Youngseuk Keehm

Digital rock physics benchmarks-part II: Computing effective properties

This is the second and final part of our digital rock physics (DRP) benchmarking study. We use segmented 3-D images (one for Fontainebleau, three for Berea, three for a carbonate, and one for a sphere pack) to directly compute the absolute permeability, the electrical resistivity, and elastic moduli. The numerical methods tested include a finite-element solver (elastic moduli and electrical conductivity), two finite-difference solvers (elastic moduli and electrical conductivity), a Fourier-based Lippmann-Schwinger solver (elastic moduli), a lattice-Boltzmann solver (hydraulic permeability), and the explicit-jump method (hydraulic permeability and electrical conductivity). The set-ups for these numerical experiments, including the boundary conditions and the total model size, varied as well. The results thus produced vary from each other. For example, the highest computed permeability value may differ from the lowest one by a factor of 1.5. Nevertheless, all these results fall within the ranges consistent with the relevant laboratory data. Our analysis provides the DRP community with a range of possible outcomes which can be expected depending on the solver and its setup.

Digital Rock Physics - Effect of Fluid Viscosity on Effective Elastic Properties

Abstract This paper is concerned with the effect of pore fluid viscosity on effective elastic properties using digitized rocks. We determine a significant velocity dispersion in wave propagation simulations by the variation of the pore fluid viscosity. Several attenuation regimes are considered which may contribute to this observation. Starting point is a virtual rock physics approach. Numerical simulations of effective transport and effective mechanical properties are applied to statistically representative rock samples. The rock microstructure is imaged by 3D X-ray tomography. Permeability values were estimated through Lattice-Boltzmann flow simulations. The dry rock moduli and the tortuosity are derived by dynamic wave propagation simulations. We apply a displacement-stress rotated staggered finite-difference 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. We give a practical description of how to use this approach and discuss the application limits. Additionally, we show the simulated signature of a theoretically predicted slow S -wave.

Computational rock physics at the pore scale: Transport properties and diagenesis in realistic pore geometries

Transport properties, such as permeability, are important in many geophysical and petroleum applications. However, complex pore geometry often makes modeling and simulation of transport properties in porous media very difficult. Conventional methods are usually based on partial differential equations, but the implementation of these techniques becomes very complicated when the geometry is extremely complex. As a result, simplified geometry is often used; thus the implementation depends heavily on the model. Solving the same problem in a different geometry often means that many parts of the implementation have to be changed. Therefore, a more robust and simple tool, which can handle complex pore space without oversimplification or modification of the model, is needed. The Lattice-Boltzmann method (LBM), based on statistical description of microscopic phenomena, is one alternative. LBM describes fluid motion as collisions of imaginary particles, which are much bigger than the real fluid molecules. These particles have nearly nothing in common with real fluids, but they show almost the same behavior at a macroscopic scale. This simple collision rule is exactly equivalent to the Navier-Stokes equation within certain appropriate limits. Figure 1 shows a synthetic pore geometry (a random dense pack of identical spheres) and the corresponding digital 3-D structure. Uniform spheres in a random dense pack are a reasonable first approximation to real sandstones. Another advantage for this model is that changing porosity is relatively easy, and laboratory measurements can be mimicked using sintered glass beads. Figure 2 shows electric flux (current) calculated by the finite-element method (FEM) and hydraulic flux calculated by LBM. Both are normalized by each maximum value. The hydraulic flux shows much more sensitivity to the grain boundary than the electric current; the hydraulic flux decreases rapidly near the boundary. Also, the high flux regions are different in Figure 2, even though pore geometry …

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

[1] 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.

Permeability-porosity transforms from small sandstone fragments

Numerical simulation of laboratory experiments on rocks, or digital rock physics, is an emerging field that may eventually benefit the petroleum industry. For numerical experimentation to find its way into the mainstream, it must be practical and easily repeatable — i.e., implemented on standard hardware and in real time. This condition reduces the size of a digital sample to just a few grains across. Also, small physical fragments of rock, such as cuttings, may be the only material available to produce digital images. Will the results be meaningful for a larger rock volume? To address this question, we use a number of natural and artificial medium- to high-porosity, well-sorted sandstones. The 3D microtomography volumes are obtained from each physical sample. Then, analogous to making thin sections of drill cuttings, we select a large number of small 2D slices from a 3D scan. As a result, a single physical sample produces hundreds of 2D virtual-drill-cuttings images. Corresponding 3D pore-space realizati...

Computational estimation of compaction band permeability in sandstone

Permeability measurements are difficult to obtain when sample availability is restricted, dimensions limited, or materials poorly consolidated. With subsurface cores of sandstone containing thin, tabular compaction bands (CBs), all three challenges can arise. Computational methods for estimating permeability from thin section provide an alternative. We evaluate a new physics-based technique in which lattice-Boltzmann flow simulations are conducted on stochastic realizations of 3D pore structure generated from thin-section images. Applied to the Aztec sandstone of southeastern Nevada, and exhumed analog for CB-rich sandstone aquifers and reservoirs, the estimates agree well with available data—a few millidarcys (CB) to a few Darcys (matrix)—capturing the range of both matrix and CB permeability from a single, representative thin-section. The technique also gives us a tool for estimating permeability anisotropy due to bed types in sandstone. For a subsurface with Aztec equivalent, this result can be invaluable, since pervasive arrays of compaction bands in sandstone have been shown capable of exerting substantial fluid flow effects at scales relevant to aquifer and reservoir management.

Analyzing Effective Thermal Conductivity of Rocks Using Structural Models

For 21 rock samples consisting of granite, sandstone and the effective thermal conductivity (TC) was measured with the LFA-447 Nanoflash, and mineralogical compositions were also determined from XRD analysis. The structural models were used to examine the effects of quartz content and the size of minerals on TC of rocks. The experimental results showed that TC of rocks was strongly related to quartz content with value of 0.75. Therefore, the proposed regression model can be a useful tool for an approximate estimation of TC only from quartz content. Some samples with similar values of quartz content, however, illustrated great differences in TC, presumably caused by differences in the size of minerals. An analysis from structural models showed that TC of rocks with fine-grained minerals was likely to fall in the region between Series and EMT model, and it moved up to ME and Parallel model as the size of minerals increased. This progressive change of structural models implies that change of TC depending on the size of minerals is possibly related to the scale of experiments; TC was measured from a disk sample with a thickness of 3 mm. Therefore, in case of measurements with a thin sample, TC can be overestimated as compared to the real value in the field scale. The experimental data illustrated that the scale effect was more pronounced for rocks with bigger size of minerals. Thus, it is worthwhile to remember that using a measured TC as a representative value for the real field can be misleading when applied to many geothermal problems.

Quantitative analysis of resolution and smoothing effects of digital pore microstructures on numerical velocity estimation

Numerical estimation of physical properties from digital pore microstructures has drawn great attention and is being used for quantifying interrelation between various physical properties. The pore microstructures are commonly obtained by the X-ray microtomographic technique, which can give fairly accurate pore geometry. However, there is minor distortion due to the limited resolution or smoothing. This distortion can cause errors in estimating physical properties by pore-scale simulation techniques. Among the properties, seismic velocity would have relatively large errors since a small amount of change in grain contacts can cause significant over-estimation. In this paper, we analyzed the errors in seismic velocity by resolution and smoothing of pore geometry using three samples: an unconsolidated sand pack and two medium-porosity sandstones with different degrees of consolidation. As the resolution becomes poor, the calculated velocity increases linearly, while smoothing gives nonlinear trends; higher errors in the early stage of smoothing. As we expected, soft rocks have higher sensitivity, since the grain contacts are small and are sensitive to minor distortion. Within similar ranges, the resolution causes larger errors than smoothing. In addition, smoothing does not cause velocity over-estimation once the resolution becomes poor, while the resolution can create considerable errors in velocity even after significant smoothing. We conclude that the resolution should be considered in the first place when obtaining digital pore microstructures to minimize errors in velocity estimation. We can also suggest that a good care should be taken when applying smoothing filters, if a sample is suspected to be poorly-consolidated or to have high porosity.

Permeability Prediction From Thin Sections Using the Lattice-Boltzmann Flow Simulation

This paper presents a new methodology for predicting permeability from thin sections. The method is based on two key components – constructing 3D porous media from 2D thin sections and a direct 3D flow simulation using the Lattice-Boltzmann (LB) method. From a thin section, statistical parameters such as porosity and autocorrelation function are calculated through image processing. We construct 3D porous media using a geostatistical method of sequential indicator simulation conditioned to the thin section. We then perform flow simulations on those 3D realizations without idealizing or simplifying the complex pore geometry. The LB flow simulation method can successfully handle realistic and very complicated 3D pore geometries. We apply our method for seven thin sections from Daqing oil field. Predicted permeabilities show excellent agreement with lab measurements. We then compare our method to another one, which also estimates permeability based on statistical parameters from thin sections, but without flow simulation. Our method gives better results and is less sensitive to statistical noise from image processing of thin sections. More importantly, our method does not require any empirical parameters.

Evolution of permeability and microstructure of tight carbonates due to numerical simulation of calcite dissolution: Permeability Trend Due to Dissolution

The current study concerns fundamental controls on fluid flow in tight carbonate rocks undergoing CO2-injection. Tight carbonates exposed to weak carbonic acid exhibit order of magnitude changes in permeability while maintaining a nearly constant porosity with respect to the porosity of the unreacted sample. This study aims to determine – if not porosity – what are the microstructural changes that control permeability evolution in these rocks? Given the pore-scale nature of chemical reactions, we took a digital rock physics approach. Tight carbonate mudstone was imaged using X-ray micro-computed tomography. We simulated calcite dissolution using a phenomenological numerical model that stands from experimental and microstructural observations under transport-limited reaction conditions. Fluid flow was simulated using the lattice-Boltzmann method, and the pore wall was adaptively eroded at a rate determined by the local surface area and velocity magnitude, which we use in place of solvent flux. We identified preexisting, high-conductivity fluid pathways imprinted in the initial microstructure. Though these pathways comprise a subset of the total connected porosity, they accommodated 80 to 99.4% of the volumetric flux through the digital sample and localized dissolution. Porosity-permeability evolution exhibited two stages: selective widening of narrow pore throats that comprised preferential pathways and development and widening of channels. We quantitatively monitored attributes of the pore geometry, namely porosity, specific surface area, tortuosity, and average hydraulic diameter, which we qualitatively linked to permeability. This study gives a pore-scale perspective on the microstructural origins of laboratory permeability-porosity trends of tight carbonates undergoing transport-limited reaction with CO2-rich fluid.