Natural Porous Media Research Articles

Application of Non-toxic Yield Stress Fluids Porosimetry Method and Pore-Network Modelling to Characterize the Pore Size Distribution of Packs of Spherical Beads

With X-ray computed tomography still being flawed as a result of limitations in terms of spatial resolution and cost, toxic mercury intrusion porosimetry (MIP) is nowadays the prevailing technique to determine PSDs of most porous media. Recently, yield stress fluids porosimetry method (YSM) has been identified as a promising clean alternative to MIP. This technique is based on the particular percolation patterns followed by yield stress fluids, which only flow through certain pores when injected at a given pressure gradient. In previous works, YSM was used to characterize natural and synthetic porous media, and the results were compared with MIP showing reasonable agreement. However, considerable uncertainty still remains regarding the characterized pore dimension with each method arising from the highly complex geometry of the interstices in real porous media. Therefore, a critical stage for the validation of YSM consists in achieving successful characterization of model porous media with well-known pore morphology and topology. With this objective in mind, a set of four packs of glass beads each with a given monodisperse bead size were characterized in the present work using different porosimetry methods: experimental YSM, numerically simulation of MIP and pore-network extraction from a 3D image. The results provided by these techniques were compared, allowing the identification of the pore dimensions being characterized in each case. The results of this research elucidate the causes of the discrepancies between the considered porosimetry methods and demonstrate the usefulness of the PSD provided by YSM when predicting flow in porous media.

Causality and Bayesian Network PDEs for multiscale representations of porous media

Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media, and the design of novel materials, e.g., for energy storage. Microscopic properties exhibit complex statistical correlations and geometric constraints that present challenges for the estimation of macroscopic quantities of interest (QoIs), e.g., in the context of global sensitivity analysis (GSA) of macroscopic QoIs with respect to microscopic material properties. We present a systematic way of building correlations into stochastic multiscale models through Bayesian Networks. The proposed framework allows us to construct the joint probability density function (PDF) of model parameters through causal relationships that are informed by domain knowledge and emulate engineering processes, e.g., the design of hierarchical nanoporous materials. These PDFs also serve as input for the forward propagation of parametric uncertainty thereby yielding a Bayesian Network PDE. To assess the impact of causal relationships and microscale correlations on macroscopic material properties, we propose a moment-independent GSA and corresponding effect rankings for Bayesian Network PDEs, based on the differential Mutual Information, that leverage the structure of Bayesian Networks and account for both correlated inputs and complex non-Gaussian (skewed, multimodal) QoIs. Our findings from numerical experiments, which feature a non-intrusive uncertainty quantification workflow, indicate two practical outcomes. First, the inclusion of correlations through structured priors based on causal relationships informed by domain knowledge impacts predictions of QoIs and has important implications for engineering design. Second, structured priors with non-trivial correlations yield different effect rankings than independent priors; these rankings are more consistent with the anticipated physics.

Effect of Cumulative Surface on Pore Development in Chalk

AbstractPore development in natural porous media, as a result of mineral dissolution in flowing fluid, generates complex microstructures. Although the underlying dynamics of fluid flow and the kinetics of the dissolution reactions have been carefully analyzed in many scenarios, it remains interesting to ask if the preferentially developed flow paths share certain general petrophysical properties. Here we combine in situ X‐ray imaging with network modeling to study pore development in chalk driven by acidic fluid flow under ambient condition. We show that the trajectory of a growing pore correlates with the flow path that minimizes cumulative surface—the overall surface area available to fluid within the residence time—calculated along streamlines. This correlation is not a coincidence because cumulative surface determines conversion of reactant and thus defines the position of dissolution front. Model simulations show that, as fluid channelizes, the growth of the leading pore in the flow direction is guided by migration of the most far‐reaching dissolution front, even in an ever‐changing flow field. In addition, we present a complete tomographic time series of microstructure erosion and show a good accord between the in situ observation and the model simulation. Our results suggest that the microscopic pore development is a deterministic process while being sensitive to stochastic perturbations to the migrating dissolution front.

Microscale Investigation of the Impact of Surfactant Structure on the Residual Trapping in Natural Porous Media

Residual trapping of a nonwetting phase in a porous medium is directly impacted by the relative magnitude of capillary, viscous, and gravity forces. Ratios of these forces control the sequence by which different pore-scale displacement mechanisms take place, which in turn govern the pore fluid occupancy and the residual nonwetting phase saturation. Parameters such as pore geometry, rock surface wettability, fluid–fluid interfacial tension, and fluids’ viscosities, densities, and flow rates determine the magnitude of the above-mentioned forces. In this study, we show that there is an additional set of factors that directly contributes to the distribution of fluids at the pore scale. We demonstrate that, under similar rock and fluid properties, interfacial repulsive and attractive interactions, caused by the adsorption of surface-active chemicals on fluid–fluid interfaces, can significantly alter pore-scale fluid occupancies. Using the microcomputed tomography (micro-CT) imaging technique integrated with a miniature core-flooding apparatus, we investigate the impact of surfactant structure on pore-scale fluid distributions in a limestone core sample subjected to injection of different wetting fluid solutions. Poly(ethylene oxide) (PEO), a nonionic surfactant, and ammonium alkyl ether sulfate, an anionic surfactant, are utilized as surface-active agents providing similar oil–brine interfacial tension (IFT) and contact angle (CA) values. Oil cluster analyses along with three-dimensional (3D) visualization of fluid distributions indicate that using the nonionic surfactant instead of the anionic surfactant results in the breaking up of the large and medium oil clusters into smaller and scattered ones. We propose a mechanism relating the stability of oil–brine interface to surfactant structure that is responsible for the breakup and/or coalescence of oil clusters inside the pore space. The suggested mechanism is confirmed by the micro-CT images and associated oil cluster analyses. This phenomenon affects the competition between the frequency of displacement mechanisms causing variations in remaining oil saturations.

Upscaling of microbially driven first-order reactions in heterogeneous porous media

Reactions mediated by microorganisms determine the fate of many chemicals in natural porous media. At the pore scale, the distribution of chemicals and microorganisms is not homogeneous, leading to heterogeneous distribution of microbial activities at the pore scale. We conducted pore scale reactive transport simulations to investigate the scaling of microbially mediated consumption reaction rates under a range of flow and reaction conditions. The results reveal that the scaling effects largely depended on Péclet and Damköhler numbers. Consumption rate estimates based on volume-averaged concentrations and reaction kinetics overestimated the true volumetric reaction rates, and large-sized biomass aggregates intensified these scaling errors. In contrast, the macroscopic rates estimated via flux-weighted concentrations underestimated the true volumetric reaction rates, with large microbial aggregates reducing scaling errors. This study also demonstrated that macroscopic rate estimates can be improved by combining information on the reaction kinetics with the flux-weighted concentrations.

Stochastic Modeling of the Permeability of Randomly Generated Porous Media via the Lattice Boltzmann Method and Probabilistic Collocation Method

The permeability of natural porous media, such as soils and rocks, usually possesses uncertainties due to the randomness and spatial variation of microscopic pore structures. It is of great importance to develop an effective methodology to obtain statistical properties of permeability for porous media. In this work, an efficient approach is developed by combining the sphere packing algorithm, lattice Boltzmann method (LBM), and probabilistic collocation method (PCM). The porous media are generated by sphere packings of a specified size distribution, and the isotropy and representative elementary volume are verified by statistical analyses. Fluid flow in the complex pore structures is numerically resolved by LBM, with the permeability calculated by Darcy’s law. The uncertainty of permeability can be quantified by PCM with only several porosity samplings required at predetermined collocation points. In addition, the porosity–permeability relationships can be acquired efficiently. Numerical results indicate that, with the proposed approach, the computational efforts are reduced by more than two orders of magnitude compared to the Monte Carlo simulations.

Modeling and Experimental Validation of Rheological Transition During Foam Flow in Porous Media

Flow of nitrogen foam stabilized by alpha olefin sulfonate (C14-16 AOS) was studied in a natural sandstone porous media using X-ray Computed Tomography. Foam was generated by a simultaneous injection of gas and surfactant solution into a porous medium initially saturated with the surfactant solution. It was found that the foam undergoes a transition from a weak to a strong state at a characteristic gas saturation of Sgc = 0.75 ± 0.02. This transition coincided with a substantial reduction in foam mobility by a two-order of magnitude and also with a large reduction in overall water saturation to as low as 0.10 ± 0.02. Foam mobility transition was interpreted by the surge of yield stress as gas saturation exceeded the Sgc. We proposed a simple power-law functional relationship between yield stress and gas saturation. The proposed rheological model captured successfully the mobility transition of foams stabilized by different surfactant concentrations and for different core lengths.

Local instabilities during capillary-dominated immiscible displacement in porous media

Fully understanding the mechanism of pore-scale immiscible displacement dominated by capillary forces, especially local instabilities and their influence on flow patterns, is essential for various industrial and environmental applications such as enhanced oil recovery, CO 2 geo-sequestration and remediation of contaminated aquifers. It is well known that such immiscible displacement is extremely sensitive to the fluid properties and pore structure, especially the wetting properties of the porous medium which affect not only local interfacial instabilities at the micro-scale, but also displacement patterns at the macro-scale. In this review, local interfacial instabilities under three typical wetting conditions, namely Haines jump events during weakly-wetting drainage, snap-off events during strongly-wetting imbibition, and the co-existence of concave and convex interfaces under intermediate-wet condition, are reviewed to help understand the microscale physics and macroscopic consequences resulting in natural porous media. Cited as : Liu, Y., Iglauer, S., Cai, J., Amooie, M.A., Qin, C. Local instabilities during capillary-dominated immiscible displacement in porous media. Capillarity, 2019, 2(1): 1-7, doi: 10.26804/capi.2019.01.01

Emerging Advances in Petrophysics: Porous Media Characterization and Modeling of Multiphase Flow

With the ongoing exploration and development of oil and gas resources all around the world, applications of petrophysical methods in natural porous media have attracted great attention. This special issue collects a series of recent studies focused on the application of different petrophysical methods in reservoir characterization, especially for unconventional resources. Wide-ranging topics covered in the introduction include experimental studies, numerical modeling (fractal approach), and multiphase flow modeling/simulations.

Capillary-Dominated Fluid Displacement in Porous Media

Liquid invasion into a porous medium is a phenomenon of great importance in both nature and technology. Despite its enormous importance, there is a surprisingly sparse understanding of the processes occurring on the scale of individual pores and of how these processes determine the global invasion pattern. In particular, the exact influence of the wettability remains unclear besides the limiting cases of very small or very large contact angles of the invading fluid. Most quantitative pore-scale experiments and theoretical considerations have been conducted in effectively two-dimensional (2D) micromodels and Hele–Shaw geometries. Although these pioneering works helped to unravel some of the physical aspects of the displacement processes, the relevance of 2D models has not always been appreciated for natural porous media. With the availability of X-ray microtomography, 3D imaging has become a standard for exploring pore-scale processes in porous media. Applying advanced postprocessing routines and synchrotron microtomography, researchers can image even slow flow processes in real time and extract relevant material parameters like the contact angle from the interfaces in the pore space. These advances are expected to boost both theoretical and experimental understanding of pore-scale processes in natural porous media.

Experimental study of pore size distribution effect on phase transitions of hydrocarbons in nanoporous media

The phase behavior of a fluid in a nanoporous system is altered from that in the bulk due to confinement effects. There have been many experimental studies on this important effect, yet the vast majority are limited to porous media with a narrow or singular pore size distribution. However, natural porous media exhibit a broad pore size distribution. For example, in shale rocks the pore size ranges from several nanometers to hundreds of nanometers. It is not clear if a broad pore size distribution has a significant effect on the phase transition of nanoconfined fluids, and, if effects are present, how and why the phase behavior is altered. The effects of a distributed pore size on the bubble point of confined fluids as measured by differential scanning calorimetry (DSC) are not known. Here, we present an experimental study on the effect of pore size distribution on the liquid-vapor phase transition of n-hexane, n-octane and n-decane confined in nonporous media. We report a method to discretize the pore size distribution of natural shale rocks so that it can be mimicked using mixtures of synthetic nanoporous media. Using DSC, we show that the presence of a broad pore size distribution significantly alters the vapor-liquid phase transition of confined hydrocarbons. In fully saturated (i.e. filled) nanoporous media, the largest pore size dictates the onset of liquid-vapor phase transition (.i.e. bubblepoint). However, when the porous media is partially saturated, smaller pore sizes influence the bubblepoint. These findings suggest that there is a dependency of the confined fluid phase behavior on the fluid saturation in nanoporous media with a broad pore size distribution, which contributes to a broader understanding of phase transitions in natural porous media.

Efficient Prediction of Multidomain Flow and Transport in Hierarchically Structured Porous Media

AbstractStructural hierarchy is a fundamental characteristic of natural porous media. Yet it provokes one of the grand challenges for the modeling of fluid flow and transport since pore‐scale structures and continuum‐scale domains often coincide independent of the observation scale. Common approaches to represent structural hierarchy build, for example, on a multidomain continuum for transport or on the coupling of the Stokes equations with Darcy's law for fluid flow. These approaches, however, are computationally expensive or introduce empirical parameters that are difficult to derive with independent observations. We present an efficient model for fluid flow based on Darcy's law and the law of Hagen‐Poiseuille that is parameterized based on the explicit pore space morphology obtained, for example, by X‐ray μ‐CT and inherently permits the coupling of pore‐scale and continuum‐scale domain. We used the resulting flow field to predict the transport of solutes via particle tracking across the different domains. Compared to experimental breakthrough data from laboratory‐scale columns with hierarchically structured porosity built from solid glass beads and microporous glass pellets, an excellent agreement was achieved without any calibration. Furthermore, we present different test scenarios to compare the flow fields resulting from the Stokes‐Brinkman equations and our approach to comprehensively illustrate its advantages and limitations. In this way, we could show a striking efficiency and accuracy of our approach that qualifies as general alternative for the modeling of fluid flow and transport in hierarchical porous media, for example, fractured rock or karstic aquifers.

Patterns of entropy production in dissolving natural porous media with flowing fluid.

The tendency for irreversible processes to generate entropy is the ultimate driving force for structure evolution in nature. In engineering, entropy production is often used as an indicator for loss of usable energy. In this study, we show that the analysis of entropy production patterns can provide insight into the diverse observations from experiments that investigate porous medium dissolution in imposed flow field. We first present a numerical scheme for the analysis of entropy production in dissolving porous media. Our scheme uses a greyscale digital model for chalk (an extremely fine grained rock), that was obtained using X-ray nanotomography. Greyscale models preserve structural heterogeneities with very high fidelity. We focussed on the coupling between two types of entropy production: the percolative entropy, generated by dissipating the kinetic energy of fluid flow, and the reactive entropy, originating from the consumption of chemical free energy. Their temporal patterns pinpoint three stages of microstructural evolution. We then showed that local mixing deteriorates fluid channelisation by reducing local variations of reactant concentration. We also showed that microstructural evolution can be sensitive to the initial transport heterogeneities, when the macroscopic flowrate is low. This dependence on flowrate indicates the need to resolve the structural features of a porous system when fluid residence time is long.

Effects of nano-confinement on Zn(II) adsorption to nanoporous silica

Nanopores (at least one dimension ≤100 nm and no dimension <1 nm) are commonly observed features of grain coatings and primary silicate minerals and can contribute substantially to the total surface area available for chemical reactions. Despite the ubiquity of nanopores in natural and synthetic porous media, a generalizable framework for evaluating the effects of nanopore confinement on both fluid and sorbate properties across the entire nanoscale has yet to emerge. As a result, we have a poor understanding of the effect of pore size on molecular-scale processes controlling nano-confinement phenomena in systems in which mineral surfaces are in contact with aqueous solutions.To address these knowledge gaps, we carried out batch experiments designed to reveal the molecular-level details of adsorption reaction products and attendant isotope fractionation of aqueous Zn(II) for synthetic, variably porous, amorphous silica (SiO2(am)) particles with average pore diameters ranging from 10 nm to 330 nm. Shell-by-shell fitting of Zn K-edge extended X-ray absorption fine structure (EXAFS) spectra reveals that Zn(II) (1) adsorbs as dominantly monodentate, corner-sharing complexes to silicate tetrahedra of all SiO2(am) particles examined, regardless of pore size, (2) is tetrahedrally coordinated by oxygen atoms in nanoporous silica with small pore sizes (≤10 nm), and (3) is present as a mixture of tetrahedrally and octahedrally coordinated surface complexes in silica with larger pore sizes (>10 nm). In addition, at low Zn(II) surface coverages (<0.9 μmol m−2) on macroporous SiO2(am), Zn(II) forms a mixture of octahedrally and tetrahedrally coordinated surface complexes, whereas tetrahedrally coordinated surface complexes predominate at higher Zn(II) coverages (>0.9 μmol m−2).Although molecular-level differences in Zn(II) adsorption complexes are apparent with respect to SiO2(am) pore size, we observed no quantifiable differences in attendant isotope fractionation or adsorption edge structure for Zn(II) uptake on nanoporous SiO2(am) surfaces. These results suggest that the differences in binding energy of tetrahedrally versus octahedrally coordinated Zn(II) complexes at the same site on SiO2(am) are small. Comparison of EXAFS spectra to the results of surface complexation modeling (SCM) of experimental Zn(II) uptake data indicates that monodentate Zn(II) adsorption on the SiO2(am) surface releases two protons through binding one site and passivating an adjacent site, which accounts for the modification of surface charge and surface complex structure during adsorption of Zn(II) cations.This study shows that adsorption of Zn(II) in variably porous SiO2(am) results in differences in surface complex geometry as pore size decreases and as surface coverage of Zn(II) increases. Although surface complexation modeling of Zn(II) adsorption edges on macroporous and nanoporous SiO2(am) does not independently identify these molecular-level differences, combination of SCM and molecular-level observations reveals unique insight into the overall adsorption reaction and neighboring surface site reactivity.

Thermal Conduction in Deforming Isotropic and Anisotropic Granular Porous Media with Rough Grain Surface

Resistance to the heat flow in solid–solid contact areas plays a fundamental role in heat transfer in unconsolidated porous materials. In the present work, we study thermal conduction in granular porous media that undergo deformation due to an external compressing pressure. The media’s grains have rough surface, with the roughness profile following the statistics of self-affine fractals that have been shown to be abundant in natural porous media. We utilize a fractal contact model of rough surfaces in order to estimate the deformation of the contact areas, which is a function of roughness fractal parameters, the grains’ Young modulus, and the compressing pressure. For porous media saturated by a single fluid, the effects of various factors, such as the porosity, the grains’ overlap (consolidation), and shapes (circular vs. elliptical), are all studied. Increasing the compressing pressure enhances heat transfer due to deformation of the rough surface of the gains. The thermal conductivity of the medium is strongly affected by the porosity, when the grains’ conductivity is much larger than that of the fluid that saturates the pore space. Furthermore, we show that thermal anisotropy is a decreasing function of roughness deformation. In other words, granular media with rougher grains exhibit larger anisotropy as measured by the ratio of the directional thermal conductivities. Whereas in one type of granular media the anisotropy eventually vanishes at very high compressing pressure, it persists in a second model of anisotropic media that we study.

Retraction of the dissolution front in natural porous media

The dissolution of porous materials in a flow field controls the fluid pathways through rocks and soils and shapes the morphology of landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive volumes in a dissolving medium, is a prerequisite for describing dissolution-induced structure emergence and transformation. Despite its fundamental importance, the report on the dynamics of a dissolution front in an evolving natural microstructure is scarce. Here we show an unexpected, spontaneous migration of the dissolution front against the flow direction. This retraction stems from infiltration instability induced surface generation, which leads to an increase in reactive surface area when a porous medium dissolves in an imposing flow field. There is very good agreement between observations made with in situ, X-ray tomography and model predictions. Both show that the value of reactive surface area reflects a balance between flow-dependent surface generation and destruction, i.e. the “dry” geometric surface area of a porous material, measured without a flow field, is not necessarily the upper limit of its reactive surface area when in contact with reactive flow. This understanding also contributes to reconciling the discrepancies between field and laboratory derived solid-fluid reaction kinetics.

Effect of physicochemical factors on transport and retention of graphene oxide in saturated media.

Fate and transport of graphene oxide (GO) have received much attention recently with the increase of GO applications. This study investigated the effect of salt concentration on the transport and retention behavior of GO particles in heterogeneous saturated porous media. Transport experiments were conducted in NaCl solutions with three concentrations (1, 20, and 50 mM) using six structurally packed columns (two homogeneous and four heterogeneous) which were made of fine and coarse grains. The results showed that GO particles had high mobility in all the homogeneous and heterogeneous columns when solution ionic strength (IS) was low. When IS was high, GO particles showed distinct transport ability in six structurally heterogeneous porous media. In homogeneous columns, decreasing ionic strength and increasing grain size increased the mobility of GO. For the column containing coarse-grained channel, the preferential flow path resulted in an early breakthrough of GO, and further larger contact area between coarse and fine grains caused a lower breakthrough peak and a stronger tailing at different IS. In the layered column, there was significant GO retention at coarse-fine grain interface where water flowed from coarse grain to fine grain. Our results indicated that the fate and transport of GO particles in the natural heterogeneous porous media was highly related to the coupled effect of medium structure and salt solution concentration.

Large time behaviour of oscillatory nonlinear solute transport in porous media

Oscillations in flow occur under many different situations in natural porous media, due to tidal, daily or seasonal patterns. In this paper, we investigate how such oscillations in flow affect the transport of an initially sharp solute front, if the solute undergoes nonlinear sorption and, disregarding molecular diffusion, mechanical dispersion. By homogenization, we show that after many cycles, the transport converges to a zero convection, pure nonlinear diffusion problem. The impact of the oscillatory flow requires an adjustment of the dispersion coefficient, where instead of the modulus of the particle velocity, we have to use its time averaged value. Physically, this agrees with a velocity defined by the distance travelled by particles in solution, divided by the time needed for that displacement. The nonlinearity of the sorption reaction is retained in the concentration distribution of the mixing zone, because in the large time limit, this distribution is not Gaussian but asymmetric. With numerical simulations, we show that this convergence may occur relatively fast (say 10 cycles). The implication of the diffusion like large time behaviour is that the transition zone continues to spread beyond the zone of convective oscillation.

Joint inversion of physical and geochemical parameters in groundwater models by sequential ensemble-based optimal design

Joint inversion of physical and geochemical parameters in groundwater reactive transport models is still a great challenge due to the intrinsic heterogeneities of natural porous media and the scarcity of observation data. In this study, we make use of a sequential ensemble-based optimal design (SEOD) method to jointly estimate physical and geochemical parameters of groundwater models. The effectiveness and efficiency of the SEOD method are illustrated by the comparison between the sequential optimization strategy and the conventional strategy (using fixed sampling locations) for two synthetic cases. Since the SEOD method is an optimization method based on the ensemble Kalman filter (EnKF), it invokes the time-consuming genetic algorithm at every assimilation step of the EnKF to obtain the optimal sampling locations. To enhance its computational efficiency, we improve the SEOD method by replacing the EnKF with the ensemble smoother with multiple data assimilation. Furthermore, the influence factors of the original and improved SEOD method are also discussed. Our results show that the SEOD method provides an effective designed sampling strategy to accurately estimate heterogeneous distribution of physical and geochemical parameters. Moreover, the improved SEOD method is more advantageous than the original one in computational efficiency, making this SEOD framework more promising for future application.

An investigation into the effects of pore connectivity on T2 NMR relaxation

Nuclear Magnetic Resonance (NMR) is a powerful technique used to characterize fluids and flow in porous media. The NMR relaxation curves are closely related to pore geometry, and the inversion of the NMR relaxometry data is known to give useful information with regards to pore size distribution (PSD) through the relative amplitudes of the fluids stored in the small and large pores. While this information is crucial, the main challenge for the successful use of the NMR measurements is the proper interpretation of the measured signals. Natural porous media patterns consist of complex pore structures with many interconnected or “coupled” regions, as well as isolated pores. This connectivity along the throats changes the relaxation distribution and in order to properly interpret this data, a thorough understanding of the effects of pore connectivity on the NMR relaxation distribution is warranted. In this paper we address two main points. The first pertains to the fact that there is a discrepancy between the relaxation distribution obtained from experiments, and the ones obtained from solving the mathematical models of diffusion process in the digitized images of the pore space. There are several reasons that may attribute to this such as the lack of a proper incorporation of surface roughness into the model. However, here we are more interested in the effects of pore connectivity and to understand why the typical NMR relaxation distribution obtained from experiments are wider, while the numerical simulations predict that a wider NMR relaxation distribution may indicate poor connectivity. Secondly, by not taking into account the pore coupling effects, from our experience in interpreting the data, we tend to underestimate the pore volume of small pores and overestimate the amplitudes in the large pores. The role of pore coupling becomes even more prominent in rocks with small pore sizes such as for example in shales, clay in sandstones, and in the microstructures of carbonates.