Homework 1

Problem 2.5 Reference Figure Data obtained from figure2.4 Data obtained from figure2.4 Year GDP Year EC 1980 22 1980 251 1981 56 1981 294 1982 90 1982 322 1983 90 1983 335 1984 157 1984 349 1985 157 1985 377 1986 258 1986 390 1987 326 1987 433 1988 360 1988 490 1989 393 1989 503 1990 461 1990 560 1991 461 1991 603 1992 528 1992 660 1993 629 1993 746 1994 629 1994 832 1995 697 1995 889 1996 730 1996 946 1997 730 1997 974 0 1000 2 0 2000 4000 6000 8000 10000 12000 f(x) = 0.00040824889 R² = 0.991819297903 GDP=f(Ele Electric GDP [U$$] GDP=f(Elect

1998 831 1998 1016 1999 865 1999 1073 2000 966 2000 1188 2001 1034 2001 1318 2002 1135 2002 1462 2003 1236 2003 1664 2004 1438 2004 1953 2005 1674 2005 2198 2006 2045 2006 2502 2007 2584 2007 2819 2008 3326 2008 3021 2010 6056 2010 3831 2012 9326 2012 4873 2013 10135 2013 5118 With an avarega rate of increase of 8% GDP (2023 =GDP (year 2013)*(1,08)^10 GDP (2023 21880.3 U$$ If GDP (2023 21880.34 U$$ I use the equation derived previously to estimate EC that year GDP per capita [U$$ PPP] = 0.0004 EC^2-0.1692EC+331.85 GDP Solver EC 21880.341 21880.34 0.00019 7554.248752 Billion kWh EC 2013 5118 Billion kWh EC 2023 7554.25 Billion kWh 0 1000 200 0 2000 4000 6000 8000 10000 12000 f(x) = 183.34837332 R² = 0.75587216691 Electricit GDP [U$$] 0 1000 2 0 2000 4000 6000 8000 10000 12000 f(x) = 1.783885 R² = 0.9004331 GDP=f(Elec Electric GDP [U$$]

The best fit for the data (R^2 closer to 1) is the polinom GDP per capita [U$$ PPP] = 0.0004 EC^2-0.1692EC+33 2000 3000 4000 5000 6000 91312 x² − 0.169164347598265 x + 331.849405083724 3595 ectricity consumption) city consumption [billion kWh] tricity consumption)

00 3000 4000 5000 6000 24279 exp( 0.000924239847607 x ) 14183 ty consumption [billion kWh] 2000 3000 4000 5000 6000 525896764 x − 907.765863850383 1332465 ctricity consumption) city consumption [billion kWh]

Problem 2.6 Reference table form the book Renewable in the world's 2014 PED [Quad] Coal in the world's 2014 PE Hydraulic 13 Coal and products Wood, biomass, and wastes 56 Total Other renewables 7.6 Total 76.6 Total Coal in 2014 [kWh] Total renwable in 2014 [kWh] 2.24438E+13 kWh generated from renwe Renewable sources in 2014

5800000 btu

Data from the problem: World's petroleum reserves Q inf 1.7E+12 bbl Global Petroleum consumption in 2015 PA (2015) 3.36E+10 bbl/year Consumption growth rate R 3.40E+08 bbl/yr^2 a) Estimate the lifetime of global petroleum reserves b) Estimate the lifetime of global petroleum reserves if the reserves increase to 3.4E+12 bbl a) I see two ways of thinking about this problem 1 The consumption growth rate is the same for every year (and the one given 3.4*10^8 bbl/ PA (time) PA (2015)+ R*(year-2015) PA (2016) PA (2015) + R*(2016-2015) PA (2017) PA (2015)+ R*(2017-2015) PA (2018) PA (2015)+ R*(2018-2015) … PA (T) PA (2015)+ R*(T) Being T the lifetime of petroleum (Last year petroleum is available - 2015)=T So, to sum up the total reserves we would multiply the consumtion of each year* 1 year Q inf= Multiplying by one doesn't make a difference, so I put together all the PA(2015)'s and the R Q inf= Using the property of geometric series (when each term is the same as the previous adding Q inf= This can easily be re-written as a quadratic equation Qinf= T^2*R/2+T*(R/2+ PA (2015) ) + PA (2015) PA (2015)* 1 year + ( PA (2015) + R*(2016-2015))* 1 year + (PA (2015)+ R*(20 (T+1)*PA (2015) + (1R + 2R + 3R + … + TR) (T+1)*PA (2015) + (T+1)*R*T/2

If I re-write the equation to leave T alone And finally Replacing for the values of the problem T 40 years If we replace Q inf for the bigger value T 69 years 𝑄 _ / 𝑖𝑛𝑓 〖 〗 𝑃𝐴 _((2015)) ∗𝑟+1 = (1+ )^( +1) 𝑟 𝑇 ( ln( _ / 𝑄 𝑖𝑛𝑓 〖 〗 𝑃𝐴 _((2015) ) +1 ∗𝑟 ))/(ln(1+𝑟)) = T+1 𝑇=( ln( _ / 𝑄 𝑖𝑛𝑓 〖 〗 𝑃𝐴 _((2015) ) +1 ∗𝑟 ))/(ln(1+𝑟))−1

/year^2). In this case, the petroleum consumtion would increase lineally R terms g a contant value) 017-2015))* 1 year + ( PA (2015)+ R*(2018-2015))* 1year + … + ( PA (2015)+ R*(T))* 1 year

ally

Data from the problem: World's natural gas reserves Q inf 5.605E+15 scf Global natural gas consumption in 2015 PA (2015) 1.25E+14 scf/year Consumption growth rate R 1.93E+12 scf/yr^2 a) Estimate the lifetime of global natural gas reserves b) Estimate the lifetime of global natural gas reserves if the reserves increase to 1.121E+16 scf a) I see two ways of thinking about this problem 1 The consumption growth rate is the same for every year (and the one given 1.93 sc PA (time) PA (2015)+ R*(year-2015) PA (2016) PA (2015) + R*(2016-2015) PA (2017) PA (2015)+ R*(2017-2015) PA (2018) PA (2015)+ R*(2018-2015) … PA (T) PA (2015)+ R*(T) Being T the lifetime of natural ga (Last year natural gas is available So, to sum up the total reserves we would multiply the consumtion of each year* 1 y Q inf= Multiplying by one doesn't make a difference, so I put together all the PA(2015)'s and Q inf= Using the property of geometric series (when each term is the same as the previous Q inf= This can easily be re-written as a quadratic equation Qinf= T^2*R/2+T*(R/2+ PA (2015) ) + PA (2015) PA (2015)* 1 year + ( PA (2015) + R*(2016-2015))* 1 year + (PA (201 (T+1)*PA (2015) + (1R + 2R + 3R + … + TR) (T+1)*PA (2015) + (T+1)*R*T/2

If I re-write the equation to leave T alone And finally Replacing for the values of the problem T 33 years If we replace Q inf for the bigger value T 56 years 𝑄 _ / 𝑖𝑛𝑓 〖 〗 𝑃𝐴 _((2015)) ∗𝑟+1 = (1+ )^( +1) 𝑟 𝑇 ( ln( _ / 𝑄 𝑖𝑛𝑓 〖 〗 𝑃𝐴 _((2015) ) +1 ∗𝑟 ))/(ln(1+𝑟)) = T+1 𝑇=( ln( _ / 𝑄 𝑖𝑛𝑓 〖 〗 𝑃𝐴 _((2015) ) +1 ∗𝑟 ))/(ln(1+𝑟))−1

cf/year^2). In this case, the petroleum consumtion would increase lineally as e - 2015)=T year d the R terms adding a contant value) 15)+ R*(2017-2015))* 1 year + ( PA (2015)+ R*(2018-2015))* 1year + … + ( PA (2015)+ R*(T))* 1 year