Energy Resource Quantification

8/13/2019 Energy Resource Quantification

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1Quitoras | Assignment 02 | Energy Resource Quantification

1. Use a Hubbert type analysis to plot annual Mexican Oil production from 195 to!" at 1 year inter#als. $ssume Q1 % 1&& x 19 barrels.

To be able to get the annual Mexican Oil Production, differentiate Qp with respect to time

!asic Principle used in differentiation"

Thus,

!# substituting the $alue of Q% & %'' x %0( barrels, data from %()0 to 20*0 will be the

following"

'ear $nnual Mexican Oil

(roduction )billion barrels*

%()0 00+)'%%(-0 00(-'-(

%(0 02)'-(%('0 0-0-)

%((0 %-%%+

2000 +2*02

20%0 *-22

2020 *%0(

20+0 2+'**

20*0 %0-(%

)}5.1940(100.0{

1

13501 −−

+

=t

p

e

QQ

dt

eQ

dt

dQ t p

1)}5.1940(100.0{1 ]13501[ −−−+

=

dxdunuu

dxd 1nn −

=

dxduee

dxd uu

=

(-0.1)]1350[]13501[)1( )}5.1940(100.0{2)}5.1940(100.0{

1

−−−−−+−= t t peeQ

dt

dQ

2)}5.1940(100.0{

)}5.1940(100.0{1

]13501[

135 t

t p

e

eQ

dt

dQ




)}1920(100.0{

1

13501 −−

+

=t

d

e

QQ

.rom the gi$en figure, it can be seen, that production of oil in Mexico, decreases annuall#starting #ear 20%0 /ame thing happens in other countries due to depletion of fossil fuelse$ertheless, the figure still pro1ects an increasing rate of production from %()0 to 20%0

!. (lot cumulati#e Mexican oil disco#eries at 1 year inter#als from 195 to !"

using a Hubbert type analysis based on+

,ote t-at t-is specifies a !.5 year lag beteen pea/ rate of disco#eries and pea/rate of production compared to a 1.5 year lag t-at Hubert uses on t-e U0 data.

!# substituting the $alue of Q% same with item number %3 and the corresponding #ears,the data will be the following"

'ear

umulati#eMexican Oil2isco#eries

)billion barrel*

umulati#eMexican Oil(roduction

)billion barrel*

%()0 2)-% 0+)(*

%(-0 +0' 0(+

%(0 %'-20' 2-2+-

%('0 *+2)) -(-*-

%((0 '*2-)- %('-2000 %2(+('- *%-%2*

20%0 %-%%)%- '%(*+

2020 %%*2( %2+-+2

20+0 %'+')*- %)(('02

20*0 %'-*)+* %--2




The figure presents graphicall# the 20) #ear lag between oil disco$er# and oil production 3. 4-e euation used in problems 1 and ! is an approximation based on Mexicanproduction data. ould parameters a and b be estimated it- a linear regression

)ordinary least suares* if sufficient number of data points are a#ailable6

7f so8 -o ould you linearie t-e euation6 0-o and pro#ide statistical euations.0ubstitute t-e data abo#e.

.irst step is to rearrange the e4uation in order to lineari5e it

.rom that, ta6e the natural logarithm on both sides

!asic Principles in law of logarithm, ln e & % and ln a 7 ln b & ln a8b

Thus,

Therefore, the linear function

.rom the linear e4uation form # & mx 9 b3, the corresponding $alue will now be"

−=

p

p

Q

QQ y

1ln bm −= 5.1940−= t x ab ln=

/ol$ing for the $alues of x and #,

)}5.1940({

1

1 −−

+

=t b

p

ae

QQ

1)}5.1940({ ]1[ QaeQ t b

p =+ −−

1)}5.1940({

] QaeQQ t b p p =+

−−

pt b

p QQaeQ −=−−

1)}5.1940({

[ ] pt b

p QQaeQ −=−−1

)}5.1940({ lnln

[ ] [ ] pt b

p QQeaQ −=++ −−

1)}5.1940({

lnlnlnln

[ ] [ ] p p QQQt ba lnln)5.1940(ln 1 −−=−−+

at bQ

QQ

p

pln)5.1940(ln

1




ote " x#, x2 and #2 will be used in determining the $alue of linear correlation coefficient, r

.rom the graph and the linear regression line e4uation # & :0%x 9 20'3, we can now

conclude the $alue of parameters a and b

;n linear regression # & a 9 bx3, # is the dependent $ariable and x is the explanator#

$ariable And as ob$ious, b % .1 and a % 135 from b & ln a wherein to get the $alue of a, it

is 1ust e raised to 20'3

Mat-ematical explanation of t-e grap- and t-e euation

'ear umulati#e Mexican

Oil (roduction)billion barrel*

x y xy :! '!

%()0 0+)(* () -2)' )(**(% (02) +(%-00-%

%(-0 0(+ %() )2)( %02)2(0) +'02) 2-*))%2

%(0 2-2+- 2() *2)' %2)-0)% '02) %'%2''-%

%('0 -(-*- +() +2)( %2'-'0) %)-02) %0-%+(%2

%((0 %('- *() 22)( %%%--0) 2*)02) )0('%%2*

2000 *%-%2* )() %2)( *'*)0) +)*02) %)'2+%2*

20%0 '%(*+ -() 02)( %(2*0) *'+02) 00--)%2*

2020 %2+-+2 () :0*2% :)'((-() -+202) 0))0%2*

20+0 %)(('02 '() :%*2% :%))(%() '0%02) +0+*(%2*

20*0 %--2 (() :2*2% :22'+'() ((002) )%(%%2*

0ummations 5"5 1;.5;&& 133.51< 3;95!.5 113."!




Note : This mathematical process can also be done directly in Microsoft Excel.

To be able to get the e4uation, get two points from the line () , -2)3 and %() , )2)3

<et the slope b# m & #2 7 #%3 8 x2 7 x%3

/lope will be e4ual to -0.1

To get the $alue of b, substitute it to # & mx 9 b considering point () , -2)3 = b will now bee4ual to 7.2 Thus, the e4uation of the line is y % =.1x > ;.!.

On the other hand, the 4uantit# >, called the linear correlation coefficient , measures thestrength and the direction of a linear relationship between two $ariables ?%@

R % n )?xy* @ )?x* )?y* A BC )n?x! @ )?x*! )n?y! @ )?y*!D

where"

n & is the number of pairs of data

The $alue of r is such that :% r 9% The 9 and 7 signs are used for positi$e linearcorrelations and negati$e linear correlations, respecti$el#

A perfect correlation of B % occurs onl# when the data points all lie exactl# on a straight line;f r & 9%, the slope of this line is positi$e ;f r & :%, the slope of the line is negati$e

A correlation greater than 0' is generall# described as strong, whereas a correlation lessthan 0) is generall# described as wea6 These $alues can $ar# based upon the Ct#peC ofdata being examined A stud# utili5ing scientific data ma# re4uire a stronger correlation thana stud# using social science data

On the other hand, the coefficient of determination, >2, gi$es the proportion of the $ariancefluctuation3 of one $ariable that is predictable from the other $ariable ;t is a measure thatallows us to determine how certain one can be in ma6ing predictions from a certainmodel8graph .or example, if > & 0(22, then >2& 0')0, which means that ')D of the total$ariation in # can be explained b# the linear relationship between x and # as described b#the regression e4uation3 The other %)D of the total $ariation in # remains unexplained ?%@Thus, based upon the graph, the data computed has a strong correlation because > 2 & %Meaning, %00D of the total $ariation in # can be explained b# the linear relationship betweenx and # as described b# the e4uation3

". ased on t-e Mexican data8 your results from 1 and !8 and any ot-er informationyou care to add8 -o applicable do you feel t-e Hubbert tec-niue is in t-is setting6F-at insig-t8 if any8 does it pro#ide you6 $s of 0eptember 19&8 Mexico -as a(otential Oil Reser#es of 1&& billion barrels and (ro#en Oil Reser#es of < billionbarrels.

'ear $ctual (roductionHubertGs Estimates

)Q1 % 1&& billion

barrels*

HubertGs Estimates)Q1 % < billion

barrels*%(*0 +(0E90 %+2E90 *20E90-




%()0 -00E90 +)'E90 %%*E90

%(-0 %0%E90' (-'E90 +0(E90

%(0 %'E90' 2)'E90' '2)E90

%() 2(*E90' *%'E90' %++E90'

%('0 E90' -0E90' 2%*E90'

%('% (+2E90' +)E90' 2+*E90'

%('2 %%0E90( '0)E90' 2)E90'

%('+ %0'E90( ''2E90' 2'%E90'

%('* %%%E90( (-)E90' +0E90'

%(') %%%E90( %0)E90( ++-E90'

%('- %02E90( %%)E90( +-E90'

%(' %0-E90( %2)E90( *00E90'

%('' %0)E90( %+E90( *+)E90'

%('( %0-E90( %*'E90( *+E90'

%((0 %0(E90( %-%E90( )%*E90'

%((% %%)E90( %*E90( ))E90'

%((2 %%*E90( %''E90( -02E90'

%((+ %%)E90( 20+E90( -)0E90'

%((* %%)E90( 2%(E90( 00E90'

%(() %%2E90( 2+)E90( )2E90'

%((- %20E90( 2)2E90( '0-E90'

%(( %2)E90( 20E90( '-2E90'

%((' %2'E90( 2'E90( (%'E90'

%((( %22E90( +0)E90( (-E90'

2000 %2-E90( +2*E90( %0+E90(

200% %+0E90( +*%E90( %0(E90(

2002 %+%E90( +)(E90( %%*E90(

200+ %+(E90( +-E90( %20E90(

200* %*%E90( +(+E90( %2)E90(

200) %+'E90( *0'E90( %+0E90(

200- %+)E90( *22E90( %+*E90(

200 %2'E90( *+)E90( %+'E90(

200' %%-E90( **-E90( %*2E90(

200( %%0E90( *))E90( %*)E90(

0ource for $ctual (roduction+ U0 Energy 7nformation $dministration




The figure pro$es that there is no significant difference when it comes to actual productionas compared with the estimates done b# Fubert Fowe$er, a change in actual productionbecame e$ident in the #ear %(0 onwards Fere, a sudden drop was obser$ed Thus, theFubbert model is accurate enough to estimate the oil production but it does not considersfactors li6e alternati$e energ# source being utili5ed in the succeeding #ears The decline inthe actual oil production ma# be due to the fact that that renewable sources of energ# hasalread# been in the mar6et

On the other hand, when it comes to oil reser$es

'ear Oil Reser#es HubertGs Estimates%(*0G '00E90' %02E90(

%()0G %00E90( 2)E90(

%(-0G 2+0E90( +0E90(

%(0 2(0E90( %'-E9%0

%() +*0E90( 2''E9%0

%('0 *)0E9%0 *++E9%0

%(') *'-E9%0 -20E9%0

%((0 )-*E9%0 '*+E9%0

%(() )0'E9%0 %0E9%%

2000 2'*E9%0 %2(E9%%200) %*-E9%0 %*E9%%

200( %0)E9%0 %)'E9%%

GHata for these #ears from two #ears earlier, ie, %(*0 data from %(+'0ource for Oil Reser#es+ U0 Energy 7nformation $dministration




Iust li6e the case of oil production, FubertJs model has a significant difference starting%('0Js

5. an you relate t-e insig-ts of t-is exercise to t-e to scenarios+ o#ernmentinter#ention and industrialiation or economic grot-8 produced by t-e Mexicano#ernment in 19&6

• o#ernment 7nter#ention

Fere is what happening to Mexico considering a good status of their oil production and

reser$es during %('0Js ?2@

• Extensi$e oil disco$eries in the %(0s increased MexicoKs domestic output and exportre$enues

• !# %() MexicoKs oil output once again exceeded internal demand, pro$iding amargin for export

• President Lpe5 Portillo announced in %(- that MexicoKs pro$en h#drocarbonreser$es had risen to %% billion barrels The# rose further to 2) billion barrels b#%('+ Lpe5 Portillo decided to increase domestic production and use the $alue ofMexicoKs petroleum reser$es as collateral for massi$e international loans, most ofwhich went to Pemex

• !etween %( and %('0, the oil compan# recei$ed N/%2- billion in internationalcredit, representing + percent of MexicoKs total foreign debt ;t used the mone# toconstruct and operate offshore drilling platforms, build onshore processing facilities,enlarge its refineries, engage in further exploration, pro$e fresh reser$es, andpurchase capital goods and technical expertise from abroad

Thus, from there, it can be seen that the go$ernment inter$ened and ma6e use of the

situation as an opportunit# for nationali5ing the petroleum industr#, gi$ing the Mexican

go$ernment a monopol# in the exploration, production, refining, and distribution of oil and

natural gas, and in the manufacture and sale of basic petrochemicals More so, the# ma6e

use their oil reser$es as exchange for massi$e international loans, which pa$ed the wa#towards reconstruction of Pemex oil industr#3






200( '(E90- %0'E90'

0ource for $nnual (roduction + U0 Energy 7nformation $dministration

Iust li6e Mexico, the Philippines do not ha$e a constant increase production of oile$ertheless, the figure pro1ects a significant increase of production from #ear %((onwards

Iinear Regression for t-e umulati#e (roduction

The linear form for the cumulati$e production of the Philippines is gi$en b# the e4uation"

where"

Q% & 0%+') billion barrel Potential Oil >eser$es of the Philippines as of 20%+according to N/ Energ# ;nformation Administration3

.rom the linear e4uation form # & mx 9 b3, the corresponding $alue will now be"

−=

p

p

Q

QQ y

1ln bm −= x & t : %(0 ab ln=

'ear umulati#e(roduction

x y xy :! '!

%('0 )'*E90- %0 +%2E900 +%2E90% %00 ()+*()%('% -(*E90- %% 2(*E900 +2*E90% %2% '-)-+%+

%('2 %02E90 %2 2)+E900 +0*E90% %** -*%0(*%

%('+ %)+E90 %+ 20(E900 2%E90% %-( *+)%2%+%('* 20%E90 %* %E900 2*'E90% %(- +%**--




%(') 2+E90 %) %)'E900 2+E90% 22) 2*'(%'(

%('- 2--E90 %- %**E900 2+0E90% 2)- 20-*0(%

%(' 2'-E90 % %+)E900 22(E90% 2'( %'%2%)'

%('' +0'E90 %' %2)E900 22)E90% +2* %)-0(%

%('( +2)E90 %( %%'E900 22)E90% +-% %+()(*

%((0 ++(E90 20 %%+E900 22)E90% *00 %2-()%%((% +*'E90 2% %0(E900 22(E90% **% %%(22%2

%((2 +)E90 22 ((%E:0% 2%'E90% *'* 0('%-**

%((+ *0+E90 2+ '(%E:0% 20)E90% )2( 0(+2--

%((* *2-E90 2* '%%E:0% %()E90% )- 0-)'*)*

%(() *+E90 2) *E:0% %(*E90% -2) 0)((2'

%((- *+2E90 2- (%E:0% 20-E90% -- 0-2)('%

%(( *2*E90 2 '%'E:0% 22%E90% 2( 0--()%'

%((' *%'E90 2' '+(E:0% 2+)E90% '* 00+**-

%((( *%)E90 2( '*(E:0% 2*-E90% '*% 020'+%

2000 *%*E90 +0 ')2E:0% 2)-E90% (00 02--'(200% **2E90 +% )'E:0% 2+)E90% (-% 0)*%()

2002 *'0E90 +2 -+*E:0% 20+E90% %02* 0*02%*)

200+ )+2E90 ++ *2E:0% %)-E90% %0'( 0222'(*

200* -2%E90 +* 20E:0% 0)E900 %%)- 00*2(*

200) %*E90 +) :-2%E:02 :2%E900 %22) 000+')'

200- '0'E90 +- :++E:0% :%2%E90% %2(- 0%%++'

200 '((E90 + :-%)E:0% :22'E90% %+-( 0+'+%

200' ('(E90 +' :(%)E:0% :+*'E90% %*** 0'++'

200( %0'E90' +( :%2-E900 :*(+E90% %)2% %)('%(

0ummation ;35 !.&E>1 "."9E>! !!55 5".;<!33

.rom the graph and the linear regression line e4uation # & :0%0)2x 9 +)%0%3, we can now

conclude the $alue of parameters a and b




;n linear regression # & a 9 bx3, # is the dependent $ariable and x is the explanator#

$ariable And as ob$ious, b % .15! and a % 33."51< from b & ln a wherein to get the $alue

of a, it is 1ust e raised to +)%0%3

/ame mathematical processes will be done item +3 to get the linear e4uation and > 2 /till, it

can be directl# computed using Microsoft Excel

!ased upon the graph, the data computed has a strong correlation because >2 & 0'-%Meaning, roughl# 'D of the total $ariation in # can be explained b# the linear relationshipbetween x and # as described b# the e4uation3

;. (resent a modified model for problem < t-at integrates tec-nology8 energy pricingand economic grot-8 and institutional inter#ention.

4ec-nology

Technolog# pla#s a $ital role in e$er# countr# /ame thing goes with oil production As

technolog# ad$ances among oil industr#, there will be an abrupt increase on the productionof oil onse4uentl#, there will also be a faster rate of depletion when it comes to oursources for crude oil e$ertheless, it can still translate to a positi$e outcome as there will bea greater chance for disco$eries when it comes to the PhilippineJs pro$en oil reser$es

More so, ad$ancement of technolog# also pa$ed the wa# towards alternati$e sources ofenerg# so as to lessen our great dependence on fossil fuels particularl# crude oil !# doingso, renewable sources will be exploited that can help in meeting the increasing demand ofenerg# in the countr#

Energy (ricing and Economic rot-



Energy Resource Quantification

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