Hubbert's theory Hubbert peak theory

1 hubbert s theory

1.1 hubbert curve
1.2 use of multiple curves
1.3 reliability

1.3.1 crude oil
1.3.2 natural gas

hubbert s theory
hubbert curve

the standard hubbert curve. applications, x , y scales replaced time , production scales.



u.s. oil production , imports 1910 2012

in 1956, hubbert proposed fossil fuel production in given region on time follow bell-shaped curve without giving precise formula; later used hubbert curve, derivative of logistic curve, estimating future production using past observed discoveries.

hubbert assumed after fossil fuel reserves (oil reserves, coal reserves, , natural gas reserves) discovered, production @ first increases approximately exponentially, more extraction commences , more efficient facilities installed. @ point, peak output reached, , production begins declining until approximates exponential decline.

the hubbert curve satisfies these constraints. furthermore, symmetrical, peak of production reached when half of fossil fuel produced has been produced. has single peak.

given past oil discovery , production data, hubbert curve attempts approximate past discovery data may constructed , used provide estimates future production. in particular, date of peak oil production or total amount of oil produced can estimated way. cavallo defines hubbert curve used predict u.s. peak derivative of:

q
(
t
)
=



q


m
a
x




1
+
a

e

−
b
t







{\displaystyle q(t)={q_{\rm {max}} \over {1+ae^{-bt}}}}

where



q


{\displaystyle q}

max total resource available (ultimate recovery of crude oil),



q
(
t
)


{\displaystyle q(t)}

cumulative production, ,



a


{\displaystyle a}

,



b


{\displaystyle b}

constants. year of maximum annual production (peak) is:

t


m
a
x



=


1
b


ln
⁡

(

a

)

.


{\displaystyle t_{\rm {max}}={1 \over b}\ln \left({a}\right).}

so cumulative production



q
(
t
)


{\displaystyle q(t)}

reaches half of total available resource:

q
(
t
)
=

q

max



/

2


{\displaystyle q(t)=q_{\text{max}}/2}



use of multiple curves

the sum of multiple hubbert curves, technique not developed hubbert himself, may used in order model more complicated real life scenarios.

reliability
crude oil

hubbert s upper-bound prediction crude oil production (1956), , actual lower-48 states production through 2014

hubbert, in 1956 paper, presented 2 scenarios crude oil production:

most estimate: logistic curve logistic growth rate equal 6%, ultimate resource equal 150 giga-barrels (gb) , peak in 1965. size of ultimate resource taken synthesis of estimates well-known oil geologists , geological survey, hubbert judged case.
upper-bound estimate: logistic curve logistic growth rate equal 6% , ultimate resource equal 200 giga-barrels , peak in 1970.

hubbert s upper-bound estimate, regarded optimistic, accurately predicted oil production peak in 1970, although actual peak 17% higher hubbert s curve. production declined, hubbert had predicted, , stayed within 10 percent of hubbert s predicted value 1974 through 1994; since then, actual production has been greater hubbert curve. development of new technologies has provided access large quantities of unconventional resources, , boost of production has largely discounted hubbert s prediction.

hubbert s 1956 production curves depended on geological estimates of ultimate recoverable oil resources, dissatisfied uncertainty introduced, given various estimates ranging 110 billion 590 billion barrels us. starting in 1962 publication, made calculations, including of ultimate recovery, based on mathematical analysis of production rates, proved reserves, , new discoveries, independent of geological estimates of future discoveries. concluded ultimate recoverable oil resource of contiguous 48 states 170 billion barrels, production peak in 1966 or 1967. considered because model incorporated past technical advances, future advances occur @ same rate, , incorporated. hubbert continued defend calculation of 170 billion barrels in publications of 1965 , 1967, although 1967 had moved peak forward slightly, 1968 or 1969.

a post-hoc analysis of peaked oil wells, fields, regions , nations found hubbert s model useful (providing best fit data), though many areas studied had sharper peak predicted.

a 2007 study of oil depletion uk energy research centre pointed out there no theoretical , no robust practical reason assume oil production follow logistic curve. neither there reason assume peak occur when half ultimate recoverable resource has been produced; , in fact, empirical evidence appears contradict idea. analysis of 55 post-peak countries found average peak @ 25 percent of ultimate recovery.

natural gas

hubbert s 1962 prediction of lower 48-state gas production, versus actual production through 2012

hubbert predicted natural gas production follow logistic curve similar of oil. @ right gas production curve united states, published in 1962.