H21L-01 INVITED
Relationship between Permeability, Elastic Moduli and Pore Structure in Porous Geological Media
The petrophysical properties of porous media, such as the permeability and the elastic moduli, are essentially controlled by the geometry of the pore space. Enormous amounts of research have been devoted over the past several decades to understanding and quantifying the relationship between pore structure and petrophysical properties (for example, see Zimmerman, Compressibility of Sandstones, 1991; Dullien, Porous Media: Fluid Transport and Pore Structure, 1992; Adler, Porous Media: Geometry and Transports, 1992; Mavko et al., The Rock Physics Handbook, 1998; etc.) Although much is now known in terms of general trends, bounds, etc., the state of knowledge is still such that existing theories can rarely provide accurate numerical estimates of the permeability or bulk modulus of a given rock. To a great extent the problem lies in the fact that micromechanics-based rock physics theories typically utilize idealized pore shapes such as circular, elliptical or triangular cylinders, for which analytical solutions can readily be obtained, whereas actual pores are irregular. In this talk I will describe recent work that utilizes actual pore geometries, as observed in electron micrographs, along with some scaling laws based on the pore areas and perimeters, and simple effective medium approximations, to predict the permeability and elastic moduli of porous sedimentary rocks. The hydraulic conductivity of the individual pores are estimated from the hydraulic radius approximation, which correlates the conductance with area3/perimeter2, with the proportionality constant chosen so as to make the relation exact for a circle. Kirkpatrick's effective medium approximation for networks of conductors is used to upscale the individual pore-scale hydraulic conductivities to yield the core-scale permeability. When applied to several data sets of sandstones and carbonates, with permeabilities ranging from 0.5-1500 milliDarcies, the methodology typically predicts the permeability to within a factor of two. The compressibilities of the individual pores are estimated from a scaling law based on perimeter2/area, with the proportionality constant again found from the known case of a circular tube. The individual pore compressibilities are then averaged, weighted by area, and the differential effective medium approximation is used to convert the mean pore compressibility into the macroscopic bulk modulus. This methodology has been applied to Berea and Fontainebleau sandstone, and typically predicts the bulk modulus to within about 10%.
H21L-02
Air entry-based characteristic length improves permeability estimates for compacted earth materials
The permeability, k, of porous media is required for quantifying flow and transport processes in hydrology, civil, agriculture and petroleum engineering and is often estimated from medium porosity and additional constraints. Changes in porosity of earth materials due to compaction by anthropogenic activities or overburden result in a reduction in mean pore sizes and a decrease of k. Permeability is often expressed as proportional to a characteristic length squared and inversely proportional to a porosity factor, pore shape, and tortuosity of the material. Various characteristic lengths for the porous medium were proposed such as the hydraulic radius of Kozeny-Carman, or limiting pore size derived from critical path analysis. We introduce a characteristic length related to the air entry value compatible with Aissen formula that accommodates complex pore shapes. The proposed model includes a geometrical (tortuosity) factor and links relative changes in porosity to concurrent changes in k. The model was evaluated for three different groups of natural porous media: sands, sandstones with different cementing agents, and unconsolidated soils. For clay-free sands and unconsolidated soils, the model provides reasonable predictions for the entire range of porosities found in laboratory or field experiments. However, for sandstones with cementing agents, the model is valid up to a critical porosity where pore structure seems to collapse and k reduces drastically. The geometrical factor for soils was influenced by silt-to-clay ratio, while for granular media, it was correlated with mean grain diameter. The model offers improvement in predicting k and provides a means for incorporating critical pore size (air entry) information in addition to porosity.
H21L-03
Evolution of unsaturated hydraulic conductivity of aggregated soils during compression
Prediction of water flow and transport processes in soils susceptible to structural alteration such as compaction of tilled agricultural lands, or newly constructed landfills rely on accurate description of changes in soil unsaturated hydraulic conductivity. Recent studies have documented the critical impact of aggregate contact characteristics on water flow rates and pathways in unsaturated aggregated soils. We developed an analytical model for aggregate contact size evolution as a basis for quantifying effects of compression on unsaturated hydraulic conductivity of aggregated soil. Relating confined one-dimensional sample strain with aggregate deformation facilitates prediction of the increase in inter-aggregate contact area and concurrent decrease in macro-pore size with degree of sample compression. The hydrologic component of the model predicts unsaturated hydraulic conductivity of a pack of idealized aggregates (spheres) based on contact size and saturation conditions under prescribed sample deformation. Calculated contact areas and hydraulic conductivity for pairs of aggregates agreed surprisingly well with measured values, determined from compaction experiments employing Neutron- as well as X-ray-radiography and image analysis.
H21L-04 INVITED
Pressure Transients in a Fluid-Filled Spherical Cavity in an Extended Porous Medium
This paper examines the problem of the pressurization of a fluid-filled cavity in a fluid-saturated porous medium of infinite extent. The problem is of interest in connection with experimental configurations that can be used to determine the permeability characteristics of low permeability materials where both the compressibility of the porous skeleton and that of the fluid are important. The paper presents theoretical results that can be used to estimate not only the permeability of the medium but also the bulk skeletal compressibility and porosity of the porous solid.
H21L-05
Incorporating Undrained Pore Fuid Pressurization Into Analyses of Off-Fault Plasticity During Dynamic Rupture
When considering dynamic fault rupture in fluid-saturated elastic-plastic materials, it is sensible to assume locally undrained behavior everywhere except in small diffusive boundary layers along the rupture surface. To evaluate undrained pore pressure changes, we consider here not just the linear poroelastic effect expressed in terms of the Skempton coefficient B, like in our previous work [Viesca et al., AGU Fall 2006], but also include plastic dilatancy, which, when positive, induces a fluid suction. We work in the context of Mohr-Coulomb-like plasticity, but with a Drucker-Prager type model. Plastic parts of strain increments are controlled by the Terzaghi effective stress, elastic parts by the Biot stress combination. Following earlier work of Rudnicki, the incremental elastic-plastic constitutive relation for undrained deformation has precisely the same form as for drained deformation, so long as we change the drained constitutive parameters into new undrained ones under transformation rules that we present. Spontaneous slip-weakening fault rupture is analyzed using the dynamic finite element procedures with ABAQUS Explicit, and undrained elastic-plastic properties. Results are shown for plastic zones and effects on rupture propagation, and how they are influenced by such parameters as B and ratio β of dilatant to shear plastic strains, for a range of principal orientations and magnitudes (relative to yield) of the pre-stress state. The undrained approximation must fail in diffusive boundary layers along the slip surface [Rudnicki and Rice, JGR 2006; Dunham and Rice, AGU Fall 2006] because the predicted pore pressures will be discontinuous at the fault. We show how to extend the Rudnicki and Rice calculation of the actual pore pressure on the fault in terms of the undrained predictions to the two sides. However, because of difficulties thus far in representing this within the ABAQUS program, all results obtained as of the time of writing neglect effects of such pore pressure changes on the fault slip-weakening strength during rupture.
H21L-06
Errors in determination of soil water content using time-domain reflectometry caused by soil compaction around wave guides
Application of time-domain reflectometry (TDR) in soil hydrology often involves the conversion of TDR-measured dielectric permittivity to water content using universal calibration equations (empirical or physically based). Deviations of soil-specific calibrations from the universal calibrations have been noted and are usually attributed with peculiar composition of soil constituents, such as high content of clay and/or organic matter. Although it is recognized that soil disturbance by TDR wave guides may have impact on measurement errors, to our knowledge, there has not been any quantification of this effect. In this presentation, we introduce a combined mechanical-hydrological method that estimates the measurement error. Our analysis indicates that soil compaction pattern depends on the mechanical properties of the soil at the time of installation. The relative error in water content measurement depends on the compaction pattern as well as the water content and water retention characteristics of the soil. Illustrative calculations based on measured soil mechanical and hydrologic properties from the literature show that the measurement errors of using a standard three-prong TDR wave guide could be up to 10 percent. We also show that the error scales linearly with the ratio of rod radius to the inter- radius spacing.