A Regional-Scale GIS-Based Modeling System for Evaluating the Potential Costs and Supplies of Biomass from Biomass Crops

From Proceedings, BIOENERGY '96--The Seventh National Bioenergy Conference. Meeting held September 15-20, 1996, Nashville, Tennessee, published by the Southeastern Regional Biomass Energy Program.

A GIS-based modeling system was developed for analyzing the geographic variation in potential bioenergy feedstock supplies and optimal locations for siting bioenergy facilities. The modeling system is designed for analyzing individual U.S. states but could readily be adapted to any geographic region.

Keywords: Feedstock, supply, siting, GIS, transportation models, feedstock costs, delivered prices, facility siting

Producing economically-competitive bioenergy from energy crops, be it electric power or liquid fuels, is strongly dependent on the availability of low-cost feedstocks. That availability will have spatial variation. We have developed a GIS-based modeling system which captures the geographic variation in the major factors that determine supply and cost of biomass feedstocks derived from energy crops. The system incorporates soil quality, climate, land use and road network information, with transportation, economic, and environmental models to predict both where energy crops would be grown and the marginal cost of supplying biomass from energy crops to specific locations. The modeling system is designed to evaluate individual U.S. states but could readily be modified to evaluate larger or smaller geographic regions. The system is an outgrowth of GIS-based modeling systems for evaluating the feedstock cost to individual plant locations (Downing and Graham, in press; Noon et al., in press; Graham et al., 1995).

Overview

The modeling system has four basic components. The first component maps cropland that is potentially available for energy crop production. The cropland map is at a 1 km² resolution (i.e., 1 km² pixel size). The second component of the system defines both expected yield (tonnes/ha/yr) and farmgate⁽¹⁾ price of energy crops of each 1 km² area. The third component calculates potential farmgate supply of feedstock and maps marginal cost of delivering specific quantities of feedstock to any destination in the state. The fourth component identifies, ranks and maps, all the sites in a state where bioenergy facilities might be co- located. The identification and ranking, which are based on minimizing the marginal cost of delivered biomass feedstock, take into account both facility size (i.e., annual demand for feedstock) and inter-site competition for potential biomass supplies.

Component 1. Mapping Cropland Availability

A GIS is used to create a digital map containing the following land availability variables for each 1 km² pixel:

1. c - the county to which the pixel belongs
2. s - the soil group found at that pixel location
3. APCT - percent of the pixel which is cropland physically suitable for growing energy crops
4. ADOPT_{a=1, c} - the proportion of the cropland in county c that could be converted to energy crop production assuming a mature bioenergy market, and
5. ADOPT_{a=2, c} - the proportion of cropland in county c that could be converted to energy crop production assuming an immature bioenergy market.

The first three variables are generated by overlaying three digital maps - a county boundary map, a soil-group map, and a land-use map. The fourth and fifth variables are linked to the digital map on the basis of their county identity and are generated using county-level information on the relative dominance of conventional crops in each county. The value of the fourth variable is defined as the percent of cropland in the county currently planted to the most dominant conventional cash crop. The value of the fifth variable is defined as the percent of cropland in the county currently planted to minor crops (i.e., crops other than the two most dominant crops). We assume that even under a mature bioenergy market, farmers would dedicate only as much land to energy crops as they currently dedicate to the dominant crop in their area. Under an immature bioenergy market, farmers would only grow energy crops on that land currently planted to minor crops. While these land availability restrictions are somewhat arbitrary they serve to recognize that farmers reduce their risk to unforeseen weather and market variations by planting multiple crops. Thus it is appropriate in modeling potential supply to restrict energy crop production to some subset of the cropland base. These five variables are later used conjunction with yield and expected farmgate price information created in component 2 to determine the potential supply of biomass from a pixel in component 3.

Component 2. Calculating expected yields and farmgate price

The model defines the farmgate price of biomass feedstock at a particular location as the price ($/harvested tonne stored on farm) that would offer a farmer a return to land and management equivalent to the current return from the mix of conventional crops grown in that geographic region. The region is defined by the location's county and soil group.

where:
FP=the farmgate price of energy crop feedstock ($/dry harvested tonne)
PB=annualized energy crop production cost ($/ha/yr)
YB=average annual energy crop yield over the lifetime of the crop (harvested dry tonnes/ha/yr)
R=returns to land and management from current mix of conventional crops ($/ha/yr)
BR=the fraction of the harvested crop that arrives at the conversion facility
s=soil group
c=county

Because many perennial energy crops do not produce a commercial harvest every year, the energy crop yield is annualized by dividing the total harvested yield of the crop over its expected lifetime by its lifetime. Lifetime refers to the duration of time between the original planting of the crop and its final harvest. The production costs are also annualized over the crop's lifetime.

Equation (1) implicitly assumes that the farmer will be paid for the feedstock that arrives at the conversion facility and thus will bear the burden of storage and transport losses. The transportation cost is, however, not borne by the farmer. The variable BR is used to account for the loss associated with the storage and transport of biomass. This loss is a function of the type of energy crop and the assumed storage and transport system.

The expected yield of energy crops is calculated using field trial results for energy crops, observed county-level variations in conventional crop yields, and soil- and climate-specific yield indices developed using the crop simulation model EPIC (Williams et al., 1989). Expected energy crop production costs are state-specific and take into account the average expected state yield for the energy crop and state-specific labor rates and farm sizes.

The expected returns to land and management from growing the location's current mix of conventional agricultural crops is calculated using equation.2

where :
R=returns to land and management from current mix of conventional crops ($/ha/yr)
Y=conventional crop yield (harvested tonnes/ha/yr)
P=market price ($/tonne) of conventional crop
C=production cost ($/ha/yr) (labor, equipment, fertilizer, seed, fuel, custom operations).
A=proportion of cropland planted to crop type I
I=type of conventional crop ( e.g. wheat, soybeans, etc)
s=soil group
c=county

Equation (2) is calculated using input tables containing county-level information on the mix of conventional crops grown at the location, market prices for those crops, and production costs (excluding costs due to land and management), and soil-group-level information on conventional crop yields. As with energy crop yields, EPIC is used in conjunction with soils and climate information and county-level crop yield statistics to predict conventional crop yields on different soil groups.

Component 3. Mapping the marginal cost of delivered energy crop feedstocks

First, the farmgate price and expected yield values derived in component 2 are linked to the map of available cropland created in component 1 on the basis of the soil and county identities. The potential feedstock supply at any pixel is then calculated using the equation (3) and land availability variable values from the cropland map.

where:
S=the amount of energy crop feedstock annually produced in the pixel (dry tonnes/yr)
ADOPT=the proportion of cropland potentially available for energy crops
YB=average annual energy crop yield over the lifetime of the crop (tonnes/ha/yr)
BR=the fraction of the harvested crop which arrives at the conversion facility
APCT=percent of 1 km² pixel which is cropland
q=pixel identity (unique to each pixel)
a=adoption choice (1=mature market or 2=immature market)
s=soil group
c=county

Once the potential feedstock supply and its associated farmgate price have been calculated and assigned to each pixel in the state, the cost of transporting the feedstock from that pixel to any other pixel within the state is calculated. A digital road network map is overlaid onto the cropland map and time and distance estimates for pixel to pixel transport are made. The per tonne cost of transporting the supply from the origination pixel to the destination pixel is calculated using equation 4.

where:
TC(x,y)=the cost of transporting feedstock from pixel x to pixel y ($/dry tonne)
KF=fixed cost of loading and unloading the feedstock ($/dry tonne)
KD=distance dependent cost ($/dry tonne-km one way)
KT=time dependent cost ($/dry tonne-hour one way)
DIST(x,y)=Road distance between pixel x and pixel y (km one way)
TIME(x,y)=Travel time between pixel x and pixel y (hours one way)

KF, KD, and KT are derived using a transport model appropriate to the energy crop and presumed transport scenario.

Once the per tonne cost of transporting the feedstock from one pixel to any other pixel has been calculated, the marginal cost of supplying a specific amount of feedstock to any destination is calculated. The marginal cost algorithm ranks (from lowest to highest) the delivered cost (farmgate price + transport price) of all the supplies from pixels within the state to the target destination and calculates the cumulative potential supply of feedstock from those ranked pixels. The marginal cost of supplying x amount of feedstock to the destination is the delivered price of the feedstock from the pixel that would supply the xth dry tonne of feedstock. The algorithm is run for all destinations (i.e., every pixel) in the state to create a surface map of delivered marginal feedstock costs for a specified feedstock amount. Different maps can be created by specifying different feedstock amounts or assuming different energy crop adoption rates.

Component 4. Mapping sites where bioenergy facilities might be co-located.

In mapping the potential locations of multiple bioenergy facilities one must account for the fact that feedstock resources used for one facility are not available to another facility. Thus to determine where and how many bioenergy facilities might be sited at what feedstock cost, we take the following approach. We calculate the marginal cost of supplying feedstock to a location in the same fashion as in component 3 but we exclude the feedstock resources that are already being used to meet the demands of another location. Potential bioenergy facility locations are selected sequentially based on lowest delivered marginal feedstock cost. For example, the first bioenergy facility location is the pixel identified in component 3 as having the lowest marginal delivered feedstock price in the state. The feedstock resources used to supply that pixel are then removed from the resource base. The marginal cost algorithm is rerun, the next lowest cost location is identified, and the feedstock resources used to supply that location are removed from the resource base. This step is repeated until the potential feedstock resources have all been allocated. The siting algorithm mimics the situation where the bioenergy facility establishes long-term contracts with farmers to produce feedstock and these contracts are not renegotiated when another facility is sited in the area.

Switchgrass (Panicum virgatum) is a native perennial C4 grass species that has shown great promise as an energy crop in the southeastern U.S.. It has produced harvested yields on research plots of up to 36 dry tonnes/ha/yr although yields of 15 to 20 tonnes are more common. Figure 1 shows the results of applying our GIS-based model system to switchgrass production in the state of Alabama. We assumed mature adoption rates and analyzed facility-demand levels of 600,000 and 100,000 dry tonnes/yr. The former demand is commensurate with the feedstock requirements envisioned by the U.S. Department of Energy for a commercial cellulosic ethanol conversion facility, while the latter demand is representative of a moderate size (20MW) combustion steam-turbine power plant. Farmgate prices (in 1993 $U.S.) over the state ranged from $20.79 to $38.83 per dry tonne. These low prices are a result of the predicted high switchgrass yields (13.0 to 23.8 tonnes/yr) and low returns to land and management from growing conventional crops in this state. The analysis showed the state could support one facility demanding 600,000 dry tonnes/yr or 27 facilities each requiring 100,000 dry tonnes with feedstock under $35/dry tonne. The analysis clearly demonstrates that in Alabama higher feedstock costs are associated with supplying larger facilities.

Fig.1. The predicted location and feedstock cost for energy facilities in Alabama needing 100,000 or 600,000 dry tonnes of switchgrass annually.

(1) The farmgate price is the price demanded by the farmer exclusive of transportation costs. The farmgate supply is the supply of feedstock at the farm as opposed to at the conversion facility. (return to text)

REFERENCES

1. Downing, M. and R.L. Graham. The potential supply and cost of biomass from energy crops in the Tennessee Valley Authority Region. Biomass and Bioenergy, in press.
2. Graham, R.L., W. Liu, M. Downing, C. Noon, M. Daly and A. Moore. (1995). The effect of location and facility demand on the marginal cost of delivered wood chips from energy crops: A case study of the state of Tennessee. In: Proceedings of the Second Biomass Conference of the Americas: Energy, Environment, Agriculture and Industry. pp 1324-1333. National Renewable Energy Laboratory, Golden CO, NREL/CP200-8098.
3. Noon, C.E. and M.J. Daly. GIS-based biomass resource assessment with BRAVO. Biomass and Bioenergy, in press.
4. Williams, J.R., C.A. Jones, J.R. Kinery and D.A. Spanel (1989). The EPIC crop growth model. Trans. of the Amer. Soc. of Agric. Engineers, 32, 497-511.

The authors appreciate the thoughtful reviews of J.H. Cushman and M. Downing. This research was supported by funds from the U.S. Dept. of Energy, the Office of Transportation Technologies and the Office of Utility Technologies. Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research Corp., for the U.S. Department of Energy under contract number DE-AC05-96OR22464.