ERTH 430 - Porosity

What is the basic water-balance equation?

Inputs = Outputs + ΔStorage.

What does steady state mean in a water balance?

ΔS = 0, so Inputs = Outputs over the time scale considered.

Does steady state mean groundwater is not moving?

No. Groundwater can still flow; steady state only means there is no net long-term change in storage.

Why are water-balance components often reported in mm?

A flow volume is divided by basin area to express it as an equivalent depth of water over the watershed.

What is a typical control volume for surface hydrology?

A watershed.

What can be used as a control volume in hydrogeology?

An aquifer, such as the aquifer underlying a watershed.

Why can groundwater flow differ from surface-water flow?

Subsurface flow is controlled by geology and hydraulic gradients, so groundwater divides do not always coincide with surface topographic divides.

What is precipitation?

Water delivered from the atmosphere to Earth's surface, commonly after warm moist air rises, cools, and condenses.

What are the four precipitation mechanisms discussed in the lecture?

Cold-frontal, warm-frontal, convective, and orographic precipitation.

What causes orographic precipitation?

Air is forced upward over topography, cools, condenses, and produces precipitation.

What is evapotranspiration (ET)?

The collective term for processes by which liquid or solid water at or near Earth's surface becomes atmospheric water vapour.

What two processes make up evapotranspiration?

Evaporation and transpiration.

What is evaporation?

Conversion of water from liquid to vapour; conversion directly from solid to vapour is sublimation.

What is transpiration?

Vaporization of water through plant stomata.

What is potential evapotranspiration (PE)?

The evaporation/ET that would occur over a large, uniformly vegetated area if the water supply were unrestricted.

What is actual evapotranspiration (AE)?

The amount of evapotranspiration that actually occurs over a land surface.

In a water-limited system, how do AE and PE compare?

AE < PE.

What four factors control evaporation rate?

Water availability, energy availability, the surface-to-air vapour-pressure gradient, and turbulent motion.

How does turbulence affect evapotranspiration?

It enhances transport of vapour away from the surface and can increase the evaporation rate.

What is precipitation partitioning?

The division of precipitation among pathways such as overland flow, infiltration, interflow, recharge, groundwater flow, evapotranspiration, and runoff.

What is the unsaturated zone?

The subsurface above the water table where pores contain both air and water.

What is the saturated zone?

The subsurface below the water table where pore spaces are saturated with water.

What is groundwater recharge?

The downward mass flux entering an aquifer at the water table.

What are possible groundwater inputs to an aquifer?

Recharge from precipitation or a river, lateral groundwater inflow, and upward/inter-aquifer flow in.

What is groundwater discharge?

Groundwater mass flux leaving an aquifer at the surface.

What are possible outputs from an aquifer?

Discharge to streams, evapotranspiration from shallow groundwater, inter-aquifer flow out, and pumping.

What is a gaining river?

A river that receives groundwater discharge from the aquifer.

What is a losing river?

A river that loses water to the aquifer and therefore provides groundwater recharge.

What is a flow-through river?

A river where groundwater enters on one side and leaves toward the aquifer on the other.

What is baseflow?

The relatively persistent component of streamflow supplied largely by groundwater.

Why are strongly gaining rivers often more stable than runoff-dominated rivers?

Groundwater-derived baseflow varies more slowly than storm runoff.

What are the main parts of a storm hydrograph discussed in the lecture?

Rising limb, peak discharge, falling limb, event flow, and baseflow.

How do surface-water and groundwater residence times generally compare?

Surface-water residence times are usually much shorter; groundwater residence times can be centuries or longer.

What is residence time?

The average length of time a parcel of water spends in a reservoir.

What is the residence-time equation at steady state?

T_R = S/q = S/i, where S is storage, q is outflow, and i is inflow.

Why can either inflow or outflow be used in the steady-state residence-time equation?

Because at steady state, inflow equals outflow.

What is the dimensional basis of residence time?

Storage [L^3] divided by flow rate [L^3/T] gives time [T].

What are typical residence-time scales for atmosphere, rivers, lakes, and groundwater?

Atmosphere: days; rivers: weeks; lakes: years; groundwater: centuries or longer.

What is a porous medium?

A material such as soil, sediment, or rock that contains solid material plus void or pore space.

What phases can occur in a porous medium?

Solid matrix, gas such as air, and fluids such as water or hydrocarbons.

What is the total-volume equation for a porous medium containing air, fluid, and solids?

V_T = V_A + V_F + V_S.

What is the total-mass equation for a porous medium?

M_T = M_A + M_F + M_S.

What is void volume in a soil containing air and water?

V_V = V_A + V_W.

Define porosity.

Porosity is the fraction of total porous-medium volume occupied by voids: n = V_V / V_T.

Is porosity dimensionless?

Yes. It is a ratio of volume to volume, L^3/L^3.

Does porosity depend on how much water is currently in the pores?

No. Porosity measures total void space, whether the voids contain water or air.

Define void ratio.

Void ratio is void volume divided by solid volume: e = V_V / V_S.

How does porosity differ from void ratio?

Porosity uses total volume in the denominator; void ratio uses solid volume.

What does porosity tell a hydrologist?

Primarily the ability of a porous medium to store water.

Does high porosity necessarily mean high ability to transmit water?

No. Water transmission also depends strongly on pore connectivity, pore-throat size, and geometry.

What is the Representative Elementary Volume (REV)?

A sample volume large enough that a measured porous-medium property becomes representative and relatively stable at the macroscopic scale.

Why do property values fluctuate at very small sample volumes?

A tiny sample may contain mostly a grain or mostly a pore, so the measured property is highly sensitive to exact location.

What can happen when the sample volume becomes very large compared with the REV?

Large-scale geological heterogeneity can cause measured properties to vary again.

Which properties were given as examples of scale-dependent properties?

Porosity, permeability, and water content.

What five geological controls on porosity were identified?

Grain-size distribution, grain shape, grain arrangement/packing, geochemical reactions, and material type.

Does grain size alone determine porosity?

No. Identically packed large and small grains can have the same porosity.

How is pore size generally related to grain size?

Larger grains generally produce larger pores; smaller grains generally produce smaller pores.

Why can two materials with different grain sizes have the same porosity?

If their grains have the same shape and packing geometry, the fraction of void space can be the same even though individual pores differ in size.

What are the approximate grain-size classes for sand, silt, and clay in the lecture?

Sand: about 2 to 0.02–0.05 mm; silt: about 0.02–0.05 to 0.002 mm; clay: <0.002 mm (2 μm).

How does sorting generally affect porosity?

Better sorting generally increases porosity.

Why do heterogeneous or poorly sorted materials often have lower porosity?

Smaller grains can fill void spaces between larger grains.

Which generally has higher porosity: uniform sand or silty sand?

Uniform sand, because the finer silt in silty sand can occupy pore space between sand grains.

What does 'well sorted' mean in geology?

The grains are mostly similar in size.

What does 'well graded' mean in engineering terminology?

The material contains a wide range of grain sizes; this is roughly opposite to geologic 'well sorted.'

What approximate composition of loam was given in the lecture?

About 40% sand, 40% silt, and 20% clay.

Why can a relatively small clay fraction strongly affect soil properties?

Clay has very fine particles and high specific surface area, so even modest amounts strongly influence texture and behaviour.

What is specific surface area (SSA)?

The total surface area of a material per unit mass.

For cubic particles, how does SSA vary with particle size?

SSA = 6/(ρ_s l), so specific surface area increases as particle size l decreases.

What soil properties are influenced by texture in the absence of large amounts of organic matter?

Surface area, bulk density, porosity, pore-size distribution, and water-holding capacity.

Why can clay have high total porosity despite very small grains?

Disk-shaped clay particles can form an open 'house-of-cards' arrangement with substantial void volume.

How do clay and sand commonly differ in water-holding capacity and drainage?

Clay generally has high water-holding capacity and very slow drainage; sand generally has low water-holding capacity and rapid drainage.

How does tighter grain packing affect porosity and bulk density?

Tighter packing decreases porosity and increases bulk density.

What porosity is associated with ideal cubic packing of spheres in the lecture?

Approximately 48%.

What porosity is associated with ideal rhombohedral packing of spheres in the lecture?

Approximately 26%.

How can mineral dissolution affect porosity?

It can increase porosity by creating or enlarging void space.

How can secondary mineral precipitation affect porosity?

It can decrease porosity by filling pore space, as during cementation or lithification.

How do compaction and cementation affect porosity?

They generally reduce porosity.

How do unconsolidated sediments generally compare with rocks in porosity?

Unconsolidated sediments usually have higher porosity, although exceptions exist.

How does porosity generally change with depth on a global scale?

It generally decreases with depth.

What total porosity range was given for sand?

About 25–50%.

What total porosity range was given for clay?

About 40–70%.

What total porosity range was given for sandstone?

About 5–30%.

What total porosity range was given for dense crystalline rock?

About 0–5%.

Define specific yield.

The volume of water that drains by gravity divided by total porous-medium volume.

Define gravimetric water content.

Mass of water divided by mass of porous-medium solids: θ_g = M_w/M_s.

Define volumetric water content.

Volume of water divided by total porous-medium volume: θ = V_w/V_T.

Define degree of saturation.

The fraction of pore volume occupied by water: S = V_w/V_V.

Define particle density.

Mass of solids divided by the volume occupied by solids: ρ_s = M_s/V_s.

What particle density is commonly assumed for many geological materials?

About 2.65 g/cm³, approximately the density of quartz.

Define dry bulk density.

Mass of dry solids divided by total sample volume: ρ_b = M_s/V_T.

Define wet bulk density.

Mass of solids plus fluid divided by total sample volume: ρ_bw = (M_s + M_f)/V_T.

What is the density-based porosity equation?

n = 1 - ρ_b/ρ_s.

Why is the equation n = 1 - ρ_b/ρ_s useful?

Particle density is relatively constant for many mineral soils, allowing porosity to be estimated from easily measured bulk density.

How are bulk density and porosity generally related?

As bulk density increases, porosity decreases.

What is primary porosity?

Porosity formed during deposition of unconsolidated material or during the original formation of a rock.

What is secondary porosity?

Additional porosity developed after formation through weathering, fracturing, dissolution, joints, faults, solution channels, or similar features.

What is a dual-porosity medium?

A medium containing both matrix/primary porosity and secondary porosity such as fractures.

How does primary porosity generally compare with secondary porosity in storage and flow?

Primary porosity generally provides more storage but often supports less flow than well-connected secondary features such as fractures.

What is total porosity?

The fraction of total volume occupied by all voids, whether or not they are connected.

What is effective porosity?

The fraction of total volume occupied by interconnected pores available for water circulation.