A lignocellulosic feedstock logistics system that supplies 800,000 dry matter tons of corn stover to a 60 Mgal/year biochemical ethanol biorefinery was modeled in Microsoft Excel using the methodology documented by Turhollow et al. (2009). The logistics system included raking and baling (large 4×4×8 ft square bales) after grain harvest, collection of bales from the field to a roadside storage stack, transportation of bales to a biorefinery over a 350 day/year delivery schedule, and preprocessing of bales at the biorefinery to a hammer-milled bulk material ready for insertion into a pretreatment reactor (Hess et al., 2009).
2.2.2 Analysis Step 2—Defining Input Parameter Probability Distributions
In order to identify and rank the importance of model input parameters, an analysis was conducted using @RISK, a commercial simulation software package used to solve Excel spreadsheet models for a probable forecasted scenario (@RISK, Palisade Corp., Ithaca, NY; Excel, Microsoft Corp., Redmond, WA). Probability distributions were defined for each model input variable, including biomass resource availabil- ity parameters (e.g., grain yield, producer participation), biomass material property parameters (e.g., moisture content, bulk density), logistics system parameters (e.g., harvest window, transportation distance, fuel and electricity prices), machinery per- formance parameters (e.g., rates, capacities, efficiencies), and biomass loss parame- ters (e.g., collection efficiencies, storage losses). Most input variables were described according to a PERT distribution function, which is commonly used when data to define a distribution is sparse (@RISK, Palisade Corp., Ithaca, NY). A PERT dis- tribution is defined by minimum, mode, and maximum values that are linked in a bell-shaped distribution, and to the extent that the minimum and maximum values are evenly distributed about the mode, this distribution mimics that of a normal distribution. Two input variables—biorefinery daily receiving hours and biorefinery feedstock inventory (i.e., tons of feedstock stored on site)—were defined by a uniform distribution that assumes all values between the defined minimum and maximum val- ues are equally likely to occur. A uniform distribution was chosen for these two variables because all values within the distribution are equally likely to occur.
Minimum, mode, and maximum values of the PERT distributions were defined according to our own research data, where available (Hess et al., 2009); other- wise, literature data and input from experienced machinery operators, manufacturers, and vendors was used. American Society of Agricultural and Biological Engineers (ASABE) Agricultural Machinery Management Data (ASABE, 2006) was used to define machinery field speeds and efficiencies, repair and maintenance costs, annual operating hours, and estimated lifetime hours. The probability distribution represents either the inherent variability or the uncertainty of the input variables, as determined by the variability in collected field data, published data (e.g., field efficiency and field speed ranges published by ASABE), or range of operating parameters suggested by skilled operators of the equipment. The most likely value included in each distribution is the benchmark value input to the feedstock logistics model (Hess et al., 2009).
2.2.3 Analysis Step 3—Perform Deterministic Computations
A Latin Hypercube sampling method was used in the @Risk simulation to gen- erate the input parameter values from the probability distribution functions. This method was chosen over the Monte Carlo technique, which samples randomly from the distribution function and causes clustering when low probability values are not sampled due to insufficient computational sampling iterations. In contrast, the Latin Hypercube stratified sampling technique systematically samples all segments (strat- ifications) of the distribution just once, resulting in fewer computational iterations required to produce a representative probability curve.
The analysis was conducted by incrementing each input parameter throughout the defined distribution while randomly varying the remaining parameters according to their own defined probability distributions. Thus, the impact of each parameter on delivered feedstock cost was determined individually, while also capturing the inter- dependence of the input parameters. Tens of thousands of scenarios were collected in this manner to generate the output shown in Figure 2.1.
This @Risk simulation was used to rank input variables based on the statistical relationship between each variable and the delivered feedstock cost. In order to resolve these rankings, the @Risk analysis results were further analyzed to isolate the individ- ual influences with respect to three parameters: sensitivity, uncertainty, and influence (Figure 2.2).Sensitivity,a measure of how responsive a unit operation/process cost is to changes in a specific variable, was determined by approximating the slope using a linear regression of each response curve in units of $/ton per percent change from the variable’s base value.
Sensitivity alone is not sufficient to rank input variables according to their impact on delivered feedstock cost because while feedstock cost may be highly sensitive to changes in a particular variable, the overall effect may be small if the range of that variable is small. This range or variability of an input variable, termedUncertainty, was measured by the horizontal run of the response curve in units of percent change from the parameter base value. An additional parameter was included, referred to as Influence, to give preference to those variables that are more influential than others.
A parameter’s influence is represented by the curvature of the response curve, with greater curvature suggesting greater interdependence (or influence). A parameter’s
Collection efficiency (%) Bale density (lb/ft3) Transport distance (mi) Storage dry matter loss (%) Harvest window (wks)
–75 52 54 56 58
$ / DM ton
60 62 64
–25 25
% change from base value
75
FIGURE 2.1 Response of delivered feedstock cost to changes in model input logistics parameters.
–30 52 54 56 58 60 62 64
–20 –10 0
% change from base value Uncertainty
Slope = sensitivity
$ / DM ton
R = 0.97042
Collection efficiency (%)
10 20 30
FIGURE 2.2 Illustrated definitions of sensitivity, influence, and uncertainty.
relative influence was estimated as the inverse of the R-squared value derived from a linear regression of the response curve.
2.2.4 Analysis Step 4—Deciphering the Results
Independent rankings of input variables according to sensitivity, uncertainty, and influence provided three disparate rankings (Figures 2.3–2.5). Bale bulk density, col- lection efficiency, and grain yield ranked highest in sensitivity; storage dry matter losses, harvest window, and bale moisture ranked the highest in uncertainty; and harvest window, collection efficiency, and stalk chopper field speed ranked high- est in influence. A combined normalized ranking was determined by taking the product of sensitivity, uncertainty, and influence and dividing by the highest value (Figure 2.6). The resulting normalized values show the combined impact of the three parameters—sensitivity, uncertainty, and influence—relative to the input variable of greatest combined effect. The variables shown in Figure 2.6 were categorized as follows: (1) biomass yield (collection efficiency, grain yield, storage dry matter loss);
(2) biomass material properties (bale bulk density, bale moisture); (3) machinery per- formance (shredder speed, baler capacity, baler field efficiency, semi speed, shredder field efficiency, loader capacity; and (4) system variables (harvest window, trans- portation distance winding factor—a multiplier applied to the transportation distance input, off-road diesel price).
Bale density (lb/ft3) Collection efficiency (%) Grain yield (bu/ac) Stalk chopping speed (mph) Stalk chopping field efficiency (%) Baling field efficiency (%) Baling moisture (%) Baling rate (bale/hr) Transport distance (mi) Off-road diesel ($/gal) Transport speed (mph) Harvest window (wks) Transport load/unload rate (bale/hr) Storage dry matter loss (%)
0 0.2 0.4
Normalized sensitivity
0.6 0.8 1
FIGURE 2.3 Normalized ranking of the sensitivity of feedstock cost to changes in input logistics parameters.
Storage dry matter loss (%) Harvest window (wks) Baling moisture (%) Stalk chopping speed (mph) Collection efficiency (%) Grain yield (bu/ac) Transport load/unload rate (bale/hr) Baling rate (bale/hr) Bale density (lb/ft3) Transport speed (mph) Baling field efficiency (%) Transport distance (mi) Off-road diesel ($/gal) Stalk chopping field efficiency (%)
0 0.2 0.4
Normalized uncertainty
0.6 0.8 1
FIGURE 2.4 Normalized ranking of the uncertainty of feedstock cost related to the variabil- ity of input logistics parameters.
0.945 0.955 0.965
Influence
0.975 0.985 0.995
Storage dry matter loss (%) Harvest window (wks)
Baling moisture (%) Stalk chopping speed (mph) Collection efficiency (%)
Grain yield (bu/ac) Transport load/unload rate (bale/hr) Baling rate (bale/hr)
Bale density (lb/ft3) Transport speed (mph) Baling field efficiency (%)
Transport distance (mi) Off-road diesel ($/gal) Stalk chopping field efficiency (%)
FIGURE 2.5 Ranking of the cumulative influence of input logistics parameters on feedstock cost.
Storage dry matter loss (%) Harvest window (wks) Baling moisture (%) Stalk chopping speed (mph) Collection efficiency (%)
Grain yield (bu/ac)
Transport load/unload rate (bale/hr) Baling rate (bale/hr) Bale density (lb/ft3)
Transport speed (mph) Baling field efficiency (%) Transport distance (mi)
Off-road diesel ($/gal) Stalk chopping field efficiency (%)
0 0.2 0.4
Normalized ranking
0.6 0.8 1
FIGURE 2.6 Normalized ranking of model input logistics parameters according to combined values of sensitivity, uncertainty, and influence.
Biomass yield variables—those that affect the mass per acre delivered to the biorefinery—are particularly important since they reside at the front end of the feed- stock supply chain and thus have broad impacts that extend through the entire supply chain. In fact, biomass yield affects many of the other variable categories identified in the analysis, including machinery performance and system variables (harvest window and transportation distance). Accordingly, uncertainties of biomass yield variables—particularly collection efficiency and storage dry matter losses—are the focus of the discussion that follows.