Digital Rock Models Research Articles

Study of the Nankai seismogenic fault using dynamic wave propagation modelling of digital rock from the Nobeoka Fault

To understand the characteristics of the Nankai seismogenic fault in the plate convergent margin, we calculated the P- and S-wave velocities (VP and VS) of digital rock models constructed from core samples of an ancient plate boundary fault at Nobeoka, Kyushu Island, Japan. We first constructed 3D digital rock models from microcomputed tomography images and identified their heterogeneous textures such as cracks and veins. We replaced the cracks and veins with air, water, quartz, calcite and other materials with different bulk and shear moduli. Using the Rotated Staggered Grid Finite-Difference Method, we performed dynamic wave propagation simulations and quantified the effective VP, VS and the ratio of VP to VS (VP/VS) of the 3D digital rock models with different crack-filling minerals. Our results demonstrate that the water-saturated cracks considerably decreased the seismic velocity and increased VP/VS. The VP/VS of the quartz-filled rock model was lower than that in the water-saturated case and in the calcite-filled rock model. By comparing the elastic properties derived from the digital rock models with the seismic velocities (e.g. VP and VP/VS) around the seismogenic fault estimated from field seismic data, we characterised the evolution process of the deep seismogenic fault. The high VP/VS and low VP observed at the transition from aseismic to coseismic regimes in the Nankai Trough can be explained by open cracks (or fractures), while the low VP/VS and high VP observed at the deeper coseismic fault zone suggests quartz-filled cracks. The quartz-rich fault zone characterised as low VP/VS and high VP in this study could partially relate to the coseismic behaviour as suggested by previous studies, because quartz exhibits slip-weakening behaviour (i.e. unstable coseismic slip).

Studies of electrical properties of low-resistivity sandstones based on digital rock technology

Electrical properties are important parameters to quantitatively calculate water saturation in oil and gas reservoirs by well logging interpretation. It is usual that oil layers show high resistivity responses, while water layers show low-resistivity responses. However, there are low-resistivity oil zones that exist in many oilfields around the world, leading to difficulties for reservoir evaluation. In our research, we used digital rock technology to study different internal and external factors to account for low rock resistivity responses in oil layers. We first constructed three-dimensional digital rock models with five components based on micro-computed tomography technology and x-ray diffraction experimental results, and then oil and water distributions in pores were determined by the pore morphology method. When the resistivity of each component was assigned, rock resistivities were calculated by using the finite element method. We collected 20 sandstone samples to prove the effectiveness of our numerical simulation methods. Based on the control variate method, we studied the effects of different factors on the resistivity indexes and rock resistivities. After sensitivity analyses, we found the main factors which caused low rock resistivities in oil layers. For unfractured rocks, influential factors arranged in descending order of importance were porosity, clay content, temperature, water salinity, heavy mineral, clay type and wettability. In addition, we found that the resistivity index could not provide enough information to identify a low-resistivity oil zone by using laboratory rock–electric experimental results. These results can not only expand our understandings of the electrical properties of low-resistivity rocks from oil layers, but also help identify low-resistivity oil zones better.

Three-dimensional printing for geoscience: Fundamental research, education, and applications for the petroleum industry

Three-dimensional (3-D) printing provides a fast, cost-effective way to produce and replicate complicated designs with minimal flaws and little material waste. Early use of 3-D printing for engineering applications in the petroleum industry has stimulated further adoption by geoscience researchers and educators. Recent progress in geoscience is signified by capabilities that translate digital rock models into 3-D printed rock proxies. With a variety of material and geometric scaling options, 3-D printing of near-identical rock proxies provides a method to conduct repeatable laboratory experiments without destroying natural rock samples. Rock proxy experiments can potentially validate numerical simulations and complement existing laboratory measurements on changes of rock properties over geologic time scales. A review of published research from academic, government, and industry contributions indicates a growing community of rock proxy experimentalists. Three-dimensional printing techniques are being applied to fundamental research in the areas of multiphase fluid flow and reactive transport, geomechanics, physical properties, geomorphology, and paleontology. Further opportunities for geoscience research are discussed. Applications in education include teaching models of terrains, fossils, and crystals. The integration of digital data sets with 3-D printed geomorphologies supports communication for both societal and technical objectives. Broad benefits that could be realized from centralized 3-D printing facilities are also discussed.

Detector-unit-dependent calibration for polychromatic projections of rock core CT.

Computed tomography (CT) plays an important role in digital rock analysis, which is a new prospective technique for oil and gas industry. But the artifacts in CT images will influence the accuracy of the digital rock model. In this study, we proposed and demonstrated a novel method to restore detector-unit-dependent functions for polychromatic projection calibration by scanning some simple shaped reference samples. As long as the attenuation coefficients of the reference samples are similar to the scanned object, the size or position is not needed to be exactly known. Both simulated and real data were used to verify the proposed method. The results showed that the new method reduced both beam hardening artifacts and ring artifacts effectively. Moreover, the method appeared to be quite robust.

Digital rock models of Precambrian and Paleozoic tight formations from Poland

Properties of selected Precambrian and Paleozoic sedimentary clastic rocks were analysed with respect to their reservoir potential. Multidimensional analysis of laboratory results and borehole logging data was used to construct digital models of pre-Mesozoic, deeply buried formations, present as tight, low-porosity and low-permeability rocks. This modern statistical and deterministic approach as applied to laboratory and borehole logging results worked to integrate data at different scales. The results obtained are useful not only in further scientific research but also found a use in industrial application. As a first step, statistical methods, including clustering and separation of homogeneous groups, enabled digital rock model creation on the basis of the results of such laboratory measurements as pycnometry, mercury porosimetry, nuclear magnetic resonance spectroscopy or computed X-ray tomography. Next, the models constructed were applied in borehole logging interpretation to find intervals with similar petrophysical properties within the group and different properties between the groups. This approach allowed implementation of upscaling procedures of laboratory experiments at micro- and nano-scale to borehole logging scale. High correlations were established between the log petrophysical parameters within the digital models. This approach can be used to divide the succession cored into intervals with different petrophysical parameters.

Modeling Oil Recovery for Mixed Macro- and Micro-Pore Carbonate Grainstones

In general, modeling oil-recovery is a challenging problem involving detailed fluid flow calculations with required structural details that challenge current experimental resolution. Recent laboratory experiments on mixed micro- and macro-pore suggest that there is a systematic relationship between remaining oil saturation (ROS) and the fraction of micro-pores. Working with experimental measurements of the pores obtained from X-ray tomography and mercury intrusion capillary pressure porosimetry, we define a digital rock model exemplifying the key structural elements of these carbonate grainstones. We then test two fluid-flow models: invasion percolation model and effective medium model. Although invasion percolation identifies the important impact of macro-pore percolation on permeability, it does not describe the dependence of ROS on micro-pore percentage. We thus modified the effective medium model by introducing a single-parameter descriptor, reff. Oil from pores r ≥ reff is fully removed, while for the remaining pores with r < reff, their contribution is scaled by (r/reff)2. Applying this straightforward physics to pore size distributions for the mixed-pore grainstones reproduces the experimental ROS dependence.

Technology Focus: Formation Evaluation (August 2017)

Technology Focus Not too long ago, horizontal drilling revolutionized the petroleum industry. Emerging logging-while-drilling and geosteering technologies helped bring about multilateral, maximum-contact, and smart-completion wells, allowing reservoirs to be developed and produced much more efficiently and economically. This increased recovery, thus boosting reserves. In the process, formation evaluation plays a critical role in determining whether a producer or an injector is successful. More recently, efficient mass horizontal drilling and optimized multistage massive fracturing have turned traditionally nonreservoir source rock into sweet spots of energy strategy on a global scale. Production from unconventional reservoirs in the last decade has dramatically changed the petroleum industry, and this movement continues to evolve. Developing unconventional resources demands unconventional thinking, mainly because of the many challenges involved in evaluating tight source rocks. The two fundamental petrophysical properties, pore structure and wettability, are completely different between conventional reservoirs and unconventional source rocks. What may be next on the horizon? It is estimated that methane hydrates contain much more gas than shale plays, and, understandably, many countries are keen to explore this vast potential. As per recent news releases, China Geological Survey geoscientists and China National Petroleum Corporation engineers may have made a great technology breakthrough by being able to test significant hydrate-gas production in the South China Sea. If this is sustainable, exploring hydrate gas may be the next game changer for the energy industry. Evaluating hydrate gas formations would not be easy, however, and producing them safely, economically, and in an environmentally friendly way would be very challenging. But, I have high hopes that future technologies will be able to resolve these challenges to produce hydrate gas conventionally so it can be used to improve living standards. Recommended additional reading at OnePetro: www.onepetro.org. SPE 182448 The Petrophysics Role of Low-Resistivity Pay Zone of Talang Akar Formation, South Sumatera Basin, Indonesia by Z. Holis, SKK Migas, et al. SPE 183883 Using Digital Rock Modeling To Estimate Permeability and Capillary Pressure From NMR and Geochemical Logs by Hao Zhang, Baker Hughes, et al. SPE 183800 An Innovative Approach for Integrated Characterization and Modeling of a Complex Carbonate Reservoir by F. Ben Amor, Schlumberger, et al.

Industrial applications of digital rock technology

This article provides an overview of the current state of digital rock technology, with emphasis on industrial applications. We show how imaging and image analysis can be applied for rock typing and modeling of end-point saturations. Different methods to obtain a digital model of the pore space from pore scale images are presented, and the strengths and weaknesses of the different methods are discussed. We also show how imaging bridges the different subjects of geology, petrophysics and reservoir simulations, by being a common denominator for results in all these subjects. Network modeling is compared to direct simulations on grid models, and their respective strengths are discussed. Finally we present an example of digital rock technology applied to a sandstone oil reservoir. Results from digital rock modeling are compared to results from traditional laboratory experiments. We highlight the mutual benefits from conducting both traditional experiments and digital rock modeling.

Hydrologic and Elastic Properties of CO2 Injected Rock at Various Reservoir Conditions: Insights into Quantitative Monitoring of Injected CO2

We calculated CO2 displacements in 3D natural sandstone (digital rock model) under various reservoir conditions using two-phase lattice Boltzmann (LB) simulations, and characterized the influence of reservoir conditions upon CO2 - water flow. The results of LB simulations under >50 conditions were used to classify the resulting two-phase flow behaviors into typical fluid displacement patterns on the diagram of capillary number (Ca) and viscosity ratio of the CO2 and water (M). In addition, the saturation of CO2 (nonwetting phase) was calculated and mapped on the Ca–M diagram. These results demonstrated that CO2 saturation is controlled by Ca and M, and the optimum CO2 saturation scales with Ca and M. When we applied similar analysis to the different type of rock, we found that CO2 saturation and behaviors are significantly different. These important differences could be due to the heterogeneity of pore geometry in the natural rock and differences in pore connectivity. By quantifying CO2 behavior in the target reservoir rock under various conditions (i.e., saturation mapping on the Ca-M diagram), our approach provides useful information for investigating suitable reservoir conditions for effective CO2 storage (e.g., high CO2 saturation). We further calculated seismic velocity of the digital rocks with injected CO2 under various reservoir conditions (e.g., Ca and M) using dynamic wave propagation simulation. By using the relation between seismic velocity and CO2 saturation parameterized by reservoir conditions, we could quantify in situ CO2 saturation in reservoir from monitoring data (seismic velocity).

Formation factor in Bentheimer and Fontainebleau sandstones: Theory compared with pore-scale numerical simulations

Accurate quantification of formation resistivity factor F (also called formation factor) provides useful insight into connectivity and pore space topology in fully saturated porous media. In particular the formation factor has been extensively used to estimate permeability in reservoir rocks. One of the widely applied models to estimate F is Archie's law (F=ϕ−m in which ϕ is total porosity and m is cementation exponent) that is known to be valid in rocks with negligible clay content, such as clean sandstones. In this study we compare formation factors determined by percolation and effective-medium theories as well as Archie's law with numerical simulations of electrical resistivity on digital rock models. These digital models represent Bentheimer and Fontainebleau sandstones and are derived either by reconstruction or directly from micro-tomographic images. Results show that the universal quadratic power law from percolation theory accurately estimates the calculated formation factor values in network models over the entire range of porosity. However, it crosses over to the linear scaling from the effective-medium approximation at the porosity of 0.75 in grid models. We also show that the effect of critical porosity, disregarded in Archie's law, is nontrivial, and the Archie model inaccurately estimates the formation factor in low-porosity homogeneous sandstones.

A novel method for estimation of remaining oil saturations in water-flooded layers

After long-term production by water injection, the conductivity features of oil reservoirs are changed, leading to difficulties in calculating remaining oil saturation by traditional well-logging techniques. There are some specific phenomena relating to petrophysical properties in water-flooded layers, and a deep investigation of them could help us understand resistivity changes of rocks during the water-injection process. We compared traditional mixed-fluid resistivity methods and determined their drawbacks. In addition, we revised the theoretical models and came up with a novel method to calculate mixed-fluid resistivity. The displacement process was divided into three stages: non-water-flooded stage, low and medium water-flooded stage, and high water-flooded stage. To study the relationships between rock resistivities and water saturations when injecting fresh-/saltwater, we used digital rock numerical methods. We first constructed 3D digital rock models based on the process-based method, and then we obtained oil and water distributions in the pore space by the pore morphology method. When resistivities of every component in digital rock models were assigned, rock resistivities could be calculated in different water saturations by the finite-element method. We found that in the case of freshwater injection, the relationship between water saturations and rock resistivities formed an S-shaped curve, but in the case of saltwater injection, if the injection water salinity was higher, the rock resistivity would be decreased by increasing the water saturation. In different rock heterogeneity and wettability conditions, these curves showed similar shapes and trends. Combined with resistivity logging data, this novel approach was used in the interpretation of a real oil well. Compared with the existing models in the interpretation practices, this new model better matched the real-field saturations and improved the accuracy of saturation interpretation in the studied water-flooded oil reservoir.

Fundamental Transport Property Relations in Porous Media Incorporating Detailed Pore Structure Description

In this article, we present fundamental transport property relations incorporating direct descriptors of the pore structure. The pore structure descriptors are defined from streamline decomposition of the numerical solutions of the transport equations. These descriptors have been introduced earlier, while the calculations are extended to voxel-based microstructures in this article. The pore structure descriptors for the respective transport equations are used in turn to obtain rigorous cross-property relations for porous media. We derive such cross-property relations exemplarily for computed tomography (CT) data and digital rock models of Fontainebleau sandstone, and CT data of two reservoir sandstone facies. Pore structure parameterizations of these porous media are given for electrical conductance and fluid permeability in the microstructure, yielding correlations for the transport property-dependent descriptors of effective porosity, tortuosity and constriction. These relations are shown to be well-correlated functions over the range of sample porosities for the Fontainebleau sandstone. Differences between the outcrop Fontainebleau sandstone and the reservoir samples are observed mainly in the derived hydraulic length descriptor. A quantitative treatment of the obtained cross-property functions is provided that could be applied for porous medium characterization. It is suggested that such cross-property investigation honoring the detailed microstructure will lead to more fundamental relations between porous medium properties, which could be exploited for example in rock typing or wire-line log interpretation.

3D printing sandstone porosity models

The petroleum industry requires new technologies to improve the economics of exploration and production. Digital rock physics is a methodology that seeks to revolutionize reservoir characterization, an essential step in reservoir assessment, using computational methods. A combination of X-ray computed microtomography, digital pore network modeling, and 3D printing technology represents a novel workflow for transferring digital rock models into tangible samples that can be manufactured in a variety of materials and tested with standard laboratory equipment. Accurate replication of pore networks depends on the resolution of tomographic images, rock sample size, statistical algorithms for digital modeling, and the resolution of 3D printing. We performed this integrated approach on a sample of Idaho Gray Sandstone with an estimated porosity of 29% and permeability of 2200 mD. Tomographic images were collected at resolutions of 30 and [Formula: see text] per voxel. This allowed the creation of digital porosity models segmented into grains and pores. Surfaces separating pores from grains were extracted from the digital rock volume and 3D printed in plastic as upscaled tangible models. Two model types, normal (with pores as voids) and inverse (with pores as solid), allowed visualization of the geometry of the grain matrix and topology of pores, while allowing characterization of pore connectivity. The current resolution of commodity 3D printers with a plastic filament ([Formula: see text] for pore space and [Formula: see text] for grain matrix) is too low to precisely reproduce the Idaho Gray Sandstone at its original scale. However, the workflow described here also applies to advanced high-resolution 3D printers, which have been becoming more affordable with time. In summary, with its scale flexibility and fast manufacturing time, 3D printing has the potential to become a powerful tool for reservoir characterization.

Multi-scale characterization of porosity in Boom Clay (HADES-level, Mol, Belgium) using a combination of X-ray μ-CT, 2D BIB-SEM and FIB-SEM tomography

The Oligocene age Boom Clay is a potential host material for radioactive waste disposal in Belgium. To better understand the physical basis of transport mechanisms of radionuclides, we aim to characterize the pore space and its connectivity at nm-scale in 3D. In the present study, X-ray μ-CT and FIB-SEM (focused ion beam scanning electron microscopy) tomography were combined, to investigate the 3D pore space of a Boom Clay sample from the Mol-1 borehole (depth corresponding to the level of the HADES-URF – ‘high activity disposal experimental site underground research facility’) at the Mol–Dessel research site for radioactive waste disposal (Belgium). BIB-SEM (broad ion beam scanning electron microscopy) was used to bridge the gap in resolutions between X-ray μ-CT and FIB-SEM and to optimize the selection of a relevant spot for FIB-SEM. Pore network extraction (PNE) modeling (Dong and Blunt, 2009 [1]) was used to simplify the results into a set of pore bodies and pore throats, which are suitable for a statistical description. Resulting pore-size distributions are interpreted to be power-law distributed over ∼6 orders of magnitude, showing the scale-invariance of the pore space. We present a conceptual model of the 3D pore network in Boom Clay. The extracted 3D pore network model can be used to estimate transport properties – in digital rock models.

Elucidating the Role of Interfacial Tension for Hydrological Properties of Two-Phase Flow in Natural Sandstone by an Improved Lattice Boltzmann Method

We investigated the interfacial tension (IFT) effect on fluid flow characteristics inside micro-scale, porous media by a highly efficient multi-phase lattice Boltzmann method using a graphics processing unit. IFT is one of the most important parameters for carbon capture and storage and enhanced oil recovery. Rock pores of Berea sandstone were reconstructed from micro-CT scanned images, and multi-phase flows were simulated for the digital rock model at extremely high resolution (3.2 $$\upmu $$ m). Under different IFT conditions, numerical analyses were carried out first to investigate the variation in relative permeability, and then to clarify evolution of the saturation distribution of injected fluid. We confirmed that the relative permeability decreases with increasing IFT due to growing capillary trapping intensity. It was also observed that with certain pressure gradient $$\Delta P$$ two crucial IFT values, $$\sigma _{1}$$ and $$\sigma _{2}$$ , exist, creating three zones in which the displacement process has totally different characteristics. When $$\sigma _{1}< \sigma < \sigma _{2}$$ , the capillary fingering patterns are observed, while for $$\sigma < \sigma _{1}$$ viscous fingering is dominant and most of the passable pore spaces were invaded. When $$\sigma > \sigma _{2}$$ the invading fluid failed to break through. The pore-throat-size distribution estimated from these crucial IFT values ( $$\sigma _{1 }$$ and $$\sigma _{2})$$ agrees with that derived from mercury porosimetry measurements of Berea sandstone. This study demonstrates that the proposed numerical method is an efficient tool for investigating hydrological properties from pore structures.

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.

Investigation of effects of clay content on F-Φ relationship by Lattice gas automation using digital rock model

The Lattice Gas Automation (LGA) method, which is improved by introducing a reflection coefficient for the border between phases to show its effect on current path, is used in this paper to simulate the current flow in digital rock for investigating the effects of clay content and clay distribution types on the relationship between formation factor(F) and rock porosity(ϕ). The digital rock model is constructed by simulating a natural deposit of matrix particles with different shapes and radius. Based on the simulation results, it was found that both dispersed clay and laminated clay can lead to a non-Archie relationship of F-ϕ. The non-Archie effect of laminated clay on the F-ϕ relationship was more significant than that of dispersed clay. Moreover, a realistic model is developed in this work for quantitatively describing the effect of clay content (Denoted as Vsh) on parameters a and m. These study results have further demonstrated the validity of LGA in study of electrical transport properties at a pore scale.

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.

Leaky mode: A mechanism of horizontal seismic attenuation in a gas-hydrate-bearing sediment

The leaky mode is a possible attenuation mechanism of seismic waves propagating along lamination in gas-hydrate-bearing sediment layers. This horizontal propagation attenuation mechanism occurs when a high-velocity layer is embedded in a low-velocity zone. This is a typical situation for gas hydrate occurrences. To quantify this attenuation mechanism, a 2D digital rock model based on the crosswell data of the Mallik 2002 Gas Hydrate Production Research Well Program is used. For simplicity, our elastic simulations exclude attenuation mechanisms like scattering loss or intrinsic absorption. We demonstrate that the leaky mode is a significant horizontal attenuation mechanism that cannot be neglected. The effective attenuation of gas-hydrate-bearing sediments is a combination of intrinsic and scattering attenuation by small-scale heterogeneties and the leaky mode.

A numerical study on reflection coefficients of fractured media

Effective-medium theories can be used to predict reflection coefficients of an interface between an unfractured layer overlying a fractured half-space. In 2D and 3D computer simulations, we analyze wavefields that are emitted by an explosion line or point source and reflected from a fractured area in a digital rock model. The reflection coefficients from the simulations are compared to several predictions given by static effective-medium theories. The agreement between our numerical results and the theoretical reflection coefficients is best for differential effective-medium schemes in 2D as well as in 3D. This result agrees with previously published numerical static and numerical transmission-time experiments. By varying the wavelength to crack-length ratio, we consider the application range of different effective-medium theories. We observe good agreement with theoretical predictions even for a ratio equal to 9. An angle-dependent analysis of the reflected amplitude of our numerical results is also compared to results given by effective-medium theory in combination with exact reflection-coefficient formulas. As expected, the fluctuations of the reflection coefficients decrease for wider angles. In our 3D digital rock models, we vary the crack density and the infill of the crack (i.e., water [cold and hot] and oil [cold and hot]).