Inaccessible Pore Research Articles

In English

The aim of this study was to compare a variety of methods to describe the textural characteristics of various materials. Several ways could be used to describe the morphological and textural characteristics of various materials in detail such as: (i) adsorption-desorption of low-molecular weight probe compounds (N 2 , CO 2 , Ar, C 6 H 6 , H 2 O, etc.) in the gaseous (vapor) phase with increasing-decreasing pressure; (ii) adsorption of low- or high-molecular weight compounds from liquid solutions with increasing concentration of a solute; (iii) small angle X-ray scattering (SAXS) or small angle neutron scattering (SANS); (iv) quantitative analysis of images recorded using TEM, SEM, AFM, CLSM, etc.; (v) thermoporometry based on DSC or TG measurements with decreasing-increasing temperature; (vi) cryoporometry based on NMR spectroscopy measurements vs. temperature; and (vii) relaxometry based on NMR spectroscopy and thermally stimulated depolarization current measurements. There are several reasons of the use of mentioned above methods in parallel. For example, a material, which is strongly hydrated in native state, can strongly change the texture upon drying; thus, it should be studied in both states. Various adsorbates can penetrate into different pores or differently fill pores of different sizes that should be taken into account upon the analyses of various data. There are accessible and inaccessible pores (such as closed or too narrow for used adsorbate molecules), but SAXS can give information on all pores in contrast to the adsorption methods. Thus, the larger the number of applied methods, the more comprehensive the morphological and textural characterization of the adsorbents, and this is clearly shown below.

Study on the Influence of Inaccessible Pore Volume of Polymer Development

In this paper, laboratory experiment and numerical simulation methods show that: (1) For reservoir formations with different permeability, there exists an optimal molecular weight for injection, and as the permeability increases, the optimal molecular weight gradually increases; (2) Inaccessible pore volume is too large, the polymer solution to reduce the volume; Inaccessible pore volume is too small, the polymer adsorption loss increases, affecting the polymer flooding effect. Therefore, there is an optimal value for the inaccessible pore volume; (3) At different times into polymer flooding, the optimal inaccessible pore volume will change, and the later the transfer time, the best access to the larger inaccessible pore volume. For example, the optimal unobtainable pore volume at 90% water injection is 0.4, while the optimal inaccessible pore volume at 30% aqueous transfer is 0.3.

Characteristics of microscopic pore structure and fractal dimension of bituminous coal by cyclic gas adsorption/desorption: An experimental study

The characteristics of micropore (0.32–2 nm), mesopores (2–50 nm) and fractal dimensions of bituminous coal during the process of cyclic gas adsorption/desorption were revealed by combining N2 (77 K) and CO2 (273 K) adsorption experiments from microscopic aspect. The results indicate that the pore structure characterization in the coal matrix are changed, resulting in decreased mesopore volumes and increased micropore volumes. The mesopore volumes are mainly constituted by the pores of 10–20, and 20–30 nm, and it will increase at first and then decrease with the increasing pressures. The maximum change of micropore volume reaches 65.6%, indicating a great effect on the micropores influenced by pressures. In addition, the main micropore size range, major peak and the model diameter of coals all increase with the increasing pressures, the higher the adsorb pressure is, the higher swelling is. With the help of the conceptual models, we then analyzed the variation reasons, which may be result from transformation of mesopores and the connection of the inaccessible pores. D1 and D2 in #1 and D2 in #2 all increase with the increasing adsorption pressures, enhancing the roughness of surface and complexity of structure, while D1 in #2 shows an opposite property. The study of variations of microscopic pore structure by cyclic adsorption/desorption was aimed at providing new understanding for the exploration of the changes of diffusion and permeability.

Cell wall microstructure, pore size distribution and absolute density of hemp shiv.

This paper, for the first time, fully characterizes the intrinsic physical parameters of hemp shiv including cell wall microstructure, pore size distribution and absolute density. Scanning electron microscopy revealed microstructural features similar to hardwoods. Confocal microscopy revealed three major layers in the cell wall: middle lamella, primary cell wall and secondary cell wall. Computed tomography improved the visualization of pore shape and pore connectivity in three dimensions. Mercury intrusion porosimetry (MIP) showed that the average accessible porosity was 76.67 ± 2.03% and pore size classes could be distinguished into micropores (3–10 nm) and macropores (0.1–1 µm and 20–80 µm). The absolute density was evaluated by helium pycnometry, MIP and Archimedes' methods. The results show that these methods can lead to misinterpretation of absolute density. The MIP method showed a realistic absolute density (1.45 g cm−3) consistent with the density of the known constituents, including lignin, cellulose and hemi-cellulose. However, helium pycnometry and Archimedes’ methods gave falsely low values owing to 10% of the volume being inaccessible pores, which require sample pretreatment in order to be filled by liquid or gas. This indicates that the determination of the cell wall density is strongly dependent on sample geometry and preparation.

Evaluation of Accessible Porosity Using Mercury Injection Capillary Pressure Data in Shale Samples

We present a novel approach to correct accessible/fluid-saturated porosity values calculated using mercury injection capillary pressure (MICP) for shale samples. On the basis of recent studies, accessible porosity of shale samples calculated from the MICP test is corrected to consider conformance and grain compressibility. However, we show here that the shale samples experience an additional phenomenon during the MICP test that has not yet been addressed, i.e., compression of inaccessible/unfilled pores. Therefore, we propose a general approach consisting of three distinct corrections to accurately estimate accessible porosity of the shale sample using MICP data: (1) conformance, (2) grain compressibility, and (3) inaccessible pore compressibility. First, we develop a mathematical model to estimate both pore and grain compressibility using MICP data and then calculate accessible porosity using the above-mentioned corrections. In the mathematical formulation, we divide the shale matrix into three constitue...

Porosity of the Marcellus Shale: A contrast matching small-angle neutron scattering study

Neutron scattering techniques were used to determine the effect of mineral matter on the accessibility of water and toluene to pores in the Devonian Marcellus Shale. Three Marcellus Shale samples, representing quartz-rich, clay-rich, and carbonate-rich facies, were examined using contrast matching small-angle neutron scattering (CM-SANS) at ambient pressure and temperature. Contrast matching compositions of H2O, D2O and toluene, deuterated toluene were used to probe open and closed pores of these three shale samples. Results show that although the mean pore radius was approximately the same for all three samples, the fractal dimension of the quartz-rich sample was higher than for the clay-rich and carbonate-rich samples, indicating different pore size distributions among the samples. The number density of pores was highest in the clay-rich sample and lowest in the quartz-rich sample. Contrast matching with water and toluene mixtures shows that the accessibility of pores to water and toluene also varied among the samples. In general, water accessed approximately 70–80% of the larger pores (>80 nm radius) in all three samples. At smaller pore sizes (~5–80 nm radius), the fraction of accessible pores decreases. The lowest accessibility to both fluids is at pore throat size of ~25 nm radii with the quartz-rich sample exhibiting lower accessibility than the clay- and carbonate-rich samples. The mechanism for this behaviour is unclear, but because the mineralogy of the three samples varies, it is likely that the inaccessible pores in this size range are associated with organics and not a specific mineral within the samples. At even smaller pore sizes (~<2.5 nm radius), in all samples, the fraction of accessible pores to water increases again to approximately 70–80%. Accessibility to toluene generally follows that of water; however, in the smallest pores (~<2.5 nm radius), accessibility to toluene decreases, especially in the clay-rich sample which contains about 30% more closed pores than the quartz- and carbonate-rich samples. Results from this study show that mineralogy of producing intervals within a shale reservoir can affect accessibility of pores to water and toluene and these mineralogic differences may affect hydrocarbon storage and production and hydraulic fracturing characteristics.

Models for Strength Prediction of High‐Porosity Cast‐In‐Situ Foamed Concrete

A study was undertaken to develop a prediction model of compressive strength for three types of high‐porosity cast‐in‐situ foamed concrete (cement mix, cement‐fly ash mix, and cement‐sand mix) with dry densities of less than 700 kg/m3. The model is an extension of Balshin’s model and takes into account the hydration ratio of the raw materials, in which the water/cement ratio was a constant for the entire construction period for a certain casting density. The results show that the measured porosity is slightly lower than the theoretical porosity due to few inaccessible pores. The compressive strength increases exponentially with the increase in the ratio of the dry density to the solid density and increases with the curing time following the composite function for all three types of foamed concrete. Based on the results that the compressive strength changes with the porosity and the curing time, a prediction model taking into account the mix constitution, curing time, and porosity is developed. A simple prediction model is put forward when no experimental data are available.

Distribution and Presence of Polymers in Porous Media

In order to better utilize the residual polymers formed after polymer flooding, the distribution and the presence of the polymers after polymer flooding were studied. This paper studied the vertical and plane distribution of the hydrophobically-associating polymer in addition to measuring the parameters after polymer flooding, which is important for numerical reservoir simulation. The results showed that the polymers mainly enter into the high permeability zone and distribute in the mainstream line area with only a small portion in the wing area. Based on the comparison of various experimental methods, double-slug experiments were chosen to measure the inaccessible pore volume and retention, which is considered to be the most accurate, most time-consuming and most complex method. Following this, we improved the processing method of experimental data by reducing it to one experiment with two parameters. At the same time, we further enhanced the accuracy of the experimental results. The results show that at 1750 mg/L, the inaccessible pore volume of the polymer is 25.8%. When the detention is 68.2 µg/g, the inaccessible pore volume constituted 22% of the total polymer, with the other 77.7% being the dissolved polymer. Moreover, the static adsorption and dynamic detention were measured, with the results showing that the static adsorption is larger than dynamic detention. Therefore, in the numerical reservoir simulation, using the static adsorption capacity instead of the dynamic detention is unreasonable. The double-slug method was chosen since it is more accurate for the determination of various parameters. Meanwhile, in order to enhance the accuracy of results, we improved the treatment of data.

Excavating hidden adsorption sites in metal-organic frameworks using rational defect engineering

Metal–organic frameworks are known to contain defects within their crystalline structures. Successful engineering of these defects can lead to modifications in material properties that can potentially improve the performance of many existing frameworks. Herein, we report the high-throughput computational screening of a large experimental metal–organic framework database to identify 13 frameworks that show significantly improved methane storage capacities with linker vacancy defects. The candidates are first identified by focusing on structures with methane-inaccessible pores blocked away from the main adsorption channels. Then, organic linkers of the candidate structures are judiciously replaced with appropriate modulators to emulate the presence of linker vacancies, resulting in the integration and utilization of the previously inaccessible pores. Grand canonical Monte Carlo simulations of defective candidate frameworks show significant enhancements in methane storage capacities, highlighting that rational defect engineering can be an effective method to significantly improve the performance of the existing metal–organic frameworks.

Computation of polymer in-situ rheology using direct numerical simulation

In-situ rheology of synthetic polymers like hydrolyzed polyacrylamide, HPAM, cannot be directly calculated from bulk rheology. The in-situ viscosity of polymers will be influenced by shear history and local pore structure contraction/expansion. Transition from flux in porous media to bulk shear rate requires empirical correlations. The conventional approach for in-situ rheology is to define apparent viscosity vs. Darcy velocity and connecting Darcy velocity to bulk shear rate by using a correction factor, which generally depends on both polymer and rock properties.Estimating polymer in-situ rheology is important for estimation of displacement pressure gradients and injectivity in the reservoir. In the following study, different models used to quantify the shear-to-flux correction factor are compared by using direct numerical simulation in 3D real rock images. We found that the models developed based on capillary bundle approach are not able to predict accurately in-situ rheology and microstructures of a rock sample can influence in-situ rheology. A novel approach is suggested to provide a more accurate prediction of in-situ rheology by adjusting appropriately bulk power index of the Carreau model before applying the correction factor. The pore scale simulations have revealed that the key parameters of porous media influencing in-situ rheology are pore aspect ratio and inaccessible pore volume.

Ultra micropores in macromolecular structure of subbituminous coal vitrinite

Pores in coal provide surface area and volume for coalbed methane storage. In this study, a 3 dimensions (3D) macromolecular structure of subbituminous coal vitrinite was constructed, which was demonstrated to be consistent with the experimental Nuclear Magnetic Resonance (NMR) data, density data and pore volume data, to study ultra micropores formed in the macromolecule. The results showed that both accessible pores and inaccessible pores existed in the macromolecular structure and that all pores were smaller than 0.62nm. Most of the accessible pores were formed by aliphatic chains and most of the atoms that directly touched the pore surface were hydrogen atoms. The accessible pores showed obvious fractal features, and the fractal dimension of pores detected by probes smaller than 0.5nm is 2.73. We also found that the volume of pores seen by helium is considerably larger than that of pores seen by methane. This would result in underestimation of methane adsorption capacity in a volumetric methane adsorption experiment, where the void volume is tested by helium. For the coal sample Y-1, the methane adsorption capacity would be underestimated by 2.7cm3/g at 10MPa.

Fractal evolution under in situ pressure and sorption conditions for coal and shale

Coalbed methane (CBM) and shale gas become two most important unconventional natural gas resources in US. The fractal dimension, known as the degree of self-similarity or irregularity, is an important parameter to quantitatively characterize gas storage capacity and gas transport properties in pores of rock matrix. In this study, two coal and two shale samples were evaluated to estimate fractal dimensions using combined small angle X-ray scattering (SAXS), small angle neutron scattering (SANS) and low-pressure N2 adsorption techniques. The results show that surface fractal dimension Ds of inaccessible pores is greater than that for total pores based on SANS results for all four tested samples. Ds of accessible pores estimated by N2 desorption is greater than that for N2 adsorption for each linear section of each tested sample. Based on in situ SANS results, Ds slightly decreases with increasing argon injecting pressure for San Juan coal. Ds decreases with increasing methane and CO2 injecting pressure for samples with high Ds. However, Ds significantly increases when CO2 became liquid phase for samples with low Ds. Furthermore, Ds almost didn’t change after methane and argon penetrations for all these samples except Marcellus outcrop shale.

Pore Compressibility of Shale Formations

Summary This study introduces a novel outlook on a shale-pore system and on the potential effect of pore compressibility on the production performance. We divide porosity of the system into accessible and inaccessible pores, and incorporate inaccessible pores with grains into the part of the rock that is not accessible. In general, accessible pores contribute to flow directly, whereas inaccessible pores do not. We present a mathematical model that uses mercury-injection capillary pressure (MICP) data to determine the accessible-pore and inaccessible part of the rock (IRP) compressibility as a function of pressure. During MICP testing in a typical shale sample, the rock sample experiences conformance, compression, and intrusion as effective pressure increases. We characterize the compressibility value dependent on MICP data as a function of pressure. The calculated compressibility values for accessible pores generally appear to be much greater (two to three orders of magnitude) than those of IRP. Next, we evaluate how calculated accessible-pore-compressibility values affect gas recovery in several shale-gas plays. Our results suggest that substitution of total pore compressibility with accessible-pore compressibility can significantly change the reservoir-behavior prediction. The fundamental rock property used in many reservoir-engineering calculations including reserves estimates, reservoir performance, and production forecasting is the total pore-volume (PV) compressibility, which has an approximate value typically within the range of 1 × 10−6 to 1 × 10−4 psi−1 (Mahomad 2014). By recognizing the part of the pore system that actually contributes to production and identifying its compressibility, we can substitute total pore compressibility with accessible-pore compressibility. The result changes the value by nearly two orders of magnitude. The outcome of the paper changes the industry's take on prediction of reservoir performance, especially the rock-compaction mechanism. This study finds that production caused by rock compaction is in fact much greater than what has often been regarded, which will change the performance evaluation on a great number of reservoirs in terms of economic feasibility.

Undesorbable residual gas in coal seams and its influence on gas drainage

The definition of “residual gas” can be found in different scenarios, such as the “fast” and “slow” desorption methods of measuring gas content and the sorption hysteresis test and gas management of coal mines, however, its meaning varies a lot in different contexts. The main aim of this paper is to discuss the existence of truly undesorbable residual gas in coal seam conditions and its impacts on sorption model and gas drainage efficiency. We believe the undesorbable residual gas does exist due to the observation of the extended slow desorption test and the sorption hysteresis test. The origin of undesorbable residual gas may be because of the inaccessible (closed or semi-closed) pores. Some gas molecules produced during coalification are stored in these inaccessible pores, since the coal is relatively intact in the coal seam condition, these gas molecules cannot escape during natural desorption and then create the undesorbable residual gas. Based on the existing adsorption models, we propose the improved desorption versions by taking into consideration the role of residual gas. By numerically simulating a gas drainage case, the gas contents after different drainage times are studied to understand the influence of residual gas content on gas drainage. The results indicate that the influence starts to be obvious even when the total gas content is at a high level, and the impact becomes more and more apparent with increasing drainage time. Our study shows that the existence of residual gas will impede the gas drainage and the total amount of recoverable coal seam methane may be less than expected.

Impact of flow rate variation in dynamic properties of a terpolymer in sandstone

The effectiveness of polymer enhanced oil recovery relies on its dynamic properties in the porous medium, such as resistance factor (RF), residual resistance factor (RRF), inaccessible pore volume (IAPV), in-situ viscosity, and retention. This paper presents a laboratory investigation of the injection flow rate on those properties of a terpolymer containing hydrolyzed polyacrylamide flowing through sandstone. We propose a methodology and evaluate the flow rate influence by both increasing and decreasing its values in different experiments. The materials, experimental setup, test protocol, and data treatment are explained thoroughly to allow reproduction. We analyze three different methodologies to measure dynamic retention, and we compare the results with one another. We report both irreversible (due to adsorption) and reversible (due to hydrodynamic effects) retentions, and also analyze their trends. In our experiments, reversible retention, RF, and RRF increase with the flow rate. The IAPV do not show any trend regarding the flow rate. We also obtain a good correlation between in-situ viscosity and a literature model. Our results indicate that the in-situ viscosity correlates to the IAPV.

Predicting the pore-filling ratio in lumen-impregnated wood

Lumen impregnation, unlike most other wood modification methods, is typically assessed by the pore-filling ratio (PFR) (i.e. the fraction of luminal porosity filled) rather than by weight percentage gain (WPG). During lumen impregnation, the impregnants act on the voids in the wood rather than on the solid mass (e.g. cell walls), but the PFR cannot be measured as conveniently as the WPG during processing. Here, it is demonstrated how the PFR can be calculated directly from the WPG if the bulk density of the untreated wood is known. The relationship between the WPG and bulk density was examined experimentally by applying a pressured impregnation on knot-free specimens from Sitka spruce with a liquid mixture of methacrylate monomers. Based on the validated model, it was possible to further study the effect of different process-related parameters, such as hydraulic pressure, on lumen impregnation. Skeletal density is another key parameter in this model, which directly reflects the amount of inaccessible pores and closed lumens, and can be independently determined by helium pycnometry. The permeability can be qualitatively evaluated by PFR as well as skeletal density. For instance, poor permeability of knotty wood, due to the large extractives content around knots, was reflected by a lower skeletal density and inefficient lumen impregnation (low PFR). Although this model was examined on a laboratory scale, it provides guidance on the precise effect of different parameters on lumen impregnation, thereby improving the fundamental understanding of and enabling better control over the modification of wood by impregnation.

Experimental study on swelling behaviour and microstructure changes of natural stiff Teguline clays upon wetting

This paper addresses the microstructure change induced by swelling for natural stiff Teguline clays. The predominant clay mineral measured by X-ray diffractometry was identified to be illite and no swelling clay minerals were found. Significant swelling occurs upon wetting, illustrating the process of suction release from a nearly fully saturated condition. Mercury intrusion porosimetry (MIP) and scanning electron microscopy were used to identify the change in microstructure with swelling during wetting. It is found that the soil swelling mainly leads to an increase of macropores (0.15–350 μm), and a slight decrease of micropores (0.006–0.15 μm) and inaccessible pores (&lt;0.006 μm and &gt;350 μm). Furthermore, swelling was found to occur in the direction perpendicular to the bedding plane, indicating an anisotropic swelling behaviour. The creation and development of cracks during wetting were also investigated. It appears that most cracks caused by swelling have the size of macropores (0.15–350 μm) identified by the MIP test. These findings call enough attention to the significant change in microstructure by wetting-induced swelling that can strongly influence the thermohydromechanical properties of stiff clays.

Laboratory Experiment on Inaccessible Pore Volume of Polymer Flooding

The research on inaccessible pore volume is completed on the basis of laboratory experiments. The experiment prepared 4 different kinds of polymers, whose molecular weight are 8 million, 12 million, 16 million and 20 million whose molecular coil size are measured by light blockage counter. Through kerosene mass method we can get pore cumulative distribution of field cores and finally plot the relation between the inaccessible pore volume and molecular coil size of polymer. The size of small pore where primary water was taken as the minimum number polymer coils can be passed. Then the polymer molecular weight with better compatibility with rock pores is optimized. The study shows with the increase of polymer relative molecular mass, pore volume increased linearly. The conclusion can better guide the selection of the polymers in practical production.

An analysis of physical models and numerical schemes for polymer flooding simulations

Chemical-enhanced oil recovery (CEOR) processes are nowadays commonly used by engineers to improve the recovery factor of an oil field. In this paper, we propose to investigate the physical and numerical singularities arising in the numerical simulation of polymer-enhanced oil recovery technique for oil fields. We assume that the polymer is only transported in the water phase or adsorbed on the rock. The polymer reduces the water-phase mobility and can change drastically the behavior of water oil interfaces. Due to its size, the polymer flows faster than water so that an inaccessible pore volume must be added in the model. After a brief description of different models for polymer adsorption, mobility reduction, and inaccessible pore volume, we discuss the mathematical singularities of the obtained system. In the framework of industrial reservoir simulators, we focus on a constant inaccessible pore volume model which may lead to severe mathematical and numerical singularities. We consider an IMPES scheme; we propose approximate Courant-Friedrichs-Levy (CFL) criteria which are required to obtain some numerical stability of the simulation. 1D numerical polymer flooding experiments are computed with a complete reservoir simulator to illustrate the validity of our approximate CFL criteria.

Fully implicit simulation of polymer flooding with MRST

The present work describes a fully implicit simulator for polymer injection implemented in the free, open-source MATLAB Reservoir Simulation Toolbox (MRST). Polymer injection is one of the widely used enhanced oil recovery (EOR) techniques, and complicated physical process is involved, which makes accurate simulation very challenging. The proposed work is intended for providing a powerful and flexible tool to investigate the polymer injection process in realistic reservoir scenarios. Within the model, the polymer component is assumed to be only transported in the water phase and adsorbed in the rock. The hydrocarbon phases are not influenced by the polymer, and they are described with the standard, three-phase, black-oil equations. The effects of the polymer are simulated based on the Todd–Longstaff mixing model, accounting for adsorption, inaccessible pore space, and permeability reduction effects. Shear-thinning/thickening effects based on shear rate are also included by the means of a separate inner-Newton iteration process within the global nonlinear iteration. The implementation is based on the automatic differentiation framework in MRST (MRST-AD), and an iterative linear solver with a constrained pressure residual (CPR) preconditioner is used to solve the resulting linear systems efficiently. We discuss certain implementation details to show how convenient it is to use the existing functionality in MRST to develop an accurate and efficient polymer flooding simulator for real fields. With its modular design, vectorized implementation, support for stratigraphic and general unstructured grids, and automatic differentiation framework, MRST is a very powerful prototyping and experimentation platform for development of new reservoir simulators. To verify the simulator, we first compare it with a commercial simulator and good agreement is achieved. Then, we apply the new simulator to a few realistic reservoir models to investigate the effect of adding polymer injection, and computational efficiency is demonstrated. Finally, we combine existing optimization functionality in MRST with the new polymer simulator to optimize polymer flooding for two different reservoir models. We argue that the presented software framework can be used as an efficient prototyping tool to evaluate new models for polymer–water flooding processes in real reservoir fields.