Unit 01 : Advanced Hydrogeology Review of Groundwater Flow Malcolm Reeves Civil and Geological Engineering

What is hydrogeology? Hydrogeology is the study of the laws governing the movement of subsurface water, the mechanical, chemical and thermal interaction of this water with the porous solid, and the transport of energy, chemical constituents and particulates by the flow. Domenico and Schwartz, 1997

Laws governing movement Darcy’s Law Q = -A.K dh/dx Q is the flow, K is the hydraulic conductivity, dh/dx is the head gradient and A is the cross sectional area normal to x. Q/A = q = -K dh/dx q is called the specific discharge v = q/n = -(K/n) dh/dx v is the advective (flow) velocity n is the porosity

Mechanical, Thermal and Chemical Interactions Mixing caused by –Hydraulic (mechanical) gradients (dh/dx) –Thermal gradients (dT/dx) –Chemical gradients (dC/dx) Interactions of fluids with the porous medium

Groundwater Transport Groundwater transports fluids. The process is called advection. Advection of fluid also carries: –Solutes (metals, organics, nutrient, etc) –Particulates (colloids, bacteria, etc) –Energy (mainly heat)

Hydrologic Cycle

Elements of the Hydrologic Cycle Condensation Precipitation Evaporation Transpiration Interception (Interception refers to precipitation that does not reach the soil, but is instead intercepted by the leaves and branches of plants and the forest floor. precipitation Infiltration Percolation Runoff

Water Profile Bound Water in Minerals Capillary Water Intermediate Vadose Water Water in Unconnected Pores Groundwater Soil Water Interstitial Zone Saturated Unsaturated

Subsurface Flow Infiltration flow entering at the ground surface Percolation vertical downward unsaturated flow Interflow sub-horizontal unsaturated and perched saturated flow Groundwater flow sub-horizontal saturated flow

Soil Moisture J F M A M J J A S O N D Millimetres of Water Spring Recharge Fall Recharge Soil Moisture Depletion Potential Evaporation Adjusted Precipitation

Infiltration Capacity Water supplied to the soil surface at an increasing rate will eventually runoff. Water supplied to the soil surface at a constant rate infiltrates at a rate that decreases with time to a limiting rate. This limiting rate (when the soil is saturated) is called the infiltration capacity of the soil surface.

Field Capacity Flow of water in an unsaturated soil cannot take place until a limiting moisture content is reached. This limiting moisture content is called the field capacity of the soil in soil science and the residual water saturation in hydrogeology.

Infiltration Infiltration Rate 0% Moisture Content 100% Infiltration Capacity Field Capacity Infiltration Capacity [ LT -1 ] Field Capacity [ % ]

Hydrograph Components Stream flow hydrographs can be broken down into three components: –Runoff (overland flow) –Interflow (unsaturated sub-horizontal flow) –Baseflow (groundwater flow) Each component has a characteristic recession (decay) rate.

Baseflow The decline of the flow in a stream in the absence of input is called recession Empirically, recession curves are exponential decay functions Q = Q o e -kt. After long periods without precipitation, the recession rate is called baseflow and is characteristic of the groundwater system feeding the stream. The groundwater recession constant is given by the equation k = ln(Q o /Q)/t

Hydrograph Analysis Point A is minimum Q gradient is determined from recession rate Point B is maximum Q Point C is Q at time T* after the peak: T* = A n where A is the drainage area and n is an empirical power. If A is in km 2, n = 0.14 If A is in mile 2, n = 0.20 Time Discharge A B C T*

Global Hydrological Equation Input – Output = Change in Storage P – E –T – R o =  S Pprecipitation E evaporation T transpiration R o runoff  Schange in groundwater storage P = I (DS) + R (Ro) + E (T+E)

Elements of the Basin Cycle Surface Soil Aquifer F PETsTs RsRs TaTa Stream Channels RoRo QoQo QiQi QsQs QaQa For the groundwater sub-system R s + Q i – T a – Q a =  S

Aquifer Types Unconfined - storage LARGE depends on specific yield Confined - storage SMALL depends on compressibilities =κρεμάμενος υδροφόρος

Porosity

Specifics of Aquifer Storage Unconfined S y = n - S r n porosity S y specific yield (gravity drainage) S r specific retention (like field capacity) Confined S = b.S s b thickness S s specific storage S s = .(  + n.  )  specific weight  matrix compressibility  water compressibility

Specific Yield

Hydraulic Conductivity

Steady-State Flow q = -K dh/dx K is hydraulic conductivity [ LT -1 ] h is hydraulic head [ L ] q = -(k  /  ) dh/dx k is intrinsic permeability [ L 2 ]  is absolute viscosity [ FL -2 T ]  is specific weight [ FL -3 ] For horizontal flow  dh/dx = dp/dx q = -(k/  ) dp/dx p is fluid pressure [ FL -2 ]

Vertical Flow For vertical flow q = -K dh/dz h = p/  + z dh/dz = (1/  ) dp/dz q = -(k  /  ) dh/dz q = -(k/  )(dp/dz + 1)

Steady-State Flow Systems

Density-Dependent Flow For density-dependent flow q = K dh/dz h = p/  + z dh/dz = (1/  )(dp/dz – (p/  )d  /dz + 1) q = -(k  /  ) dh/dz q = -(k/  )(dp/dz + 1 – (p/  )d  /dz)

Unsaturated Flow For unsaturated flow q = -K(  ) dh/dz h =  + z  is the pressure head z is the elevation head h is the total hydraulic head The pressure head,  depends on saturation. At full saturation,  increases with depth. In the unsaturated zone,  is negative and is called suction pressure.

Soil Water Characteristic Curve - Pressure + Depth Water Table 0% Saturation 100% + Pressure - Water Table Hydraulic Conductivity

Steady-State and Transient Flow Steady-State Inflow = Outflow dq/dx = d(K dh/dx)/dx = 0 Transient Inflow - Outflow = Change in Storage dq/dx = d(K dh/dx)/dx = S.dh/dt K is hydraulic conductivity [ LT -1 ] S is storage coefficient[ ] h is hydraulic head [ L ]