for the BHPP, costs for the pipeline have to be regarded. Gas induction Biogas can be inducted into the gas grid, using qualitatively high processed biogas. This method is applied in pilot projects already and supported by the German government. It is assumed that it becomes technically mature within the modelling time frame of the project (2020) and is thus included in the location model. The possibility of induction depends on several standards and legislation, as well as on the technical and economic side on the gas net at hand with different gas qualities and gas pressures. The costs for induction of gas (parameter pc) and possible counties of gas induction are included in the model. 3 Pre-selection of potential locations When analysing population density, counties with more than 500/km 2 habitants were excluded, as no biogas production is possible in urbanized areas due to availability of raw material and restrictions in building laws. For the choice of location (independent of the size) it is assumed, that the availability of raw materials and the usage of the produced energy (gas injection or heat sink) are the most important factors for location a biogas facility. Using a Geographical Information System these potential locations are identified using an analysing tool. Maize areas As in RAUMIS climatic data and data on soil are not explicitly modelled, in a first step we tried to identify areas advantageous for maize cultivation using a Geographic information system (GIS) by a spatial analysis of heat sums and water availability. Maize is a crop that does not request high fertility of soil, but demands a certain climate and availability of water (LÜTKE ENTRUP et al. 2000, p. 405). Especially from the starting of bloom water deficiency can lead to an insufficient impregnation and blocking of assimilation (ibid.). Thus, heat sums and precipitation are chosen as location factors: Heat sums: The growing period of maize is mainly determined by regionally differing temperatures in Germany (LÜTKE ENTRUP et al. 2000, p. 404). For germination it needs a soil temperature of 4

5 8-10 C. According to the maximum-minimum-method with a basic temperature of 8 C, heat sums are calculated summing up daily air temperature from middle of April to middle of November (AUGTER 1994). They are presented in a map by the German Weather Service. Water availability: Water is most important during the period from middle of July to the end of August. In an extreme example, in this period of time 6mm/m 2 and day are needed (LÜTKE ENTRUP et al. 2000, p. 405), which sums up to 180mm/m 2 per month. To determine thresholds for advantageous areas of maize cultivation, an expert interview was held with representatives of the German Maize Committee. The interview resulted in the statement that no areas can be classified as advantageous or disadvantageous as different varieties of maize are bred, that are well adapted to different natural conditions. (A map of the German Maize Committee which additionally includes the factors soil and geology to determine the optimal harvesting time exists.) Thus, a pre-selection of relevant areas according to availability of maize could not be realized. Areas with heat sinks For biogas facilities with 100KW and 500KW it is assumed that CHG is needed for cost efficiency. Currently, most biogas facilities do not have a concept for usage of produced heat. Further, most existing facilities have been constructed in areas with poor possibilities for heat disposal (BREMER ENERGIE INSTITUT 2007, p. 1). A study of the BREMER ENERGY INSTITUT (2007) examined possibilities for heat disposal, which are technically and economically feasible. All of these possibilities assume an existing facility can be improved or heat can be used after a facility is constructed. With existing data the amount of heat sinks cannot be assessed on a county level. Another option for heat disposals are heating networks and bigger heat users like swimming pools, retirement homes, schools etc. Based on this, the heat demand is still prohibitively difficult to estimate for each county, as there are different kinds (e.g. full-day/half-day), and sizes of buildings and therewith different demands on heat. Thus, we decided to calculate potential heat demand for each county using data offered by the German Federal Ministry of Economy and Technology (2006) on heat relevant energy use. The results were then compared with produced heat by biogas facilities. They indicate that, theoretically, in all counties heat demand exceeds potential heat produced by biogas facilities. 5

6 Areas of gas injection In order to determine counties with suitable gas pipelines for the injection of biogas, studies from the INSTITUT FÜR ENERGETIK UND UMWELT (2005) and ARBEITSGEMEINSCHAFT WUP- PERTAL INSTITUT, FRAUNHOFER GESELLSCHAFT-UMSICHT, GASWÄRME-INSTITUT ESSEN (2007) were reviewed. Following a study on the structure of the gas grid, the gas grid can be assumed to cover on average 85% of Germany, but an assessment of numbers of municipalities, which are suitable for an induction of biogas is not possible with this information as a direct induction is dependant on the location of induction, the structure of the gas grid and consumers at hand (INSTITUT FÜR ENERGETIK UND UMWELT 2005, p. 115). Thus, in a GIS-analysis counties with access to gas pipelines were selected, and for those the option of gas induction was included in the model. 4 Choice of a facility location model A literature review of different facility location models (see Annex) resulted in the choice of a Capacitated Facility Location Problem (CFLP). CFLP are classified as Mixed-integer programming models. Starting with a given set of potential facilities, many location problems can be modeled as mixed-integer programming models. KLOSE (2005) gives a rough classification of discrete facility location models: (a) single- vs. multistage models, (b) uncapacitated vs. capacitated models, (c) multiple- vs. single-sourcing, (d) single- vs. multi-product models, (e) static vs. dynamic models, and, last but not least, (f) models without and with routing options included. Of relevance for the location model in our context is the Capacitated Facility Location Problem (CFLP), which is described in the following sections. The objective of the CFLP is to minimize costs considering the trade-off between fixed operating and variable delivery cost. Assuming a single-stage model (=simple plant location problem) it has to be decided, whether to establish facilities and which quantities to supply from facility i to customer j such that the total cost (including fixed and variable costs) is minimized. min m i= 1 n c x + m ij ij j= 1 i= 1 f i yi d j xij j j s i y i Assumptions: One stage, one product, considers a set of candidate sites for facility location, and a set of customers. Each facility i I has a fixed cost fi. Every customer j J has a de- 6

7 mand b j, and c ij is the unit transportation cost from i to j. Each open facility can provide a limited amount of commodity. d= distance, s= capacity. 5 Description of the location model The first version of the location model is a modified Capacitated Facility Location Problem, where profit is maximised. Modifications are employed for production and processing costs per unit. They are assumed to be constant in regular CFLPs, but data for biogas shows increasing returns of scale. Furthermore, in regular CFLPS, a linear relation between transportation costs per tonne and distance is assumed. This is not the case for biogas, as variables like yields, and numbers of transportation units have to be considered. Objective function max ( λ q f y ) ( c n ) lu jl l jl k kjl j J l L u U k K Indices / Sets: k K: regions (319 counties) j J: facilities within counties (30975) l L: classes of capacities (100, 500, 1000, 2000kW) u U: pathways for usage subsets j_county(j,k) subset to relate facilities to regions u_option(l, u) subset to define utilization options gas(k,u) subset to define regions where gas induction is possible Given data/ Parameters: λ lu profit per produced kwh in eeg l feed in prices for electricity (in /kwh) nawaro subsidy for usage of RPP (in /kwh) techn subsidy for technology (in /kwh) heat u subsidy for usage of heat (in /kwh) v l : variable production costs ( /kwh) pc lu costs for the different processing ways, depending on capacity and possibility of gas induction (in /kwh) st l costs for storing silage in drive-in silo (in /kwh) 7

8 q jl: f l : c k : production output of j at capacity l (in kwh) fixed costs (in per year) transport costs per transportation unit in (different cost in regions, differences in farm size initially neglected) e k : yield in k (in tons per m 2 ) s k : share of maize on agricultural area in use in k b k : amount of maize produced in k (in tons) m: demand of maize in tonnes per kwh p: speed of transportation unit (in km/h) sp: speed of cutting unit (in m/min) u: time for unloading the trucks (in min) t: additional time for intersections (in min) d k : time for filling the trucks (in min) a kj total time for driving (in min) wd width of cutting machine (in m) tgr size of truck (in m 3 ) A circular area in k around facility (in m 2 ) Decision variables / Variables y jl : decision variable (opened or closed) z kjl : transported amount of maize from k to j depending on l (in tons) n kjl : number of rides (integer) r kjl : transport radius around j (in km) Side conditions for all k K (1) zkjl bk j J l L (2) q * m= z for all j J and l L jl k K kjl (3) zkjl 1.08 m* qjl yjl for all l L k K (4) y jl 1 for all j J j J (5) z kjl 0 for all k K, j J and l L (6) q jl 0 for all j J and l L (7) y {0,1 } for all j J and l L jl 8

9 (8) n kjl Z for all k K, j J and l L (9) r kjl 0 for all k K, j J and l L where λ = ( eeg + nawaro + tech + heat ) ( v + st + pc ) lu l u l l lu d k tgr = sp* wd* e k zkjl 100 A = * e s r kjl k A = (in km) π k rkjl akjl = (60* + u+ t)*2 p The objective function maximises profits over all regions and facilities. It is special in that it does not include per unit gross revenue from market activities. This is due to the fact that per unit gross income net of subsidies is not dependent on location or capacity and is thus not relevant for the location problem. Therefore, income from different subsidies is subtracted by production costs including fixed, variable, processing costs, and costs for storing silage in drive-in silo, and transportation costs, which consist of costs for chaff cutting and transporting harvested maize to the facility. The condition 1 ensures that not more maize is transported from a region to facilities than is produced in that region. Input with maize and the facility s output are related with condition 2. With condition 3 it is made sure, that the capacity of facilities is kept and closed facilities are not provided with maize. 8% are added, as these are silage losses. That every facility produces at only one class of capacity is taken care of with constraint 4. Constraints 5 to 9 determine the rage of value for variables. The filling time for trucks is calculated by dividing the truck s size by the width and speed of the cutting machine times the yield in a region. To receive the radius around a facility where maize is transported from, the circular area around a facility is determined by dividing the transported amount of maize by the yield, including the share of maize on the agricultural area. The total driving time of a transportation unit is obtained by adding driving time of a truck from the cutting machine to the facility, time for intersections and unloading. This derivation assumes that each vehicle always drives to the margin of a circle. 9

10 The number of needed transportation units result from dividing the driving time by the filling time. Iteratively, fist z and y are determined by the model, and thereafter r and n. 6 References AUGTER, G. (1994): Maisanbauregionen in der Bundesrepublik Deutschland. Berechnung und Regionalisierung von Mais-Wärmesummen. Projekt AM/258. Offenbach a. M.. BOYSEN, O. & C. SCHRÖDER (2006): Economies of Scale in der Produktion versus Diseconomies im Transport. Zum Strukturwandel im Molkereisektor. In: Agrarwirtschaft (55), pp BREMER ENERGIE INSTITUT (2007): Leitfaden: Verwertung von Wärmeüberschüssen bei landwirtschaftlichen Biogasanlagen. Bremen. DREZNER, Z. & H. W. HAMACHER (2002): Facility location: applications and theory. Berlin: Springer. DREZNER, T., DREZNER, Z. & S. SALHI (2002): Solving the multiple competitive facilities location problem. In: European Journal of Operational Research (142), pp FACHAGENTUR NACHWACHSENDE ROHSTOFFE e.v. (ed.) (2005): Basisdaten Biogas Deutschland. Gülzow. FACHAGENTUR NACHWACHSENDE ROHSTOFFE e.v. (ed.) (2006): Handreichung. Biogasgewinnung und -nutzung. Gülzow. INSTITUT FÜR ENERGETIK UND UMWELT (2005): Evaluierung der Möglichkeiten zur Einspeisung von Biogas in das Erdgasnetz. Forschungsvorhaben im Auftrag der Fachagentur Nachwachsende Rohstoffe e.v.. Leipzig: Institut für Energetik und Umwelt ggmbh. KLOSE, A. (2001): Standortplanung in distributiven Systemen. Modelle, Methoden, Anwendungen. Heidelberg: Physica. KLOSE, A. & A. DREXL (2005): Facility location models for distribution system design. In: European Journal of Operational Research (162), pp LÜTKE ENTRUP, N. & J. OEHMICHEN (2000): Lehrbuch des Pflanzenanbaus. Band 2: Kulturpflanzen. Gelsenkirchen: Th. Mann. 10

11 Annex Overview over dismissed models for facility locations (based on DREZNER et al. 2002a, KLOSE 2001, KLOSE et al. 2005) Facility location models can be classified according to the shape or topography of plant, objectives (minsum or maxsum), capacity restriction, stages (single or multiple), products (homogenous or inhomogeneous), demand (elastic or inelastic), static or dynamic, deterministic or probabilistic, and quality of demand allocation (KLOSE et al. 2005, p. 5). In literature, location models are mainly categorized by topography (see e.g. KLOSE et al. 2005, KLOSE 2001, DREZNER et al. 2002a) into: Models in the plane (continuous location models) Continuous location problems arise, when the locations space is described by way of continuous variables (DREZNER et al. 2002a, p. 37). They are characterized by a continuous solution space which states, that each point in the space represents a feasible location. Further, the measurement of distances is carried out by a suitable metric (mainly by lp-standards) (KLOSE 2001, p. 13). The objective is a minimization of the sum of distances between the facilities and given demand points (KLOSE et al. 2005, p. 5). It is assumed that one cannot give an exhaustive list of all individual available places (DREZNER et al. 2002a, p. 37). Demand points are fixed. Continuous location models were debarred, as the study area Germany is not homogenous regarding e.g. agricultural area, heat sinks and others. Discrete location models or network location models Discrete location models have a given underlying network, given locations of demands to be served by the facilities and the locations of existing facilities. They can be divided regarding their considerations of distance into maximum distance models (equity objective) and total or average distance models (DREZNER et al. 2002a, S. 82). In the first class, a maximum distance is defined a priori, e.g. in a maximum distance of 500m students must walk to school, and public transportation must cover those student not living within the maximum distance. The location of a school should be found to minimize the number students who must use the bus. Set covering location models aim to locate the minimum 11

12 number of facilities required to cover all of the demand nodes. This is not suitable for our problem. The objective of Maximal covering location problems is to locate a predetermined number of facilities, and to maximize the demand that is covered. Similar to the p-center problem the aim of which is to locate p facilities such that the maximum distance is minimized (min. costs for consumers), this model cannot solve our optimization problem. In the p-dispersion problem only distance between new facilities are regarded. The objective is to maximize minimum distance between any pair of facilities. Examples are military installations, where a separation makes them more difficult to attack (DREZNER et al. 2002a, p. 89). For biogas facilities it is advantageous to be located far from other users for maize, but in this model economic variables and existing old facilities are not included. In the group of total or average distance models (efficiency objective) models deal with the total travel distance between facilities and demand nodes. The p-median model locates facilities such that the demand-weighted total distance between demand nodes and the facilities to which they are assigned are minimized (min. costs for consumers). It is assumed that some facilities exist, new facilities are added. Potential facilities sites are nodes on the network. Each potential site has the same fixed costs for locating a facility at it. Facilities being sited do not have capacities on demand that they serve (uncapacitated). The number of facilities to be opened is known. The Multiple competitive facilities location problem is in many ways equal to the p-median or p-center problems, but here, facilities compete against each other aiming to attract as many customers as possible in order to maximize market share. There is a given set of facilities, and new facilities added. Customers patronize the closest facility or in the gravity based formula: customers divide patronage according to distance and attractiveness. Market share is determined by a gravity model. New facilities p are planned, searching for location where total market share is maximized. Unknown locations are X (DREZNER et al. 2002b). The objective of the fixed charge location problem is to minimize total (summed) facility and transportation costs in order to determine the optimal number and locations of facilities, as well as the assignments of demand to a facility. Assumptions of the p-median problem are relaxed: facilities have capacity, thus demand may not be assigned to its closest facility. Fixed costs for locating are not similar; one does not know a priori how many facilities should be opened. 12

13 In the hub location problem, the sum of the costs of moving items between a non-hub node and the hub to which the node is assigned is minimized. As all operational costs are neglected, the model is not suitable. Maxisum location problem aims to maximize the demand-weighted total distance and hence to locate the facilities far from demand points. Being close to another facility is not desirable. A clear distinction of network location models and mixed-integer programming models (MIPM) is not possible, because the former ones can be stated as discrete optimization models. While parameters like the structure of potential facilities and the distance metric are explicitly taken by network location models, MIPL use them as exogenous input parameters (KLOSE et al. 2005, p. 8ff). 13