The Application of Numerical Simulation on Groundwater Yield Calculation of Seepage Well

Transcription

1 The Application of Numerical Simulation on Groundwater Yield Calculation of Seepage Well Xu Jialu 1, Wang Wei 1, School of Environmental Science and Engineering, Chang an University, No. 16 Yanta Road, Xi an , China 1, Key Laboratory of Subsurface Hydrology and Ecology in Arid Areas, Ministry of Education, No.16 Yanta Road, Xi an , China Abstract In regions where rivers are not perennial or have low flow conditions during most part of the year(like banks of the Yellow River), the seepage wells are placed in the riverbed to obtain uninterrupted supply of naturally filtered groundwater through highly permeable saturated riverbed aquifers. Due to the complexities of flow, no exact analytical solution exists to provide steady state discharge drawdown relationship for seepage well. To overcome this difficulty, in this study a numerical model was developed for seepage well by adapting the equivalent hydraulic conductivity and the coupled seepage-pipe flow model. The numerical model is proposed to be applied for groundwater exploitation in Zaolinping Village which locates at Shenmu County, China. By calculation, the water yield of study area is m 3 /d. The results show that the proposed methodology based on the application of the coupled seepage-pipe flow model has been found to be efficient in constructing riverbed aquifer model with seepage well, which has a positive theoretical significance for guiding the design and construction of seepage well. Keywords seepage well, equivalent hydraulic conductivity, the coupled seepage-pipe flow model, groundwater yield I. INTRODUCTION The Quaternary alluvium of the Yellow River Valley is relatively thick with good permeability. Under the leakage recharge by the Yellow River, it is a favorable water source for centralized water supply. However, the water yield produced by traditional vertical wells is small, which can not meet the need of urban water consumption. According to the experience of regions with similar conditions, seepage wells can be adopted as the method for groundwater exploitation at the banks of the Yellow River. A seepage well consists of a vertical well, chamber, gallery and a number of radiation holes. Each seepage well has several chambers to which the radiation holes are connected. The radiation holes spread laterally through an aquifer and collect water when groundwater abstraction occurs at the vertical well. Usually the vertical well is constructed at the bank of the river with a depth of 0-30m, which is the water intake of seepage well. Seepage wells have the following advantages over traditional vertical wells: the drawdown is lower, groundwater tends to enter the wells at low velocities, the wells do not need frequent cleaning, and the operating cost of the wells tends to be low(bakker et al., 005). Owing to these benefits, in recent years, seepage wells have attracted considerable attention as groundwater supply wells. A number of studies on seepage wells have been carried out. Therefore, in this paper a methodology of numerical model is developed to construct the seepage well. The proposed model is applied in Zaolinping Village which locates at Shenmu County, China. II. FLOW CHARACTERISTICS OF SEEPAGE WELL Diverse flow regimes coexist in the seepage well system. Usually the groundwater flow through a porous medium is laminar flow with low Reynolds number(re<1~10), which can be explained on the basis of mass conservation and Darcy s law. In contrast, flow within a well pipe with great hydraulic radius and great Reynolds number can not be represented on the basis of Darcy s law, which is only valid for laminar flows, thus other flow regimes can not be expressed. The quantity of water intake is mostly from saturated riverbed aquifer in the early days, while the river infiltration is little. With the continuation of work time, the water level of the aquifer is lower than that of the river, then the river infiltration increases. When the pumping intensity is not too large and the seepage well system reach a steady state in a short period of time, the quantity of water intake is almost entirely from the river leakage supply. Groundwater flow around a seepage well has significant three dimensional flow characteristics. III. CALCULATION MODEL OF SEEPAGE WELL Due to the complex flow characteristics, it is difficult to describe the boundary condition of the seepage well system. 6

2 Chen et al. proposed a new numerical approach that a well can be represented by an equivalent hydraulic conductivity that depends on the Reynolds number within the pipe, which is called the coupled seepage-pipe flow model. According to the coupled seepage-pipe flow model, different flow regimes can be expressed and connected by the equivalent hydraulic conductivity. When the water flow is laminar flow, the equivalent hydraulic conductivity K l in the well pipe can be expressed as: K l = d 3 (1) Where is heavy rate of water, d is equivalent diameter of the well pipe is the dynamic viscosity coefficient of water. When the water flow is turbulent flow, the equivalent hydraulic conductivity K n in the well pipe can be expressed as: K n = gd fv () Where g is the acceleration due to gravity, f is the coefficient of friction, is the seepage velocity in well pipe. From the formula above, the flow law of a seepage well system can be expressed as the form of Darcy s law, which means that the seepage flow can be coupled with the pipe flow. Thus a numerical model for seepage well is constructed: H H H Khe Khe Kve 0 x, y, z D x x y y z z H 0 zero flow boundary n Kr H r H qr river boundary M r Qe CH p H exchange flow between pipeand aquifer d d g H laminar flow 4 3 l d gd d 1 H Q p smooth turbulent flow pipeflow v l d d 1 H 8gd log 3.71 rough turbulent flow 10 4 e v l H z H water table boundary 0 n p H x, y, z H s vertical well boundary K K e = K K l n hydraulicconductivity in aquifer medium, laminar flow equivalent hydraulicconductivity in" WellPipe", laminar flow equivalent hydraulicconductivity in" WellPipe", turbulent flow 7

3 Where H is head; K is hydraulic conductivity; n is exterior normal vector of the second boundry; n p is internal normal vector of the water table boundary; C is the conductance of pipe screen material; Q e is the exchange flow rate between well pipe and aquifer; Q p is the flow rate in well pipe; K r is the vertical hydraulic conductivity of medium in riverbed; M r is the thickness of medium in riverbed; q r is specific river leakage; q is the specific flow rate of the second boundry of per unit area; H is head loss and υ is fluid viscosity coefficient. IV. APPLICATION The study area is located in Shenmu County, Shaanxi Province, China, longitude110 50, latitude38 83, where the aquifer medium is mainly Quaternary Holocene gravel layer and Triassic clastic bedrock weathering zone. The Yellow River lies on the northeast of the study area. Under natural conditions, the groundwater discharges to the Yellow River after the areal precipitation infiltration recharge; under the conditions of future exploitation, massive exploitation of groundwater will stimulate massive leakage recharge of the Yellow River. Thus the Yellow River can be conceptualized as the third kind of boundary. The southwest boundary of the study area is the interface between Mesozoic bedrock and alluvia of the river valley, which can be conceptualized as the non-flow boundary due to underdeveloped fractures of Mesozoic bedrock; the bottom surface is complete Mesozoic bedrock constituting regional impervious base. Under natural conditions, after being recharged through the infiltration of precipitation, groundwater is flowing from west to the east on the whole and finally discharging into the Yellow River. Under the condition of riverside exploitation, the stimulated leakage of the Yellow River becomes the dominating recharge source, and the manual exploitation is the major discharge(chen Chongxi et al.,008). According to the experience of regions with similar conditions, seepage wells can be adopted as the method for groundwater exploitation at the banks of the Yellow River. To depict the complex structure of the seepage well accurately, rectangular units are used in the fine discretization of the calculation domain. Zaolinping model area is discretized into 300 columns along the east-to-west direction and 60 rows along the north-to-south direction. The horizontal interval of the discretization grid is 5m. The number of active cells in a single-layer is 7550, and the horizontal area actually represented is m. The model domain is subdivided into 11 layers vertically; in which the Quaternary aquifer is discretized into 3 layers and the bedrock fractured aquifer is discretized into 8 layers. Thus, the total number of active cells is According to local hydrogeology conditions, seven seepage wells(two vertical wells are 400m apart) are laid in the study area. Each seepage well has five chambers and the spacing between two chambers is 60m or 70m. A threedimensional finite difference method is used to calculate the water yield of the study area when the drawdown of seepage well is 5m. The calculation results are shown in Table I. The total yield in the normal is m 3 /d and the steady state flow fields under the pumping of 7 seepage wells is shown in Fig I. 8

4 Table I. Results of simulation for Seepage Well s Pumpage Well number Water yield composition(m3/d) Total yield(m 3 /d) Proposed yield(m 3 /d) Chamber1 Chamber Chamber3 Chamber4 Chamber5 gallery Vertical well ZLP ZLP ZLP ZLP ZLP ZLP ZLP Total wells As the recession of water boundary of the Yellow River in the dry season, the water yield will decrease obviously. In order to calculate the water yield of seepage wells during the dry season, reset the condition of water boundary and water level in the model. Thus the water yield in the dry season can be calculated. The results show that the total yield in the dry season is 47600m 3 /d, decreases by.07%. With a storage facility, the infiltration replenishment of the river in the normal season can be stored, which can be used in the dry season, thus the water utilization rate of the region will increase markedly. Fig I. Drawdown contour map of seepage wells, normal season V. CONCLUSIONS A coupled seepage-pipe flow model for seepage well was proposed by introducing the concept of equivalent hydraulic conductivity. The proposed model was applied in Zaolinping Village for water supply field of seepage wells. The water yield of study area was calculated by adopting the three-dimensional groundwater flow finite difference method. The total water yield is 61300m 3 /d in the normal season, which is 47600m 3 /d in the dry season. The results show that the mathematic model can greatly reflect the flow characteristics of seepage well. 9

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