Hubbert model

Production Peaks, Depletion Signals [2] Lynch, M.C. Petroleum Resources Pessimism Debunked in Hubbert Model and Hubbert Modelers Assessment. Oil and Gas Journal, July 14, 2003 [3],... 

Nashawi, I.S., Malallah, A., and Al-Bisharah, M. (2010) Forecasting wolrd crude oil production using multicyclic Hubbert model. Enery Fuels, 24,1788-1800. 

Once the hydrocarbons have been solubilized in the formation water, they move with the water under the influence of elevation and pressure (fluid), thermal, electroosmotic and chemicoosmotic potentials. Of these, the fluid potential is the most important and the best known. The fluid potential is defined as the amount of work required to transport a unit mass of fluid from an arbitrary chosen datum (usually sea level) and state to the position and state of the point considered. The classic work of Hubbert (192) on the theory of groundwater motion was the first published account of the basinwide flow of fluids that considered the problem in exact mathematical terms as a steady-state phenomenon. His concept of formation fluid flow is shown in Figure 3A. However, incongruities in the relation between total hydraulic head and depth below surface in topographic low areas suggested that Hubbert s model was incomplete (193). Expanding on the work of Hubbert, Toth (194, 195) introduced a mathematical mfcdel in which exact flow patterns are... 

Figure 3. Development of fluid flow models (A) Hubbert (192), (B) Toth (194,195), (C) Freeze and Witherspoon (196-198)...

Figure 2.18 depicts a cross-section of a model that has been much quoted in the hydrological literature from Hubbert (1940) to most recent textbooks and articles. The modeling is restricted to a valley flank in a small drainage basin. The cross-section is through half a valley, from a local divide to a nearby low-order valley. The three marked planes are assumed in the model to be impermeable (no water is assumed to flow across the vertical planes... 

Fig. 2.18 A cross-section of a much-quoted model (following Freeze and Cherry, 1979, who cited Hubbert, 1940). The surface is described as undulating in a mode that can be expressed by a simple mathematical equation, and the water table is assumed to follow topography in a fixed mode. The stippled section describes a water system from a low-order divide to a nearby low-order valley the thick lines mark there impermeable planes that are an intrinsic part of the U-shape flow paths model, enlarged in Fig. 2.19. The cross-section emphasizes topographic undulations and disregards the location of the terminal base of drainage and the location of the main water divide.

Figure 7.4. The historical global consumption of oil (top) and the historical price levels of crude oil (bottom), supplemented with 3 models for future behaviour a extrapolates the expected growth in demand, notably carried by countries such as China and India, b assumes a constant usage of oil (i.e. all growth substituted) and c is a Hubbert (1962) model based on the assumption of generously available substitute fuels at prices similar to that of current oil. The rapid price increases in the models a and b simply reflect the lack of available substitutes for oil at equivalent prices under 100 US /bbl. The figure uses historical consumption data from Fig. 5.6 and historical prices from Enquete Kommission des Deutschen Bundestages (1995) and Energy Information Administration of the US DoE (2004) (cf. Sorensen, 20041).

M. King Hubbert s Resource Model (Hubbert, 1981), which I will call the HR Model, will be used to project fossil fuel production into the future. Projections of future fossil fuel production will be converted to CO2 emissions. There is a 3-month lag between fossil fuel production and use, which is negligible compared to the time frame of this study. In the simplest sense, the HR Model for an exhaustible resource shows the production curve will rise to some peak and them come back down, eventually to zero. The area under the production curve is the ultimate cumulative production of the resource. An aggressive rise in the future fossil fuel production curve will be chosen to set an upper limit for future atmospheric CO2 levels. 

For the purpose of developing the long-term projections in this paper, all fossil fuel resource data used will be that available in 1993 and projections shown in the figures start at 1990. Published data from 1990 to 2001 for anthropogenic CO2 emissions and atmospheric CO2 levels will be used to test the model. The cumulative production of world fossil fuel (oil, gas and coal) and a projection into the future are shown in Fig. 1. The projection was made using the HR Model (Hubbert, 1981) and is based on known, proved reserves only. The total area under the curve in Fig. 1 is47,330 quads (Barabba, 1989 Taylor, 1989 Kilgore, 1993 West, 1993). The curve in Fig. 1 will be used to develop the low estimate of fossil fuel production. 

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