Development of an on-demand foaming printhead for biofabrication of constructs with heterogeneous porosity

The heterogeneity maps for micropyretic synthesis of Ni–Al composite

Impacts of hydrological heterogeneities on caprock mineral alteration and containment of CO2 in geological storage sites

SummaryUnsaturated soils are solid‐water‐air systems that include a solid skeleton, pore water, and pore air. Heterogeneities in porosity or degree of saturation are salient features of unsaturated soils. These heterogeneities may trigger localized deformation (eg, shear banding) in such materials as demonstrated by numerical simulations via a pseudo three‐phase model. In this article, we formulate a true three‐phase mathematical framework implemented via stabilized low‐order mixed finite elements. With this mathematical framework, we study the evolution of pore air pressure and its role in the inception of strain localization triggered by initial heterogeneity either in porosity or suction. The numerical simulations show that pore air pressure is nonzero and nonuniform in the process of progressive failure in unsaturated soils. The heterogeneity of pore air pressure may also play a significant role in the onset of localized deformation of unsaturated soils. Therefore, a three‐phase model considering the pore air phase is physically more appropriate for modeling strain localization in unsaturated soils.

Evolution of sealing efficiency for CO2 geological storage due to mineral alteration within a hydrogeologically heterogeneous caprock

Sand sediments are inherently heterogeneous due to the random packing of the grains. For sound propagation through fluid-saturated sediments, these heterogeneities may lead to scattering from the coherent fast compressional wave into incoherent slow compressional waves or shear waves. This loss of energy from the fast compressional wave may account for the increase in high-frequency attenuation above that predicted by Biot theory. In a previous talk, we presented preliminary results of applying perturbation theory to Biot theory in order to model scattering from heterogeneities in the porosity [Hefner et al., J. Acoust. Soc. Am. 120, 3098 (2006)]. This theory has since been refined to properly account for scattering into both the slow compressional wave and the shear wave. In order to apply this theory to a given sand sediment, knowledge of the covariance function for the spatial variations in the porosity is required. Results of the theory will be presented for several different analytic covariance functions, as well as for covariance functions measured in simulated and real unconsolidated granular materials.

The numerical simulation of effects of the heterogeneities in composition and porosity on micropyretic synthesis

The influence of heterogeneous porosity on silicon nitride/steel wear in lubricated rolling contact

Effects of spatially heterogeneous porosity on matrix diffusion as investigated by X-ray absorption imaging

Numerical and experimental modelling of fluid–rock interactions with heterogeneous porosity

Reservoir heterogeneity is one of the key geological problems in the process of oil and gas exploration and development of clastic rocks. Understanding reservoir heterogeneity is imperative to improve the effectiveness of exploration and development. The primary porosity calculation model proposed by the authors in the previous study is used to calculate the primary porosity of samples from modern braided river sands and sandstone outcrops of braided sand bodies, and the primary porosity heterogeneity (PPH) model of the braided sand body is established. The architectural-elemental structures of braided sand bodies have obvious control effects on the distribution of its primary porosity heterogeneity. The central braided channel and braid bars have strong primary physical properties; the primary porosity is high and always greater than 38%. The contact areas between the braided channel and braided bars have a low value of primary porosity and are always lesser than 33%. The distribution characteristics of the present porosity of braided river reservoirs are also influenced by sedimentary architecture. To compare the relationship between PPH, present porosity heterogeneity (pPH), and sedimentary architecture (SA), the images of PPH, pPH, and SA were digital, graying, and normalized. The digital image Q-Q plots of the distribution probability of PPH, pPH, and SA are calculated. The results show that: the Q-Q plots of the probability distribution of present porosity and architectural-elemental structures (or lithofacies) can reflect the influence and degree of primary porosity and diagenesis on the present heterogeneity of the reservoir. The Q-Q plots of distribution probability primary porosity and present porosity identify the distribution areas; the points are always distributed on different lines. The line ‘y = x’, is derived from compaction and primary porosity; the line ‘y = ax, a > 1’, is derived from diagenesis, which is unfavorable to the reservoir porosity preservation (such as cementation); the line ‘y = ax, a < 1’ is derived from diagenesis, which is beneficial to reservoir porosity preservation (such as dissolution). Based on the Q-Q plots of distribution probability, the influence from primary porosity and diagenesis can be quantitatively analyzed. The influence of primary porosity on pPH in braided sand bodies of Ahe formation (Kuqa depression), middle Jurassic fluvial sandstone (Datong basin), and Karamay Formation (Junggar basin) were 19%, 90%, and 10%, respectively. A quantitative probability distribution Q-Q model of reservoir PPH and pPH is effective for reservoir physical modeling.

Influence of porosity and permeability heterogeneity on liquid invasion in tight gas reservoirs

The Meramec interval within the Sooner Trend Anadarko Canadian Kingfisher (“STACK”) play of the Anadarko Basin in central Oklahoma has recently been at the epicenter of increased exploration and production of oil and gas. It has become one of the top target intervals of the “mid-continent” aided by technological advancements in horizontal drilling and completion techniques. The Meramec interval, mainly composed of argillaceous siliciclastic sediments with varying amounts of carbonate cement, exhibits high porosity heterogeneity, which is theorized to be caused by varying amounts of clay and postdepositional calcite cement. Characterization of the porosity heterogeneity in the Meramec interval will improve our understanding of the wide range in Meramec oil and gas production volumes and reduce the risk associated with drilling and completion techniques. We completed an initial interpretation followed by inversion of 3D seismic data in which we generated a detailed characterization of the porosity heterogeneity and overall reservoir quality within the Meramec interval over an area of approximately 150 square kilometers. We then used the 3D seismic volume and available well logs to map the vertical and lateral extents of the Meramec interval and identify possible structural elements that could affect the reservoir quality. A petrophysical analysis of the well logs confirmed porosity heterogeneity and variations in volumetric calculations of clay and carbonate minerals. Finally, we generated a set of porosity volumes using the acoustic impedance from seismic inversion and probabilistic neural network methods. The derived porosity volume helped us identify porous and nonporous intervals within the Meramec throughout the study area. The results improved our understanding of Meramec heterogeneity, further reducing the risk associated with well planning, drilling, and completion.

Porosity heterogeneities in carbonate reservoirs occur at all scales, from the size of a reservoir delineated by seismic data and/or well-to-well correlations, down to microscales which can only be revealed by scanning electron microscopy. The origin of porosity heterogeneities is varied; some result from the depositional system, while others are products of burial, diagenesis and tectonism. Defining the three-dimensional distribution of textures and facies in a carbonate reservoir is exceedingly difficult. At present, carbonate specialists rely on cores to provide an understanding of decimetre to micron-scale textures and fabrics in carbonate reservoirs. Cores are rarely available from every well in a reservoir and usually do not cover the entire reservoir interval. Thus, the characterization of carbonate textures, fabrics, pore types, and porosity distribution using wireline well logs in uncored wells provides additional valuable information. Such an approach requires the integration of all of the available data, including acoustic, nuclear, electric, and dielectric measurements for reliable geological and petrophysical analyses. The wide range of possibilities coupled with the complexity of many carbonate reservoirs, however, generally means that both core and logs have to be acquired, at least in a few key wells. The evaluation of borehole electrical imagery in carbonate reservoirs from different depositional settings with a variety of diagenetic histories, indicates that this technique is providing valuable, and sometimes new, information about porosity heterogeneities. Electrical imagery, which has a high resolution and provides three-dimensional data, usually reveals more of the complexity of pore distributions than standard well logs are capable of. Large individual pores, fractures, and vugs are often directly visible in these images, although microscopic pores are below the resolution of the technique. The porosity fabric, or decimetre-scale distribution of microscopic integranular, intercrystalline and mouldic pores, is routinely defined, much as oil-saturated porosity in a core can be revealed by ultraviolet light. The correlation of electrical imagery with core samples, or drill cuttings in uncored intervals, can help to quantify the porosity fabric and also the geological interpretation of electrical texture and fabrics. On a decimetre-scale of examination, porosity is sometimes distributed homogeneously but is more commonly heterogeneous. In addition to vugs and fractures, there are four basic geometrical fabrics of decimetre-scale porosity. Layering is the most common, sometimes clearly associated with stratification. However, the thickness of porosity layers can be uniform or quite variable within the same formation. The next most common heterogeneous fabric is patchy porosity distribution. This fabric can either be patches of high porosity within low-porosity intervals or patches of low-porosity rock within porous reservoir zones. A common porosity fabric in Cretaceous and Tertiary carbonate shelf reservoirs is a three-dimensional convoluted continuous mixture of low- and high-porosity rock volumes. This porosity fabric is sometimes associated with isolated patches of either high- or low-porosity rock, although no obvious genetic transitions of these two fabrics have been observed in images, cores, or outcrops. The characteristics observed in electrical images must be summarized in a log format for large-scale correlation studies. Log summary plots of carbonate texture and fabric help to correlate long intervals of imagery with a variety of other data, including drill-cutting sample logs, other well-log data from the same well, and data from other wells. As specific porosity fabrics are generally associated with certain depositional or diagenetic facies, these log summaries also aid well-to-well correlation of facies. Many diagenetic and depositional facies with distinctive electrical fabrics are often not clearly defined by standard well logs because of the decimetre-scale averaging of rock properties by these logs.

A coupled thermal–hydraulic–chemical (THC) model was carried out in this paper to study the influence of rock heterogeneity and the coupling effect of temperature, groundwater, and hydrochemistry on rock damage. Firstly, the hydrochemical and hydraulic erosion equations were established. The equations of the coupled THC model were established by combining the hydrochemical and hydraulic erosion equations, the flow equations, and the heat transfer equations. Weibull distribution was adopted to govern the heterogeneity of initial rock porosity distribution. Secondly, the influence of the hydrochemistry, the temperature and the initial porosity heterogeneity on porosity and fluid velocity change was studied. Then the rock damage rule changed with time at different pH values and temperature was studied. Finally, an actual deep coal mine model was established to apply the THC model to predict water inrush. Results indicate that: (1) The average porosity and average fluid velocity approximately show linear growth and exponential growth with time, respectively, and their growth rates increase with decreasing pH value and increasing temperature in a certain acidity and temperature range. (2) The increase of initial porosity heterogeneity has little influence on porosity change, but it can increase the fluid velocity growth rate. The porosity heterogeneity and fluid velocity heterogeneity approximately show exponential growth with increasing time, and the rock heterogeneity growth contributes to form cracks. The increase of temperature and decrease of pH value have little influence on the porosity heterogeneity, but they can increase the growth rate of the fluid velocity heterogeneity. (3) The rock damage shows linear growth with time, and its growth rate increases with decreasing pH value and increasing temperature in a certain acidity range and temperature range. (4) The increase of rock heterogeneity can increase the possibility of water inrush.

A novel approach for modeling permeability decline due to mineral scaling: Coupling geochemistry and deep bed filtration theory