Showing papers in "Transport in Porous Media in 2015"

Anisotropy and Stress Dependence of Permeability in the Barnett Shale

Abstract: We document vertical permeability of $$2.3 \times 10^{-21}\, \hbox {m}^{2}$$ (2.3 nd) and horizontal permeability of $$9.5 \times 10^{-20}\, \hbox {m}^{2}$$ (96.3 nd) in two Barnett Shale samples. The samples are composed predominantly of quartz, calcite, and clay; have a porosity and a total organic content of $$\sim $$ 4 % each; and have a thermal maturity of 1.9 % vitrinite reflectance. Both samples exhibit stress-dependent permeability when the confining pressure is increased from 10.3 to 41.4 MPa. We measure a permeability anisotropy, the ratio of the horizontal to the vertical permeability, of $$\sim $$ 40. We find that the permeability anisotropy does not vary with effective stress. Multiscale permeability, as demonstrated by pressure dissipation, is related to millimeter-scale stratigraphic variation. We attribute the permeability anisotropy to preferential flow along more permeable layers and attribute the stress dependence to pore closure. A determination of permeability anisotropy allows us to understand flow properties in horizontal and vertical directions and assists our understanding of upscaling. Characterization of stress dependency allows us to predict permeability evolution during production.

Free Convection in a Square Cavity Filled with a Porous Medium Saturated by Nanofluid Using Tiwari and Das’ Nanofluid Model

Abstract: Free convection in a square differentially heated porous cavity filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation. The Tiwari and Das’ nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids has been used for numerical analysis. The governing equations have been solved numerically on the basis of a second-order accurate finite difference method. The developed algorithm has been validated by direct comparisons with previously published papers and the results have been found to be in good agreement. The results have been presented in terms of the streamlines, isotherms, local, and average Nusselt numbers at left vertical wall at a wide range of key parameters.

The Imaging of Dynamic Multiphase Fluid Flow Using Synchrotron-Based X-ray Microtomography at Reservoir Conditions

Abstract: Fast synchrotron-based X-ray microtomography was used to image the injection of super-critical \(\hbox {CO}_{2}\) under subsurface conditions into a brine-saturated carbonate sample at the pore-scale with a voxel size of \(3.64\,\upmu \hbox {m}\) and a temporal resolution of 45 s. Capillary pressure was measured from the images by finding the curvature of terminal menisci of both connected and disconnected \(\hbox {CO}_{2}\) clusters. We provide an analysis of three individual dynamic drainage events at elevated temperatures and pressures on the tens of seconds timescale, showing non-local interface recession due to capillary pressure change, and both local and distal (non-local) snap-off. The measured capillary pressure change is not sufficient to explain snap-off in this system, as the disconnected \(\hbox {CO}_{2}\) has a much lower capillary pressure than the connected \(\hbox {CO}_{2}\) both before and after the event. Disconnected regions instead preserve extremely low dynamic capillary pressures generated during the event. Snap-off due to these dynamic effects is not only controlled by the pore topography and throat radius, but also by the local fluid arrangement. Whereas disconnected fluid configurations produced by local snap-off were rapidly reconnected with the connected \(\hbox {CO}_{2}\) region, distal snap-off produced much more long-lasting fluid configurations, showing that dynamic forces can have a persistent impact on the pattern and sequence of drainage events.

Wettability Alteration in Carbonate Rocks by Implementing New Derived Natural Surfactant: Enhanced Oil Recovery Applications

Abstract: One of the robust and high-performance EOR methods which use chemical agents is chemical flooding. Environmental impacts, surfactant cost, and oil price are the three main parameters that affect on the robustness of the surfactant flooding in oil reservoirs. Interfacial tension reduction and wettability alteration of the reservoir rocks are the two main mechanisms of the oil recovery via employing surfactant flooding. The preliminary study about adsorption and environmental impacts of the new natural-based surfactant which derived from roots of Glycyrrhiza Glabra was investigated systematically by the authors and proved the ability of the aforementioned surfactant for EOR goals. Thanks to this point that throughout the current study, core displacement tests and qualitative and quantitative wettability experiments were carried out to specify performance of the above-mentioned natural surfactant in oil recovery. For wettability alteration measurements, contact angle measurement as a quantitative method, and floatation and two-phase separation experiments as qualitative methods were utilized. In addition, three commonly industrial surfactants were implemented throughout the wettability alteration experiments to contrast performance of the used surfactants. Thanks to the outcomes obtained from qualitative and quantitative wettability alteration experiments, and the surfactant suggested in this study could change wettability of carbonate rock from strongly oil-wet toward water-wet state. In addition, based on the core displacement experiments, it is robust, cheap, and high performance in comparison with other conventional industrial surfactants for surfactant flooding purposes. There is a hypothesis that the addressed raw surfactant can be utilized in chemical flooding of oil reservoirs owing to very low cost and availability around the world compared to other currently implemented surfactants.

Three-Dimensional Stochastic Characterization of Shale SEM Images

Abstract: Complexity in shale-gas reservoirs lies in the presence of multiscale networks of pores that vary from nanometer to micrometer scale Scanning electron microscope (SEM) and atomic force microscope imaging are promising tools for a better understanding of such complex microstructures Obtaining 3D shale images using focused ion beam-SEM for accurate reservoir forecasting and petrophysical assessment is not, however, currently economically feasible On the other hand, high-quality 2D shale images are widely available In this paper, a new method based on higher-order statistics of a porous medium (as opposed to the traditional two-point statistics) is proposed in which a single 2D image of a shale sample is used to reconstruct stochastically equiprobable 3D models of the sample Because some pores may remain undetected in the SEM images, data from other sources, such as the pore-size distribution obtained from nitrogen adsorption data, are integrated with the overall pore network using an object-based technique The method benefits from a recent algorithm, the cross- correlation-based simulation, by which high-quality, unconditional/conditional realizations of a given sample porous medium are produced To improve the ultimate 3D model, a novel iterative algorithm is proposed that refines the quality of the realizations significantly Furthermore, a new histogram matching, which deals with multimodal continuous properties in shale samples, is also proposed Finally, quantitative comparison is made by computing various statistical and petrophysical properties for the original samples, as well as the reconstructed model

A Lattice Boltzmann Model for Simulating Gas Flow in Kerogen Pores

Abstract: Nanoscale phenomena in kerogen pores could result in complicated non-Darcy effects in shale gas production, and so classical simulation approaches based on Darcy’s law may not be appropriate for simulating shale gas flow in shale. In general, understanding the shale gas transport mechanisms in a kerogen pore is the first and most important step for accurately simulating shale gas flow in shale. In this work, we present a novel lattice Boltzmann (LB) model, which can take account of the effects of surface diffusion, gas slippage, and adsorbed layer, to study shale gas flow in a kerogen pore under real gas conditions. With the Langmuir isothermal adsorption equation and the bounce-back/specular-reflection boundary condition, the gas–solid and gas–gas molecular interactions at the solid surface are incorporated into the LB model. Furthermore, the effects of surface diffusion and gas slippage on the free-gas velocity profile and mass flux in a kerogen pore are studied via the LB model. It is found that the free-gas velocity profile appears as a parabolic profile in a kerogen pore and the free-gas velocity at the center of the kerogen pore is apparently higher than that near the wall. In particular, we find that both surface diffusion and gas slippage can enhance the mass flux. Compared with gas slippage, surface diffusion is a more important factor on the shale gas transport in small pores, while it can be negligible in large pores.

Conjugate Heat Transfer in an Annulus with Porous Medium Fixed Between Solids

Abstract: Conjugate heat transfer is an important area of research which has been in demand due to its applications related to various scientific and engineering fields. The current research is focused to study the heat transfer in a porous medium sandwiched between two solid walls of an annular vertical cylinder. The prime focus of the current study was to evaluate the effect of solid wall thickness, the influence of variable wall thickness at inner and the outer radius, the conductivity ratio and the solid wall conductivity ratio on the heat transfer characteristics of the porous medium. The surface at inner and outer radii of the annulus is maintained isothermally at $$T_{h}$$ and $$T_{\infty }$$ such that $$T_{h}>T_{\infty }$$ . The governing partial differential equations for the conjugate heat transfer in porous medium and that of solid walls are converted into a set of algebraic equations with the help of finite element method and then solved simultaneously to predict the temperature variation in the solid wall as well as the porous region of the annular domain.

Computational Permeability Determination from Pore-Scale Imaging: Sample Size, Mesh and Method Sensitivities

Abstract: In this work, a complete work flow from pore-scale imaging to absolute permeability determination is described and discussed. Two specific points are tackled, concerning (1) the mesh refinement for a fixed image resolution and (2) the impact of the determination method used. A key point for this kind of approach is to work on enough large samples to check the representativity of the obtained evaluations, which requires efficient parallel capabilities. Image acquisition and processing are realized using a commercial micro-tomograph. The pore-scale flows are then evaluated using the finite volume method implemented in the open-source platform OpenFOAM®. For this numerical method, the influence of the different aspects mentioned above are studied. Moreover, the parallel efficiency is also tested and discussed. We observe that the level of mesh refinement has a non-negligible impact on permeability tensor. Moreover, increasing the refinement level tends to reduce the gap between the methods of computational measurements. The increase in computation time with the mesh is balanced with the good parallel efficiency of the platform.

Assessing the Water Migration and Permeability of Large Intact Bituminous and Anthracite Coals Using NMR Relaxation Spectrometry

Abstract: Although extensive literature has emerged on the use of nuclear magnetic resonance (NMR) relaxation spectrometry for the determination of various petrophysical properties of clastic rocks, relatively few papers have reported the use of NMR to determine the moisture migration process and permeability of large intact coals. In this study, evaporation experiments simultaneously with NMR measurements were conducted for seven coal core plugs. Differences in the relaxation time distribution at the various saturation stages provide both qualitative and quantitative information on the saturation state and migration of moisture in the coal samples. Moisture migration accrues first in the larger pores, whereas the smaller pores appear to remain water-saturated. The evaporation of moisture in large intact coals undergoes three continuous processes: Migration of free water, macro-capillary water, and micro-capillary water, among which, the migration rates of both macro-capillary water and micro-capillary water are related to the coal pore size distribution and porosity. The results of the NMR measurements also indicate that coal permeability has a relationship with the moisture migration characteristics, which make it possible to develop an NMR-derived permeability model. The Timur–Coates and the Schlumberger-Doll Research (SDR) equations, which are commonly used in NMR logging evaluations of the permeability of clastic rock reservoirs, were discussed concerning their application to coals. It is found that a modified SDR permeability evaluation model $$[K_\mathrm{SDR}=0.0224(\hbox {T}_\mathrm{2gm}^\mathrm{b})^{0.182}(\hbox {T}_\mathrm{2gm}^\mathrm{a})^{1.534}]$$ , which is a double-exponential relationship with the $$T_{2}$$ geometric mean in the full water-saturated state and in the bound water state, fits the analyzed coal samples well. The NMR-derived methods provide a framework for the determination of the moisture migration and permeability of coals.

Nanoscale Pores in Coal Related to Coal Rank and Deformation Structures

Abstract: Experimental results show that nanoscale pores in coal are affected by coal rank and deformation structures. In terms of pore volume, the transitional pores occupy the largest proportion, and in terms of specific surface area, the sub-micropores take up the largest proportion. For weak brittle deformed coal (including normal structured coal), when the coal rank increases, the volume and specific surface area of pores in different sizes firstly decrease and then increase. The volume and specific surface area of transitional pores and micropores in coal reach the minimum at about $${R}_\mathrm{O, ran} = 2.0\,\%$$ . After that, a slow increasing trend is observed. The volume of sub-micropores reaches the minimum at about $${R}_\mathrm{O, ran}= 1.5\,\%$$ and then shows a trend of rapid growth as coal rank increases. As the degree of coal deformation increases, both pore volume and specific surface area have a significant increase. Under strong tectonic deformation, both the volume and total specific surface area of the nanoscale pores and of sub-micropores increase significantly; the volume of transitional pores increases moderately, and their specific surface area shows a decreasing trend; the volume and specific surface area increments of micropores decline rapidly as the degree of metamorphism increases.

Free-Flow–Porous-Media Coupling for Evaporation-Driven Transport and Precipitation of Salt in Soil

Abstract: Evaporative salinization of soil is a common issue observed in arid and coastal regions. This process is driven by mass, momentum and energy exchange between the porous medium and the free-flow region. To analyze such coupled systems, we present a representative elementary volume-scale model concept for coupling non-isothermal multi-phase compositional porous-media flow and single-phase compositional laminar free flow. Our numerical results illustrate evaporation behavior from a porous medium initially saturated with NaCl solution, manifesting its influence on dissolved salt distribution, salt precipitation and porous-media properties. We show that the new model is capable to capture the evaporation physics for different stages of evaporative salinization and compare the numerical results to two different experimental datasets: (1) cumulative mass loss of water and dissolved salt during stage-1 of saline water evaporation and (2) evaporation rate for different stages of evaporative salinization. In addition, influence of the initial salt concentration on the saline water saturation vapor pressure and transition to stage-2 evaporation are analyzed and discussed.

Wettability Alteration of Reservoir Rocks from Liquid Wetting to Gas Wetting Using Nanofluid

Abstract: Well productivity in gas condensate reservoirs is reduced by condensate banking when the bottom hole flowing pressure drops below the dew point pressure. Among the several methods which have been proposed for condensate removal, wettability alteration of reservoir rock to intermediate gas wetting in the near wellbore region appears to be one of the most promising techniques. In this work, we report use of a nanofluid to change the wettability of the carbonate and sandstone rocks to intermediate gas wetting. Application of nanofluid in the wettability alteration of carbonate and sandstone rocks to gas wetting has not been reported previously and is still an ongoing subject. Static and dynamic contact angle measurements, along with imbibition tests, have been performed to investigate the wettability of carbonate and sandstone rocks in presence of nanofluid. It was found that the nanofluid used in this work can considerably change the wettability of both surfaces to preferentially gas wetting in just one day of ageing time. We also report the effect of initial oil saturation and ageing time on the nanofluid capability for wettability change. Initial oil saturation reduces the impact of the nanofluid on wettability change, and hence, a pre-treatment before using nanofluid is necessary. In addition to these small slab-scale experiments, applicability of nanofluid in wettability alteration of sandstone rocks to gas wetting is also investigated in core scale. The results of core displacement tests confirm the ability of nanofluid to change the rock wettability from liquid wetting to gas wetting in core samples. They also show the effectiveness of chemical treatment in subsurface conditions.

Field-Scale Simulation of Production from Oceanic Gas Hydrate Deposits

Abstract: The quantity of hydrocarbon gases trapped in natural hydrate accumulations is enormous, leading to a significant interest in the evaluation of their potential as an energy source. It has been shown that large volumes of gas can be readily produced at high rates for long times from some types of methane hydrate accumulations by means of depressurization-induced dissociation, and using conventional horizontal or vertical well configurations. However, these resources are currently assessed using simplified or reduced-scale 3D or 2D production simulations. In this study, we use the massively parallel TOUGH+HYDRATE code (pT+H) to assess the production potential of a large, deep ocean hydrate reservoir and develop strategies for effective production. The simulations model a full 3D system of over $$38\hbox { km}^{2}$$ extent, examining the productivity of vertical and horizontal wells, single or multiple wells, and explore variations in reservoir properties. Systems of up to 2.5 M gridblocks, running on thousands of supercomputing nodes, are required to simulate such large systems at the highest level of detail. The simulations reveal the challenges inherent in producing from deep, relatively cold systems with extensive water-bearing channels and connectivity to large aquifers, mainly difficulty of achieving depressurization and the problem of enormous water production. Also highlighted are new frontiers in large-scale reservoir simulation of coupled flow, transport, thermodynamics, and phase behavior, including the construction of large meshes and the computational scaling of larger systems.

Drying, Shrinkage, and Cracking of Cementitious Materials

Abstract: Concrete is a heterogeneous, reactive, viscoelastic material whose shrinkage during drying often results in cracking that compromises its durability. This paper reviews the principles of shrinkage and stress development during drying of cement paste and concrete, taking particular account of the changes in microstructure as the cement hydrates, which profoundly influence the transport and mechanical properties of the body.

Relative Permeability of Coal: A Review

Abstract: Coalbed methane (CBM), once a hazard to the undermining safety, is becoming an important addition to the global energy supply. Injecting carbon dioxide \((\hbox {CO}_{2})\) into coal seams not only aids to enhance CBM production but also offers an option of \(\hbox {CO}_{2}\) sequestration helpful for the reduction of greenhouse gas release. Multiphase flow occurs in those cases as most coalbeds are initially saturated with water. Accurate determination of relative permeability of coal plays an important role in the prediction and evaluation of those operations because it is in effect the effective permeability (absolute permeability multiplied by relative permeability) to gas/water rather than absolute permeability that controls the flow in coal seams. To date, varying methods have been reported of obtaining relative permeability curves of coals through either laboratory tests or field data analysis, which are reviewed in this paper. Also, this paper includes a summary of the characteristics of relative permeability curves of coals, relative permeability models, effects of varying factors on curves and effects of the curves on CBM production. This paper concludes that despite the importance of relative permeability in CBM-related operation process, limited research efforts have been paid on improvements concerning this subject in the past two decades: the advance in the research of relative permeability-related subjects can barely keep up with the rate at which the developments of CBM and \(\hbox {CO}_{2}\)-ECBM projects are booming worldwide. More efforts are needed to conduct related investigations such that a reliable standard or workflow can be established that can as accurately determine coal relative permeability with repeatability.

An Integrated Method for Upscaling Pore-Network Characterization and Permeability Estimation: Example from the Mississippian Barnett Shale

Abstract: Although pore-network characterization of shale rock systems is being actively investigated, a detailed understanding of the pore network at the nanometer-to-millimeter scale has not been completed. This is because of the technical limitations of collecting and integrating data at the wide spectrum of scales necessary to understand the pore network. Permeability for a micrometer-scale volume can be estimated based on pore-scale modeling for the focused ion beam/scanning electron microscope (FIB/SEM) milled 3D pore network; however, it is not clear how representative this permeability is for larger volumes. In this study, an integrated method employing FIB/SEM, helium ion microscopy, and synchrotron X-ray micro-computed tomography (micro-CT) was developed and applied to a Barnett Shale sample for pore and organic-matter distribution network characterization and upscaling. Organic-matter particle network characterization using synchrotron micro-CT scanning is the key step that bridges the gap between nanometer-scale and macroscopic observations. A conceptual model and an empirical equation were developed for permeability estimation based on FIB/SEM and micro-CT image analysis and mercury intrusion data. Upscaled permeability estimation was produced based on the empirical equation and parameters from the image and mercury intrusion analysis. The resulting permeability values of 2–22 and 0.6–3 nD for parallel and perpendicular to bedding planes, respectively, are comparable to laboratory measurements of the same sample. The proposed technique provides a method for more basic understanding of the pore network and pore-permeability relationship for organic-rich shale samples, and can serve as a basis for further upscaling to core and formation scale.

Drying with Formation of Capillary Rings in a Model Porous Medium

Abstract: Modelling of drying processes without adjustable parameters is still a challenge. As emphasized in several previous works, this might partly be due to the impact of liquid films trapped in corners of the pore space. In this study, we present and analyse a drying experiment with a micromodel, which clearly shows the presence of corner films. In contrast with previous works, however, the corner films do not form a system of interconnected corner films extending over large regions in our micromodel. They rather form isolated capillary rings surrounding the solid blocks of the device, and thus, a quasi-two-dimensional version of liquid bridges often observed in the contact regions between grains in soils and packings of particles. These capillary rings essentially remain confined in the two-phase region. As a result, their impact on drying rate is much smaller than in systems favouring films hydraulically connected over long distances. The capillary liquid ring formation is taken into account in a pore network model of drying leading to satisfactory agreement with the experiment provided that the lateral pinning of liquid phase observed in the experiment is included in the model. Based on this, the model enriches the family of pore network models of drying and can be considered as a step towards the modelling of secondary capillary effects in drying in more complex geometry.

Effects of Organic Micromolecules in coal on its Pore Structure and Gas Diffusion Characteristics

Abstract: Coal has complex pore structures including micro-, meso-, and macropores and cracks, and contains organic micromolecules. To in-depth study the effects of organic micromolecules in coal on the pore structure and gas diffusion characteristics, organic micromolecules were extracted by tetrahydrofuran using microwave-assisted method from anthracite and bituminous coal samples to obtain the residual coal samples at 50 $$^{\circ }$$ C and atmospheric pressure. Changes in raw and residual coal samples were explored using a series of methane desorption and low-temperature nitrogen adsorption experiments and their pore structure parameters were compared using samples with same granule size (0.180–0.250 mm). The results showed that (1) although the micropores of both raw and residual coal granules are characterized by fractal, residual coal has lower fractal dimension than raw coal; (2) residual coal samples have higher gas emission amount and rate than the raw coal samples and lower gas diffusion resistance, indicating that gas in residual coal is easier to flow from micropores through mesopores into macropores and cracks. Based on the fractal theory and the diffusion model, extraction of organic micromolecules increased the number and diameter of pores and cracks and dredged the rawly clogged pores and cracks, all of which decreased the resistance of gas diffusion in the coal matrix. In addition, extraction of organic micromolecules has the most obvious effect on diffusion pores. After extraction, the proportion of meso-/macropores increased, while that of micropores reduced, thereby reducing the resistance of gas flowing from micropores through mesopores into macropores and cracks, and subsequently increasing the amount and rate of gas emission. The study is of great significance for pushing forward the boundary of our recognition of the influences exerted by micromolecules on gas diffusion.

Hydraulic Operating Conditions and Particle Concentration Effects on Physical Clogging of a Porous Medium

Abstract: The effects of the hydraulic operating conditions and the concentration of suspended particles (SP) in pore fluid on the filtration and physical clogging of a porous medium were investigated. Polydisperse kaolinite SP was injected into a sand-filled column under two different operating conditions: constant flow rate and constant head. The retention rate was observed to be greater under the condition of constant head than under the condition of constant flow rate, mainly for the high concentrations. Under constant head, the porous medium were clogged more rapidly; the pore velocities decreased with time and the permeability reduction occurred in fewer pore volumes injected than under constant flow rate. Under the same hydraulic condition, an increase of the concentration leads to a more rapid reduction in permeability. Regardless of the hydraulic operating conditions, particle-size analysis shows an increase with time of the median diameter of the particle-size distribution of the recovered particles. At the beginning of the filtration process, larger particles are mainly retained in the column. As the injection volume increases, the larger particles are better transported and the size of particles observed in the effluent gradually increases. It appears that the median diameter of the recovered SP increases more rapidly with time under constant flow rate.

Coupled THM Modeling of Hydroshearing Stimulation in Tight Fractured Volcanic Rock

Abstract: In this study, we use the TOUGH-FLAC simulator for coupled thermo–hydro-mechanical modeling of well stimulation for an Enhanced Geothermal System (EGS) project. We analyze the potential for injection-induced fracturing and reactivation of natural fractures in a porous medium with associated permeability enhancement. Our analysis aims to understand how far the EGS reservoir may grow and how the hydroshearing process relates to system conditions. We analyze the enhanced reservoir, or hydrosheared zone, by studying the extent of the failure zone using an elasto-plastic model, and accounting for permeability changes as a function of the induced stresses. For both fully saturated and unsaturated medium cases, the results demonstrate how EGS reservoir growth depends on the initial fluid phase, and how the reservoir extent changes as a function of two critical parameters: (1) the coefficient of friction, and (2) the permeability-enhancement factor. Moreover, while well stimulation is driven by pressure exceeding the hydroshearing threshold, the modeling also demonstrates how injection-induced cooling further extends the effects of stimulation.

Anti-correlated Porosity–Permeability Changes During the Dissolution of Carbonate Rocks: Experimental Evidences and Modeling

Abstract: The dissolution of carbonate rocks usually leads to both porosity $$(\phi )$$ and permeability $$(k)$$ increase We present experimental evidences and physical-based models of positive and anti-correlated dynamics of $$k$$ and $$\phi $$ observed during dissolution experiments of carbonate rocks We study the way the rate of change of $$\phi $$ and $$k$$ is controlled by the degree of undersaturation of the percolating solution for two different types of carbonate rocks We document the occurrence of an anti-correlated $$k-\phi $$ trend when the flowing fluid (deionized water) has a weak capacity of dissolution A positive correlation is found when $$\hbox {CO}_{2}$$ is added to the deionized water to increase the potential dissolution rate Detailed analyses of the microstructures of the rock performed by X-ray microtomography reveal that low dissolution rate favors detachment of solid particles and their subsequent accumulation at the pore-throat inlet Particles are detached from the rock matrix due to the differential dissolution rate of the indurated grains and the microporous cement We then propose a simple phenomenological model to interpret the effect of the pore-throat clogging by the accumulation of partially dissolved carbonate particles We conjecture that permeability is controlled by the decrease of the effective hydraulic radius and the increase of the tortuosity due to partial and localized obstruction of the pore network Conversely, increasing the level of undersaturation of the flowing solution leads to an augmented potential of dissolving most of the transported particles before they reach the throats In this case, both $$k$$ and $$\phi $$ increase and display power-law correlations

Double-Diffusive Mixed Convection in a Porous Open Cavity Filled with a Nanofluid Using Buongiorno’s Model

Abstract: This work examines the steady double-diffusive mixed convection flow in a porous open cavity filled with a nanofluid using mathematical nanofluid model proposed by Buongiorno. The analysis uses a two-dimensional square cavity of size $$L$$ with an inlet of size $$0.2\cdot L$$ in the bottom part of the left vertical wall and an outlet of the same size in the upper part of the right vertical wall. The mathematical problem is represented by non-dimensional governing equations along with the corresponding boundary conditions, which are solved numerically using a second-order accurate finite difference method. The developed algorithm has been validated by direct comparisons with previously published papers, and the results have been found to be in good agreement. Particular efforts have been focused on the effects of the key parameters on the fluid flow, heat and mass transfer characteristics. In addition, numerical results for the average Nusselt and Sherwood numbers are presented in tabular forms for various parametric conditions and discussed.

Effects of Grain and Pore Size on Salt Precipitation During Evaporation from Porous Media

Abstract: Salt precipitation in saline porous media during evaporation is important in many processes including $$\hbox {CO}_{2}$$ sequestration, soil salinity which is a global problem as well as the preservation of monuments and buildings. In this study, X-ray micro-tomography was used to investigate the evolution of salt precipitation during evaporation to study the effects of particle and pore sizes on salt precipitation patterns and dynamics. The packed beds were saturated with NaCl solution of 3 Molal, and the time-lapsed X-ray imaging was continued for one day to obtain pore- scale information associated with the evaporation and precipitation dynamics and patterns. The results show that the presence of preferential evaporation sites (associated with fine pores) on the surface of the sand columns influences significantly the patterns and dynamics of NaCl precipitation. They confirm the formation of an increasingly thick and discrete salt crust with increasing grain size in the sand column due to the presence of fewer fine pores (preferential precipitation sites) at the surface compared to the sand packs with finer grains. Fewer fine pores on the surface also result in shorter stage-1 precipitation for the columns with larger grain sizes. A simple model for the evolution of salt crust thickness based on this principle shows a good agreement with our experiments. The findings of this study offer new insights about the dynamics and patterns of salt precipitation in drying porous media.

Stress-jump and Continuity Interface Conditions for a Cylinder Embedded in a Porous Medium

Abstract: The selection of interface boundary conditions between porous-medium and clear-fluid regions is very important for the wide range of engineering applications. In this paper, the difference between two common types of fluid flow interfacial conditions between clear fluid and porous medium is analyzed in detail. These two types of fluid flow interfacial condition are stress-jump and stress-continuity conditions. The effects of porosity on these types of interface condition are studied. The results are presented for different Reynolds numbers in the range 1–40, porosity equal to 0.4 and 0.8 and Darcy number $$Da=5\times 10^{- 4}$$ . In this study, the Darcy–Brinkmann–Forchheimer model is used to model the momentum transfer in the porous medium. The dimensionless governing equations consisting of continuity and momentum equations are discretized using control volume technique. The set of algebraic discretized coupled equations is solved using SIMPLE algorithm. It was found that for high porosity (i.e., $$\varepsilon =0.8)$$ , there is a large difference between two boundary conditions for the velocity profile along the horizontal and vertical directions in the porous layer.

Patterns of Desiccation Cracks in Saline Bentonite Layers

Abstract: Formation of cracks as a result of desiccation is a ubiquitous phenomenon in nature which is influenced by various factors including the environmental conditions, the properties of soil and the evaporating fluid. In this work, a comprehensive series of experiments is conducted to investigate the salinity effects on patterns formation during desiccation of bentonite layers. To do so, mixtures of bentonite and NaCl solutions were prepared with salt concentrations ranging from 3 to 15 %. The mixture was placed in a petri dish mounted on a digital balance to record the evaporation dynamics in an environmental chamber in which the ambient temperature and relative humidity were kept constant. An automatic digital camera was used to record cracking dynamics formed during the desiccation of clay layers. Results illustrated that the salt concentration had significant effects on the initiation, propagation, morphology and general dynamics of cracks. It was found that higher salt concentrations resulted in larger crack lengths due to the effects of NaCl on colloidal interactions among particles as well as the drying behavior. Additionally, using scanning electron microscopy, the influence of salt concentration on the patterns of cracks was investigated at different scales down to a few hundred nanometers. The present results provide new insights into the salinity effects on the cracking patterns and dynamics during desiccation of clay layers.

A Multi-Scale Investigation of Pore Structure Impact on the Mobilization of Trapped Oil by Surfactant Injection

Abstract: The evolution of the residual oil saturation as a function of the trapping number $$N_\mathrm{t}$$ (capillary number plus Bond number), is generally known as the capillary desaturation curve (CDC) and constitutes an important input parameter in chemical enhanced oil recovery flooding. However, less importance has been paid to the investigation of the influence of oil ganglia evacuation on relative permeabilities. We report on an experimental investigation dealing with the effect of flooding parameters, fluid interfacial properties and rock structure on the CDC and on the water relative permeability. Experiments were performed on a set of water-wet sandstone plugs with different petrophysical properties, and X-ray computed tomography (CT-scan) imaging was used to accurately measure the local oil saturation. Oil ganglia size distribution as well as pore scale geometrical properties was also quantified at the scale of the micrometer using high-resolution micro-computed tomography (MCT). Results showed that the CDC depends on the pore structure and specifically on the average throat radius and the inverse of the relative permeability. Oil ganglia size distribution obtained by MCT follows a typical power law as suggested by percolation theory. We also showed that CDC obtained from macroscopic measurements can be predicted from the measured oil ganglia size distribution and rock structure geometrical parameters. In parallel, we observed that for low trapping numbers, water relative permeability is independent of the trapping number. However, for intermediate trapping numbers, a strong dependence of the water relative permeability on the latter can be noticed. In this range, we showed that water relative permeability has a specific scaling with the trapping number.

Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data

Abstract: A new method is proposed for geostatistical simulation and reconstruction of porous media by integrating hard (quantitative) and soft (qualitative) data with a newly developed method of reconstruction. The reconstruction method is based on a cross-correlation function that we recently proposed and contains global multiple-point information about the porous medium under study, which is referred to cross-correlation-based simulation (CCSIM). The porous medium to be reconstructed is represented by a reference image (RI). Some of the information contained in the RI is represented by a training image (TI). In unconditional simulation, only the TI is used to reconstruct the RI, without honoring any particular data. If some soft data, such as a seismic image, and hard data are also available, they are integrated with the TI and conditional CCSIM method in order to reconstruct the RI, by honoring the hard data exactly. To illustrate the method, several two- and three-dimensional porous media are simulated and reconstructed, and the results are compared with those provided by the RI, as well as those generated by the traditional two-point geostatistical simulation, namely the co-sequential Gaussian simulation. To quantify the accuracy of the simulations and reconstruction, several statistical properties of the porous media, such as their porosity distribution, variograms, and long-range connectivity, as well as two-phase flow of oil and water through them, are computed. Excellent agreement is demonstrated between the results computed with the simulated model and those obtained with the RI.

Pore-Morphology-Based Simulation of Drainage in Porous Media Featuring a Locally Variable Contact Angle

Abstract: Since the first publications by Hazlett (Transp Porous Med, 20:21–35, 1995) and Hilpert and Miller (Adv Water Res, 24:243–255, 2001), the pore-morphology-based method has been widely applied to determine the capillary pressure–saturation curves of porous media. The main advantage of the method is the simulation of a primary drainage process for large binary images using moderate computational time and memory compared to other two-phase flow simulations. Until now, the pore morphology model was restricted to totally wetting materials or those with a constant contact angle. Here, we introduce a similarly computationally efficient extension of the model that now enables the calculation of capillary pressure–saturation curves for porous media, where the contact angle varies locally within, due to a composite structure.

A Sensitivity Study of the Effect of Image Resolution on Predicted Petrophysical Properties

Abstract: Micro-CT scanning is a nondestructive technique that can provide three-dimensional images of rock pore structure at a resolution of a few microns We compute petrophysical properties on three-dimensional images of benchmark rocks: two sandstones (Berea and Doddington) and two limestones (Estaillades and Ketton) We take scans at a voxel size of approximately 27 $$\upmu \hbox {m}$$ and with $$1024^3$$ voxels for both sandstone and limestone rocks We numerically upscale the images to image sizes of $$512^3, 256^3$$ and $$128^3$$ , representing voxel sizes of around 54, 108, and 216 $$\upmu \hbox {m}$$ respectively, covering the same domains with coarser resolution We calculate porosity and permeability on these images by using direct simulation and by extracting geometrical equivalent networks We find that the predicted porosity is fairly insensitive to resolution for sandstones studied with the selected range of resolutions but sensitive for limestones with lower porosity for larger voxel sizes For the permeability predictions, we do not observe a clear trend in permeability as a function of voxel size; however, sandstones, roughly, have comparable permeability regardless of the voxel size On the other hand, for limestones, we generally see a decreasing trend in permeability as a function of upscaled voxel size

Effects of Airflow Induced by Rainfall Infiltration on Unsaturated Soil Slope Stability

Abstract: The aim of this study was to investigate the characteristics of airflow induced by rainfall infiltration and their effects on unsaturated soil slope stability using numerical methods. The TOUGH2/EOS3 simulator was used to analyze the features of water–air two-phase flow in a soil slope under rain conditions. The results show that when the rain infiltrates the soil, the air is pushed into the soil by the advancing wetting front, the pore-air pressure in the unsaturated zone increases firstly, then the airflow is reversed, and the pore-air pressure decreases until it is close to atmospheric pressure. The features of water single-phase flow (i.e., the gas phase is neglected) were also simulated using the TOUGH2/EOS9 simulator. When the infiltration of rainwater into the soil slope in the water single-phase flow model is set as same as that in the water–air two-phase flow model, the water saturation and the capillary pressure distributions in the unsaturated zone are probably the same. Slope stability studies were then performed based on the simulated water–air two-phase and water single-phase seepage conditions, respectively. The slope stability analysis on a given slip surface based on the simulated water–air two-phase seepage condition shows that the safety factor decreases during rainfall, reaches the lowest value when rain stops, generates immediately a sudden rise, and then increases slowly to a steady value. The capillary pressure is beneficial to slope stability, while the pore-air pressure is unfavorable to slope stability. The variation tendency of the safety factor is similar to that of the negative total air pressure acting on the slip surface. The slope stability analysis on the given slip surface based on the water single-phase seepage condition shows that the safety factor is approximate to FS1 (is the safety factor for the case that does not take into account the air pressure based on the water–air two-phase seepage condition). Therefore, difference between the safety factor and FS1 based on the water–air two-phase seepage condition can approximately represent the effects of airflow induced by rainfall on unsaturated soil slope stability under the condition that the infiltration of rainwater into the soil slope remains unchanged.