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Physical modeling and computer graphic simulation of the depletion of world energy reserve
Mathematics and Computers in Simulation XXIII (1981) 56-62 North-Holland Publishing Company
PHYSICALM~DELIN~ANDC~MPUTERGRA~HICS~MULATIONOFTHEDEPLETI~NOF WORLD ENERGY RESERVE Chih WU Mechanical
Engineering
Department.
U.S. Naval Academy,
Annapolis.
MD 21402,
U.S.A
A physical modeling device and a computer graphic simulation program of the depletion of world energy reserve are developed to demonstrate how rapidly our energy reserve is depleted, how quickly and enormously our demands for energy grows, and how important energy conservation is to us. In both modeling and simulation cases, the total world energy reserve, the current energy usage annual growth rate, and the current energy consumption rate are given as parameters. One can view the energy shortage in terms of the rapidly falling levels in the physical water tank or the simulated oil barrels.
awareness demonstration aimed at midshipmen at the U. S. Naval Academy, through his teaching energy courses. To make the students energy conscious, the author also uses the demonstration to motivate and challenge his students. Further material in energy conservation, energy and environment, direct energy conversion, alternative energy sources, energy and economy, energy planning and societal implications are also covered in the energy courses.
INTRODUCTION Abundant and cheap enerqv has been a decisive element in the creation of modern world economics. Since the industrial revolution, fossil fuel energy has increasingly replaced human labor in industry, supported a qrowinq population, and led to-a spectacular growth-in the productivity and higher standards of living beings. There are physical and economical limits on the world's supply of oil. The total world oil. reserve is estimated to be two trillion barrels and more than 360 billion barrels have already been consumed. World consumotion of oil has arown at an averaae rate of 6.6% since 1940, and-it grew by as much as 8% annually during the 1960's. If it could be assumed that demand for oil would grow at an annual rate of only 3%, the world's presently estimated recoverable oil resources would be exhausted before 2020 rather than 2010 at a conjectural growth rate of 5% [l]. At any rate, however, the fact is clear that within a few generations, the bulk of the world's supply of oil, which has been created over hundreds of millions of years, will have been substantially exhausted.
In the energy awareness demonstration, total world oil reserve, current oil consumption rate, and current oil usage annual growth rate are given. Students can view the oil energy shortage in terms of the rapidly falling levels in oil barrels either physically or on the screen of a cathode ray tube which is connected to a computer. Oil (water in the physical modelinq case) is made.to drain from'a-reservoir at an exponentially increasing flow rate, providing an analogue to the depletion of world oil reserve in the face of a continuously increasing demand. A student can also choose a lower annual growth (conserve) rate than the current growth rate, a large difference in energy requirements is shown. The varying annual growth rate mentioned above is further compared with a zero annual growth rate. Students are required to find the 'doubling time' of energy consumption. They are also supposed to find out how much energy is going to be consumed compared with what we have used so far. All students who have been involved in the demonstration are very impressed by the energy depletion situation and respond with a much better understanding of the energy crisis. Further, this demonstration stimulates students' interest in the energy conversion field.
The oil energy crisis gives no indication of going away. Instead, it shows every sign of increasing in severity and complexity in the years to come. It is necessary to persuade public opinion that our oil energy reserves are limited. To avoid a much more severe oil crisis, people must become more energy conscious and learn to conserve energy while scientists and technologists attempt to discover andincrease the supply of new energy resources. An appropriate starting point in this education process is in college. It is the intention of the author to create an energy 56
57
C. Wu / Sirmtlation of the deplrtiorl of r4orld etmg.v rc3ei-W
Let tf be the time from now that the total energy reserve is completely depleted.
MATHEMATICAL ALGORITHM Energy consumption rate for the past years has nearly constant growth rate. A constant percentage growth rate implies that increase in future energy consumption is proportional to the current energy consumption. An exponential relation can be easily derived. P = Poexp(at)
PHYSICAL MODEL
1
where PO is the current power consumption, a
is the annual growth rate,
t
is time, and
P is the future power consumption at time t. The energy consumed for all time up to now, E and from all time up to a future time t, Et, a%:
0 E. =
where ET is the total energy reserve.
Pdt = ; PO
(2)
-m
Poeat.
The physical model of the depletion of world energy reserve is shown in Figure 1. A fluid flow to the energy flow analogy is also shown. The mechanical device is a very simple one with water stored in a plastic tank. The water is drained out from a hole in the bottom of the plastic tank. The hole is resulted from two over-lapped plates as shown in Figure 2. Figure 2 is the top view of two flate plates. The lower plate has a hole which increases in size exponentially. The upper plate has a hole of constant area. The lower plate is pulled by an electric motor across the bottom of the upper plate and as it moves the water flow will increase by an exponential amount. The double shaded area is the effective area of draining water flow. It is found from the fluid analog that the opening area of the lower plate is given by the following equation:
(3)
is defined to be The doubling time, t that the power consumptio . 8’ at tD is double the current power consumption
where (e
!!?=
2
=
eatD.
J
pO Therefore
(e
atf at f
- 1) -e
tf = i In (>+ t
D
= 0.693
0
-a--'
The doubling time is particularly significant when the consumption of a fuel is conFor a constant annual growth rate, it sidered. can be shown that the total energy consumption in the next doubling time period is equal to the total energy consumption for all time up to now.
Eo=j;.Pdt=ED=j;Pdt=;Po.
(6)
As one can see, even for seemingly reasonable growth rate, the doubling period can be relatively short.
at
)
is the water velocity correction factor due to various water level in the plastic tank,
1) is the time from now to the time that the total energy is completely depleted,
A0 = Current Cross Section Area, ET = The Total Energy Reserve. A computer program may be written to determine the dimension of the exponential hole. The plastic tank constructed is 20.25 in. tall and 8 in. square and it contains approximately 5.8 gal of water. Based on these sizes, the dimension of the hole has been computed and a graph of the values has been plotted. The program is fed directly into the computer operated drill press in the machine shop to make the lower plate. The upper plate is 5" x l/2". The exponential plate is the sliding plate and the upper plate is secured in the bottom of the tank and is immovable. A stand for the electric motor is constructed and attached to the legs of
58
C. Wu /Simulation of the depletion of world energy reserve
of the tank. A collecting tank is also constructed. This tank must be able to hold the entire volume of the demonstration tank and is able to demonstrate doubling time. COMPUTER GRAPHICS SIMULATION ihe computer program is written in the Graphic System BASIC language, and runs interactively on Tektronix 4051. The program is separated into two files in order to save memory space at run time. Oil barrels are drawn on CRT. Energy depletion is shown by the failing levels in barrels for the current annual growth rate. The energy depletion for zero growth rate is shown aside to emphasize the conservation effects of a lower growth rate. Students can also choose a lower annual growth (conserve) rate than the current rate to compare with the zero growth rate. Students are required to find out how much energy is going to be consumed compared with what we have used so far. The program first print out the following instruction so that students know what to do. A PROGRAM TO SHOW DEPLETION OF THE WORLD'S ENERGY SUPPLY ********************* INSTRUCTIONS: 1. ON THE NEXT PAGE YOU WILL SEE TWO BARRELS OF FOSSIL FUEL. THEY REPRESENT SCHEDULES OF FUEL CONSUMPTION IN WHICH, ON THE LEFT THE DEMAND FOR ENERGY INCREASES CONTINUOUSLY AT A CONSTANT RATE, AND ON THE RIGHT THE DEMAND REMAINS CONSTANT AT ITS CURRENT LEVEL 2. TO VIEW THE PICTURE FOR FUEL IN THE FUTURE THE TIME MAY BE INCREMENTED BY PRESSING THE USER DEFINABLE KEY l-5 CORRESPONDING TO THE NUMBER OF YEARS INTO THE FUTURE YOU DESIRE TO MOVE THE PICTURE. 3. TO END THE DISPLAY AND TURN TO THE NEXT PAGE HIT USER DEFINABLE *6. 4. TO TURN THE PAGE PRESS 'RETURN' Computer Program 1 4 5 6 a 9
10
12
;z 1'; :; 21 22 24 100 110 120 130
GO TO 100 T=T+l P=l GO TO 930 T=T+2 P=l GO TO 930 T=T+3 P=l GO TO 930 T=T+4 P'0 GO TO 930 T=Tt5 P'0 GO TO 930 GO TO 1240 INIT SET DEGREES PAGE SET KEY
140 PRINT "JJJJJJJJ" A PROGRAM TO SHOW DEPLETION OF THE WORLD'S ENERGY SUPPLY" 160 PRINT ***************************II 170 PRINT ” 180 PRINT 190 PRINT "INSTRUCT.ION." ON THE NEXT PAGE you WILL SEE 200 PRINT "1 TWO BARRELS OF FOSSIL FUEL." THEY REPRESENT SCHEDULES OF FUEL 210 PRINT " CONSUMPTION IN WHICH, ON" THE LEFT THE DEMAND FOR ENERGY 220 PRINT ' INCREASES CONTINUOUSLY AT" 230 PRI 'I A CONSTANT RATE, AND ON THE RIGHT THE DEMAND REMAINS CONS-" AT ITS CURRENT LEVEL." 240 PRINT ” 250 PRINT "2. TO VIEW THE PICTURE FOR FUEL IN THE FUTURE THE TIME MAY" 260 PRINT ” BE INCREMENTED BY PRESSING THE USER DEFINABLE KEY 1-5" 270 PRINT ” CORRESPONDING TO THE NUMBER OF YEARS INTO THE FUTURE YOU" 280 PRINT ' DESIRE TO MOVE THE PICTURE." 290 PRINT "3. TO END THE DISPLAY AND TURN TO THE NEXT PAGE HIT USER" 300 PRINT ' DEFINABLE 06." 310 PRINT "4 TO TURN THE PAGE PRESS 'RETURN'" 320 INPUT A$' 330 A=0.073 340 T=fl 350 Fl=@ 360 FZ=@ 370 Y0=1978 380 E0=3.76E+14 390 P0=3.1E+12 400 01=0.693/A 410 TP=E0P0 420 Y2=Yfl+INT(T2) 430 PAGE 440 R=20 450 B=l 460 MOVE 5,10 470 GOSUB 1690 480 GOSUB 1690 490 GOSUB 1690 500 DRAW 5,95 510 MOVE 5,10 520 B=-1 530 DRAW 55,10 540 GOSUB 1690 550 GOSUB 1690 560 GOSUB 1690 570 DRAW 55,95 580 B=l 590 MOVE 70,1@ 600 GOSUB 1690 610 GOSUB 1690 620 GOSUB 169a 630 DRAW 70,95 640 MOVE 70,10 650 DRAW 120,10 660 B=-1 670 GOSUB 1690 680 GOSUB 1690 690 GOSUB 1690 70b DRAW 120,95
150 PRINT 'I
fhl ~B!ET~~A'$ ICTURE OF WORLD ENERGY DEPLETION"
59
730
740
MOVE 5,7.5 PRINT "ANNUAL GROWTH RATE=";A MOVE 5,5 1MAGE"USE DOUBLES EVERY" X2D.D , "YEARS." PRINT USING 760:Dl ’ MOVE 70,7.5 PRINT "ZERO ANNUAL GROWTH RATE" MOVE 70,5 PRINT 'IiUEL EXHAUSTED IN YEAR";Y2 MOVE 5,90 DRAW 55,90 MOVE 6,90.3 PRINT Y0 MOVE 70,90 DRAW 120,910 MOVE 71,90,3 PRINT Y0 MOVE 0,2.5 REM GO TO 910 Cl=l/A*P0(EXP(A*T)-1) El=E0-Cl IF El>0 THEN 1010 MOVE 6,10.2 IF F1<>0 THEN 1000
750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 Fl=l 990 b!kNT INT (l/A*LOG(E0*A/P0+l))+Y0 1000 1010 1020 1030 1040 1050
1060 1070
1080 1090 1100
1110 1120 1130 1140 1150 1160 1170 1180 1190
1200
1210 1220 1230 1240 1250 1260 1270
;' FUEL EXHAUSTED","G" GO TO 1000 H=El/E0*80+10 CS=INT(El/E0*100) MOVE 5,H DRAW 55,H IF P=l THEN 1000 MOVE 6,H+8.3 ";C9;"% LEFT" PRINT Y0+T;" E2=E0-P0*T C8=INT(E2/E0*100) IF ~2$ THEN ii@ MOVE 71,10.3 IF F2<>0 THEN 1150 F2=1 PRINT "FUEL EXHAUSTED" IF Fl=l THEN 1230 GO TO 1240 H=E/E0*80+10 MOVE 70,H DRAW 120,H IF P=l THEN 1230 MOVE 71,H+0.3 ";C8,"% LEFT" PRINT Yb+T;" GO TO 910 PAGE PRINT "HERE IS A SUMMARY OF WHAT HAPPENS TO THE FUEL SUPPLY WHEN" PRINT PRINT " THE CONSTANT RATE OF INCREASE
1280 ;fM"& 1290 s(l)=i 1300 S(2)=2 1310 s(3j=5 1320 S(4)=10 1330 S(5)=15 1340 S(s)=20 1350 S(7)=25 1360 S(8)=30
’
1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590
S(9)=35 PRINT "JJJJ" A$="YEAR" B$="CONSUMPTION RATE" C$="ENERGY USED SO FAR" D$="PERCENT LEFT" IMAGE 2X,4A,3X,16A,3X,18A,3X,12A PRINT USING 1430; A$,B$,C$,D$ FOR I=1 to 61 PRINT "-'I. NEXT I ’ PRINT "-" IMAGE 3T,4D,12T,3E,31T,3E,52T,5D FOR I=1 TO 9 Y=Y@+S( I) P=P0*EXP(A*S(I) E=l/A*P0*(EXP(A*S(I))=l) L=(E0-E)/E0*100 IF L<0 THEN 1590 PRINT USING 1490;Y,P,E,L PRINT NEXT I PRINT "JJJ" 1600 PRINT "DO YOU WISH TO MAKE PROJECTIONS WITH ANOTHER GROWTH RATE?" 1610 ;N";;; ;;Y OR N)" 1620 1630 IF A$="N" THEN 1670 1640 PRINT "INPUT YOUR bECIMAL GROWTH RATE." 1650 INPUT A 1660 GO TO 340 1670 PRINT "SO LONG THEN, AND BE SURE TO CONSERVE ENERGY!" 16813 END 1690 RDRAW O,R 1700 FOR I=1 to 9 1710 RDRAW -B*0.4,0 1720 ROTATE 20*1*-B 1730 NEXT I 1740 ROTATE 0 1750 REMOVE B*0.4,0 1760 RETURN
Then oil barrels are drawn on CRT, energy depletion is shown by the falling levels in the barrel for the current annual growth rate. The energy depletion for zero growth rate is shown on the side to emphasize the conservation effects of a lower growth rate. Some of the depletion pictures for different annual growth rates are shown here: DISCUSSION The physical modeling and computer graphics program illustrate the consumption of fuel oil, based on the present (1978) world consumption rate, with no growth and also with a constant growth rate. The graphical presentation can be advanced in steps from one to five years, until The two presentaall of the fuel is depleted. tions (no growth and constant growth) are shown simultaneously and have printouts of the percentage of fuel left, after steps of four or five years. Along with this, the graphs also list the growth rates, the time for doubling consumption for the constant growth rate, and
60
C. Wu / Simulation of /he depletion of world energy vesen~c
the fuel is exhausted for zero growth. After advancing this presentation as far in time as is desired, the operator can change to another presentation, which gives a tabular summary of what happens to the worlds fuel supply at the This constant growth rate being considered. table shows years, consumption rate, energy used so far, and the percentage of fuel left. Following this presentation the operator, student, has the option of running through the program, using other growth rates, as many times as desired. In considering or evaluating what will or will not be an effective means of teaching any large number of individuals there are many variables, which in general cannot be compiled into one overall viewpoint. This program is an effective means of presenting the facts that energy is being depleted on a worldwide basis, and that without some degree of conservation the known reserves will be gone before the year 2099, which is the projected date for exhaustion of supplies at the present consumption rate, with no growth. The presentation of these facts should have a positive impact on most educated people, and especially on midshipmen due to the Navy's heavy use of energy. Almost as much as any single training aid can accomplish, in teaching energy awareness is accomplished by this program. This statement is based on the fact that the program allows the operator to vary the consumption growth rate to a great degree and compare the results of each growth rate to the others, as well as zero growth. This comparison clearly illustrates the degree of change in time energy exhaustion for any change in growth rate, and this illustration is the primary point that must be conveyed to produce a change in a The facts presented must be person's attitude. directly relatable to the range of experience or knowledge of the individuals to whom they are presented and, for the most part, the material presented in this program is so relatable.
alarmingly fast the energy levels fall off even with a small annual growth rate. And how desirable it is to have a zero growth rate. It is believed that demonstrations like these, should be made more readily available to the general public. Many more demonstrations can be developed. The only limit is our imagination. REFERENCE 1.
Krenz, J. H., Energy Conversion and Utilization, Allyn & Bacon, Bost (1976).
lEr-EI
Fig.
1
As an overall impression, the author feels that the program is an effective means of illustrating the energy problem in the world today and that it is an excellent form of teaching midshipmen, at the Naval Academy, just how much a small change in consumption affects the time to deplete the world's energy reserves, thereby accomplishing it's task of making them energy aware.
Energy
and Fluid
Flow Analogy
Fixed
ving ection
CONCLUSION The adequancy of our energy supply has become one of the most frequently discussed The first step to meet subjects in the world. the energy problem is to have public well aware of the crisis. There is the old saying that one picture is worth a thousand words. These demonstrations allow the students to see how
‘Vr -VI
Moving opening
Fig. 2
lower area
plate
Hole Opening Area of the Physical Modeling Device
61
A PROCRM
TO SHDY
DEPLETIOtd
OF THE UORLD’S
ENERGY
SUPPLY
MRE
IS R O”““(uY
__ _ .__ __. TO TWN
THE PRCE
Fig. 3
PRESS
‘RETLW’
Computer Graphic Instruction
OF “MI
MPPPEW I0 THE FUEL SUPPLY WE!,
THE COWSTpI(T RRTE OP tWCRER(LI
I9
9.973
E”EllGY USED 90 WAR CO”S”“PTlON RllTE ___________________________________________________________--,979 ,.139E+9,2 1.2*6E*9,2
FOR
tttt:tttttttttttt:ttttttttt
PEICEWT
LEFT
99 99
,989
1.597E*9*2
6.675E+912
,993
..,66E19,2
,.W,E+B,J
99
,998
6.43x*9*2
*.%1E+913
*9
,993
9.2661+9,2
9.147E*9,3
79
,999
*.,WE+B,J
,.494E+9,4
63
Simulation
Fig. 6
Sumnary
1 PtCfUt
< ‘9s3
of Simulation
O+ UYLD
EWICY
Result
DFPLETtDU
I
‘m ~
199n
71% LEFT
2a3
so: LEFT
(
Fig. 4
Computer
Graphic
Simulation
Fig. 7
(I PlCfUI
OP “ML0
MtKY
DEPLETIOY
Rm
ts
Computer
1 8uMRr mr
OP wr
COWTN’T
Graphic
WPEME ““m
Simulation
TO TWE FUEL
OP tHC”En9E
I9
SUPPLY
YEly coNgllrrtm RaTE EMERCY WED SO F(Y( ----__--------___--_~~~-~~~-~~~___________________-_______ ,979 3.259E*.12 3.179R912
Fig. 5
Computer
Graphic
Simulation
1964
3.4tLE+112
1983
3.999EMlZ
1.76,El@,J
1999
9. L,IE+9,2
4.W.?E+O,l
,993
L.scaE+9,2
6.9258+@,3
9. e??Eb9,Z
1.@65E+@,4
z-3
,.992E+9,J
*.s44E+s,,
a.9
,.399E+9n
2. ,59E+,*4
nn
1.794E+9,3
2.949E*e,4
Summary
PEI)CE”T LEFT 99
6.52,E*e*2
,999
Fig. 8
mw
9.99
of Simulation
Result
62
C. Wu /Simulation o.f the depletion of world energy reserve
Fig. 9
Fig. 10
Computer Graphic Simulation
Summary of Simulation Result
PHYSICALM~DELIN~ANDC~MPUTERGRA~HICS~MULATIONOFTHEDEPLETI~NOF WORLD ENERGY RESERVE Chih WU Mechanical
Engineering
Department.
U.S. Naval Academy,
Annapolis.
MD 21402,
U.S.A
A physical modeling device and a computer graphic simulation program of the depletion of world energy reserve are developed to demonstrate how rapidly our energy reserve is depleted, how quickly and enormously our demands for energy grows, and how important energy conservation is to us. In both modeling and simulation cases, the total world energy reserve, the current energy usage annual growth rate, and the current energy consumption rate are given as parameters. One can view the energy shortage in terms of the rapidly falling levels in the physical water tank or the simulated oil barrels.
awareness demonstration aimed at midshipmen at the U. S. Naval Academy, through his teaching energy courses. To make the students energy conscious, the author also uses the demonstration to motivate and challenge his students. Further material in energy conservation, energy and environment, direct energy conversion, alternative energy sources, energy and economy, energy planning and societal implications are also covered in the energy courses.
INTRODUCTION Abundant and cheap enerqv has been a decisive element in the creation of modern world economics. Since the industrial revolution, fossil fuel energy has increasingly replaced human labor in industry, supported a qrowinq population, and led to-a spectacular growth-in the productivity and higher standards of living beings. There are physical and economical limits on the world's supply of oil. The total world oil. reserve is estimated to be two trillion barrels and more than 360 billion barrels have already been consumed. World consumotion of oil has arown at an averaae rate of 6.6% since 1940, and-it grew by as much as 8% annually during the 1960's. If it could be assumed that demand for oil would grow at an annual rate of only 3%, the world's presently estimated recoverable oil resources would be exhausted before 2020 rather than 2010 at a conjectural growth rate of 5% [l]. At any rate, however, the fact is clear that within a few generations, the bulk of the world's supply of oil, which has been created over hundreds of millions of years, will have been substantially exhausted.
In the energy awareness demonstration, total world oil reserve, current oil consumption rate, and current oil usage annual growth rate are given. Students can view the oil energy shortage in terms of the rapidly falling levels in oil barrels either physically or on the screen of a cathode ray tube which is connected to a computer. Oil (water in the physical modelinq case) is made.to drain from'a-reservoir at an exponentially increasing flow rate, providing an analogue to the depletion of world oil reserve in the face of a continuously increasing demand. A student can also choose a lower annual growth (conserve) rate than the current growth rate, a large difference in energy requirements is shown. The varying annual growth rate mentioned above is further compared with a zero annual growth rate. Students are required to find the 'doubling time' of energy consumption. They are also supposed to find out how much energy is going to be consumed compared with what we have used so far. All students who have been involved in the demonstration are very impressed by the energy depletion situation and respond with a much better understanding of the energy crisis. Further, this demonstration stimulates students' interest in the energy conversion field.
The oil energy crisis gives no indication of going away. Instead, it shows every sign of increasing in severity and complexity in the years to come. It is necessary to persuade public opinion that our oil energy reserves are limited. To avoid a much more severe oil crisis, people must become more energy conscious and learn to conserve energy while scientists and technologists attempt to discover andincrease the supply of new energy resources. An appropriate starting point in this education process is in college. It is the intention of the author to create an energy 56
57
C. Wu / Sirmtlation of the deplrtiorl of r4orld etmg.v rc3ei-W
Let tf be the time from now that the total energy reserve is completely depleted.
MATHEMATICAL ALGORITHM Energy consumption rate for the past years has nearly constant growth rate. A constant percentage growth rate implies that increase in future energy consumption is proportional to the current energy consumption. An exponential relation can be easily derived. P = Poexp(at)
PHYSICAL MODEL
1
where PO is the current power consumption, a
is the annual growth rate,
t
is time, and
P is the future power consumption at time t. The energy consumed for all time up to now, E and from all time up to a future time t, Et, a%:
0 E. =
where ET is the total energy reserve.
Pdt = ; PO
(2)
-m
Poeat.
The physical model of the depletion of world energy reserve is shown in Figure 1. A fluid flow to the energy flow analogy is also shown. The mechanical device is a very simple one with water stored in a plastic tank. The water is drained out from a hole in the bottom of the plastic tank. The hole is resulted from two over-lapped plates as shown in Figure 2. Figure 2 is the top view of two flate plates. The lower plate has a hole which increases in size exponentially. The upper plate has a hole of constant area. The lower plate is pulled by an electric motor across the bottom of the upper plate and as it moves the water flow will increase by an exponential amount. The double shaded area is the effective area of draining water flow. It is found from the fluid analog that the opening area of the lower plate is given by the following equation:
(3)
is defined to be The doubling time, t that the power consumptio . 8’ at tD is double the current power consumption
where (e
!!?=
2
=
eatD.
J
pO Therefore
(e
atf at f
- 1) -e
tf = i In (>+ t
D
= 0.693
0
-a--'
The doubling time is particularly significant when the consumption of a fuel is conFor a constant annual growth rate, it sidered. can be shown that the total energy consumption in the next doubling time period is equal to the total energy consumption for all time up to now.
Eo=j;.Pdt=ED=j;Pdt=;Po.
(6)
As one can see, even for seemingly reasonable growth rate, the doubling period can be relatively short.
at
)
is the water velocity correction factor due to various water level in the plastic tank,
1) is the time from now to the time that the total energy is completely depleted,
A0 = Current Cross Section Area, ET = The Total Energy Reserve. A computer program may be written to determine the dimension of the exponential hole. The plastic tank constructed is 20.25 in. tall and 8 in. square and it contains approximately 5.8 gal of water. Based on these sizes, the dimension of the hole has been computed and a graph of the values has been plotted. The program is fed directly into the computer operated drill press in the machine shop to make the lower plate. The upper plate is 5" x l/2". The exponential plate is the sliding plate and the upper plate is secured in the bottom of the tank and is immovable. A stand for the electric motor is constructed and attached to the legs of
58
C. Wu /Simulation of the depletion of world energy reserve
of the tank. A collecting tank is also constructed. This tank must be able to hold the entire volume of the demonstration tank and is able to demonstrate doubling time. COMPUTER GRAPHICS SIMULATION ihe computer program is written in the Graphic System BASIC language, and runs interactively on Tektronix 4051. The program is separated into two files in order to save memory space at run time. Oil barrels are drawn on CRT. Energy depletion is shown by the failing levels in barrels for the current annual growth rate. The energy depletion for zero growth rate is shown aside to emphasize the conservation effects of a lower growth rate. Students can also choose a lower annual growth (conserve) rate than the current rate to compare with the zero growth rate. Students are required to find out how much energy is going to be consumed compared with what we have used so far. The program first print out the following instruction so that students know what to do. A PROGRAM TO SHOW DEPLETION OF THE WORLD'S ENERGY SUPPLY ********************* INSTRUCTIONS: 1. ON THE NEXT PAGE YOU WILL SEE TWO BARRELS OF FOSSIL FUEL. THEY REPRESENT SCHEDULES OF FUEL CONSUMPTION IN WHICH, ON THE LEFT THE DEMAND FOR ENERGY INCREASES CONTINUOUSLY AT A CONSTANT RATE, AND ON THE RIGHT THE DEMAND REMAINS CONSTANT AT ITS CURRENT LEVEL 2. TO VIEW THE PICTURE FOR FUEL IN THE FUTURE THE TIME MAY BE INCREMENTED BY PRESSING THE USER DEFINABLE KEY l-5 CORRESPONDING TO THE NUMBER OF YEARS INTO THE FUTURE YOU DESIRE TO MOVE THE PICTURE. 3. TO END THE DISPLAY AND TURN TO THE NEXT PAGE HIT USER DEFINABLE *6. 4. TO TURN THE PAGE PRESS 'RETURN' Computer Program 1 4 5 6 a 9
10
12
;z 1'; :; 21 22 24 100 110 120 130
GO TO 100 T=T+l P=l GO TO 930 T=T+2 P=l GO TO 930 T=T+3 P=l GO TO 930 T=T+4 P'0 GO TO 930 T=Tt5 P'0 GO TO 930 GO TO 1240 INIT SET DEGREES PAGE SET KEY
140 PRINT "JJJJJJJJ" A PROGRAM TO SHOW DEPLETION OF THE WORLD'S ENERGY SUPPLY" 160 PRINT ***************************II 170 PRINT ” 180 PRINT 190 PRINT "INSTRUCT.ION." ON THE NEXT PAGE you WILL SEE 200 PRINT "1 TWO BARRELS OF FOSSIL FUEL." THEY REPRESENT SCHEDULES OF FUEL 210 PRINT " CONSUMPTION IN WHICH, ON" THE LEFT THE DEMAND FOR ENERGY 220 PRINT ' INCREASES CONTINUOUSLY AT" 230 PRI 'I A CONSTANT RATE, AND ON THE RIGHT THE DEMAND REMAINS CONS-" AT ITS CURRENT LEVEL." 240 PRINT ” 250 PRINT "2. TO VIEW THE PICTURE FOR FUEL IN THE FUTURE THE TIME MAY" 260 PRINT ” BE INCREMENTED BY PRESSING THE USER DEFINABLE KEY 1-5" 270 PRINT ” CORRESPONDING TO THE NUMBER OF YEARS INTO THE FUTURE YOU" 280 PRINT ' DESIRE TO MOVE THE PICTURE." 290 PRINT "3. TO END THE DISPLAY AND TURN TO THE NEXT PAGE HIT USER" 300 PRINT ' DEFINABLE 06." 310 PRINT "4 TO TURN THE PAGE PRESS 'RETURN'" 320 INPUT A$' 330 A=0.073 340 T=fl 350 Fl=@ 360 FZ=@ 370 Y0=1978 380 E0=3.76E+14 390 P0=3.1E+12 400 01=0.693/A 410 TP=E0P0 420 Y2=Yfl+INT(T2) 430 PAGE 440 R=20 450 B=l 460 MOVE 5,10 470 GOSUB 1690 480 GOSUB 1690 490 GOSUB 1690 500 DRAW 5,95 510 MOVE 5,10 520 B=-1 530 DRAW 55,10 540 GOSUB 1690 550 GOSUB 1690 560 GOSUB 1690 570 DRAW 55,95 580 B=l 590 MOVE 70,1@ 600 GOSUB 1690 610 GOSUB 1690 620 GOSUB 169a 630 DRAW 70,95 640 MOVE 70,10 650 DRAW 120,10 660 B=-1 670 GOSUB 1690 680 GOSUB 1690 690 GOSUB 1690 70b DRAW 120,95
150 PRINT 'I
fhl ~B!ET~~A'$ ICTURE OF WORLD ENERGY DEPLETION"
59
730
740
MOVE 5,7.5 PRINT "ANNUAL GROWTH RATE=";A MOVE 5,5 1MAGE"USE DOUBLES EVERY" X2D.D , "YEARS." PRINT USING 760:Dl ’ MOVE 70,7.5 PRINT "ZERO ANNUAL GROWTH RATE" MOVE 70,5 PRINT 'IiUEL EXHAUSTED IN YEAR";Y2 MOVE 5,90 DRAW 55,90 MOVE 6,90.3 PRINT Y0 MOVE 70,90 DRAW 120,910 MOVE 71,90,3 PRINT Y0 MOVE 0,2.5 REM GO TO 910 Cl=l/A*P0(EXP(A*T)-1) El=E0-Cl IF El>0 THEN 1010 MOVE 6,10.2 IF F1<>0 THEN 1000
750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 Fl=l 990 b!kNT INT (l/A*LOG(E0*A/P0+l))+Y0 1000 1010 1020 1030 1040 1050
1060 1070
1080 1090 1100
1110 1120 1130 1140 1150 1160 1170 1180 1190
1200
1210 1220 1230 1240 1250 1260 1270
;' FUEL EXHAUSTED","G" GO TO 1000 H=El/E0*80+10 CS=INT(El/E0*100) MOVE 5,H DRAW 55,H IF P=l THEN 1000 MOVE 6,H+8.3 ";C9;"% LEFT" PRINT Y0+T;" E2=E0-P0*T C8=INT(E2/E0*100) IF ~2$ THEN ii@ MOVE 71,10.3 IF F2<>0 THEN 1150 F2=1 PRINT "FUEL EXHAUSTED" IF Fl=l THEN 1230 GO TO 1240 H=E/E0*80+10 MOVE 70,H DRAW 120,H IF P=l THEN 1230 MOVE 71,H+0.3 ";C8,"% LEFT" PRINT Yb+T;" GO TO 910 PAGE PRINT "HERE IS A SUMMARY OF WHAT HAPPENS TO THE FUEL SUPPLY WHEN" PRINT PRINT " THE CONSTANT RATE OF INCREASE
1280 ;fM"& 1290 s(l)=i 1300 S(2)=2 1310 s(3j=5 1320 S(4)=10 1330 S(5)=15 1340 S(s)=20 1350 S(7)=25 1360 S(8)=30
’
1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590
S(9)=35 PRINT "JJJJ" A$="YEAR" B$="CONSUMPTION RATE" C$="ENERGY USED SO FAR" D$="PERCENT LEFT" IMAGE 2X,4A,3X,16A,3X,18A,3X,12A PRINT USING 1430; A$,B$,C$,D$ FOR I=1 to 61 PRINT "-'I. NEXT I ’ PRINT "-" IMAGE 3T,4D,12T,3E,31T,3E,52T,5D FOR I=1 TO 9 Y=Y@+S( I) P=P0*EXP(A*S(I) E=l/A*P0*(EXP(A*S(I))=l) L=(E0-E)/E0*100 IF L<0 THEN 1590 PRINT USING 1490;Y,P,E,L PRINT NEXT I PRINT "JJJ" 1600 PRINT "DO YOU WISH TO MAKE PROJECTIONS WITH ANOTHER GROWTH RATE?" 1610 ;N";;; ;;Y OR N)" 1620 1630 IF A$="N" THEN 1670 1640 PRINT "INPUT YOUR bECIMAL GROWTH RATE." 1650 INPUT A 1660 GO TO 340 1670 PRINT "SO LONG THEN, AND BE SURE TO CONSERVE ENERGY!" 16813 END 1690 RDRAW O,R 1700 FOR I=1 to 9 1710 RDRAW -B*0.4,0 1720 ROTATE 20*1*-B 1730 NEXT I 1740 ROTATE 0 1750 REMOVE B*0.4,0 1760 RETURN
Then oil barrels are drawn on CRT, energy depletion is shown by the falling levels in the barrel for the current annual growth rate. The energy depletion for zero growth rate is shown on the side to emphasize the conservation effects of a lower growth rate. Some of the depletion pictures for different annual growth rates are shown here: DISCUSSION The physical modeling and computer graphics program illustrate the consumption of fuel oil, based on the present (1978) world consumption rate, with no growth and also with a constant growth rate. The graphical presentation can be advanced in steps from one to five years, until The two presentaall of the fuel is depleted. tions (no growth and constant growth) are shown simultaneously and have printouts of the percentage of fuel left, after steps of four or five years. Along with this, the graphs also list the growth rates, the time for doubling consumption for the constant growth rate, and
60
C. Wu / Simulation of /he depletion of world energy vesen~c
the fuel is exhausted for zero growth. After advancing this presentation as far in time as is desired, the operator can change to another presentation, which gives a tabular summary of what happens to the worlds fuel supply at the This constant growth rate being considered. table shows years, consumption rate, energy used so far, and the percentage of fuel left. Following this presentation the operator, student, has the option of running through the program, using other growth rates, as many times as desired. In considering or evaluating what will or will not be an effective means of teaching any large number of individuals there are many variables, which in general cannot be compiled into one overall viewpoint. This program is an effective means of presenting the facts that energy is being depleted on a worldwide basis, and that without some degree of conservation the known reserves will be gone before the year 2099, which is the projected date for exhaustion of supplies at the present consumption rate, with no growth. The presentation of these facts should have a positive impact on most educated people, and especially on midshipmen due to the Navy's heavy use of energy. Almost as much as any single training aid can accomplish, in teaching energy awareness is accomplished by this program. This statement is based on the fact that the program allows the operator to vary the consumption growth rate to a great degree and compare the results of each growth rate to the others, as well as zero growth. This comparison clearly illustrates the degree of change in time energy exhaustion for any change in growth rate, and this illustration is the primary point that must be conveyed to produce a change in a The facts presented must be person's attitude. directly relatable to the range of experience or knowledge of the individuals to whom they are presented and, for the most part, the material presented in this program is so relatable.
alarmingly fast the energy levels fall off even with a small annual growth rate. And how desirable it is to have a zero growth rate. It is believed that demonstrations like these, should be made more readily available to the general public. Many more demonstrations can be developed. The only limit is our imagination. REFERENCE 1.
Krenz, J. H., Energy Conversion and Utilization, Allyn & Bacon, Bost (1976).
lEr-EI
Fig.
1
As an overall impression, the author feels that the program is an effective means of illustrating the energy problem in the world today and that it is an excellent form of teaching midshipmen, at the Naval Academy, just how much a small change in consumption affects the time to deplete the world's energy reserves, thereby accomplishing it's task of making them energy aware.
Energy
and Fluid
Flow Analogy
Fixed
ving ection
CONCLUSION The adequancy of our energy supply has become one of the most frequently discussed The first step to meet subjects in the world. the energy problem is to have public well aware of the crisis. There is the old saying that one picture is worth a thousand words. These demonstrations allow the students to see how
‘Vr -VI
Moving opening
Fig. 2
lower area
plate
Hole Opening Area of the Physical Modeling Device
61
A PROCRM
TO SHDY
DEPLETIOtd
OF THE UORLD’S
ENERGY
SUPPLY
MRE
IS R O”““(uY
__ _ .__ __. TO TWN
THE PRCE
Fig. 3
PRESS
‘RETLW’
Computer Graphic Instruction
OF “MI
MPPPEW I0 THE FUEL SUPPLY WE!,
THE COWSTpI(T RRTE OP tWCRER(LI
I9
9.973
E”EllGY USED 90 WAR CO”S”“PTlON RllTE ___________________________________________________________--,979 ,.139E+9,2 1.2*6E*9,2
FOR
tttt:tttttttttttt:ttttttttt
PEICEWT
LEFT
99 99
,989
1.597E*9*2
6.675E+912
,993
..,66E19,2
,.W,E+B,J
99
,998
6.43x*9*2
*.%1E+913
*9
,993
9.2661+9,2
9.147E*9,3
79
,999
*.,WE+B,J
,.494E+9,4
63
Simulation
Fig. 6
Sumnary
1 PtCfUt
< ‘9s3
of Simulation
O+ UYLD
EWICY
Result
DFPLETtDU
I
‘m ~
199n
71% LEFT
2a3
so: LEFT
(
Fig. 4
Computer
Graphic
Simulation
Fig. 7
(I PlCfUI
OP “ML0
MtKY
DEPLETIOY
Rm
ts
Computer
1 8uMRr mr
OP wr
COWTN’T
Graphic
WPEME ““m
Simulation
TO TWE FUEL
OP tHC”En9E
I9
SUPPLY
YEly coNgllrrtm RaTE EMERCY WED SO F(Y( ----__--------___--_~~~-~~~-~~~___________________-_______ ,979 3.259E*.12 3.179R912
Fig. 5
Computer
Graphic
Simulation
1964
3.4tLE+112
1983
3.999EMlZ
1.76,El@,J
1999
9. L,IE+9,2
4.W.?E+O,l
,993
L.scaE+9,2
6.9258+@,3
9. e??Eb9,Z
1.@65E+@,4
z-3
,.992E+9,J
*.s44E+s,,
a.9
,.399E+9n
2. ,59E+,*4
nn
1.794E+9,3
2.949E*e,4
Summary
PEI)CE”T LEFT 99
6.52,E*e*2
,999
Fig. 8
mw
9.99
of Simulation
Result
62
C. Wu /Simulation o.f the depletion of world energy reserve
Fig. 9
Fig. 10
Computer Graphic Simulation
Summary of Simulation Result