CVEN 5838 Aug 28, 2008CVEN 5838 Aug 28, 2008

Lecture 2Lecture 2

Reservoir Capacity Yield AnalysisReservoir Capacity Yield Analysis(how to size a reservoir and measure its (how to size a reservoir and measure its

performance)performance)

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Reservoir Yield: Controlled Release from a Reservoir Yield: Controlled Release from a reservoir (or system of reservoirs). reservoir (or system of reservoirs).

Often expressed as a ratio of % of mean annual flow. E.g., 70% yield means the Often expressed as a ratio of % of mean annual flow. E.g., 70% yield means the reservoir can provide a regulated release of 70% of the mean annual flow.reservoir can provide a regulated release of 70% of the mean annual flow.

The Yield depends on the active The Yield depends on the active storage capacitystorage capacity of the reservoir of the reservoir

Reliability of Yield: probability that a reservoir will be able to meet the demand in any particular time interval (usually a year)

Reliability = Ns/N

Ns is number of intervals in which demand was met; N is the total number of intervals

Firm Yield: can be met 100% of time

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Estimating Active Storage CapacityEstimating Active Storage Capacity

Mass Balance Equation of ReservoirsMass Balance Equation of Reservoirs SSt-1t-1 + Q + Qtt – R – Rtt – L – Ltt = S = Stt

Where Where SSt-1 t-1 is storage at end of previous time intervalis storage at end of previous time interval SSt t is storage at end of current time intervalis storage at end of current time interval QQt t is inflows at current time intervalis inflows at current time interval RRtt is release at current time interval is release at current time interval LLt t is loss (evap/seepage) at current time intervalis loss (evap/seepage) at current time interval

Reservoirs have a fixed storage capacity, K, soReservoirs have a fixed storage capacity, K, so

SStt <= K for each interval <= K for each interval

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Mass Diagram Analysis (Rippl) MethodMass Diagram Analysis (Rippl) Method

1.1. Plot cumulativesPlot cumulatives

2.2. Add demand lineAdd demand line

3.3. Find max deficitFind max deficit

Find the maximum positive cumulative difference between a sequence of pre-Find the maximum positive cumulative difference between a sequence of pre-specified (desired) reservoir releases Rspecified (desired) reservoir releases R tt and known inflows Q and known inflows Qtt. .

Record of historical inflows is used, typicallyRecord of historical inflows is used, typically

Example: Nine period-of-record flows: Example: Nine period-of-record flows:

[1, 3, 3, 5, 8, 6, 7, 2, 1][1, 3, 3, 5, 8, 6, 7, 2, 1]

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6 7 8 9

time

infl

ow

vo

lum

e

InflowCumulative Inflow

Rt=4

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Mass Diagram Analysis (Rippl) MethodMass Diagram Analysis (Rippl) MethodRepeat the hydrologic sequence in case critical period is at endRepeat the hydrologic sequence in case critical period is at end

Start demand line at full reservoirStart demand line at full reservoir

Rt=4

Calculate Active Calculate Active Storage KStorage Kaa as max as max

accumulated storage accumulated storage over 2 successive over 2 successive periods of recordperiods of record

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Mass Diagram Analysis (Rippl) MethodMass Diagram Analysis (Rippl) MethodThe maximum capacity is determined by the Critical PeriodThe maximum capacity is determined by the Critical Period

Critical Drawdown Period:Critical Drawdown Period:

Longest period from full Longest period from full reservoir condition to reservoir condition to emptinessemptiness

Critical Period:Critical Period:

Longest period from full Longest period from full condition, through condition, through emptiness and to a full emptiness and to a full condition againcondition again

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Problems with Mass Diagram MethodProblems with Mass Diagram Method

Reservoir release needs to be constant (this is not Reservoir release needs to be constant (this is not accurate for monthly interval as demands are often accurate for monthly interval as demands are often seasonal)seasonal)

Assumes that future hydrology is like the pastAssumes that future hydrology is like the past

Cannot compute storage size for a given reliabilityCannot compute storage size for a given reliability

Evaporation and other losses that depend on level in Evaporation and other losses that depend on level in reservoir cannot be factored into analysisreservoir cannot be factored into analysis

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Reservoir Planning by SimulationReservoir Planning by Simulation

Simulation models are based on mass balance equations Simulation models are based on mass balance equations and take into account all time-varying processes as well as and take into account all time-varying processes as well as elevation-based processes (losses) elevation-based processes (losses) Simulation based techniques are called Simulation based techniques are called Behavior AnalysisBehavior Analysis

Why is it difficult to use simulation for reservoir sizing?Why is it difficult to use simulation for reservoir sizing?

Another type of “simulation” is based on deficit instead of Another type of “simulation” is based on deficit instead of storage. This solves some of the simulation problems.storage. This solves some of the simulation problems.

Approach is called Approach is called Sequent Peak AlgorithmSequent Peak Algorithm

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Sequent Peak AnalysisSequent Peak AnalysisLet KLet Ktt be the maximum total storage requirements needed; Set K be the maximum total storage requirements needed; Set K00 = 0 = 0

Example: Nine period-of-record flows: [1, 3, 3, 5, 8, 6, 7, 2, 1]Example: Nine period-of-record flows: [1, 3, 3, 5, 8, 6, 7, 2, 1]

Apply the equation consecutively for up to 2x the total length of the record.

The maximum of all Kt is the required storage capacity for the specified releases Rt and inflows Qt

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Accounting for LossesAccounting for LossesEvaporation and Rainfall (net losses) depend on Surface AreaEvaporation and Rainfall (net losses) depend on Surface Area

Surface area depends on storage non linearly: Surface area depends on storage non linearly:

But can be approximated linearly: But can be approximated linearly:

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Accounting for lossesAccounting for losses

Losses can alter the critical period and change the storage Losses can alter the critical period and change the storage capacitycapacity

Net evap (equations) can be included in storage based Net evap (equations) can be included in storage based simulations directlysimulations directly

Lele and Montaseri developed methods for including evap Lele and Montaseri developed methods for including evap in SPA in an interative approachin SPA in an interative approach(See McMahon et al., Sequent Peak Algorithm paper on (See McMahon et al., Sequent Peak Algorithm paper on class website)class website)

An alternative evap model An alternative evap model can be used directly with SPAcan be used directly with SPA

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ReliabilityReliability

ReliabilityReliability (time-based) - Ns/N (time-based) - Ns/N

Resiliance Resiliance – Speed of recovery– Speed of recovery

Vulnerability Vulnerability – severity of failure (volumetric reliability)– severity of failure (volumetric reliability)

(Tradeoffs on these 3 lead to very tricky design; several authors have developed indices (Tradeoffs on these 3 lead to very tricky design; several authors have developed indices that attempt to combine these (Loucks, 1997; Zongxue, 1998)that attempt to combine these (Loucks, 1997; Zongxue, 1998)

Reliability and Vulnerability can be integrated into SPA:Reliability and Vulnerability can be integrated into SPA:

Determine number of failure periods permitted (from reliability)Determine number of failure periods permitted (from reliability)

Determine reduced maximum reduced capacity permitted (from Determine reduced maximum reduced capacity permitted (from vulnerability)vulnerability)

See example in McMahonSee example in McMahon

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Classification of S-Y-P ProceduresClassification of S-Y-P Procedures(Storage – Yield – Performance)(Storage – Yield – Performance)

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Behavior Analysis – storage based simulationBehavior Analysis – storage based simulation(detailed simulations of processes)(detailed simulations of processes)

Case 1: Estimate System PerformanceCase 1: Estimate System PerformanceActive capacity of reservoir is known. Active capacity of reservoir is known. Series of demands is given (could be stochastic). Series of demands is given (could be stochastic). Starting condition is known or assumed.Starting condition is known or assumed.Historical or synthetic inflows are used Historical or synthetic inflows are used

(could be many traces) (index sequential or monte carlo)(could be many traces) (index sequential or monte carlo)

Case 2: Find size of reservoir under considerationCase 2: Find size of reservoir under considerationSSeries of demands is known (could be stochastic)eries of demands is known (could be stochastic)series of inflows is given (historical or generated stochastic)series of inflows is given (historical or generated stochastic)Performance criterion is specifiedPerformance criterion is specifiedEstimate reservoir capacity; do simulations; adjust until get performance Estimate reservoir capacity; do simulations; adjust until get performance desireddesired

Case 3: Estimate Yield of an existing reservoirCase 3: Estimate Yield of an existing reservoirSpecify performance criteria (reliability, vulnerability, maybe resiliance)Specify performance criteria (reliability, vulnerability, maybe resiliance)Use historic or stochastic hydrologyUse historic or stochastic hydrologyEstimate demand (yield) and iterate until meet performance criteriaEstimate demand (yield) and iterate until meet performance criteriaNeed to know and model detailed operating proceduresNeed to know and model detailed operating procedures

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Additional important topicsAdditional important topics

Optimization techniquesOptimization techniquessimple ones can give identical results to SPAsimple ones can give identical results to SPAmore complex methods can include cost more complex methods can include cost functionsfunctions

Multiple reservoir systemsMultiple reservoir systemssingle-reservoir techniques can be extended to multi-single-reservoir techniques can be extended to multi-

reservoir systems reservoir systems determine size at each sitedetermine size at each sitespecify operating policies for releases and demands specify operating policies for releases and demands

(heuristic policies have been developed)(heuristic policies have been developed)typical objective is to keep reservoirs balancedtypical objective is to keep reservoirs balanced