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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.

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.

Accurate estimation of physical properties of prospective formations is essential for the successful geological CO2 storage. Important physical properties such as porosity, permeability and electrical resistivity are typically obtained through laboratory measurements on core plugs or well-log data. When prospective formations for geological CO2 storage are poorly-consolidated, core recovery and well logging are very difficult and the estimation of physical properties becomes the main obstacle to evaluating the prospective formation. In this paper, we present a new approach to estimating physical properties of poorly-consolidated formation, which consists of acquiring undisturbed samples with epoxy impregnation, obtaining pore microstructures by X-ray CT, and numerically estimating physical properties using pore-scale simulations. To verify the reliability and applicability of the proposed method, we applied the method to a poorly-consolidated sample from a prospective formation in Korea. We also chose two more samples for comparison, one unconsolidated and one consolidated whose properties are known. Results showed that the computational estimation agrees well with the laboratory measurements for two comparative samples, and that for the test sample with unknown properties also lies in the expected ranges. This implies that the estimated properties of poorly-consolidated formation are reliable enough to use for the initial characterization of CO2 storage formations. We also performed two-phase flow simulations, which mimics the CO2 injection at the pore scale. From the simulations, we can roughly estimate the change in transport properties as a function of CO2 saturation. In conclusion, the proposed method can be a good tool to estimate transport properties for poorly-consolidated formations for geological CO2 storage.

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.

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.

The performance of the ATES (aquifer thermal energy storage) system primarily depends on the thermal interference between warm and cold thermal energy stored in an aquifer. Additionally the thermal interference is mainly affected by the borehole distance, the hydraulic conductivity, and the pumping/injection rate. Thermo-hydraulic modeling was performed to identify the thermal interference by three parameters and to estimate the system performance change by the thermal interference. Modeling results indicate that the thermal interference grows as the borehole distance decreases, as the hydraulic conductivity increases, and as the pumping/injection rate increases. The system performance analysis indicates that if η (the ratio of the length of the thermal front to the distance between two boreholes) is lower than unity, the system performance is not significantly affected, but if η is equal to unity, the system performance falls up to ∼22%. Long term modeling for a factory in Anseong was conducted to test the applicability of the ATES system. When the pumping/injection rate is 100 m3/day, system performances during the summer and winter after 3 years of operation are estimated to be ∼125 kW and ∼110 kW, respectively. Therefore, 100 m3/day of the pumping/injection rate satisfies the energy requirements (∼70 kW) for the factory.

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.

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 realizations are generated statistically from these 2D images; fluid flow is simulated in three dimensions, and the absolute permeability is computed. The results show that small fragments of medium– to high-porosity sandstones that are statistically subrepresentative of a larger sample will not yield the exact porosity and permeability of the sample. However, a significant number of small fragments will yield a site-specific permeability-porosity trend that can then be used to estimate the absolute permeability from independent porosity data obtained in the well or inferred from seismic techniques.

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 …

Summary We have presented results on formation modeling of gas hydrates (GH) using pore-scale simulation techniques and the comparison to similar laboratory experiments by KIGAM last year. The preliminary results showed that the pore-scale modeling technique can be effective on GH formation and corresponding property changes, and that GH seemed to be formed at the pore throats. In the previous study, we used 100% water-saturated sample to determine the location of GH nucleation and growth; however, there were two fluids – water and methane in the lab experiment. Thus we applied two-phase flow simulation using the lattice-Boltzmann (LB) method on our pore-scale modeling to mimic lab experiment more accurately. In addition, we use a mixed sand sample with two different grain sizes to investigate the effect of sorting on GH formation and property changes. We found that the new modeling method with the two-phase flow simulation rigorously replicated the lab experiment, and that the physical properties of GHbearing sample (permeability, electrical conductivity and velocity changes) matches the lab data especially at hydrate saturation < 20%. There were discrepancy at higher GH saturation between calculated properties by our method and lab data, and we are investigating the reason by redoing numerical modeling and lab experiments. The effect of sorting on GH formation at the pore scale does not seem to be great. We found that the property changes of mixed sample follows those of the uniform sample with the smaller grain size. In conclusion, the numerical modeling of GH formation using pore-scale simulation technique can accurately mimic the GH formation and dissociation and corresponding physical property changes. We think that this method can help to understand the quantitative relation between GH saturation and physical properties of GHbearing sediments.

In this work, we present elastic property computations on a rock microstructure obtained by using granular dynamics simulation. The granular dynamics simulation in this case models gravity sedimentation and compaction of spherical quartz grains. We focus on studying the interrelationship of elastic and fabric properties in the regime just above critical porosity, which is difficult to model in a laboratory experiment. We find that the elastic properties near the critical porosity depend more on the grain rearrangements and less on the pressure. We also investigate the relation between fabric anisotropy and coordination number. The final fabric tensor shows transverse isotropy symmetry for the simulated pack.

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.

[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.

P161 Z-99 FLUID EFFECTS ON WAVE PROPAGATION: A VISCOELASTIC MODELING APPROACH Summary 1 ERIK H. SAENGER 1 YOUNGSEUK KEEHM 2 OLIVER S. KRUGER 1 and SERGE A. SHAPIRO 1 1 Freie Universitat Berlin Fachrichtung Geophysik Malteserstr. 74-100 12249 Berlin Germany 2 Stanford University Department of Geophysics 397 Panama Mall Stanford CA 94305-2215 USA 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. Viscosity is implemented by using a generalized Maxwell body. This approach allows us to

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. Viscosity of the fluid is implemented by using a generalized Maxwell body. With this approach we consider the predictions of effective elastic properties (i.e. velocities) by the Biot velocity relations of different digital rock samples. To distinguish between the low and the high frequency range we also determine the effective permeabilities by a flow simulation. Our numerical results indicate that the viscous Biot-coupling is visible in the synthetics. Moreover, the important influence of other solidfluid interactions (e.g. Squirt flow) is also discussed.

[1] We present results and methodology for predicting permeability from thin sections. The method consists of two key components–reconstruction of 3D porous media from 2D thin sections, and 3D flow simulation using the Lattice-Boltzmann (LB) technique. We construct 3D porous media using sequential indicator simulation (SIS), a geostatistical method, with conditional data and input statistical parameters from thin sections. Permeability is then estimated through flow simulation on the reconstructed porous media. The LB flow simulation successfully handles very complex reconstructed 3D pore geometries. Computed permeabilities from seven thin section samples show good agreement with laboratory measurements over a wide range of permeability. We compare our method to one that uses only thin sections without 3D reconstruction. The comparison shows that our method gives better prediction of permeability, and is less sensitive to statistical errors from discrepancy between thin sections and core samples.

Summary We present results on two-phase flow simulation by Lattice-Boltzmann method. In this paper we focus on the steady state simulation that has a fixed saturation of nonwetting and wetting fluids. We used three rock models; Finney’s random dense pack of spheres and two samples of X-ray tomographic Fontainebleau sandstone. These were binary digital models describing the complex pore space. We investigated three aspects of two-phase flow; effect of initial distribution of two fluids on relative permeability, role of wetting fluid at low wetting fluid saturation, and relative permeability under different pressure gradient and surface tension. We found very small differences in relative permeability with various initial distributions of two fluids. Although the final distributions were a little different due to different initial distributions, the relative permeability was almost identical. At high water saturation, even though the nonwetting phase is not connected, they form blobs and move with the wetting phase. Thus the relative permeability of non-wetting phase is still considerable. In the next step, we investigated the role of wetting fluid at low wetting fluid saturation. Many studies and laboratory measurements have shown that small amount of water does not affect relative permeability of non-wetting phase. We observed same results from our simulation. In our digital rock samples, the permeability of non-wetting phase changed very little at a range of less than 10% wetting saturation. However, if we replace the small amount of water trapped in small pores by solid grain, the relative permeability of non-wetting phase decreases dramatically even for very small reduction of porosity. The small amount of wetting phase effectively reduces the viscous effect between grain boundary and nonwetting phase. Lastly, we explored two different regimes of pressure gradient (∆P) and surface tension (σ); when ∆P ≈ σ and when ∆P >σ . We observed the relative permeability of non-wetting phase increases with pressure gradient, while that of wetting phase stays almost the same. The amount of the relative permeability increase strongly depends on the details of pore geometry. In conjunction with lab calibration, this two-phase flow simulation provides a powerful computational tool for efficient estimation of multiphase fluid-flow with different physical parameters, and can complement physical lab measurement.

This paper is concerned with numerical considerations of effective transport and effective mechanical properties of rocks. We derive these properties directly from rock microstructure using 3D tomographic images. Permeability values were estimated through