Complex Pore Geometry Research Articles

Complex resistivity spectra and pore geometry for predictions of reservoir properties in carbonate rocks

Measurements of complex resistivity spectra (CRS) are performed on core plugs from a wide variety of carbonates in a log sweep from 0.1 to 100,000Hz inside a pressurized chamber at varying effective pressures up to 20MPa. We quantify the CRS curves by extracting the slope of both real and imaginary part of complex resistivity in the 10,000–100,000Hz range. Pore geometries are quantified with thin-section digital image analysis (DIA) from optical light microscopy. The dataset includes 330 carbonate core plug samples from twelve different study areas and hence includes a highly diverse range of carbonate rock types. This should make our results applicable to most carbonate rocks.Pore geometry parameters derived from DIA, such as Dominant Pore Size (DOMsize) and Perimeter over Area (PoA), correlate well with petrophysical properties such as cementation factor and permeability. However, when modeling those properties, higher correlation coefficients are achieved with CRS than with DIA parameters. Using CRS and model constants tuned to the sub-datasets, cementation exponents are predicted with R2=0.91 and permeability with R2=0.84. The correlation coefficient of a universal equation for all 330 samples is still high for cementation factors with R2=0.80, but less for permeability with R2=0.48.The results show that CRS in carbonates are directly related to permeability and formation factors, and greatly improve reservoir property estimates. This study also highlights the usability of low-frequency CRS data as a measure of flow and storage properties in carbonate rocks. The transfer of this methodology to wireline applications would result in more accurate and continuous permeability and cementation factor predictions from well logs.

Use of differential scanning calorimetry to study phase behavior of hydrocarbon mixtures in nano-scale porous media

The phase behavior of petroleum fluids is a challenging problem in shale oil and gas production. Due to strong surface-fluid interactions and complex pore geometries in shale nanopores, PVT properties of fluids in shale are altered from those of conventional reservoirs and cannot be described by bulk-phase thermodynamics. To our best knowledge, the experimental data for hydrocarbon phase behavior in shale systems is severely absent. The experimental difficulty lies in introducing the nanoporous environment and finding an effective technique to study the fluid-nanoporous media system.In this work, we investigate the phase change of mixtures of hydrocarbons in nano-scale capillaries using a thermal laboratory technique, differential scanning calorimetry (DSC), which probes the thermal properties by measuring the heat exchange evolution of a sample during a temperature ramp. Porous media controlled-pore glasses (CPGs) are applied to model the nano-porous structure of shale reservoirs. CPGs (pore diameters 4.1 and 37.9nm) infiltrated with hydrocarbons (octane and decane binary mixtures) are subjected to DSC. It is observed that at 37.9nm the bubble point shift is negligible, but at 4.1nm two distinct vaporization incidents occur with deviations as great as ∖xB120K relative to the bulk. The unusual observation of bubble points for mixtures in 4.1nm pores suggests compositional heterogeneity in the nanopore.The bubble point is modeled using Peng-Robinson equation of state (PR EOS) with the capillary pressure considered. The flash calculation is performed based on isofugacity and an interfacial tension model is accommodated. The modeling gives an exaggerated bubble point temperature shift and does not match the experimental results. This suggests the poor accuracy of the PR EOS/capillary pressure model in describing the behavior of nanoconfined fluid mixtures.

Directional-Permeability Assessment in Formations With Complex Pore Geometry With a New Nuclear-Magnetic-Resonance-Based Permeability Model

Summary This paper proposes a new method for directional-permeability assessment with nuclear-magnetic-resonance (NMR) measurements. Conventional techniques for permeability assessment from NMR measurements include empirical correlations such as SDR (Schlumberger-Doll-Research) and Coates models. However, carbonate rocks are known for lack of good correlations between pore-body-size and pore-throat-size, which makes it challenging and often unreliable to estimate permeability from NMR T2 (spin-spin relaxation time) distribution in carbonate formations with complex pore structure. It also was proposed that conventional permeability models can be improved by incorporating an estimated pore-connectivity factor. However, none of the previously introduced techniques reflects the anisotropic characteristics of rock permeability. The new NMR-based directional-permeability model, introduced in this paper, incorporates a directional pore-connectivity factor into a conventional NMR-based permeability model. We introduce two approaches to quantify the directional pore-network connectivity of rock samples with pore-scale images. The first approach calculates directional pore connectivity in 3D pore-scale images with a topological technique. The second approach combines image analysis and electrical formation factor. The new NMR-based permeability model enables assessment of rock permeability in any desired direction. We successfully calibrated and tested the introduced NMR-based permeability model on carbonate, sandstone, and sandpack samples with complex pore geometry or anisotropic permeability. The anisotropic permeability used for calibration and test purposes was obtained by the lattice Boltzmann method (LBM) simulations on microcomputed tomography (CT) images of rock samples. The comparison between the permeability estimates with our new NMR model and conventional NMR models (e.g., SDR and Coates models) demonstrated that the NMR-based directional-permeability model significantly improves assessment of rock permeability, by reflecting rock's anisotropic characteristics and minimizing calibration efforts. The outcomes of this research can significantly improve permeability assessment in complex carbonate reservoirs and anisotropic sandstone reservoirs, and can be extended further to organic-rich mudrock formations.

Does Biot’s theory have predictive power?

Biot’s theory of elastic waves in fluid-saturated porous solids has two free parameters: the tortuosity α, characterizing the dynamic coupling between the solid and the fluid, and the structural factor δ, representing the geometric properties of the porous space. The meaning and significance of these parameters have not been sufficiently understood. The tortuosity has the physical meaning of the normalized mean square of the velocity of the pore fluid relative to the solid wall; it has a low-frequency but no high-frequency limits. The analytical calculation of the tortuosity for Biot’s slit-like pore provides its range of variability from approximately 1–100 in the frequency range of practical interest. The tortuosity has a significant effect on the properties of the Biot waves of the second kind in the high-frequency range. On the other hand, in realistically complex pore geometries, the values of the tortuosity are virtually unpredictable. This limits the usefulness of the Biot theory in predicting the wave propagation at high frequencies. At all frequencies, the effect of the structural factor is insignificant relative to the effect of the tortuosity. The conventional compressional wave (the wave of the first kind) is insensitive to both parameters at all frequencies. The frequencies of interest to seismic exploration are also free of the uncertainty imposed by the lack of constraints on the tortuosity as the only free parameter in Biot’s theory.

Direct simulation of supercritical gas flow in complex nanoporous media and prediction of apparent permeability

Mudrocks and shales contain pores within the size range of 2–100nm. Flow of supercritical gas in these pores at reservoir pressure–temperature conditions falls within the slip-flow and early transition-flow regime (0.001<Kn<1.0). Currently, the description of supercritical gas flow in these flow regimes is mostly limited to simple tube and channel geometries that are of limited applicability to the sponge-like or platy nanoporous geometry in organic matter or clays. Here, we present a local-effective-viscosity multi-relaxation-time lattice Boltzmann model (LEV-LBM) designed to simulate gas flow in the slip- and early-transition-flow regimes in complex geometries. The LEV-LBM is informed with local effective viscosities at each node to capture the variance of the mean free path of gas molecules in a bounded system. The corrected mean free path for each lattice node is determined using a three-dimensional wall function adaptable to complex pore geometries. To enforce a non-zero slip velocity at solid boundaries, a combined diffusive bounce-back scheme is applied to the pore-walls. The LEV-LBM is first validated in simple tube geometries, where good agreement is found for Knudsen numbers up to 1.0. We then use the LEV-LBM to quantify the finite tube length effect and comment on the implications for pore-network models. We finally demonstrate the utility of the LEV-LBM by simulating pure methane flow in digital reconstructions of nanoporous organic matter at reservoir conditions, and compare the results to bundle of tubes models. We show that the bundle of tubes models overestimate apparent permeability by factors between 1.52 and 153, due to the non-trivial dependence of flow on pore space connectivity and shape.

Improved Assessment of Interconnected Porosity in Multiple-Porosity Rocks by Use of Nanoparticle Contrast Agents and Nuclear-Magnetic-Resonance Relaxation Measurements

Summary Nuclear-magnetic-resonance (NMR) measurements are considered among the most-reliable methods to evaluate porosity and pore-size distribution in fluid-bearing rocks. However, in reservoirs with complex pore geometry, there is still a challenge to interpret accurately NMR relaxometry data to evaluate petrophysical properties of these reservoirs such as interconnected porosity. In this paper, we introduce the application of nanoparticle contrast agents to improve assessment of interconnected porosity with NMR measurements. The comparison of NMR relaxometry data before and after nanoparticle injection enables distinguishing connected and isolated pore volumes (PVs), which might not be possible in the absence of contrast agents. The use of these contrast agents was demonstrated successfully in the magnetic-resonance-imaging (MRI) technique for clinical diagnosis. We used superparamagnetic iron oxide nanoparticles (SPION) as contrast agents injected into rock samples with a multiple-porosity system (including intra-/intergranular pores and natural fractures) and then quantified their impact on NMR measurements with laboratory experiments and numerical simulations. We injected contrast agents in sandstone and organic-rich mudrock samples, and measured NMR T2 (spin-spin relaxation time) distributions before and after contrast-agent injection. We simulated the NMR responses in sandstone and organic-rich mudrock samples before and after injection of contrast agent with a random-walk algorithm. The simulated NMR T2 distribution was cross validated by experimental results. We also documented the simulation results in a carbonates sample before and after injection of contrast agents, and characterized the pore-network connectivity with the simulation T2 distribution. The results show that the comparison of NMR relaxometry data before and after SPION injection improves characterization of interconnected porosity and connectivity of natural fractures in rock samples with complex pore geometry such as those from carbonate and organic-rich mudrock formations. We observed that the long-relaxation-time peaks in NMR T2 distribution significantly shift to short relaxation time after SPION injection, indicating that interconnected large pores/fractures are most easily invaded by SPION. However, the original short-relaxation-time peaks remained at the same position with almost the same amplitude and shape, indicating that small pores are not invaded by SPION. The accumulative porosity of the rock remains almost the same before and after SPION injection, indicating that SPION invasion in the rock only results in the downshifting of T2 relaxation time, but does not affect the NMR estimates of total porosity. We conclude from the experimental and numerical-simulation results that interconnected large pores/fractures, isolated large pores, and small pores can be differentiated in NMR T2 distribution with the aid of contrast agents. The outcomes of this paper are promising for the successful application of the introduced technique for pore characterization in heterogeneous multiple-porosity systems containing natural fractures.

An Incompressible, Depth-Averaged Lattice Boltzmann Method for Liquid Flow in Microfluidic Devices with Variable Aperture

Two-dimensional (2D) pore-scale models have successfully simulated microfluidic experiments of aqueous-phase flow with mixing-controlled reactions in devices with small aperture. A standard 2D model is not generally appropriate when the presence of mineral precipitate or biomass creates complex and irregular three-dimensional (3D) pore geometries. We modify the 2D lattice Boltzmann method (LBM) to incorporate viscous drag from the top and bottom microfluidic device (micromodel) surfaces, typically excluded in a 2D model. Viscous drag from these surfaces can be approximated by uniformly scaling a steady-state 2D velocity field at low Reynolds number. We demonstrate increased accuracy by approximating the viscous drag with an analytically-derived body force which assumes a local parabolic velocity profile across the micromodel depth. Accuracy of the generated 2D velocity field and simulation permeability have not been evaluated in geometries with variable aperture. We obtain permeabilities within approximately 10% error and accurate streamlines from the proposed 2D method relative to results obtained from 3D simulations. In addition, the proposed method requires a CPU run time approximately 40 times less than a standard 3D method, representing a significant computational benefit for permeability calculations.

Some Remarks on Bimodality Effects of the Hydraulic Properties on Shear Strength of Unsaturated Soils

Hydraulic properties affect the shear strength of unsaturated soils in terms of suction, predicted as a function of water volume in the pores. In complex pore geometries, such as soils with bimodal pore‐size distributions, suction effects on shear behavior are poorly understood. We present an analytical approach to define how a bimodal suction stress originates in such soils, which are conceptually divided into micro and macrostructures due to aggregation of a wide range of particle sizes. The results were compared with data from the literature for other soils with aggregated macrostructure or with a prevailing coarse fraction. A physically based dependence of soil shear behavior on the bimodal hydraulic behavior was observable, with the extension of the suction stress theory to a bimodal soil hydraulic response in agreement with the suction and moisture change. Depending on the soil type and the range of suctions investigated, the micro and macrostructures should prevail affecting the mechanical soil response subject to environmental loading, such as rainfall events. From a practical point of view, taking into account the bimodal structure network should be fundamental in the set‐up of proper prediction models for shallow landslides induced by rainfall.

Integrated rock classification in carbonate formations based on elastic and petrophysical properties estimated from conventional well logs

A reliable rock classification in a carbonate reservoir should take into account petrophysical, compositional, and elastic properties of the formation. However, depth-by-depth assessment of these properties is challenging because of the complex pore geometries and significant heterogeneity caused by diagenesis. Common rock-classification methods in carbonate formations do not incorporate the impact of both depositional and diagenetic modifications on rock properties. Furthermore, elastic properties, which control fracture propagation and the conductivity of fracture under closure stress, commonly are not accounted for in conventional rock-classification techniques. We apply an integrated rock-classification technique, based on both depositional and diagenetic effects that can ultimately enhance (1) assessment of petrophysical properties, (2) selection of candidates for fracture treatment, and (3) production in carbonate reservoirs. We apply the conductive and the elastic self-consistent approximation theories to estimate depth-by-depth volumetric concentration of interparticle (e.g., interconnected pore space) and intraparticle (e.g., vugs) pores, as well as elastic bulk and shear moduli, in the formation. This process takes into account the impact of shape and volumetric concentrations of rock components on electrical conductivity and elastic properties. We document a successful application of the introduced technique in two wells in the upper Leonardian carbonate interval of Veterans field in west Texas. The identified rock types were verified using thin-section images and core samples. We estimate elastic moduli as well as interparticle porosity with average relative errors of approximately 8% and 10% compared to the core measurements, respectively. Furthermore, the well-log-based estimates of permeability and water saturation are improved by approximately 50% and 20%, respectively, after considering rock classification. Finally, we explain that the fracture propagation failure in the second well (i.e., well B) could be the result of relatively lower Young’s modulus in the rock class corresponding to fracture locations.

A computational analysis for quantitative evaluation of petrol-physical properties of rock fluids based on Bloch NMR diffusion model for porous media

Estimating permeability from grain-size distributions or from well logs is attractive but very difficult. The difficulties are inherent in many petroleum-bearing reservoirs and complex mineralogy earth formations where existing nuclear magnetic resonance (NMR) models require modifications to work effectively. In this paper, we present a generally applicable and simple approach which may yield useful information from NMR signals of different petro-physical properties and porosity. This approach is a model of the Bloch NMR diffusion equation for complex pore geometries in which the transverse magnetization is obtained as function of reservoir chemical (relaxation) and physical properties. The NMR signal is also shown to be dependent on the tortuosity and relaxation rate of rocks fluid so that reservoirs comprised of mixed lithology and mineralogy can be easily evaluated. The computational tools obtained in this study are useful for repetitive data processing which is otherwise difficult due to hardware limitations and logistic issues. • We model NMR diffusion equation for quantitative analyses of complex pore geometry. • We obtained expression for M y as function of T 1 , T 2 and petrol-physical properties. • The colour maps show the model is able to differentiate components of fluid mixture. • The model interpolates (colour maps) for points of interest not on the data table. • The model could not show contrast between brine and oil via diffusion process.

3D mapping of water in oolithic limestone at atmospheric and vacuum saturation using X-ray micro-CT differential imaging

Determining the distribution of fluids in porous sedimentary rocks is of great importance in many geological fields. However, this is not straightforward, especially in the case of complex sedimentary rocks like limestone, where a multidisciplinary approach is often needed to capture its broad, multimodal pore size distribution and complex pore geometries. This paper focuses on the porosity and fluid distribution in two varieties of Massangis limestone, a widely used natural building stone from the southeast part of the Paris basin (France). The Massangis limestone shows locally varying post-depositional alterations, resulting in different types of pore networks and very different water distributions within the limestone. Traditional techniques for characterizing the porosity and pore size distribution are compared with state-of-the-art neutron radiography and X-ray computed microtomography to visualize the distribution of water inside the limestone at different imbibition conditions. X-ray computed microtomography images have the great advantage to non-destructively visualize and analyze the pore space inside of a rock, but are often limited to the larger macropores in the rock due to resolution limitations. In this paper, differential imaging is successfully applied to the X-ray computed microtomography images to obtain sub-resolution information about fluid occupancy and to map the fluid distribution in three dimensions inside the scanned limestone samples. The detailed study of the pore space with differential imaging allows understanding the difference in the water uptake behavior of the limestone, a primary factor that affects the weathering of the rock.

Ionic Liquids Confined in a Realistic Activated Carbon Model: A Molecular Simulation Study

Classical molecular dynamics simulations were performed to study the structure and dynamics of the ionic liquid (IL) [emim+][NTf2–] inside a slit graphitic nanopore and a realistic model of a coconut shell activated carbon (CSAC), which was generated using a reverse Monte Carlo protocol and matches the experimental radial distribution function from the real adsorbent. The CSAC model material consists of semigraphitic carbon sheets with different sizes and shapes, which form irregularly connected pores of roughly rectangular shape. In general, the ions inside the CSAC model material form layers parallel to the walls, as observed for the IL inside slit pores; however, the distribution of pore sizes and the complex pore geometry of the CSAC model materials cause the density profiles and the orientation of the ions to depart significantly from the uniform behavior observed for these properties of the IL inside slit pores. The presence of interconnected pores with a distribution of sizes in the CSAC model materials also causes confinement effects to be weaker than in slit pores of the same size; as a result, the ions inside CSAC model materials have a liquid structure similar to that of the bulk IL and have faster dynamics than those of ions inside slit pores of the same size. The ions near the pore walls of the CSAC model material move slower than the ions that are farther away from the walls, as observed for the IL inside slit pores; however, the complex pore geometry and variations of pore size with position within the CSAC model material cause the dynamics of the confined IL to exhibit significant spatial heterogeneities and depart significantly from the uniform, regular behavior observed in slit nanopores. Our results suggest that the structure and dynamics of ILs confined inside porous materials having heterogeneities in pore size, pore shape, and pore interconnectivity can depart significantly from the properties of ILs confined inside ideal pores of simple geometries.

A dual-porosity theory for solute transport in biofilm-coated porous media

In this work, we derive a Darcy-scale model for solute transport in porous media colonized by biofilms. Biofilms refer to structured communities of microbial cells that grow attached to an aqueous interface, e.g., the pore walls of a water-saturated porous medium. First, we present the pore-scale description of mass transport within and between the phases (water phase and biofilm phase) including the biologically-mediated reactions. Then, a two-equation Darcy-scale mass balance model (classically referred to as dual-porosity model), suitable both for local equilibrium and non-equilibrium conditions, is obtained from the method of volume averaging. Application of this macroscopic model to complex pore geometry of a two-dimensional porous medium supporting biofilms is presented. Comparisons with direct numerical simulation results confirm the large range of validity of the model. Finally, an illustrative example based on a scenario of reactive transport experimental tests is used to point out conditions for when the use of the proposed model is required.

Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations

A significant body of current research is aimed at developing methods for numerical simulation of flow and transport in porous media that explicitly resolve complex pore and solid geometries, and at utilizing such models to study the relationships between fundamental pore-scale processes and macroscopic manifestations at larger (i.e., Darcy) scales. A number of different numerical methods for pore-scale simulation have been developed, and have been extensively tested and validated for simplified geometries. However, validation of pore-scale simulations of fluid velocity for complex, three-dimensional (3D) pore geometries that are representative of natural porous media is challenging due to our limited ability to measure pore-scale velocity in such systems. Recent advances in magnetic resonance imaging (MRI) offer the opportunity to measure not only the pore geometry, but also local fluid velocities under steady-state flow conditions in 3D and with high spatial resolution. In this paper, we present a 3D velocity field measured at sub-pore resolution (tens of micrometers) over a centimeter-scale 3D domain using MRI methods. We have utilized the measured pore geometry to perform 3D simulations of Navier–Stokes flow over the same domain using direct numerical simulation techniques. We present a comparison of the numerical simulation results with the measured velocity field. It is shown that the numerical results match the observed velocity patterns well overall except for a variance and small systematic scaling which can be attributed to the known experimental uncertainty in the MRI measurements. The comparisons presented here provide strong validation of the pore-scale simulation methods and new insights for interpretation of uncertainty in MRI measurements of pore-scale velocity. This study also provides a potential benchmark for future comparison of other pore-scale simulation methods. © 2012 Elsevier Science. All rights reserved.

Numerical Simulation of 3D Liquid–Gas Distribution in Porous Media by a Two-Phase TRT Lattice Boltzmann Method

The 3D description of the soil structure at the pore scale level can help to elucidate the biological functioning of soil. The water–air distribution in the 3D-pore space is of particular interest because it determines the diffusion pathways of nutrients and the localisation of active soil microorganisms. We used the Shan–Chen interparticle-potential approach to simulate spontaneous phase separation in complex academic and real 3D-porous media using the advanced TRT lattice Boltzmann scheme. The equation of state and phase diagram were calculated and the model was verified using hydrostatic laws. The 3D pattern of water/air interface in two complex academic pore geometries was accurately computed. Finally, 3D maps of static liquid–gas distribution were simulated in a real 3D X-ray computed tomography image obtained from an undisturbed soil column sampled in a silty clay loam soil. The simulated soil sample of 1.7 cm3 was described at a voxel-resolution of 60 μm. The range of the simulated saturations (from 0.5 to 0.9) was in a good agreement with the expected saturations calculated from the phase diagram.

Tracking colloid transport in real pore structures: Comparisons with correlation equations and experimental observations

Accurate prediction of colloid transport in porous media under environmentally relevant conditions requires incorporation of complex pore geometries into particle trajectory simulations. Advances in pore structure characterization and numeric flow simulations have the potential to take real pore geometries into account. In this work, a scheme was developed to extract pore structures (grain radii and center positions) from X‐ray microtomography images of glass beads. Lattice Boltzmann flow simulations were performed to derive flow fields in pore spaces. On the basis of the derived flow fields, particle tracking was carried out in the absence of an energy barrier to deposition and under a wide range of colloid size and flow conditions. Simulated depositions agree reasonably well with predictions by applicable correlation equations and experimental observations at groundwater flow regimes, indicating that the particle tracking algorithm is able to simulate colloid trajectories in porous media with reasonable accuracy in the absence of an energy barrier and may also be able to do so in the presence of an energy barrier (which is more environmentally relevant). The simulated depositions are much greater than both predicted and experimentally observed values at high fluid velocities (&gt;1 × 10−3 m s−1). Simulations under selected unfavorable conditions at groundwater flow regimes indicated that temporary retention of colloids by low‐flow zones in pore spaces could play a predominant role in colloid removal at low ionic strengths. As the ionic strength increases (deposition condition becomes less unfavorable), the contribution of temporary retention to overall removal decreases.

Combining X-ray CT and 3D printing technology to produce microcosms with replicable, complex pore geometries

Measurements in soils have been traditionally used to demonstrate that soil architecture is one of the key drivers of soil processes. Major advances in the use of X-ray Computed Tomography (CT) afford significant insight into the pore geometry of soils, but until recently no experimental techniques were available to reproduce this complexity in microcosms. This article describes a 3D additive manufacturing technology that can print physical structures with pore geometries reflecting those of soils. The process enables printing of replicated structures, and the printing materials are suitable to study fungal growth. This technology is argued to open up a wealth of opportunities for soil biological studies.

Water retention of repellent and subcritical repellent soils: New insights from model and experimental investigations

Soil organic matter can modify the surface properties of the soil mineral phase by changing the surface tension of the mineral surfaces. This modifies the soil’s solid-water contact angle, which in turn would be expected to affect its water retention curve (SWRC). Here we model the impact of differences in the soil pore-water contact angle on capillarity in non-cylindrical pores by accounting for their complex pore geometry. Key outcomes from the model include that (i) available methods for measuring the Young’s wetting angle on soil samples are insufficient in representing the wetting angle in the soil pore space, (ii) the wetting branch of water retention curves is strongly affected by the soil pore-water contact angle, as manifest in the wetting behavior of water repellent soils, (iii) effects for the drying branch are minimal, indicating that both wettable and water repellent soils should behave similarly, and (vi) water retention is a feature not of only wettable soils, but also soils that are in a water repellent state. These results are tested experimentally by determining drying and wetting branches for (a) ‘model soil’ (quartz sands with four hydrophobization levels) and (b) five field soil samples with contrasting wettability, which were used with and without the removal of the soil organic matter. The experimental results support the theoretical predictions and indicate that small changes in wetting angle can cause switches between wettable and water repellent soil behavior. This may explain the common observation that relatively small changes in soil water content can cause substantial changes in soil wettability.

Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach

The accurate estimation of hydraulic conductivity is important for many geotechnical engineering applications, as the presence of fluids affects all aspects of soil behaviour, including its strength. Darcy’s law is the key experimental (or phenomenological) equation employed to model ground water flow. Yet, this phenomenological equation can be linked to a more fundamental microscale model of flow through the pore spaces of the porous material. This paper provides an experimental verification of the relationships between Darcy’s law (macroscale) and the Navier–Stokes equations (microscale) for actual complex pore geometries of a granular material. The pore geometries are experimentally obtained through state-of-the-art X-ray computer assisted micro-tomography. From the numerical modelling of the microscale flow based on actual pore geometries, it is possible to quantify and visualize the development of pore-scale fluid preferential flow-paths through the porous material, and to assess the importance of pore connectivity in soil transport properties.

Numerical simulation of non-Archie electrophysical property of saturated rock with lattice Boltzmann method

The electrophysical property of saturated rocks is very important for reservoir identification and evaluation. In this paper, the lattice Boltzmann method (LBM) was used to study the electrophysical property of rock saturated with fluid because of its advantages over conventional numerical approaches in handling complex pore geometry and boundary conditions. The digital core model was constructed through the accumulation of matrix grains based on their radius distribution obtained by the measurements of core samples. The flow of electrical current through the core model saturated with oil and water was simulated on the mesoscopic scale to reveal the non-Archie relationship between resistivity index and water saturation (I-Sw). The results from LBM simulation and laboratory measurements demonstrated that the I-Sw relation in the range of low water saturation was generally not a straight line in the log-log coordinates as described by the Archie equation. We thus developed a new equation based on numerical simulation and physical experiments. This new equation was used to fit the data from laboratory core measurements and previously published data. Determination of fluid saturation and reservoir evaluation could be significantly improved by using the new equation.