Porosity and Effective Porosity

2.3.1 Porosity and Effective Porosity

The nature of the porosity of porous media (sediments and all rocks in general) is the single most important factor in determining the storage and movement of groundwater

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F IGURE 2.9 Three-dimensional conceptual site model showing different stratigraphic layers and ready for transfer into a numeric groundwater model. (Modified from Oostrom et al., 2004.)

in the subsurface. Many quantitative parameters describing “life cycle” of water and contaminants (when present) within a groundwater system directly or indirectly depend on porosity. Here are just a few: infiltration of precipitation into the subsurface, rock (sediment) permeability, groundwater velocity, volume of water that can be extracted from the groundwater system, and diffusion of contaminants into the porous media solids.

Porosity (n) is defined as the percentage of voids (empty space occupied by water or air) in the total volume of rock, which includes both solids and voids:

where V v = volume of all rock voids and V = total volume of rock (in geologic terms, rock refers to all the following: soils, unconsolidated and consolidated sediments, and any type of rock in general). Assuming the specific gravity of water equals unity, total porosity, as a percentage, can be expressed in four different ways (Lohman, 1972):

= V w = V−V m =

n=

GroundwaterSystem

where n = porosity, in percent per volume

V = total volume

V i = volume of all interstices (voids)

V m = aggregate volume of mineral (solid) particles

V w = volume of water in a saturated sample Porosity can also be expressed as:

where ρ m = average density of mineral particles (grain density) and ρ d = density of dry sample (bulk density). The shape, amount, distribution, and interconnectivity of voids influence the per- meability of rocks. Voids, on the other hand, depend on the depositional mechanisms of unconsolidated and consolidated sedimentary rocks, and on various other geologic processes that affect all rocks during and after their formation. Primary porosity is the porosity formed during the formation of rock itself, such as voids between the grains of sand, voids between minerals in hard (consolidated) rocks, or bedding planes of sedi- mentary rocks. Secondary porosity is created after the rock formation mainly due to tectonic forces (faulting and folding), which create micro- and macrofissures, fractures, faults, and fault zones in solid rocks. Both the primary and secondary porosities can be successively altered multiple times, thus completely changing the original nature of the rock porosity. These changes may result in porosity decrease, increase, or altering of the degree of void interconnectivity without a significant change in the overall void volume.

The following discussion by Meinzer (1923), and the figure that accompanies it (Fig.

2.10) is probably the most cited explanation of rock porosity, and one can hardly add anything to it:

The porosity of a sedimentary deposit depends chiefly on (1) the shape and arrangement of its con- stituent particles, (2) the degree of assortment of its particles, (3) the cementation and compacting to which it has been subjected since its deposition, (4) the removal of mineral matter through solution by percolating waters, and (5) the fracturing of the rock, resulting in joints and other openings. Well- sorted deposits of uncemented gravel, sand, or silt have a high porosity, regardless of whether they consist of large or small grains. If, however, the material is poorly sorted small particles occupy the spaces between the larger ones, still smaller ones occupy the spaces between these small particles, and so on, with the result that the porosity is greatly reduced (A and B). Boulder clay, which is an unassorted mixture of glacial drift containing particles of great variety in size, may have a very low porosity, whereas outwash gravel and sand, derived from the same source but assorted by running water, may be highly porous. Well-sorted uncemented gravel may be composed of pebbles that are themselves porous, so that the deposit as a whole has a very high porosity (C). Well-sorted porous gravel, sand, or silt may gradually have its interstices filled with mineral matter deposited out of so- lution from percolating waters, and under extreme conditions it may become a practically impervious conglomerate or quartzite of very low porosity (D). On the other hand, relatively soluble rock, such as limestone, though originally dense, may become cavernous as a result of the removal of part of its substance through the solvent action of percolating water (E). Furthermore hard, brittle rock, such as limestone, hard sandstone, or most igneous and metamorphic rocks, may acquire large interstices through fracturing that results from shrinkage or deformation of the rocks or through other agencies (F). Solution channels and fractures may be large and of great practical importance, but they are rarely abundant enough to give an otherwise dense rock a high porosity.

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F IGURE 2.10 Diagram showing several types of rock interstices and the relation of rock texture to porosity. (a) Well-sorted sedimentary deposit having high porosity; (b) poorly sorted sedimentary deposit having low porosity; (c) well-sorted sedimentary deposit consisting of pebbles that are

themselves porous and thus the deposit as a whole has a very high porosity; (d) well-sorted sedimentary deposit whose porosity has been diminished by the deposition of mineral matter in the interstice’s; (e) rock rendered porous by solution; ( f ) rock rendered porous by fracturing (Meinzer, 1923).

The porosity of unconsolidated sediments (gravel, sand, silt, and clay) is often called intergranular porosity because the solids are loose detritic grains. When such rocks become consolidated, the former intergranular porosity is called matrix porosity. In general, the term matrix porosity is applied to primary porosity of all consolidated (hard) rocks, such as porosity between mineral grains (minerals) in granite, gneiss, slate, or basalt. Some unconsolidated or loosely consolidated (semiconsolidated) rocks may contain fissures and fractures, in which case the nonfracture portion of the overall porosity is also called matrix porosity. Good examples are fractured clays and glacial till sediments, or residuum deposits, which have preserved the fabric of the original bedrock in the form of fractures and bedding planes. Sometimes, microscopic fissures in rocks are also considered part of the matrix porosity as opposed to larger fissures and fractures called macroporosity. In general, rocks that have both the matrix and the fracture porosity are referred to as dual-porosity media. This distinction is important in terms of groundwater flow, which has very different characteristics in fractures and conduits compared to the bulk of the rock. It is also important in contaminant fate and transport analysis, especially when contaminant concentrations are high causing its diffusion into the rock matrix where it can remain for long periods of time. Plots of average total porosity and porosity ranges for various rock types are shown in Figs. 2.11 and 2.12.

When analyzing porosity from the groundwater management perspective, it is very important to make a very clear distinction between the total porosity and the effective porosity of the rock. Effective porosity is defined as the volume of interconnected pore space that allows free gravity flow of groundwater. The following anthological discussion by Meinzer (1932) explains why it is important to make this distinction between the total and the effective porosity:

GroundwaterSystem

Drif t

Loes s

0 10 20 30 40 50 60 70 Sandstone

Quartzit e 2.1 Cher t 2.9

Claystone

Limestone 8.2 Chal k

Dolomite 7.0 Marble 2.2 0 10 20 30 40 50 60 70

Anhydrit e 6.1 Gypsum

8.7 Halite 2.5 Salt (Rock) 1.5

F IGURE 2.11 Porosity range (horizontal bars) and average porosities (circles) of unconsolidated and consolidated sedimentary rocks. (Kresic, 2007a; copyright Taylor & Francis Group, LLC; printed with permission.)

To determine the flow of ground water, however, a third factor, which has been called the effective porosity, must be applied. Much of the cross section is occupied by rock and by water that is securely attached to the rock surfaces by molecular attraction. The area through which the water is flowing is therefore less than the area of the cross section of the water-bearing material and may be only a small fraction of that area. In a coarse, clean gravel, which has only large interstices, the effective porosity may be virtually the same as the actual porosity, or percentage of pore space; but in a fine- grained or poorly assorted material the effect of attached water may become very great, and the effective porosity may be much less than the actual porosity. Clay may have a high porosity but may

be entirely impermeable and hence have an effective porosity of zero. The effective porosity of very fine grained materials is generally not of great consequence in determinations of total flow, because in these materials the velocity is so slow that the computed flow, with any assumed effective porosity, is likely to be relatively slight or entirely negligible. The problem of determining effective porosity, as distinguished from actual porosity, is, however, important in studying the general run of water- bearing materials, which are neither extremely fine nor extremely coarse and clean. Hitherto not much work has been done on this phase of the velocity methods of determining rate of flow. No distinction has generally been made between actual and effective porosity, and frequently a factor of 33 1/3 per cent has been used, apparently without even making a test of the porosity. It is certain that the effective porosity of different water-bearing materials ranges between wide limits and that it must be at least roughly determined if reliable results as to rate of flow are to be obtained. It would seem that each

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Granite 1.6 Granodiorite 0.6 Monzonite

Diabase 0.6 Latite

Pumice >75 Rhyolite

Tuff 32.4 58.4 0 10 20 30 40

Gneiss 1.9 Greenstone 0.7 Schist 1.6 Serpentine

Shale 13.5 42.3 Scarn

F IGURE 2.12 Porosity range (horizontal bars) and average porosities (circles) of magmatic and metamorphic rocks. (Kresic, 2007a; copyright Taylor & Francis Group, LLC; printed with permission.)

field test of velocity should be supplemented by a laboratory test of effective porosity, for which the laboratory apparatus devised by Slichter (1905) could be used.