The key paradigm of digital rock physics (DRP) “image and compute” implies imaging and digitizing the pore space and mineral matrix of natural rock and then numerically simulating various physical ...processes in this digital object to obtain such macroscopic rock properties as permeability, electrical conductivity, and elastic moduli. The steps of this process include image acquisition, image processing (noise reduction, smoothing, and segmentation); setting up the numerical experiment (object size and resolution as well as the boundary conditions); and numerically solving the field equations. Finally, we need to interpret the solution thus obtained in terms of the desired macroscopic properties. For each of these DRP steps, there is more than one method and implementation. Our goal is to explore and record the variability of the computed effective properties as a function of using different tools and workflows. Such benchmarking is the topic of the two present companion papers. Here, in the first part, we introduce four 3D microstructures, a segmented Fontainebleau sandstone sample (porosity 0.147), a gray-scale Berea sample; a gray-scale Grosmont carbonate sample; and a numerically constructed pack of solid spheres (porosity 0.343). Segmentation of the gray-scale images by three independent teams reveals the uncertainty of this process: the segmented porosity range is between 0.184 and 0.209 for Berea and between 0.195 and 0.271 for the carbonate. The implications of the uncertainty associated with image segmentation are explored in a second paper.
► We propose four rock microstructure images as benchmark geometries for digital rock tools. ► The digital samples are Fontainebleau and Berea sandstone, a vuggy carbonate and a pack of spherical beads. ► Sample porosities range from 14.7% and 18.3% for the sandstones to 24.3% for the sphere pack.
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.
► We conduct micro-scale simulations on digital rock samples. ► We simulate elastic, hydraulic and electrical properties for four samples. ► Simulated effective properties are affected by the details of image segmentation. ► Simulation results are consistent with laboratory measurements.
Matrix acidizing is a widely applied stimulation process in carbonate reservoirs to remove damaged parts of the formation and enhance wellbore productivity. Few studies considered the impact of acid ...on the deterioration of mechanical rock properties considering different carbonate types. Assessment of the wellbore stability and the sustainability of the wormhole structure depends on the mechanical rock properties after acidizing. In this study, three rock lithologies (chalk, limestone, and dolomite) were treated with acid at different injection rates to establish acid efficiency curves. The acid was injected in a coreflooding setup until wormhole breakthrough, indicated by zero pressure drop across the sample. The rock petrophysical (i.e., porosity, permeability) and mechanical properties were measured before and after the treatment. XRD was used to estimate the mineralogical compositions of each rock type. Then, the impulse hammer technique was implemented to measure the rock surface hardness at ambient pressure. Also, acoustic measurements were used to quantify the dynamic Young’s modulus and Poisson ratio at high confining pressures. To estimate the deformation in the samples with wormholes under varying confining stress, a finite element model was constructed. Results indicate that the acid treatment significantly reduces the rock surface hardness (by 47 to 77 %), while Young’s modulus decreases by 18 to 33 % at ambient stress. The treated rock samples showed higher Young’s modulus under high confining stress. Chalk samples were the most impacted by the treatment, while dolomite specimens were the least. The finite element numerical model indicates that rock deformation is more significant in chalk samples, especially at high confining stress that acts perpendicular to the wormhole.
By examining wireline data from Woodford and Wolfcamp gas shale, we find that the primary controls on the elastic-wave velocity are the total porosity, kerogen content, and mineralogy. At a fixed ...porosity, both
V
p
and
V
s
strongly depend on the clay content, as well as on the kerogen content. Both velocities are also strong functions of the sum of the above two components. Even better discrimination of the elastic properties at a fixed porosity is attained if we use the elastic-wave velocity of the solid matrix (including kerogen) of rock as the third variable. This finding, fairly obvious in retrospect, helps combine all mineralogical factors into only two variables,
V
p
and
V
s
of the solid phase. The constant-cement rock physics model, whose mathematical form is the modified lower Hashin-Shtrikman elastic bound, accurately describes the data. The inputs to this model include the elastic moduli and density of the solid component (minerals plus kerogen), those of the formation fluid, the differential pressure, and the critical porosity and coordination number (the average number of grain-to-grain contacts at the critical porosity). We show how this rock physics model can be used to predict the elastic properties from digital images of core, as well as 2D scanning electron microscope images of very small rock fragments.
Rock physics diagnostics (RPD) established based upon the well data are used to deterministically predict elastic properties of rocks from measured petrophysical rock parameters. However, with the ...recent advances in statistical methods, machine learning (ML) can help to build a shortcut between raw well data and rock properties of interest. Several studies have reported the comparison of rock physics and machine learning methods for the prediction of rock properties, but the scale dependence of the ML models was never investigated. This study aims at comparing the results from rock physics and machine learning models for predicting elastic properties such as bulk density (
ρ
b
), P-wave velocity (
V
p
), S-wave velocity (
V
s
), as well as Poisson’s ratio (
v
) and acoustic impedance (
I
p
) in a well from the Gulf of Mexico (GOM) in two different scale scenarios: the well log and seismic scales. The well data under examination was split into training and testing subsets to optimize and test the developed ML models. The RPD approach was also used to validate and compare the accuracy of predicted elastic properties. Backus averaging was later applied to upscale the well data to the seismic scale to examine the scale dependence and prediction accuracy of aforementioned physics-driven and data-driven approaches. Results show that RPD and ML methods provided consistent results at both well log and seismic scales, suggesting the scale independence of both approaches. Moreover, ML models showed better estimation of rock properties due to their “apparent” match with measured data at both scales compared to the RPD approach where a significant mismatch between measured and predicted rock properties was found in the reservoir section of the well. However, by conducting further quality control of the sonic data, it was found that the measured Poisson’s ratio was extremely high in the gas-saturated interval. Hence, the prediction from ML models in this particular case cannot be trusted as ML models were trained based on poor-quality well data with non-realistic
V
s
and
v
values. Such an issue, however, could be identified and corrected using RPD as presented in this study. We demonstrate the importance of incorporating domain knowledge, i.e., rock physics, to check data quality and validate results from data-driven models.
Sonic and dipole wireline tools measure
V
p
and
V
s
along the vertical direction. The state of stress in the subsurface is predominantly anisotropic, while most laboratory experiments measuring the ...dynamic elastic properties are conducted under hydrostatic stress. The question we ask is whether such laboratory experiments provide the velocities that are close to those measured in the vertical wellbore where the stresses are anisotropic. To address this question, we conducted ultrasonic pulse transmission experiments on several room-dry rock samples. The comparison was made between the P- and S-wave velocities obtained at pure hydrostatic loading conditions and those at a smaller hydrostatic stress with added axial stress, so that the total stress along the axis of a cylindrical plug was the same as under pure hydrostatic loading. These differences were significant in the extreme case of only 1 MPa hydrostatic confining stress with the axial stress increasing up to 40 MPa. However, as the hydrostatic (confining) stress increased, the differences between the velocities along the axis of the sample became smaller and smaller. For example, at 1 MPa confining and 30 MPa axial stress, the relative difference in
V
p
was about 10%, while that in
V
s
was about 20%. However, at 10 MPa confining stress, these differences became about 3% and 6%, respectively, and further decreased as the confining stress increased. This means that even at strong
in-situ
contrasts between the vertical and horizontal stresses, the results of laboratory hydrostatic experiments can be used for
in-situ
velocity estimates. These results also appear to be consistent with a theoretical model that predicts the directional velocities at any triaxial stress conditions from those measured versus hydrostatic stress.
A rock physics based seismic interpretation workflow has been developed to extract volumetric rock properties from seismically derived P- and S-wave impedances,
I
p
and
I
s
. This workflow was first ...tested on a classic rock physics velocity-porosity model. Next, it was applied to two case studies: a carbonate and a clastic oil field. In each case study, we established rock physics models that accurately relate elastic properties to the rock’s volumetric properties, mainly the total porosity, clay content, and pore fluid. To resolve all three volumetric properties from only two inputs,
I
p
and
I
s
, a site-specific geology driven relation between the pore fluid and porosity was derived as a hydrocarbon identifier. In order to apply this method at the seismic spatial scale, we created a coarse-scale elastic and volumetric variables by using mathematical upscaling at the wells. By using
I
p
and
I
s
thus upscaled, we arrived at the accurate interpretation of the upscaled porosity, mineralogy, and water saturation both at the wells and in a simulated vertical impedance section generated by interpolation between the wells.
SUMMARY
Published laboratory elastic-wave velocity versus porosity data in carbonate rocks exhibit significant scatter even at a fixed mineralogy. This scatter is usually attributed to the strong ...variability in the rock-frame or pore-space geometry, which, in turn, is driven by the richness and complexity of diagenetic alteration in these very reactive sediments. Yet, by examining wireline data from oil-bearing high-to-medium porosity chalk deposits, we find surprisingly tight velocity–porosity trends. Moreover, these trends are continued into the low-porosity domain by data from a location thousands of miles away from the chalk field. This congruence implies a universality of diagenetic trends, at least in the massive deposits under examination. We also find that the elastic bulk and shear moduli of the pure-calcite end member are somewhat smaller than such values reported in the literature. Using the end-member elastic constants relevant to the data under examination, we establish a theoretical rock physics model to match and generalize these data.
We offer an effective medium model for the elastic moduli of high‐porosity ocean‐bottom sediments. The elastic constants of the dry‐sediment frame depend on porosity, elastic moduli of the solid ...phase, and effective pressure. The model connects two end points in the elastic‐modulus‐porosity plane: the Hertz‐Mindlin modulus of a dense elastic sphere pack at critical porosity; and zero at 100% porosity. The elastic moduli of saturated sediment are calculated from those of the dry frame using Gassmann's equation. Unlike the suspension model, our model assigns non‐zero elastic constants to the dry‐sediment frame and can predict the shear‐wave velocity. Unlike various modifications of the travel‐time‐average equation, it is first‐principle‐based and contains only physical parameters. We justify this model by matching sonic data in shallow marine sediments and in an ODP well.
In arid countries such as Saudi Arabia, aeolian sand often covers a large area of the country. Understanding the variations of sand properties in dunes, including grain size, sorting, mineral ...composition and water content, can be important for groundwater recharge, environmental, and construction applications. Earlier studies examined properties of sand dunes by collecting samples from the surface. This study aims to investigate variations of sand properties within a Barchan sand dune in the coastal area of Saudi Arabia, by collecting samples and measurements from two vertically drilled boreholes up to the ground water level; one drilled in the dune crest and another one in the limb. Representative samples were collected and analyzed for their texture parameters, water content, and mineralogy. Electrical resistivity survey data was also acquired to map water content variation in the dune limb, and for comparison with well bore data. The reported results show no vertical variations in grain size or sorting in the dune crest. In contrast, the upper 0.5 m of the dune limb shows a relatively poorer sorting than found in deeper parts of the dune. Laterally, no variations in minerology were observed between crest and limb sands while grain size tended to be slightly coarser in the dune limb compared to the crest. Regarding the water content, it was found to vary vertically, probably due to previous cycles of rainfall infiltration through the sand body. Such observed variation in water content is consistent with the measured resistivity profile which could clearly identify the water table and areas with higher water content. This study concludes that beyond the upper 0.5 m, the Barchan sand dune body can be treated as a homogeneous medium in terms of mineralogy and sorting while grain size increases slightly toward the limb side.
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