Calculation Of Porosity Research Articles

Identifying clay mineral using angular competitive neural network: A machine learning application for porosity estimative

In the daily practice of Formation Evaluation for porosity calculation considering the shale volume is common the adoption of simple hypotheses about the physical properties of the reservoir rock constituents. In this paper, it is argued that an accurate estimate of clay mineral physical properties in the reservoir rock are essential for a realistic porosity calculation, once it may be different from the physical properties of clay minerals present in nearby shale layers. Geologically, the assumption of similarity between the clay mineral physical properties in the reservoir rock and adjacent shales properties means to presume a depositional continuity in sedimentary process and disregarded the innumerous postpositional processes involved in the sedimentary basin. By applying the angular competitive neural network to the Density-Neutron method to identify the clay mineral in the reservoir rock based on all identifiable clay minerals in the oil field, it is shown that a particular clay mineral signals a characteristic angular pattern in the Density-Neutron cross-plot. The methodology is presented with synthetic data and evaluated with actual well logs and core analysis from a borehole drilled in the Namorado oil field, Campos basin, Brazil.

RAYLEIGH WAVE AND WELL HEAD RESPONSE TO CALCULATE POROSITY IN THE EDWARDS AQUIFER OF SOUTH-CENTRAL TEXAS, USA.

We use the magnitude and centroid period of Rayleigh wave along with the amplitude of fluctuations of water level in a well to calculate effective porosity of a karst aquifer at the site scale. The radial and vertical displacements of Rayleigh wave are first related to the confining pressure of rock, which is then related to fluid pressure via the Gassmann equation. Three seismograms recorded at station 633A of the USARRAY and the induced responses of Well J-17 in the Edwards Aquifer (Texas) allow the calculation of an effective porosity between 17.0 and 24.4 percent, the average of which is close to the total porosity of core samples determined by geophysical well logs. This paper provides an innovative method to measure effective porosity in aquifers. Because of the long wavelengths of Rayleigh wave, the interdisciplinary approach is advantageous in that the resulting effective porosity is at the site scale which includes large conduits or voids.

Modeling of pharmaceutical filtration and continuous integrated crystallization-filtration processes

As continuous manufacturing is evolving in the pharmaceutical industry, continuous filtration has emerged as a bottleneck for connecting the crystallization of the active pharmaceutical ingredient with the formulation of the final drug product. This work aims the modeling of filtration to improve the understanding of the process, to support the development of continuous filtration methodologies, and to aid the integration of crystallization and filtration. The presented model utilizes the generalized form of Darcy’s law together with the calculation of the cake porosity and specific cake resistance based on the full crystal size distribution (CSD) of the slurry, without the need for experimental filtration data. The model is applied the first time for the dynamic simulation of an automated batch- type continuous filtration, which is also integrated with a population balance model of crystallization. The effect of the slurry properties (solid concentration, CSD) and the crystallization and filtration process parameters (crystallization temperature, flow rates, filter pressure difference, carousel rotation time) on the specific cake resistance, filtration time and residual moisture content are determined. It is concluded that continuous filtration facilitates the filtration of slurries with bad filterability through the modification of the rotation time and provides an opportunity to control the filtration when connected to a continuous crystallization. The simulation results show good agreement with real integrated continuous crystallization and filtration experiments of acetylsalicylic acid. The presented methodology could be used for both batch Nutsche filtration and continuous filtration to predict filterability and for optimization, risk analysis and control purposes.

Estimation of in situ hydrocarbon saturation of porous rocks from borehole measurements of spontaneous potential

It has been previously shown that Nernst’s equation is not reliable for the interpretation of spontaneous potential (SP) measurements acquired in hydrocarbon-bearing rocks. We have examined whether the difference between borehole SP measurements and Nernst-equation predictions could be used to estimate in situ hydrocarbon saturation of porous rocks. For this purpose, a new petrophysical model and a mechanistic finite-difference algorithm for simulating SP borehole measurements in the presence of mud-filtrate invasion are used to establish the limits of detectability of hydrocarbon saturation using only SP logs. We find that the optimal conditions for the detection of hydrocarbon saturation from SP borehole measurements are when (1) capillary forces dominate the process of mud-filtrate invasion, (2) the matrix-pore interface region, known as the electrical double layer, has a relevant impact in the diffusion of counterions, and (3) the electrolyte concentration of drilling mud is greater than that of formation water. We also determine why high values of the endpoint of the water relative permeability favor the detection of hydrocarbon-saturated rocks with the SP log. Using measurements acquired in three key wells within a mature and active hydrocarbon field, three blind tests find that our petrophysical model together with the mechanistic SP simulation algorithm enable the estimation of hydrocarbon saturation from SP borehole measurements without the need for resistivity logs or porosity calculations. The estimation is reliable when the volumetric concentration of shale is negligible, the pore network structure is constant throughout the reservoir, and radial invasion profiles are similar to those observed in the calibration key wells.

Synthetic geochemical well logs generation using ensemble machine learning techniques for the Brazilian pre-salt reservoirs

Geochemical logs are an essential tool for hydrocarbon reservoir characterization. The rock composition given by these logs is useful for porosity calculation, stratigraphic modeling, diagenesis estimation, and well acidification. In reduced logging operations performed in carbonate reservoirs of the Brazilian pre-salt, the geochemical tool is no longer acquired, aiming at optimization and cost reduction. This research aims the development of synthetic geochemical logs using machine learning algorithms. The database includes 22 wells with complete logging acquisition, and the input logs are natural gamma-ray, gamma-ray spectroscopy, density, photoelectric factor, neutron porosity, nuclear magnetic resonance, and sonic. The chemical elements chosen as output are Al, Ca, Fe, Mg, Na, Si, S, and Ti. Five models based on machine learning are trained using 19 wells: Support-vector machine, Multilayer perceptron, Random Forest, AdaBoost, and XGBoost. AdaBoost represents the best algorithm because, in addition to showing the best results, it allowed for a more simplified preprocessing and hyperparameter tuning. The evaluation of the models applies R2 and root mean squared error (RMSE) in validation data and cross-validation. Robust models are acquired for Al, Ca, Fe, Mg, Si, S, and Ti, with R2 above 0.80. Na shows R2 slightly above 0.70. All the models have RMSE between 10-2 to 10-4. The most important logs during training are density, photoelectric factor, K, Th, U, and neutron porosity. Synthetic geochemical logs created for three test wells show a good agreement with acquired logs, being able to reproduce general trends of the pre-salt formations. The machine learning model is capable of substituting the acquisition of geochemical logs with high confidence, representing cost reduction, and supplying engineers and geoscientists with quality data to be used in formation evaluation.

Multifractal analysis of coal pore structure based on NMR experiment: A new method for predicting T2 cutoff value

Nuclear magnetic resonance (NMR) is a commonly used method to quantitatively characterize the pore structure of coal. T2 cutoff value is closely related to the microscopic pore structure of coal reservoirs, which directly affects the calculation of porosity, permeability, movable and irreducible fluid saturation. In this study, the pore structure of four types of coal samples were studied based on NMR experiments and the multifractal characteristics of saturated coal samples were analyzed with multifractal theory. Furthermore, the correlation between T2 cutoff values and multifractal characteristic parameters were discussed. The results show that the pore structure characteristics of CZ, GD and GHS coal samples are basically the same, all of which are mainly micropores, with relatively less content of mesopores, macropores and microcracks, while PDS coal samples have relatively more content of mesopores, macropores and microcracks. Different types of coal samples have similar multifractal characteristics and all coal samples are dominated by micropores. There is an obvious linear relationship between T2 cutoff values and the multifractal characteristic parameters. Five models of T2 cutoff values changing with the multifractal characteristic parameters are obtained by linear fitting. The error range between T2 cutoff values calculated by the five models and the experimental values are within 0.1 ms, among which T2 cutoff values calculated by model 5 are highly consistent with the experimental values, indicating that model 5 can better predict T2 cutoff values. The results can provide theoretical reference for the characterization of coal pore structure and the prediction of T2 cutoff values.

An unconventional method for calculating porosity of marine clay deposits using the 2D resistivity method

ABSTRACTVarious methods were earlier designed to calculate porosity of a formation, but many of them are reliant on physical soil sampling and/or laboratory measurements. The present work examines a recently proposed method, which we call here as Sample‐free Porosity Calculation from Resistivity Imaging Data (SPyCRID), to calculate porosity of unconsolidated soils. By conjoining Archie's and Waxman–Smits’ equations, SPyCRID can achieve high accuracy in porosity calculation, while requiring no physical soil‐sampling data. Two‐dimensional resistivity data acquired at Segantang Garam were modelled to calibrate SPyCRID's workflow and to devise data constraints for marine clay and brackish pore‐fluid conditions. Measured porosities from soil samples were used only for calibration and validation purposes. With data transformation added into the workflow, the performance of SPyCRID was improved as it was possible to achieve more precise value for the calculated porosity (error ≤3.1%). The final step to establish SPyCRID's competency was implemented through testing SPyCRID at the Nibong Tebal test site that has similar geological conditions to the model. Results from this test site showed nominal errors (≤3.9%) in the calculated porosity. SPyCRID could successfully calculate the porosity of the unconsolidated, marine clayey soils with a confidence limit exceeding 96%, while requiring no physical sampling data.

Fabrication and Characterization of Polylactic Acid Electrospun Scaffolds Modified with Multi-Walled Carbon Nanotubes and Hydroxyapatite Nanoparticles.

The solution electrospinning process (SEP) is a cost-effective technique in which a wide range of polymeric materials can be electrospun. Electrospun materials can also be easily modified during the solution preparation process (prior SEP). Based on this, the aim of the current work is the fabrication and nanomodification of scaffolds using SEP, and the investigation of their porosity and physical and mechanical properties. In this study, polylactic acid (PLA) was selected for scaffold fabrication, and further modified with multi-walled carbon nanotubes (MWCNTs) and hydroxyapatite (HAP) nanoparticles. After fabrication, porosity calculation and physical and mechanical characterization for all scaffold types were conducted. More precisely, the morphology of the fibers (in terms of fiber diameter), the surface properties (in terms of contact angle) and the mechanical properties under the tensile mode of the fabricated scaffolds have been investigated and further compared against pristine PLA scaffolds (without nanofillers). Finally, the scaffold with the optimal properties was proposed as the candidate material for potential future cell culturing.

FRACTAL ANALYSIS OF DIGIT ROCK CORES

The rock cores of low permeability reservoirs have special pore structures, which are the essential factors to determine the seepage capacity and oil displacement efficiency and directly affect oil and gas reserves and oil well productivity. This paper studies 16 digital rock core samples. Based on the fractal theory for porous media, we carried out the fractal characterization of the pore structure of the samples by an approach combined with binarized CT images and fractal theory. The computing software based on the Box-counting method was used to measure and calculate the fractal dimension and porosity of the samples, and the calculated results were compared with the binarized CT data from the laboratory. It was found that among the tested samples, the results of 12 rock core samples were in good agreement with the experimental data, indicating that the fractal theory is effective in the measurement of fractal dimension and in the calculation of porosity of digital rock core samples. For the results with larger errors compared to laboratory data, we also analyzed and elaborated the reasons from the relevant binarized images and pore distribution images of samples. It is also found that the minimum pore size has a significant impact on the results when the fractal theory was applied to analyze the digital rock core samples. Finally, a standard or criterion is established whether the pore/particle size distribution in a digit rock core/porous medium is fractal or non-fractal.

New vuggy porosity models-based interpretation methodology for reliable pore system characterization, Ordovician carbonate reservoirs in Tahe Oilfield, North Tarim Basin

Carbonate rocks are in general complex and commonly contain compound pore systems that can significantly affect the variations of physical properties; their petrophysical evaluation remains challenging, and the results are often uncertain.This paper presents a new approach developed to establish vuggy porosity models that can be applied to successfully estimate vuggy porosity, both connected and separate vug fraction. It involves mainly partitioning the total porosity into fractions of its basic components, such as fractures, matrix porosity, and vugs. To estimate and decompose the total porosity, wireline methods involving standard porosity and borehole electrical image logs are integrated based on rock-physics modeling and image analysis techniques through a series of steps, which specifically have particular set of procedures performed rigorously to obtain accurate results. The determined fractions of the total-vug and separate-vug porosities are related to acoustic parameters to establish total-vug and separate-vug porosity models, respectively. Core analysis and thin-section-derived optical porosity (PHIO) are used to verify the log-derived porosities and validate the newly-established total porosity partition procedure.The newly proposed vuggy porosity models yield optimal estimates that significantly match the measured quantities. They also show statistically better prediction accuracy, compared with previous models in literature, especially typical Lucia vug porosity models. In addition, the results indicate that the density log, which its combination to sonic and resistivity logs can enable separate-vug porosity calculation, is a good-total porosity estimator at least in low-touching vug zones. Together, this has proven the effectiveness of the present approach for porosity partitioning in carbonate rocks, and the vuggy porosity models derived could therefore be applied to other similar carbonate reservoir studies.

Optimal X-ray micro-CT image based methods for porosity and permeability quantification in heterogeneous sandstones

Summary 3-D X-ray micro-CT (XCT) is a non-destructive 3-D imaging method, increasingly used for a wide range of applications in Earth Science. An optimal XCT image-processing workflow is derived here for accurate quantification of porosity and absolute permeability of heterogeneous sandstone samples using an assessment of key image acquisition and processing parameters: image resolution, segmentation method, representative elementary volume (REV) size and fluid-simulation method. XCT image-based calculations obtained for heterogeneous sandstones are compared to two homogeneous standards (Berea sandstone and a sphere pack), as well as to the results from physical laboratory measurements. An optimal XCT methodology obtains porosity and permeability results within ±2 per cent and vary by one order of magnitude around the direct physical measurements, respectively, achieved by incorporating the clay fraction and cement matrix (porous, impermeable components) to the pore-phase for porosity calculations and into the solid-phase for permeability calculations. Two stokes-flow finite element modelling (FEM) simulation methods, using a voxelized grid (Avizo) and tetrahedral mesh (Comsol) produce comparable results, and similarly show that a lower resolution scan (∼5 µm) is unable to resolve the smallest intergranular pores, causing an underestimation of porosity by ∼3.5 per cent. Downsampling the image-resolution post-segmentation (numerical coarsening) and pore network modelling both allow achieving of a REV size, whilst significantly reducing fluid simulation memory requirements. For the heterogeneous sandstones, REV size for permeability (≥1 mm3) is larger than for porosity (≥0.5 mm3) due to tortuosity of the fluid paths. This highlights that porosity should not be used as a reference REV for permeability calculations. The findings suggest that distinct image processing workflows for porosity and permeability would significantly enhance the accurate quantification of the two properties from XCT.

Comparison of phosphor screen autoradiography and micro-pattern gas detector based autoradiography for the porosity of altered rocks

This study aims to further develop the 14C-PMMA porosity calculation method with a novel autoradiography technique, the Micro-pattern gas detector autoradiography (MPGDA). In this study, the MPGDA is compared with phosphor screen autoradiography (SPA). A set of rock samples from Martinique Island exhibiting a large range of connected porosities was used to validate the MPGDA method. Calculated porosities were found to be in agreement with ones from the SPA and the triple-weight method (TW). The filmless nature of MPGDA as well as straightforward determination of C-14 radioactivity from the source rock makes the porosity calculation less uncertain. The real-time visualization of radioactivity from C-14 beta emissions by MPGDA is a noticeable improvement in comparison to SPA.

Measuring Open Porosity of Porous Materials Using THz-TDS and an Index-Matching Medium

The porosity of porous materials is a critical quality attribute of many products ranging from catalysis and separation technologies to porous paper and pharmaceutical tablets. The open porosity in particular, which reflects the pore space accessible from the surface, is crucial for applications where a fluid needs to access the pores in order to fulfil the functionality of the product. This study presents a methodology that uses terahertz time-domain spectroscopy (THz-TDS) coupled with an index-matching medium to measure the open porosity and analyze scattering losses of powder compacts. The open porosity can be evaluated without the knowledge of the refractive index of the fully dense material. This method is demonstrated for pellets compressed of pharmaceutical-grade lactose powder. Powder was compressed at four different pressures and measured by THz-TDS before and after they were soaked in an index-matching medium, i.e., paraffin. Determining the change in refractive index of the dry and soaked samples enabled the calculation of the open porosity. The results reveal that the open porosity is consistently lower than the total porosity and it decreases with increasing compression pressure. The scattering losses reduce significantly for the soaked samples and the scattering centers (particle and/or pore sizes) are of the order of or somewhat smaller than the terahertz wavelength. This new method facilitates the development of a better understanding of the links between material properties (particles size), pellet properties (open porosity) and performance-related properties, e.g., disintegration and dissolution performance of pharmaceutical tablets.

Non-Autoclaved Aerated Concrete Porosity and Factors Affecting it

The total volume of cellular porosity, which comprises pores, interpore partitions, and air-entrained pores, depends on the spatial packing of pores, size distribution, maximum and average size, their shape, and the thickness of interpore partitions. Interpore partitions contain gel and capillary pores, which have a significant impact on the total porosity, thus affecting the operating properties of aerated concrete. This paper presents the calculations of gel, capillary, air, and total porosity in non-autoclaved aerated concrete of average-density grades D100...D1200 for different cement hydration degrees (0.6; 0.8, and 1) and water-cement ratios (0.5; 0.6, and 0.7); calculations use the author-developed methodology. Cement consumption depends on the average-density grade as well as on cement hydration degree. Reducing the latter from 1 to 0.6 in D500 concrete raises cement consumption by 7.4 %; other grades have similar patterns. This is why aerated concrete should be conditioned to maximize the utilization of the binder by enabling its complete hydration. The amount of water in the mixture is what determines the cement consumption and the water-cement ratio, whereby the density of cement dough will not depend on the average-density grade provided that the hydration degree and the WC ratio are constant. The finding is that the ability of cement to form its own pore structure is crucial to D500 and D400 aerated concrete if the mixture has high initial water content.

Effect of Mineral Composition on Transverse Relaxation Time Distributions and MR Imaging of Tight Rocks from Offshore Ireland

In this paper, we investigate the effect of magnetic field strength on the transverse relaxation time constant (T2) in six distinct core plugs from four different rock types (three sandstones, one basalt, one volcanic tuff and one siltstone), retrieved from offshore Ireland. The CPMG pulse-sequence was used at two different magnetic field strengths: high-field at 4.70 T and low-field at 0.28 T. Axial images of the core plugs were also acquired with the RAREst sequence at high magnetic field strength. Thin-sections of the core plugs were prepared for optical imaging and SEM analysis, and provided qualitative information on the porosity and quantification of the elemental composition of the rock material. The content of iron varied from 4 wt. % to close to zero in the rock samples. Nevertheless, the effective T2 distributions obtained at low-field were used to successfully predict the porosity of the core plugs. Severe signal attenuations from internal magnetic gradients resulted in an underestimation of the porosity at high-field. No definitive trend was identified on the evolution of discrete relaxation time components between magnetic field strengths. The low-field measurements demonstrate that NMR is a powerful quantitative tool for petrophysical rock analysis as compared to thin-section analysis. The results of this study are of interest to the research community who characterizes natural gas hydrates in tight heterogeneous core plugs, and who typically relies on MR imaging to distinguish between solid hydrates and fluid phases. It further exemplifies the importance of selecting appropriate magnetic field strengths when employing NMR/MRI for porosity calculation in tight rock.

Micropore structure characteristics and quantitative characterization methods of lacustrine shale-A case study from the member 2 of Kongdian Formation, Cangdong sag, Bohai Bay Basin

To better understand the micropore characteristics of lacustrine shale and develop quantitative methods for characterizing lacustrine shale, the reservoir space types, structures and spatial distribution patterns of effective pores in the shale of Member 2 of Kongdian Formation in Cangdong sag are studied using cores, thin sections, scanning electron microscopy (SEM), confocal laser scanning microscopy (CLSM), nuclear magnetic resonance (NMR), whole-rock X-ray diffraction (XRD) data, etc. Various shale porosity calculation methods are evaluated. The study results show that the reservoir spaces of the shale mainly include three types, i.e., matrix pores, organic pores and fractures. Flaky pore throats formed by dissolution-induced pores and mould pores can improve the pore connectivity. NMR effective porosity of the shale varies from 0.59% to 4.42% with an average of 2.38%, accounting for 49.54% of the total NMR porosity and 34.53% of the gas porosity. The shale is divided into the unimodal-type felsic shale, bimodal-type felsic shale, carbonate shale and mixed shale. The different lithologies exhibit linear correlations among NMR, gas and effective porosities. The shale has effective porosity of 0.56%–4.53% with an average of 2.12%. Furthermore, the shale reservoir is divided into four classes: Class I reservoir with effective porosities of more than 2.5%; Class II1 reservoir with effective porosity of 2.0%–2.5%; Class II2 reservoir with effective porosity of 1.5%–2%; and Class III reservoir with effective porosity of less than 1.5%.

ESTIMASI NILAI POROSITAS DAN PERMEABILITAS DENGAN PENDEKATAN DIGITAL ROCK PHYSICS (DRP) PADA SAMPEL BATUPASIR FORMASI NGRAYONG, CEKUNGAN JAWA TIMUR BAGIAN UTARA

Reservoir rock permeability and porosity are physical properties of rocks that control reservoir quality. Conventionally, rock porosity and permeability values are obtained from measurements in the laboratory or through well logs. At present, calculation of porosity and permeability can be calculated using digital image processing / Digital Rock Physics (DRP). Core data samples are processed by X-ray diffraction using CT-micro-tomography scan. The result is an image model of the core sample, 2D and 3D images. The combination of theoretical processing and digital images can be obtained from the value of porosity and permeability of rock samples. In this study, we calculated porosity and permeability values using the Digital Rock Physics (DRP) approach in sandstone samples from the Ngrayong Formation, North East Java Basin. The results of the digital image simulation and processing on the Ngrayong Formation sandstone samples ranged in value from 33.50% and permeability around 1267.02 mDarcy.

Groundwater aquifer potential using electrical resistivity method and porosity calculation: a case study

ABSTRACT This study uses aquifer characteristics such as the aquifer thickness, depth to the aquifer, and the subsurface porosity calculated from 1-D vertical electrical sounding data to evaluate groundwater potential. Thirty geoelectric investigations were carried out using Schlumberger-vertical-electrical-sounding (VES). The VES data were plotted against their respective current electrode spacing (AB/2) and presented as curves. The curves were interpreted quantitatively by partial curve matching and 1-D computer-assisted forward modelling using the WINRESIST version1.0 software. Isopach and isoresistivity maps of aquifer units in the area were generated from 1-D vertical electrical sounding data. The investigated area was subdivided into three zones of high (C); medium (B) and low (A) groundwater potential. Zone A overburden thickness <20 m has 30%, zone B with overburden thickness <30 m, which is the most predominant occupies 55% while 15% overburden thickness for zone C is <40 m. The subsurface porosity is calculated using Archie’s Law. The aquifer in the northeastern and southeastern parts of the study area were determined to be of good quality and can yield reasonable quantities of water that can serve the community.

Effect of Reinforcement Material on Properties of Manufactured Aluminum Matrix Composite Using Stir Casting Route

Composite is a lightweight material that used and developed in various industries. The use of aluminum matrix composites as structural and automotive materials has increased in recent years. One of the obstacles in the development of aluminum matrix composites is high-cost production, especially raw material for reinforcing particles. One innovation is the use of natural materials and waste as reinforcement in aluminum matrix composites. Sea sand is one of the natural materials containing ceramic or oxide compounds so that it has the potential to be used as reinforcement in aluminum matrix composites. This paper compares the physical and mechanical properties of aluminum composite production using sea sand particles and composites with commonly used ceramic particle reinforcement, such as alumina and SiC. Calculation of density and porosity shows that Al6061/sea sand composites have higher density and lower porosity compared to Al6061/Al2O3 and Al6061/SiC composites. The hardness of Al6061/sea sand composite is higher compared to Al6061/Al2O3 and Al6061/SiC composites.

Research of Formation of Macro-Damages on Surface of Basalt Fiber Reinforced Polymer Rebar in an Extremely Cold Climate

In the work, basalt fiber reinforced polymer rebars exposed in the climatic conditions of the North for 51 months have been investigated. To study the formation of macrodamages, fractographic and structural studies of longitudinal sections of the rebars were carried out. The open porosity of basalt fiber reinforced polymer rebars was investigated by the method of hydrostatic weighing. The influence of microdamages on the formation of open porosity of basalt fiber reinforced polymer rebars during their aging is shown. It has been found that degradation of basalt fiber reinforced polymer rebars leads to a significant increase in their open porosity. A linear expression is proposed to assess the average porosity of basalt fiber reinforced polymer rebars depending on their diameter, the concentration of reinforcing fiber rovings, etc. Estimated calculations of the average porosity of basalt fiber reinforced polymer rebars with their uniform degradation from the outer surface under the influence of the external environment have been carried out. A satisfactory correlation of estimated calculations and experimental data of average porosity at small diameters of basalt fiber reinforced polymer rebars (with diameters of 6 and 8 mm.)