Digital Rock Samples Research Articles

Estimates of olivine–basaltic melt electrical conductivity using a digital rock physics approach

Estimates of melt content beneath fast-spreading mid-ocean ridges inferred from magnetotelluric tomography (MT) vary between 0.01 and 0.10. Much of this variation may stem from a lack of understanding of how the grain-scale melt geometry influences the bulk electrical conductivity of a partially molten rock, especially at low melt fraction. We compute bulk electrical conductivity of olivine–basalt aggregates over 0.02 to 0.20 melt fraction by simulating electric current in experimentally obtained partially molten geometries. Olivine–basalt aggregates were synthesized by hot-pressing San Carlos olivine and high-alumina basalt in a solid–medium piston-cylinder apparatus. Run conditions for experimental charges were 1.5 GPa and 1350 °C. Upon completion, charges were quenched and cored. Samples were imaged using synchrotron X-ray micro-computed tomography (μ-CT). The resulting high-resolution, 3-dimensional (3-D) image of the melt distribution constitutes a digital rock sample, on which numerical simulations were conducted to estimate material properties. To compute bulk electrical conductivity, we simulated a direct current measurement by solving the current continuity equation, assuming electrical conductivities for olivine and melt. An application of Ohm's Law yields the bulk electrical conductivity of the partially molten region. The bulk electrical conductivity values for nominally dry materials follow a power-law relationship σbulk=Cσmeltϕm with fit parameters m=1.3±0.3 and C=0.66±0.06. Laminar fluid flow simulations were conducted on the same partially molten geometries to obtain permeability, and the respective pathways for electrical current and fluid flow over the same melt geometry were compared. Our results indicate that the pathways for flow fluid are different from those for electric current. Electrical tortuosity is lower than fluid flow tortuosity. The simulation results are compared to existing experimental data, and the potential influence of volatiles and melt films on electrical conductivity of partially molten rocks is discussed.

Prediction of Transport Properties of Deformed Natural Fracture Through Micro-scale Hydro-mechanical Modeling

To study the effect of fracture properties on mechanical and fluid flow behavior of fractured rocks, we developed a micro-scale hydro-mechanical model. Modeling grains and studying their interactions are used to predict the mechanical response of digital rock samples. Fluid flow behavior is obtained through a realistic network model of the pore space in the compacted assembly. As a result of grain deformation and micro-crack development in a rock sample, the geometric description of the complex pore structure is regenerated to predict fluid flow performance of the rock sample using a dynamic pore network model. In our numerical model, the first step consisted of constructing a Berea sandstone sample. Then, fractures with different properties such as orientation, dilation angle, roughness, and cementing materials are introduced. Mechanical properties of the fractured sample are measured as functions of deformation by performing numerical triaxial tests. Applying a dynamic pore network provides a tool to investigate the important role of fracture parameters on transport behavior. Our results show that shearing along the fracture dilates the sample, and increases its permeability, which is a complex function of fracture mechanical properties.

A new non-Archie model for pore structure: numerical experiments using digital rock models

SUMMARY Tortuosity is a key parameter for investigating the pore structure of sedimentary rock. The conventional model for calculating the tortuosity is derived from Archie’s law which is only valid for one conductive phase contained in a porous rock. However, there have been increasingly cases to show the non-Archie phenomenon in instances where the rock matrix has extra conductive phases such as surface conductivity caused by the electrical double layer. Therefore, such model may be inapplicable in these cases and in calculations involving partial melting. We investigated the relation between formation factor and porosity (F–φ )o ver aw ide range of porosities by the lattice-gas automata method (LGA) with the electrical double layer. The digital rock samples were constructed by packing up solid grains with different shapes and size distribution, as previously measured in the laboratory on real rock specimens. Our purpose was to identify the origin of non-Archie behaviour of the F–φ relation sometimes observed. The simulations show that Archie’s law may only be an approximation of the F–φ relation in a high porosity range. Based on our LGA simulations and additional laboratory experimental data, we developed new equations for non-Archie F–φ relation and tortuosity potentially useful for improving the evaluation of pore structure.

Digital core approach to the effects of clay on the electrical properties of saturated rocks using lattice gas automation

Clay has a significant influence on the relationship between resistivity index I and water saturation Sw (i.e, I-Sw relationship) of reservoir rocks because it complicates the current paths of these rocks. It is difficult to reveal the physical mechanisms of these clay effects on the conductivities of various rocks by physical laboratory measurements because the pore structure, micro distribution and content of clay inside a rock can not be observed and controlled during the experiments. We present a digital rock approach to study these clay effects on the electrical transport properties of reservoir rocks at pore scale using lattice gas automation (LGA) method. The digital rock samples are constructed with the information of grain size distribution from SEM images of reservoir rocks. The LGA is then applied on these digital rocks fully saturated with fluids to simulate the electrical transport properties for revealing the effects of volume and distribution patterns of clay on the non-Archie behaviors of the I-Sw relationship. The very good agreement between the simulated results and the laboratory measurements clearly demonstrates the validity of the LGA in numerical research of rock physics. Based on these studies, a new model has been developed for quantitatively describing the relationship between the saturation exponent and the volume of clay (Vsh). This development may improve the evaluation for the fluid saturations in reservoir rocks.

2-D numerical simulation of digital rock experiments with lattice gas automation for electrical properties of reservoir formation

SUMMARY The lattice gas automation (LGA) simulations for electrical transport properties have been performed on digital rock samples virtually saturated with oil and water to investigate the relationship between resistivity index and water (oil) saturation (I–Sw) of reservoir rocks at micropore scale. The digital rocks were constructed by the pileup of matrix grains with a radius distribution obtained by laboratory measurements on reservoir rock samples. The LGA was then applied to simulate the flow of electrical current through the pores of these virtually saturated digital rocks to reveal the non-Archie relation of I–Sw. The results from LGA simulation indicate that the I–Sw relation is generally a non-linear function changing with the decrease of water saturation and porosity on a log–log scale. Archie’s equation is an approximation in high water saturation range. Based on this study, we developed a new equation for non-Archie relation of I–Sw to improve the calculation of pore fluid saturation. Thecalculatedresultswiththisnewequationhaveshownbetterfittolaboratorymeasurements.

Finite-difference modeling of wave propagation on microscale: A snapshot of the work in progress

Digital rock methodology combines modern microscopic imaging with advanced numerical simulations of the physical properties of rocks. Modeling of elastic-wave propagation directly from rock microstructure is integral to this technology. We survey recent development of the rotated staggered grid (RSG) finite-difference (FD) method for pore-scale simulation of elastic wave propagation in digital rock samples, including the dynamic elastic properties of rocks saturated with a viscous fluid. Examination of the accuracy of this algorithm on models with known analytical solutions provide an additional accuracy condition for numerical modeling on the microscale. We use both the elastic and viscoelastic versions of the RSG algorithm to study gas hydrates and to simulate propagation of Biot’s slow wave. We applyRSG method ology to examine the effect of gas hydrate distributions in the pore space of a rock. We compare resulting P-wave velocities with experimentally measured data, as a basis for building an effective-medium model for rocks containing gas hydrates. We then perform numerical simulations of Biot’s slow wave in a realistic 3D digital rock model, fully saturated with a nonviscous fluid (corresponding to the high-frequency limit of poroelasticity), and placed inside a bulk fluid. The model clearly demonstrates Biot’s slow curve when the interface is open between the slab and bulk fluid. We demonstrate slow wave propagation in a porous medium saturated with a viscous fluid by analyzing an idealized 2D porous medium represented alternating solid and viscous fluid layers. Comparison of simulation results with the exact solution for this layered system shows good agreement over a broad frequency range.

Electrical Transport Properties of Fluid-Saturated Porous Rocks by 2D Lattice Gas Automata

Summary We have studied the electrical transport properties of porous media and the physical meaning of Archie's parameters with 2D lattice gas automata (LGA). On the basis of our simulations, we have developed a set of new equations to calculate fluid saturation from electrical measurements. The calculations from the new equations show very good agreement with laboratory measurements and published data on sandstone samples. There are limitations for this study in applying mesoscale modeling to the resistivity-index/ water-saturation (I/Sw) relationship for porous rocks because only 2D models of sandstone rock were simulated. Some important factors like wettability were not modeled. However, current flow simulations on the 3D digital rock samples of various types reconstructed from thin sections and high-resolution CT scans of real rocks have been ongoing in our laboratory as the next step to address these issues.

Seismic effects of viscous Biot‐coupling: Finite difference simulations on micro‐scale

This paper is concerned with numerical considerations of viscous fluid effects on wave propagation in porous media. We apply a displacement‐stress rotated staggered finite‐difference (FD) grid technique to solve the elastodynamic wave equation. An accurate approximation of a Newtonian fluid is implemented in this technique by using a generalized Maxwell body. With this approach we consider the velocity predictions of the Biot theory for elastic waves in different digital rock samples. To distinguish between the low and the high frequency range we estimate the effective permeabilities by a flow simulation. Our numerical results indicate that the viscous Biot‐coupling is visible in the numerical experiments. Moreover, the influences of other solid‐fluid interactions (e.g., Squirt flow) are also discussed.