Critical Porosity Research Articles

Velocity-Porosity-Mineralogy Model for Unconventional Shale and Its Applications to Digital Rock Physics

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, bothVpandVsstrongly 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,VpandVsof 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.

Size effect on the fracture of sintered porous nano-silver joints: Experiments and Weibull analysis

Nano-silver paste is a promising alternative of high temperature solder material for the next generation electronic devices, which is composed of organic solvent and silver nanoparticles/sheets. The mechanical properties of nano-silver interconnections are essential for the bonding between chip and substrate by sintering. During sintering process, volatilization and combustion of organic solvent in nano-silver paste lead to development of abundant voids in the joint, forming a three-dimensional network structure, which has strong influence on the mechanical properties. Sintering temperature and cross section area can affect the distribution of voids in solder joint. In the current study, effects of sintering temperature (200 °C, 250 °C, 300 °C) on the tensile and shear failure strength of sintered nano-silver joints were investigated, the size effect caused by different cross section area (i.e. (0.5, 1, 2, 3) × 5 mm2) was studied. The volatilization of organic solvent in nano-silver paste is the main reason for the porosity diversity, and the difference of porosity is one of the key factors causing size effect. It also leads to dispersion of experimental data of failure strength, thus, statistical analysis was performed to the experimental data. Four universal estimators and Weibull distributions were adopted to analyze the tensile and shear failure strength of sintered nano-silver joints. Based on the Gurson-Tvergaard-Needleman model, the critical porosity equation of fracture was developed. Furthermore, the relationship between critical porosity and size effect was established considering porosity increases with the increasing of cross section area, and a modified Weibull model containing size effect was proposed, which showed good agreement compared with the experimental data.

Porosity-dependent velocities of longitudinal and transverse waves in dry porous materials

New relations are presented to better evaluate the longitudinal and transverse velocities in porous materials under the dry state, respectively. The models are based on semi analytically derived bulk and shear moduli-porosity correlations for dry porous materials. The accuracy and robustness are validated by fitting the published elastic waves-porosity data of different porous materials and a further sensitivity analysis, respectively. The accuracy of the proposed models is averagely higher than that of the empirical Phani’s equation and theoretical Ramakrishnan’s equation. There is an advantage over the Ramakrishnan’s equation to predict the zero-porosity velocity from the data lack of dense porous specimens. The proposed models have a good predictive performance for porous materials with critical porosity and can provide the value of critical porosity, but attention also should be paid to increased sensitivity in this case.

Rock physics modelling in unconsolidated sandstone reservoir based on contact theory method case study: FRR Field, Kutai Basin

The study of rock physics modeling has been successfully carried out in FRR Field, Kutai Basin. This study aims to predict elastic parameters of rock such as V p, V s, and density which represent the characteristic of reservoir. The Contact Theory (CT) method was used for conducting rock physics modeling at the unconsolidated reservoir. CT method combines the elastic modulus of Hertz Mindlin at the critical porosity (Φ0) and Hashin Shtrikman Walpole lower bound (HSW−) to interpolate the elastic modulus from the critical porosity to the minerals modulus. Gassman model has been applied to estimate bulk modulus of a fluid-saturated rock with variation water and gas saturation. The data used in this study is log data coming from one well in FRR Field, Kutai Basin. The targeted reservoir was identified as gas sand reservoir that was deposited in the channel complex of turbidity system. Based on the data, the reservoir has the majority of sandstone rock marked by low density and low gamma-ray at the upper part of log data. The results show correlation between elastic properties estimation and log data with the correlation of V p was 0.66; V s was 0.5310, and density was 0.99. This result was indicated that the CT method successfully predicts elastic parameter in unconsolidated sandstone reservoir of the FRR Field, Kutai Basin.

Relationship between percolation mechanism and pore characteristics of recycled permeable bricks based on X-ray computed tomography

Abstract The relationship between percolation mechanism and pore characteristics for recycled permeable bricks with different porosities is investigated in this study based on X-ray computed tomography (X-CT). Permeability coefficients are measured and some characteristics including size, amount, and distribution of the pore are analysed. The results show that the effective porosity and permeability coefficient of the recycled permeable bricks exhibit a linear relationship first and then a quadratic curve relationship, where the critical effective porosity is 12%. Meanwhile, we discovered that nonlinear channels in permeable bricks are larger and fewer compared with linear percolation channels, regardless of whether the percolation stage is linear or nonlinear. Additionally, when the area and number ratios of the linear and nonlinear percolation channels reached 80% and 10%, respectively, the overall percolation state of the permeable bricks changed from linear to nonlinear percolation. This research is helpful to improve the mechanical and percolation properties of recycled concrete bricks and promote the application of porous permeable material.

The critical control of arkosic sandstone porosity on deformation band formation: Insights from the Shulu across-fault borehole in the Bohai Bay Basin, China

Fewer studies have focused on subsurface deformation bands than deformation bands in outcrops. In this work, we studied the subsurface deformation bands in high-porosity sandstones from the Shulu borehole in the Bohai Bay Basin. The Shulu borehole was drilled through the Xicaogu normal fault with a displacement of 140 m, and the recovered core contains deformation bands and fractures in the damage zones. This study focused on the structural characteristics of subsurface deformation bands with burial depths between 2504.4 m and 2506.2 m. The critical porosity limit of host sandstone for the formation of deformation bands and fractures was determined. The host sandstones in the Shulu borehole are predominantly arkose. The subsurface deformation bands in the Shulu borehole are suggested to be compactional shear bands. We find that the subsurface deformation bands have identical characteristics to those in outcrops, except that they do not show strong positive reliefs. These bands are characterized by protocataclasis and cataclasis and organized into localized and conjugate networks. Compared to the host rocks, the subsurface deformation bands show porosity reductions of 7.7–27.7% and permeability reductions of 1–3 orders of magnitude. Three porosity intervals of the host-rock with different deformation styles can be identified in the Shulu borehole core: 1) host sandstone with porosities greater than 14.3%, which develop deformation bands exclusively; 2) host sandstone with porosities less than 10.8%, which develop fractures; and 3) the transition zone, where the porosities of host sandstone are 10.8–14.3%, and the deformation styles are characterized by both deformation bands and fractures. The critical porosity limit of host rocks in terms of the formation of deformation bands and fractures suggests that porosity is a major factor controlling the formation of fractures and deformation bands. Deformation bands and fractures have counteracting effects on the fluid flow in the transition zone.

ROCK QUALITY GROUPING IN SANDSTONE FORMATION USING A CRITICAL POROSITY APPROACH AT FORMATION PRESSURE CONDITIONS

The methods of grouping reservoir rock types based on the physical properties of rocks that have been studied by previous researchers still have a relatively large value of uncertainty. This uncertainty arises in conditions where rock type grouping is carried out in wells that do not have core sample data. Where we know that in the oil and gas field, not all wells in the field are subjected to rock sampling, either routine core analysis or special core analysis. From these problems, the authors feel the need to carry out this study to create a method for classifying reservoir rock types based on the physical properties of rocks that can be used in wells that do not have core sample data. The rock types in the wells that do not have core samples will be grouped based on the critical porosity value of the rock obtained from the vp value in the acoustic log data owned by these wells. By making an approach model through the critical porosity of rocks from wells that have core sample data, wells that only have acoustic log data can be grouped by using the critical porosity approach which is generated from the vp value of the acoustic log.

Assessment of the properties of polycrystalline rock salt synthesized under nominally dry and wet conditions

Polycrystalline rock salt’s compression is a function of applied stresses, exposure duration to the applied stresses, ambient temperature, and water content. Rock salt’s compressional behavior under different conditions and its effects on the specimens’ mechanical properties have been investigated in the literature. However, the one-dimensional (1D) compression behavior of polycrystalline rock salt at various water contents and how the specimen’s compression at different water contents further affects its physical and mechanical properties are not fully understood yet. In this study, polycrystalline rock salt specimens were prepared under nominally dry and wet conditions and some of the dry and wet specimens were annealed after the preparation. The relationship between the porosity of the specimens and the logarithm of the applied axial stresses during the 1D compression was found to follow a linear relationship after reaching unique critical porosities of 32% and 37% for the dry and wet specimens, respectively. Unloading and reloading the specimens did not result in any major changes in the porosity of the specimens. The specimens compressed under wet condition showed an average final porosity of 2.6% compared to 6.9% for the dry specimens. The dry and wet specimens that were annealed after the compression exhibited a lower porosity in comparison to the dry and wet specimens, respectively. Unconfined compression experiments on the specimens showed dry and wet specimens possess averaged unconfined compressive strengths ( σ u ) of 64.3 and 16.2 MPa, respectively. Annealing decreased σ u of the dry specimens to 39.6 MPa and increased σ u of the wet specimens to 41 MPa. • Rock salt’s porosity vs. stress follows a linear trend during consolidation. • Unloading or reloading rock salt does not change the porosity significantly. • Wet consolidated rock salt has a lower porosity than dry. • Dry consolidated rock salt has higher compressive strength than wet. • Annealing influences dry and wet rock salt’s compressive strength differently.

Silica-rich spinel harzburgite residues formed by fractional hybridization-melting of the intra-oceanic supra-subduction zone mantle: New evidence from TUBAF seamount peridotites

Recent studies of serpentine-free, spinel peridotite xenoliths from the mantle lithosphere beneath the active Kamchatka and West Bismarck arcs have shown that these rocks are enriched in silica and highly depleted in incompatible elements in comparison with melting residues of either primitive or mid-ocean ridge mantle. It has been suggested that the silica-rich nature of peridotites from the intra-oceanic, fore- and sub-arc mantle lithosphere, collectively referred to as ‘Supra-Subduction Zone (SSZ) peridotites’, is primarily of residual origin and inherited from source processes during partial melting in the SSZ mantle asthenosphere (mantle wedge). However, quantifying the contribution of post-melting processes to the silica-rich nature of SSZ peridotites has remained challenging.Here we report petrological and major and trace element data for a new suite of spinel harzburgite xenoliths from the mantle lithosphere beneath TUBAF seamount, located in the fore-arc region of New Ireland (Papua New Guinea area). All samples are fresh peridotites displaying coarse-grained protogranular textures, and sometimes high orthopyroxene (up to ∼29 wt%) at low clinopyroxene (≤4 wt%) contents, which are typical for SSZ peridotites worldwide. TUBAF peridotites in this study have suffered very little post-melting metasomatism through the formation of ≤1 wt% amphibole, which subsequently experienced decompression-induced breakdown during the xenolith ascent. Otherwise, the rocks display a high degree of inter-mineral equilibration and melting signatures preserved through sub-solidus re-equilibration. The bulk-rock chemistry of TUBAF peridotites record a Fe-Al correlation along the 25–30% melting isopleths from ∼2 to <1 GPa, in combination with the distinctive enrichment in silica and (TiO2, Al2O3, Na2O)-depletion of SSZ peridotites. This strongly supports the melting origin of these ‘residual SSZ signatures’. Bulk-rock and mineral lithophile trace element compositions of TUBAF xenoliths are similar to those of other residual SSZ peridotites, consistent with 25–30% of nearly-pure fractional melt extraction (critical mass porosity <0.001%) in the presence of a fluxing agent enriched in highly incompatible elements.We re-assess earlier interpretations of the origins of TUBAF peridotites by melting at mid-ocean ridges. Instead, we show that these rocks have experienced their last melting event in the mantle wedge, similar to samples from the Izu-Bonin-Mariana fore-arc and the Kamchatka and West Bismarck arcs. We also demonstrate that post-melting metasomatism (including fibrous orthopyroxene that are absent from the samples in this study) is unrelated to the residual SSZ mantle signatures, for which we present the results of polybaric and isothermal flux-melting models including minor element partitioning parameterizations. These models imply that residual SSZ signatures form when previously depleted mantle protoliths are hybridized by hydrous, silica-rich liquids. From the unique Fe-Al correlation in TUBAF peridotites and their low temperatures of equilibration, it appears that fractional hybridization-melting processes forming these rocks occurred in a fore-arc environment with shallow mantle decompression, likely during Oligocene to Miocene subduction along the Manus-Kilinailau trench.

Sulfate resistance of Portland dolomite cement: performance and mechanisms

This study investigated the sulfate resistance of Portland-dolomite cement (PDC) cured at different temperatures. Mortars of Portland cement (PC) and PDC with different dosages of dolomite, 10, 20, 30% by weight, were cured in water at 20 °C and 60 °C for 28 days before immersed in 50 g/L Na2SO4 solution at 20 °C. In addition to monitoring the length changes of mortars, MIP and XRD were performed to investigate microstructure and evolution of phase assemblages. Results show that PDC mortars cured at 20 °C give a poorer sulfate resistance than PC, and the higher the dosage of dolomite, the worse the sulfate resistance. On the contrary, when cured at 60 °C, PDC gives a much better sulfate resistance than PC, and the higher the dosage of dolomite, the better the sulfate resistance. The increases of critical pore size and porosity with the incorporation of dolomite lead to a poor sulfate resistance of PDC cured at 20 °C. However, for PDC cured at 60 °C, it is not the pore structure but the lack of available aluminate caused by the formation of hydrotalcite contributes to its sound sulfate resistance. The higher the dosage of dolomite from 10 to 30%, the larger amounts of hydrotalcite formation and the better the sulfate resistance. Hydrotalcite is stable in the presence of sulfate.

Investigations on three-dimensional pore-structure in cementitious materials using metal centrifugation porosimetry and simulation

Cementitious material is a vital composite for infrastructure, its 3D pore-structure determines its cement hydration as well as structural performance. However, the quantitative characterization of 3D pore-structure has yet been investigated in depth. In this study, the 3D pore-structure in hardened cement-paste is investigated systematically using innovative experiment and simulation methods. The experiment implements nano X-ray techniques combined with metal centrifugation porosimetry (X-MCP) for visualizing the 3D pore-structure and compared to that obtained by CEM3D-based model. The 3D pore-structure parameters containing the critical pore-diameter (dc) and porosity by X-MCP and CEM3D are counted and compared to those by mercury intrusion porosimetry (MIP). The results show that the dc values by X-MCP and CEM3D are both higher than those by MIP, and the porosity values obtained by the three methods agree with each other.

Seismic AVO statistical inversion incorporating poroelasticity

Seismic amplitude variation with offset (AVO) inversion is an important approach for quantitative prediction of rock elasticity, lithology and fluid properties. With Biot–Gassmann’s poroelasticity, an improved statistical AVO inversion approach is proposed. To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients, the AVO equation of reflection coefficients parameterized by porosity, rock-matrix moduli, density and fluid modulus is initially derived from Gassmann equation and critical porosity model. From the analysis of the influences of model parameters on the proposed AVO equation, rock porosity has the greatest influences, followed by rock-matrix moduli and density, and fluid modulus has the least influences among these model parameters. Furthermore, a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity, rock-matrix modulus, density and fluid modulus. Besides, the Laplace probability model and differential evolution, Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework. Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters, which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.

A Workflow Incorporating an Artificial Neural Network to Predict Subsurface Porosity for CO2 Storage Geological Site Characterization

The large scale and complexity of Carbon, Capture, Storage (CCS) projects necessitates time and cost saving strategies to strengthen investment and widespread deployment of this technology. Here, we successfully demonstrate a novel geologic site characterization workflow using an Artificial Neural Network (ANN) at the Southeast Regional Carbon Anthropogenic Test in Citronelle, Alabama. The Anthropogenic Test Site occurs within the Citronelle oilfield which contains hundreds of wells with electrical logs that lack critical porosity measurements. Three new test wells were drilled at the injection site and each well was paired with a nearby legacy well containing vintage electrical logs. The test wells were logged for measurements of density porosity and cored over the storage reservoir. An Artificial Neural Network was developed, trained, and validated using patterns recognized between the between vintage electrical logs and modern density porosity measurements at each well pair. The trained neural network was applied to 36 oil wells across the Citronelle Field and used to generate synthetic porosities of the storage reservoir and overlying stratigraphy. Ultimately, permeability of the storage reservoir was estimated using a combination of synthetic porosity and an empirically derived relationship between porosity and permeability determined from core.

Cake formation and filtration characteristics of a cyclone-granular bed filter

The dust cake is critical to improve the fine particle collection efficiency in the gas-solid separation process of the granular bed filter (GBF). In this work, the dust cake formation and the corresponding filtration characteristics in a cyclone-granular bed filter (C-GBF) were investigated by experiments under a constant-velocity filtering condition. It was found that cake filtration, deep-bed filtration and the corresponding transitional phenomena could be observed in the C-GBF. A critical porosity was defined to identify the transition from cake filtration to deep-bed filtration. A following parametric study showed that a higher filtration gas velocity could increase the critical porosity and made it more difficult to form a dust cake. It was also demonstrated that the critical porosity was little affected by the dust concentration. However, the time point of the transition of different filtration modes was earlier with a higher dust concentration. The inlet gas velocity ultimately resulted in the different dust concentrations into the GBF. The similar dynamic processes of cake formation were obtained for different granular sizes. These results provided a deeper understanding of the dynamic behaviors of cake formation and filtration mode transition, which played an important role in the design and the scaling-up of the C-GBF filtration systems.

On the bifurcation buckling and vibration of porous nanobeams

In the present paper, effects of porous material on bifurcation buckling and natural vibrations of nanobeams are investigated based on the higher-order nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. The displacements gradients are assumed to be small so that the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded porous material are expressed by nonlocal and length scale parameters and power-law variation of material parameters in conjunction with cosine functions to create a possibility to investigate the effect of diverse distributions of porosity on mechanics of nanostructures. Effect of Winkler-Pasternak foundation on mechanics of nanobeam is also considered. The Hamilton’s variational principle is utilized to derive governing equations of motion of the composite nanobeam. For the first time, the critical porosity is defined and examined for bifurcation buckling analysis of elastically supported nanobeams with symmetric distribution of porosity. Influence of axial forces and types of porosity distributions on eigenfrequencies of functionally graded nanobeams is studied. Classical theory without nonlocal effects is obtained as a special case and valid for all considered distributions of functionally graded material and volume fractions of voids.

Reservoir quality determination by using critical porosity and volume of clay: a case study in the Talang Akar Formation in the NW Java Basin, Indonesia

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Calibration of two rock-frame models using deterministic and probabilistic approaches: Application to a carbonate reservoir in south-west Iran

Calibration of the rock-frame elastic properties is an important step in establishing the rock-physics models for quantitative seismic reservoir characterization. While several empirical and theoretical rock-frame models have been proposed in the literature, their applicability to carbonate rocks is challenged due to their specific textural and varied pore type characteristics. Here, the suitability of an empirical model (Nur’s critical porosity), and a semi-empirical inclusion-based model (Keys-Xu) for a hard rock carbonate reservoir in south-west Iran is examined. Wireline log data in conjunction with deterministic and probabilistic optimization algorithms are employed to calibrate the free parameters in these models, as well as the minerals’ effective elastic moduli and density. The optimum values derived from the very fast simulated annealing algorithm were comparable to the estimated values from a probabilistic calibration workflow (Markov chain Monte Carlo sampling-based method). The uncertainty quantification via the probabilistic approach indicates higher uncertainty is associated with the calibrated clay elastic parameters (10%–13%) compared to the uncertainty associated with the calcite elastic moduli (1%–3%) in both rock-frame models. This could be attributed to the dominance of the calcite mineral and lack of variability in clay volume fraction in the interval of interest. The uncertainty associated with critical porosity and pore aspect ratio are 3% and 7%, respectively. The results of this case study show that simple rock frame models with only one free parameter (critical porosity or pore aspect ratio) could successfully model the elastic logs without resorting to more sophisticated rock-frame models.

Detachment of dilatant soil due to high hydraulic shear stresses explained

When soil surfaces are exposed to high shear stresses induced by high-velocity water flows, they erode. Erosion consists of the detachment, entrainment and transport of soil particles. When exposed to high shear stresses the process of soil detachment is no longer given by the pick-up of individual particles but by the continuous shear failure of layers of soil. The understanding of how soil properties influence the detachment rate of soil is lacking. This paper presents how the bed shear stress, initial and critical porosity, hydraulic conductivity, and density influence the detachment rate of dilatant soils which are subjected to high-velocity flows. Based on the constitutive mass and momentum balance equations it is hypothesized that the exchange of mass and momentum during soil detachment corresponds with that situation for which the dilatancy induced shear resistance of the soil is maximum. The hypothesis is validated against high-velocity erosion experiments on sand.

Critical conditions of tight oil charging and determination of the lower limits of petrophysical properties for effective tight reservoirs: A case study from the Fengcheng Formation in the Fengcheng area, Junggar Basin

Studying the lower limits of petrophysical properties is important to evaluate the exploration and development potentials of tight oil reservoirs. At present, the evaluation criteria are based on a large number of cores and logging data, and rules are based on collections of empirical statistics and displacement pressure experiments. However, there have been few studies on the lower limits of the petrophysical properties of tight reservoirs based on force balance conditions for the hydrocarbon charging process. In this paper, the critical condition for hydrocarbon charging is determined using the oil expansion pressure as the main driving force, with the capillary pressure as the major resistance, via an analysis of the dynamic mechanism of tight oil reservoirs. A force-balance model for judging the lower limits of the petrophysical properties of tight reservoirs can be established by assuming that the oil expansion pressure is equal to the capillary force. This discriminant method is applied to calculate the critical pore-throat radius of the effective reservoirs of the Lower Permian Fengcheng Formation in the Fengcheng area, Junggar Basin, which are 0.310 μm, 0.248 μm, 0.208 μm, and 0.135 μm, when the buried depths are 2500–3000 m, 3000–3500 m, 3500–4000 m, and 4000–4500 m, respectively. The corresponding critical porosities are 6.15%, 4.84%, 3.81%, and 1.20%, respectively. The lower limits of the petrophysical properties of effective tight reservoirs gradually decrease with increasing burial depth. This method is of great significance for resource evaluations of tight oil reservoirs and the selection of exploration zones.

Exploring the wet granulation growth regime map – validating the boundary between nucleation and induction

A methodological approach to define the regime map boundaries does not exist, and while some experimental data has been reported previously the boundaries have not been “validated”. The present study explored and quantified the boundary between the nucleation and induction growth regimes for a model high drug load formulation. It was postulated that the induction period could be decreased by increasing the liquid saturation of the system, with the effect of introducing additional binder liquid to the surface of the granules, which facilitates consolidation and growth. An increase in liquid saturation was achieved by increasing the liquid to solid ratio, or by densifying the granules to squeeze intragranular liquid to the surface. The densification was achieved by subjecting the granules to an extended wet massing period and by varying the impeller speed. By characterizing the response in granule porosity as a function of liquid to solid ratio, wet massing time and impeller speed the boundary between the nucleation and induction growth regimes was defined. Granules formed in the induction growth regime were shown to suffer significantly reduced compactibility. Further analysis of liquid saturation and compactibility data allows a critical granule porosity to be established as a basis for developing a control strategy. The attention to granule porosity allows a mechanistic interpretation of the growth behavior, rather than simply relying upon size measurements. The porosity based approach was successfully superimposed onto the existing growth regime map framework, and established that the boundary between regimes is a gradual transition rather than the conventionally visualized abrupt binary state.