ASSESSMENT OF HYDROELECTRIC POTENTIALS AT THE OWU AND ERO-OMOLA FALLS IN KWARA STATE
B. F. Sule K. M. Lawal K. A. Adeniran
TECHNICAL REPORT NO. 7 ISBN: 978-978-915-055-7
NATIONAL CENTRE FOR HYDROPOWER RESEARCH AND DEVELOPMENT ENERGY COMMISSION OF NIGERIA
UNIVERSITY OF ILORIN, ILORIN, NIGERIA
MAY, 2011 Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
TABLE OF CONTENTS 1. EXECUTIVE SUMMARY 3 CHAPTER ONE 1.0 Introduction 5 1.1 General Introduction 5 1.2 Sources of Energy 6 1.3 Statement of Problem 6 1.4 Why Small Hydro 7 1.5 Aim of the Study 7 1.6 Objective of the Study 7 1.7 Physical Characteristics and Description of the Study Areas 7 1.8 Demographic Data 8
2. CHAPTER TWO 2.0 Theory of Hydropower Generation 10 2.1 Energy Production 11 2.2 Hydropower System 14
3. CHAPTER THREE 3.0 Study Approach and Technology 14 3.1 Data Collection 14 3.2 Determination of Energy Demand 14 3.3 River Stage Measurement 16 3.4 Measurement of Discharge 16
4. CHAPTER FOUR 4.0 Field Output and Data Analysis 17 4.1 Introduction 17 4.2 Instrumentation Details 17 4.3 Stream Discharge 19 4.4 Development of a Monthly Flood Rating Curve 19 4.5 Extension of Streamflow Data at Ero-omola Fall 23 4.6 Model Development 25 4.7 Determination of the Required Reservoir Capacity 28 4.8 Evaluation of Sediment Load or Sediment transport 29
5. CHAPTER FIVE 5.0 Potential Energy Assessment 31 5.1 Potential Energy Assessment of Ero-omola Fall 31 5.2 Potential Energy Assessment of Owu Fall 33 5.3 Hydropower Power Demand 34
6. CHAPTER SIX 6.0 Financial Justification 35 6.1 Introduction 35 6.2 Engineering Economics 35 6.3 Economics Analysis 35 6.4 Cost of Generation Per Kilowatt 36 6.5 Internal Rate of Return 36 6.6 Amortization Analysis 36
7. APPENDIX 1 40 APPENDIX 2 41 APPENDIX 3 48 APPENDIX 4 49 APPENDIX 5 55 APPENDIX 6 56 APPENDIX 7 57 APPENDIX 8 58 APPENDIX 9 59 APPENDIX 10 60 APPENDIX 11 61
8. REFERENCES 61
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
EXECUTIVE SUMMARY 1. General The study for the assessment of potential hydropower development of Owu and Ero-omola Falls commenced effectively by 20th of June, 2009. Various site visits were undertaken to facilitate gauge installation and hydraulic head survey. Gauge readers were recruited to monitor gauges, with provision of a motorbike for the gauge reader at Owu Fall, due to long distance of site from urban centre. Gauge readers were effectively engaged by 26th of November, 2009 and have since continued to monitor the gauge till date. Signboards were installed to indicate ownership of the measuring instrument at both sites. Ero-Omola has recorded about 450 days (15 months) of records while Owu Fall has about 217 days (7months) of records. The fewer months of records were due to conflict between the gauges readers employed for the site. Discharge measurement from both sites were evaluated to generate the discharge rating curves on excel programme and to establish the minimum and the maximum water level. 2. Discharge Computation Method There are different methods of determining river discharge. The choice of computation methods depends upon the equipment and observational method used during the gauging, flow conditions at the time of gauging, type of stream and the accuracy required. The arithmetic method is preferred, because it offers sufficient accuracy and quicker to perform than other methods. For the purpose of this report the Mean Section Method was utilized to evaluate the discharge. The raw data is presented in the annexure to this report. 3. Hydropower Potential a. Owu Fall with a hydraulic head of 95.5m has a potential hydro capacity of 8.81MW and annual generating capacity of 15425.12MWh. The minimum flow available for about 100% of the time from the flow duration curve is estimated at 9.9m3/s. Therefore a single pelton turbine is recommended. The total amount of energy so generated can be sold to National grid is estimated at N216,091,680.00 at N14.00/kWh. The internal rate of return was however negative. Owu Fall has a difficult terrain with relatively low runoff but consistent runoff yield. It is therefore suitable for only runoff river system as it is practically difficult to impound water behind the Fall. More so the distance to the 33kva National Grid at Omu Aran is about 189km, while that of Ero-Omola is just 48km. b. Ero-Omola Fall with an averages discharge of 22.8m3/s and a hydraulic head of 59.4m has a potential hydropower capacity of 8.64MW. The 100% flow rate from Ero-Omola may be bifurcated by 3 unit draft tube into the turbines at 7m3/s each. The total annual energy was estimated at 15137.28MWh at an economics cost of N211,921,820.00/annum using the NIPP multi-year tariff order of N14.00/Kwh. The total amount derivable from the power generation excluding other charges amount to about N213million with an internal rate of return (IRR) of 18.00%. This IRR although lower than the prevailing interest rate of 21% is still acceptable on the premise that, the present commercial interest rate in Nigeria is relatively high. Ero-Omola water
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
year is between April to March with a two to three month break of hydrological cycle. It is therefore necessary to provide a reservoir, sufficient enough to regulate flow for the turbines and to provide domestic and irrigation water supply to the host communities downstream. This off course is an additional cost to the investor. The benefit/cost ratio is however encouraging. 4. Constraints The Centre must collaborate with State Government to see that the only access roads to Owu Fall are rehabilitated. The deplorable condition of the road makes it un-passable during the rainy season and make site visit difficult. The present security situation of Owu site does not encourage installations of expensive instrument for now, due to constant vandalization, removal or theft. 5. Financial Positions The total budgetary provision for the two sites would have been draw down completely by the end of April 2011. It is therefore important to provide fund for the salary and wages of the gauge readers beginning from May 2011. The budgetary provision for the two site is estimated at N650,000.00 each, bringing the total sum required annually to about N1,300,000.00(this includes salary and wages of gauge readers, fuelling of motorbikes, instrument maintenance, site visits etc.). This request becomes necessary if the centre is to continue to sustain continuous and uninterrupted data acquisition of both sites. 6. Recommendations a. The next phase of this study is to provide detail topography of the site and to locate position of power house, fore bay, penstocks with detail engineering drawing and subject the overall cost to economic analysis. b. Thereafter this report will be publicly presented to provide the necessary information to investors to appraise and executes the project. c. An automatic data logger should be provided at Ero-omola. This is to minimize research cost and expenditure on data acquisition. Self-recording gauges that maintain a continuous record of stage are based on various types of sensors. The three most commonly used types of sensors are float- driven, pressure, and ultrasonic. In a typical installation of a float-driven, water-level sensor, the vertical movement of a float in a stilling basin, resulting from fluctuations in water level, is translated by a mechanical movement or an electronic signal. Ultrasonic sensors use acoustic pulses to sense water levels either by contact or noncontact methods. Stage-discharge relations may have to be periodically updated due to changes in the hydraulic characteristics of a stream reach over time, caused by erosion and sedimentation, bank vegetation, and other changes. It is therefore extremely important to make provision for continuous regular site visits, whenever the need arises.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
CHAPTER ONE
1.0 INTRODUCTION 1.1 General Introduction
Power is a very important infrastructural development of a nation. It is widely believed that an appropriate level of energy generation has always gone hand in hand with industrialization and economic development. Similarly a functional energy generation system often serves as an effective tool for National Economic Development. The need for comprehensive studies of hydropower operation of large water resources system is increasing at rapid pace because of the increasing interest in all facets of resources use and management. Complexity of water resource planning, design and operations studies, demand for a mathematical procedure that will select the optimum sizes and characteristics of components to produce a desired result. Many failures of water related projects are due to project planning on the basis of inadequate hydrological data, due in part to two factors: a. Data which are not accurately measured b. Too short time series of hydrological data not allowing reliable estimates of system performance In the later case some scientist suggests the postponement of the project until more reliable and accurate data are available. Although this suggestion is theoretically sound, it however lacks the requirement and needs of engineering practice. A better way to solving the problem may be the use of hydrological data from synoptic station within the same catchment which in combination with available hydrological data may improve the planning results. This is the basis of the stochastic theory approach utilized to extend flood data. The purpose of this research is to demonstrate the value of such deficit data in the optimization process of hydropower development. Inadequate hydrological data may lead to over or under design of the power plant. Stochastic theory is applied in order to minimize the risk of such uncertainties. The stochastic theory provides opportunity to forecast and extend short duration data in a planning process. In this context we have to distinguish between two types of hydrological uncertainty. a. The natural uncertainty due to random variation of hydro meteorological processes; b. If hydro-power project are planned and designed on the basis of rather short time series of observed hydrological data the danger of inaccurate solutions is high. 1.2 Sources of Energy
The three most important sources, which have become common and therefore referred to as conventional, are: (i) Thermal power (ii) Hydro-power (iii) Nuclear power The other sources of power generation are also valuable but the quantum of power produced by these sources is limited. Such other sources are: (i) Tidal power (ii) Solar energy (iii)
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Geo-thermal energy (iv) Wind power (v) Magneto-hydro-dynamic plants and (VI) Biomass Energy The focus of this research was limited to design of potentials hydropower generation only. Table 1.1, 1.2 and shows the status of hydropower generation and Electricity demand Scenarios in Nigeria. Table 1.1: Status of Hydropower Generation in Nigeria (Install Capacity) Year Generation Capacity Actual Losses generation(Peak) 2005 5,880 MW 2,500 MW 57% 2009 6,021 MW 3,700 MW 38% 2009(NIPP) 6,814 MW ------2011 (P) 11,000 MW ???? Source:Energy Commission of Nigeria
Table 1.2 Nigeria Electricity Demand Scenarios Scenarios Demand MW Period 2010 2015 2020 2025 2030 Reference (7%) 15,730 28,360 50,820 77,450 119,200 High Reference (10%) 15,920 30,210 58,180 107,220 192,000 Optimistic (11.5%) 16,000 31,240 70,760 137,370 250,000
Source: Energy Commission of Nigeria (2006)
1.3 Statement of Problem
Fresh water supplies, energy and environmental preservation are three of the most pressing issues facing humanity. In Nigeria poor planning and under investment had created a huge generation and supply deficit over time, despite improved routine maintenance for the existing hydro infrastructures. There is a heavy reliance on public electricity supply while demand for electricity keeps outstripping supply. The response to address irregular public power generation and transmission failure was the importation of various brands of gasoline generators into the country to augment supply, it is however obvious that a new approach and fresh initiatives to development of energy producing resources and the implementation of developmental plans has to be accelerated, if vision 2020 target is to be met.
1.4 Why Small Hydro
Hydroelectricity enjoys several advantages over most other sources of electrical power. These include high levels of reliability, proven technology, high efficiency, very low operating and maintenance cost, and the ability to easily adjust to load fluctuations. Hydropower project often provide flood control and recreational benefits. Hydropower does not produce waste
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
products that contribute to air quality problems, acid rain, and green house gases; it is a renewable resource that minimizes the use of other fuels (oil, gas and coal).
Poverty in Nigeria is associated with high unemployment, poor governance, corruption, lack of accountability, and gross violation of human rights, nepotism and a skewed income inordinate distribution. Additional factors include poor infrastructure and impaired access to productive and financial assets by women and vulnerable groups. In the framework of the Millennium Development Goals Report, the latest estimates revealed that over 70% of the population lives below the International income poverty line of $1 a day. (World Bank, 2007) A common belief is that guaranteeing a sustainable supply of affordable energy is one of the best ways to address poverty, inequality and environmental degradation everywhere on the planet. However, energy cannot be affordable unless its production and availability are sustainable. Increasingly, energy sustainability amongst others also means: connecting the entire urban and rural poor to reliable, sustainable economical sources of energy. This way we can guarantee improved living standard for a better quality of life. (World Bank, 2007) It is in response to these challenges, that the study was initiated
1.5 Aim of the Study The main purpose of this study is to establish, explore and optimize the hydropower potentials of Owu and Ero-omola Falls for the use of the rural communities.
1.6 Objectives of the Study In achieving the main aim stated above, the following objectives are covered. a. Installation of hydrologic instruments for data collection. b. Collection of hydrologic data and topographical maps of the two sites and adjoining catchments. c. Rainfall and run-off data studies. d. Development of flood duration curve. e. Estimation of energy generation potential with the runoff. f. Determination of potential hydropower generation capacity of Owu Falls. g. Economic analysis and financial assessment of both hydropower projects.
1.7 Physical Characteristics and Description of the study Areas: Owu Fall is located at Owa Kajola in Ifelodun LGA of Kwara State near Oro-Ago about 127km from Ilorin, the state capital (figure 1 shows the LGAs of Kwara State). The run-off is ׳perennial from a hill of about 95.5 m high. Owu Fall lies between Latitude North N08 20 .״34.7 ׳and E005° 08 ״34.8 ׳and between Longitude East E005° 08 ״23.1 ׳and N08° 20 ״23.2
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
The rainfall is moderate with general annual average of about 1,250mm with maximum rainfall occurring in the months of June and August and a low humidity of about 50%. The Ero-Omola Fall is located along Osi- Isolo-Ajuba Road off Osi-Idofin road in Ekiti LGA, (Araromi-Opin) about 116 km from Ilorin. The runoff is perennial and of higher unit discharge than Owu-Falls. The height of the Fall is about 59.4m high. The catchment area of Ero-omola Fall is about 45km2 with contribution from two rivers namely, Ero-river from Iddo- Faboro near Ifaki in Ekiti state and Odo-Otun from Ajuba itself. Ero-Omola Falls lies and between Longitude East E005° ״30.8 ׳and N08°09 ״34.6 ׳between Latitude North N08° 09 .״06.7 ׳and E005° 14 ״07.4 ׳14 1.8 Demographic Data
Population is a major driver of energy demand. The most important determinant of energy demand is the level of economic activity and its structure, measured by the Gross Domestic Product (GDP). The evolution of the GDP was guided by the projections assumed in the National Economic Empowerment and Development Strategy (NEEDS). The local government areas within the catchment areas of the proposed project are listed in Table 1.4 along with other LGAs in Kwara State. Table 1.3: Population of Kwara State (NPC, 2006) LGAs MALES FEMALES POPULATION Baruten 108153 101306 209459 Kaiama 68240 55924 124164 Moro 55630 53162 108792 Edu 104944 96525 201469 Pategi 62639 49678 112317 *Ifelodun 106056 99986 206042 Ilorin South 104504 104187 208691 Ilorin East 104402 99908 204310 Ilorin West 181875 182791 364666 Asa 64982 61453 126435 Oyun 48601 45652 94253 Offa 46266 43408 89674 *Irepodun 75539 73071 148610 *Isin 30833 28905 59738 *Oke-Ero 29515 28104 57619 *Ekiti 28402 26448 54850 Total 1220581 1150508 2371089 *Study Areas
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Fig. 1:Map of Kwara State showing Local Government Areas. Owu and Ero-Omola Falls are located in Ifelodun and Ekiti LGAs.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
CHAPTER TWO
2.0 THEORY OF POWER GENERATION
2.1 Energy Production
Hydroelectric power production from a given reservoir at any time, t depends on the installed capacity of the turbine (generators), turbine release, generating head, the number of hours of power generation in a period, the plant factor, the efficiency of the turbine. In hydropower, the potential energy of the Falling water is converted to mechanical energy which is used in rotating the turbine. The Potential energy is given as: (Loucks et al, 1981). PE= mgh (2.1) where m =is the mass of the Falling water g =is the acceleration due to gravity h =is the Falling head A cubic meter of water, weighing 103 kg, accelerating at a rate of 9.81m/s2 over a distance of one meter, results in 9.81 x 103 joules (Newton-meter) of work. The work done in one second equals (joules per second) is of power produced in watts. Hence an average flow of tqˆ (m3/s) 3 Falling a height of Ht (m) in period t yields 9.81 x 10 tqˆ Ht watts or 9.81 tqˆ Ht Kilowatts. Multiplying by the number of hours in period t yields the kilowatt-hours of energy produced from an average flow of tqˆ in period t. The total kilowatt-hours of energy KWHt produced in period t, assuming 100% efficiency is (Sharma, 1979)
E=KWHt =9.81 qˆ H(seconds in period t) (2.2) 3.6 x 103
Since the total flow qt in period t, in units of 106 m3, equals the average flow rate tqˆ (m3/s) times the number of seconds in the period divided by 106, the total kilowatt-hours of energy produced in period t given a plant efficiency of e is equals
E = KWHt = 2730qtHt (2.3)
Equation (2.3) implies that the kilowatt-hours of energy KWHt produced in period t, are proportional to the product of the plant efficiency, the productive storage head Ht and the flow qt through the turbine. The amount of electrical energy produced also depends on the installed kilowatts of plant capacity P as well as on the plant factor Ft. The plant factor is a measure of hydroelectric power plant use and is usually dictated by the characteristics of the power system supply and demand.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
The plant factor F is given as: Ft =Average load on the plan(2.4) Installed plant capacity
The plant factor accounts for the variability in the flow rate during each period t and this variability is pre specified by those responsible for energy production and distribution. It may or may not vary for different period’s t. The total energy produced cannot exceed the product of the plant factor Ft, the number of hours in the period ht and the plant capacity P, measured in kilowatts.
KWH = ft ht P (2.5)
FIRM ENERGY = Pdesign x x 24 x 365 kWh (2.6)
= 0.2 (A reduction factor due to streamflow fluctuations)
2.2 Hydropower system. 2.2.1 The major types of hydroelectric power development are (Sharma, 1979): a. Run-of river development The runoff river plant are such plant that do not substantially alter the flow regime of the river, this implies that the river is not diverted materially away from its natural course, since no impoundment is envisaged. b. Pondage development (Dam toe based) Pondage developments are reservoirs developed to provides uninterrupted or balance inflow for day to day fluctuations in the amount of inflow available for power productions. Most often the power plant is located at the dam toe. c. Storage development is similar to pondage development as described above. d. Regulating development (canal Fall based) This are the hydropower plant fed through a regulated outlet from the reservoir. e. Pumped storage development (diversion) The pumped storage plant as the name implies are those plants whose inflow for power generation is augmented through a system of pumping unit. Regulating development is proposed at Ero-omola Fall, while Owu Fall is suitable for Runoff River plant. The proposed typical schematic design diagram for the two sites is as shown in Figure 2.1 and 2.2: The major components in the scheme are: a) Gross head (H). The gross head is the difference of the water level in the head race and the
water level in the tail race.( for a run-off river plant) b) Net Head (h). The net head (or effective head) is the head available for the turbine. It is equal
to the difference of total head at the point of entry and at the point of exit of the turbine.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
i. For a pelton wheel or impulse turbine,
h=H –Z –hf (2.7) Where:
H =gross head (m)
Z= is the height of the pelton wheel exit above the tail race level and hf= is the loss of head in the penstock.
2 ii. For a reaction turbine. h=H-(Vd) - hf(2.8)
2g-
Where Vd = is the exit velocity and other terms are as defined above.
c) Operating Head. The operating head is equal to the difference of the
water level in the forebay (or foreway) and that in the tail race.
FIGURE 2.1: OWU FALL
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
FIGURE 2.2: ERO-OMOLA FALL
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
CHAPTER THREE
3.0 STUDY APPROACH AND METHODOLOGY
3.1 Data Collection Topographical map, Stream flow, hydraulic head and pipeline length must be estimated or measured, before one can calculate the power that could be developed from a stream. Stream flow is the most difficult to measure or estimate. Understanding of its sources, its fluctuations and flow measurements is important.
3.2 Determination of Energy Demand A constant monthly energy demand is defined from an assumed installed capacity and chosen plant factor. The monthly energy demand as follows:
FE (t) = IC * n hours * PF(t) (3.1)
Where FE (t) is the target monthly firm energy demand (MWh) and other variables are previously defined.
IC=installed capacity MW
N =no of operating hours
PF=Plant factor
Monthly firm energy demand was computed from the above equation: Owu Fall with installed capacity of 8.81MW over assumed 8 hours of operation and plant factor of 0.25 is estimated at 17.62MWh or 211.14MWh/annum, while Ero-omola Fall with installed capacity of 19.93MW over an assumed 8 hours of operations and plant factor of 0.25 is estimated at 39.86MWh or 478.32MWh/annum.
a) Population Estimate Population is a major driver of energy demand. From the demographic data, the projected population figure was deployed in the estimation of energy demand of the communities. The project catchment areas comprises of about five local government areas namely; Ekiti,Oke-ero, Isin, Irepodun, and Ifelodun LGAs with a combined population of 526,859 by the 2006 population census. This is projected to 2036 at a National population growth rate of 2.83% and in consideration of 25 years life span of the proposed project. The projection was achieved with the relation: n Pn =Po (1 + r) (3.2)
526,859 X (1.0283)25 = 1,058,499
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
b.) Electricity Demand per Capital
The electricity demand per capital of 321.59Kwh published by Energy Commission of Nigeria (2006) was adopted for this study.
c.) Peak Domestic Electric Load demand Using the annual electric energy demand, load factor of 0.75, transmission and distribution losses; approximate estimates of the peak load demand was obtained. The highest growth scenarios gives a peak demand 0f 3157MW.(NERC, 2009)
d.) Projected Electricity Demand
In accordance with the National Energy Policy (2003), access to electricity by household is expected to increase to 75% by year 2020 for urban centre while that of rural was put at 55%. This study assumed an average projected electricity demand of the community to grow by about 55% due to development of many small agro businesses within the project area.
3.3 River Stage Measurement The river stage is the height of the water surface above the mean sea level (msl). For convenience, the datum was arbitrarily selected at the lowest point on the river bed. The river stage was measured to compute the cross-sectional area of the river so that the discharge can be determined using the OTT current metre obtained from Lower Niger River basin Development Authority.
3.4 Measurement of Discharge A river discharge is the rate at which water flows through a cross section and is expressed as volume per unit time.
The following methods are commonly used for the measurement of discharge in a river. 1. Area-velocity method 2. Slope-area method 3. Salt-concentration 4. Moving-boat method 5. Electromagnetic and ultrasonic 6. Indirect methods A relationship between stage and discharge is required to convert stage measurements to flow rates. Measurements of head were converted to flow rates. In this report the velocity-area method was used for measuring the discharge of both sites. 3.4.1 In this method, the discharge is determined from the area of cross section and the mean velocity. The area of cross section of the stream is determined from the profile of the stream bed obtained by survey.(Appendix 1) The river cross section was divided in to a suitable number of vertical segments (or strips).About 10 segments were taken in the case of Owu, while Ero-omola had about 15 segments. The total discharge in the river is the total sum of
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
various segments. The discharge in each segment is equal to the area of the segment multiplied by the mean velocity of flow. The mean section method was used to estimate the discharge, in this method; the segment is taken between two vertical lines on which the velocity and depth are measured. The velocity in the segment is taken as the average of the
mean velocities V1and V2 determined at the two adjacent verticals. Similarly the depth is also
taken as the average of two depth d1and d2. Thus the discharge in the segment is given by
푑 + 푑 푉 + 푉 ∆푄 = 푏 1 2 1 2 (3.3) 2 2 푇표푡푎푙푑푖푠푐ℎ푎푟𝑔푒 푄 = 푄 (3.4)
3.4.2 Determination of Velocity (V): For the measurement of discharge, the mean velocity (V) is required at various vertical lines as stated above. The following methods were used for the sites.
1. Floats Method 2. Current Meter Method both float and current metre method was undertaken on the field for accuracy checks. a.) Floats method: In this method, a straight and uniform reach of the river was selected for the float to travel. The time t taken by a float to travel a certain distance L is measured. There are three types of floats commonly used in practice. (i) Surface floats, (ii) Double floats (iii) Velocity rods. The study adopted surface floats. The surface floats are generally made of wood (or any other light material) so that they can float. Wooden discs of 7 – 15 cm diameters were used. As the surface floats travel at the water surface, they give the surface velocity. The mean velocity is usually taken as 0.85 times the surface velocity. b.) Current Meter
A current meter is generally used for the measurement of velocity in a river. The current meters are basically of two types.
(ii). Cup-type current meter (iii). Propeller-type current meter.
The accuracy of the cup-type current meter is about 0.3% for the velocity greater than 1 m/s. The main disadvantage of a cup-type current meter is that its accuracy is low when there is an appreciable vertical component of the velocity.
The basic principle of both types of current meters is the same; namely, when a current meter is inserted in flowing water, there is an unbalanced drag on the rotating element (cup or propeller) which starts rotating. As the velocity increases, the speed of rotation increases. The current meter is calibrated to give the velocity corresponding to different speeds of rotation. Manufacturers also provide the calibration chart which gives the relationship between the velocity and the number of revolutions per second. Generally, it follows a linear relationship,
푣 = 푎푁 + 푏 (3.5) where v is the velocity at the instrument location, N is the number of revolutions per second, and a and b are the constants of meter obtained by calibration. These constants are determined by towing the instrument in a towing tank in the laboratory. The current meter gives the velocity (v) at a point. For determination of the discharge in the river, the mean velocity (V) along a vertical line is required.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
CHAPTER FOUR
4.0 FIELD WORK OUTPUT AND DATA ANALYSIS 4.1 Introduction Several visits were undertaken by the research team to Ero-omola and Owu Falls project between September 2009 and March 2011. The purpose of the visit was to obtain stage- discharge relation and preliminary peak discharge data for the two sites. Stream flow measurement were undertaken to determine the extent and dependability of the flow. 2 Nos. metric steel gauges were installed at the bottom of Fall at Owu and Ero-omola site as well. Table 4.1: Details of Gauge at Owu and Ero-omola Falls 1. Item Owu Fall Ero-omola Fall 2. Purpose River Stage River Stage 3. Type Self illuminated steel gauge Self illuminated steel gauge 4. Station Bench +455.51m +451.60m Mark 5. Datum Nigeria Ordinance Nigeria Ordinance Datum/Universal Traverse Datum/Universal Traverse Mercator (UTM) Mercator (UTM) 6. Gauge +480.7m +449.996m Elevation(m) 7. Water level +426.2m +449.8m (m) 8. Gauge Height 3 4 (m) 9. Location N080 20’ 40’’ and E050 08’ 56’’ N080 09’ 48’’ and E050 13’ 09’’ 10 Date 12th September 2009 11th September 2009 Established
4.2 Instrumentation Details
An OTT current metre obtained from the Lower Niger River Basin Development Authority was deployed for the streamflow measurement. The instrument specification is as indicated below:
Type: Propeller Current Metres (OTT-C31-BAREL 17929)
Propeller Diameter: 125mm
Impulse: 1
Error: +/- 0.25
The calibration equation of the instrument is given as;
V = 0.2483 n +0.011 for n=< 0.59 where n revolution per seconds
V = 0.2619 n + 0.003 for n= < 9.21
Discharge measurement trials were carried out with the instrument on both sites to determine its level of accuracy. The float method was equally carried out as a check on the calibrated instrument. The
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
float method involves the use of floating material moving under the drag of the river flow, so as to evaluate or compute the speed or velocity of the river-flow. The float method trials result at Ero- Omola Fall is as indicated in Table 4.2.The float method was carried out over a uniform distance of 5m along the stream. Stop watch was used to determine the time of travel of the float along the stream. The computation of the discharge is as follows: T=Time lapse (in seconds)
Velocity =Distance (L)/Time
Discharge=Area x Velocity
Table 4.2: Discharge computation of float method Trials at Ero-omola Fall from 21-26th October 2009
Distance(m) 5 5 5 5 5 5 Segment Area 4.75 4.25 4.75 4.3 4.8 4.75 (m2) T(Time)(S) 8.43 3.55 3.38 3.67 3.85 3.29 V(m/s) 0.59 1.41 1.48 1.36 1.29 1.52 Q(m3/s=VA 2.802 5.992 7.030 5.848 6.192 7.22 35.084
The time travel by the float along subdivision of 5m segment on the stream was determined with a stop watch. The total discharge of 35.084m3/s was obtained during the trials. Similar trials were also carried out with the current metre. The trials result is as indicated in Table 4.3
Table 4.3: Result of Current Metre Trials at Ero-omola Fall
Date 18/10/2009 19/10/2009 20/10/2009 21/10/2009 22/10/2009 Water level(m) 1.98 1.98 1.95 1.89 1.87 Discharge 48.79 48.60 47.31 41.75 35.4
Similar trials carried out at Owu Fall are indicated in Table 4.4 and 4.5 respectively.
Table 4.4: Results of trial of float method at Owu Fall from11th-15th November 2009 Distance(m) 3 3 3 3 3 3 Segment Area 6.8 6.8 6.4 5.35 6.8 6.5 (m2) T(Time)(S) 12.13 11.97 7.60 5.53 12.00 24.9 V(m/s) 0.25 0.25 0.39 0.54 0.25 0.12 Q(m3/s 1.70 1.70 2.50 2.89 1.70 0.78 11.27
Total Discharge = 11.27m3/s (November Peak)
Table 4.5Result of Current Metre Trials at Owu Fall
Date 11/9/2009 12/9/2009 13/9/2009 14/9/2009 15/9/2009 Water level(m) 0.98 0.97 0.95 0.92 0.89 Discharge 11.02 10.88 10.58 10.14 9.703
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Subsequent discharge measurements were carried out each month in order to have a relatively spread of the flood discharge throughout the year. The rating curve equations were developed from the discharge so obtained each month.
4.3 Stream Discharge
Subsequent discharge measurement at Ero-Omola and Owu Falls were computed on the bases of arithmetic method using the current meter measurements provided. The horizontal distance across the stream was measured from the edge of the water at one bank. Depths were measured from the water surface.
The cross-section at Owu Fallis shown in Figure 4.1, with the location of each of the current meter measurements of point velocity. The Qi for each of the ten 1.0-m wide flow subareas are estimated and summed to obtain the total flow. The cross-section area Ai for each subarea is estimated as depth multiplied by 1-m width. The mean velocity in each subarea is estimated as the average of the flows at measured depth. The measured value is as indicated in Table 4.6
Table 4.6: Result of discharge measurement carried out at Owu Fall
2 Ai m 0.5 2.2 3.7 4.3 3.7 2.8 2.4 1.8 1.1 0.7 Vi (m/s) 0.030 0.044 0.070 0.070 0.065 0.060 0.054 0.049 0.041 0.035 3 Qi=m /s 0.0150 0.0968 0.3010 0.3010 0.2405 0.1680 0.1296 0.0882 0.0451 0.0245 Q = 0.0150 + 0.0968 + 0.2294 + 0.3010 + 0.2405 + 0.2405 + 0.1680 + 0.1296 + 0.0882 + 0.0451 + 0.0245
Q = 1.34 m3/s (January, 2010)
Distance across Owu stream in meters
1 2 3 4 5 6 7 8 9 10
Figure 4.1: Owu-Fall Stream Cross-section (Ero-Omola Fall cross section is presented in Appendix 1)
Similar stream flow measurements were carried out at Ero-Omola Fall. The stream cross-section or profile is shown in Appendix 1. The details computation is as indicated in Appendix 2. The total discharge of 5.40m3/s (January, 2010) were obtained from 15Nos. sub-divided segment of the profile.
4.4 Development of a monthly flood Rating Curve 4.4.1 A staff gage is the simplest device for measuring river stage or water surface elevation. The staff gauge is a graduated self illuminated strip of metal marked in metres and fractions thereof. Water levels were read daily, recorded and collated on monthly basis by the observer employed. Streamflow discharge measurement normally involves: (1) establishing the relationship (rating curve) between water surface elevation or height above a reference datum (stage) and discharge (flow rate) at a gauging station.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
(2) continuously or periodically measuring stage at the gauging station (3) transforming the record of stage into a record of discharge by applying the rating curve. Limited numbers of discharge measurements (10Nos.) were undertaken each month for a range of stage to define a relationship between stage and discharge at the two gauging station. The stage- discharge relation, which is the rating curve, is then combined with continuous periodic stage measurements to record discharge as well as stage simultaneously. The rating curve was converted to discharge by Excel software and was subsequently extended for about 25 years. The extension became necessary so as to ascertain the viability of the two sites for hydropower development. 3 For a gauge height H (m) at point of zero flow Ho ; the Discharge Q (m /s) is related to height H(m) as follows: n Q =K (H - Ho) (4.1) The rating equations (Sharma, 1979) relation is giving as: n Q = K H (when Ho=0) (4.2) Where
Q = Discharge (m3/s)
H = Gauge Height (m)
Ho = Zero Gauge Height (m) n & k = Constants
This is a parabolic equation which plots as a straight line on double logarithmic graph sheet. K &n are determined using the least square method
The procedure for estimating discharge from the gauge height measurements is the Least Square Method.
n 4.4.2 Let Q = KH (since Ho =0 from installation) be the function to be fitted to the given data. Taking logarithms of both sides, we obtain the relation
log Q = log K + n log H (4.3) which is of the form Q = a0 + a1, where Q = log Q, a0 = log K, a1 = n log H. Then k and n can be calculated from the formulae a0 = log K and n = a1.
∑Log Q =NLog K + n∑Log H (4.4)
∑Log Q Log H = Log K ∑Log H + n ∑(Log H) 2 (4.5)
Where: N = Numbers of pairs of observation
These two equations are solved simultaneously to determine constant k & n respectively for each rating equation of each month. The computation for January rating curve is as indicated in Table 4.7 while February to December is presented in Appendix 3. While Owu Fall Least Square (LSM) Computation for November rating curve is shown in Table 4.8.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Table 4.7:Ero-omola January Flood Rating Curve (LSM) S/n H (m) Q(m3/s) LogH Log Q (Log H)2 Log Qlog H 1 0.47 6.5 -0.327902142 0.812913 0.107519815 0.266556031 2 0.47 6.5 -0.327902142 0.812913 0.107519815 0.266556031 3 0.47 5.5 -0.327902142 0.740363 0.107519815 0.242766512 4 0.46 6.4 -0.337242168 0.80618 0.11373228 0.271877882 5 0.46 6.4 -0.337242168 0.80618 0.11373228 0.271877882 6 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013 7 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013 8 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013 9 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013 10 0.45 6.3 -0.346787486 0.799341 0.120261561 -0.2772013 SUM -3.392128194 7.975252 1.151331808 2.705640838
∑Log Q =NLog K + n∑Log H------1 ∑Log Q Log H = Log K ∑Log H +n ∑(Log H)2 ------2
7.975252 = 10 log K + n (-3.392128194)1 2.705640838 = (-3.392128194) log K + n (1.151331808) 2
By solving these equations simultaneously k & n are estimated thus:
K = 9.206 n = 0.491
Q = K Hn Q = 9.206 H 0.491(4.6)
The twelve rating equations obtained from Ero-omla records was utilized to convert the gauge readings to streamflow data (Appendix 4). The streamflow data generated by the Owu Fall rating equations is indicated in Appendix 5. The January rating curve is shown in Figure 4.2. While that of Owu Fall is shown in Figure 4.3.The summary of rating curve coefficient is presented in Table 4.9
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Figure 4.2:Ero-omola January Flood Rating Curve
JANUARY FLOOD RATING CURVE 0.35 y = -0.02ln(x) + 0.286 R² = 0.997 0.345
0.34
0.335
LOG H (m) H LOG GAUGE HEIGHT GAUGE 0.33
0.325 0 0.05 0.1 0.15 0.2 LOG Q (m3/S)
Table 4.8: Owu Fall November Flood rating Curve H(m) Q(m3/s) log Q log H (log H)2 logQlogH 0.27 1.986 0.298 0.103 0.011 0.0307 0.29 2.184 0.339 0.11 0.012 0.0373 0.24 1.698 0.229 0.093 0.009 0.0214 0.22 1.512 0.179 0.086 0.007 0.0154 0.21 1.42 0.152 0.083 0.007 0.0126 0.98 11.02 1.042 0.297 0.088 0.3095 0.97 10.88 1.037 0.294 0.086 0.3049 0.95 10.58 1.024 0.29 0.084 0.297 0.92 10.14 1.006 0.283 0.08 0.2847 0.89 9.703 0.987 0.276 0.076 0.2724 Total 6.293 1.915 0.46 1.5859
1.586=1.915 log k + 0.46n------1 6.294=10log k +1.915n ------2 by resolving above equation simultaneously we have k=11.33 n=1.33 Ho=0 Which gives the rating equations as : Q=11.33*H^1.33 for H> 0.20
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Figure 4.3: Owu Flow Duration Curve
OWU NOVEMBER FLOOD RATING CURVE 0.35 0.3 0.25 0.2 0.15 0.1
GAUGE HEIGTH (m) HEIGTH GAUGE 0.05 0 0 0.2 0.4 0.6 0.8 1 1.2 DISCHRGE Qm3/s
Table 4.9: Summary of Coefficient of Rating Equations.(Ero-omola)
Months K N Coefficient of Determinant *(R2) January 9.206 0.491 0.0463 February 9.253 0.765 0.815 March 9.089 0.934 0.9857 April 10.496 1.049 0.8318 May 10.229 1.455 0.9954 June 8.539 2.258 0.9727 July 0.610 7.789 0.9834 August 12.65 1.517 0.941 September 25.308 0.400 0.8949 0ctober 1.166 5.505 0.9285 November 17.167 2.753 0.9471 December 1.617 5.977 0.8902 *R2=This is a measure of the strength of relationship between the predictive and response variables
4.5 Extension of Streamflow Data at Ero-omola Fall
One year stream flow data generated by the rating equation at Ero-omola has to be extended in order to fulfill other hydrological analysis requirement. In order to achieve this, the Model proposed by Thomas and Fierring in 1962 according to McMachon and Mein (1978) was adopted. The model utilized Markov model to represent actual stream flow when the monthly stream flow, qi, are normally distributed and follow a first – order auto regressive model. The algorithm for the Thomas and Fierring model is giving as:
2 1/2 푞푖+1 = 푞 푗 +1 + 푏푗,푗+1 푞1푞 푗 + 푍푖+1푆푗 +1 1 푟푗 ,푗 +1 (4.7)
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
th th where qi+1, qi = monthly flows during (i + 1) , i from the start of the synthesized sequences,
th th 푞 푗 +1, 푞 푗 = mean monthly flows during (j + 1) , j ( j =1,2,--- 12 ),
th th 푏푗,푗 +1 =least squares regression coefficient for estimating (j+1) flow the j flow
푆푗 +1 ÷ 푏푗,푗 +1 = 푟푗,푗 +1 ÷ (4.8) 푆푗
Zi+1 = normal random number with mean of zero and variance of unity
th th Sj+1, Sj = standard deviations of flows during the (j+1) , j seasons, and
th th rj,j+1 = correlation coefficient between flows in , j and (j+1) seasons.
If N years of data is available, the calculation for the terms in the Thomas – Fierring model for each month, j = 1, 2, 3 ……………………… 12 in accordance to McMahon and Mein (1978) include:
(a) The mean flow
푞 푞 = 푗푖 ÷ (4.9) 푗 푁 ÷
(b) The standard deviation
2 푞 푞 푆 = 푖 푗푖 푗 (4.10) 푗 (푁 1)
(c) The correlation coefficient with flow in the preceding month
푖 푞푗푖 푞 푗 (푞푗+푖,푖푞 푗+1) 푟푗,푗 +1 = (4.11) 2 2 푖 푞푗푖 푞 푗 푖(푞푗 +푖,푖푞 푗+1)
To use the model to generate monthly flows at a site, the monthly means, standard deviations and lag one serial correlations are required and these parameters were obtained from analysis of monthly historical flows of River Akamo and River Oshin. In order to run the model, q1 is set as: 푞1 = 푞 퐽퐴푁 and the synthetic flow q1, q2, q3, q4, ……… was computed successively. The model is restricted to normally distributed flows, that is Zi is considered to be a Normal random number and is the only unknown in the model and for each step it can be calculated as a pseudo-random normal number. The model is the set of twelve regression equations following the pattern of equation (4.7) and presented in equations 4.12(a) – 4.12(l).
푞1 = 푞 퐽퐴푁 (4.12a)
2 1/2 푞2 = 푞 퐹퐸퐵 + 푏퐽푎푛 /퐹푒푏 (푞1푞 퐽푎푛 ) + 푍2푆퐹푒푏 1 푟퐽푎푛 /퐹푒푏 (4.12b)
2 1/2 푞3 = 푞 푀푎푟 + 푏퐹푒푏 /푀푎푟 (푞2푞 퐹푒푏 ) + 푍3푆푀푎푟 1 푟퐹푒푏 /푀푎푟 (4.12c)
2 1/2 푞4 = 푞 퐴푝푟 + 푏푀푎푟 /퐴푝푟 (푞3푞 푀푎푟 ) + 푍4푆퐴푝푟 1 푟푀푎푟 /퐴푝푟 (4.12d)
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
2 1/2 푞5 = 푞 푀푎푦 + 푏퐴푝푟 /푀푎푦 (푞4푞 퐴푝푟 ) + 푍5푆푀푎푦 1 푟퐴푝푟 /푀푎푦 (4.12e)
2 1/2 푞6 = 푞 퐽푢푚 + 푏푀푎푦 /퐽푢푛 (푞5푞 푀푎푦 ) + 푍6푆퐽푢푛 1 푟푀푎푦 /퐽푢푛 (4.12f)
2 1/2 푞7 = 푞 퐽푢푙 + 푏퐽푢푛 /퐽푢푙 (푞6푞 퐽푢푛 ) + 푍7푆퐽푢푙 1 푟퐽푢푛 /퐽푢푙 (4.12g)
2 1/2 푞8 = 푞 퐴푢𝑔 + 푏퐽푢푙 /퐴푢𝑔 (푞7푞 퐽푢푙 ) + 푍8푆퐴푢𝑔 1 푟퐽푢푙 /퐴푢𝑔 (4.12h)
2 1/2 푞9 = 푞 푆푒푝 + 푏퐴푢𝑔/푆푒푝 (푞8푞 퐴푢𝑔 ) + 푍9푆푆푒푝 1 푟퐴푢𝑔 /푆푒푝 (4.12i)
2 1/2 푞10 = 푞 푂푐푡 + 푏푆푒푝 /푂푐푡 (푞9푞 푆푒푝 ) + 푍10 푆푂푐푡 1 푟푆푒푝 /푂푐푡 (4.12j)
2 1/2 푞11 = 푞 푁표푣 + 푏푂푐푡 /푁표푣 (푞10푞 푂푐푡 ) + 푍11푆푁표푣 1 푟푂푐푡 /푁표푣 (4.12k)
2 1/2 푞12 = 푞 퐷푒푐 + 푏푁표푣 /퐷푒푐 (푞11푞 푁표푣 ) + 푍12푆퐷푒푐 1 푟푁표푣 /퐷푒푐 (4.12l)
Z is calculated for each step as a pseudo – random normal variate.
4.6 Model Development
The multiple linear regression theory is based on the assumed distribution of all variables in accordance with the Gaussian normal distribution. Therefore, mathematical integrity requires that each variable be transformed to a normal distribution. It has been established that logarithms of streamflow are approximately normally distributed in most cases, however for computational efficiency, it is convenient to establish the model from a transform logarithms of streamflow data. The data from the two synoptic stations (Oro and Omu Aran) were converted to natural logarithms before the data was analyzed for the determination of various model coefficient variables. The data for Ero-omola were extended for 25 years based on the twelve model equations generated from the analysis. In accordance with the above basic procedure, historical streamflow data with relatively long years of records obtained from the Lower Niger River Basin Development Authority was utilized in extending the short data from Ero-omola. The data was obtained from the 1982 Hydrological Year Book published by the hydrology department. The raw data and the flood hydrograph is attached in Appendix 10 of this report. The method of Least Square method was used to obtain the Regression Coefficient and other statistical parameters between the short streamflow data from Ero-omola and the long historical streamflow data from River Oshin and River Akamo. These two rivers are located between Oro and Omuaran a similar catchment characteristics to Ero-omola. The monthly streamflow parameters between historical streamflow and Ero-omola are shown in Table 4.9 while the equivalent transformed data to natural logarithm is shown in Table 4.10. In modeling the monthly streamflow data the Thomas and Fierring model based on a first order Markov model is used and the synthetic streamflow series were calculated in Table 4.9 using historical flow data from River Akamo and Oshin. The series of equation derived from the model is presented in equations 4.13(a)-4.13(l) as follows:
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Table 4.10: Monthly Streamflow Parameters for River Oshin (1979) Month Mean STD Corr. Coeff. Coeff. Of Lag One
qj Sj Cv Skewness Corr.Coeff.rj JANUARY 6.4706 0.0662 -0.169 -1.984 0.075 FEBRUARY 4.2696 0.1794 -0.28 -0.686 0.359 MARCH 0.9294 0.4885 0.3568 -0.235 -0.425 APRIL 10.386 0.0855 -0.265 2.1991 0.1358 MAY 15.422 0.1533 -0.438 1.8573 -0.243 JUNE 18.662 0.2224 0.1695 -1.339 -0.249 JULY 14.463 0.3254 0.0137 0.3426 0.142 AUGUST 15.398 0.2634 -0.391 0.4197 0.2095 SEPTEMBER 21.499 0.2634 -0.187 0.465 0.2487 OCTOBER 18.527 0.2598 0.1096 -0.42 0.0951 NOVEMBER 13.415 0.3264 0.5877 0.1667 0.1198 DECEMBER 7.7923 0.0677 0.5371 -0.032 -0.525
q1 = 6.470645 + 0.39210 (q122.89452) + 2.13421z1 (4.13a)
q2 = 4.269643 + 0.52523 (q,1 7.792258) + 4.199054z2 (4.13b)
q3 = 0.929355 + 0.169519 (q2 6.470645) + 2.166747z3 (4.13c)
q4 = 10.38645 + 0.095148 (q3 0.929355) + 0.259820z4 (4.13d)
q5 = 15.42161 + 0.222417 (q4 10.38645) + 3. 537140z5 (4.13e)
q6 = 18.66167 + 0.013661 (q5 15.42161) + 3.326388z6 (4.13f)
q7 = 14.46258 + 0.325371 (q6 18.66167) + 5.420320z7 (4.13g)
q8 = 15.39839 + 0.095148 (q7 14.46258) + 4. 259820z8 (4.13h)
q9 = 21.49900 + 0.179392 (q8 15.39839) + 6.067661z9 (4.13i)
q10 = 18.52742 + 0.03172 (q9 21.499) + 8.98356 z10 (4.13j)
q11 = 13.41467 + 0.587739 (q10 18.52742) + 5.074972z11 (4.13k)
q12 = 7.792258 + 0.525230 (q11 13.41467) + 4.325371z12(4.13l)
Table 4.10 :Transformed Natural Logarithmic Monthly Streamflow Parameters for River Oshin
By(1979) setting q1= 6.470645 Mean The hisSTDtorical streamflow data from only Oshin River, which was found to give a reliable statistical parameterCorr.Coff. similar to Ero-omola was used to run the model. The above set of equations was used to extendCoeff.of the streamflow flow data in an excel programme to 25 years. (2009-2034) The extended streamflowLag one Corr data generated by the excel programme is giving in Appendix 6. Similarly historical streamflow data from River Oshin and Akamo is shown in Appendix 7. The equivalent transform to qj natural logarithm is shown in Appendix 8. Sj C v Skewness
rj JANUARY Page 26 1.867276 -2.7154 -0.12691 0.108505 Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Table 4.11 Transformed Natural Logarithmic Monthly Streamflow Parameters for River Oshin (1979) Month Mean STD Corr. Coeff. Coeff. Of Lag One
qj Sj Cv Skewness Corr.Coeff.rj JANUARY 1.8673 2.715 -0.127 0.1085 0.2384 FEBRUARY 1.4515 1.718 -0.104 0.132 0.2434 MARCH -0.073 0.716 -0.107 0.1298 0.2277 APRIL 2.3405 2.459 -0.109 0.1287 0.2428 MAY 2.7358 1.875 -0.11 0.1293 0.239 JUNE 2.9265 1.503 -0.11 0.1287 0.2346 JULY 2.6716 1.123 -0.111 0.132 0.2379 AUGUST 2.7343 1.334 -0.112 0.1262 0.2394 SEPTEMBER 3.068 1.334 -0.112 0.1262 0.2403 OCTOBER 2.9193 1.348 -0.112 0.129 0.2319 NOVEMBER 2.5963 -1.12 -0.113 0.1267 0.2399 DECEMBER 2.0531 2.693 -0.114 0.1228 0.2298
Table 4.12: Monthly Streamflow Parameters for River Akamo (1981) Month Mean STD Corr. Coeff. Coeff. Of Lag One
qj Sj Cv Skewness Corr. Coeff.rj JANUARY 5.5168 0.3138 -0.209578889 -1.092 0.166323484 FEBRUARY 7.2808 0.1876 -0.174896707 -5.231 -0.174896707 MARCH 3.4519 0.4144 1 1.0393 0.761907351 APRIL 12.342 0.4144 0.761907351 1.0393 0.747056989 MAY 18.467 0.8012 1 0.2401 0.770461678 JUNE 22.246 0.7847 0.753907959 0.2265 0.655500363 JULY 16.596 0.4229 0.622736154 0.9587 0.229111101 AUGUST 20.552 1.0804 0.543791067 -0.346 0.675861256 SEPTEMBER 25.802 0.7272 0.554306075 -0.048 0.559931888 OCTOBER 22.35 0.9066 0.669627026 0.4298 0.736537432 NOVEMBER 18.52 1.0366 0.983150118 0.9183 -0.157603747 DECEMBER 12.635 1.178 -0.07175952 0.0267 -0.115143984
Table 4.13: Natural Logarithmic Transformed Monthly Streamflow Parameters for Akamo
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
River(1981) Month Mean STD Corr. Coeff. Coeff. Of Lag One
qj Sj Cv Skewness Corr. Coeff.rj JANUARY 1.7078 -1.159 0.094296843 0.2336 0.338208832 FEBRUARY 1.9852 -1.674 0.080529482 0.2256 0.333803756 MARCH 1.2389 -0.881 0.102455523 0.2386 0.342761931 APRIL 2.513 -0.881 0.100029495 0.2372 0.342858112 MAY 2.916 -0.222 0.0827014 0.2269 0.353779166 JUNE 3.1021 -0.242 0.068728441 0.2188 0.34791206 JULY 2.8092 -0.861 0.075363026 0.2227 0.351357211 AUGUST 3.0229 0.0773 0.120742773 0.2317 0.351461525 SEPTEMBER 3.2504 -0.319 0.095364927 0.2348 0.34791206 OCTOBER 3.1068 -0.098 0.159226005 0.2744 0.360897776 NOVEMBER 2.9188 0.0359 0.116877947 0.248 0.354409363 DECEMBER 2.5365 0.1638 0.147501602 0.2671 0.349307898
4.7Determination Of The Required Reservoir Capacity
It is imperative to make provision for compensation reservoir due to 3 months break of runoff at Ero- omola. The regulated reservoir will then provide the needed flow of to the turbines uninterrupted through out the year. The capacity required for a reservoir depends upon the inflow available and the demand. If the available inflow in the river is always greater than the demand, there is no storage required. On the other hand, if the inflow in the river is small but the demand is high, a large reservoir capacity is required. The required capacity for the reservoir at Ero-omola was evaluated or determined by the following methods: 1. Graphical method, using mass curves and 2.Flow-duration curves method
4.7.1 Determination of Ero-omola Reservoir Capacity
The yield from a reservoir of a given capacity can be determined by the use of the mass inflow curve. The following procedure was used.
Table 4.14: Mass Inflow Curve Computation for Ero-omola Fall using average monthly discharge data. Month Average Monthly Discharge Cumulative Volume (m3/s) (m3/s) JAN. 6.04984 6.04984 FEB. 4.939395 10.98924 MAR. 3.755002 14.74424 APR. 12.84037 27.58461 MAY 19.64738 47.23199 JUNE 21.39122 68.62321 JULY 24.09706 92.72027 AUG. 36.95531 129.6756 SEPT. 49.07125 178.7468
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
OCT. 39.91781 218.6646 NOV. 32.30785 250.9725 DEC. 19.97958 270.9521 Sum 1316.955
Figure 4.4: Ero-omola Inflow Mass Curve
ERO-OMOLA INFLOW MASS CURVE 300 y = 18.96x 250 R² = 0.848
200
150
100
50 Cummulative flow (M3/s) flow Cummulative
0 JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. Months
The maximum storage capacity computed from the mass inflow curve above is 60m3/s. The reservoir is expected to fill up in the middle of September. Further computation is needed to convert the discharge into an inflow volume:
1 m3/ year = 1 x 365 x 24 x 60 x 60 = 31.536 x 106m3
Reservoir Capacity = 31.536mcm x 60 = 1892.16mcm
Inflow volume in 2009 = 13I6.955 x 31.536mcm = 41531.49mcm
4.8 Evaluation of Sediment Load or Sediment Transport
In order to established the sediment load into the reservoir. It assumed that the reservoir capacity will terminate when 80% of initial capacity is filled with sediment.
Average sediment inflow to River Ero is giving as 36000 tonnes (LNRBDA, 2003)
Specific weight of sediment taken from laboratory =1200kg/m3(LNRBDA, 2003)
Reservoir Capacity = 1892.16mcm
Annual Inflow = 41531.49mcm
Trap Efficiency = Sediment Deposited x 100% (US Bureau of Reclamation, 1987) Sediment Inflow
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Trap Efficiency = Reservoir Capacity/Mean Annual Inflow
Trap Efficiency = 1892.16/41531.49 =0.045
Annual sediment inflow = 36000 푡표푛푛푒푠 = 3.6 × 106 푘𝑔. (LNRBDA, 1999)
3.6 ×106 Volume of sediment inflow = = 3000 푚3 1200
Annual Sediment Deposited = Trap Efficiency x Sediment inflow =0.045 x 3000 = 135m3
Therefore, in 25years the sediment deposited will amount to 3,375m3which suggest the need to provide sluice gate at the headworks for sediment discharge. This is to avoid a situation where the reservoir is filled up before the expected project life of 25 years. Nevertheless, a more details assessment is required to ascertain the useful life of the reservoir.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
CHAPTER FIVE
5.0 POTENTIAL ENERGY ASSESSMENT
5.1 Potential Energy Assessment of Ero-OmolaFall In order to evaluate potential energy at Ero-omola. Twenty years ofstreamflow record (2009-2034) was utilised from the projected 25 years records in Appendix 6. The streamflow data was arranged in ascending order. The percentage of exceedence and annual projected hydropower generation potential was computed in Table 5.1. The Flow Duration Curve as well as the Power Duration Curve plotted is shown in Figure 5.1 and 5.2 Table 5.1:Computation of Flow Duration Curve using the projected 20 years figures
Flow in P{ower=9.8 x 59.4 x % of time of No. Year Flow(m3/s) Ascending Order F(kw) availability N +1 -n % N 1 2009 22.57 21.97 12789.18 100 2 2010 22.82 21.98 12795 95 3 2011 23.14 22.03 12824.1 90 4 2012 22.99 22.57 13138.45 85 5 2013 23.71 22.79 13266.51 80 6 2014 24.39 22.82 13283.98 75 7 2015 23.34 22.99 13382.94 70 8 2016 21.98 23.14 13470.26 65 9 2017 21.97 23.34 13586.68 60 10 2018 22.03 23.61 13743.85 55 11 2019 22.79 23.71 13802.07 50 12 2020 23.61 24.34 14168.8 45 13 2021 24.49 24.39 14197.91 40 14 2022 24.94 24.49 14256.12 35 15 2023 24.8 24.8 14436.58 30 16 2024 24.34 24.83 14454.04 25 17 2025 24.83 24.94 14518.07 20 18 2026 26.06 25.39 14780.03 15 19 2027 25.39 26.06 15170.05 10 20 2028 26.07 26.07 15175.87 5
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Figure 5.1: Ero-omola Flow Duration Curve
ERO-OMOLA FLOW DURATION CURVE 27 26 25 24
23 Flow (m3/s) Flow 22 21 0 20 40 60 80 100 120 Percentage of Exceedence
Figure 5.2: Ero-omola Power Duration Curve ERO-OMOLA POWER DURATION CURVE 15500 15175.868415170.0472 15000 14780.0268 14500 14518.072814454.039614436.576 14256.118814197.906814168.8008 14000 13802.065213743.8532 13586.6808 Power (kw) Power 13500 13470.2568 13382.938813283.978413266.5148 13000 13138.448412824.1036 12789.1764 12500 12794.9976 0 20 40 60 80 100 120 Percentage of Exceedence
The minimum flow available for 100% of the time is estimated at 21.8m3/sfrom the flow duration curve over an hydraulic head of 59.4m. Generator and Turbine Efficiency is assumed at 85% and 80%
Plant Efficiency = 0.85 x 0.80 = 0.68
From Equation (2.1) PE= 9.81QHe
Hydropower of Ero –Omola = 59.4 m x 21.8 m3/sx 9.81 x0.68 =8638.15kw or 8.64MW
FIRM ENERGY = Pdesign x 24 x 365 kWh (Equation 2.6)
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Annual Firm Energy = 8.64 x 24 x 365x 0.2 = 15137.28MWh (Analytical) Also from the Power Duration Curve in Figure 5.2 the firm energy or plant capacity at 100% of time is computed as 12794.9976kw or 12.794MW Annual Firm Energy =12.794 x 0.68 x 24 x 365 x 0.2=15242.26MWh.(Graphical)
Using the new NIPP, Multi Year Tariff Order (MYTO) of Nigeria Regulatory Energy Commission (Appendix 9) of N14.00/kWh. The total cost of bulk energy, excluding other charges is estimated at 15137280Kwh x N14.00/kWh = N211,921,920/Annum 5.2 Potential Energy Assessment of Owu Fall The streamflow discharge data (Appendix 5) generated from the rating equation at owu was utilized to develop the Flow Duration Curve (FDC) as well as Power Duration Curve (PDC). The minimum flow available for 100% of the time from the FDC/PDC curve(Figure 5.3 and 5.4) amount to 9.9m3/s over an hydraulic head of 95.5m. The computational procedures is shown in Table 5.2 Hydropower potentials for Owu Fall= 95.5m x 9.9m3/s x 9.81 x 0.95 = 8,811.12 kW or 8.81 MW (with 95% efficiency plans). Annual Firm Energy =8.81MW x 24 x 365 x 0.2 = 15435.12MWh Using the NIPP tariff order of N14.00/Kwh. Annual energy generated is estimated at N216,091,680.00/Annum.
Table 5.2 : Owu FDC/PDC Computation Flow in Ascending Power=9.8 x 59.4 % of time of No. Year Flow(m3/s Order x F(kw) availability N +1 -n % N 1 JANUARY 4.1856 10.955 3917.3133 100 2 FEBRUARY 0 91.667 3 MARCH 3.6371 10.342 3403.958 83.333 4 APRIL 3.6414 10.237 3407.9883 5 MAY 3.8497 4.1856 3602.9737 66.667 6 JUNE 3.5605 4.1856 3332.2596 58.333 7 JULY 0 8 AUGUST 10.237 3.8497 9580.4755 41.667 9 SEPTEMBER 4.1856 3.6414 3917.3133 33.333 10 OCTOBER 0 11 NOVEMBER 10.955 3.6371 10252.694 16.667 12 DECEMBER 10.342 3.5605 9679.3501 8.3333
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Figure 5.3: Owu Flow Duration Curve
OWU FLOW DURATION CURVE 14
12
10
8
6
FLOW (Qm3/S) FLOW 4
2
0 0 20 40 60 80 100 120 PERCENTAGE OF EXCEDENCE
Figure 5.4:Owu Fall Power Duration Curve
OWU POWER DURATION CURVE 12000 10000 8000 6000
POWER(kw) 4000 2000 0 0 20 40 60 80 100 120 PERCENTAGE OF EXCEEDENCE
5.3 Hydropower Water Demand
From the flow duration curve(Ero-omola) the peak hydropower demand was estimated at 21.80m3/s, hence 7m3/s is expected to be drafted by draft tube into bifurcated penstocks making a total of 7 x 24 x 3600 x 365 =220.752 MCM or 662.256mcm for the three turbines annually.
The storage capacity required to meet the peak hydropower demand of 21.80m3/s throughout the year is given thus;
Yearly demand = 31.536 x 21.80 = 687.48mcm
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
CHAPTER SIX
6.0 FINANCIAL JUSTIFICATION
6.1 Introduction
Economic feasibility and optimality represent just one of many considerations in the decision- making process. However, economic analysis does play an important central role in decision- making at many levels, in various settings. Economic evaluation of hydropower development plans combines basic methods of engineering economics with benefit estimation procedures. Analyses of economic costs and benefits provide important information for use, along with various other forms of information, in making a myriad of decisions in planning, design, operations, and other water resources engineering activities. (Printinger, 1972) The economic objectives for comparing alternative plans may be in either of the following alternative forms:
Maximize net benefits, which are benefits less costs Minimize cost required to provide a specified level of service Maximize benefits derived from fixed resources.
In this study, both benefits and costs are relevant and are included in the analysis.
6.2 Engineering Economics
Engineering economics is a set of principles applied in comparing alternative plans to determine the economically optimal design. Equivalence of kind and equivalence of time are required so that all relevant costs and benefits of each alternative are comparable. Equivalence of kind is achieved by expressing all benefits and costs included in the analysis in both local and foreign currencies. Equivalence of time is achieved through discounting techniques using compound interest formulas. Having a Naira today is worth more than obtaining a Naira at some future time, because the Naira in hand today can be invested to accrue interest. 6.3 Economic Analysis
Benefits and costs associated with water projects occur at various times, Initial investment costs occurring at the beginning of the project life are associated with construction or implementation. Operation and maintenance costs continue throughout the life of the project. Major replacement and rehabilitation costs may occur periodically. Benefits typically accrue over long periods of time. Time streams of benefits and costs may be converted to other equivalent cash flows for purposes of comparison using discounting formulas, with a special fixed discount rate. The discount rate is often linked to the concept of marginal internal rate of return in National Integrated Power Project or National Independent Power Project industry. If funds were committed to the project yielding the highest return first, and then to subsequent projects in order of rate of return, the rate of return of the last project selected before funds
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
ran out would be the marginal internal rate of return. The discount rate used by the National Economic Planning Department is based on the market interest rate for risk free investment, with the limitation that the rate may not be changed too rapidly. The financial analysis in this study shall be limited to only Ero Omola project due to its obvious advantage of Owu Fall Project.
6.4 Hydro Power Generation Benefit
The entire benefit envisaged from this project is generation of Hydro-power electricity. The peak power generation contemplated of the project is 8638.15kw or 8.64 MW. This power would be utilized for electrifying five LGAs town and neighboring villages.
The total capability of hydropower generation (number of Kilowatt hour units) in a year of 90% dependability would be 15137.28MWh. With 70% load factor, the total units generated would be 0.7 x 15137.28 = 10596.096MWh.
6.5 Cost of generation per Kilowatt
The total cost of the project, except for the equivalent cost of 48 Km. long 133 KVA High Tension Transmission line, equipments & distribution system, which is entirely for power generation works out to 1809 million Naira. (Abstractive Cost) With the above investment, the installed capacity to be provided is 8638.15kw; hence the cost per kW installed capacity works out to N209,419.84\kW
6.6 Internal Rate Return.
Internal rate of return is that discount rate that makes the net present value of a net benefit or cash flow equal zero or is the maximum interest rate that a project could pay on invested capital, if the project is to recover its investments and operating costs and still break even. It could also be defined as the rate of return on capital outstanding per period while it is invested in the project. 6.6.1 Assumptions:
Reservoir capital costs are given as input data and their operation and maintenance costs are expressed as a fraction of their capital costs. Power house, penstock and forebay costs are based on maximum draft tubes flow. Operation and maintenance costs are a fraction of this value. Power and imported turbines spare parts costs are determined from abstractive market value. Present worth is obtained from the actual cost (sum of the costs of actual Capital, operation and maintenance, power, imported turbines parts, and deficit minus the hydroelectric power benefits). The cost abstract is presented in Table 6.1.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
TABLE – 6.1: Consolidated Abstract of Cost
S.No Unit Description Cost in Millions(N)
1. Unit – I Civil Works 109
2. Unit – II Electrical Works 483
3. Unit – III Compensation and Honourariums 450
4. Unit – IV Design and Construction 568
5. Unit-V Operation and Maintenance 199
Total 1809
The preliminary cost of development of Ero-omola Fall is estimated at N1,809,000,000.00 which include the Headworks, Civil, Electrical and the mechanical component. Using the current Central Bank of Nigeria annual interest rate of 21% at a repayment period of 25years. The Internal Rate of Return was interpolated between 16% and 20% to guess the true Rate of Return. The details computational procedure is indicated in Table 6.2.
(1+푖)푁 − 1 (1+0.16)− 1 퐷푖푠푐표푢푛푡 퐹푎푐푡표푟 = = = =0.8620 (i=16%) 푖(1+푖)푁 0.16(1+0.16)
(1+0.20)− 1 (1+0.21)− 1 = =0.833 (i=20%) = =0.8264 (i=21%) 0.20(1+0.20) 0.21(1+0.21)
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
TABLE 6.2: COMPUTATION OF INTERNAL RATE OF RETURN FROM CASH FLOW (ABSTRACTIVE COST) METHOD:INTERPOLATION METHOD YEAR CAPITAL O & M (N)*M GROSS(N)M VALUE OF IN C REMENTAL 16% D.F 16% PW 20% D.F 20% PW COMPONENT(N)M INCREMENTAL NET GROSS BENEFIT BENEFIT(N)M CASH FLOW(N)M 1 1.09 0 1.09 -1.09 0.862 -0.94 0.833 -0.91 2 4.83 0 4.83 -4.83 0.743 -3.59 0.694 -3.35 3 5.68 0 5.68 -5.68 0.641 -3.64 0.579 -3.29 4 4.5 0 4.5 -4.5 0.552 -2.48 0.482 -2.17 5 1.99 0 1.99 -1.99 0.476 -0.95 0.402 -0.8 6 0 0.67 0.67 1 0.41 0.41 0.335 0.34 7 0 0.97 0.97 2.37 0.354 0.84 0.279 0.66 8 0 1.3 1.3 3.7 0.305 1.13 0.233 0.86 9 0 1.62 1.62 5.06 0.263 1.33 0.194 0.98 10 0 1.95 1.95 6.43 1.57 10.1 0.948 6.1 TOTAL 18.09 6.51 24.6 0.47 6.176 2.21 4.979 -1.58 (*M=million) Interpolation Procedures: Internal Rate of Return= Lower Discount rate +Difference Between the Discount rate x Ratio of Present Worth of Incremental benefit cash flow at Lower Discount Rate and Sum of the Incremental Net Benefit Stream Cash flow of the two Discount rate (when the signs are ignored)
Present Worth of Benefit @ 16% = 2.21 Million Present Worth of Benefit @ 20% = 1.58 Million The Sum of the Streams at the two Discount rates Ignoring the signs=2.21+1.58=3.79 INTERNAL RATE OF RETURN =16 (4)2.21/3.79=16 + 4(0.58) = 18.62 OR 18%
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
The internal rate return of 18% with an abstractive cash flow analysis suggests a promising profit outlook. Accurate Internal Rate of Return will be achieved when both structural and non-structural design of all hydropower components is completed and the true Bill of Engineering Measurement and Evaluation is incorporated in the Economic Analysis. The amortization of various hydropower components at the prevailing interest rate of 21% is computed below:
6.7 Amortization Analysis
The projected hydropower cash flow is presented in Appendix 11. The cash flow indicates that Ero- omola project is expected to grow by 5% profit beginning from year 2015. The total Kilo Watt Hour units available annually at 90% dependability excluding Power-Station requirement is 15137.28 MWh. Taking the estimated life span of electrical works (generation), civil, operation and maintenance and other works as 25 years. Amortization of various component of hydropower project outlined above was computed in consideration of prevailing interest rate of 21%. The discount factor computed at 21% interest rate is presented thus:
푖 0.21 퐴 = 퐹 = 퐴 = 퐹 =0.0018 (when n=25years) (1+푖)푁 − 1 (1+0.21)25− 1
1. Amortization Cost Amount(N)
(a) Electrical Works (21% Interest, 25 yrs. life) = 0.0018 x 1090000 = N1,962.00
a) (b) Civil Works. (21% Interest, 25 yrs. life) = 0.0018 x 4830000 = N8,694.00
(c) Design and Construction = 0.0018 x 5680000 =N10,224.00
(d) Compensation and Honourariums = 0.0018 x 4500000 =N8,100.00
(a) (e)Operation and Maintenance(1.5% of Total Cost) = 0.015 x 1990000 =N29,850.00
Total = N58,830.00
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 1: CROSS-SECTION OF ERO-OMOLA STREAM
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 2
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
Streamflow Discharge Computation with Current Metre (Arithmetic Method)
The calibration equation of the instrument is given as;
V = 0.2483 n +0.011 for n=< 0.59 where n revolution per seconds
V = 0.2619 n + 0.003 for n= < 9.21
Segment 1
푟푒푣표푙푢푡푖표푛 푛 = 푡푖푚푒 5 = = 0.125 40
푣1 = 0.2483 × 푛 + 0.011 = 0.2483 × 0.125 + 0.011 = 0.034푚푙푠. 1 퐴1 = 2 푏푑 1 = 2 × 3 × 0.95 = 1.43푚3
푞1 = 푣1퐴1 = 0.03 × 1.43
= 0.049푚3/푠
Segment 2
7 푛 = = 0.163 43
푉2 = 0248 × 0.163 + 0.011 = 0.043푚/푠
푄 + 푄 퐴 = 2 3 푏 2 2 0.095 + 1.4 = 3 2 = 3.53푚2
푞2 = 푉2퐴2 = 0.043 × 3.53
= 0.152푚2/푠
Segment 3
7 푛 = = 0.135 52
푣3 = 0.2483 × 0.135 + 0.011
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
= 0.036푚/푠 (푄 + 푄 ) 퐴 = 3 4 푏 3 2 (1.4 + 2.0) = 2 = 5.0푚2
3 푞3 = 푉3퐴3 = 0.184푚 /푠
3 푞3 = 0.184푚 /푠 Segment 4
7 푛 = = 0.175 40
푣4 = 0.2483 × 0.175 + 0.011 = 0.046푚/푠
(2.0 + 2.1)3 퐴 = 4 2 = 6.15푚2
푞4 = 푉4퐴4 = 0.046 × 6.15
= 0.283푚3/푠
Segment 5
10 푛 = = 0.182 55
푣5 = 0.2483 × 0.182 + 0.011 = 0.048푚/푠
(2.1 + 2.3)3 퐴 = 5 2 = 6.6푚2
푞5 = 푉5퐴5 = 0.048 × 6.6
= 0.317푚3/푠
Segment 6
10 푛 = = 0.189 53
푣6 = 0.2483 × 0.189 + 0.011
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
= 0.049푚/푠
(2.3 + 2.25)3 퐴 = 6 2 = 6.83푚2
푞6 = 푉6퐴6 = 0.049 × 6.83
= 0.334푚3/푠
Segment 7
10 푛 = = 0.208 48
푣7 = 0.2483 × 0.208 + 0.011 = 0.054푚/푠
(2.25 + 2.2)3 퐴 = 7 2 = 6.68푚2
푞7 = 푉7퐴7 = 0.054 × 6.68
= 0.360푚3/푠
Segment 8
15 푛 = = 0.3 푉8 = 0.2483 × 0.3 + 0.011 1 50 1 = 0.077푚/푠
10 푛 = = 0.2 푉8 = 0.2483 × 0.2 + 0.011 2 50 2 = 0.0524푚/푠
푉8푎푣𝑔 = 0.065푚/푠
(2.2 + 2.5)3 퐴 = 8 2 = 7.05푚2
푞8 = 푉8퐴8 = 0.065 × 7.0
= 0.458푚3/푠
Segment 9
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
15 푛 = = 0.33 푉9 = 0.2483 × 0.33 + 0.011 1 45 1 = 0.085푚/푠
10 푛 = = 0.2 푉9 = 0.2483 × 0.21 + 0.011 2 48 2 = 0.054푚/푠
푉9푎푣𝑔 = 0.069
(0 + 0 ) (2.5 + 2.8) 퐴 = 9 10 푏 퐴 = 2 9 2 9 2 = 5.3푚2
푞9 = 푉9퐴9 = 0.069 × 5.3
= 0.366푚3/푠
Segment 10
15 푛 = = 0.35 푉10 = 0.2483 × 0.35 + 0.011 1 43 1 = 0.089푚/푠
10 푛 = = 0.22 푉10 = 0.2483 × 0.22 + 0.011 2 46 2 = 0.057푚/푠
푉10푎푣𝑔 = 0.073푚/푠
(0 + 0 ) (2.8 + 3.0) 퐴 = 10 4 푏 퐴 = 2 10 2 10 2 = 5.8푚2
푞10 = 푉10퐴10 = 0.073 × 5.8
= 0.423푚3/푠
Segment 11
20 푛 = = 0.38 푉11 = 0.2483 × 0.38 + 0.011 1 52 1 = 0.098푚/푠
10 푛 = = 0.25 푉11 = 0.2483 × 0.25 + 0.011 2 40 1 = 0.065푚/푠
푉11푎푣𝑔 = 0.081푚/푠
(0 + 0 ) (3.0 + 2.95 퐴 = 11 12 푏 퐴 = 2 11 2 11 2
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
= 5.95푚2
푞11 = 푉11퐴1 = 0.081 × 5.95
= 0.482푚3/푠
Segment 12
20 푛 = = 0.40 푉12 = 0.2483 × 0.40 + 0.011 1 50 1 = 0.102푚/푠
10 푛 = = 0.24 푉12 = 0.2483 × 0.24 + 0.011 2 42 2 = 0.062푚/푠
푉12푎푣𝑔 = 0.082푚/푠
(0 + 0 ) (2.95 + 3.1 퐴 = 12 13 푏 퐴 = 2 12 2 12 2 = 6.05푚2
푞12 = 푉12퐴12 = 0.082 × 6.05
= 0.496푚3/푠
Segment 13
20 푛 = = 0.42 푉13 = 0.2483 × 0.42 + 0.011 1 48 1 = 0.106푚/푠
10 푛 = = 0.22 푉13 = 0.2483 × 0.22 + 0.011 2 46 2 = 0.057푚/푠
푉13푎푣𝑔 = 0.081푚/푠
(0 + 0 ) (3.1 + 3.2 ) 퐴 = 13 14 푏 퐴 = 2 13 2 13 2 = 6.3푚2
푞13 = 푉13퐴13 = 0.081 × 6.3
= 0.51푚3/푠
Segment 14
20 푛 = = 0.38 푉14 = 0.2483 × 0.38 + 0.011 1 52 1
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
= 0.098푚/푠
15 푛 = = 0.27 푉14 = 0.2483 × 0.27 + 0.011 2 55 2 = 0.07푚/푠
푉14푎푣𝑔 = 0.084푚/푠
(0 + 0 ) 퐴 = 14 15 푏 14 2 = 6.25푚2
푞13 = 푉14퐴14 = 0.084 × 6.25
= 0.525푚3/푠
Segment 15
15 푛 = = 0.36 푉15 = 0.2483 × 0.36 + 0.011 1 42 1 = 0.091푚/푠
10 푛 = = 0.22 푉15 = 0.2483 × 0.22 + 0.011 2 46 2 = 0.057푚/푠
푉15푎푣𝑔 = 0.074푚/푠
(0 + 0 ) (3.05 + 3.1) 퐴 = 15 16 푏 퐴 = 2 15 2 9 2 = 6.15푚2
푞15 = 푉15퐴15 = 0.074 × 6.15
= 0.46푚3/푠
Total Discharge Q
Q = 0.049 + 0.152 + 0.184 + 0.283 + 0.317 + 0.334 + 0.360 + 0.458 + 0.366 + 0.423 + 0.482 + 0.496 + -.510 + 0.525 + 0.460 = 5.40m3/s.
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 3
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 4
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 4a: ERO-OMOLA DAILY GAUGE RECORDS
JA FE MA AP MA JN JL AU SE OC NO DE 1. 0.470 0.710 0.610 0.520 0.560 1.350 1.36 0.840 0.980 1.370 1.360 1.260 2. 0.470 0.690 1.360 0.520 1.320 1.320 1.340 0.810 0.970 1.350 1.350 1.240 3. 0.470 0.680 1.330 0.510 1.290 1.260 1.310 1.780 1.420 1.320 1.310 1.210 4. 0.460 1.270 1.310 0.50 1.260 1.210 1.280 1.760 1.380 1.280 1.270 1.190 5. 0.460 1.250 1.280 0.690 1.180 1.120 1.250 1.760 1.360 1.240 1.240 1.170 6. 0.460 1.230 1.250 0.670 1.130 0.940 1.210 1.710 1.320 1.460 1.210 1.140 7. 0.460 1.220 1.210 0.640 0.970 0.890 1.170 1.650 1.190 1.430 1.170 1.110 8. 0.460 1.210 1.180 0.630 0.960 0.850 1.120 1.620 1.190 1.390 1.165 0.970 9. 0.460 1.190 1.140 0.630 0.950 0.810 1.240 1.530 1.370 1.350 1.140 0.940 10. 0.460 1.430 1.110 0.620 0.980 0.780 1.210 1.480 1.340 1.310 1.120 0.910 11. 0.460 1.410 0.950 0.60 0.940 1.240 1.150 1.440 1.310 1.260 0.960 0.860 12. 0.460 1.380 0.890 0.590 0.910 1.220 1.110 1.410 1.290 1.225 0.930 0.830 13. 0.460 1.350 0.830 0.580 0.880 1.180 0.940 1.320 1.230 1.180 0.880 0.790 14. 0.460 1.330 0.780 0.560 0.870 1.130 0.920 1.170 1.890 1.130 0.880 0.750 15. 0.450 1.290 1.150 0.530 0.840 1.10 0.920 1.140 1.860 1.110 0.870 0.730 16. 0.450 1.260 1.140 0.510 0.810 0.890 0.790 0.970 1.810 0.960 0.850 0.710 17. 0.450 1.180 1.120 0.740 0.980 0.850 0.750 0.930 1.640 0.950 1.230 0.670 18. 0.450 1.120 0.880 0.710 0.960 0.970 1.560 1.590 0.930 1.190 0.630 19. 0.450 0.940 0.940 0.620 0.940 0.920 1.470 1.530 0.880 1.160 1.160 20. 0.450 0.860 0.890 0.610 0.910 0.8750 1.430 0.840 1.480 0.840 1.110 1.120 21. 0.450 0.770 0.850 0.80 0.870 1.460 1.350 0.790 1.480 1.260 0.970 0.980 22. 0.450 0.690 0.810 0.780 0.860 1.410 1.310 0.780 1.560 1.240 0.940 0.960 23. 0.450 0.650 0.760 0.940 0.840 1.380 1.260 0.780 1.510 1.210 0.910 0.940 24. 0.450 0.630 0.730 0.890 0.830 1.340 1.190 0.760 1.490 1.180 0.870 25. 0.450 0.610 0.650 0.840 0.810 1.290 1.130 1.540 1.440 1.160 0.830 26. 0.450 0.630 0.820 0.8150 1.230 1.110 1.510 1.30 1.130 27. 0.50 0.940 0.80 1.170 0.980 1.430 1.280 1.130 28. 0.580 0.780 1.140 0.970 1.370 1.250 1.110 29. 0.580 1.10 0.940 1.280 1.220 1.350 30. 0.950 0.880 1.220 1.180 1.330 31. 0.850 1.280
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APPENDIX 4b: ERO-OMOLA DAILY DISCHARGE DATA GENERATED FROM RATING EQUATIONS
JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV. DEC.
6.177174 4.908227 3.220095 5.285807 4.39994 16.81515 6.69059 9.710066 25.10431 6.596982 40.0246 6.436129 6.177174 4.866968 3.580008 5.285807 15.32033 15.98317 5.961412 9.188874 25.00153 6.083954 39.21961 5.849132 6.177174 4.846234 3.526813 5.179227 14.81635 14.38943 4.997536 30.33735 29.11878 5.375985 36.10292 5.052638 6.143801 4.977332 3.491306 5.072749 14.31767 13.13217 4.172423 29.82176 28.78787 4.538261 33.14867 4.573558 6.143801 4.941396 3.437978 7.111751 13.01432 11.02913 3.468662 29.82176 28.62025 3.810526 31.03733 4.132919 6.143801 4.905325 3.384568 6.895667 12.21975 7.425568 2.692434 28.54602 28.28052 9.363992 29.01366 3.538591 6.143801 4.887238 3.313222 6.572137 9.785568 6.563412 2.07219 27.04043 27.13168 8.352634 26.44905 3.017209 6.143801 4.869116 3.25961 6.464457 9.63913 5.916092 1.47465 26.29813 27.13168 7.144881 26.13904 1.34786 6.143801 4.832767 3.187988 6.464457 9.493383 5.305987 3.258302 24.1139 28.70424 6.083954 24.62371 1.117108 6.143801 4.260239 3.134162 6.356861 9.932695 4.872554 2.692434 22.9286 28.45114 5.155574 23.45263 0.920239 6.143801 4.225299 3.845396 6.141925 9.348334 13.87884 1.811779 21.99512 28.19463 4.16139 15.34218 0.656458 6.143801 4.17267 3.736305 6.034587 8.917403 13.3785 1.375151 21.30374 28.02165 3.56359 14.05814 0.530933 6.143801 4.119771 3.626727 5.927339 8.492889 12.40842 0.376723 19.2753 27.49286 2.900073 12.07411 0.395209 6.143801 4.084351 3.535013 5.713116 8.352831 11.25274 0.31862 16.05198 32.64694 2.285048 12.07411 0.289702 6.110057 4.013134 3.205908 5.392488 7.937058 10.58941 0.31862 15.43175 32.43867 2.071102 11.70014 0.246485 6.110057 4.959381 3.187988 5.179227 7.527987 6.563412 0.097263 12.07878 32.08701 0.931326 10.9745 0.208776 6.110057 4.814538 3.152114 7.653285 9.932695 5.916092 0.064891 11.33128 30.84575 0.879158 30.35311 0.147625 6.110057 4.704389 3.718077 7.328141 9.63913 7.971455 19.47948 0 30.46609 0.781983 27.71247 0.102181 6.110057 4.365158 3.827246 6.356861 9.348334 7.073591 12.26209 0 30.00091 0.576867 25.83136 3.926227 6.110057 4.209575 3.736305 6.24935 8.917403 6.316277 9.891046 9.710066 29.60483 0.446536 22.88066 3.183363 6.110057 4.030405 3.663309 8.305489 8.352831 20.06854 6.316835 8.846894 29.60483 4.16139 15.78618 1.433073 6.110057 4.866968 3.590086 8.087812 8.213503 18.54999 4.997536 8.677568 30.23484 3.810526 14.47823 1.266908 6.110057 4.783594 3.49822 9.836372 7.937058 17.67071 3.690762 8.677568 29.84342 3.329906 13.24144 1.117108 6.110057 4.741457 3.44291 9.288251 7.79995 16.53521 2.36464 8.34228 29.68468 2.900073 11.70014 0 6.110057 4.699005 3.294663 8.741637 7.527987 15.17465 1.580367 24.35339 29.28214 2.63961 10.27818 0
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SUM 78.32396 64.08454 48.59602 166.9248 241.1845 284.7805 102.4264 423.8826 726.7812 97.94532 557.6962 49.48943 MEAN 6.02492 4.92958 3.738155 12.84037 9.647381 11.39122 4.097057 16.95531 29.07125 3.917813 22.30785 1.979577 MIN 3.110057 1.699005 1.220095 5.072749 4.39994 4.872554 0.064891 0 25.00153 0.446536 10.27818 1.793888 MAX 3.177174 3.260239 2.580008 9.836372 15.32033 20.06854 19.47948 30.33735 32.64694 97.94532 40.0246 5.849132
APPENDIX 5a: OWU FALL DAILY GAUGE READINGS
JA FE MA AP MA JN JL AU SE OC NO DE 1. 0.48 0.42 0.43 0.42 0.43 0.88 0.48 0.88 2. 0.48 0.42 0.43 0.44 0.43 0.87 0.48 0.87 3. 0.48 0.42 0.43 0.44 0.43 0.87 0.48 0.87 4. 0.48 0.42 0.43 0.44 0.43 0.89 0.48 0.89 5. 0.48 0.42 0.43 0.44 0.42 0.88 0.48 0.88 6. 0.48 0.42 0.43 0.44 0.42 0.87 0.48 0.87 7. 0.48 0.42 0.43 0.45 0.42 0.86 0.48 0.86 8. 0.48 0.42 0.43 0.45 0.42 0.86 0.48 0.865 9. 0.47 0.42 0.43 0.44 0.42 0.85 0.47 0.85 10. 0.47 0.42 0.42 0.44 0.42 0.84 0.47 0.84 11. 0.47 0.42 0.43 0.44 0.42 0.84 0.47 0.84 12. 0.47 0.42 0.43 0.44 0.42 0.63 0.47 0.83 13. 0.47 0.43 0.43 0.44 0.43 1.52 0.47 1.52 14. 0.47 0.43 0.43 0.44 0.42 1.49 0.47 1.49 15. 0.47 0.43 0.43 0.43 0.42 1.42 0.47 1.42 16. 0.47 0.43 0.42 0.43 0.42 1.3 0.47 1.3 17. 0.47 0.43 0.42 0.44 0.42 1.11 0.47 1.11 18. 0.47 0.43 0.41 0.44 0.42 0.95 0.47 0.95 19. 0.47 0.43 0.43 0.48 0.43 0.92 0.47 0.92 20. 0.47 0.43 0.41 0.48 0.43 0.83 0.47 0.83
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
21. 0.47 0.43 0.42 0.46 0.43 0.79 0.47 0.79 22. 0.47 0.43 0.42 0.44 0.48 0.76 0.47 0.76 23. 0.47 0.43 0.42 0.44 0.46 0.76 0.47 0.76 24. 0.47 0.43 0.44 0.44 0.46 0.74 0.47 0.74 25. 0.47 0.43 0.43 0.44 0.45 0.69 0.47 0.69 26. 0.47 0.43 0.42 0.47 0.45 0.67 0.47 0.98 0.67 27. 0.47 0.43 0.42 0.44 0.67 0.47 0.97 0.675 MEAN NO OF DAYS=217
APPENDIX 5b: OWU STREAMFLOW DISCHARGE DATA GENERATED FROM THE RATING EQUATIONS
JANUARY FEBRURY MARH APRIL MAY JUNE JULY AUGUST SEPTEMBE R 4.268554 3.573975 3.687593 3.573975 3.687593 9.558547 4.268554 4.268554 3.573975 3.687593 3.802086 3.687593 9.414354 4.268554 4.268554 3.573975 3.687593 3.802086 3.687593 9.414354 4.268554 4.268554 3.573975 3.687593 3.802086 3.687593 9.703281 4.268554 4.268554 3.573975 3.687593 3.802086 3.573975 9.558547 4.268554 4.268554 3.573975 3.687593 3.802086 3.573975 9.414354 4.268554 4.268554 3.573975 3.687593 3.917442 3.573975 9.270707 4.268554 4.268554 3.573975 3.687593 3.917442 3.573975 9.270707 4.268554 4.150688 3.573975 3.687593 3.802086 3.573975 9.12761 4.150688 4.150688 3.573975 3.573975 3.802086 3.573975 8.985068 4.150688 4.150688 3.573975 3.687593 3.802086 3.573975 8.985068 4.150688 4.150688 3.573975 3.687593 3.802086 3.573975 6.128481 4.150688 4.150688 3.687593 3.687593 3.802086 3.687593 19.77342 4.150688 4.150688 3.687593 3.687593 3.802086 3.573975 19.25607 4.150688 4.150688 3.687593 3.687593 3.687593 3.573975 18.06231 4.150688
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
4.150688 3.687593 3.573975 3.687593 3.573975 16.06107 4.150688 4.150688 3.687593 3.573975 3.802086 3.573975 13.01696 4.150688 4.150688 3.687593 3.461246 3.802086 3.573975 10.58284 4.150688 4.150688 3.687593 3.687593 4.268554 3.687593 10.14069 4.150688 4.150688 3.687593 3.461246 4.268554 3.687593 8.843084 4.150688 4.150688 3.687593 3.573975 4.033646 3.687593 8.280831 4.150688 4.150688 3.687593 3.573975 3.802086 4.268554 7.86524 4.150688 4.150688 3.687593 3.573975 3.802086 4.033646 7.86524 4.150688 4.150688 3.687593 3.802086 3.802086 4.033646 7.591159 4.150688 4.150688 3.687593 3.687593 3.802086 3.917442 6.916704 4.150688 4.150688 3.687593 3.573975 4.150688 3.917442 6.651344 4.150688 4.150688 3.687593 3.573975 3.802086 0 6.651344 4.150688 4.185611 3.637096 3.641402 3.849742 3.560487 10.23664 4.185611
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APPENDIX 5: OWU FALL STREAM FLOW DATA
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 6: EXTENDED STREAMFLOW DATA (2009-2034) AT ERO-OMOLA
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Assessment of Hydroelecric Potentials of Owu and Ero-omola Falls in Kwara State, Nigeria
APPENDIX 7: STAGE DISCHARGE RECORDS OF RIVER AKAMO AND OSHIN
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APPENDIX 8: STREAMFLOW DATA TRANSFORM TO NATURAL LOGARITHM
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APPENDIX 9: PHCN TARIFFS
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APPENDIX 10: SCANED COPY OF HYDROGRAPH OF RIVER OSIN AND AKAMO INCLUDING THE RAW DATA AS OBTAINED FROM THE LOWER NIGER RIVER BASIN AUTHORITY
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