# Porosity

Porosity is a measure of the volume of void space in a rock as a fraction of the total volume of the rock. In geology, this void space is always filled with a fluid such as water or hydrocarbon.

The total porosity can be defined as:

${\displaystyle \phi ={\frac {V_{V}}{V_{T}}}=1-{\frac {V_{M}}{V_{T}}}}$

Where VV is the volume of void space, VM is the volume of rock matrix, and VT is the total volume of the rock.

## Types of porosity

There are many specific definitions of porosity that may refer to a subset of the total porosity. Each is measured with different methods and is important in different geophysical applications.

### Total porosity

The total amount of void space as a fraction of the total rock volume.

### Connected porosity

Void space through which a physical path exists that connects the pores to the outside of the volume.

### Disconnected porosity

Void space not connected to the outside of the volume. Total porosity minus connected porosity.

### Effective porosity

Connected porosity that can store and produce fluids. The definition of effective porosity varies depending on what can actually be produced in a reasonably short amount of time. For example, a porosity that allows fluid flow in a period of a million years is not considered effective even though the fluids can technically flow out of the rock.

### Trapped porosity

Porosity that contains fluids that cannot flow in a reasonably short amount of time. This can be due to trapped porosity or due to pore throats that are too small to let the fluids flow.

### Vuggy porosity

Porosity with high aspect ratio (spherical) commonly caused by the dissolution of calcareous material. This type of porosity can resist compression very effectively due to its shape.

### Vesicular porosity

Porosity due to gas bubbles.

### Dissolution porosity

Porosity caused by the dissolution of mineral grains during diagenesis.

### Moldic porosity

Porosity caused by the stacking of biogenic shells.

### Intergranular porosity

Porosity between grains.

### Intragranular porosity

Porosity within grains.

### Fracture porosity

Porosity caused by fractures. This type of porosity has very low aspect ratio and is therefore more easily compressed.

### Micro porosity

Porosity in very small pores. It is generally ineffective.

### Primary porosity

Porosity available due to sedimentary deposition. Original porosity.

### Secondary porosity

Porosity created after burial. It generally refers to diagenetic porosity (dissolution, etc.) and fracture porosity.

## Measuring porosity

One can measure porosity directly or indirectly. It is much more common to measure porosity using indirect methods because these can be done in situ. There are many property changes caused by taking a core sample to the surface (different temperature and pressure) for a direct porosity measurement. Among these changes are the expansion of the sample, the introduction of fractures and the expulsion of the saturating fluids.

### Porosity from sonic log

Using the Wyllie time-average equation one can approximate the porosity from sonic velocities. The equation is as follows:

${\displaystyle \phi ={\frac {1/v-1/v_{m}}{1/v_{f}-1/v_{m}}}={\frac {\Delta t-\Delta t_{m}}{\Delta t_{f}-\Delta t_{m}}}}$

where, ${\displaystyle \phi }$ is the total porosity, ${\displaystyle v}$ is the wave's measured phase velocity, ${\displaystyle v_{m}}$ is the velocity of the rock matrix, and ${\displaystyle v_{f}}$ is the velocity of the fluid in the pores, ${\displaystyle \Delta t}$ is the measured interval travel-time, ${\displaystyle \Delta t_{m}}$ is the interval travel-time of the rock matrix, ${\displaystyle \Delta t_{f}}$ is the interval travel-time of the saturating fluid. By measuring the wave velocity of the rock and assuming velocities for the rock matrix and saturating fluids, one can estimate the porosity of such rock.

### Porosity from density log

Using the mass balance equation, porosity can be estimated from measured density values assuming a density for the rock matrix and the saturating fluid. The equation is as follows:

${\displaystyle \phi ={\frac {\rho -\rho _{m}}{\rho _{f}-\rho _{m}}}}$

where ${\displaystyle \phi }$ is the total porosity, ${\displaystyle \rho }$ is the measured bulk density, ${\displaystyle \rho _{m}}$ is the density of the rock matrix, and ${\displaystyle \rho _{f}}$ is the density of the saturating fluid.