Enter the void volume and the total volume into the Porosity Calculator. The calculator will evaluate the Porosity.
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Porosity Formulas
Porosity (n) is the fraction of a material’s total volume occupied by voids or pore spaces, expressed as a value between 0 and 1 or as a percentage.
Basic porosity from volumes:
n = V_v / V_t
Where V_v is void volume and V_t is total (bulk) volume. Since solid volume V_s = V_t - V_v, this is equivalent to n = 1 - (V_s / V_t).
Porosity from densities:
n = 1 - (\rho_{bulk} / \rho_{grain})Standard in petrophysics and soil mechanics. Bulk density is sample mass divided by total volume; grain density is the density of solid particles alone. For quartz sand, grain density is typically 2.65 g/cm3. For limestone, approximately 2.71 g/cm3.
Porosity-void ratio conversion:
n = e / (1 + e) \quad \text{and} \quad e = n / (1 - n)Void ratio (e) is the ratio of void volume to solid volume. Geotechnical engineers often prefer it because it can exceed 1.0, making it more practical for tracking volume changes in compressible soils.
Types of Porosity
Total (Absolute) Porosity accounts for every void in the material, connected or isolated. Pumice may have total porosity above 80%, yet much of it consists of sealed gas bubbles fluids cannot enter.
Effective Porosity counts only interconnected pore space through which fluids can flow. In clean sandstones, effective porosity nearly equals total porosity. In clay-rich shales, total porosity can reach 40 to 70%, but effective porosity may be below 5% because tiny pores are poorly connected and water is bound to clay mineral surfaces.
Primary porosity forms during deposition: intergranular space between sand grains or between oolitic carbonate grains.
Secondary porosity develops after formation. Dissolution by acidic groundwater creates vugs (vugular porosity) in carbonates. Tectonic stress produces fracture porosity, typically only 1 to 2% of total porosity but dominating permeability because fracture apertures are orders of magnitude larger than matrix pore throats. In naturally fractured reservoirs, the matrix holds 96 to 99% of stored fluid while fractures provide the primary flow pathways.
Typical Porosity Values by Material
| Material | Total Porosity (%) | Effective Porosity (%) |
|---|---|---|
| Well-sorted gravel | 25 - 40 | 22 - 35 |
| Well-sorted sand | 25 - 50 | 22 - 40 |
| Silt | 35 - 50 | 1 - 20 |
| Clay | 40 - 70 | 1 - 5 |
| Glacial till | 10 - 25 | 5 - 15 |
| Sandstone | 5 - 30 | 5 - 25 |
| Limestone / Dolomite | 1 - 20 | 1 - 15 |
| Shale | 5 - 30 | 0.5 - 5 |
| Granite (unfractured) | 0.1 - 1.5 | 0.05 - 0.5 |
| Basalt (unfractured) | 1 - 12 | 0.5 - 5 |
| Pumice | 50 - 85 | 10 - 40 |
| Peat / Organic soil | 60 - 90 | 50 - 80 |
| Concrete | 8 - 15 | 2 - 8 |
| Brick | 12 - 25 | 5 - 15 |
Clay has the highest total porosity of any common soil, yet its effective porosity is among the lowest. Clay particles are under 2 micrometers, creating pores so small that capillary forces and surface adsorption immobilize the water. Sand and gravel transmit water far more readily despite lower total porosity.
Porosity and Permeability: The Kozeny-Carman Relationship
Porosity measures storage capacity; permeability measures flow ease. The Kozeny-Carman equation (Kozeny 1927, Carman 1937) links them for granular media:
k = \frac{d^2}{180} \cdot \frac{n^3}{(1 - n)^2}Where k is intrinsic permeability (m2), d is representative grain diameter (m), and n is porosity (fraction). Valid for laminar flow in unconsolidated granular materials with porosity in the 0.08 to 0.50 range. The n3/(1-n)2 term makes permeability extremely sensitive to porosity: reducing porosity from 0.40 to 0.30 cuts permeability by more than half.
How Porosity Is Measured
Helium Gas Expansion (Boyle’s Law): Standard lab technique. Helium expands into the pore space of a core sample, and the pressure change reveals grain volume. Helium’s small molecular size (0.26 nm) penetrates all connected pores. Accuracy: +/- 0.5%.
Mercury Intrusion Porosimetry (MIP): Mercury is forced into samples at increasing pressure. The pressure needed to enter each pore is inversely proportional to pore throat diameter (Washburn equation). Maps pore sizes from 3 nm to 1000 micrometers. Common for ceramics, cements, and tight rocks.
Water Saturation (Archimedes): Oven-dry, weigh, vacuum-saturate with water, weigh again. Mass difference gives pore volume. Simple and inexpensive for construction materials.
Density Logging: Borehole gamma-ray tools measure bulk density in situ. Combined with known grain density, porosity is computed continuously along the well without extracting cores.
Neutron Logging: Neutron sources in the borehole interact with hydrogen in pore fluids. Count rate at the detector inversely correlates with porosity. Especially sensitive to water- and hydrocarbon-filled pores.
Factors That Control Porosity
Grain size uniformity: Well-sorted sediments have higher porosity. Rhombohedral packing of uniform spheres yields 25.95% porosity; loose random packing yields 36 to 40%.
Grain shape: Angular particles pack less efficiently than rounded ones, producing slightly higher porosity.
Depth and compaction: Surface muds start at 60 to 80% porosity; at 3,000 m burial they compact to 10 to 20%. Sandstones decline from about 40% at the surface to 15 to 25% at depth.
Cementation: Mineral precipitation (quartz overgrowths, calcite, iron oxides) fills pore throats. A sandstone with 30% initial porosity may drop to 10 to 15% after cementation.
Dissolution: Acidic groundwater dissolves calcite in carbonates, creating secondary vugular porosity and forming karst landscapes.
Applications by Industry
Petroleum engineering: Porosity determines storage volume. Original oil in place: OOIP = A * h * n * (1 - S_w) / B_o, where A is area, h is pay thickness, S_w is water saturation, B_o is formation volume factor.
Groundwater hydrology: Effective porosity controls specific yield. Sand aquifers with 25 to 35% effective porosity are among the most productive; clay aquitards yield almost no water despite high total porosity.
Geotechnical engineering: Consolidation settlement depends on void ratio change under load: delta_H = H * (delta_e / (1 + e_0)).
Construction materials: Lower concrete porosity reduces chloride penetration, carbonation, and freeze-thaw damage. High-performance concrete targets porosity below 10%.
Environmental science: Contaminant transport velocity: v = K * i / n_e. Overestimating effective porosity underestimates contaminant speed, with consequences for wellhead protection zones.
