3.2 Effective Porosity

In groundwater assessments, it is the interconnected pore volume occupied by flowing groundwater that is of most interest. Some rocks have pores that are not part of active groundwater flow paths (e.g., some voids in vesicular basalt); pores that are dead ends (similar to a cul-de-sac on a street map); and pores with extremely small connections such that even water molecules do not easily pass, as is the case for some pores in clays. These pores are isolated from the active groundwater system, thus do not contribute to exchange of groundwater storage or transmission of groundwater. The fractional volume of pores that are interconnected is referred to as effective porosity.

Effective porosity (ne) is defined as the ratio of the volume of interconnected pore spaces (VI) to the total volume (VT) as defined in Equation 6 and illustrated in Figure 7. Interconnected void space allows groundwater to move into and out of porous material.

\displaystyle n_e=\frac{V_I}{V_T} (6)

where:

ne = effective porosity (dimensionless)
VI = volume of interconnected pore space (L3)
VT = volume of sample (L3)

 

Figure showing relationship between total porosity and effective porosity
Figure 7 – Relationship between total porosity and effective porosity where the total sample volume, VT, is represented by the area inside the gray circle. a) Water occupies all pore spaces (light blue spaces, VV) and the total porosity is n = VV / VT ; b) Some pore spaces are disconnected from other pores (red hatched spaces) and groundwater can only access the connected pore spaces (blue area, VI), thus effective porosity is ne = VI / VT .

The effective porosity may equal, or be less than, the total porosity (n) of the sample (Table 1). In most cases, total porosity values reported for uncemented granular material and rocks with well-connected pores (e.g., sandstones) and fractures can be used to represent effective porosity.

Measuring Effective Porosity

Effective porosity can be determined at the laboratory scale when sediment and rock samples of a given volume are dried and then the pore spaces are filled with water (Figure 8). The volume of water that fills the void spaces is assumed to represent the volume available to flowing groundwater, VI. For example, to determine the effective porosity of a granular earth material, a sample volume is collected, allowed to dry completely, and then water is introduced slowly to the base of the sample (so that air can escape from the top). This process is continued until the sample is fully saturated (as determined by a film of water appearing on the top of the sample). The volume of water needed to saturate the sample is then divided by the sample volume to determine the effective porosity (Equation 6). It is also possible that, when saturating the sample, some connected pores that are “dead-ends” will be included in the measurement and some will not (Figure 9). Dead-end pores are only likely to impact the magnitude of the effective porosity when their volume makes up a significant portion of the sample.

 

Figure showing simple laboratory set up to measure effective porosity of a sample of earth material
Figure 8 – A simple laboratory set up to measure effective porosity of a sample of earth material. a) Initially the sample volume (VT) is determined using the length of the sample and inside radius of the cylinder, then the sample is dried such that no residual water is present in the pore space. b) Then, water is introduced slowly from the bottom of the sample to displace air in the pores and the volume of water required to saturate the sample, as indicated by the appearance of a thin film of water on the top of the sample, is determined. The volume of water required to fill the voids is the VI and effective porosity is computed as ne = VI / VT .

 

Figure showing the geometry of dead-end pores
Figure 9 – The geometry of dead-end pores may complicate an effective porosity measurement, but generally the infrequency of such situations will introduce only minor errors in the measurement: a) orientation of pore allows displacement of air; and b) pore orientation traps air and the air-filled pore space is not included in the effective porosity.

Effective porosity can also be determined by submerging a fully dried sample in a beaker filled with a measured quantity of water and applying suction to draw air out of the sample. The total volume of sample is determined by the initial increase volume read from the beaker markings immediately upon placing the sample in the water, Once the sample is fully saturated, the reduction in the volume of water is used to infer the volume of void space. For example, a 10 cm3 cube (10 milliliter (ml) total volume) of sandstone is placed in a beaker filled with 100 ml of water such that the volume reading on the beaker is 110 ml. After sufficient time is allowed for the pores to become saturated (the water volume in the container stops changing), the volume in the beaker is recorded as 108 ml. The volume of void space is 2 ml (2 cm3). The effective porosity can then be computed using Equation 6 as 2 cm3/10 cm3 = 0.20. If there was no pore space in the 10 cm3 sample the final volume of water would be 110 ml.

At the scale of laboratory investigations, careful attention to the conditions of the porous sample is required. Ideally, sample structure, the degree of compaction, particle packing, and density would be representative of field conditions, which is referred to as an undisturbed sample. However, in some cases, physical sampling methods may increase or decrease the sample porosity. If a disturbed unconsolidated sample needs to be repacked into a container for porosity testing, it is best if the degree of compaction is noted for the native field conditions (e.g., by using a cone penetrometer or a standard penetration test). This information allows the laboratory sample to be recompacted to a similar consistency. Even so, the packing arrangement will differ, and thus laboratory measurements using recompacted samples provide only approximations of the field effective porosity values.

Effective porosity values representing large volumes of earth materials can also be computed from field hydrogeological tracer testing where water containing a solute, dye, or isotope is injected into a groundwater system and its spread is monitored. Ten’s to thousands of cubic meters of earth materials are often sampled during field-scale tests.

Values of Effective Porosity

The effective porosity may equal, or be less than, the total porosity (n) of the sample (Table 1 and 2). In most cases, total porosity values reported for uncemented granular material and rocks with well‑connected pores and fractures can be used to represent effective porosity. Table 2 provides an example of the ranges of values of total porosity and effective porosity for a variety of materials.

Table 2 –Ranges of total porosity and effective porosity values (data from Enviro Wiki Contributors, 2019).

Total and Effective Porosity
Total Porosity Effective Porosity
Unconsolidated Sediments
Gravel 0.25 – 0.44 0.13 – 0.44
Coarse Sand 0.31 – 0.46 0.18 – 0.43
Medium Sand 0.16 – 0.46
Fine Sand 0.25 – 0.53 0.01 – 0.46
Silt, loess 0.35 – 0.50 0.01 – 0.39
Clay 0.40 – 0.70 0.01 – 0.18
Sedimentary and Crystalline Rocks
Karst and reef limestone 0.05 – 0.50 —
Limestone, dolomite 0.00 – 0.20 0.01 – 0.24
Sandstone 0.05 – 0.30 0.10 – 0.30
Siltstone — 0.21 – 0.41
Basalt 0.05 – 0.50 —
Fractured crystalline rock 0.00 – 0.10 —
Weather granite 0.34 – 0.57 —
Unfractured crystalline rock 0.00 – 0.05 —

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Hydrogeologic Properties of Earth Materials and Principles of Groundwater Flow Copyright © 2020 by The Authors. All Rights Reserved.