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Intro. Hydrogeology (GEO 346C) Lecture 5: Ground Water Flow

Intro. Hydrogeology (GEO 346C) Lecture 5: Ground Water Flow. Instructor: Bayani Cardenas TAs: Travis Swanson and John Nowinski. www.geo.utexas.edu/course/geo346c/. What drives groundwater flow? What do you need in order to induce flow?. ENERGY, more specifically energy gradients.

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Intro. Hydrogeology (GEO 346C) Lecture 5: Ground Water Flow

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  1. Intro. Hydrogeology (GEO 346C) Lecture 5: Ground Water Flow Instructor: Bayani Cardenas TAs: Travis Swanson and John Nowinski www.geo.utexas.edu/course/geo346c/

  2. What drives groundwater flow? What do you need in order to induce flow? ENERGY, more specifically energy gradients What types of energy are present in a groundwater system? chemical, thermal, nuclear, mechanical Total mechanical energy per unit volume Etv=1/2rv2 +rgz + P Divide by density r Total mechanical energy per unit mass Etm= v2 +gz + P 2 r

  3. For steady flow (no acceleration and deceleration) and when the fluid is incompressible (no significant changes in r), the sum of the three components is constant: v2 +gz + P = constant 2 r The equation above is also known as the Bernoulli equation Divide by g Total mechanical energy per unit weight v2 +z + P = constant 2g rg

  4. Hydraulic head (h) = total mechanical energy per unit weight v2 +z + P = h 2g rg h = velocity head + elevation head + pressure head h = elevation head + pressure head = z + P/(g) What are the units or dimensions of h? h is expressed in terms of length

  5. Hydraulic head (h) components pressure head P/rg total head h elevation head z datum piezometer –small diameter well with a very short screen or section of slotted pipe at the end

  6. Hydraulic head (h) components

  7. Importance of accounting for head components

  8. Head distribution in 2D

  9. Head distribution in 2D

  10. Equipotential and flowlines along K boundaries This looks like Snell’s Law

  11. Refraction of equipotential and flowlines along K boundaries K1 << K2 K1 < K2 K1 > K2

  12. Refraction of equipotential and flowlines along aquifer boundaries

  13. Refraction of equipotential and flowlines along aquifer boundaries

  14. h=90 cm 70 80 60 50 Anisotropy in K, ground water flow and equipotential lines

  15. Anisotropy in K, ground water flow and equipotential lines Under anisotropic condictions, flow lines may be non-perpendicular to equipotential lines.

  16. Derivation of the Groundwater Flow Equations

  17. The Groundwater Flow Equations (transient flow, 3-dimensional, heterogeneous, anisotropic)

  18. The Groundwater Flow Equations under different conditions Steady-state (vs transient)

  19. The Groundwater Flow Equations under different conditions Steady-state (vs transient), homogeneous (vs heterogeneous)

  20. The Groundwater Flow Equations under different conditions Steady-state (vs transient), homogeneous (vs heterogeneous), isotropic (vs anisotropic) Divide everything by K

  21. Regional Groundwater Flow: Simple Aquifers

  22. Regional Groundwater Flow: Periodic Topography

  23. Regional Groundwater Flow: Periodic Topography

  24. Regional Groundwater Flow: Periodic Topography

  25. Regional Groundwater Flow: Different Topography

  26. Regional Groundwater Flow: Effect of permeability contrasts

  27. Regional Groundwater Flow: Aquifer Heterogeneity From Weissmann et al (SEPM, 2004)

  28. Groundwater Flow to Wells: Horizontal Flow Aquifers

  29. Groundwater Flow to Wells • Basic Assumptions • The aquifer is bounded on the bottom by a confining layer. • All geologic formations are horizontal and have infinite horizontal extent. • The potentiometric surface of the aquifer is horizontal prior to start of pumping. • The potentiometric surface of the aquifer is not changing with time prior to the start of pumping. • All changes in the position of the potentiometric surface are due to the effect of the pumping well alone. • The aquifer is homogeneous and isotropic. • All flow is radial toward the well. • Ground water flow is horizontal. • Darcy’s Law is valid. • Ground water has a constant density and viscosity. • The pumping well and the observation wells are fully penetrating; they are screened over the entire thickness of the aquifer. • The pumping well has an infinitesimal diameter.

  30. Radial Flow to Wells

  31. Groundwater Flow Equations in Radial Coordinates

  32. s=ho-h Drawdown and Cone of Depression ho h s is drawdown

  33. Pumping-induced flow in a CONFINED aquifer(steady-state or equilibrium conditions) Thiem equation

  34. Pumping-induced flow in a CONFINED aquifer(steady-state or equilibrium conditions) Q Requires 2 observation wells

  35. Pumping-induced flow in an UNCONFINED aquifer(steady-state or equilibrium conditions) Thiem equation

  36. Q Pumping-induced flow in an UNCONFINED aquifer(steady-state or equilibrium conditions) Requires 2 observation wells

  37. Transient or non-equilibrium conditions

  38. Pumping-induced flow in a CONFINED aquifer(transient or non-equilibrium conditions) Theis Method Requires 1 observation with head measurements at several times h is head at a given time t after pumping begins W(u) is the Theis well function, aka Theis curve u=r2SW(u) also known as exponential integral 4Tt S is storativity T is transmissivity r is radial distance to well

  39. Pumping-induced flow in a CONFINED aquifer(transient or non-equilibrium conditions) Theis Method • Plot time and drawdown field data in log-log paper (y= drawdown, x= time) • Place the Theis curve (i.e., W(u) well function) on top of the field data and until the Theis curve and the field data match • After “matching”, pick any “piercing point” on the overlain graphs. A convenient choice is to pick W(u)=1, and u=1. • Write down the corresponding time t and drawdown h to the picked W(u) and u values. • Convert the pumping rate/ discharge Q to volume per day • Convert time t to days • Compute T and S

  40. Pumping-induced flow in a CONFINED aquifer(transient or non-equilibrium conditions) Cooper-Jacob straight-line Method Requires 1 observation with head measurements at several times D(h-ho) is drawdown per log cycle tois the time where the straight line intersects the zero-drawdown axis

  41. Pumping-induced flow in a CONFINED aquifer(transient or non-equilibrium conditions) Cooper-Jacob straight-line Method • Plot time and drawdown field data in a semi-log paper with drawdown (linear y-axis) increasing in the negative y-direction and beginning at 0; time is in logarithmic scale (x-axis) • Draw a straight line through the late-time data • Get the drawdown per log cycle D(h-ho) • Project the line to the x-axis, the intercept at s=0 is time to • Convert the pumping rate/ discharge Q to volume per day • Convert time toto days • Compute T and S

  42. Pumping-induced flow in a CONFINED aquifer(transient or non-equilibrium conditions) Jacob straight-line Distance-Drawdown Method Requires 3 or more observation wells with simultaneous head measurements D(h-ho) is drawdown per log cycle t is time at which the observations are simultaneously made rois the distance where the straight line intersects the zero-drawdown axis

  43. Pumping-induced flow in a CONFINED aquifer(transient or non-equilibrium conditions) Jacob straight-line Distance-Drawdown Method • Plot drawdown as a function of radial distance of observation well in a semi-log paper with drawdown (linear y-axis) increasing in the negative y-direction and beginning at 0; distance r is in logarithmic scale (x-axis). The drawdown should be recorded at the same times. • Draw a straight line through the data • Get the drawdown per log cycle D(h-ho) • Project the line to the x-axis, the intercept at s=0 is ro • Convert the pumping rate/ discharge Q to volume per day • Compute T and S

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