Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis

A unified analysis method for small-angle scattering data is demonstrated by surveying complex systems that display multiple size-scale structures. Using this approach the relationship between micro- and nano-structures can be ascertained. The method uses a function that is general enough to adequately describe systems ranging from particulates with fractally rough interfaces to mass fractals such as polymer coils. Additionally multiple Guinier and power-law regimes can be treated. The unified method can distinguish Guinier regimes buried between two power-law regimes. Data from particulate filled systems, low crystallinity polymers and low density polymer foams are analyzed.

Structural studies of complex systems using small-angle scattering: a unified Guinier/power-law approach☆

The self-similarity of rocks on the macro-scale is well known—traditionally, the photographs of rock formations usually include a scale-defining object such as a coin, a hammer, a human silhouette, etc. We know now that rock self-similarity, expressed in the quantitative language of fractal geometry, is also ubiquitous in the micro-world as well. In fact, sedimentary rocks are some of the most extensive microstructural fractal systems found in nature. Much of the knowledge of self-similarity on the micro-scale has been accumulated over the last two decades using small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS).

In the family of neutron scattering techniques, small-angle scattering has the lowest spatial resolution (Vogel and Priesmeyer 2006, this volume)—it cannot detect the position of individual atoms. It can, however (using two different experimental designs), explore the internal microarchitecture of the pore space over an impressive linear scale range (from nanometers to tens of micrometers). The technique is non-invasive and gives an average value for a given sample volume.

In the following, it is demonstrated how SANS can be used to explore the microstructure of sedimentary and igneous rocks and help gain insights into internal specific surface area, porosity, pore size distribution, mercury intrusion porosimetry, compaction, subsurface generation of oil and gas, adsorption of gases, imbibition of water, distribution of crystalline precipitates and the microstructural effects of heat treatment.

It is the author’s intention to provide both a comprehensive introduction for newcomers to the subject and a reference text for those already familiar with small-angle scattering techniques. The article includes a review of theoretical results, selected examples, description of experimental procedures, examples of interpreted data for various types of rocks and references to original work.

### Small-angle scattering (SAS) techniques

SANS (Small-Angle Neutron Scattering) and SAXS (Small-Angle X-ray Scattering), have been used for decades to study the geometry of …

Small-Angle Neutron Scattering and the Microstructure of Rocks

Development of the meso- and macroporous structure of coals with rank as analysed with small angle neutron scattering and adsorption experiments

The concept of fractals, introduced by Mandelbrot ( 1 982), has proven to be a highly useful way to describe the statistics of naturally occurring geometries. Fluid flow, whether it be the rise and fall of rivers (Bridge & Jarvis 1 982), turbulence in air or water (Nelkin 1989), or precipitation (Mandelbrot & Wallis 1 968), is found to follow self-similar patterns in time and space. Natural objects, from mountains and coastlines (Mandel­ brot 1982) to the perimeters of forests (Loehle 1 983), are found to have boundaries best described as self-similar, appearing the same on all length scales and having a measured size that depends on the scale ofthe measure­ ment. Microscopic processes of diffusion (Orbach 1 989) and chemical reaction kinetics (Kopelman 1988) can lead to fractal structures, while the scale independence of natural processes can lead to the ubiquitous I/! noise and stretched exponential relaxation (West & Shlesinger 1 990). Many review articles and books have been written on fractals [see Hurd (1 988) for a bibliography], and reviews (Wong 1 988) and conference proceedings (Scholz & Mandelbrot 1 989, Aharony & Feder 1 989, Fleischmann et al 1 989, Avnir 1 989) have appeared on various aspects of fractal applications in geophysics. I do not attempt to review here basic fractal concepts as they are covered in the cited literature but rather concentrate on fractal structure at the microscopic scale in sedimentary porous rock and on the geometry of flowing fluids. One objective of this work is to develop models for rock pore geometry that will distinguish rocks from other porous materials. The length scales of interest include the submicron structure on pore walls,

Fractals in Rock Physics

The small-angle scattering from fractally rough surfaces has the potential to give information on the surface area at a given resolution. By use of quantitative neutron and x-ray scattering, a direct comparison of surface areas of fractally rough powders was made between scattering and adsorption techniques. This study supports a recently proposed correction to the theory for scattering from fractal surfaces. In addition, the scattering data provide an independent calibration of molecular adsorbate areas.

Surface areas of fractally rough particles studied by scattering.

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Surface areas of fractally rough particles studied by scattering.