Nuclear magnetic resonance has been applied in well logging to investigate pore size distribution with high resolution and accuracy based on the relaxation time distribution. However, due to the heterogeneity of natural rock, pore surface relaxivity, which links relaxation time and pore size, varies within the pore system. To analyze and alter pore surface relaxivity, we saturated Boise sandstone cores with positively charged zirconia nanoparticle dispersions in which nanoparticles can be adsorbed onto the sandstone pore wall, while negatively charged zirconia nanoparticles dispersions were used as a control group to provide the baseline of nanoparticle retention due to nonelectrostatic attraction. We have performed core flushing with deionized water, pure acid, and alkali with different pH values; compared properties of zirconia nanoparticles before and after exposure to Boise sandstone; analyzed the portion of zirconia nanoparticles retained in the rock; altered pore surface relaxivity; and linked the adsorbed nanoparticle concentration on the pore surface to the modified surface relaxivity. Our work has indicated that after two pore volumes of core flooding, there was approximately 1% of negatively charged nanoparticles trapped in the Boise sandstone core, whereas approximately 8%–11% of positively charged nanoparticles was retained in the Boise sandstone cores. Our results indicated that besides van der Waals attraction, electrostatic attraction was the driving force for retention of nanoparticles with a positive surface charge in sandstone cores. The attachment of nanoparticles onto sandstone surfaces changed the mineral surface relaxivity. Exposure to acidic or strong alkaline conditions increased the Boise sandstone surface relaxivity. After contact with Boise sandstone, the nanoparticles themselves exhibited increased relaxivity due to interactions between nanoparticles dispersion and mineral surface under different pH conditions.
Porous materials such as rocks, soils, and peats are typically complex mixtures built up of more than one component, with intrinsic permeabilities that depend on factors such as pore shape and surface area, tortuosity, and connectivity. In such media, the macroscopic permeability is an integrated combination of the permeabilities of the individual components. In this study, we numerically simulated fluid flow in binary mixtures of low- and high-permeability components constructed of spheres and ellipsoids using the lattice-Boltzmann (LB) method to model permeability in porous media. We then applied the effective-medium approximation (EMA) to predict permeability in the simulated binary mixtures. Our results indicate a very good match between predicted permeabilities by EMA and those simulated by LB in simple and body-centered cubic packs as long as the permeability of the high-permeability component Kh is not substantially different than that of the low-permeability component Kl. The upper limit of Kh/Kl for which the EMA approach results in very accurate permeability predictions depends on several factors, such as packing arrangement, grain shape, and porosity. Including all data, we found the EMA permeability predictions still within a factor of two of the LB simulations.
Most existing models for predicting relative permeability in the presence of hydrate are either empirical or based on simplistic representations of the pore system and hydrate growth. Multiple models are often needed to explain relative permeability behavior observed in the laboratory over different ranges of hydrate saturation. Critical path analysis (CPA) offers a framework for predicting relative permeability based on pore system properties, including the percolation threshold and breadth of the pore size distribution. Using an existing method developed for partially saturated soils, I show that CPA can accurately predict relative permeability to either water or gas over the entire range of measured hydrate saturation for several suites of laboratory measurements. The method does not require any assumption of hydrate growth habit, and assumes that hydrate tends to grow in the largest pores first. This work represents an improvement in understanding the link between pore structure and transport properties of hydrate-bearing sediment.
Two methane migration mechanisms have been proposed for coarse‐grained gas hydrate reservoirs: short‐range diffusive gas migration and long‐range advective fluid transport from depth. Herein, we demonstrate that short‐range fluid flow due to overpressure in marine sediments is a significant additional methane transport mechanism that allows hydrate to precipitate in large quantities in thick, coarse‐grained hydrate reservoirs. Two‐dimensional simulations demonstrate that this migration mechanism, short‐range advective transport, can supply significant amounts of dissolved gas and is unencumbered by limitations of the other two end‐member mechanisms. Short‐range advective migration can increase the amount of methane delivered to sands as compared to the slow process of diffusion, yet it is not necessarily limited by effective porosity reduction as is typical of updip advection from a deep source.
Knowledge of porosity and saturation‐dependent thermal conductivities is necessary to investigate heat and water transfer in natural porous media such as rocks and soils. Thermal conductivity in a porous medium is affected by the complicated relationship between the topology and geometry of the pore space and the solid matrix. However, as water content increases from completely dry to fully saturated, the effect of the liquid phase on thermal conductivity may increase substantially. Although various methods have been proposed to model the porosity and saturation dependence of thermal conductivity, most are empirical or quasiphysical. In this study, we present a theoretical upscaling framework from percolation theory and the effective‐medium approximation, which is called percolation‐based effective‐medium approximation (P‐EMA). The proposed model predicts the thermal conductivity in porous media from endmember properties (e.g., air, solid matrix, and saturating fluid thermal conductivities), a scaling exponent, and a percolation threshold. In order to evaluate our porosity and saturation‐dependent models, we compare our theory with 193 porosity‐dependent thermal conductivity measurements and 25 saturation‐dependent thermal conductivity data sets and find excellent match. We also find values for the scaling exponent different than the universal value of 2, in insulator‐conductor systems, and also different from 0.76, the exponent in conductor‐superconductor mixtures, in three dimensions. These results indicate that the thermal conductivity under fully and partially saturated conditions conforms to nonuniversal behavior. This means the value of the scaling exponent changes from medium to medium and depends not only on structural and geometrical properties of the medium but also characteristics (e.g., wetting or nonwetting) of the saturating fluid.
Gas transport from shale matrix to fractures depends on the topology of the pore space, which is very difficult to measure directly in large samples. We applied conventional techniques (mercury intrusion capillary pressure (MICP) and N2 adsorption/desorption) to obtain indirect measurement of shale pore structure in samples from the Barnett Shale. We exploit the facts that N2 adsorption is sensitive to pore size distribution (PSD) but not pore topology, while MICP and N2 desorption are sensitive to both topology and PSD. Our model assumed that the bulk rock is composed of an impermeable matrix with embedded pore conduits. Conduits may or may not be connected to form a 3D network. For simplicity the conduits were composed of cylindrical tube elements with sizes assigned from the PSD inferred from N2 adsorption. A tree-like structure, a 3D cubic lattice, and bundles of short conduits models were tested to examine the role of connectivity by optimizing reconstructions of N2 adsorption/desorption and MICP intrusion/withdrawal simultaneously. The bundle of short conduits model with some constrains on pore sizes predicted both the measured MICP and N2 desorption curves very well; the other models failed to account for both measurements.
Existing models for shale permeability couple advection and diffusion but do not include the effects of fluid saturations on the permeability. Using a combination of critical path analysis, effective medium theory, and percolation theory, we modeled shale relative permeability by considering the effects of pore structure on unsaturated advection and diffusion. Relevant percolation properties were determined from N2 adsorption-desorption measurements. We considered samples of Green River Shale, Woodford Shale, and Cameo Coal, and isolated kerogens from the Green River and Woodford. We considered gas to be the wetting phase in the kerogens and coal and the nonwetting phase in the bulk shales. We found that the nonwetting phase relative permeability scales linearly with the nonwetting phase saturation, while the wetting phase relative permeability exhibits a highly nonlinear relationship with wetting phase saturation due to the large pore space fractal dimensions (>2.68) of the shales. Based on our model, we predict that water production from the shales is expected to be minor until the gas phase reaches its residual saturation, and that the rate of gas transport out of the kerogen and into the shale matrix should decrease rapidly following the onset of production. This may explain in part why shale gas wells typically produce little formation water and exhibit rapid production decline rates.
We assembled a data set of permeability measurements from 317 subduction zone and reference site samples worldwide made over nearly 25 years of scientific drilling. This data set allowed us to examine the influence of grain size, structural domain, and measurement type on permeabilities ranging from 10−21 to 10−14 m2. We found that porosity–permeability behavior is a function of clay‐size fraction, which is consistent with previous work. Sediments within the slope, accretionary prism, and fault‐zone structural domains are strongly affected by shearing, which alters the permeability behavior with burial. Consolidation, flow‐through, and transient pulse decay measurements all provide comparable results. Measurements of horizontal and vertical permeability show significant cm‐scale permeability anisotropy (ratio of horizontal to vertical permeability >10) in the slope and accretionary prism structural domains, further indicating shear deformation in these domains. Laboratory consolidation trends match large‐scale (102 m) field trends in structural domains with negligible shear, but tend to underestimate the rate of permeability reduction with porosity loss where shear is significant. Comparison with downhole measurements shows that permeability is controlled by higher‐permeability (>10−15 m2) layers at the meter to tens of meters scale, while wireline formation tester measurements closely match laboratory results. Sediments from the underthrust and reference structural domains exhibit similar porosity–permeability trends, which suggests that shallow subduction (total burial <1 km) does not significantly alter the porosity–permeability behavior of incoming sediments. Comparison with measurements of deeper analog data from 14 passive‐margin samples show that porosity–permeability trends are maintained through burial and diagenesis to porosities <10%, suggesting that behavior observed in shallow samples is informative for predicting behavior at depth following subduction.
In this rapid communication, we address two important issues regarding the calculation of fragment mass-size distribution fractal dimension. We particularly focus on particle-size distribution, as a special case of fragment mass-size distribution, and demonstrate that the arithmetic mean concept frequently used in the literature is not supported. We also show that ignoring lower and upper cutoffs of fractal scaling may significantly alter the mass fractal dimension value. For these purposes, two examples using experiments available in the literature are given, and critical analyses are discussed in detail. We also reanalyze three databases reported in the literature, recalculate the mass fractal dimension, and show that applying the arithmetic mean concept and/or ignoring the lower and upper cutoffs may result in substantially different fractal dimension values. We note that the lower and upper cutoffs have to be reported in addition to the mass fractal dimension value. We also emphasize that accurate determination of the fractal scaling parameters, such as fractal dimension and lower and upper cutoffs requires precise characterization of the mass-size distribution.
Understanding and accurate prediction of gas or liquid phase (solute) diffusion are essential to accurate prediction of contaminant transport in partially saturated porous media. In this study, we propose analytical equations, using concepts from percolation theory and the Effective Medium Approximation (EMA) to model the saturation dependence of both gas and solute diffusion in porous media. The predictions of our theoretical approach agree well with the results of nine lattice Boltzmann simulations. We find that the universal quadratic scaling predicted by percolation theory, combined with the universal linear scaling predicted by the EMA, describes diffusion in porous media with both relatively broad and extremely narrow pore size distributions.
Herein, we report on a novel dual-site adsorption model to determine state of methane in shale formations and coalbeds. By considering two surface energy terms, the model distinguishes methane adsorption in the intrinsic micropore volume of the organic matter from that of the inorganic structure. One energy term describes methane adsorption in micropores (< 2 nm) whereas the other one concerns with meso-macropores. This study showed that at storage conditions, 150 bar and 50.4 °C, where methane is in supercritical state, the surface energy plays the major role to influence methane adsorption capacity whereas the effect of lateral forces between adsorbed molecules has a minor influence on overall adsorption capacity. We applied the model on experimental methane adsorption data in three organic-rich samples including Woodford shale, Woodford isolated kerogen and Cameo coal to quantify their methane storage state. Textural properties of shale and coal samples were analyzed by N2 porosimetry at − 196 °C. The samples had a weak micropore peak followed by a broader peak stretched over meso and macropore regions up to nearly 120 nm. Fitting the dual-site model to experimental methane adsorption data revealed that, among all, the coal sample, with the average heat of adsorption of 24.5 kJ/mol, had the highest interaction energies with both micro- and mesopore sites. Further, we find that 37%, 81% and 83% of methane was stored in the organic matter of Woodford shale, Woodford isolated kerogen and Cameo coal, respectively. Considering low maturity, and hence low micropore volume of the samples, and based on significant methane storage in the organic content we estimated that more than 50% of methane gas is being dissolved into the organic matter rather than just being adsorbed into the micropore volume.
Nuclear magnetic resonance (NMR) measurements are routinely used to characterize pore size distributions in fluid saturated porous media. The principle of the NMR measurement is that the result is linked with pore size by a parameter named surface relaxivity. However, in natural porous media, surface relaxivity is not constant or well-known due to heterogeneous distributions of impurities on pore surfaces. To control pore surface relaxivity, we injected paramagnetic zirconia nanoparticles into silica porous media: glass bead packs and sandstone core samples. Adsorption of the nanoparticles onto the pore surfaces altered their surface relaxivity due to differences in relaxivity between the silica surfaces and the nanoparticles. NMR measurements of porous media saturated with zirconia nanoparticle dispersions and deionized (DI) water were compared to calculate amount of adsorbed zirconia nanoparticles and quantify the alteration of pore surface relaxivity. Our results indicate that adsorption of nanoparticles onto pore surfaces leaves fewer nanoparticles in dispersion within the pore space and alters surface relaxation on pore wall with attached nanoparticles. The overall relaxation rate of the porous medium is thus affected by adsorption, which changes the surface relaxation rate and the relaxation rate of the fluid within the pore space. Electrostatic interactions drive nanoparticle adsorption onto pore walls. When silica porous media, which have negative surface charge, are saturated with positively charged nanoparticles, the nanoparticles adsorb onto the pore surface. When the porous media are saturated with negatively charged nanoparticles, no adsorption occurs. Our work highlights the importance of surface chemistry and adsorption on nanoparticle behavior in porous media and suggests that fundamental NMR behavior of media may be controlled with targeted adsorption of suitable nanoparticles.
Hydrate-bearing sands are being actively explored because they contain the highest concentrations of hydrate and are the most economically recoverable hydrate resource. However, relatively little is known about the mechanisms or timescales of hydrate formation, which are related to methane supply, fluid flux, and host sediment properties such as permeability. We used logging-while-drilling data from locations in the northern Gulf of Mexico to develop an effective medium theory-based model for predicting permeability based on clay-sized sediment fraction. The model considers permeability varying between sand and clay endpoint permeabilities that are defined from laboratory data. We verified the model using permeability measurements on core samples from three boreholes, and then used the model to predict permeability in two wells drilled in Walker Ridge Block 313 during the Gulf of Mexico Gas Hydrate Joint Industry Project Leg II expedition in 2009. We found that the cleanest sands (clay-sized fraction <0.05) had intrinsic (hydrate-free) permeability contrasts of 5–6 orders of magnitude with the surrounding clays, which is sufficient to provide focused hydrate formation due to advection of methane from a deep source or diffusion of microbial methane from nearby clay layers. In sands where the clay-sized fraction exceeds 0.05, the permeability reduces significantly and focused flow is less pronounced. In these cases, diffusion of dissolved microbial methane is most likely the preferred mode of methane supply for hydrate formation. Our results provide important constraints on methane supply mechanisms in the Walker Ridge area and have global implications for evaluating rates of methane migration and hydrate formation in hydrate-bearing sands.
We expanded an existing model for permeability in mudrocks and shaly sands to include computation of effective grain radius and the Archie’s law parameter m">m in granular media composed of two different grain sizes. We found that the effective grain radius is the harmonic mean of the endmember grain radii and that m">m can be computed as the geometric mean of the endmember m">m values. We tested our model with three-dimensional lattice-Boltzmann simulations of flow through dilute and concentrated systems, and with comparison to measurements of laboratory-prepared and natural samples as well as field data. Modeled permeabilities matched the simulated and measured permeabilities over a wide range of porosities, grain sizes, and grain shapes. We additionally found that the model is independent of grain packing and aspect ratio, as these parameters only affect the endmember m">m values. Our predicted permeabilities generally fall within previously determined bounds, and we derive approximations for permeability as a function of endmember permeability for cases when endmember m">m values are equal and when endmember grain radii are very different. Our results advance our understanding of permeability in heterogeneous porous media.
Using end‐member permeabilities defined by a worldwide compilation of sediment permeabilities at convergent margins, we compare permeability predictions using a geometric mean and a two‐component effective medium theory (EMT). Our implementation of EMT includes a threshold fraction of the high‐permeability component that determines whether flow occurs dominantly in the high‐ or low‐permeability component. We find that this threshold fraction in most cases is equal to the silt + sand‐sized fraction of the sediment. This suggests that sediments undergoing primary consolidation tend to exhibit flow equally distributed between the high‐ and low‐permeability components. We show that the EMT method predicts permeability better than the weighted geometric mean of the end‐member values for clay fractions <0.6. This work provides insight into the microstructural controls on permeability in subducting sediments and valuable guidance for locations which lack site‐specific permeability results but have available grain‐size information.
Electrical conductivity is a fundamental characteristic describing how strongly a network opposes flow of electrical current. In fully water‐saturated porous media the conductivity, represented by the formation factor, is mainly controlled by porosity, connectivity of the conducting phases, and the tortuosity of electrical current paths. Previous work has shown that universal scaling derived from percolation and effective medium theories accurately describes the relationship between formation factor and porosity when the percolation threshold is taken account, as well as the porosity value at which the scaling switches from percolation theory to effective medium theory. We determined the formation factor in clay‐rich sediments based on cation exchange capacity measurements on samples from five scientific ocean drilling sites in the Nankai Trough. We then compared the results to predictions from universal scaling after determining the volume of clay‐bound water and the percolation threshold. We found that the previously reported universal scaling relations hold in these clay‐rich sediments once the corrections are made for the clay‐bound water and that percolation scaling appears to be valid over the entire range of observed porosities, probably due to relatively broad pore size distributions or low pore system connectivity. Our results show that universal scaling can be applied to describe the porosity dependence of the formation factor in clay‐rich sediments when appropriate corrections are made for the presence of clay‐bound water.
Characterizing the quality and quantity of hydrocarbons associated within shales is important for evaluating a formation for future production. Traditional methods utilizing Nuclear Magnetic Resonance (NMR) which rely on the use of T2 relaxation are not sufficient in shales due to the nano-scale nature of the pores. Instead, we propose the use of differential T1 and T2 maps to represent a characteristic change in the sample. We performed thermogravimetric analysis (TGA) along with Pyrolysis Gas Chromatography-Mass Spectrometry (Py-GC-MS) measurements of Bakken, Utica, and Eagle Ford cores at various temperatures and compared them to these T1 and T2 differential maps in order to correlate fluid type. Additionally, at higher temperatures, we believe the maturation of kerogen is evident via a gradual change in peak locations in the T1 and T2 maps, which is difficult to quantify with T2 and diffusion maps due to the low diffusion rates of kerogen.
We performed uniaxial, constant-rate-of-strain consolidation experiments; grain size analyses; specific surface measurements; and mercury injection capillary pressure (MICP) measurements to characterize transport and deformation properties of 30 specimens from Integrated Ocean Drilling Program Expedition 333 Sites C0011, C0012, and C0018. Permeability, compression index, and overconsolidation ratio were determined from consolidation experiments. Permeability values range from 2.3 × 10–14 m2 to 5.9 × 10–19 m2 and generally decrease with increasing depth. Compression indexes, which define stress-strain behavior during consolidation, range from 0.26 to 2.7. Overconsolidation ratios, defined as the ratio of the preconsolidation stress to the in situ vertical effective stress under hydrostatic conditions, range from 0.20 to 4.1 and generally decrease with increasing depth. Median grain sizes determined by Stokes settling analysis range from 1.10 to 15.4 µm, and samples consist mainly of silt- and clay-sized particles. Specific surface values determined by methylene blue adsorption range from 25.7 to 77.7 m2/g. MICP measurements on a subset of 14 samples yield median pore throat radii of 0.087 to 0.36 µm and air-water capillary entry pressure values of 64 to 770 kPa.
Pore size distributions in rocks may be represented by fractal scaling, and fractal descriptions of pore systems may be used for prediction of petrophysical properties such as permeability, tortuosity, diffusivity, and electrical conductivity. Transverse relaxation time (T2) distributions determined by nuclear magnetic resonance (NMR) measurements may be used to determine the fractal scaling of the pore system, but the analysis is complicated when internal magnetic field gradients at the pore scale are sufficiently large. Through computations in ideal porous media and laboratory measurements of glass beads and sediment samples, we found that the effect of internal magnetic field gradients was most pronounced in rocks with larger pores and a high magnetic susceptibility contrast between the pore fluid and mineral grains. We quantified this behavior in terms of pore size and Carr-Purcell-Meiboom-Gill (CPMG) half-echo spacing through scaling arguments. We additionally found that the effects of internal field gradients may be mitigated in the laboratory by performing T2 measurements with different CPMG half-echo spacings and fitting the apparent fractal dimensions determined by the NMR measurements with a model to determine the true pore system fractal dimension.
Our work shows how pore size affects the quantity of methane dissolved in pore fluid in sediments from the Nankai Trough offshore Japan. Integrating log and laboratory data from shallow sediments in the Nankai Trough, we determined that the range of pore sizes in this region leads to methane hydrate equilibrium temperature depressions of about 1–3 degrees C at Site C0011, 2–5 degrees C at Site C0012, and 1-5 degrees C at Site C0018. Methane solubility was determined to increase by 10–30 percent at Sites C0011 and C0012, while solubility increases at Site C0018 were predicted to be between 10 and 50 percent throughout the methane hydrate stability zone. Further, the increase in methane solubility due to the Gibbs-Thomson effect was found to significantly decrease the mass of methane deposited as hydrate as well as decrease the thickness of the methane hydrate stability zone.