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Reservoir Sizing
Water stored in reservoir, lakes and stream are most important source of fresh water supply
If river discharges were constant in time, surface water resources is simple, no reservoir required
Unfortunate, river flow are stochastic in nature and variable with time
Two extreme condition occurs High flow caused flood Low flow caused water shortage (drought)
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The practical problem A water supply,
irrigation or hydroelectric project drawing from river may unable to satisfy the demands during low flow
Therefore, the main function of a reservoir is to stabilize the flow of water especially during dry spell
Streamflow, Q(t)
Spill
Diverted (Demand Area) Reservoir
(with storage Capacity, C)
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Reservoir defined Impoundment of
surface water across a river
Storage capacity estimated from the area-elevation curve (topography)
Various zones of storage in a reservoir
Spillway crest
U M N S
D Stream Bed
Sluiceway
D: dead storage M: minimum pool level U: Useful storage S: surcharge storage N: Normal pool level
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Reservoir/Dam from the sky
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SEMENYIH DAM, SELANGOR
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PROPOSED DAM SITE
dh
The topo map Q
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Storage capacity of a reservoir
Storage capacity of a reservoir is estimated using topographic map of the reservoir site
S = {(Ai+1 + A i)/2}* (dh) S i+1 = Si + S S i+1 = Si + (A i+1 + Ai) dh/2
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0
200000
400000
600000
800000
1000000
1200000
525 530 535 540 545 550 555 560
Ketinggian Pugak (m)
K
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u
a
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P
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m
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a
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T
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a
n
(
m
2
)
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
0 200000 400000 600000 800000 1000000
1200000
Luas Permukaan Takungan (m2)
S
t
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r
a
g
e
T
a
k
u
n
g
a
n
(
m
3
)
h (m)
A (m2)
A (m2)
S (m3)
dtt cSA baSA tt
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What and why low flow Low flow defined: Streamflow of less than
average flow Flow of water in a stream during prolonged dry
period The basic question:
How much water (Yield) can a reservoir collect water during low flow condition?
Yield defined the amount of water that a reservoir can supply during a specified time interval
Thus knowledge in storage-yield relationship (S-Y) of a reservoir is required
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Further questions a. Can the given demand be met from natural river flow or is reservoir required?
b. How much water can be reliably pumped from a river in a given time?
c. What is the probability that streamflow Q(t) will be less that a specified amount during a given period?
d. If the storage is necessary, how large the reservoir capacity, C, need to be to provide for a given controlled release or draft D(t) with acceptable level of reliability?
e. Therefore, the relationship between Q(t), C, D(t) and reliability must be found.
a. Question (a-c) is solved using concept, yield of unregulated streams (natural flow condition)
b. Question (d-e) is solved using storage-yield relationship ERT 246 Hydrology and Water
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Streamflow, Q(t)
Spill (Hydropower)
Diverted Controlled Release, D(t) (Demand Area)
Reservoir (with storage Capacity, C)
Q(t), D(t), C Optimization
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Yield of unregulated streams Those without artificial storage. Give example of
an artificial storage Source of inflow to the artificial storage
(reservoir) Source of water: slow flow or baseflow of the
rainfall hydrograph Tool of analysis
Flow duration curves Low flow frequency curves
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Flow duration curve Simplest and most informative mean of
showing the low flow characteristic of an unregulated stream
Defined: the percentage of time during which specified discharge were equalled or exceeded during the period of the record
Is a cumulative frequency distribution
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(1) (2) (3) (4)
Q(m3/s) Frequency
Cumulative frequenc
y %Cumulative
frequency Over 475 3 3 0.21 420-475 5 8 0.55 365-420 5 13 0.89 315-365 8 21 1.44 260-315 25 46 3.15 210-260 36 82 5.61 155-210 71 153 10.47 120-155 82 235 16.08 105-120 52 287 19.64 95-105 42 329 22.52 85-95 50 379 25.94
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(1) (2) (3) (4)
Q(m3/s) Frequency Cumulative frequency
%Cumulative frequency
65-75 83 520 35.59
50-65 105 625 42.78
47-50 72 697 47.71
42-47 75 772 52.84
37-42 73 845 57.84
32-37 84 929 63.59
26-32 103 1032 70.64
21-26 152 1184 81.04
16-21 128 1312 89.80
11-16 141 1453 99.45
Below 11 8 1461 100.00
Total days 1461
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Flow duration curve: procedure a. Group all data into class intervals (Column 1) b. Count the number of occurrence (frequency) of each
class interval (column 2) c. Class frequencies are accumulated beginning with the
largest discharge (column 3) d. Each cumulated frequency is expressed as a percentage
(column 4) e. Discharge is plotted against cumulated percentage of
frequency on normal graph paper or normal-probability paper or log-normal-probability paper
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Flow Duration Curve (Normal-normal graph)
050
100150200250300350400450500
0 20 40 60 80 100
%time equalled or exceeded
Q
(
t
)
m
3
/
s
.
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Flow Duration Curve plotted on log-probability paper
Q(t)
%tage of time exceeded 0.1 2 50 90 99.5
10
100
1000
- Flow duration curve Based on 4 years (1461 days) period - 2% of the 4 years period, Flow exceeded 290 m3/s - 96% of the 4 years period, The flow is between 12-290 m3/s - 50% time point provides the median value (45 m3/s) - Is the flow normally distributed?
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Uses of flow duration curves in reservoir design
90, 95, 96 and 99% - measures of a streams low flow 90% of time discharge exceeded
a measure of groundwater and river bank storage contribution to streamflow
Use to estimate hydropower potential If the slope of the curve in low flow portion is flat, groundwater
contribution is significant Steep curve poor baseflow or cease to flow condition Valuable tool for comparing basic characteristics of the catchment area
in particular the geology groundwater Related to water quality
Indicate the %tage of time that various levels of water pollution will occur following of the introduction of a pollutant of a given volume. Eg. Total Maximum Daily Load (TMDL).
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050
100150200250300350400450500
0 20 40 60 80 100
%time equalled or exceeded
Q
(
t
)
m
3
/
s
.Flat slope
Steep slope
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Assignment
A. You are required to obtain a topographic map of an area in Johor State. The lower reach of the river is the main outlet (intake) of the proposed reservoir. You are required to propose a reservoir to serve people at the downstream area of the river. Estimate the potential storage capacity of the proposed reservoir and plot graphs showing:
a). Water surface area-elevation relationship and b) Storage- surface area relationship of the reservoir c) Establish the reservoir equation
B. You are provided with a river flow data sets taken from the proposed project area
stated in Question A. Prepare the duration curve (for all data set given) using normal graph and log-
probability graph, of the selected river and discuss on the finding in relation to water resources. The discussion must be supported by at least two journal papers of the related subject.
baSA tt
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LOW FLOW FREQUENCY CURVE
Flow duration curves: use all kind of data Low flow duration curve: based on data sequence
(in order or in series) that are independent and homogenous
With independent and homogenous data, the probabilistic analysis of occurrence of a low flow can be determined
The data required Annual series (based on minimum flow event in each
year of record)
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Assignment # 2
Use the same data you used in Assignment #1, develop a low flow frequency curve of the selected river. For each year, divide the data into quarterly and use minimum mean monthly flow as low flow record.
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Storage-yield-performance (S-Y-P) relationship
Streamflow, Q(t)
Spill
D(t), Diverted (Demand Area) Reservoir
(with storage Capacity, S)
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Estimation of the capacity-yield relationship for a reservoir on a stream
Study the relationship between storage capacity (S), Release or draft D(t) and Reliability
Question: Given active capacity S and streamflow Q(t), how much yield D(t) is available for a given reliability, or
Given Q(t) and D(t) for a given reliability, what is the size of S
Storage-yield-performance (S-Y-P) relationship
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Flow conditions defined
Natural streamflow (virgin, unimpacted, unimpaired): flow in stream has not been affected by human influence like inter-basin transfer, diversions or land use change in the catchment or climate change
Unregulated stream; one does not have upstream diversions nor is regulated by an upsteram reservoir.
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Reservoir outflow and yield defined Yield is the controlled release from a reservoir
system Expressed as a ratio or % of the mean annual
flow to the reservoir Eg: 70% yield means that during the period of
analysis the system will provide a regulated yield of 0.7 times mean annual flow
Other terms: release, draft and regulation Demand: the amount of water required by a
demand center (irrigation scheme or township) Required design demand: the demand at a given
level of security or reliability Reservoir yield is the water available for
distribution to a demand center for a given storage capacity and a given level of security
Streamflow, Q(t)
Spill
D(t), Diverted (Demand Area) Reservoir
(with storage Capacity, S)
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Firm yield: the most important term in reservoir design
The yield that can be met over a particular planning period with a specified no-failure reliability
The largest quantity of flow that is dependable at the given site along the stream at all time
Usually based on historical record
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Safe yield
The yield from a water supply system after a detailed storage-yield analysis
100% reliability mean the yield is safe, but it is never occur
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Operational yield
To describe the yield of a system as obtained from simulation taking into account seasonal variations in demand and any restriction placed on supply
No knowledge of future inflows is assumed and decision are based only on the available water in storage
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Type of storage
Spillway crest
U M
N S
D
Stream Bed
Sluiceway
D: dead storage M: minimum pool level U: Useful storage S: surcharge storage N: Normal pool level
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Total storage, active storage, dead storage
a) Total storage: volume of reservoir at full supply equal the sum of active storage size and dead storage
b) Active storage: use for conservation purposes; water supply, navigation, irrigation
c) Full supply level is the level of the invert of fixed spillways
d) Dead storage is the volume of water held in the reservoir below lowest off-take (below this level, sediment may trapped)
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Finite storage Using a reservoir Peclet dimensionless number
(P), measure the relative importance of the mean and variance of the net inflows, i.e. reservoir inflow less the outlow
P>+1, the stored contents almost never reaches the lower boundary and the reservoir can be regarded as bottomless
P
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Date Q(in)m3/s Q(out)m3/s NetinflowJ 400 550 150F 550 496 54M 474 474 0A 591 626 35M 936 765 171J 1437 832 605J 1502 939 563A 1203 817 386S 662 905 243O 334 483 149N 251 466 215D 243 560 317
mean 56var 98039
d
d SP 22
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Critical period and critical drawdown period
Refer to the period from a full reservoir condition to emptiness
The period from a full condition through to emptiness and to a full condition again
The period from full to empty is known as critical drawdown period (US)
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Reservoir performance It is importance to characterize the likely future performance under the
wide range of possible demand and hydrologic conditions that are expected to occur during the reservoirs operating life
Performance criteria based on unsatisfactory operation (failure) during period of low reservoir inflow
failure is defined as the inability to provide the target demand during a given period
The main term to describe the performance of a reservoir system is reliability, i.e. the probability that the system can meet the target demand
Vulnerability quantifies the consequences of failure Resilience quantifies the ability of a reservoir to recover after a failure
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Unsatisfactory region
Range of Satisfactory performace value System performance
Indicator, e.g. release
Unsatisfactory region
Hypothetical numbers indicate by how much the target is over-supplied: a desirable outcome for water supply situation
Hypothetical numbers indicate by how much the releases deviate from the target demand due to under-performance
3 3
4 4
2
6
4
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Time-based reliability
NNsNF )(
NNsRt Rt = time-based reliability Ns = total number of intervals during which the demand was met
N = total number of time intervals in simulation
F = the shortage frequency Ns = total number of intervals during which the demand was met N = total number of time intervals in simulation
RtF 1
ERT 246 Hydrology and Water Resources
Time-based reliability
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Q(m3/s)
month
41
Volumetric Reliability
Nj
j
fjjj
V D
DDR
)(1
'
1 if Dj is 100% satisfied, i.e Dj=Dj Rv = volumetric reliability f = no of failure periods (=N-Ns) Dj = actual supply from reservoir system during jth failure period Dj = target demand during jth period N = number of periods in the simulation
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Resilience
It is necessary to know how readily a system will recover following failure
An indicator of the speed (probability) of recovery following failure
10;1
d
s
s
d ff
ff
is resilience, f s number of continuous sequences of failure period, fd is the total duration of the failure, i.e. N-Ns
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Critical Period Method
Based on continuity equation in which the required storage equals the maximum difference between outflow (draft) and inflow during a critical period.
The reservoir is assumed to be at full supply level at the beginning of the worst critical period
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Storage-yield relationship
Estimation of the capacity-yield relationship for a reservoir on a stream
Study the relationship between storage capacity (C), Release or draft D(t) and Reliability
Streamflow, Q(t)
Spill
Diverted (Demand Area) Reservoir
(with storage Capacity, C)
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Definition of Terms Critical period: a period during which a reservoir goes
from a full to an empty, without spilling The start of a critical period is full condition, the end is
the first empties Thus, only one failure can occur during a critical period
1980 1981 1982 1983 1984 1985 1986 1987 1988 1999
Full Storage Critical period
Critical period
Empty Storage
ERT 246 Hydrology and Water Resources
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