Fontainebleau Sandstone Research Articles

Experimental study of acoustic anisotropy and birefringence in dry and saturated Fontainebleau sandstone

The velocities of ultrasonic P, SH, and SV waves have been measured in two perpendicular directions, in samples of Fontainebleau sandstone as received or thermally cracked, dry, or saturated, under uniaxial stress. We have investigated the effect of cracking, saturation, and uniaxial stress on the velocity of P and S waves in two orthogonal directions (anisotropy) and the velocity of S waves with two orthogonal polarizations in each direction of propagation (birefringence). The effect of cracking, saturation, and uniaxial stress on Poisson’s ratio has also been investigated. The velocity anisotropy is larger for S waves than for P waves and practically disappears in saturated samples. Birefringence is attenuated in saturated samples. Inversion of the results using Crampin’s model gives values of the crack densities in three directions, in qualitative agreement with the state of cracking observed by scanning electron microscopy. In particular, the crack density is found to be near zero in sandstones with rounded pores only. After thermally induced cracking the crack density is found to be ≈20 percent; uniaxial stress closes the cracks in the plane normal to the stress. Also, in naturally cracked samples the crack density is found to be quite high. Uniaxial stress causes the density of cracks to decrease, mostly in the plane normal to the stress.

Flow in simulated porous media

Two average statistical properties of the pore space of Fontainebleau sandstones are measured on thin sections. They are used to generate fictitious porous media which share the same statistical properties as the real ones; the simulation process is thoroughly presented and discussed. The Stokes flow of a Newtonian fluid in such media can be numerically determined by a finite-difference scheme in three dimensions; the permeability of these media is easily derived from these flow fields. The numerical values of permeability are compared to the experimental data. With no adjustable constant, the predicted permeabilities were found to be in acceptable agreement with the experimental ones.

Effective medium theory and network theory applied to the transport properties of rock

The effective medium theory (EMT) proposed by Kirkpatrick (1973) is known to be a useful tool to describe the conducting properties of heterogeneous media. We check the validity of the theory on several probability distribution functions. The accuracy of the theory is inferred by comparing the results given by the EMT to those obtained when using an exact method based on the resolution of two‐dimensional conducting networks. It turns out that the EMT approximation is quite good for quasi‐uniform distributions of conducting elements, whereas large discrepancies appear for highly contrasted distributions such as decreasing exponential functions. The reason is that ensemble averaging and spatial averaging are not equivalent for broad, nonuniform distributions. Therefore the effective medium theory may not be appropriate for the calculation of the transport properties of rocks which exhibit this type of distribution. The nature of the distribution varies, however, depending on the rock type and the length scale of interest. Critical path analysis can be a complementary tool to deal with highly heterogeneous conducting media. The accuracy of such a technique appears to be better than that of the EMT approximation. But it depends also on the representativity of the input data. Finally, an example of data relative to Fontainebleau Sandstone is developed in this paper. It is concluded that for this rock, network theory is the most accurate tool for calculating transport properties from statistically averaged observations on two‐dimensional sections.

Fundamental modes of strength development for Fontainebleau sandstone (In French) : Luong, M P Proc International Symposium on Rock at Great Depth, Pau, 28–31 August 1989V1, P157–163. Publ Rotterdam: A A Balkema, 1989

Fundamental modes of strength development for Fontainebleau sandstone (In French) : Luong, M P Proc International Symposium on Rock at Great Depth, Pau, 28–31 August 1989V1, P157–163. Publ Rotterdam: A A Balkema, 1989

Direct tensile and direct shear strengths of Fontainebleau sandstone : Luong, M P Key Questions in Rock Mechanics: Proc 29th US Symposium, Minneapolis, 13–15 June 1988P237–246. Publ Rotterdam: A A Balkema, 1988

Direct tensile and direct shear strengths of Fontainebleau sandstone : Luong, M P Key Questions in Rock Mechanics: Proc 29th US Symposium, Minneapolis, 13–15 June 1988P237–246. Publ Rotterdam: A A Balkema, 1988

Permeability, conductivity, and pore geometry of sandstone

Using Bruggeman's effective medium theory, the hydraulic permeability and dc electrical conductivity of sandstone are both expressed in terms of the ratio of two microscopic lengths, which are the dimensions of a characteristic pore throat and pore chamber, respectively. The theory is consistent with Kozeny‐Carman formulas in the limit of a perfectly microscopically homogeneous pore structure. Based on the effective medium approximation, the transport properties of Fontainebleau sandstone are predicted from a quantitative study of the pore space morphology. A series of epoxy‐impregnated thin sections of Fontainebleau sandstone was prepared from cores with porosity ranging between 5 and 22%. Using an image analyzer, throat and pore size distributions were constructed from the digitized and segmented microsections. For each sample the transport coefficients are calculated from the characteristic lengths, which are estimated directly from the experimental size histograms. The changes of both permeability and conductivity are predicted within a factor of 3 over the whole range of porosity. The variations of transport coefficients with porosity are interpreted from the contrasting evolution of pores and throats during diagenesis. Large pore chambers alternate with narrow passages in Fontainebleau sandstone. With decreasing porosity, some of the large pores remain stable, while the throats gradually shrink and are finally eliminated. The microscopic inhomogeneity of the pore geometry of Fontainebleau sandstone implies that its flow properties deviate from Kozeny‐Carman predictions.

EXPERIMENTAL COMPARISON BETWEEN SPECTRAL RATIO AND RISE TIME TECHNIQUES FOR ATTENUATION MEASUREMENT*

ABSTRACTTwo techniques for the measurement of attenuation–spectral ratio and rise time techniques–were tested and compared in the laboratory. The spectral ratio technique proved to be reliable and easy to implement for intermediate values (5 < Q < 50) of attenuation. For low (Q > 50) and high attenuations, the spectral ratio technique is inaccurate. Calculating the rise time on simulated signals, we found a relation between rise time τ and the ratio travel‐time to quality factor T/Q which could be approximated in intervals by the linear relation τ=τ+C*T/Q. The constants τ and C depend on the absolute value of T/Q and on the initial source signal. The rise time technique, performed on the first quarter period of the signal, enables high attenuations (Q < 5) to be measured. The determination of the relation between τ and T/Q is possible if one knows the initial source. We theoretically approximate this relation through a simulation using a realistic propagation model. With laboratory measurements made on Fontainebleau sandstone, we show that the rise time technique using the theoretical relation τ=τ(T/Q) gives comparable values of Q to those obtained from the spectral ratio technique. In borehole seismics, where it is often difficult to remove undesired signals, the rise time technique applied with the right (τ, T/Q) relation is the best method to use.

Hydraulic and acoustic properties as a function of porosity in Fontainebleau sandstone : Bourbie, T; Zinszner, B J Geophys ResV90, NB13, 10 Nov 1985, P11524–P11532

Hydraulic and acoustic properties as a function of porosity in Fontainebleau sandstone : Bourbie, T; Zinszner, B J Geophys ResV90, NB13, 10 Nov 1985, P11524–P11532

Hydraulic and acoustic properties as a function of porosity in Fontainebleau Sandstone

Laboratory measurements have been made of the permeability (k), free porosity (ϕL), compressional velocities (VPorVE), and compressional attenuations (QPorQE) in Fontainebleau sandstone over a continuous range of porosities ϕ from 3 to 28%. This large variation was achieved without any composition change: Fontainebleau sandstone is made of fine quartz grains with regular grain size (≈250 μm). Permeability was measured with a falling head permeameter. Velocities and attenuations were obtained either through an ultrasonic experiment for frequencies around 500 kHz or through a resonant bar technique experiment for frequencies around 5 kHz and in both cases with varying water saturation. The results show an excellent correlation between permeability k and total porosity ϕ for all our samples. For low porosities (ϕ = 3% to 9%), permeability (in millidarcies) is 2.75×10−5(ϕ)7.33, while for high porosities (ϕ = 9% to 28%), permeabilityk(in millidarcies) is given by 0.303(ϕ)3.05. The correlation is also excellent between free porosity and total porosity. On the other hand the correlation between acoustic properties and total porosity is not as clear as for hydraulic properties whatever the frequency (500 kHz or 5 kHz) or the water saturation. On the average, velocity decreases, and attenuation roughly increases with increasing total porosity. Velocity and attenuation values are related to the variation of grain contact structure, and two samples with the same porosity and permeability may exhibit different velocities and attenuations. The clear correlation between hydraulic properties and porosity is related to constant grain size, while the lack of correlation for acoustic properties emphasizes the importance of the microstructure.

On the permeabilty of low porosity sandstones

A Klinkenberg correction is derived for granular porous media and applied to published experimental air permeability data to obtain liquid permeability at low porosities. Various cut-off and threshhold porosity combinations are then examined to obtained an optimal theoretical prediction for the liquid permeability of Fontainebleau sandstone. The results are extremely promising and point to specific objectives which should be addressed in future experimental work.

Stone Polygons beside Loch Lomond

STONE polygons are polygonally arranged bands of flat pebbles, usually surrounding a core of mud, common in Arctic regions in soils composed of mud and stones. They may be associated with curved arcs of stones, each of which is also standing on end. These structures are well known in Spitsbergen, Norway, Iceland*, and Antarctica, and have been found in the Alps. Their formation has been discussed in a long and scattered literature. The chief theories of their formation have been clearly summarized in a paper by Professor J. S. Huxley and Dr. N. E. Odell, in this Journal (vol. 63,1924, pp. 207-229). The most widely accepted explanation attributes these struc? tures to the repeated outward push of the pebbles whenever the ground is frozen, and the flow back of the mud during thaw. That theory was advanced by Professor Hogbom (Bull. Geol. Inst. Upsala, ix, 1908, pp. 41-59) and has been widely adopted, as by Professor Hawkes for a case on a raised beach in Iceland (GeoL Mag., 1924, pp. 509-513, pl 28)and by Dr. C. S. Elton (Q.J.G.S., vol. 83,1927, pp. 163-193, pl. 10-12), Nansen (En Ferd til Spits? bergen, 1920 ; Spitsbergen, 1921) on the other hand regarded the polygons as due not to the migration of the pebbles but to the reduction to powder of those in the centre of a group by repeated freezing. This comminution of the stones no doubt takes place to some extent when they consist of soft shale; and both processes are regarded by Huxley and Odell as having shared in the formation of these structures. A modification of the frost-push theory has been advanced by Thoroddsen for the examples in Iceland, where they are known as rudemarks. His account of the phenomenon, although one of the earliest, has been often overlooked (Thoroddsen, 'The Botany of Iceland,' Pt. I. Physical Geography, 1914, pp. 259-261). He attributed these structures to the combined effect of irregular evaporation from sodden stony clay which has been cracked by frost into clay prisms, and of the pebbles being pushed by repeated frost and thaw into the shrinkage cracks. My interest in these formations was arowsed the day Sir Martin Conway's expedition landed at Green Harbour, Spitsbergen, on 18 June 1896. From the observations made there and at other places in Spitsbergen Professor Garwood and I concluded that these polygons were due to the repeated freezing and thawing of the ground. The stone hexagons appear due to the water freezing into large ice crystals charged with mud and stones, like the sand-charged calcite of the Fontainebleau Sandstone. We did not describe the structures as we expected to find examples of them in the English boulder clays; but to my repeated surprise I have failed to find them in the British glacial drifts, and I am not aware of any definite case of them having been described in glacial deposits, though vertical stones in such are not nixconftnion. Embryonic frost-formed stone polygons I have frequently observed in recent deposits in Scottish valleys, and I have occasionally seen them well dbveJoped, as on the summit of the Merrick (2764 feet), the highest summit in Scotland south of the Highknds (as remarked Q.J.GJS., vol. 83,1927, p. 193), and on Ben Lawers.

Notes on the Nature of the Containing Rocks

The “bluestone” which is found in the central parts of some of the concretions associated with the large spiral bodies described by Mr. B. B. Woodward is found, on microscopical examination, to be a calcareous sandstone. Sabangular grains of quartz, averaging 0·04 mm. in diameter, constitute over 50 per cent of the rock, and are set in a cement of carbonates which have crystallized in plates very much as in the Fontainebleau sandstone. These plates are sometimes 3 cm. across, and give a characteristic lustre to the stone. The quartz-grains are evenly distributed through the plates of crystalline carbonate, and are so closely packed as to be almost in contact. It is easy to imagine that with the complete removal of the carbonates by solution there would remain a friable sandstone, very porous, but still occupying almost the same volume as the bluestone.

Note on the occurrence of a calcareous sandstone allied to Fontainebleau Sandstone at Rock Lily, near Narrabeen

Note on the occurrence of a calcareous sandstone allied to Fontainebleau Sandstone at Rock Lily, near Narrabeen