q0q0 baseflow recession. baseflow recession q = q 0 e –at q = flow at time t after recession...

Q0

Baseflow Recession

Baseflow recession

• Q = Q0 e–at

• Q = flow at time t after recession started (L3/T; ft3/s or m3/s).

• Q0 = flow at the beginning of recession.

• a = recession constant (1/T; d-1).

• t = time since recession began. (T; d)

Meyboom method

• Vtp = Q0t1/2.3• Vtp = Volume of total potential groundwater

discharge during a complete ground water recession (L3, ft3 or m3).

• Q0 = baseflow at start of recession (L3/T, ft3/s or m3/s).

• T1 = time it takes baseflow to go from Q0 to 0.1Q0

Increase of Recharge

• find t1

• tc = 0.2144 t1

• find QA & QB

Vtp = QBt1/2.3 – QAt1/2.3

• 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 (L3, cm3, m3)

• 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 = d60/d10

• d60 = grain size that is 60% finer by weight.• d10 = grain size that is 10% finer by weight.• Cu = 4 => well sorted; Cu > 6 => poorly

sorted.

d60

d60

d10

d10

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 = Sy + Sr.• 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)] [ L3/T/[L2(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.


• Q d2

• Q γ.

• Q 1/μ.

• d = mean pore diameter.

• γ = specific weight.

• μ = viscosity.

Darcy’s Law, cont.

• Q = -[Cd2γA/ μ](dh/dl).

• C = shape factor.

• C, d = properties of porous media.

• γ and μ = properties of the fluid.

Intrinsic Permeability

• Intrinsic permeability Ki = Cd2 (L2).• K = Ki (γ/μ) or K = Ki (ρg/ μ)• Petroleum industry 1 Darcy = unit of intrinsic

permeability Ki

• 1 darcy = 1 cP x 1 cm3/s / (1 atm/ 1 cm). cP – centipoise - 0.01 dyn s/cm2

atm – atmospheric pressure – 1.0132 x 106 dyn/cm2

• 1 darcy = 9.87 x 10-9 cm2 ~ 10-8 cm2

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(d10)2.

• K = hydraulic conductivity.

• d10 = effective grain size (0.1 – 3.0 mm).

• C = coefficient (see table on P 86).

Hazen method (General)

• K = C(d50)j.

• K = hydraulic conductivity.

• d50 = 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 = [dt2L/dc

2t]ln(h0/h).

• K = Hydraulic conductivity.• L = sample length.

• h0 = initial head in the falling tube.

• h = final head in the falling tube.

• t = time that it takes for head to go from h0 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.



• Potentiometric surface – surface at which water will rise in a well cased to the aquifer.

Aquifer – Cont.



• 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 = bK• T = transmissivity.• b = saturated thickness.• K = hydraulic conductivity.• Multilayer => T1 + T2 + … + Tn

Compressibility and Effective Stress

• σT = σe + 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 + dP => 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 => dP = - dσe

Bulk Modulus = (P/)

… where = dilatation = V/V and 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]/dP• 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)

Kh avg

Kv avg

Average vertical conductivity:

Kv avg = b / m=1,n (bm /Kvm)

O

Y

X dh/dx

dh/dy

Grad h = [(dh/dx)2 + (dh/dy)2]0.5

θ = arctan ((dh/dy)/(dh/dx))

θ