Minimum Pore Radius Research Articles

A novel analytical model for porosity-permeability relations of argillaceous porous media under stress conditions

Argillaceous rocks, such as sandstones, shales, and mudstones, are widely distributed in nature and constitute approximately 50% of the global sedimentary rocks. They are the conventional reservoir rocks for hydrocarbon resources. To better characterize hydrocarbon resources, it is essential to understand the fundamental physical properties of argillaceous porous media (APM), and one of the most crucial properties is the porosity-permeability relationship (PPR). However, due to the enormous complexity of pore structures in APM, the effects of relevant factors on PPR remains unclear, and the major factors controlling PPR are still open questions. In this work, experimental tests were carried out on 43 artificial argillaceous sandstone samples to evaluate the porosity and permeability relations under stress dependence. An analytical model was then proposed to interpret the experimental results. The analytical solutions are consistent with the experimental data and the simulation results obtained from the Lattice Boltzmann method. It indicates that the derived model can precisely capture the PPR of APM. The analysis results show that the PPR of APM under stress dependence is related to clay volume content, effective stress, initial irreducible water saturation, rock lithology, and pore structure parameters (e.g., the maximum pore radius, the minimum pore radius, pore fractal dimension and tortuosity fractal dimension). These findings can enhance the understanding of the PPR and coupled flow-deformation behavior in APM and set the stages for a proper investigation of PPR in APM.

Пористость консолидированных методом газовой экструзии компактов из никелевых нанопорошков

The method of hot gas extrusion differs from other methods of metal pressure treatment in that the processed material is subjected to intense plastic deformation by extrusion under conditions of high isostatic pressure of inert gas and heating in the area of plastic deformation. The method makes it possible to process powder materials, while inevitably there is a need to control mechanical properties by controlling porosity and pressure inside the pores. The paper presents a method for calculating the pressure inside the pores from the minimum size of the closed pore. The pore pressure was evaluated on materials obtained by the consolidation of nickel nanopowders by hot gas extrusion. Quantitative processing of the material cross-section view images obtained by scanning electron microscopy showed that the minimum pore size is 220 nm. The formula for calculating the pore pressure is derived from the formula for calculating the critical pore radius. It takes into account the external impact pressure (the gas pressure during the extrusion process was equal to 400 MPa), the surface tension coefficient and the yield strength of nickel (at the extrusion start temperature of 910 °С), as well as the minimum pore radius. The proposed method for calculating the pressure inside a closed pore will allow us to evaluate the mechanical properties of materials obtained by various methods of powder metallurgy.

Fractal wave velocity evolution model of ultrasonic propagation and attenuation in water-bearing coal

A fractal wave velocity evolution model of the water-bearing coal is constructed to explore the relationship between the complex pore and fissure structure parameters of the water-bearing coal mass and the ultrasonic P-wave velocity, based on the fractal theory and with consideration of the attenuation of ultrasonic waves propagating in the porous media of coal. In addition, experimental study and numerical analysis of the model are carried out, the following conclusions are reached. (1) The P-wave velocity increases with the increase of the coal sample length, the water content, the wave velocity in the coal matrix and the maximum pore radius, and decreases with the increase of the minimum pore radius. (2) The experimental results also show that the P-wave velocity increases with the increase of the water content and fractal dimension of the coal sample, indicating that the wave velocity prediction model has high accuracy. (3) The fractal dimension, water content, wave velocity in the coal matrix and coal sample length have great effects on the P-wave velocity of coal samples, while the minimum pore radius and the maximum pore radius have relatively little influences on the P-wave velocity.

Investigation on pore structure, fluid mobility and water huff-n-puff oil recovery of tight volcanic oil reservoir

The pore structure of tight volcanic oil reservoirs is very complex and the permeability is extremely low. The oil recovery effect of traditional water-driven and gas-driven development is not ideal. In this paper, we first analyzed the pore structure characteristics and fluid movability characteristics of tight volcanic rocks. Then, the feasibility of water huff-n-puff in tight volcanic rocks was analyzed. Finally, we investigated the oil recovery characteristics, pore motility characteristics, and ORM of water huff-n-puff in tight volcanic rocks by using a high temperature and ultra-high pressure water huff-n-puff physical simulation experimental device under NMR monitoring. The study shows that the mineral composition of tight volcanic rocks is relatively simple, but the pore structure is very complex. The pores are mainly amygdule pores, and contain some vesicular pores and matrix pores. The fractures include structural fractures, dissolution fractures, and shrinkage fractures. Fractures are of great significance for communicating relatively independent pores and improving the seepage ability of fluids in tight volcanic rocks. The fluid movable saturation of tight volcanic rocks is 32.93%–83.75%, and the minimum movable pore radius is 0.0178 μm. The seepage capacity of large pores (r > 0.1 μm) is 2.19–7.75 times that of middle pores (0.001 μm < r < 0.1 μm). The oil recovery efficiency (the ratio of the volume of recovered oil to the volume of injected water) of the first two cycles of water huff-n-puff of tight volcanic rocks exceeds 20%, which is high-efficiency oil recovery period. However, with the increasing huff and puff cycles, the recovery factor and oil change rate both decrease rapidly. After five cycles of water huff-n-puff, the recovery factor of tight volcanic rocks increases by 29.13%. For the selected experimental core, middle pores are the main oil-producing pores, and their contribution rates in natural energy depletion and five cycles of water huff-n-puff are 59.665% and 78.173%. In five cycles of water huff-n-puff, the contribution rates of elastic displacement are 96.491%, 93.846%, 86.667%, 64.706%, and 55.556%, and the effect of imbibition displacement is relatively small. Increasing the water injection pressure is beneficial to water huff-n-puff oil recovery of tight volcanic rocks. The research can provide a good theoretical basis for the efficient development of tight volcanic oil reservoirs.

Microstructural variations and damage evolvement of salt rock under cyclic loading

Fatigue tests under different maximum cycling stresses were performed on salt rock specimens to study the microstructural variations and damage evolvement of salt rock under cyclic loading. A nuclear magnetic resonance (NMR) instrument was utilized to record the microstructural variations in the specimens. The results indicated that with an increase in the number of cycles, the maximum pore radius in the salt rock initially increased and then remained constant, whereas the minimum pore radius initially decreased and then increased. The minimum pore size in the salt rock after 12,000 cycles was closely related to the maximum cycling stress. The porosity and permeability of the salt rock exhibited a two-stage change of “rapid increase – slow increase” and “slow increase – rapid increase”, respectively, with an increase in the number of cycles. In contrast, the tortuosity presented a two-stage process of “rapid decrease – slow decrease” with an increase in the number of cycles. With an increase in the maximum cycling stress, the porosity and permeability of the salt rock after 12,000 cycles increased nonlinearly, whereas the tortuosity decreased linearly. The permeability exhibited a gradually ascending trend with an increase in the porosity. However, a critical porosity was observed. When the porosity was lower than that of the threshold, the change in porosity had a minor effect on permeability, whereas the effect of porosity on the permeability gradually increased when the porosity exceeded the threshold. The value of critical porosity of the salt rock specimens used in this paper was approximately 0.35%. The fatigue damage evolvement equation of salt rock under cyclic loading was established based on the change in porosity. The damage evolvement process of the salt rock specimens under different maximum stresses was analyzed. The results demonstrated that the fatigue damage evolvement process of salt rock consisted of three stages. However, the damage in the first two stages was relatively small, and the damage increased rapidly only when the salt rock was close to failure.

AN IMPROVED FRACTAL PERMEABILITY MODEL FOR POROUS GEOMATERIALS WITH COMPLEX PORE STRUCTURES AND ROUGH SURFACES

Permeability is a critical parameter for characterizing the migration behavior of a fluid in porous media, thus being of great importance in guiding the geotechnical engineering practice. In this study, an improved permeability model was developed on the basis of the fractal features of the porous geomaterials. It further takes into account the periodic variation of the cross-section of the pore path in the flow direction and the roughness of the pore surfaces. This model indicates that the permeability is a function of the porosity, maximum pore radius, proportion of minimum pore radius to the maximum pore radius, roughness of the capillary tube, and variation in the cross-sectional characteristics of the tube. It provides a better insight into the transport mechanism of fluids in porous geomaterials. The permeability of the model is related to the variable cross-sectional characteristics of the pore channel, i.e. the belly-to-throat ratio and the roughness, as a quadratic function. These two parameters are the key to affecting the level of permeability. The model was verified over a wide range of permeability variations by changing from high-permeability media (102 mD) to low-permeability media (10−3 mD). Accurate permeability prediction of high–low-permeability porous media can be achieved by considering the variation of parameters.

Calculation Model of Relative Permeability in Tight Sandstone Gas Reservoir with Stress Sensitivity

During the development of tight gas reservoir, the irreducible water saturation, rock permeability, and relative permeability change with formation pressure, which has a significant impact on well production. Based on capillary bundle model and fractal theory, the irreducible water saturation model, permeability model, and relative permeability model are constructed considering the influence of water film and stress sensitivity at the same time. The accuracy of this model is verified by results of nuclear magnetic experiment and comparison with previous models. The effects of some factors on irreducible water saturation, permeability, and relative permeability curves are discussed. The results show that the stress sensitivity will obviously reduce the formation permeability and increase the irreducible water saturation, and the existence of water film will reduce the permeability of gas phase. The increase of elastic modulus weakens the stress sensitivity of reservoir. The irreducible water saturation increases, and the relative permeability curve changes little with the increase of effective stress. When the minimum pore radius is constant, the ratio of maximum pore radius to minimum pore radius increases, the permeability increases, the irreducible water saturation decreases obviously, and the two-phase flow interval of relative permeability curve increases. When the displacement pressure increases, the irreducible water saturation decreases, and the interval of two-phase flow increases. These models can calculate the irreducible water saturation, permeability and relative permeability curves under any pressure in the development of tight gas reservoir. The findings of this study can help for better understanding of the productivity evaluation and performance prediction of tight sandstone gas reservoirs.

Predicting water flow in fully and partially saturated porous media: a new fractal-based permeability model

Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many models have been proposed in the literature to estimate the permeability from properties of the porous media such as porosity, grain size or pore size. In this study, we develop a model of the permeability for porous media saturated by one or two fluid phases with all physically-based parameters using a fractal upscaling technique. The model is related to microstructural properties of porous media such as fractal dimension for pore space, fractal dimension for tortuosity, porosity, maximum radius, ratio of minimum pore radius and maximum pore radius, water saturation and irreducible water saturation. The model is favorably compared to existing and widely used models from the literature. Then, comparison with published experimental data for both unconsolidated and consolidated samples, we show that the proposed model estimate the permeability from the medium properties very well.

A New Method to Determine the Lower Limit of Reservoir Physical Properties—Corrected Minimum Flow Pore-throat Radius Method

The lower limit of reservoir physical properties is an important parameter for identifying reservoirs and determining effective thickness in reserves evaluation, and is also an important basis for selecting perforated test intervals in oilfield exploration and development. There are many methods to determine the lower limit of reservoir physical properties, and the minimum flow pore throat radius method is one of the commonly used methods. The method uses 0.1μm as the minimum flow pore-throat radius, and uses this to calibrate the lower limit of reservoir physical properties. However, according to the water film theory, the minimum radius of the reservoir's flowing pore throat is not a definite value, but varies with the displacement dynamics. Therefore, there is no exact basis for using 0.1μm as the minimum flow pore-throat radius, so it needs to be corrected. To this end, a new method for determining the lower limit of reservoir physical properties—the corrected minimum flow pore-throat radius method is proposed. The correction method comprehensively considers the factors of oil and gas accumulation dynamics, and determines the lower limit of reservoir physical properties by obtaining the minimum flow pore-throat radius value suitable for oil and gas accumulation dynamics. A case study of Chang 63 reservoir in A Oilfield shows that the minimum flow pore radius of oil and gas determined by the correction method is 0.08 μm, and the lower limit of reservoir physical properties (porosity 9.1%, permeability 0.117 × 10-3 μm2). The traditional method has a minimum flow pore-throat radius of 0.1 μm and a lower limit of reservoir physical properties (porosity of 9.8% and permeability of 0.133 × 10-3 μm2). Due to full consideration of the impact of oil and gas accumulation dynamics, the minimum flow pore-throat radius determined by the correction method is more reliable than the traditional method, and the lower limit of the reservoir physical property calibrated by it has practical significance.

Effect of Water Distribution on Spontaneous Imbibition of Tight Rocks: A Fractal Approach

The original water distribution characteristic plays an important role in the fracturing liquid retention in actual tight reservoirs. In this paper, an analytical model was proposed to characterize the water distribution and its effect on the spontaneous imbibition, based on the capillary tube model and fractal theory. Furthermore, the effect of the water film and the non-piston-like front related to the pore size are included in our model. The proposed model was successfully validated with the experimental results of core imbibition tests. Our work demonstrates that water distribution is influenced by displacement pressure and pore structure. For a small differential pressure, the porous media with richer large pores usually possesses a lower water saturation, and this difference will decrease with the increase of differential pressure. Moreover, compared with previous studies, the proposed imbibition model can not only distinguish the valid pores and invalid pores for imbibition but it can also predict the initial imbibition rate and equilibrium time of tight porous media with different water saturation. The results show that the equilibrium time is controlled by the minimum effective pore radius while the initial imbibition rate is mainly controlled by the large pores. Both of these two parameters will decrease with an increase of water saturation; the former is more sensitive to a low water saturation, while the latter decreases more quickly for a middle-high water saturation.

A Novel Analytical Model for Pore Volume Compressibility of Fractal Porous Media

Over the past decades, many scholars have been studying the pore volume compressibility (PVC) of porous media. However, the fundamental controls on PVC of porous media are not yet definitive. Some scholars suggest a negative correlation between PVC and initial porosity, while others suggest a positive correlation. Motivated by this discrepancy, this paper presents a new analytical model to study the PVC of fractal porous media. The predictions are compared with test results and thereby validated to be accurate. In our attempt not only to complement but also to extend the capability beyond available models, the derived model accounts for multiple fundamental variables, such as the microstructural parameters and rock lithology of porous media. Results suggest that, there is a negative correlation between PVC and initial porosity, if all other parameters are fixed, the relationship between initial porosity and PVC is not monotonic. In addition, PVC decreases with rougher pore surfaces and smaller initial minimum pore radius. Besides providing theoretical foundations for quantifying PVC of porous media, this analytical model could be applied to estimate pore structure parameters of porous media using inverse modeling.

Hydrodynamic resistance model of oil flow in nanopores coupling oil–wall molecular interactions and the pore-throat structures effect

Clarifying enhanced oil flow behaviors is crucial because of the large number of pore-throat structures and the complex oil–wall molecular interactions in shale/tight reservoirs. According to the single pore model with pore-throat structures, total hydrodynamic resistance and enhanced oil flow models are established by coupling the molecular interaction effect and the entrance effect (caused by pore-throat structures). The results show that, with decreasing oil–wall molecular interactions, the total hydrodynamic resistance decreases because of increasing slip length and decreasing near-wall oil viscosity and the hydrodynamic resistance of the entrance effect gradually dominates. Additionally, the enhanced flow capacity when considering the entrance effect can be several times smaller than that without considering it. With decreasing minimum pore radius and increasing variation trend of radius, the hydrodynamic resistance of the entrance effect increases, and the enhanced oil flow capacity decreases with increase of minimum pore radius and variation trend of radius.

Effect of clay content on permeability behavior of argillaceous porous media under stress dependence: A theoretical and experimental work

Prediction of permeability behavior of argillaceous porous media (APM) is a major challenge for science and engineering, despite considerable advances in using both theoretical and experimental means over the last few decades. Specifically, the effect of clay content on stress sensitivity of APM is still an open question. In this paper, laboratory tests are conducted to investigate the effect of clay content on behavior of permeability for artificial argillaceous sandstone samples under stress dependence. Then a corresponding theoretical model for stress dependent permeability of APM based on fractal theory is derived to interpret the experimental results. The predicted results from the developed theoretical model are consistent with those determined by experimental tests, which verifies the developed model. The proposed model can be invoked to effectively study the coupled flow-deformation behavior in APM. The results show that the normalized permeability increases with increasing the power law index, increasing elastic modulus, increasing rock initial porosity, and decreasing clay content at a given effective stress. This work provides a comprehensive experimental and theoretical study on stress-dependent permeability in APM, which is beneficial to study the effect of clay content on permeability behavior of APM under stress dependence. In addition, with this proposed model, we can conduct the estimation of specific parameters (e.g., the structure of pore surface, the fractal dimension of pore, the maximum pore radius, the minimum pore radius, clay content, initial irreducible water saturation, and rock elastic modulus) using inverse modeling approaches.

A fractal study for the effective electrolyte diffusion through charged porous media

Electrolyte diffusion in electrolyte solutions exists in various areas including rechargeable batteries, soil physics and chemical engineering. In this paper, a fractal model based on the capillary model and fractal theory of porous media is proposed to quantify the effective electrolyte diffusivity in porous media with consideration of the electrical double layer (EDL) effects. The present model explicitly relates to the micro-structural parameters of porous media and electrokinetic parameters. To validate this model, a comparison is carried out with experimental data and semi-analytical model results, and yields satisfying agreement. Besides, the influences of the parameters (the porosity, equivalent particle diameter, ratio of the minimum pore radius to the maximum pore radius, molar concentration, zeta potential, and dimensionless parameter β) are discussed in details.

Establishment and application of fractal capillary tube bundle model of porous media

In view of the problem of statistical regression constant in the model of capillary tube bundles in the porous media, a capillary bundle percolation model with fractal geometry was reconstructed. The function expressions of the fractal coefficient and Kozeny constant were deduced. The relationship between the macroscopic fractal properties of porous media and the fractal dimension and the micro pore parameters were obtained. Results show: Fractal coefficient is a function of fractal dimension, maximum pore radius and minimum pore radius; The macroscopic physical properties of porous media are a function of the fractal dimension and the radius of the capillary (the maximum capillary radius and the minimum capillary radius). The expression does not contain any empirical or experimental constants. In the fractal capillary percolation model, the relationship between the three kinds of surface volume, skeleton volume and pore volume are the same as the traditional equal diameter straight capillary bundle model. The Kozeny constant can be accurately described by the function expression of the z-h coefficient, which is used for correcting the difference between real and ideal porous media model.

A FRACTAL PERMEABILITY MODEL COUPLING BOUNDARY-LAYER EFFECT FOR TIGHT OIL RESERVOIRS

A fractal permeability model coupling non-flowing boundary-layer effect for tight oil reservoirs was proposed. Firstly, pore structures of tight formations were characterized with fractal theory. Then, with the empirical equation of boundary-layer thickness, Hagen–Poiseuille equation and fractal theory, a fractal torturous capillary tube model coupled with boundary-layer effect was developed, and verified with experimental data. Finally, the parameters influencing effective liquid permeability were quantitatively investigated. The research results show that effective liquid permeability of tight formations is not only decided by pore structures, but also affected by boundary-layer distributions, and effective liquid permeability is the function of fluid type, fluid viscosity, pressure gradient, fractal dimension, tortuosity fractal dimension, minimum pore radius and maximum pore radius. For the tight formations dominated with nanoscale pores, boundary-layer effect can significantly reduce effective liquid permeability, especially under low pressure gradient.

Ion-pulling simulations provide insights into the mechanisms of channel opening of the skeletal muscle ryanodine receptor

The type 1 ryanodine receptor (RyR1) mediates Ca2+ release from the sarcoplasmic reticulum to initiate skeletal muscle contraction and is associated with muscle diseases, malignant hyperthermia, and central core disease. To better understand RyR1 channel function, we investigated the molecular mechanisms of channel gating and ion permeation. An adequate model of channel gating requires accurate, high-resolution models of both open and closed states of the channel. To this end, we generated an open-channel RyR1 model using molecular simulations to pull Ca2+ through the pore constriction site of a closed-channel RyR1 structure determined at 3.8-Å resolution. Importantly, we find that our open-channel model is consistent with the RyR1 and cardiac RyR (RyR2) open-channel structures reported while this paper was in preparation. Both our model and the published structures show similar rotation of the upper portion of the pore-lining S6 helix away from the 4-fold channel axis and twisting of Ile-4937 at the channel constriction site out of the channel pore. These motions result in a minimum open-channel pore radius of ∼3 Å formed by Gln-4933, rather than Ile-4937 in the closed-channel structure. We also present functional support for our model by mutations around the closed- and open-channel constriction sites (Gln-4933 and Ile-4937). Our results indicate that use of ion-pulling simulations produces a RyR1 open-channel model, which can provide insights into the mechanisms of channel opening complementing those from the structural data.

Effect of Meniscus Recession on the Effective Pore Radius and Capillary Pumping of Copper Metal Foams

An experimental study is performed to characterize the effect of meniscus recession on the effective pore radius and capillary pumping of copper metal foams which are to be used as wicks in heat pipes for electronic cooling. Knowledge of the effective pore radius is critical in defining the capillary pumping of a wicking material but is rarely measured under operating conditions. It is known that the meniscus of a liquid recedes when evaporating from a porous media, which could impact the effective pore radius and therefore the capillary pumping capabilities of the foam. To elucidate this impact, the evaporation rate is measured from foam strips wicking ethanol from a reservoir while applying heat fluxes to the foam. Using thermocouple and IR camera measurements, the measured evaporation rates are corrected to account for different thermal losses, including natural convection, direct thermal conduction to the liquid, and evaporation from the container. An analytical model is then developed to relate the evaporated mass to the maximum capillary pressure (minimum effective pore radius) provided by the foam. It is shown for the first time, that just before the onset of dryout, the recessed meniscus will lead to 15%, 28%, and 52% decrease in effective pore radius for samples with 68%, 75%, and 82% porosities, respectively. The capillary pumping therefore increases during evaporation. This can have significant impact on the prediction of the capillary limits in two phase capillary driven devices.

Permeability of Aluminium Foams Produced by Replication Casting

The replication casting process is used for manufacturing open-pore aluminum foams with advanced performances, such as stability and repeatability of foam structure with porosity over 60%. A simple foam structure model based on the interaction between sodium chloride solid particles poorly wetted by melted aluminum, which leads to the formation of air pockets (or “air collars”), is proposed for the permeability of porous material. The equation for the minimum pore radius of replicated aluminum foam is derived. According to the proposed model, the main assumption of the permeability model consists in a concentration of flow resistance in a circular aperture of radius rmin. The permeability of aluminum open-pore foams is measured using transformer oil as the fluid, changing the fractions of initial sodium chloride. Measured values of minimum pore size are close to theoretically predicted ones regardless of the particle shape. The expression for the permeability of replicated aluminum foam derived on the basis of the “bottleneck” model of porous media agrees well with the experimental data. The obtained data can be applied for commercial filter cells and pneumatic silencers.

Mesoporous Aerogels Synthesized with an Ionic Liquid [Hmim]Br as Template via Ambient Pressure Drying

Mesoporous silica aerogels with a high surface area and narrow pore size distribution were prepared from tetraethylorthosilicate (TEOS) precursor at ambient pressure by using a water miscible ionic liquid (IL) [Hmim]Br as a template. The aerogels were characterized by scanning electron microscopy (SEM) and N2 gas adsorption-desorption isotherms (BET and BJH analyses), and the effect of the IL on gel structure was also studied. The results showed that IL plays an important role in regulating the nanostructure of the aerogels, in particular, pore sizes and their distribution. By increasing the IL/Si molar ratio from 4 to 7, the specific surface area of the resultant aerogel increased from 822.38 to 992.43 m2/g, while the pore volume decreased from 1.568 to 1.031 cm3/g. More importantly, the pore size distribution became narrower with minimum average pore radius centralized at 20 nm as the IL/Si molar ratio of 7. Compared with other IL templating methods previously reported, notable attributes of this method include gelation at a much wider range of the IL/Si molar ratios (up to 7) and the formation of homogeneous porous structure whose size can be up to meso-scale (2 nm - 50 nm).