Permeability of granite under high pressure
TL;DR: In this article, the authors measured the porosity of Westerly granite as a function of effective pressure to 4 kb and found that porosity is correlated with the electrical resistivity of the granite.
Abstract: The permeability of Westerly granite was measured as a function of effective pressure to 4 kb. A transient method was used, in which the decay of a small incremental change of pressure was observed; decay characteristics, when combined with dimensions of the sample and compressibility and viscosity of the fluid (water or argon) yielded permeability, k. k of the granite ranged from 350 nd (nanodarcy = 10−17 cm2) at 100-bar pressure to 4 nd at 4000 bars. Based on linear decay characteristics, Darcy's law apparently held even at this lowest value. Both k and electrical resistivity, ρs, of Westerly granite vary markedly with pressure, and the two are closely related by k = Cρs−1.5±0.1, where C is a constant. With this relationship, an extrapolated value of k at 10-kb pressure would be about 0.5 nd. This value is roughly equivalent to flow rates involved in solute diffusion but is still a great deal more rapid than volume diffusion. Measured permeability and porosity enable hydraulic radius and, hence, the shape of pore spaces in the granite to be estimated. The shapes (flat slits at low pressure, equidimensional pores at high pressure) are consistent with those deduced from elastic characteristics of the rock. From the strong dependence of k on effective pressure, rocks subject to high pore pressure will probably be relatively permeable.
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TL;DR: In this article, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed, and two different modeling approaches to these phenomena are compared.
Abstract: In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.
946 citations
TL;DR: In this paper, the authors analyzed the accessibility of the rock matrix to radio-nuclides and showed that the diffusion of the nuclides into the rock matrices and their sorption onto the surfaces of the microfissures are the main mechanisms retarding migration from a repository.
Abstract: This paper discusses migration of radionuclides in the bedrock surrounding a repository. Currently available models use either a surface reaction or a bulk reaction concept to describe the retardation of migrating nuclides. The first model assumes that the nuclide reacts only with the surface of the fissures. This implies that the rock matrix is not utilized as a sink. The other model implies that the whole bulk of the rock is accessible to the nuclides. The paper analyzes the accessibility of the rock matrix to the radio-nuclides. The transport mechanisms are shown to be flow of water and nuclides in the fissures and transport of nuclides from the water in the fissures into water in the microfissures of the rock by pore diffusion. The diffusion of the nuclides into the rock matrix and their sorption onto the surfaces of the microfissures are the main mechanisms retarding migration from a repository. The diffusivity of the nuclide may be as important as its sorption equilibrium constant. Diffusivities in the pores and microfissures in such dense rocks as granite under confining pressure of hundreds of bars can be expected to be 6–20% of the diffusivity in water. These data are obtained from electrical resistivity measurements of saltwater-filled granites. Porosity of such granites varies from 0.4 to 0.9%. The apparent diffusivities in the granites will then vary between 0.25 · 10−12/Kdρp and 10 · 10−12/Kdρp m2/s, where Kdρp is the volume equilibrium constant. This varies from the porosity of the rock for nonsorbing species to up to and over 104. For a 100-year contact time a nonsorbing nuclide can be expected to penetrate tens of meters of the rock matrix and a strongly sorbing nuclide with Kdρp larger than 104 will penetrate a few millimeters. The diffusion into the rock matrix can enhance the retardation by many orders of magnitude as compared to retardation by surface reaction in fissures only. The retardation may, on the other hand, be many orders of magnitude smaller than the maximum value that could be obtained if all the rock matrix were accessible. This depends very much on the fissure widths and spacings.
810 citations
TL;DR: In this article, the effective pressure p e for measurements of fluid permeability is shown to be ( p c − sp p ) where p c is confining pressure, p p is pore pressure, and s depends on the topography of the fracture surfaces and rock type.
668 citations
TL;DR: In this article, the authors compared laboratory, in situ, and inferred values of permeability, k, of crystalline and argillaceous rocks, and found that in situ k ranged from about 1 μd (10−14 cm2) to 100 md; this is close to the permeability of many sandstones and about 103 times greater than laboratory measurements for intact crystalline rocks.
647 citations
TL;DR: In this article, the authors consider gas adsorption in the measurement of porosity and diffusivity of very tight reservoir rocks, such as gas shales, coal, and tight gas sands, as well as rocks considered as seals for nuclear waste repositories and strata for geological sequestration.
Abstract: Permeability and diffusivity are critical parameters of tight reservoir rocks that determine their viability for commercial development. Current methods for measuring permeability and/or diffusivity may lead to erroneous results when applied to very tight rocks including gas shales, coal, and tight gas sands, as well as rocks considered as seals for nuclear waste repositories and strata for geological sequestration of CO2. The use of He as routinely applied to measure porosity, permeability, and diffusivity may result in non-systematic errors because of the molecular sieving effect of the fine pore structure to larger molecules such as reservoir gases. Utilizing gases with larger adsorption potentials than He, such as N2, and including all reservoir gases to measure porosity or permeability of rocks with high surface area is a viable alternative, but requires correcting for adsorption in the analyses. This study expands several approaches to measure permeability and diffusivity with considerations for gas adsorption, which has not been explicitly considered in previous studies. We present new models that explicitly correct for adsorption during pulse-decay measurements of core under reservoir conditions, as well as on crushed samples used to approximate permeability or diffusivity. We also present a method to determine permeability or diffusivity from on-site drill-core desorption test data as carried out to determine gas in place in coals or gas shales. Our new approach utilizes late-time data from experimental pressure-decay tests, which we show to be more reliable and theoretically (and practically) accurate than the early-time approach commonly used to estimate gas-transport properties.
632 citations
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TL;DR: In this article, it was shown that the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. This can be further simplified by expressing p in terms of S by means of the equation which, when introduced into equation (4), gives
Abstract: Promise of resolving the paradox of overthrust faulting arises from a consideration of the influence of the pressure of interstitial fluids upon the effective stresses in rocks. If, in a porous rock filled with a fluid at pressure p, the normal and shear components of total stress across any given plane are S and T, then are the corresponding components of the effective stress in the solid alone.
According to the Mohr-Coulomb law, slippage along any internal plane in the rock should occur when the shear stress along that plane reaches the critical value where σ is the normal stress across the plane of slippage, τ 0 the shear strength of the material when σ is zero, and ϕ the angle of internal friction. However, once a fracture is started τ 0 is eliminated, and further slippage results when This can be further simplified by expressing p in terms of S by means of the equation which, when introduced into equation (4), gives From equations (4) and (6) it follows that, without changing the coefficient of friction tan ϕ , the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. In a horizontal block the total weight per unit area S zz is jointly supported by the fluid pressure p and the residual solid stress σ zz ; as p is increased, σ zz is correspondingly diminished until, as p approaches the limit S zz , or λ approaches 1, σ zz approaches 0. For the case of gravitational sliding, on a subaerial slope of angle θ where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6) Then, equating the right-hand terms of equations (7) and (8), we obtain which indicates that the angle of slope θ down which the block will slide can be made to approach 0 as λ approaches 1, corresponding to the approach of the fluid pressure p to the total normal stress S .
Hence, given sufficiently high fluid pressures, very much longer fault blocks could be pushed over a nearly horizontal surface, or blocks under their own weight could slide down very much gentler slopes than otherwise would be possible. That the requisite pressures actually do exist is attested by the increasing frequency with which pressures as great as 0.9 S zz are being observed in deep oil wells in various parts of the world.
1,871 citations
30 Jun 2012
1,428 citations
Journal Article•
TL;DR: The standard procedure for determining the permeability of porous media according to APZ Code No. 27 (first edition, October 1935) is based on the fundamental assumption that, as long as the rate of flow is proportional to the pressure gradient as mentioned in this paper.
Abstract: The standard procedure for determining the permeability of porous media according to APZ Code No. 27 (first edition, October 1935) is based on the fundamental assumption that, as long as the rate of flow is proportional to the pressure gradient, the permeability constant of a porous medium is a property of the medium, and is independent of the fluid used in its
1,297 citations
TL;DR: In this article, it was shown that porosity can be determined quite precisely from compressibility measurements, in particular for material in which all porosity occurs as narrow cracks, and that a crack increases compressibility nearly as much as a spherical pore of the same diameter as the length of the crack.
Abstract: Compressibility of porous material is greater than that of solid material of the same composition, and the difference is shown to be equal to rate of change of porosity with pressure, for any pore shape or concentration. Expressions for compressibility are given for two special cases for material of low pore concentration: for spherical pores and for narrow cracks. Comparison of the two cases shows that a crack increases compressibility nearly as much as a spherical pore of the same diameter as the length of the crack, although porosity in these two cases differs enormously. For material in which all porosity occurs as narrow cracks, it is shown that porosity can, in certain cases, be determined quite precisely from compressibility measurements.
1,220 citations
TL;DR: In this article, the Mohr-Coulomb-law was used to study the influence of the pressure of interstitial fluids upon the effective stresses in rocks, and it was shown that the critical value of the shearing stress can be made arbitrarily small by increasing the fluid pressure p.
Abstract: Promise of resolving the paradox of overthrust faulting arises from a consideration of the influence of the pressure of interstitial fluids upon the effective stresses in rocks. If, in a porous rock filled with a fluid at pressure p, the normal and shear components of total stress across any given plane are S and T, then ![Formula][1] ![Formula][2] are the corresponding components of the effective stress in the solid alone.
According to the Mohr-Coulomb law, slippage along any internal plane in the rock should occur when the shear stress along that plane reaches the critical value ![Formula][3] where σ is the normal stress across the plane of slippage, τ the shear strength of the material when σ is zero, and ϕ the angle of internal friction. However, once a fracture is started τ is eliminated, and further slippage results when ![Formula][4]
This can be further simplified by expressing p in terms of S by means of the equation ![Formula][5] which, when introduced into equation (4), gives ![Formula][6]
From equations (4) and (6) it follows that, without changing the coefficient of friction tan ϕ , the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. In a horizontal block the total weight per unit area S zz is jointly supported by the fluid pressure p and the residual solid stress σzz; as p is increased, σzz is correspondingly diminished until, as p approaches the limit S zz, or λ approaches 1, σzz approaches 0.
For the case of gravitational sliding, on a subaerial slope of angle θ ![Formula][7] where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6) ![Formula][8]
Then, equating the right-hand terms of equations (7) and (8), we obtain ![Formula][9] which indicates that the angle of slope θ down which the block will slide can be made to approach 0 as λ approaches 1, corresponding to the approach of the fluid pressure p to the total normal stress S .
Hence, given sufficiently high fluid pressures, very much longer fault blocks could be pushed over a nearly horizontal surface, or blocks under their own weight could slide down very much gentler slopes than otherwise would be possible. That the requisite pressures actually do exist is attested by the increasing frequency with which pressures as great as 0.9 S zz are being observed in deep oil wells in various parts of the world.
[1]: /embed/graphic-1.gif
[2]: /embed/graphic-2.gif
[3]: /embed/graphic-3.gif
[4]: /embed/graphic-4.gif
[5]: /embed/graphic-5.gif
[6]: /embed/graphic-6.gif
[7]: /embed/graphic-7.gif
[8]: /embed/graphic-8.gif
[9]: /embed/graphic-9.gif
908 citations