1 Intelligent Well Technology: Status and Opportunities for Developing Marginal Reserves SPE
MODELLING THE COSTS OF BIOFUELS: A CASE STUDY OF U.S. CORN AND BRAZILIAN SUGAR CANE
Aurélie Méjean, University of Cambridge, +44 (0) 7910245208,
Chris Hope, University of Cambridge, +44 (0) 1223 338194,
Overview
High crude oil prices, uncertainties about the consequences of climate change and the eventual decline of conventional oil production raise the issue of alternative fuels, such as biofuels. This paper describes a simple probabilistic model of the costs of energy crops, drawing on the user's degree of belief about a series of parameters as an input. This forward-looking analysis quantifies the effects of production constraints and experience on the costs of corn and sugar cane, which can then be converted to bioethanol. Land is a limited and heterogeneous resource: the crop cost model builds on the marginal land fertility, which is assumed to decrease as more land is taken into production, driving down the marginal crop yield. Also, the maximum achievable yield is influenced by technological change, while the yield gap between the actual yield and the maximum yield decreases through improved management practices.
Methods
The aim is to express our uncertainty about the future costs of supplying alternative liquid fuels. A model is introduced that draws on the user’s degree of belief about a series of parameters as an input (see Hope, 2006). A probability distribution is assigned to these parameters based on “up-to-date knowledge from science and economics”, (Stern, 2007). We look at the uncertainty associated with the validity of the input data and the influence of each parameter on the output.
Land is heterogeneous and of limited supply, and it is economically rational to produce the low cost, high quality resources first.The approach taken by modellers is to try to reflect how the marginal productivity of land could evolve as more land is brought into production.Our model will focus on the marginal cost of producing crops, i.e. the cost of producing crops on the marginal hectare of land. The marginal production cost is relevant in this case as it will reflect the costs faced by land renting farmers on every type of land under cultivation. The maximum achievable marginal yield is a decreasing function of the area of land Q, as the most fertile land is used first (equation 1). The maximum yield will also benefit from technological developments (equation 2).The yield gap between the actual marginal yield the maximum achievable marginal yield will decrease with cumulative production, through improved production technologies and management practice (equation 3).
Equation / Parameter / Description(1) / YMAX / maximum achievable marginal yield
Ymin / minimum value of the achievable yield
Yinitial / initial (maximum) value of the achievable yield
Q / area of land used for crop production
QT / total suitable land
/ exponent of the land productivity curve
(2) / bYMAX / learning coefficient (LRYMAX)
X / cumulative production
X0 / initial cumulative production
(3) / Yactual / actual marginal yield
bYa / learning coefficient (LRYactual)
g / yield gap
g0 / initial yield gap
A literature review is conducted in order to define the ranges of estimates associated with each parameter for U.S. corn and Brazilian sugar cane. These ranges are fed into the model to obtain some preliminary results.
Results
The model reveals the kind of uncertainties that need to be dealt with when designing policies. The results show large uncertainties in the future costs of producing corn and sugar cane, with a 90% confidence interval of 2.5 to 7.5 US$/GJ in 2025 for average corn costs, and 1 to 2 US$/GJ in 2025 for average sugar cane costs. The influence of each parameter on these supply costs is examined.
The sensitivity analysis shows that parameters C0 and g0 have the biggest influence on corn costs in 2025 and C0 and LRYMAX have the biggest influence on corn costs in 2050. Parameters C0 and g0 also have the biggest influence on sugar cane costs in 2025, but α replaces LRYMAX in 2050. Learning and the decreasing fertility of land are driven by production: costs decrease with experience and the marginal productivity of land decreases as more land is brought into production. The correlation sensitivity associated with demand suggests that the dominant effect on corn costs switches from the decreasing fertility of land to learning around 2035: As the maximum marginal yield comes closer to its theoretical minimum, the potential for further cost increase linked to the decreasing fertility of land is reduced, and the main effect of higher production rates is to build experience, driving down average costs. In the case of sugar cane costs, the influence of higher demand increases over the whole period. However, when the time frame of the model is expanded, the influence of higher demand reaches a peak around 2060, when all suitable land for sugar cane production is used as in the case of corn. This shift in the effect of demand growth between corn and sugar cane is explained by the fact that the initial share of suitable land used for sugar cane production in Brazil is much lower than the initial share of suitable land used for corn production in the U.S.
Conclusions
This research ultimately aims to reveal the effects of experience, technological developments and production constraints on the costs of supplying alternative fuels. In this paper, a first model describing the effects of learning and decreasing marginal land fertility on the costs of supplying corn and sugar cane was introduced. The learning, resources and production parameters of the model are not known precisely, and uncertainty was introduced by assigning a distribution to each parameter.
The results show large uncertainties in the future costs of supplying corn and sugar cane, with a 90% confidence interval of 2.5 to 7.5 $/GJ in 2025 for average corn costs, and 1 to 2 $/GJ in 2025 for average sugar cane costs. Learning and the decreasing fertility of land are driven by production: costs decrease with experience while the marginal productivity of land decreases as more land is brought into production. The sensitivity analysis shows that in both cases, production is first driving the costs up, as the productivity of the marginal land decreases. As the maximum marginal yield comes closer to its theoretical minimum, the potential for further cost increase linked to the decreasing fertility of land is reduced, and the main effect of higher production is to build experience. The effect of the decreasing fertility of land is thus overcome by experience in the longer term.
Bioethanol is obtained by the fermentation of sugars found in the crop feedstock. A model for conversion costs will be introduced. The environmental costs associated with the production of biofuels are not included in the cost estimates. In particular, the cost of carbon should be considered when assessing the cost-competitiveness of these fuels. Like high oil prices, high carbon prices will impact on investment into alternative fuels supplies, and will therefore influence the scale of production and trend in supply costs.
It is expected that the study will inform decision makers on the type of policy and the scale and timing of investments that will be needed to meet the growing demand for liquid fuels while satisfying CO2 constraints, and the first model described here is a step in this direction.
References
Hope, Chris (2006) The marginal impact of CO2 from PAGE2002: An integrated assessment model incorporating the IPCC's five reasons for concern, Integrated Assessment, 6 (1) 19-56
Stern, Nicholas (2007) The Economics of Climate Change - The Stern Review. CUP, Cambridge, U.K.