Porosity plays a clearly important role in geology. It controls fluid storage in aquifers, oil and gas fields and geothermal systems, and the extent and connectivity of the pore structure control fluid flow and transport through geological formations, as well as the relationship between the properties of individual minerals and the bulk properties of the rock. In order to quantify the relationships between porosity, storage, transport and rock properties, however, the pore structure must be measured and quantitatively described. The overall importance of porosity, at least with respect to the use of rocks as building stone was recognized by TS Hunt in his “Chemical and Geological Essays” (1875, reviewed by JD Dana 1875) who noted:

> “Other things being equal, it may properly be said that the value of a stone for building purposes is inversely as its porosity or absorbing power.”

In a Geological Survey report prepared for the U.S. Atomic Energy Commission, Manger (1963) summarized porosity and bulk density measurements for sedimentary rocks. He tabulated more than 900 items of porosity and bulk density data for sedimentary rocks with up to 2,109 porosity determinations per item. Amongst these he summarized several early studies, including those of Schwarz (1870–1871), Cook (1878), Wheeler (1896), Buckley (1898), Gary (1898), Moore (1904), Fuller (1906), Sorby (1908), Hirschwald (1912), Grubenmann et al. (1915), and Kessler (1919), many of which were concerned with rocks and clays of commercial utility. There have, of course, been many more such determinations since that time.

There are a large number of methods for quantifying porosity, and an increasingly complex idea of what it means to do so. Manger (1963) listed the techniques by which the porosity determinations he summarized were made. He separated these into seven methods for …

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Characterization and Analysis of Porosity and Pore Structures

The three-dimensional geometry and connectivity of pore space controls the hydraulic transport behavior of crustal rocks. We report on direct measurement of flow-relevant geometrical properties of the void space in a suite of four samples of Fontainebleau sandstone ranging from 7.5 to 22% porosity. The measurements are obtained from computer analysis of three-dimensional, synchrotron X-ray computed microtomographic images. We present measured distributions of coordination number, channel length, throat size, and pore volume and of correlations between throat size/pore volume and nearest-neighbor pore volume/pore volume determined for these samples. In order to deal with the ambiguity of where a nodal pore ends and a channel begins, we apportion the void space volume solely among nodal pores, with the channel throat surfaces providing the nodal pore delineations. Pore channels thus have length but no associated volume; channel length is defined by nodal pore center to nodal pore center distance. For a sample of given porosity our measurements show that the pore coordination number and throat area are exponentially distributed, whereas the channel length and nodal pore volume follow gamma and lognormal distributions, respectively. Our data indicate an overall increase in coordination number and shortening of pore channel length with increasing porosity. The average coordination number ranges from 3.4 to 3.8; the average channel length ranges from 200 to 130 μm. Average throat area increases from 1600 to 2200 μm 2 with increasing porosity, while average pore volume remains essentially unchanged at around 0.0004 mm 3 .

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900208

Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones

Characterization of pore systems in seal rocks using Nitrogen Gas Adsorption combined with Mercury Injection Capillary Pressure techniques

Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks

Durability estimation of porous building stones from pore structure and strength

Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, Fourth Edition provides users with tactics that will help them understand rock-fluid interaction, a fundamental step that is necessary for all reservoir engineers to grasp in order to achieve the highest reservoir performance. The book brings the most comprehensive coverage on the subject matter, and is the only training tool for all reservoir and production engineers entering the oil and gas industry. This latest edition is enhanced with new real-world case studies, the latest advances in reservoir characterization, and a new chapter covering unconventional oil and gas reservoirs, including coverage on production techniques, reservoir characteristics, and the petrophysical properties of tight gas sands from NMR logs.Strengthened with a new chapter on shale oil and gas, adding the latest technological advances in the field todayCovers topics relating to porous media, permeability, fluid saturation, well logs, Dykstra-Parson, capillary pressure, wettability, Darcy's law, Hooke's law, reservoir characterization, filter-cake, and moreUpdated with relevant practical case studies to enhance on the job trainingContinues its longstanding, 20-year history as the leading book on petrophysics

Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties

This chapter discusses that the point-load test is designed to provide a rapid, portable index test for rock strength. A sample is compressed among solid steel cones that generate tensile stress normal to the axis of loading. The point-load strength index (Is) is defined as the load measured at the point of failure of the rock sample (Fa) divided by the distance among the conical platens at the moment of failure (Ls). Empirical testing has revealed a direct correlation of the Is index to the uniaxial compressive rock strength when the test is performed using a cylindrical core the length of the core is greater than 1.4 times the diameter of the core and the diametral test is performed.

Point-Load Strength Test

The knowledge of the two properties—porosity and permeability—of rocks is essential to determine the types of fluids, amount of fluids, rates of fluid flow, and fluid recovery estimates in rocks. The porosity of a reservoir rock is defined as that fraction of the bulk volume of the reservoir that is not occupied by the solid framework of the reservoir. The porosities of petroleum reservoirs range from 5% to 30%, but most frequently are between 10% and 20%. Any porosity less than 5% is very seldom commercial, and any porosity more than 35% is extremely unusual. During sedimentation and lithification, some of the pore spaces initially developed became isolated from the other pore spaces by various diagenetic and catagenetic processes such as cementation and compaction. Thus, many of the pores will be interconnected, whereas others will be completely isolated. This leads to two distinct categories of porosity—total and effective—depending upon which pore spaces are measured in determining the volume of these pore spaces. In addition to being porous, a reservoir rock must have the ability to allow petroleum fluids to flow through its interconnected pores. The rock's ability to conduct fluids is termed as permeability. The permeability of a rock depends on its effective porosity and consequently, it is affected by the rock grain size, grain shape, grain size distribution (sorting), grain packing, and the degree of consolidation and cementation.

Porosity and Permeability

An air-water capillary pressure curve may be used to obtain a distribution of the average pore entry radii of a porous medium. Air is non-wetting; therefore, the contact angle can be considered to be 90°, which makes the cos θ in Equation A15.1 equal to 1.0. Thus, the equation to measure the average pore entry radius is as follows:

Pore Size Distribution

Today well logging is basically a suite of electrical, acoustic, and nuclear measurements that provide data, as accurately as possible, to permit the solution of Archie’s equation. Archie’s equation is composed of four parameters that define the interstitial water saturation of subsurface geologic structures. The quantity of petroleum is then inferred by the deviation of the water saturation from 100%. Archie’s formation resistivity factor ( F ) is a direct function of porosity and cementation, and it is determined using one or more logs that directly, or indirectly, furnish the value of the formation porosity as a function of depth (acoustic, density, neutron). The water resistivity, bed boundaries, and percentage of shale (clay) of the geologic formation are determined by the self-potential log (SP log). The gamma ray log (GR log) is used for lithology identification and percent shale. The true, overall, resistivity of the undisturbed (by drilling fluids) zone of the hydrocarbon reservoir is determined using electrical devices that make these measurements several feet away from the wellbore. When all of the values are obtained, Archie’s equation yields a quantitative evaluation of the hydrocarbons present in the reservoir. FORTRAN programs are provided for analyses of reservoir data.

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Papers

Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties

Point-Load Strength Test

Porosity and Permeability

Pore Size Distribution

Basic Well-Log Interpretation