Estimation of Water Seepage from Upper Reservoir of Rudbar Pumped Storage Power Plant T. Abadipoor a and H. Katibeh a and A. Alianvari b a Dept. of Mining & Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran b Dept. of Mining Engineering, University of Kashan, Kashan, Iran abadipoor.ta90@yahoo.com Abstract One of the major problems during the construction and operation of reservoirs, which can undermine the water maintainability, is related to water seepage from the reservoir. In pumped storage power plant, due to connect between upper and main reservoir, water seepage from upper reservoir have a significant effect on the efficiency of the power plants to produce energy. The objective of this research is to estimate water seepage from the upper reservoir of Rudbar pumped storage power plant, based on combined geological and geotechnical investigations using numerical and analytical methods. Geological investigations show that the upper reservoir consists of limestone and marly limestone. Obtained data of seven exploratory boreholes and seven joint measurement stations have been considered as the main source for seepage calculations in analytical method and distinct element method (DEM, respectively. The input data such as permeability of layers and the hydraulical and mechanical properties of discontinuities has been obtained from measured data. Results from both methods (analytical and numerical have an appropriate consistency together. The estimated seepage from analytical method and DEM is around 348,000 m 3 /day and 80,000 m 3 /day, respectively. Due to the high amount of water seepage and economical value of Water in this region, water tightening is necessary. Keywords: Water seepage, Dam reservoir, Pumped storage power plant, Distinct element method 1. Introduction Generally, dams are constructed for two main goals, including surface water control and water storage. One of the applications of water storage is power generation that provides about 15% the world's total electricity. This important source of electricity generation is appropriately flexible and products energy in a relatively short time and low losses (Bondarchuk et al., 01. The pumped storage power plant is one type of powerhouses that have two reservoirs, which, according to the topographic changes are located at two different heights. Whatever the difference in elevation between the reservoirs is greater; the work efficiency will increase. These power plants reach to their capacity maximum at less time than any other nuclear and fossil power plants (www.darvill.clara.net, 014. During periods of the low electricity usage, the water is transferred to the upper reservoir and at peak periods, the water is moved to the lower reservoir, therefore, electrical energy be generated. Given the importance of electricity generated by these plants, in both of the reservoirs particularly in the upper reservoir, the storage of water is an important problem. Water storage of reservoirs is impressed by the seepage phenomenon that appears due to many factors including the high permeability of the surrounding rocks and the presence of discontinuities and faults. In order to evaluate the water seepage through reservoir, information such as geological formations and hydraulic properties of the surrounding rocks should be examined. Factors contain the fluid pressure difference and height differences, which determine the hydraulic gradients as well as geological and hydrogeological properties control water flow through rock masses. Hence, once data related to the hydraulic and geometric parameters and geological condition are available, the seepage quantity can be estimated. Based on the data, the flow network within rock mass is modeled and water seepage through the reservoir is determined. Escaped water from the reservoir may percolate to groundwater aquifers and not appear in the ground surface or may discharge at the downstream as visible (Shamsayi and Rasoly, 005.
Rudbar power plant is located in Zagros Mountain in West of Iran. After Siyah-Bishe plant power, it is second pumped storage power plant in Iran, which is under construction. The upper reservoir of Rudbar plant is included of formations as Elam-Sarvak, Dalan and Garo, which mainly has dolomite and limestone rocks. Lugeon test results in the site shows high values of permeability. In addition, the surface surveys data indicate the existence of different types of discontinuities and joints. This preliminary data demonstrate that reservoir is located in a highly tectonic area and is prone to water seepage. Therefore, in order to predict the water storage ability of the upper reservoir of Rudbar pumped storage power plant a seepage analysis is done. In this study, two methods containing a discrete element method (UDEC 4.0 and an analytical method are used to estimate the water seepage quantity. Finally, the results obtained from two methods are compared with each other and according to estimated values in both methods; a final assessment of the seepage quantity and seepage condition within the rock mass surrounding the reservoir is obtained.. Rudbar pumped storage power plant The Rudbar pumped storage power plant is located 9 Km of Aligoodarz city in Lorestan province in the West of Iran (Fig.1a. Rudbar dam is currently under construction over the Rudbar River (in upper East of Dez River catchment area. The dam type is as gravel with clay core that have a crest 185 m length, crest width of 15 meters and height is 155 meters. For the given power plant, two areas were proposed to specify the upper reservoir location including Chaleh-Hatam and Galeh-Mu, which their location is shown in Fig.1b. Due to the inappropriate topographical condition in the Galeh-Mu, this option was rejected and Chaleh-Hatam area was considered to construction the reservoir. It is predicted that the reservoir located in Chaleh-Hatam area has a capacity approximately 3 million cubic meters and the power plant will be produces 450 MW electricity. (a (b Fig. 1. a Location of Rudbar pumped storage power plant in Iran geology and Zagros zone, b Chaleh-Hatam and Galeh-Mu location. 3. Analytical method Analytical methods that predict water seepage from reservoirs are based on the governing mathematical equations with assumptions such as isotropic environment, homogeneous and deep-water surface. These methods are sometimes related to particular conditions and places, but due to the simplicity of calculations, can be used as a preliminary estimation of the seepage. In seepage analysis, it is better that beside the seepage rate also seepage path, general mechanism of seepage, seepage velocity and water surface position to be determined. It is noteworthy that determining these cases using analytical methods is often difficult or impossible. There are several analytical methods to measure the seepage rate and in all of them, the reservoir simulates as cross section of a channel which length of the channel is considered as unit. Seepage in these channels is affected by parameters such as permeability, channel geometry and position of the water surface in the channel (ICID, 1967. In general, to minimize seepage rate should be the channels designing optimally. According to studies, the trapezoidal cross section have minimum seepage rate among of the three main cross sections (trapezoidal and rectangular (Swammee et al., 000. Therefore, it is more appropriate that in the design stage, a trapezoidal cross section be chosen.
In given analytical method, the total seepage rate as laminar flow in a channel with deep water level is calculated as follows (Vedernikov equation (Swammee et al., 000: (1 Where, is seepage rate per unit length (m 3 /s/m, K is hydraulic conductivity of the media (m/s, y is maximum water depth in the channel (m and F s is seepage function which using Vedernikov equations for trapezoidal cross section as follows (Harr, 196: F s 1 m cos 1 5 t t 1 1 t 1 tdt 5 t t 1 1 tdt Where, σ and channel cross slope (m is shown in Fig., t is index variable between 1 and -1 and deformation variable (β is calculated as follows (Harr, 196. b y 1 m 1 cos 0 1 sin 1 t( 1 t t( 1 t ( 5 ( 5 ( t ( t ( 1 ( 1 tdt tdt (3 ( T 1 m y πσ b Fig.. trapezoidal cross-section (Swamee et al., 001. In order to calculate F s, Eq. (4 is simplified by combination of Eq. ( and Eq. (3 (Swammee et al., 000: F ( 77 46m ( 1 6m 1. 3 1. 3 ( 1. 3 6m b ( 1. 3 6m s (( 4 ( m ( y ( 1. 3 6m ( 1 6m This equation can be used when the water surface is deep and values m and b/y are between 0-1000 (Swammee et al., 000. Assumption of deep water level is true if the water depth is greater than T +3y (Swamee et al., 001. The error maximum of this equation is 1.8%, however in field practices in which 5<m<5 and 5<b/y<10, the error be less than 6% but when one of below three cases occurs, the error increases (Swammee et al., 000; 001: Case 1 :( b/y=10 and m=, case : (b/y=5 and m=1 and case 3: (b/y=1.3 and m=5 Once water level is not deep, Eq. (4 transforms as follow (Swamee et al., 001: (4 F s 1. 81 m 1. 3 b 1. 43 y 1. 3 4 m 93 9 77p 1. 3 b 100my. b 47. 6my 1. 57bm b y p p1 p 5 p1 d 1 y p1 p3 1 p1 (5
Where, p 1, p, p 3 are expressed as following equations:. 38b 7. 48my p1 b 8my p 3 p 1 6m 1. 3 6m 318b 6my 461b my (6 (7 (8 3.1 Results of seepage estimation using analytical method In analytical methods, main parameters to estimate the seepage are reservoir geometry and permeability of surrounding rocks. In this study, due to the changes of section size along the reservoir and difference in geological conditions, it is necessary which according to the boreholes location; the reservoir is divided to five parts (Fig.3. Fig. 3. Sections and the boreholes along the reservoir (MGCE, 010. To use the analytical equations in seepage estimation, first Lugeon number should be converted to according to permeability coefficient: 7 K 1. 310 Lu (9 Where, K is permeability coefficient (m 3 /day and Lu is Lugeon number obtained from Lugeon test in boreholes within the reservoir. Lugeon test is performed in the boreholes for different depths, which their results are given in Table 1 as mean, maximum and minimum values of Lugeon number. Table1 Lugeon test data from the boreholes (MGCE, 010. Boreholes BH BH3 BH4 BH5 BH6 BH7 BH8A Depth (m 10-5 4-30 17-45 4-50 40-45 -75 4-85 Lugeon number Minimum Mean Maximum 100 100 100 6 45.6 111 5 75 100 67.8 100 100 100 100 99 99.6 100 1 55. 100 In order to predict the upper and lower limits of seepage and most likely seepage rate, in each section the seepage rate calculated for the mean, minimum and maximum Lugeon number in each borehole. To calculate the seepage rate, first the values of b/ y and m for each section are placed in equation 6 and seepage factor (F s is calculated. Then, by placing y and K (mean, maximum and minimum
values in respective holes in Eq. (5 and multiplying the obtained value in length of the reservoir that is attributed to each section, the seepage is obtained for mean, maximum and minimum permeability coefficients. Summing the seepage values in five parts, total seepage from the reservoir is calculated. The values of parameters needed for this method and the obtained results of seepage estimation are shown in Table. Table Parameters required in analytical method (Vedernikov equation and seepage estimation results. Vedernikov parameters Section Section Section Section Section 1 3 4 5 y 50 50 45 45 45 b 344 84 45 54 55 b/y 6.88 5.68 5.44 5.64 5.67 m 1.6 1.6 1.6 1.6 1.6 F s 13. 11.9 11.63 11.85 11.89 K max 741.3 668.3 587.83 664.83 6097 q (m 3 /day/m K mean 44.77 4098 4487 73.1 598.56 7.413 13.366 146.96 35.94 594.96 K min L (Channel length Q (m 3 /day K max 160 118610 148363 100 58783 135 8975 184 110578 Reservoir 56086 K mean 67963 89018 44087 36871 110135 348074 1186 967 14696 485 109473 133174 K min Result shows, using the analytical method, in maximum permeability around 17.5%, in mean permeability around 11.6% and in minimum permeability around 4.5% of water volume of the reservoir is seeped as daily. 4. Seepage analysis using discrete method In many of the geological structures, the permeability of the rock matrix compared to fractures available at the rock mass is very negligible and a major part of the flow is through the fractures. In such cases, using method basis on discontinuous approach is necessary to obtain realistic estimations of flow (Mayer, 008. Since continuous methods do not properly take into account influence fractures in behavior of the flow through rock mass, in fractured rocks, discontinuous methods (discrete methods are an appropriate choice than continuous methods (Priest, 1993; Chaoshui and Dowd, 010. In a discrete method, fractures are considered as distinct structures. This issue requires to detailed data about the fractures properties and properties of fracture sets and distribution functions related to the properties. One of the numerical methods, which frequently used in discontinuous media, is distinct element method that its principles are used in the UDEC two-dimensional software. In this software rock mass are considered as a combination of intact rock and discontinuities in which intact rock is as rigid or deformable blocks that are placed between discontinuities (Itasca, 004. To evaluate the flow condition in rock mass around the given reservoir, first the reservoir geometry is defined and after determination the rock mass properties and boundary conditions governing to the problem, the flow equations may be solved. 4.1 Model geometry To estimate the seepage rate from upper reservoir of Rudbar dam, the rock mass be divided to several part based on the geological formations situation and lithological changes. Related data is collected at eight stations, but it is notable that station number 7 data is not used in this study (Fig.4. At each station, in order to determine the discontinuities condition, data are measured for
discontinuities that are shown in Table 3 (MGCE, 010. Among the discontinuities, those that control hydraulic and mechanical behavior of the rock mass have been used to modeling. Station name Sta.1 Sta. Sta.3 Sta.4 Sta.5 Sta.6 Sta.8 Table 3 Available discontinuities in stations One Two Three Bedding joint set joint set joint set Four joint set Fig. 4. Data Stations (Sta and modeling sections (Sec along the reservoir axis (MGCE, 010. Based on data collection stations, to optimize the computational time and best resolution, four sections along the reservoir are considered (Fig.4. Since at three of these sections, a data station was located on each side of them, in order to achieve estimations that have more accurate, each section is divided into two parts and each part according to the data related to station were separately simulated. In addition, this dividing makes smaller the models and subsequently increases the calculation speed. Since in the boreholes within the reservoir no groundwater had observed, to model the studied area, groundwater level is not applied in considered models. In order to construct the initial models, first according to the topography, modeling block is constructed. Then, geometrical properties of fracture sets such as orientation, spacing, length of fractures and length of rock bridges are applied to the models. 4. Mechanical properties of the rock mass and joints After constructing the initial models, mechanical properties of the rock mass and joints in saturated conditions should be applied to the model. The mechanical properties of intact rock and joints were determined for three major geological formations in the area including Dalan, Garo and Elam-Sarvak, which related data are shown in Tables 4 and 5, respectively. It is common that characteristic of weaker rock is used to model the rock mass (Bondarchuk et al., 009. Table 4 The intact rock mechanical properties of the formations within the reservoir in saturated condition. Formation type Garo Elam-Sarvak Dalan Friction angle ( 0 55 51 50 Cohesion (MPa 8.1 139 7.57 Elastic module (GPa 9..4 5 Poisson's ratio 7 1 Saturation density(kg/cm 3.71.71.75
Table 5 The mechanical properties of intact rock of the formations within the upper reservoir of Rudbar dam in saturated condition. Formation type Garo Elam-Sarvak Dalan Friction angle( 0 9.3 4.5 35.7 Cohesion (MPa 18 03 14 4.3 Static analysis After constructing the initial blocks of the models and apply the mechanical properties of the rock mass and discontinuities to models, boundary conditions include of situ stresses and displacement condition in the boundaries are applied and at this stage, the model should be reach to primary stability then run to the next stages. To simulate the initial state of ground without the water flow, excavation of the reservoir goes forward in multi stages until reach to the reservoir floor. At each stage of the excavation, the stresses changes and induced stresses concentration arises which made the model unbalance. Therefore, before going to next stage, the model should be stable and unbalance forces be near to zero. This process is performed for each and the results of these excavations are depicted in Fig.5 for the models 1-8. Model No.1 Model No. Model No.3 Model No.4 Model No.5 Model No.6 Model No.7 Model No.8 Fig. 5. Constructed models for dual parts of sections along the reservoir. 4.4 Flow analysis Due to reservoir water filling and water level changes, load cycles and considerable displacements arise in the rock mass. These changes are modeled as that pore water pressure is applied to the model
boundaries with increasing the water level in reservoir. Fig.6 shows an example of the boundary conditions applied to the model No.1 in the final stage of water filling. Fig. 6. Boundary conditions applied in model No. 1 Also at each stage of the water filling, the model should be stable and the flow becomes as steady state. For this purpose, a history of unbalanced forces in model and a history of the flow stability for each model are evaluated that an example of these evaluations is shown in Fig.7 for model No.1. (a (b Fig. 7. The histories of model No.1 after water filling stages in model 1: a Unbalanced forces, b Flow stability. After complete water filling and all the time derivatives of the flow field vanish (steady-state flow, seepage quantity from the reservoir and flow condition within rock fractures are specified. As is shown in Fig.8, the flow vectors direction, which are from walls and floor of the reservoir to outside it, indicate the water seepage condition at this section of the reservoir. (a (b Fig. 8. (a and (b are flow simulation in fractures of floor and wall of reservoir, respectively.
Based on the flow quantities through fractures intersected with the floor and walls of the reservoir, seepage rate can be calculated for each model and with sum of the values obtained from two models that constitute a section, the seepage rate for each section was determined. According to that, the seepage quantity is expressed as ratio of seepage rate per unit length, by multiplying seepage quantity of a section in length of the reservoir that is located in impact zone of the section; seepage rate is obtained for a certain length of the reservoir. By summing the values obtained for the different length of the reservoir, total seepage rate of the reservoir is calculated that the results are given in Table 6. It is noted that due to reach considered water level, parts of the reservoir walls need to concrete placement. Therefore, in models that are included these parts, concrete parts are modeled as impermeable. Table 6 The estimated seepage rate in different parts and total reservoir using UDEC Software. Sections q (m 3 /s/m L (channel length (m Q(m 3 /day Model 1 00383 163 33560 Model 0048 163 67539 Model 3 00501 171 36951 Model 4 Model 5 000809 000988 171 66 1195 707 Model 6 00694 66 61915 Model 7 Model 8 000437 001768 0 0 767 30857 Total reservoir 73108 5. Conclusion In the Chaleh-Hatam reservoir site, which is under construction as upper reservoir of Rudbar pumped storage power plant, Lugeon test performed in seven boreholes to determine the media permeability and discontinuities properties were collected using seven stations. At first, assuming continuity of media, seepage prediction using analytical method (Vedernikov equation for mean permeability were 348074 and 348880 m 3 /day, respectively. Then, as regards the reservoir site can be considered as discontinuous, using UDEC software, which is based on distinct element method, water seepage from the reservoir is estimated about 73108 m 3 /day. The results shown, in order to estimate the seepage rate using analytical method, choice the mean permeability coefficient was more acceptable and is more compatible with reality. If in analytical methods, minimum or maximum permeability coefficient is used, difference between obtained results in numerical and analytical methods will be more. In analytical method, a mean permeability coefficient is used and it is assumed that water level in is deep, this is way that the seepage rate calculated by analytical methods is larger than numerical methods. In this study, the seepage rate from the upper reservoir of Rudbar dam using the analytical method is about 31.5% larger than the numerical method. According to that, analytical methods are simple and save time and money, as a preliminary estimation of seepage rate can be useful. In environments where discontinuities are dominant structures to flow control within rock mass, discontinuous method is an appropriate solution to evaluate the flow condition in rock mass. The accuracy of analysis result obtained of discontinuous method is depends on available data and its quality. Using distinct element method, it was found that approximately 9% of the reservoir volume daily leaks. The results obtained of analytical and numerical methods show significant values of seepage. According to the importance of keeping the water in the Rudbar dam upper reservoir to provide electricity during peak hours of power consumption, a sealing method in this reservoir must be used.
6. References Bondarchuk, A., Ask, M. V. S. and Dahlström, L. O. and Nordlund, E., 01, Rock Mass Behavior Under Hydropower Embankment Dams: A Two-Dimensional Numerical Study, Rock Mechanics and Rock Engineering, 45(5, 819-835. Bondarchuk, A., Ask, M., Dahlström, L. O., Nordlund, E. and Knutsson, S, 009, Hydro-Mechanical Numerical Analyses of Rock Mass Behavior Under A Swedish Embankment Hydropower Dam, na. Harr, M. E., Groundwater and Seepage, 196, Chap, 10, 49-64. http:// www.darvill.clara.net/altenerg/pumped.htm, 014, Pumped Storage Reservoirs: Storing Energy To Cope With Big Demands. International Commission on Irrigation and Drainage (ICID, 1967, Controlling Seepage Losses from Irrigation Canals, Worldwide Survey, New Delhi. Itasca Consulting Group, Inc., 004, UDEC, Universal Distinct Element Code, Ver. 4.0 Theory and Background Manual, Minneapolis: Itasca. Mayer, J. (008. A Double-Continuum Approach for Two-Phase Flow in Macro porous Media: Parameter Study and Applications. Fachgebiet für Wasserwirtschaft und Hydrosystemmodellierung, Technische Universität Berlin. Mahab Ghodss Consulting Engineering (MGCE co., 010, Preliminary report of engineering geological studies, The first stage studies of Rudbar pumped storage power plant, Water and Power Resources Development Company, Iran. Priest, S. D., 1993, Discontinuity Analysis for Rock Engineering, Springer. Shamsayi, A. and Rasoly, K., 005, Detection and Protection Against Seepage From Dams, Publications Center of Science And Technology, University of Tehran, Iran. Swamee, P. K., Mishra, G. C. and Chahar, B. R., 000, Design of minimum seepage loss canal section, Irrigation and Drainage Engineering, 1, 16, 8-3. Swamee, P. K., Mishra, G. C. and Chahar, B. R., 001, Design of minimum seepage loss canal sections with drainage layer at shallow depth, Journal of Irrigation and Drainage Engineering, 17(5, 87-94. Xu, C. and Dowd, P., 010, A new computer code for discrete fracture network modeling, Computers & Geosciences, 36(3, 9-301.