8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 1/33
INTRODUCTION
History Of Petroleum Energy
Petroleum ( petroleum,from Greek : petra (rock) + Latin : oleum or crude oil is a
naturally occurring,flammable liquid consisting of a complex mixture of hydrocarbons of various
molecular weights and another liquid organic compounds ,that are fundin geologic formation
beneath the Earth’s surface.
The team petroleum is found (in the spelling is “petraoleum”) in tenth-century Old
English sources.It was used in the treatise De Natura Fossilium, published in 1548 by the
German mineralogist Geog Baoer, also known as Georgius Agricola. In the 19th
Century , the
term petroleum was frequently used to refer to mineral oils produced by distillation from mined
organic solids such as canned coal (and later oil shale), and refined oils produced from them; in
the United Kingdom, storage (and later transport) of these oils were regulated by a series of
Petroleum Acts , from the Petroleum Acts 1862 c, 66 onward.
Petroleum,in one form or another,has been used since ancient times,and is nowimportant across society, including in economy, politics and technology.The rise in importance
was mostly due to the invention of the internal combustion engine , the rise in commercial
aviation and the increasing
More than 4000 years ago,according to Herodotus and Diodorus Siculion,asphait
as used in the construction of walls and towers of Babylon: there were oil pits near Ardericca
(near Babylon), and a pitch spring on Zacynthus .Great quantites of it were found on the river
issus,one of the tributaries of the Euphrates.Ancient Persian tablets indicate the medicinal and
lightning uses of petroleum in the upper levels of their society .By 347 CE,oil was produced
from bamboo-drilled wells in China.
In the 1850s, the process kerosene from petroleum was invented by Ignancy
Lukasiewicz,providing a cheaper alternative to whale oil. The demand for the petroleum as a fuel
for lighting in North America and around the world quickly grew. The world’s first commercial
oil well was drilled in Poland in 1853. Oil exploration developed in many parts of the world with
the Russian Empire,particulary the Branobel company in Azerbajin (Asia’s first modern
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 2/33
borehole oil production began in 1848 at the Bibi-Heybat field near Baku), taking the lead in
production by the end of the 19th
century.
Access to oil was and still is a major factor in several military conflicts of the
twentieth century including World War II, during which oil facilities were a major strategics
asset and were extensively bombed. Operation Barbossa included the goal to capture the Bakuoilfields as it would provide much needed oil-supplies for the German military which was
suffering from blockades. Oil exploration in North America during the early 20th century later
led to the U.S becoming the leading producer by the mid 1900s. As petroleum production in the
U.S peaked during the 1960’s , however , the United States was surpassed by Saudi Arabia and
Russia.
Today,90% of vehicular fuel needs are met by oil. Petroleum also makes up 40%
of total energy consumption in the United States, but is responsible for only 2% of electricity
generation.Petroleum’s worth as a portable,dense energy source powering the vast majority of
vehicles and as the base of many industrial chemicals makes it one of the world’s most importantcommodities.
The top three oil producing countries are Saudi Arabia,Russia and United States.
About 80% of the world’s readily accessible reserves are located in the Middle Eas t, with 62.5%
coming from the Arab 5:Saudi Arabia,UAE,Iraq,Qatar and Kuwait. A large portion of the
world’s total oil exists as unconventional sources, such as bitumen in Canada and Vanezuela and
oil shale.White significant volumes of oil are extracted from oil sands, particulary in Canada,
logistical and technical hurdles remain,as oil extraction requires large amounts of heat and water,
making its net energy content quite low relatives to conventional crude oil.Thus, Canada’s oil
sands are not expected to provides more than a few million barrels per day in the foreseeablefuture.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 3/33
Alternative energy source
Energy development is the effort to provide sufficient primary energy sources and secondary
forms for supply,cost,impact on air pollution and water pollution,miligation of climatechange
with renewable energy.
Technology advanced societies have become increasingly dependent on external energy sources
for transportation,the production of many manufactured goods, and the delivery of energy
services. This energy allows people who can afford the cost to live under otherwise unfavorable
climatic conditions through the use of heating, ventilation,and/or air conditioning.Level of use
of external energy sources differs across societies,as do the climates,convienience,levels of
traffic congestion, pollution and availability energy sources.
A wind farm is a group of wind turbines in the same location used for production of electric
power. A large wind farm may consist of several hundred individual wind turbines , and cover an
extended area of hundreds of square miles, but the land between the turbines may be used for
agricultural or other purposes. A wind farm may also located offshore to take advantage of
strongs winds blowing over the surface of an ocean or lake.
As a general rule,economic wind generators require windspeed of 10 mph (16 km/h) or
greater.An ideal location would have a near constant flow of non-turbulent wind throughout the
year, with a minimum likehood of sudden powerful burst of wind.An important factor of turbine
sitting is also access to local demand or transmission capacity.
Floating wind farms are similar to a wind farm,but the difference is that they float in the middleof the ocean.Offshore wind farms can be placed in water up to 40 metres (130 ft) deep,whereas
floating wind turbines can float in water up 700 meters (2,300 ft) deep.The advantage of having
a floating wind farm is to be able to hardness the winds from the open ocean. Without any
obstructions such as hills,trees and buildings, winds from the open ocean can reach up to speeds
twice as fast as coastal ureas.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 4/33
AIM
The aims of carrying out this project work are:
i. To apply and adapt a variety of problem-solving strategies to solve problems;
ii. To improve thinking skills;
iii. To promote effective mathematical communication;
iv. To develop mathematical knowledge through problem solving in a way that increases
students interest and confidence;
v. To use the language of mathematical to express mathematical ideas precisely
vi. To provide learning environment that stimulates and enhances effective learning;
vii. To develop positive attitude towards mathematics
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 5/33
By using Phythagoras Theorem,we can calculate the length of any sides of a triangle.The theory can be
concluded that any right triangle, the area of the square whose side is the hypothanus (the side opposite
the right angle) is equal to the sum of the areas of the areas of the squres whose sides are the two legs
(the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a,b and c,often called the
Phytagorean equation:
a²+b²=c²
where c represents the length of the length of the hypotenuse, and a and b represent the lengths of the
other two sides.
Therefore,the calculation of the distance is as follows:
ROUTE 1
Section 1 Section 2 Section 3
6² + 8² = c² 10² + 2² = c² 6² + 9² = c²
36 + 64 = c² 100 + 4 = c² 36 + 81 = c²
100 = c² 104 = c² 117 = c²
10 = c 10.198 = c 10.817 = c
Total distance = 10 + 10.198 + 10.817
= 31.015 km
ROUTE 2
Section 1 Section 2 Section 3
26² + 2² = c² 11² + 15² = c² 6² + 9² = c²
676 + 4 = c² 121 + 225 = c² 36 + 81 = c²680 = c² 346 = c² 117 = c²
26.076 = c 18.601 = c 10.817 = c
Total distance = 26.076 + 18.601 + 10.817
= 55.494 km
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 6/33
ROUTE 3
Section 1 Section 2 Section 3
20² + 2² = c² 8² + 2² = c² 6²+9² = c²
400 + 4 = c² 64 + 4 = c² 36 + 81 = c²
404 = c² 68 = c² 117 = c²
20.100 = c 8.246 = c 10.817 = c
Total distance = 20.100 + 8.246 + 10.817
= 39.181 km
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 7/33
BEARINGS
To calculate bearings,we must first find the length of the horizontal line and vertical
line.Then,we could use tangent of the lengths to get the angle.Lastly,we must calculate the angle
from the True North rotating clockwise to the desired location.
N 360° / 000°
W 270 ° E 090°
S 180 °
Route 1
Section 1 Section 2 Section 3
Horizontal length 8 km 2 km 9 km
Vertical length 6 km 10 km 6 km
Calculation of angle tan = 8/6
= 8/6
= 53.13
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 8/33
Route 2
Section 1 Section 2 Section 3
Horizontal length 26 km 11 km 9 km
Vertical length 2 km 15 km 6 km
Calculation of length = 15
Route 3
Section 1 Section 2 Section 3
Horizontal length 2 km 8 km 9 km
Vertical length 20 km 2 km 6 km
Calculation of angle ⁄ ⁄
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 9/33
Coordinates
After calculating the distance and the bearings of the course , we need to find out the
coordinates of which the boat needed to turn.
Route 1
From the coordinates ( 0 , 0 ) , the boat is needed to turn 53.13 from North.Then, at the
coordinates ( 8 , 6 ) , the boat is turned bearing 11.31 . Lastly, just before reaching the offshoreoil rig,the boat is turned bearing 56.31 at coordinate ( 15 , 18 )
Route 2
From the coordinates ( 0 , 0 ) , the boat is needed to turn 86.50 from North.Then,at
coordinates ( 26 , 2 ) , the boat is turned bearing 323.75 . Lastly,just before reaching the
offshore oil rig,the boat turned bearing 56.31 at coordinate ( 15 , 18 )
Route 3
From the coordinates ( 0 , 0 ) , the boat is needed to turn 5.71 from North. Then, at
coordinates ( 2 , 20 ) , the boat is turned bearing 104.04 . Lastly,just before reaching the
offshore oil rig the boat turned bearing 56.31 at coordinates ( 15 , 18 )
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 10/33
Possible dangers
There are many possible dangers that lays in the journey. Besides that,there are also severalpreserved and conserved areas that have high risk of being intruded.
Route 1
Coral reef
Sunken ship
Giant octopus
Route 2
Shark infested water
Thunderstorm
Sunken ship
Giant octopus
Route 3
Coral reef
Sunken ship
Giant octopus
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 11/33
Time estimation
To calculate the time estimation of arrival of the boat,we must use the formula :
Distance travelled Speed = Time of arrival
Route 1
31.015 km km/hr = 0.87 hours
= 53.17 minutes
Route 2
55.494 km km/hr = 1.59 hours
= 95.13 minutes
Route 3
39.181 km 35 km/hr = 1.12 km
= 67.17 minutes
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 12/33
Conclusion
Types of routes Route 1 Route 2 Route 3
Distance 31.015 km 55.494 km 39.181 km
Bearings 53.13
11.31
56.31
85.60
323.75
56.31
5.71
104.04
56.31
Coordinates ( 0 , 0 )
( 8 , 6 ) ( 15 , 18 )
( 0 , 0 )
( 26 , 2 ) ( 15 , 18 )
( 0 , 0 )
( 2 , 20 ) ( 15 , 18)
Possible danger Coral reef
Sunken ship
Giant octopus
Shark infestedwater
Thunderstorm
Sunken ship
Giant octopus
Coral reef
Sunkentreasure
Giant octopus
Time estimation 0.87 hours
53.17 minutes
1.59 hours
95.13 minutes
1.12 hours
67.17 minutes
Based on the table above , we can conclude that route 1 is the best route to travel to the offshore
oil rig . Not only has the shortest distance overall,it also has the lowest bearing overall meaning
that the boat doesn’t need to turn so hard . Furthermore , it also has one danger which is the giant
octopus and two preservation and conservation site which is the coral reef and the sunken ship.
Lastly,it also needed the lowest time needed to arrive to the offshore oil rig which is 0.87
hours,equivalent to 53.17 minutes.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 13/33
Part 2
Before we can find the time arrival of the boat,we must first calculate the resistance of the seacurrent or drag to effect on the speed of the boat .
Desired Destination
Actual Movement
Sea current
Boat movement
If the boat was to move directly to the desired destination, the coming sea current will push the
boat away from the move a bit further away to another location.This can be shown in Diagram 1(above)
Desired Destination
Actual Movement
Sea current
Boat movement
Now,if the boat was to move towards the incoming sea current will push the boat to its
destination as shown in Diagram 2 (above)
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 14/33
Section 1 Vc 15
Vr 10
6 Vb
Vy
Cos = Vx / Vr
Vx = Vr cos ……………………….. 1
Sin = Vy / Vr
Vy = Vr sin ………………………… 2
Vr = =
= ()
Vb = () Vc = (
)
Vr = Vb + Vc
= () + ( )
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 15/33
Vr 8/10 = 36 cos ………………………. 1
Vr 6/10 = 36 sin
= 60 sin …………………………….. 2
Combine those two equation and we can find the ( use the Formula = 1 )
+
= 1 -
8/10 ( 60 ) = 36 cos
48 sin
2304 ( 1 - ) = ( 36
2304 – 2304 ̃ + 225
3600
Because the value
= 22.4 of is 90
Vr = 60 sin 22.4
= 22.855 km/h
Time taken = 10/22.855
= 0.4375
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 16/33
Section 2 Vc 15
V104
10 Vb
Vr Vy
Vx
Vx = Vr ………………………………………….. 1
= Vy / Vr
Vy = Vr ………………………………………….. 2
Vr = =
= ( )
Vb = ( ) Vc = (
)
Vr = Vb + Vc
= (
) + ( )
Vr 2 / = 36 - 15 …………………………………… 1
Vr 10 / = 36
Vr = / 10 ……………………………….. 2
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 17/33
Combine those two equation and we find the
(use the Formula
9 / / 6 = 36
54 = 36
54 ( 1 - = (36
54 – 54 1296 – 1080
1350
Vr = / 10
= 29.915 km/h
Time taken = /
= 0.341 hours
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 18/33
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 19/33
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 20/33
Journey start at 10.00 a.m
Distance from starting point ( 0 , 0 ) to Wind Farm ( 11 , 16 ) is 20.198 km
Distance from Wind Farm ( 11 , 16 ) to Oil Rig ( 25 , 23 ) is 10.817 km
The boat will arrive at the Oil Rig
= 10.00 a.m + t1 + t2 + 2 hours ( maintaining wind farm ) + t3
= 10.00 a.m + 0.4375 hours + 0.3410 hours + 2 hours + 0.48 hours
= 1.15.31 p.m
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 21/33
Part 3
a) To find the machine constant , c , we must first utilize the formula given which is :
P = cAu²
the value of the other unknown has been given :
Wind speed,u = 13 m/s
Surface area of the turbine = 10 m²
Power output = 10 kW
P = cAu
10 000 = c(10) (13) (13)
C = 10 000 1690
C = 5.917
b) The determine the time taken to produce 50 MJ of energy,we must use the other formula
given,which is :
E = ∫ dt
E = ∫ dt
E =
50 000 000 = (5.917) (10) (13) (13) t
t = 50 000 000 10 000
= 5000 seconds
= 250/3 minutes
= 25/18 hours
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 22/33
b)ii) 50 000 000 = ∫ dt
50 000 000 = ∫
= 4/169 (t³) / 3
= 4/507 t
t = 1850.6 seconds
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 23/33
Part 4
a) To find the average rate of oil production in hours that can last 10 years,we must first find
the number of hours in 10 years.
Number of hours =Hours in a day × Days in a year × 10
= 24 × 365 ×10
= 87 600 hours
Then we should divide the number of barrels by the total hours to find the average rate of oilproduction.
Average rate = Number of barrels ÷ Total hours
= 100 000 000 ÷ 87600
= 1142 barrels per hour
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 24/33
b)
1 metre
0.5 metre
To find the rate of increase of oil , we must utlize the formula :
dh / dt = dh / dv × dv / dt
From the question ,it given that :
Time = 5 minutes
Diameter = 0.5 metre
Height = 1 metre
dh / dv = 100 / ( 25 ) ( 25 ) ( 100 )
= 100 / 62500
= 0.0016 / ………………………………….1
dv / dt = ( 25 ) ( 25 ) ( 100 ) / 5
= 125 00
…………………………………2
dh / dt = dh / dv × dv / dt
= 0.0016/ × 12500
= 20 cm / minutes
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 25/33
PART 5
a ) Oil Productions and Consumption
As we can see from the charts above , Russian Federation is the second largest producer of oil
seconded only to the major producer og oil which is Saudi Arabia with a production of 10 . 5
million barrels a day.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 26/33
b ) Oil Imports and Exports
In the previous charts , Saudi Arabia is the largest producer of oil , thus Saudi Arabia is the
largest exporter og oil globally which is 9.1 billion barrels per year , about 24% of global export.
The second largest exporter is Rusia which is also second largest oil producer of the world .
Russsia exported 21 % of world oil export , 7.9 billion barrels per year
Eventhough our country , Malaysia is a producer of oil , the export of oil is insignificant in
global scale that we did not enter the pie chart for the major oil exporter.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 27/33
Crude Oil Imports by Country of Origin, 2005
Based from the pie chart above , we can conclude that the country that import the most oil is
Canada which is 16.3 % of global oil import.Second , Mexico imports about 15.4 % of total oil
import in the world .
In third place is Saudi Arabia which imports 14.3 % of global oil imports eventhough it is the
largest producer of oil . The other countries imports a total of 16.5 % of world oil imports.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 28/33
c ) Oil Reserves
In the Asia pacific , China holds the most oil reserves abaut 2 .0 billion barrels . Seconds, India
which have about 6 billion barrels in its reserves. Our country , Malaysia shared third place with
Indonesia for the most oil reserve. Both of the countries have 4 billion barrels each. Lastly,
Australia is the last of the top 5 oil reserves holders in Asia pacific.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 29/33
FURTHER EXPLORATION
Careers in Petroleum Industry that requires a good foundation in Additional Math :
- Petroleum Engineer
Petroleum Engineers help locate natural reservoirs of petroleum deposits. They work with
teams of specialist to develop more effective, cost-efficient methods of petroleum
recovery. Petroleum Engineers require at least a bachelor’s degree in Petroleum
Engineering or related field.
Petroleum Engineers apply principles from chemistry, mathematics, engineering and
geology to develop new processes and methods of petroleum extraction.
- Engineering GeologistAn engineering geologist is a geologist is a geologist trained in the discipline of
engineering geology. Many organizations and governments have programs for the
qualifications, testing and certification of engineering geologists as a protection to the
public.
Engineering geologist commonly works with civil engineers, architects, developers and
planners, to ensure that the geologic factors affecting the location, design, construction,
operation and maintenance of engineering works are recognized and adequately provided
for.
One of the most important roles of the engineering geologist is the interpretation of
landforms and earth processes to indentify potential geologic and related manmade
hazards that may impact civil structures and human development.Nearly all engineering
geologist are initially trained and educated in geology, primarily during their
undergraduate education.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 30/33
HYDROLOGIST
Hydrology is the study of the movement, distribution, and quality of water on earth and
other planets, including the hydrologic cycle, water resources and environmental
watershed sustainability. A practitioner of hydrology is a hydrologist, working within the
fields of earth environmental engineering.
The main jobs of a hydrologist are to assess contaminant transport risk and establish
environmental policy guidelines, part of the hazard module in catastrophe modeling,
designing riparian restoration projects. They also involved determining the water balance
of a region.
GEOPHYSICIS
Geophysicis is the physics of the earth and its environment in space . Its subjects include
the shape of the earth , its gravitational ang magnetic fields, the dynamics of the earth as
a whole and of its component parts, the earth’s internal structure, composition and
tectonics, the generation of magmas, volcanism and rock formation, the hydrological
cycle including snow and ice, all aspects of the oceans, the atmosphere, ionosphere,
magnetosphere and solar-terrestrial relations, and analogous problems associated with the
moon and other planets
Geophysics is a highly interdisciplinary subjects and geophysicist contribute to every
area of the earth sciences such as Gravity, heat flow and magnetism.
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 31/33
SOURCES / REFERENCES
http://en.wikipedia.org/wiki/hydrologist#branches_of_hydrology
http://en.wikipedia.org/wiki/engineering_geologist
http://www.energyzone.net/downloads/career%20path%20o%20&%20g%20rev2.pdf
http://educationportal.com/articles/petroleum_engineer_job_description_and_info_abaut_
a_career_in_petroleum_engineering.html
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 32/33
CONCLUSION
Oil industry plays a very important part in our life. Oil powers our cars, electcity and
many others things. Just imagine a world without petroleum. That is why oil exploration
and research is important and must be continued by future generations.
I learnt many things from this coursework such as :
- Additional Math can be used in daily life
- Additional Math is not very hard to learn
- We must keep on finding newer renewable energy sources to replace oil reserves that are
depleting.
- Careers that involved in oil industry requires a basic knowledge of Additional Math
8/4/2019 Add Math Maya
http://slidepdf.com/reader/full/add-math-maya 33/33
ACKNOWLEDGEMENT
I would like to express my gratitude and thanks to my teacher, Puan Halimaton Saadiah Bt Saad
for her wonderful guidance for me to able to complete this project work. Next, is to my parents
for their continuous support to me throughout this experiment. Special thanks to my friends for
their help, and to all those who contributed directly or indirectly towards the completion of this
project work.
Throughout this project, I acquired many valuable skills, and hope that in years to come, those
skills will be put to good use.
Recommended