Baseflow Recession Q 0 Baseflow recession Q Q

Baseflow Recession Q 0

Baseflow recession • Q = Q 0 e–at • Q = flow at time t after recession started (L 3/T; ft 3/s or m 3/s). • Q 0 = flow at the beginning of recession. • a = recession constant (1/T; d-1). • t = time since recession began. (T; d)

Meyboom method • Vtp = Q 0 t 1/2. 3 • Vtp = Volume of total potential groundwater discharge during a complete ground water recession (L 3, ft 3 or m 3). • Q 0 = baseflow at start of recession (L 3/T, ft 3/s or m 3/s). • T 1 = time it takes baseflow to go from Q 0 to 0. 1 Q 0

Increase of Recharge • • find t 1 tc = 0. 2144 t 1 find QA & QB Vtp = QBt 1/2. 3 – QAt 1/2. 3 • G = 2 Vtp

Porosity • Porosity is percent of rock or soil that is void of material. • n = 100 Vv/V • n = porosity (percentage) • Vv = volume of void space (L 3, cm 3, m 3) • V = unit volume of material including voids and solids.

Factors affecting porosity • Packing • Grain-size distribution - sorting

Sediment Classification • Sediments are classified on basis of size of individual grains • Grain size distribution curve • Uniformity coefficient Cu = d 60/d 10 • d 60 = grain size that is 60% finer by weight. • d 10 = grain size that is 10% finer by weight. • Cu = 4 => well sorted; Cu > 6 => poorly sorted.

d 60 d 10

d 60 d 10 d 60 d 10

Aquifer • Properties: Porosity, specific yield, specific retention. • Potential: Transmissivity, storativity. • Types: confined, unconfined. • Hydraulic conductivity, Physical Laws controlling water transport.

Specific Yield and Retention • Specific yield – Sy: ratio of volume of water that drains from a saturated rock owing to the attraction of gravity to the total volume of the rock. • Specific retention – Sr: ratio of the volume of water in a rock can retain against gravity drainage to the total volume of the rock. • n = S y + S r. • Sr increases with decreasing grain size.

Darcy’s Law

Darcy’s Experiment • • • Q ha – hb. Q 1/L. Darcy’s Law: Q = -KA(ha-hb)/L. Q = -KA(dh/dl). dh/dl = Hydraulic gradient. dh = change in head between two points separated by small distance dl.

Hydraulic conductivity • K = hydraulic conductivity (L/T). • K is also referred to as the coefficient of permeability. • K = -Q[A(dh/dl)] [ L 3/T/[L 2(L/L)] = L/T] • V = Q/A = -K(dh/dl) = specific discharge or Darcian velocity.

Factors influencing hydraulic conductivity • Porous medium. • Fluid passing through the medium.

Factors influencing hydraulic conductivity • • • Q d 2 Q γ. Q 1/μ. d = mean pore diameter. γ = specific weight. μ = viscosity.

Darcy’s Law, cont. • • Q = -[Cd 2γA/ μ](dh/dl). C = shape factor. C, d = properties of porous media. γ and μ = properties of the fluid.

Intrinsic Permeability • Intrinsic permeability Ki = Cd 2 (L 2). • K = Ki (γ/μ) or K = Ki (ρg/ μ) • Petroleum industry 1 Darcy = unit of intrinsic permeability Ki • 1 darcy = 1 c. P x 1 cm 3/s / (1 atm/ 1 cm). c. P – centipoise - 0. 01 dyn s/cm 2 atm – atmospheric pressure – 1. 0132 x 106 dyn/cm 2 • 1 darcy = 9. 87 x 10 -9 cm 2 ~ 10 -8 cm 2

Factors affecting permeability of sediments • Grain size increases permeability increases. • S. Dev. Of particle size increase poor sorting => permeability decrease. • Coarse samples show a greater decrease of permeability as S. Dev. Of particle size increases. • Unimodal samples (one dominant size) vs. bimodal samples.

Hazen method • Estimate hydraulic conductivity in sandy sediments. • K = C(d 10)2. • K = hydraulic conductivity. • d 10 = effective grain size (0. 1 – 3. 0 mm). • C = coefficient (see table on P 86).

Hazen method (General) • • • K = C(d 50)j. K = hydraulic conductivity. d 50 = effective grain size (mm). C = coefficient. j = an exponent (1. 5 – 2).

Permeameters • • Constant-head permeameter Qt = -[KAt(ha-hb)]/L. K = VL/Ath. V = volume of water discharging in time. L = length of the sample. A = cross-sectional area of sample. h = hydraulic head. K = hydraulic conductivity

Falling head permeameter • • K = [dt 2 L/dc 2 t]ln(h 0/h). K = Hydraulic conductivity. L = sample length. h 0 = initial head in the falling tube. h = final head in the falling tube. t = time that it takes for head to go from h 0 to h. dt = inside diameter of falling head tube. dc = inside diameter of sample chamber.

Aquifer • Aquifer – geologic unit that can store and transmit water at rates fast enough to supply amounts to wells. Usually, intrinsic permeability > 10 -2 Darcy. • Confining layer – unit with little or no permeability … < 10 -2 Darcy. aquifuge – absolutely impermeable unit. aquitard - a unit can store and transmit water slowly. Also called leaky confining layer. Raritan formation on Long Island. -- all these definitions are in a relative sense.

Aquifer – Cont. • Unconfined aquifer – water-table aquifer.

Aquifer – Cont. • Unconfined aquifer. • Confined or artesian aquifers.

Aquifer – Cont. • Unconfined aquifer. • Confined or artesian aquifers. • Potentiometric surface – surface at which water will rise in a well cased to the aquifer.

Aquifer – Cont. • Unconfined aquifer. • Confined or artesian aquifers. • Potentiometric surface – surface at which water will rise in a well cased to the aquifer. • Perched aquifer.

Aquifer

Water table • • • Water table map – unconfined aquifer. Rivers, lakes as reference Contouring – use topographic information. Contours V-upstream for gaining streams. Contours bend downstream for losing streams.

Potentiometric surface maps • Potentiometric surface map – confined aquifer. • Not influenced by topography, surface water features, river

Transmissivity • The amount of water that can be transmitted horizontally through a unit width by the full saturated thickness of the aquifer under a hydraulic gradient of 1. • T = b. K • T = transmissivity. • b = saturated thickness. • K = hydraulic conductivity. • Multilayer => T 1 + T 2 + … + Tn

Compressibility and Effective Stress • σT = σ e + P • σT = total stress produced by weight of overlying rock and water. • P = fluid pressure. • σe = effective stress (actual stress borne by aquifer skeleton).

Changes in Stress • dσT = dσe + d. P => change in total stress produces change in effective stress and pressure. • Confined aquifer => change in pressure but very little change in thickness of saturated water column => d. P = - dσe

Bulk Modulus = ( P/Q) … where and Q = dilatation = V/V P = pressure

Aquifer Compressibility • Reduction in pressure P => effective stress will increase => compaction of aquifer skeleton. • Consolidation depends on aquifer compressibility α. • α = [-db/b]/dσe = [db/b]/d. P • b = original aquifer thickness, • db = change in aquifer thickness.

Elasticity • Change in pressure due to change in head affects mineral grain arrangement and water density => elasticity. • Water contracts as pressure increases and expands as pressure decreases. • Decline in head => aquifer skeleton compresses => reduces effective porosity => expels water. • Additional water expels as water expands due to pressure drop.

Specific Storage • Specific storage Ss = amount of water per unit volume stored or expelled owing to compressibility of mineral skeleton and pore water per unit change in head (1/L). • Ss = ρwg(α+nβ) • α = compressibiliy of aquifer skeleton. • n = porosity. • β = compressibility of water.

Storativity • When head of saturated aquifer or confining unit changes => water is stored or expelled. • Storage coefficient = volume of water that permeable unit will absorb or expel per unit surface area per unit change in head • Storage coefficient or storativity is dimensionless.

Storativity of confined Unit S = b Ss • Ss = specific storage. • b = aquifer thickness. • All water released in confined, saturated aquifer comes from compressibility of mineral skeleton and pore water.

Storativity in Unconfined Unit • Changes in saturation associated with changes in storage. • Storage or release depends on specific yield Sy and specific storage Ss. • S = Sy + b Ss

Volume of water drained from aquifer • • • Vw = SAdh Vw = volume of water drained. S = storativity (dimensionless). A = area overlying drained aquifer. dh = average decline in head.

Homogeneity and Isotropy • Homogeneous – same properties – hydraulic conductivity, specific storage, specific yield – at all locations. • Heterogeneous – hydraulic properties change spatially.

Isotropic and Anisotropic • Isotropic – same intrinsic permeability in all directions. • Anisotropic – direction dependent.

High K K=0

Average horizontal conductivity: Kh avg = m=1, n (Khmbm/b) Kv avg Kh avg Average vertical conductivity: Kv avg = b / m=1, n (bm /Kvm)

Grad h = [(dh/dx)2 + (dh/dy)2]0. 5 Y dh/dy θ X dh/dx O θ = arctan ((dh/dy)/(dh/dx))