SEES 503 SUSTAINABLE WATER RESOURCES GROUNDWATER. Instructor. Assist. Prof. Dr. Bertuğ Akıntuğ

Transcription

1 SEES 503 SUSTAINABLE WATER RESOURCES GROUNDWATER Instructor Assist. Prof. Dr. Bertuğ Akıntuğ Civil Engineering Program Middle East Technical University Northern Cyprus Campus SEES 503 Sustainable Water Resources 1/70

2 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources /70

3 Introduction Groundwater Hydrology: deals with the existence, movement, quantity, and quality of water in the soil formations below the ground surface. Application areas the water supply through the wells, water storage in underground reservoirs, solution of groundwater contamination problems, lowering the groundwater table etc. SEES 503 Sustainable Water Resources 3/70

4 Introduction Number of wells and their depths in different regions of Turkey (DSI, 1995) Groundwater: 0.76% of all waters 30% of the total fresh water generally free from pollution useful for domestic and irrigation use In Turkey 40% of total fresh water In USA 5% of total fresh water The surface water and groundwater feed each other. Therefore the exchange between ground and surface water source must be understood clearly. SEES 503 Sustainable Water Resources 4/70

5 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources 5/70

6 Occurrence of Subsurface Water In general, the water below the surface of the soil occurs in two major zones separated by ground table. Zone of aeration. The pores contain water and air. The pores completely full of water SEES 503 Sustainable Water Resources 6/70

7 Occurrence of Subsurface Water Aeration Zone: There are three different parts in aeration zone. There are four types of water in the aeration zone. gravity water capillary water hygroscopic water water vapor Root zone: Thickness depends on the type of vegetation. Thickness depends on the size of the soil particles. SEES 503 Sustainable Water Resources 7/70

8 Occurrence of Subsurface Water Field Capacity: The amount of water remaining in the soil after percolation. Wilting Point: The lower limit of water content in the soil at which plants cannot extract water any more. Irrigation should be applied before wilting point is reached. Equilibrium points in the soil SEES 503 Sustainable Water Resources 8/70

9 Occurrence of Subsurface Water Saturation Zone: Water in the saturation zone is called groundwater. The geologic formations which contain water are called aquifers. They are generally sand and gravel formations and classified as Confined Aquifers Unconfined Aquifers SEES 503 Sustainable Water Resources 9/70

10 Occurrence of Subsurface Water There are mainly four different formations in saturated zones: Aquifer is the saturated permeable geologic formation, which contains and transmits water in economic amounts, under ordinary hydraulic gradients for water supply and has generally sand and gravel. Aquifuge is sold granite type formation and it neither contains nor transmits water, therefore totally accepted as totally impervious. Aquiclude is relatively impermeable saturated material like clay. It generally contains but not transmit it, therefore it is also accepted as impervious. Aquitard is a formation, which may not transmit water to a well in economic amounts but may feed an adjacent aquifer through the leakage especially if it is thick. Such formations generally contain sandy clay or gravel in them. SEES 503 Sustainable Water Resources 10/70

11 Occurrence of Subsurface Water Types of Aquifers: SEES 503 Sustainable Water Resources 11/70

12 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources 1/70

13 Storage Characteristics of Aquifer Porosity: The ratio of pore volume to the total volume. The amount of water stored in an aquifer is a function of its porosity. Pore size vary greatly in different soils. Clay and shale very small pores Limestone and lava very large pores SEES 503 Sustainable Water Resources 13/70

14 Storage Characteristics of Aquifer The productivity of the aquifer is not directly related to its porosity. A different characteristics is defined to represent aquifers total water storage and also ability to transmit it. Storage coefficient (storativity, S) volume of water released from storage (or added to it) / unit horizontal area of the aquifer / unit decline (or rise) in the piezometric head. SEES 503 Sustainable Water Resources 14/70

15 Storage Characteristics of Aquifer S b S s S s : Specific Storativity b: thickness of the aquifer. The mechanism of releasing water in confined and unconfined aquifer are completely different. SEES 503 Sustainable Water Resources 15/70

16 Storage Characteristics of Aquifer Water Release in Unconfined Aquifer As water is pumped from a well (water release) the piezometric surface, which is ground water table, drops. However pores are not completely drain. (The specific storativity of unconfined aquifer) < (the porosity) Specific storativity Specific Yiled SEES 503 Sustainable Water Resources 16/70

17 Storage Characteristics of Aquifer Water Release in Unconfined Aquifer Specific Retention Porosity - Specific Yield Retantion clay % Retantion sand(coarse) % SEES 503 Sustainable Water Resources 17/70

18 Storage Characteristics of Aquifer Water Release in Confined Aquifer The storage coefficient is a function of the elasticity and compressibility of the aquifer. Total stress: σ T σ s + p σ s : skeleton stress p: water pressure When water is pumped from a well, the water pressure drops (dp). Since the load above is unchanged and has to be carried, the extra part is carried by the skeleton of the medium and therefore there will be an increase in the skeleton stress with in the same amount. dσ s - dp SEES 503 Sustainable Water Resources 18/70

19 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources 19/70

20 Fundamentals of Groundwater Flow For easy processing, the actual porous medium is replaced by an imaginary medium which has the same characteristics. In the imaginary medium, variables and the characteristics are averaged and assumed to represent the whole porous medium for groundwater flow. This is called continuum approach. A sample of porous medium SEES 503 Sustainable Water Resources 0/70

21 Fundamentals of Groundwater Flow The flows in a actual porous medium occurs between particles as seen in figure (a), having and actual velocity distribution as shown in figure (b). The actual velocity will be a function of all three cartesian coordinates plus time, which is difficult to deal with. Therefore, a simple velocity definition is given for groundwater flow analysis. It is named as discharge velocity, specific discharge or superficial velocity. SEES 503 Sustainable Water Resources 1/70

22 Fundamentals of Groundwater Flow discharge velocity superficial velocity specific discharge Discharge through a representative area of porous medium Representative area From here on in the following parts the term velocity will mean discharge velocity as it is defined above. SEES 503 Sustainable Water Resources /70

23 Fundamentals of Groundwater Flow Total head, h is constant for a liquid at rest or in uniform horizontal flow. This is also valid for a saturated continuous porous medium. Velocity head (v /g) is neglected, since the velocity is very small. p z + γ h (constant) Heads in unconfined and confined aquifers SEES 503 Sustainable Water Resources 3/70

24 Fundamentals of Groundwater Flow Darcy Law Q h h1 AK L AK dh dl Where Q: flow rate (m 3 /s) A: cross sectional area (m ) K: Hydraulic conductivity or permeability (m/s) h: Hydraulic head L: Length dh/dl: hydraulic gradient Darcy s experiment SEES 503 Sustainable Water Resources 4/70

25 Fundamentals of Groundwater Flow Permeability or hydraulic conductivity is the measure of resistance of the medium to the flow and it is a function of the characteristics of both fluid and porous medium. Permeability or hydraulic conductivity change with time and location. SEES 503 Sustainable Water Resources 5/70

26 Fundamentals of Groundwater Flow SEES 503 Sustainable Water Resources 6/70

27 Fundamentals of Groundwater Flow Heterogeneity and Anisotropy Isotropic anisotropic: If the hydraulic conductivity is the same in all directions of flow at a certain point, the medium is said to be isotropic, otherwise anisotropic. In an anisotropic medium directions at which the hydraulic conductivity gets its maximum and minimum value are called principal directions of anisotropy. Homogeneous Heterogeneous: If in a medium hydraulic conductivity does not change from one point to the other, the medium is said to be homogeneous, otherwise heterogeneous SEES 503 Sustainable Water Resources 7/70

28 Fundamentals of Groundwater Flow Possible combinations of heterogeneity and isotropy (Sevuk, 1986) SEES 503 Sustainable Water Resources 8/70

29 Fundamentals of Groundwater Flow When hydraulic conductivity is considered to be different in the three cartesian directions, then the velocity components in these directions will be given with corresponding conductivity value in Darcy s Law. V x K x dh dx V y K y dh dy V z K z dh dz SEES 503 Sustainable Water Resources 9/70

30 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources 30/70

31 Groundwater Flow Equations Confined Aquifers Groundwater flow equations Continuity Equation + Darcy s Law q v Leakage into the aquifer / unit horizontal area. Thickness of the aquifer Control Volume SEES 503 Sustainable Water Resources 31/70

32 Groundwater Flow Equations Confined Aquifers The net flux through the control volume is equal to the rate of change of mass, which is given as: where ρ : density of the fluid S: storage coefficient of the aquifer : change of head with time dx, dy: elementary horizontal distance h / t NET FLUX ρ S h t dx dy SEES 503 Sustainable Water Resources 3/70

33 SEES 503 Sustainable Water Resources 33/70 8. GROUNDWATER 8. GROUNDWATER Groundwater Flow Equations Confined Aquifers For two-dimensional unsteady flow case in confined aquifers, the equation will be as when velocity components are expressed as given by Darcy s Law, and the aquifer thickness times the permeability (b x K) is defined as transmissivity, T of the aquifer the following equation will be obtained ( ) ( ) t h S q bv y bv x v y x + t h S q y h T y x h T x v y x +

34 SEES 503 Sustainable Water Resources 34/70 8. GROUNDWATER 8. GROUNDWATER Groundwater Flow Equations Confined Aquifers This equation is called general differential equation of groundwater When the aquifer is homogeneous, transmissivity does not change with location t h S q y h T y x h T x v y x + t h S q y h T x h T v y x +

35 SEES 503 Sustainable Water Resources 35/70 8. GROUNDWATER 8. GROUNDWATER Groundwater Flow Equations Confined Aquifers In addition to homogenity, if aquifer is also isotropic then T x will be equal to T y which will be a constant transmissivity value T If there is no leakage to the aquifer, the term q v will also drop Finally if the flow is steady, the change in head with respect to time will be zero and Laplace equation for two dimensional groundwater flow will be obtained. t h T S T q y h x h v + + t h T S y h x h y h x h

36 Groundwater Flow Equations Unconfined Aquifers In unconfined aquifers there is also a vertical velocity component. To avoid this difficulty, Dupuit approximation is made which assume the slope of the water table as negligible. This way the flow is assumed to be horizontal as seen in the figure. The general equation for anisotropic, heterogeneous and unconfined aquifer x K x h h x y K y h h + y q v S y h t S y : specific yield h: depth of the aquifer SEES 503 Sustainable Water Resources 36/70

37 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources 37/70

38 Unsteady Radial Flow (Well Hydraulics) For the solution of the problems, groundwater equation is used considering the following assumptions. 1. Aquifer is homogeneous, isotropic and infinite in areal extent.. The thickness of the aquifer is constant. 3. Pumping is continuous with a constant rate. 4. Well diameter is infinitely small. 5. Initially piezometric surface is horizontal. The solution for the following two case will be presented here. Fully penetrating well in a confined aquifer. Fully penetrating well in a leaky confined aquifer. SEES 503 Sustainable Water Resources 38/70

39 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer When the well penetrates, the flow towards the well will be in horizontal direction only. Theis and Cooper - Jacob Methods An infinite, homogenous, and isotropic aquifer having constant thickness. The drawdown, s, can be found by the solution of the following equation: s + 1 r r s r S T s t Fully penetrating well in a confined aquifer. SEES 503 Sustainable Water Resources 39/70

40 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Theis and Cooper - Jacob Methods (continued) s + 1 r r s r Equation is subject to the following initial and boundary conditions: S T s t 1. s(r,0)0 Drawdown is zero at any point at time zero.. s(,t)0 Drawdown is zero at any time when the point is infinitely far away. lim s r r 3. Point sink condition r 0 Q π T SEES 503 Sustainable Water Resources 40/70

41 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Theis and Cooper - Jacob Methods (continued) For the solution, Boltzman variable is defined u r S 4Tt Then the drawdown, s: s Q 4π T W ( u) where x e W ( u) dx This solution type is called x u Theis method. Q: discharge (m 3 /s), s: drawdown (m) r : radial distance (m), S: storage coefficient, T: transmissivity (m /s) t: time from the start of pumping (s) SEES 503 Sustainable Water Resources 41/70

42 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Theis and Cooper - Jacob Methods (continued) W(u) well function: W(u) u for a confined aquifer. SEES 503 Sustainable Water Resources 4/70

43 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Theis and Cooper - Jacob Methods (continued) Well function can be expressed as an infinite series as W ( u) ln u + u u +! 3 u ±K 3 3! When u is small, u<0.01, the terms after the first two, become very small and therefore well function can be approximated by the first two terms. Then drawdown equation will be s Q 4π T ln r S 4Tt SEES 503 Sustainable Water Resources 43/70

44 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Theis and Cooper - Jacob Methods (continued) After rearranging and converting the ten-base logarithm equation will be.3q 4π T log.5tt r S s the drawdown This solution is first given by Cooper and Jacob (1946) and is valid for small u values. As it is seen from the definition of u, it will be small if r is small or t is large. u r S Tt SEES 503 Sustainable Water Resources 44/70

45 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Theis and Cooper - Jacob Methods (continued) Both methods has some practical applications such as Determination of aquifer characteristics, S and T, by performing pumping tests with observations of discharge and corresponding drawdown and time. For an aquifer with known characteristics, S and T, determination of drawdown for a certain discharge at a certain location and time. Determination of maximum discharge for a maximum permissible drawdown at a certain location and time within an aquifer, whose characteristics are known. SEES 503 Sustainable Water Resources 45/70

46 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Determination of Aquifer Characteristics Aquifer characteristics, S and T, can be determined graphically by 1. Theis Method, or. Cooper Jacob Method Theis Method s Q 4π T W ( u) u r S 4Tt r T 4 t S u log s Q log logw ( u) 4π T + log r t log 4T S + logu SEES 503 Sustainable Water Resources 46/70

47 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Determination of Aquifer Characteristics Theis Method Using the similarity of these two equations and conducting a pumping test with constant rate for a long duration S and T can be determined with the following procedure 1. A plot of W(u) u (type curve) is prepared on log-log paper graph a. Theis graphical method SEES 503 Sustainable Water Resources 47/70

48 Unsteady Radial Flow (Well Hydraulics) Determination of Aquifer Characteristics Theis Method. From the pumping test data, a plot of r /t s is prepared on a transparent log-log paper (graph b). The length of cycle in both graphs should be the same. Theis graphical method SEES 503 Sustainable Water Resources 48/70

49 Unsteady Radial Flow (Well Hydraulics) Determination of Aquifer Characteristics Theis Method 3. The plot of data is superimposed on type curve keeping the coordinate axes parallel to each other and adjusting as many points as possible on the curve. 4. An arbitrary point is selected and corresponding four coordinate values are obtained form the four axes: W(u) *, u *, values from graph a and (r /t) * and s * values from graph b. Theis graphical method SEES 503 Sustainable Water Resources 49/70

50 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Determination of Aquifer Characteristics Theis Method T QW ( u) 4π s S 4Tu ( r / t) SEES 503 Sustainable Water Resources 50/70

51 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Determination of Aquifer Characteristics Cooper - Jacob Method Plot s t on a semi-log paper where s will be on linear axis. Slop of the line gives transmissivity. T. 3Q 4π s SEES 503 Sustainable Water Resources 51/70

52 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Determination of Aquifer Characteristics Cooper - Jacob Method Plot s t on a semi-log paper where s will be on linear axis. The line is extended to find t 0. S.5t r 0 T SEES 503 Sustainable Water Resources 5/70

53 Unsteady Radial Flow (Well Hydraulics) Fully Penetrating Well in a Confined Aquifer Determination of Aquifer Characteristics Cooper - Jacob Method For Cooper Jacob method, u mast be small. u should be checked after T and S are determined. If u is not less than 0.01, the new straight line should be tried for larger time portion of the data points The procedure is then repeated to determine satisfactory S and T. SEES 503 Sustainable Water Resources 53/70

54 Overview Introduction Occurrence of subsurface water Storage characteristics of aquifers Fundamentals of groundwater flow Groundwater flow equations Unsteady radial flow (well hydraulics) Generalization of solutions SEES 503 Sustainable Water Resources 54/70

55 Generalization of Solutions The following assumptions were made for the analytical solutions: 1. There is a single well. The well is pumping with a constant rate continuously 3. Aquifer is infinite in areal extent. To be able to solve practical cases one more assumption has been made. 4. Aquifer system and governing groundwater flow equations are linear and superposition method is applied. SEES 503 Sustainable Water Resources 55/70

56 Generalization of Solutions Multiple Well Case The drawdown at any point in an aquifer is equal to the summation of all drawdowns occurring due to each of the wells independently. Drawdown in a confined aquifer with two pumping wells SEES 503 Sustainable Water Resources 56/70

57 SEES 503 Sustainable Water Resources 57/70 8. GROUNDWATER 8. GROUNDWATER Generalization of Solutions Multiple Well Case ) ( 4 ) ( u W T Q u W T Q s s s π π + + Tt S r u Tt S r u 4 and n i i i u W T Q s 1 ) ( 4π In general

58 Generalization of Solutions Multiple Well Case Q 1 Q Q 3 Drawdown in a three well system SEES 503 Sustainable Water Resources 58/70

59 Generalization of Solutions Variable Pumping Assuming that pumping started with discharge Q 0 at time t 0 and increased with amounts Q 1, Q,, Q n, at time t 1, t,, t n. The drawdown at a distance r from the well will be: s n Q0 1 W ( u + 0) Qi W ( u i ) 4π T 4π T i 1 u 0 r S 4Tt * and u i ri 4T ( t * S t i ) t * the time at which drawdown is required SEES 503 Sustainable Water Resources 59/70

60 Generalization of Solutions Variable Pumping Superposition of drawdowns for stepwise pumping SEES 503 Sustainable Water Resources 60/70

61 Generalization of Solutions Variable Pumping (Recovery of a well) s Q 4 π T ( W ( u ) W ( )) 1 u Drawdown for recovery after pumping is stopped t d time after pumping is stopped. u 1 r S 4Tt * and u r 4T ( t * S t d ) SEES 503 Sustainable Water Resources 61/70

62 Generalization of Solutions Finite Aquifer One of the assumptions for the solution of the groundwater equation was the infinity of aquifer in areal extent. But this may not be true in reality. There may be a recharge (wet) boundary (i.e. river, lake, reservoir) nearby the well or There may be a barrier (impervious) boundary (i.e. rocky area) nearby the well. For the solution of such cases image well concept is used together with superposition assumptions. In this concept, the aquifer with a boundary is replaced by an imaginary aquifer with infinite areal extend and an imaginary well located at a point symmetrical to the real well with respect to the boundary. SEES 503 Sustainable Water Resources 6/70

63 Generalization of Solutions Finite Aquifer In case of impervious boundary, the image well is assumed to be pumping with the same rate as real well and having the same drawdown curve. Then actual drawdown will be determined by summation of the two drawdowns as shown in the figure. Q s + 4 π T ( W ( u ) W ( )) r u i u r rr S 4Tt and u i ri S 4Tt Effect of impervious boundary SEES 503 Sustainable Water Resources 63/70

64 Generalization of Solutions Finite Aquifer In case of recharge boundary, the image well is assumed to be recharging, instead of discharging, with the same rate as the real well so that its effect will decrease the drawdown as shown in the figure. The two drawdowns will cancel their effect at the boundary location. s Q 4 π T ( W ( u ) W ( )) r u i u r rr S 4Tt and u i ri S 4Tt Effect of recharge boundary SEES 503 Sustainable Water Resources 64/70

65 Generalization of Solutions Finite Aquifer The image well approach more than one boundary around the well A well with two impervious boundaries on both sides. i.e. a well in an alluvial valley with parallel impervious sides Image wells in a confined valley aquifer SEES 503 Sustainable Water Resources 65/70

66 Generalization of Solutions Finite Aquifer In parallel boundary case, if on one side there is a river while the other boundary is impervious, then the type of the images will change. Image wells system for parallel boundaries SEES 503 Sustainable Water Resources 66/70

67 Generalization of Solutions Finite Aquifer Another case may be semi-infinite strips aquifer, where two parallel boundaries end at right angle at a third boundary. Image wells system for semi infinite aquifer SEES 503 Sustainable Water Resources 67/70

68 Generalization of Solutions Finite Aquifer Another case my be a rectangular aquifer. Image wells system for rectangular aquifer SEES 503 Sustainable Water Resources 68/70

69 Generalization of Solutions Finite Aquifer When the boundaries converge to each other wedge shaped aquifers are produced. Image wells system for wedge shape aquifers with 90º angle. SEES 503 Sustainable Water Resources 69/70

70 Generalization of Solutions Finite Aquifer When the boundaries converge to each other wedge shaped aquifers are produced. Image wells system for wedge shape aquifers with 45º angle. SEES 503 Sustainable Water Resources 70/70