Porosity and Permeability of Reservoir Rocks

Oil and gas are not found in underground lakes. They fill tiny spaces between grains of sand or within fractures and cavities in carbonate rocks. How much fluid those spaces hold, and how easily it can move towards a well, decides whether a discovery is commercial. Reservoir engineers, geologists and petrophysicists therefore spend a great deal of effort measuring porosity and permeability.

Porosity

Porosity is the ratio of pore volume to total (bulk) rock volume:

$$\phi = \frac{V_p}{V_b}$$

It is expressed as a fraction or a percentage. Typical reservoir sandstones have 10 to 30% porosity; carbonates range widely from a few percent to over 30%.

Types of porosity

• Total porosity: all pore space, connected or isolated.
• Effective porosity: only interconnected pores that contribute to flow. This is what matters for production.
• Primary porosity: formed when the sediment was deposited, such as spaces between sand grains.
• Secondary porosity: formed later by dissolution (vugs in limestone), fracturing or dolomitisation.

Factors controlling porosity

• Sorting: well sorted grains of similar size leave more pore space than poorly sorted ones, where small grains fill the gaps.
• Grain packing: loosely packed (cubic) spheres give about 47.6% porosity; tightly packed (rhombohedral) about 26%.
• Cementation: minerals such as quartz and calcite precipitate between grains and reduce porosity.
• Compaction: burial under thick sediment squeezes grains together, so porosity generally decreases with depth.

Grain size alone does not control porosity for ideal packing: uniform small spheres and uniform large spheres have the same porosity. It does strongly control permeability.

Permeability and Darcy’s law

Henry Darcy discovered in 1856, while designing water filters for Dijon, that flow through a sand pack is proportional to the pressure difference and the area, and inversely proportional to the length. For a fluid of viscosity μ flowing through rock of permeability k:

$$q = \frac{k A \,\Delta P}{\mu L}$$

where q is the flow rate, A the cross sectional area, ΔP the pressure drop over length L.

One darcy is the permeability that allows 1 cm³/s of a 1 cP fluid to flow through 1 cm² under a gradient of 1 atm/cm. Because reservoir values are usually much smaller, the millidarcy (mD) is common. One darcy is about 0.987 × 10⁻¹² m².

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Porosity and permeability relationship

Porosity and permeability are related but not the same. Permeability depends mainly on pore throat size and connectivity, not just pore volume. Coarse, well sorted sands have large throats and high permeability. Fine grained rocks can have the same porosity but far lower permeability. Fractures can give tight rocks high permeability despite low porosity. Within one rock type, engineers often fit a log linear trend of permeability against porosity from core data, then use it to estimate permeability from porosity logs.

Permeability is also often anisotropic: horizontal permeability is usually higher than vertical because of layering, which affects coning of gas or water towards wells.

How porosity and permeability are measured

Core analysis

Rock samples (cores) cut during drilling are tested in the laboratory following practices such as API RP 40:

• Porosity: helium porosimetry using Boyle’s law, or saturating the sample with liquid and weighing it.
• Permeability: flowing gas or brine through a plug and applying Darcy’s law, as in the example above.

Well logs

Continuous measurements down the borehole estimate porosity from density, neutron and sonic logs, as described in well logging methods. Permeability is harder to log directly; it is estimated from correlations, nuclear magnetic resonance logs or formation testers.

Well tests

Pressure transient tests, where a well is flowed and then shut in while pressure is recorded, give the average permeability of the reservoir around the well, a much larger volume than any core. Accurate downhole and surface pressure measurement is essential for these tests.

Fluid saturation and reservoir quality

Porosity tells how much space exists, but not what fills it. Water saturation is the fraction of pore volume filled with water; the rest holds oil or gas. Fine grained rocks with small pores hold more water by capillary forces, so poor permeability often comes with high water saturation. Engineers therefore combine porosity, permeability and saturation into net pay: the thickness of rock that meets cut offs for all three and can contribute to production. Thin, high quality layers can matter more than thick, tight ones.

Why they matter

Porosity, together with reservoir area, thickness and water saturation, gives the volume of hydrocarbons in place. Permeability, with fluid viscosity and pressure, controls how fast wells can produce, how many wells are needed, and whether techniques such as artificial lift or hydraulic fracturing are required. Together, porosity and permeability shape every major decision in developing an oil or gas field, from drilling with a rotary rig to designing the surface facilities.