Fontainebleau Sandstone Research Articles

Investigating 3D geometry of porous media from high resolution images

We present spatial distributions for pore path length and coordination number, pore throat size and nodal pore volume obtained for a 1.53 mm3 volume of 12.1% porosity Fontainebleau sandstone. The sandstone was imaged using Synchrotron X-Ray computed microtomography at 6 micron resolution. The spatial distributions were computed based upon three dimensional medial axis analysis of the void space in the image. We also present vesicle size and vesicle-vesicle contact surface area distributions for a 1.36 mm length of a 6.36 mm diameter core of basalt from a vesiculated lava flow imaged at 20 micron resolution.

Reconstructing random media. II. Three-dimensional media from two-dimensional cuts

We report on an investigation concerning the utilization of morphological information obtained from a two-dimensional (2D) slice (thin section) of a random medium to reconstruct the full three-dimensional (3D) medium. We apply a procedure that we developed in an earlier paper that incorporates any set of statistical correlation functions to reconstruct a Fontainebleau sandstone in three dimensions. Since we have available the experimentally determined 3D representation of the sandstone, we can probe the extent to which intrinsically 3D information (such as connectedness) is captured in the reconstruction. We considered reconstructing the sandstone using the two-point probability function and lineal-path function as obtained from 2D cuts (cross sections) of the sample. The reconstructions are able to reproduce accurately certain 3D properties of the pore space, such as the pore-size distribution, the mean survival time of a Brownian particle, and the fluid permeability. The degree of connectedness of the pore space also compares remarkably well with the actual sandstone. However, not surprisingly, visualization of the 3D pore structures reveals that the reconstructions are not perfect. A more refined reconstruction can be produced by incorporating higher-order information at the expense of greater computational cost. Finally, we remark that our reconstruction study sheds light on the nature of information contained in the employed correlation functions.

The characterisation of fluid transport in porous solids by means of pulsed magnetic field gradient NMR

The determination, by pulsed field gradient (PFG) nuclear magnetic resonance (NMR), of the probability distributions (propagators) of displacements for fluids undergoing transport by both flow and self-diffusion within porous solids is outlined. The nature of the observed propagator, P Δ (Z), for the transport of a single aqueous phase through an outcrop sandstone (Fontainebleau) is described. Recent measurements of the propagators for both aqueous and oil phase flow in the limiting saturation states of irreducible water ( S wi ) and residual oil ( S or ) in the same sample are illustrated through the use of difference propagators. These are shown to emphasise the regions of the propagators most affected by the presence of the second, stationary, phases in these limiting saturation conditions. Measurement of the propagators for both oil and aqueous phases undergoing simultaneous flow are also described for the same sandstone sample and the effect of increasing S wi on the nature of the oil flow is briefly discussed. Finally, a new two-dimensional (2-D) experiment is introduced which measures the propagator P Δ (X, Z). This is the joint probability for displacements X and Z in time Δ. Some preliminary observations of these two-dimensional propagators are shown for single-phase flow in the Fontainebleau sandstone sample, where Z and X are, respectively, displacements in the axial and radial direction for the cylindrical sample for which the pressure gradient is along Z and where bulk radial flow is constrained to be zero.

Study of wettability and spreading impact in three-phase gas injection by cryo-scanning electron microscopy

Much has been already done and written on the effect of wettability and spreading in three-phase displacement properties and efficiency. However, a direct visualization of the impact of these parameters in the distribution of the three fluids (water–oil–gas) within the pore space and consequently on the recovery mechanisms has been lacking. The objective of this paper is to obtain at the pore scale the necessary information to interpret the macroscopic behavior and to predict ultimate oil recovery for well controlled wetting and spreading conditions. To this end cryo-scanning electron microscopy (cryo-SEM) observations are performed in water-wet and oil-wet Fontainebleau sandstone plugs for spreading and non-spreading conditions. It is demonstrated that cryo-SEM can be used as a tool to study at the pore scale the fluid distributions and efficiency of oil recovery processes involving three phases. It is also proved that in a real porous medium both wettability and spreading affect gas injection efficiency by controlling three-phase distributions at the pore level and phase connectivity.

An Experimental Study of the Reactive Surface Area of the Fontainebleau Sandstone as a Function of Porosity, Permeability, and Fluid Flow Velocity

An Experimental Study of the Reactive Surface Area of the Fontainebleau Sandstone as a Function of Porosity, Permeability, and Fluid Flow Velocity

Reconstructing random media

We formulate a procedure to reconstruct the structure of general random heterogeneous media from limited morphological information by extending the methodology of Rintoul and Torquato [J. Colloid Interface Sci. {bold 186}, 467 (1997)] developed for dispersions. The procedure has the advantages that it is simple to implement and generally applicable to multidimensional, multiphase, and anisotropic structures. Furthermore, an extremely useful feature is that it can incorporate any type and number of correlation functions in order to provide as much morphological information as is necessary for accurate reconstruction. We consider a variety of one- and two-dimensional reconstructions, including periodic and random arrays of rods, various distribution of disks, Debye random media, and a Fontainebleau sandstone sample. We also use our algorithm to construct heterogeneous media from specified hypothetical correlation functions, including an exponentially damped, oscillating function as well as physically unrealizable ones. {copyright} {ital 1998} {ital The American Physical Society}

The characterization of multiphase fluid transport in a porous solid by pulsed gradient stimulated echo nuclear magnetic resonance

Pulsed magnetic field gradient stimulated echo nuclear magnetic resonance (NMR) measurements are reported for the steady-state flow and diffusion of two and three phases (water, dodecane, N2 gas) within a sample of a Fontainebleau sandstone. The stimulated echo dependence on the gradient pulse area, q, is used to derive the displacement probability, PΔ(X) for fixed observation times Δ, with the displacements X being measured along the macroscopic pressure gradient. An extensive range of NMR experiments was carried out, starting with single-phase flow of either water (an aqueous solution of NaCl 3% w/v) or oil (dodecane) for various relative saturation states. Following these experiments, PΔ(X) were acquired for water and oil when both phases were forced to flow through the sandstone. Finally, NMR measurements were performed in which three phases (oil, water and N2 gas) were flowing simultaneously. Using the NMR data it was possible to evaluate the physical importance of parameters such as wettability, spreading and phase saturations on the transport phenomena. To our knowledge, these experiments represent the first comprehensive NMR study of multiphase flow in porous media, and the extent of the information obtained is providing a strong experimental basis to validate and develop accurate modelling of fluid transport in porous solids.

Laboratory measurements anomalous 0.1–0.5 Hz streaming potential under geochemical changes: Implications for electrotelluric precursors to earthquakes

Streaming potentials resulting from flow of various salt solutions in rock were measured on saturated sediments (Fontainebleau sandstones). The streaming potential ΔV was found to be proportional to the driving pore pressure ΔP. Pulses of amplitude 15–40 mV in the frequency range of 0.1 to 0.5 Hz were observed when the conductivity of the injected water was decreased and the fluid flow rate was relatively low, corresponding to a Darcian velocity of 17 to 30 cm/h. The amplitudes of these pulses are 47% to 133% of the corresponding steady components of the ΔV values. Such geochemically induced effects may possibly be responsible for the frequency signals from 0.1 to 0.5 Hz that were sometimes observed before an earthquake.

NMR measurements and numerical simulation of fluid transport in porous solids

AbstractPulsed magnetic field gradient stimulated echo NMR measurements are performed for diffusion and flow of an aqueous phase both within a sample of packed spherical beads and within a 25% porosity Fontainebleau sandstone. The stimulated echo dependence on the gradient pulse area q is used to derive the displacement probability distributions PΔ(X) for fixed observation times Δ. The shape of PΔ(X) as a function of Δ is simulated for computer‐generated porous media, and a good agreement is obtained between the experimental NMR data and the simulations.

Three-phase flow in water-wet porous media: gas/oil relative permeabilities for various spreading conditions

This paper addresses the impact of oil-on-water spreading energy (which governs the ability of the oil phase to spread on water in the presence of gas) on three-phase gas/oil relative permeabilities and residual oil saturation. Experimental tests, including simultaneous injections of oil and gas in porous media (steady state) as well as displacements of oil by gas (unsteady state) in the presence of connate water, were performed in two different rocks, Fontainebleau and Clashach sandstones. Gas and oil relative permeabilities were calculated directly from the steady-state data or evaluated by history matching of the experimental displacement production curves. The values obtained by the two methods often differ significantly; the relative permeabilities obtained by the steady-state method cannot represent a displacement. Oil recovery and relative permeabilities are higher for spreading than for non-spreading conditions for gas drainage displacements. Gas relative permeabilities at low oil saturations seem to be lower for non-spreading than for spreading conditions due to an important gas blocking effect caused by the oil/gas menisci. In this case, the measured relative permeabilities include a capillary effect. Oil relative permeabilities are compared to theoretical curves derived from an analytical model that takes into account, through the fractal dimension, the surface irregularities of a real porous medium; the model presented in this paper can be used to calculate the relative permeability of the intermediate phase (oil) during gas injection in a porous medium in the presence of water, for low oil saturations where film flow predominates; very good agreement is obtained for spreading conditions. Gas and oil relative permeabilities obtained by fitting the displacement curves for experiments performed with the reservoir rock and fluids under representative conditions may thus be used for prediction or modeling purposes on a reservoir scale.

Influence of change in physical state on elastic nonlinear response in rock: Significance of effective pressure and water saturation

We describe Young's mode resonant bar results obtained under effective pressure at two saturation states: dry and water saturated. We monitor primary manifestations of nonlinear response in these experiments: the harmonic content, the source extinction intensity, and fundamental resonant frequency shift. In addition, we describe the hysteretic behavior of the static pressure response, the linear modulus, and Q. Because we currently lack a complete theoretical description of nonlinear behavior under resonance at pressure, we provide relative measures of nonlinear response rather than absolute values. The rocks include Fontainebleau and Meule sandstones and Lavoux limestone. Dynamic strain levels range from 10−8 to 10−5 and frequencies range from 1 to 10 kHz. The elastic nonlinear response of each of the rocks is markedly different over the range of physical property states explored. The different responses are related to differences in mechanical response resulting from rock type, grain cement type, etc. In all of the samples studied, the change in resonant frequency as a function of excitation intensity is not measurable above approximately 10 MPa; however, harmonics are observed at larger effective pressure levels. Hysteresis in velocity and Q versus pressure vary considerably between the rocks. The effect of Q on the experiments is marked. When Q is low (<10) as for some saturated samples, relative excitations must be large in order to induce equivalent dry sample strains.

Strain localization in Fontainebleau sandstone: Macroscopic and microscopic investigations

Two small-scale models simulating an opening in a flat-lying layered rock mass were manufactured in the laboratory using ilmenite sand and gypsum mixtures and tested on a loading frame until failure. It was observed that the failure of the opening was initiated by tensile cracking at the mid-section of the immediate roof layer. The loading frame test results have been back-analysed using a Cosserat Continuum Finite Element code. In the finite element formulation, the layers have been assumed to be elastic with equal thickness and equal mechanical properties; whereas the inter-layer interfaces (joints) have been assumed to be elastic perfectly-plastic. It is observed that the present Cosserat continuum model accurately predicts the experimental displacements everywhere, except for the roof region where the prediction is accurate up to a certain load level beyond which the experimental displacements increase more rapidly than those predicted by the numerical model. It is shown that the load, at which the measured displacements start to deviate noticeably from those obtained from the numerical prediction corresponds to the critical load that may initiate cracks in the roof layer.

Strain localization in Fontainebleau sandstone: Macroscopic and microscopic investigations

The paper concerns a study of strain localization in a sandstone. At first, the material properties and the experimental device are described. The experimental method for detecting strain localization is based on multiple measurements of strains and displacements. By comparisons, these measurements give indications on a strain inhomogeneity. First tests have been performed on cylindrical samples and the results shown that the procedure is not systematically efficient for this kind of experiments. Prismatic samples are then used. In order to control the localization initiation and to follow up the shear banding the last tests are performed on prismatic samples containing a little hole. The shear bands characteristics (onset, orientation, width) are given for all these tests on prismatic sample. Their variation with confining pressure is emphasized. Finally, some details on the deformation mechanisms inside the bands are provided by visual and microscopic observations.

Lattice-Boltzmann simulations of flow through Fontainebleau sandstone

Lattice-Boltzmann simulations of flow through Fontainebleau sandstone

The effective mechanical properties of random porous media

The effective mechanical properties of homogeneous porous media can be theoretically determined by a multiple scale expansion. In such a scheme, the media are modelled as being spatially periodic. The elastic equations with appropriate boundary conditions are numerically solved on the unit cell to determine the macroscopic mechanical properties of the medium. Three types of unit cell were investigated: deterministic, fractal and random; the last type includes media derived from site percolation, random packings of spheres and a real sample of Fontainebleau sandstone. A systematic comparison is made with existing numerical data and with the predictions of various types of renormalization models.

A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect

A three-dimensional model of anisotropic damage by mesocrack growth is first described in its basic version, employing a second-order tensorial damage variable. The model—concerning rate-independent, small strain, isothermal behaviour—allows to take into account residual effects due to damage and reduces any system of mesocracks to three equivalent orthogonal sets. This first version is then extended to account for elastic moduli recovery due to crack closure. Micromechanical considerations impose to employ a fourth-order crack-related tensor when the mesocracks are constrained against opening. Unlike some models which do not avoid (or rectify a posteriori) discontinuities of the stress-strain response, the approach herein ensures a priori the stress continuity and allows to express a convenient macroscopic opening-closure criterion. Nevertheless, the new formulation maintains the orthotropy of the effective properties (instead of an eventual, more general form of anisotropy). Finally, it appears that the extended version does not introduce additional material constants compared to the basic version. The model is tested by simulating the behaviour of Fontainebleau sandstone.

Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis

We present a study of the morphology and bulk physical properties of a Fontainebleau sandstone via an X ray tomographic analysis. Synchrotron‐based X ray tomographic techniques provide us with a high‐resolution (7.5 μm), three‐dimensional digitized representation of the sandstone that leaves the sample intact and unaltered. To estimate a wide spectrum of bulk properties of the Fontainebleau sandstone specimen, we extract from this image a number of different correlation functions that statistically characterize the pore‐space morphology and relevant pore‐space length and time scales. These statistical measures are obtainable from lineal, plane, and/or volume measurements and include the porosity, specific surface, two‐point and three‐point probability functions, lineal‐path function, chord‐length distribution function, pore‐size distribution function, and coarseness. The pore‐size distribution function, in particular, contains a certain level of connectedness information and accordingly can only be obtained from a three‐dimensional representation of the sample. Many bulk properties of the sandstone, such as the mean survival time τ (obtainable from Nuclear Magnetic Resonance relaxation studies), fluid permeability k, effective electrical and thermal conductivities, and effective elastic moduli, can be estimated using the aforementioned statistical correlation functions. Specifically, the electrical conductivity (or, equivalently, the formation factor F), mean survival time, and fluid permeability are determined using rigorous bounds. The mean survival time and fluid permeability are also found using direct simulation techniques and cross‐property relations, respectively. One such cross‐property relation for k depending on τ and F gives a permeability estimate that is within a factor of 2 of the experimental result.

Modelling of simulated clay precipitation within reservoir sandstones

The purpose of this study was to investigate whether a previously developed computer model, named Pore-Cor, could simulate the subtle changes in void space dimensions which occur during the artificial deposition of small amounts of illite and kaolinite within Fontainebleau sandstone. Clay precipitation was carried out by placing a sandstone plug in a gold capsule, with an aluminosilicate gel, and treating the plug hydrothermally with potassium hydroxide solution. Using experimental conditions of 350°C and 1.0 kbar (100 MPa), illite, illite-smectite and kaolinite were precipitated in parts of the sandstone void space with morphologies similar to those of authigenic clay minerals in sandstone petroleum reservoirs. Mercury intrusion curves were then measured for the untreated and clay precipitated sandstones. The Pore-Cor package simulated these intrusion curves, and generated void space models of the correct porosity. By this means, subtle changes in void space dimensions and connectivity could be identified, which give rise to large changes in permeability.

Lattice-Boltzmann simulations of flow through Fontainebleau sandstone : B. Ferreol & D. H. Rothman, Transport in Porous Media, 20(1–2), 1995, pp 3–20

Lattice-Boltzmann simulations of flow through Fontainebleau sandstone : B. Ferreol & D. H. Rothman, Transport in Porous Media, 20(1–2), 1995, pp 3–20

The effective mechanical properties of reconstructed porous media

The purpose of the present paper is two-fold. First, a method of simulating geological porous media is presented ; the two first moments of the pore space phase function are measured on thin sections of Fontainebleau sandstones and used to reconstruct artificial media wsith the same average geometreical properties. Then, the effective elastic properties of the reconstructed samples are determined by solving the local equations of elasticity using a second-order finite difference formulation ; the local equations are discretized using the finite volume technique which incorporates the boundary conditions in such a way that the discretization holds for any geometry. Finally, the comparison between these effective elastic properties and the experimental results obtained on the same materials is presented and discussed.