06美赛建模论文.doc

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number186 ? Problem ChosenC For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2005 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.) Type a summary of your results on this page. Do not includethe name of your school, advisor, or team members on this page. Summary This paper aims to predict the depletion of crude oil reserve. In our prediction, we analyze the relationship between production, reserve and some exogenous factors in detail. Analyzing the data from website of Organization of Petroleum Exporting Countries (OPEC) and U.S. Energy Information Administration (EIA), we propose three models to forecast the annual petroleum production and peak production years. Our first model is a short-term prediction for regional annual production. Based on the Hubbert model, we obtain a differential equation for the cumulative production. Using the least squares fits, we obtain the values of parameters for the differential equation. Solving the equation, we get a rough prediction of the oil production. The second one is used for long-term forecast. Firstly, we model the accumulative discovery by logistic regression; then we introduce the reserve-to-production ratio concept to describe the relationship between the reserve and production; finally, we design a recursion of time to predict the production year by year. According to the variation of reserve-to-production ratio, we consider two scenarios and find the peak year of production is 2010 and 2015 respectively and even till the year of 2100, the annual production can be at the level of 5.5 billion barrels. The third model takes some exogenous factors impacting production into account. We divide those factors into three categories: Supply factors, Demand factors and Modulation factors. Cho