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460724 A Composite-Curve-Based Biomass Procurement Planning Approach

**A
Composite-Curve-Based Biomass Procurement Planning Approach**

**Wenzhao Wu, Daniel Kurniawan, WenBo Zhu,
Christos T. Maravelias***

Dept. of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706

The production of fuels
and chemicals from biomass has received considerable attention recently due to
environmental concerns^{1}. Since the production of biofuels involves
relatively expensive feedstock and energy-intensive biomass transportation, any
biomass-to-fuels strategy should include an efficient, both in terms of cost
and environmental impact, biomass (feedstock) supply chain. Unlike fossil
fuels, biomass, as a low-energy density resource, is sparsely distributed. The
efficient biomass transportation thus requires biomass procurement planning
methods^{2}. In many studies, the farms are treated as points without
shape or area^{3}. This is a reasonable assumption when the
transportation distance is so large that the shape and size of the farms can be
neglected. In this case, the transportation problem is modeled as a
point-to-point (farm-to-refinery) problem. However, the shape and size of the
farms cannot be neglected when the refinery is close to the farm, which means
that the size of the farm is not significantly smaller than the transportation
distances, which in turn means that the error in approximating the real
transportation distance with the distance between the center of the farm and
the bio-refinery can be quite large. In this case, transportation should be
treated as a region-to-point problem. To this end, we discuss a novel approach
to biomass procurement planning on a region-to-point basis.

In terms of
transportation, we propose a region-to-point modeling approach based on
mathematical integration (in a polar coordinate system) over the sourcing
region that has unique characteristics such as shape, location, and
productivity. The transportation cost is correlated with the amount of biomass
(“mass”) procured from each farm. The final result is a function *C* = *f
*(*M*), where *M* is the mass, and *C* is the transportation
cost. In other words, the proposed methods generate a function that returns the
total cost of procuring *M* mass, which is graphically represented by a
“procurement curve”. Both algebraic and numerical solution methods are
discussed and demonstrated with examples.

In terms of system-level
procurement planning, we develop a composite-curve-based approach that
incorporates the regional transportation modeling method, and aims at
identifying the biomass procurement plan that minimizes the total procurement
cost (including biomass purchasing, harvesting and transportation). The
specific steps for the generation of the composite curve using the individual
procurement curves, as well as insights into the procurement planning problem
are discussed. An analogy to the cold/hot composite curves in the pinch design
method for heat exchanger networks^{4} is also presented. A case study
involving 12 farms (which are approximated as polytopes) and one refinery is
presented (see Figure 1A). The corresponding composite curve is shown in Figure
2, and the final procurement strategy is graphically represented in Figure 1B.

**Fig****ure 1.** (**A**) Map of farms (the polytopes)
surrounding a bio-refinery (the black dot at the origin) for the case study; (**B**)
procurement strategy (represented by the green dashed areas) for a 11800 T/year
demand. The farm numbers are labeled accordingly.

**Figure ****2.** Individual procurement curves and the composite
curve for the case study. The composite curve is marked thick. The demand of
11800 T/year and the corresponding per-mass supply cost () on the y-axis are marked
with dashed lines. The farm numbers are labeled accordingly.

The proposed
composite-curve-based method allows us to more accurately calculate
transportation distance, and thus transportation costs and GHG emissions due to
transportation. It also provides some key insights into the design of biofuel
supply chains. In addition, the methods proposed in this work are integrated
with mathematical programming to address complicated problems involving, for
example, multiple feedstocks, multiple refineries, and multiple periods. We can
solve such problems by either generating multiple composite curves, or directly
incorporating the *C* = *f *(*M*) function for each farm into a
general supply chain optimization model.

**References**

[1] DOE Bioenergy Technologies Office, 2014. Multi-year program plan, Washington DC, USA: DOE.

[2] DOE/EERE, 2013c. Feedstock supply and logistics: biomass as a commodity, US: Department of Energy, Office of Energy Efficiency & Renewable Energy.

[3] You, F., Tao, L., Graziano, D. & Snyder, S. W., 2012. Optimal Design of Sustainable Cellulosic Biofuel Supply Chains: Multiobjective Optimization Coupled with Life Cycle Assessment and Input-Output Analysis. AIChE Journal, Volume 58, pp. 1157-1180.

[4] Linnhoff, B. & Hindmarsh, E., 1983. The pinch design method for heat exchanger networks. Chemical Engineering Science, 38(5), pp. 745-763.

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