Porosity

Porosity is the proportion of the bulk volume of a porous material occupied by pores or voids rather than solid matter. These spaces may contain gases, liquids, or mixtures of fluids; they need not be empty. Usually represented by $\phi$ or $n$, porosity is a dimensionless quantity expressed as a fraction or percentage. It describes how much pore space a material contains, but not, by itself, how readily fluid can move through that space. (water.usgs.gov)

Definition and related quantities

Total porosity is defined as

where $V_p$ is pore volume, $V_s$ is solid volume, and $V_b$ is bulk volume. For example, a specimen with a bulk volume of $100\ \mathrm{cm^3}$ and a pore volume of $25\ \mathrm{cm^3}$ has a porosity of $0.25$, or 25%. The denominator includes both the solid material and its pores. (pubs.usgs.gov)

Porosity is distinct from fluid saturation. Water saturation is the fraction of pore volume occupied by water, whereas porosity is the fraction of bulk volume occupied by all pores. A material can therefore become wetter or drier without a corresponding change in porosity, provided its solid structure and pore volume remain unchanged. (water.usgs.gov)

Porosity can also be calculated from density:

where $\rho_b$ is dry bulk density and $\rho_s$ is the density of the solid material, excluding pore space. This relationship requires consistent definitions of solid and bulk volume; it is widely used for soils. (nrcs.usda.gov)

Total, open, and effective porosity

Different descriptions of porosity distinguish the amount of pore space from its accessibility and contribution to transport:

• Total porosity includes all pores, regardless of whether they are connected.
• Open porosity comprises pores communicating with the exterior of a specimen.
• Closed porosity comprises cavities isolated from the exterior.
• Effective porosity, in groundwater-flow studies, is the fraction of bulk volume occupied by interconnected voids available for fluid transmission. (pubs.usgs.gov)

These quantities are not necessarily interchangeable. An accessible cavity may be connected to the exterior through only one opening and need not form a continuous flow pathway through the material. Measurements of accessible pore space also depend on the size of the probe molecules and the conditions under which they enter the pores. Consequently, an effective or accessible porosity should be accompanied by its operational definition and measurement method. (pubs.usgs.gov)

Pore size and permeability

Porosity measures the quantity of pore space, not its size distribution. In the terminology used by the International Union of Pure and Applied Chemistry for adsorption in porous solids, micropores have widths not exceeding approximately 2 nanometres, mesopores have intermediate widths of approximately 2–50 nanometres, and macropores have widths exceeding approximately 50 nanometres. These boundaries are conventional and relate to differences in pore-filling behavior. (goldbook.iupac.org)

Permeability describes a material’s capacity to transmit fluid. Materials with similar porosities may have very different permeabilities because their pore dimensions, constrictions, connectivity, and flow-path geometry differ. Porosity–permeability relationships therefore depend on the material and its formation history rather than following a universal conversion. (usgs.gov)

Porosity is likewise different from specific surface area, which measures surface area per unit mass or volume. Characterizing a porous solid commonly requires both pore-volume information and surface-area or pore-size measurements. (publications.iupac.org)

Factors controlling porosity

In soils and sediments, porosity depends on particle packing, grain-size distribution, aggregation, and organic matter. Fine-textured soils can have greater total pore space than sandy soils even though their individual pores are generally smaller. A larger grain size therefore does not necessarily imply greater porosity. (nrcs.usda.gov)

Compaction generally reduces pore volume and increases bulk density. In sedimentary rocks, mineral cement deposited within pores can also reduce porosity. Grain sorting, compaction history, and mineral changes influence both porosity and permeability, but not always in the same proportion. (nrcs.usda.gov)

In geology, intergranular pore space formed with a sediment is commonly described as primary porosity, while fractures formed subsequently contribute secondary porosity. Fractures can provide important flow pathways even where the surrounding rock has little interconnected pore space. (pubs.usgs.gov)

Measurement and applications

Porosity is determined through measurements of bulk volume, solid volume, or accessible pore volume. Soil investigations commonly combine dry bulk-density and particle-density measurements. Gas adsorption provides information about accessible pore volume and pore-size distribution, while liquid-intrusion methods characterize pores accessible to an invading liquid. Image-analysis methods provide another approach to pore characterization. No single method necessarily captures every pore size or closed cavity. (directives.nrcs.usda.gov)

In groundwater studies, total porosity describes the space potentially occupied by water, while effective porosity helps characterize movement through an aquifer. Effective porosity is distinct from specific yield, the fraction of bulk volume represented by water released through gravity drainage. (pubs.usgs.gov)

In soil science, porosity is important to water storage and movement, aeration, and root growth. In porous-material characterization, pore volume is considered alongside pore size and accessible surface area to describe fluid uptake and transport. (directives.nrcs.usda.gov)

References

1. Water Resources of the United States — SUTRA Glossarywater.usgs.gov
2. Understanding the Hydrologic System — USGS Circular 1224pubs.usgs.gov
3. Department of the Interior — Hydrologic Atlas 659, Plate 3pubs.usgs.gov
4. Soil Survey Laboratorynrcs.usda.gov
5. Soil–Plant–Water Relationshipsdirectives.nrcs.usda.gov
6. Soil Quality Indicators: Bulk Densitynrcs.usda.gov
7. Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosityarxiv.org