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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.

Ultrasonic elastic‐wave velocities, as well as the stress‐strain behavior, were measured on dry dune sand from Saudi Arabia under hydrostatic loading from 0 to 50 MPa. The samples came from the dune's crest, limb, and base. The experiments included several loading and unloading cycles. All samples exhibited irreversible deformation and porosity reduction during the tests due to grain repacking in low‐stress regimes and grain breakage at higher stress. The loading behavior was plastic, while the unloading/reloading behavior was elastic. In spite of noticeable porosity variations during the experiments, the elastic‐wave velocities mainly depended on the stress rather than on porosity. Our velocity versus stress data is very close to earlier published results, although the provenance of the sand is very different, pointing at a universality of such behavior in loose sand. Our results were matched by the contact Hertz‐Mindlin theory with varying coordination number and shear‐stiffness adjustment. We also offer a new theoretical model for the static bulk modulus measured in these experiments. This model is based on the concept of stress heterogeneity (stress chains or patches) in a granular pack and uses elastic bound averaging of the respective moduli of stressed and unstressed parts of the pack. The same model is used to describe the velocity versus stress behavior. These results and theory constitute a new installment into the published sparse data of the mechanical properties of unconsolidated sand as well as theoretical analyses thereof and are the first ever such data generated in Saudi Arabia. New dataset on dune sand, velocity and deformationNew theory for elastic‐wave velocityNew theory for static bulk modulus

A quantitative seismic interpretation workflow based on rock physics was developed for an organic-rich mudrock formation in order to estimate porosity, and organic matter and clay contents from seismically-derived acoustic and shear impedances. This deterministic workflow consists of: developing a rock physics model that accurately estimates the elastic properties of the formation; finding inter-relationships between the formation's petrophysical properties; and validating the model after upscaling and applying it to seismically-derived acoustic and shear impedances. By analyzing wireline data from this organic-rich mudrock formation, we find that the P-wave velocity at fixed porosity may vary by as much as 1.0 km/s, while the respective variation in the S-wave velocity reaches 0.5 km/s. A robust discriminator for velocity appears to be, in addition to the total porosity, the volumetric fraction of the soft components of the solid matrix where the kerogen is included, namely the sum of the clay and kerogen. The ensuing velocity-porosity-mineralogy relations are accurately described by the soft-sand rock physics model. Thus, an attempt to interpret seismically-derived impedance volumes based on rock physics modeling is performed after simplifying the rock's petrophysical variables by building site-specific internal relations between mineral's volume fractions that comprise the rock's solid matrix. This workflow helps in hydrocarbon exploration by identifying favorable areas with relatively high porosities and organic matter content.

We measured the permeability of 30 samples extracted from 6 sets of compaction bands and the adjacent host rocks of the Jurassic aeolian Aztec Sandstone exposed in the Valley of Fire State Park in Nevada using core flooding experiments. The results show that the permeability within the high-angle compaction bands (three sets) is consistently three orders of magnitude lower than that of the host rocks. For the bed-parallel compaction bands, the measured permeability reduction is about half an order to three orders of magnitude for two sets of bands, and there is no detected permeability reduction for the samples from one set. For the samples that show permeability reduction within high-angle and bed-parallel compaction bands, the results are generally consistent with the data estimated from two-dimensional segmented image analyses in previous studies. Permeability of the samples used in the laboratory experiments was also obtained numerically based on three-dimensional tomographic images scanned from micro-samples and lattice-Boltzmann flow simulations. In addition, backscatter electron images (BEI) and energy dispersive spectroscopy images (EDSI) of thin sections were used to estimate the clay content inside and outside the bands. Large differences exist between the lab-based and image-based permeability and porosity measurements of compaction bands and host rocks. Possible factors causing these differences are different sample sizes and heterogeneities within the host rocks, calibration on the image segmentation, and incomplete characterization of clay minerals and fines migration during lab-based experiments. Given the wide range of permeability reductions within compaction bands of different orientations by different investigators, their impact on fluid flow should be evaluated case by case, one should consider their dimensions and distributions. [ABSTRACT FROM AUTHOR]

We offer a first-principle-based, effective medium model for elastic-wave velocity in unconsolidated, high porosity, ocean bottom sediments containing gas hydrate or free gas. The dry sediment frame elastic constants depend on porosity, elastic moduli of the solid phase, and effective pressure. Elastic moduli of saturated sediment are calculated from those of the dry frame using Gassmann's equation. To model the effect of gas hydrate on sediment elastic moduli we use two separate assumptions: (a) hydrate modifies the pore fluid elastic properties without affecting the frame and (b) hydrate becomes a component of the solid phase, reducing porosity and modifying the elasticity of the frame. The goal of the model is to predict the amount of hydrate in sediments from sonic or seismic velocity data. We apply the model to sonic and VSP data from ODP Hole 995 and obtain hydrate concentration estimates from assumption (b) that are consistent with estimates obtained from resistivity, chlorinity, and evolved gas data.

Analytical solutions are presented to predict the intergranular contact load transfer in cemented granular media where both grain material and cement are elastic. The grains can be separated, have a direct point contact, or be compacted prior to cement deposition. For all these cases contact stress distributions are obtained for normal, tangential and torsional deformation of two cemented deformable grains. An important result is that intergranular cement, even if very soft, is load-bearing. Thus cementation reduces contact stress concentration (as compared with direct Hertzian interaction). Contact stresses are maximum near the center of the contact region when the cement is soft relative to the grains, and are maximum at the periphery of the contact region when the cement is stiff. These results allow us to predict the following modes of static and dynamic failure of the grains and intergranular bonds in a particulate material. (1) Uncemented grains will tend to shatter whereas cemented grains will stay intact, and the cement will fail. (This conclusion is supported by hydrostatic loading experiments where intensive crushing of uncemented glass beads was observed at about 50 MPa, whereas grains cemented at their contacts with small amounts of epoxy stayed intact.) (2) Where intergranular cementation is present, grain failure may still be expected if the cement is strong and stiff. In this case, grain damage will be initiated at the periphery of the cement layer. (3) Yielding of a cement material that is soft (as compared with the grain material) will initiate at the center of the contact region, whereas stiff cement will yield at the periphery.

The role of cementation, porosity, permeability and consolidation on acoustic properties of unconsolidated sands and poorly consolidated sandstones has been investigated. Partially and fully water saturated Ottawa sand and poorly consolidated sandstone samples were measured in a bench-top ultrasonic assembly in permafrost conditions at several ice saturation states to determine the variations in wave velocities associated with the degree of cementation. A Berea sandstone sample was also measured in permafrost conditions to investigate the role of consolidation on the measured wave velocities. Permeability and porosity of the samples were found to have significant effect on the variation of the wave velocities. Freezing water creates thin ice layers surrounding the grains resulting cement-like response in poorly consolidated sands allowing grains to be in contact even at large ice saturations. This response can be predicted using a modified cementation model presented here. The model is designed based on the cementation model of Dvorkin et al.1994. There are two extreme schemes where the ice is located in pore space in the modified model. In the first scheme, ice acts like cementing material deposited only at the grain contacts in pendular ring form resulting high velocities that agree with the observed trends for low saturations in both low and high permeability sands. In the second scheme, ice envelopes the grains corresponding to the variations in high permeability sands at intermediate to high saturations. Ice acts as the load-bearing cementation material which strongly increase the stiffness of the sands tested. Wave velocities obtained from frozen drainage tests indicate a plateau at the intermediate saturations in all samples studied. The width of the plateau is controlled by the permeability of the sample tested. The higher the permeability, the smaller the plateau becomes and the corresponding velocity reduction is more gradual.

Sand and glass bead samples were monotonically loaded from 0 to 50 MPa and then monotonically unloaded, all under hydrostatic stress conditions. Sand deformed irreversibly and its porosity loss was permanent. In contrast, the glass bead deformation was almost fully reversible with the initial porosity recovered. During loading, the static bulk modulus in all sand samples increased from 0 to about 0.5 GPa between 0‐ and 15‐MPa stress and remained constant for the remainder of the loading. Such behavior, somewhat unexpected in a granular system, means that sand deforms as a linear elastic body during loading from 15 to 50 MPa. The unloading behavior was very different—the static bulk modulus almost linearly decreased from about 4 GPa at 50 MPa to zero as the stress was reduced. Once again, this behavior was very different from that observed in glass beads, where the static bulk modulus during loading was essentially the same as during unloading and appeared to be a unique function of stress, independent of the direction of its variation. Moreover, the static and dynamic bulk moduli in glass beads, the latter computed from Vp, Vs, and density measured during the loading/unloading cycle, were very close to each other. In contrast, the dynamic bulk modulus in dry sand exceeded the static modulus during unloading by a factor of 1.5 to 2.0. We used a quantitative theory based on contact mechanics and the concept of stress heterogeneity in particulates to analytically match the observed results. Measurements of static moduli of granular materialsDeformation of sand and glass beadsTheoretical explanation of results

A patchy saturated two‐layered porous rock, with each layer filled with a different fluid, is examined. We assume that this system is probed by an elastic wave having a wavelength much larger than the layers' thicknesses. We also assume that the diffusion length is smaller than the thickness of an individual layer, which implies hydraulic disconnection between layers. In the context of Gassmann's fluid substitution theory, we analytically derived an exact expression for the effective fluid bulk modulus assuming that both layers have the same porosity, dry frame, and mineral matrix properties. In addition we derived an approximate solution that works well at relatively high porosities. Both solutions are expressed as a weighted average of the arithmetic and harmonic averages of individual bulk moduli of the pore fluid. These weights are explicitly given as functions of the porosity, the fractional thicknesses of both layers, and the elastic moduli of the constituents. For the approximate solution, one does not require explicit knowledge of the shear modulus of the rock. The comparison with laboratory data showed that, in the case where a porous, isotropic rock is filled with water and gas, the approximate solution can be used to model the measured data for high values of water saturation. We derive exact and approximate analytic solutions to model the effective fluid bulk modulus of patchy saturated porous rocksWe compare and validate the solutions with stochastic simulation and laboratory data

The shapes of particles play a crucial role in the transport and mechanical behavior of granular media. How densely particles of a specific shape can be arranged in a given volume has an enormous practical significance for many scientific and industrial fields. We developed a numerical workflow to investigate the effects of irregularly shaped frictionless, convex particles combined with the polydispersity of particle sizes on the porosity, permeability, and elastic bulk modulus of granular porous media. The workflow is based on the computationally generated three‐dimensional granular assemblies of both regular and irregularly shaped particles and pore‐scale simulation of physics to estimate the absolute permeability and elastic bulk modulus of the generated digital granular porous media. Our numerical results show that the porosity decreases by 14–25%, absolute permeability decreases by 45–76%, and elastic bulk modulus increases by 20–66% as we deviate from the regular‐shaped particle with the specified particle size distribution. How rapidly and to what degree these properties of granular assemblies of irregularly shaped particles change depends on particle size distribution. However, once the maximal densest packings of irregularly shaped particles with the prescribed aspect ratio are generated, any further change in the shape of particles has either a minimal impact or an opposite effects are observed. Overall, our numerical observations suggest that the irregular shape of particles has the greatest effect on permeability and the least effect on porosity in both monodisperse and polydisperse granular media. We developed a numerical workflow to investigate the effects of irregularly shaped frictionless, convex particles combined with the polydispersity of particle sizes on the physical properties of granular porous mediaHow rapidly and to what degree the properties of granular packings of irregularly shaped particles change depends on the particle size distributionThe irregular shape of particles has the greatest impact on permeability and the least effect on porosity in both monodisperse and polydisperse granular assemblies

We present a deterministic methodology for mapping the lithology, pore fluid, and porosity from seismic data. The input is the P‐ and S‐wave data volumes that may come, e.g., from acoustic and elastic inversion or cross‐well measurements. The output is the pore fluid type (hydrocarbon versus water), total porosity, and clay content. The key element of this methodology is a site‐specific rock physics model that provides the needed transforms from the elastic rock properties to the reservoir properties. This model is established by comparing model‐based predictions, such as impedance versus porosity, to the relations present in well log data. Once selected, the model is used to identify the presence of hydrocarbons from a combination of the P‐wave impedance and Poisson's ratio. Then the P‐wave impedance is used to map porosity and clay content assuming that a deterministic relation exists between the latter two properties. All deterministic equations are calibrated at a well and then are applied to upscaled well log data to confirm their validity at the seismic scale. This methodology is applied to log data from a fluvial environment. The results indicate that the relative error in porosity determination is 14%, which is acceptable for reservoir characterization purposes.

A finite‐element microstructure analysis code was used to model the geoacoustic properties of shallow marine clay sediments in Eckernfoerde Bay which has been the subject of an intensive geoacoustic and geotechnical study (Coastal Benthic Boundary Layer—Special Research Program). Uniaxial strain and pure shear were applied to two‐phase microstructure models with generalized, periodic plane‐strain boundary conditions to generate anisotropic bulk and shear moduli. Analyses were carried out on two length scales: clay microfabric (μm) and gas‐filled inclusions (mm). The clay microstructure was modeled as a random lattice of Illite platelets with a density and porosity equivalent to average values observed in shallow Eckernfoerde Bay sediments. Saturated and dry framework moduli were calculated and the effective medium velocities were compared with observed velocities. The analysis suggests that shear wave propagation in these sediments is not supported by the framework structure but by differential compression of fluid‐filled pores. Radiographic images of pressurized cores containing gas‐filled inclusions with dimensions of a few millimeters were also analyzed. The analysis indicates a shear wave velocity anomaly related to the inclusion structure. The calculated effective medium velocities are compared with analytical models of spheroidal inclusions. [Work supported by ONR.]