Hydropower

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Hydropower
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Hydropower Source Rainfall at high altitudes
Reservoir/river Kinetic energy gt 0.4 m/yr
History BC 100 Water wheels in Middle
East, Greek/Roman empires 1000 AD gt 5000
waterwheels in S England 1700 20,000
waterwheels in England 1830
Fourneyron radial flow turbine 1880
Pelton wheel (Californian Gold Rush)
Current Usage 20 of worlds electric power is
generated by hydropower
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Power Conversion Process Incident Power
(mass/sec) g (head)
P (dm/dt)g h (dm/dt) r
Q
Q is (volume of water)/sec and r is the density
of water Q u A where u is
the speed of the water and A is the
cross-sectional area of the pipe (penstock)
feeding the water turbine P
r g Q h Power depends on product Q h
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Pumped Storage eg Dinorwig, N Wales h 500 m V
7 106 m3 P 1600 MW Efficiency 80 Full
power within 10 secs (Surge in demand of 2800
MW 2mins after World Cup penalty shoot-out)
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Mountain Reservoirs large h, small Q High Dams
large h, large Q River Barrage small h,
large Q Each situation needs a particular design
of turbine
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Measurement of the flow Q
p0
p0
t
ut
D
z
s
p0
W
ps
u0
Weir
S
Bernoullis Theorem ½u2 - gz p/r constant
along a streamline
½u02 - gs ps/r ½ut2 - gt p0/r
u0 independent of s, so ps p0 rgs and ut
(u02 2gt)1/2
u02 ltlt 2gt so Qth W?utdt (8g/9)1/2WD3/2
Qexp kQth where k 0.6 (turbulence)
S 1m, D 0.2m, W 1m, then for u0 0.3ms-1
u02 0.1 lt 2gt 20t for t gt 0.005
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Fourneyrons turbine First successful water
turbine 1830
Water flows outwards between vanes and across the
runner blades.
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Turbine runners
Francis developed from Fourneyron 2 mlt h lt200 m
Pelton (not submerged) h gt 200 m
Kaplan (variable pitch) fixed pitch
propellers h lt 2 m
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Pelton Wheel Impulse Turbine (large h, small Q)
Power Optimisation Speed of water jet u , of cup
uc Assume jet reflected by 1800 Change in
velocity 2(u - uc) Force on cup 2(u -
uc)(dm/dt) F 2rQ(u - uc)
Power P Fuc 2rQ(u - uc)uc P is
max/min when dP/duc 0 ie u - 2uc
0 or u ½uc Pmax
½rQu2 All the kinetic energy of the water jet
imparted to cup
u2 2gh
(conservation of energy) where h is the head.
Substituting gives Pmax(kW) 45 A
h3/2 where A is the cross-sectional area of the
water jet
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Three Gorges Project on Yangzi River in China
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Environmental Impact Low-carbon
electricity Silting, loss of natural
irrigation Population shift (Yangtze River, China
106 people)
Risks Dam bursts (not infrequent!)- 1975 230,000
died following collapse of Banqiao Dam on Huai
river China. Earthquakes- Vaoint dam, Italy
tremor set off landslide, 2000 killed
Limits to Efficiency- typically 80, old 60 new
90 Losses in pipework, turbines (small) Flow
conditions (10-20)
Economics High civil engineering costs (National
Funding) Low operating cost, long life (50-100
years)
Installations About 1/3 global potential
utilised- rest mainly in LDC 1.4 GW in UK (90 in
Scotland) 8 GW in Switzerland, 12 GW on Parana
River in Brazil 105 dams in China
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Tidal Power
Sources a) Gravitational attraction of Moon
b) Rotation of Earth-Moon system
Earth
Centre of rotation of Earth-Moon distance x from
centre of Earth
Moon
A
B
w
x
w
m
M
Radius of Earth is r
R
-GmM/R2 M xw2 0 for equilibrium Centrifugal
force same at all points of Earth Tidal force
at a point is difference in gravitational
attraction of Moon at the point from that at the
centre of the Earth
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Tidal Range
M
s
r
q
R
m
Tidal force per unit mass F Fs - FR FR
GmR/R3 F Gms/s3 s2 R2 r2 - 2rRcosq 1/s2 ?
1/R2(1 2rcosq /R) Tangential component of tidal
force Fq Fsinq Fq 2Gmrcosq sinq /R3
Potential energy change in going from q 90 to q
q DV - ?Fq rdq gh - Gmr2cos2q /R3
gh where h is height of water surface.
Equilibrium when DV 0 g GM/r2 h mr4cos2q
/MR3 Maximum value is 0.36 m
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• Sun is in phase with Earth-Moon twice a year
  (neap tides)
• Tides do not keep pace with the rotation of the
  Earth-Moon,
• gives rise to friction and slow down of period
  of rotation of
• Earth 1/600 sec/century (equatorial speed 464
  m/s)
• Resonance effects possible
• across Atlantic causes tidal range (height) to
  increase
• from 0.5 m to 3 m
• Estuaries eg Bristol Channel increase range to
  10 m

Exploitation of Tidal Power Kinetic Energy -
Power per unit area, P with flow speed u
P (mass/unit area/sec)(kinetic energy per unit
mass) P (ru)(½u2) P ½ru3
(maximum efficiency 59, 40 typical) Restricted
application to regions of large flow speed eg
between Islands. Need large area Kaplan turbines
(v. expensive)
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Speed of Tidal Wave
Pressure p po rg(z - z) Pressure difference
dp rg ?z/?x dx dF dpArea -rg ?z/?x dx bh
rbhdx ?u/?t (massacceleration) so -g
?z/?x ?u/?t
z
z
h
b
b
Flow Q uA ubh (volume per second) dQ bh
?u/?x dx ?dV/?t bdx ?z/?t -dQ so ?z/?t -h
?u/?x
dx
x
Therefore ? 2z/?x2 (1/gh) ? 2z/?t2 so
speed c (gh)1/2
Atlantic Ocean width 4000 km, depth 4000 m so
speed 200 ms-1 Tidal frequency 210-5 s-1
ln c so l 10000 km Resonance as l twice
width, so tides enhanced from 0.5 m to 3m
Bristol Channel continental shelf length 300
km, average depth 80 m corresponds to a l/4
resonance standing wave
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Tidal Resonance in Estuary
l/4
y a sin kx sin wt
Standing wave
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Potential Energy Create tidal barrier different
water level on each side of barrier
Basin level
h
f
h
Tide level
Average power extracted from turbines, PA PA
(mass) g (fall of centre of mass)/(time
generating) (rAh) g f/t PA rAhfg/t , where A
is the area of the tidal basin
eg Bristol Channel and River Severn h 10 m, A
480 km2, PA 2 GW La Rance, France h
8 m, A 20 km2, PA 0.07 GW
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Bristol Channel
Open sea tidal range 0.5m

• Tidal wave Amplification
• due to
• funnelling in estuary
• reducing depth
• resonant coupling
• (modelling very complex)

Global Potential 3000 GW but only about 3 in
areas where tidal range enhanced Environmental
impact Major impact on environment and ecology of
estuary and surrounds- impedes ships, affect
fish, habitat altered, water quality affected
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Tidal Current Projects
Prototype 10 KW tidal current Turbine, Loch
Linne, 1994 UK Potential 10 GW 19 of
UKs electricity, but expensive harsh
environment
Tidal current/stream projects less environmental
impact than barrage schemes
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Tidal Power
Severn Barrage
Limited global potential 100-1000 GWe Good
around UK
8.6 GWe capacity
Significant local environmental impact but
improves flood defences
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Wave Power
Origin Wind-induced on free surface of
sea History None before 1970s. Sudden
development due to Oil crisis UK resource
(Technical potential) Shallow water
30 GW Deep water 80
GW (cf UK generating capacity of 55
GW) Predictable up to 24 hrs in advance good
availability high power density
Wave characteristics y a sin(k x -
wt) where k 2p/l , w 2pu and u 1/t
Typically a /l lt 0.1, l 100m and period t
5-10 secs Phase speed c (g /k)1/2 Real sea
waves are superposition of simple waves
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Wave energy Consider element of wave of unit
width, extent in the direction of travel dx, and
amplitude y. Loss in PE dU if elements c-of-m
falls from z/2 at x to -z/2 at x - l/2 is
dU (rzdx)gz rgz2dx z
a sink x so integrating over x from 0 to l /2,
corresponding to one wavelength, gives
U ¼ rga2l Equipartition of
energy KE PE so total energy/unit width E
in one l is E ½ rga2l
c-of-m at z/2
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Group velocity cg dw/dk d(kc)/dk c
kdc/dk c (g /k)1/2 so cg ½c
Power/unit width of wave P given by
P ½ E/T ¼ rga2l /T where T wave period
and l /T c so P ¼ rga2c

• Example
• 103 kg/m3 , a 1 m , l 50 m
• Period T l /c l /(g/k)1/2 (2pl /g)1/2
  5.7 sec, c 9 ms-1
• P 22 kW/m

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Wave-Energy Extraction

• A plane wave can be represented by a sum of
  spherical waves
• eikz eikrcosq ?at large r ?n cosnq
  (1/2pkr)1/2eiX e-iX
• where X kr - p/4 - np/2, n -88
• The power per unit width
• P ¼ rga2c
• so power of incoming spherical (n0) wave
• ¼ rg(1/2pkr)a2c ? 2pr ¼ rga2c/k
• Consider a plane wave incident on a small
  absorber which causes it to oscillate up and down
  and generate a circular outgoing wave. When this
  wave cancels the outgoing circular wave part of
  the incoming plane wave then the ingoing circular
  part of the incoming plane wave can be absorbed.
• i.e the energy in the width 1/k l/2p of
  the incident plane wave can be absorbed.

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Various types of wave energy converter
Surface devices All vulnerable in storms 50 yr
peak 10 ? height of average wave, so device must
be able to withstand 100 ? normal power
intensity Submersion is expensive Frequency 0.2
Hz is very low for electricity transmission-gt
stepped up
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Bristol cylinder
Cylinder moves in orbit in response to
waves Power taken away via hydraulic
pipes Conversion to electric power at land-based
generating station Barnacles can be a problem!
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Oscillating Water Column Device
No moving parts except for turbine Turbines spins
in air, not water, gives high revs (50 Hz)
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The Wells Turbine
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Tapered Channel TAPCHAN Norway 350 kW
Wave height amplification overspill into upper
reservoir Power from reservoir recovered using
conventional Kaplan (low head) turbine. Sea water
discharged to sea after passage through turbine
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Environmental impact Offshore - low visual
impact, little potential for pollution Coastal -
more visual impact, concrete disposal
Economics UK 6 GW practical potential (2020)
World 1-10 TW Offshore expensive- but Pelamis
device looks encouraging Coastal viable if
conventional power uneconomic Power
(amplitude)2 so variable and backup necessary-
more predictable though than wind and solar
Risks Surface devices can be vulnerable to
storms- but Pelamis dives through very large
waves. Potential shipping hazard high insurance
Potential Limited due to cheaper alternatives
(especially wind) but technology in RD phase
and a large resource. Expect cost reduction with
increased production (learning curve)
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Pelamis sea snake wave energy converter
30 MW per square km
130 m long 750 kW 700 tonnes
 Always there seems to be a layer, or indeed
layers, of senior people with negative views
about renewables and the power to make them
stick. This power seems to be inversely related
to technical knowledge of the subject or
technology in general. Professor Salter in
evidence to a Science and Technology select
committee 2001
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Salter Duck
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Wave Power
130 m long 750 kW 700 tonnes
Global potential about 2000 GWe Developing
technology By 2050 about 50 GWe
Pelamis sea snake
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Ocean Thermal Energy Conversion (OTEC)
Seasonal average temperature difference DT
between sea surface and 1000 m depth Zones with
DT gt 20 C are most suitable for OTEC
Top 100 m constant, below that level
temperature decreases At 1000 m it is 5 C and
remains that temperature to all depths
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Schematic of an OTEC system
eg Ammonia
Th
Tc

• So Pout lt (rcQ/ Th)(DT)2
  (note quadratic dependence)
• 1000 kg/m3, c 4200 J/kg/K so for DT 20 C
  and Pout 1 MW
• requires Q gt 0.18 m3/s 180 l/s

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Environmental Dredging up the cold water from
the deep will release some CO2 dissolved in the
sea water. However, amount is lt1 of the amount
generated burning coal to produce the same
amount of energy It may affect the climate, the
fauna and marine life of the region
Economic Needs large and expensive equipment
pumps and in particular very efficient heat
exchangers Encrustation by marine organisms,
biofouling, is a serious problem - Manufacture of
long large diameter cold water pipe is
difficult Not yet economically competitive, but
with global warming and technical developments it
is closer to becoming competitive.
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Biomass
Rate of energy storage by land biomass 3000 EJ/y
95 TW Total consumption of all forms of
energy 400 EJ/y 12 TW Biomass energy
consumption 55 EJ/y 1.7 TW Food energy
consumption 10 EJ/y 0.3 TW World
population 5.5 billion (109)
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Energy content of fuels GJ/tonne (?kJ/g) Wood
(air dried 20 moisture) 15 Sugar cane (air
dried stalks) 14 Commercial wastes (UK
average) 16 Oil (petroleum) 42 Coal (UK
average) 28 Natural gas 55
Biomass Resource in 2050 Potential EJ/y Energy
crops 128 Dung 25 Forestry
residues 14 Cereal residues 13 Sugar
cane residues 12 Existing forests
10 Urban refuse 3 TOTAL 205 (35 of
World Total)
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Solid Fuel Boilers
Energy to heat one litre of water from 20 oC to
100 oC 804200 J 336 kJ
Wood 15 MJ/kg or 10 kJ/cc So only need 34 cc of
wood to boil one litre of water
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Biomass is vegetable and organic waste that has
been generated in recent times When biomass is
grown CO2 is removed and the same amount
is released when it is burnt as a fuel. Fast
growing Willow can be used.
Ethanol produced from sugar-cane in Brazil. Used
as substitute for petrol. Liquid fuel from woody
biomass is more difficult than from sugar cane
because of cellulose component in wood.
Fermentation is final step in converting biomass
into fuel. For woody biomass the cellulose is
converted to sugars by acid-catalysed
hydrolysis before being converted to alcohol-
enzyme hydrolysis in development
Generally hardy broad leaf plants requiring
little fertiliser or water are preferred -
genetically modified (GM) crops Storage and water
content can be a problem
Water rather than land can be used to grow
biomass eg kelp or algae Need for cheap liquid
transportation fuel to replace petrol and diesel
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Photosynthesis

• CO2 H2O light ? O2 CH2O Carbohydrate
• Minimum of 8 photons each 1.8 eV, so 14.4 eV in
  all
• ? O2 and C fixed in carbohydrate that stores
  4.8 eV
• per C equivalent to 16 MJ/kg
• Maximum efficiency 33 (4.8/14.4)

(1000/30)(6 1023)(4.8)(1.6 10-19) J/kg
Only 50 of the energy of the solar photons can
be absorbed Losses (25) from the leaves -
reflection and transmission Maximum efficiency
is 12
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Photosynthesis in the Field
In the field the conversion efficiency is much
less 33 of solar radiation falls in growing
period 20 lands on the leaves 60
converted to biomass 40 on respiration.
Overall efficiency of 0.5
Useful estimate is 0.5 MW/ sq km
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Bioethanol
Sugar fermented to alcohol. Alcohol substitute
for gasoline C2H5OH 3O2 ? 2CO2 3H2O 30.5
MJ/kg cf C8H18 11.5O2 ? 8CO2 9H2O 48.2 MJ/kg

• Corn feedstock
• Corn contains starch a glucose polymer.
• Linkages are a-glycosidic - easily broken apart
  using human and animal enzymes.
• Enzymes catalyse decomposition of starch to
  glucose by hydrolysis
• C12H22O11 H2O ? C6H12O6 C6H12O6
• Sugar fermented by yeast or bacteria
• C6H12O6 ? 2C2H5OH 2 CO2 0.4 MJ/kg

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Biofuels
Forest burned for palm oil plantation in Indonesia
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Cost of bioethanol ? Cost of gasoline when oil
41/barrel 1.5 x1010 litres produced in US
(corn) and in Brazil (sugar) Only ? 2.5 of
gasoline used in US 4 litres/person/day
To produce another 2.5, 1/3 EJ/yr of ethanol,
would require 5 106 ha. This area is 3 of
the US cropland.

• Fossil Energy Ratio (FER)
• FER Energy supplied to customer / Fossil energy
  used
• Corn has FER of only 1.34
• Energy used in farming- harvesting, planting,
  fertilisers plus energy used in processing corn
  into alcohol

Need plants that have good FERs and are cheap to
produce
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Cellulosic Plants
Maltose Cellubiose a-glycosidic
b-glycosidic

• Cellulose, 40-60 of biomass, is a glucose
  biopolymer
• Linkages are b-glycosidic resistant to
  cleavage because of hydrogen bonding
• Hemicellulose, 20-40 of biomass, mainly the
  5-sugar xylose, interlinks the cellulose
• Hemicellulose and lignin enclose the cellulose
  bundles and protect them from microbial attack

eg Switchgrass- grows on marginal land,
perennial, little fertiliser or water required.
Cheap to produce
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Ethanol from Cellulose
Pretreatment with dilute acid to expose cellulose
and separate hemicellulose and lignin.

• Hydrolysis
• acid catalysed requires heat and pressure
• enzyme catalysis at low temperatures and
  atmospheric
• pressure - but currently enzymes too expensive
  and slow

Glucose then fermented. Yeasts recently
developed to ferment xylose. Bacteria under
investigation as fermentation can be quicker
Sugar yield
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Combustion of fuels

• Petrol (gasoline) principal component octane
  C8H18 12.5O2 ? 8CO2 9H2O
• On combustion 114 kg octane produces 352 kg
  carbon dioxide or 96 kg carbon

• Diesel, main component cetane (hexadecane) C16H34
  24.5O2 ? 16CO2 17H2O
• On combustion 226 kg cetane produces 704 kg
  carbon dioxide or 192 kg carbon

Need to take into account FER value of fuel to
calculate total carbon dioxide or carbon
produced.
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US annual consumption of Petrol

• Each year 5?1011 litres used . Petrol has an
  FER of 0.83. How much carbon is emitted?

114 kg octane produce 96 kg carbon, so 1 kg of
octane produces 0.84 kg of carbon. Petrol has an
FER of 0.83, so assuming petrol is pure octane
means 1 kg of petrol emits 1 kg of carbon.
The density of petrol is 0.73 kg per litre so
5?1011 litres corresponds to 3.7?1011 kg .This
amount would produce 0.37 Gt of carbon per
year. cf globally 7 Gt of carbon are emitted per
year
Petrol car engines 30 efficient Diesel car
engines 40 efficient
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Main bioenergy conversion routes
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Extraction and composition of landfill gas