Porosity, Specific Yield & Capillary Rise

[Pages:13]Lab 1 - Porosity, Specific Yield & Capillary Rise

Porosity, Specific Yield & Capillary Rise

Laboratory 1 HWR 431/531

1-1

Lab 1 - Porosity, Specific Yield & Capillary Rise

Introduction:

In this lab you will be introduced to some of the fundamental concepts in the study of hydrogeology. Porosity and specific yield are two of the basic characteristics which define a porous medium and its ability to facilitate flow. Capillary rise occurs at the fringe of the saturated zone. This area is an important interface between the saturated and vadose zones.

Background:

I) Total Porosity:

Total porosity (n) is defined as the ratio of the volume of void space (VV) in a sample to its total

volume (VT).

n = VV VT

[ -

]

=

[L]3 [L]3

(1)

(a)

(c)

(e)

(b)

(d)

(f)

FIGURE 1 ? Some examples of porosity in nature (a) a well sorted sedimentary material (high porosity) (b) a poorly sorted sedimentary material (low porosity) (c) a well sorted sedimentary material with porous grains, e.g. soil with aggregates (high porosity) (d) a well sorted sedimentary deposit which has a reduced primary porosity due to chemical precipitation (low porosity) (e) rock rendered porous by solution, e.g. karstic limestone (porosity may be high or low) (f) matrix (sedimentary or crystalline) rendered porous by fracturing (porosity may be high or low)

(After Freeze and Cherry, 1979)

1-2

Lab 1 - Porosity, Specific Yield & Capillary Rise

Many factors determine the porosity of a particular sample. The original porosity created during the deposition is called the primary porosity. After deposition, physical, chemical or biological processes may create fractures, dissolution pathways and other new voids resulting in secondary porosity.

It is difficult to predict a sample's porosity, especially given variability in crystallization processes and the evolution of secondary porosity. However, for sedimentary structures, there are some basic factors that control primary porosity.

i) Grain Size Though it may seem logical that if one were to take two boxes, one full of golf balls and the other basketballs, the box with the bigger 'grains' should have a higher porosity since it would now have a greater void volume. This is not so. Rather, the ratio of void space to total volume (i.e. porosity) does not change with scale (given that the packing of the grains does not change). It is shown in Figure 2 that two systems of different scale have the same porosity. Therefore, for a given geometry, porosity is independent of grain size.

4r1 2r1

4r1 = 8r2 2r2 = 4r1

spherical grain

n = VV VT

= VT

- Vsolids VT

=1-

8 43 r 3 (4r)3

=1-

6

0.476

FIGURE 2 - Calculating porosity for two systems with different grain sizes. Note that the porosity in both systems is independent of the grain diameter.

1-3

Lab 1 - Porosity, Specific Yield & Capillary Rise

ii) Grain Size Distribution (i.e. degree of sorting) In general, poorly sorted sediments will have a much lower porosity than uniforms ones. This is due to the fact that small grains may be able to fit inside the pore spaces created by larger grains. iii) System Geometry Another important factor in determining the porosity is the packing. In Figure 3a, it is evident that porosity may be reduced by simply rearranging the grains so that more fit in a given volume. The shape of the grains also plays an important role. For example, clays generally have a very high porosity, 40 - 70% (Freeze & Cherry, 1971) due to bridging of the clay's plate-like grains (Figure 3b). During consolidation to shale high pressures cause the plates to align themselves in an ordered manner drastically reducing the porosity to 0-10%.

Clay

Shale

(a) reduced porosity due to change in packing of spheres

(b) platelets in clay are rearranged to yield a reduced porosity in shale

FIGURE 3 - Packing of grains plays an important role in determining porosity. Consolidation of sediments causes a rearrangement of grains which results in a denser packing (i.e. lower porosity).

Other Related Parameters:

The void ratio (e) is defined as the ratio of the volume of the voids (Vv) to the volume of the solids

(Vs):

e = Vv Vs

[ -

]

=

[L]3 [L]3

(2)

Saturation (S) is the fraction of the void space occupied by water, i.e. it is the ratio of the volume of water (Vw) to the total volume of the void spaces (Vv):

1-4

S = Vw Vv

S [0,1]

Lab 1 - Porosity, Specific Yield & Capillary Rise

(3)

Volumetric Water content () is given by:

= Vw Vt

[ -

]

=

[L]3 [L]3

(4)

Gravimetric water content is given by:

G.W .C. = mw ms

[-]

=

[M] [M]

or

G.W .C. = 1 b

(5a) & (5b)

where mw is the mass of water in the sample and ms is the mass of the dry sample. The two water contents

( and GWC) differ mainly in the method of measurement. They are closely related to each other by the

bulk density (b) of the sample which is the ratio of sample mass to total sample volume:

b

=

ms Vt

LM3

=

[ [

M] L]3

(6)

1-5

Lab 1 - Porosity, Specific Yield & Capillary Rise

II) Specific Yield

Specific yield, Sy, is the ratio of the volume of water that can be drained (Vdrained) by gravity from

a saturated sample to the total volume of sediment (Vt) which contributed that water.

Sy

= Vdrained Vt

[ -

]

=

[L]3 [L]3

(7)

Formally, it is defined as:

"the volume of water that an unconfined aquifer releases from storage

per unit surface area of aquifer per unit decline in the water table."

Freeze and Cherry, Groundwater, p. 61

Consistent with this definition, storage in an unconfined aquifer comes from changes in the saturation of

individual pore spaces within the soil.

Not all of the pores in a saturated sample will contribute to drainage since some of them are isolated from

the rest and some water inevitably clings (is attracted) to particle surfaces. The ratio of the volume of water

remaining in the sediment sample after drainage to the sediment volume is the specific retention (Sr):

Sr

= Vretained Vt

[ -

]

=

[L]3 [L]3

(8)

Specific yield and specific retention sum to the total porosity:

n = Sy + Sr

(9)

The specific yield reflects the effective porosity (ne) of an unconfined aquifer because only those pores which are interconnected and available for fluid flow will conduct (or yield) water.

1-6

Lab 1 - Porosity, Specific Yield & Capillary Rise

III) Capillary Rise

The rise of water in a capillary tube above a free water surface is due to surface tension. Water in

the tube forms a meniscus across which exists a pressure difference, and therefore a net force, which drives

the fluid up the tube.

The equilibrium height of capillary rise (hc) is given by:

hc

=

2cos rw g

[ L]

=

[Mt - [L][ML- 3

2] ][Lt

-

2

]

(10)

where is the surface tension (72.7 g/s2 @ 20oC), is the angle of wetting between the liquid and solid

(assumed to be zero for water-air-glass systems), r is the tube radius, w is the density of water and g is the

acceleration due to gravity.

A similar phenomenon occurs in porous media where the continuous pore spaces between the

grains act like capillary tubes. In an unconfined aquifer there is a region above the water table, i.e. above

the free water surface, which is saturated. This region is called the capillary fringe and represents a portion

of the aquifer where water is held under tension.

Soils are sometimes modelled as bundles of tubes since their complex pore geometry is difficult to

describe (Figure 4). By using such a model the thickness of the capillary fringe is determined by the soil's

capillary radius. The capillary radius is a parameter that conceptually represents the radius of the largest

imaginary tube. Since the capillary radius cannot be measured directly in the field, an indirect method is

used to estimate its value. In practice, the capillary radius is taken as one-half of the d10 (tenth percentile) particle size of the grains.

FIGURE 4 ? A soil with complex pore geometry may be represented by a model composed of a bundle of tubes.

1-7

Lab 1 - Porosity, Specific Yield & Capillary Rise

Laboratory Assignment:

Experiment 1 - Porosity: Measure the porosity of uniform glass beads under different packing arrangements and the

porosity of a mixture of beads.

A. Weigh the 50mL graduated cylinder and record the mass in the data table provided. Pour 30mL of dry large glass beads into the cylinder and reweigh. (Make sure you note the way in which the beads are arranged.) Put 100mL of water into another graduated cylinder. Pour from the 100mL cylinder into the 50mL until the water level is coincident with the top of the beads. Record the volume of water added.

(B) Repeat (A) using a 500mL beaker instead of the 50mL cylinder and about 250mL of beads. (You may need to use more than 100mL of water.)

(C) Repeat (A) again using the 50mL cylinder and small glass beads.

For each test (A, B and C) do the following: (1) Calculate the dry bulk density (b) of the sample (2) Calculate the density of the solids (s) as the mass of beads divided by their volume (3) Calculate the total porosity of the sample using the following equation:

n = 1 - b s

(4) Determine the void ratio (e) for each sample

1-8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download