Journal articles on the topic 'Rocks Testing Mathematical models'
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1
Andjelkovic, Vladimir, Zarko Lazarevic, and Velimir Nedovic. "Application of analogous models in civil engineering." Facta universitatis - series: Architecture and Civil Engineering 9, no. 3 (2011): 395–405. http://dx.doi.org/10.2298/fuace1103395a.
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The paper describes the results of making the mathematical and physical models of the authors, by using analogous methods and materials. There is the mathematical rock mass deformability model as a base for foundation engineering a concrete arch dam and the physical rock slope model which was tested by loading until failure and the results were compared with the calculation procedure. In the first example the correlation is established between the static and the analogous dynamic in situ investigations for creating the mathematical rock mass deformability model. In the second example there is application of the analogous materials for the discontinuity shearing simulation on the physical slope model. The results of the geotechnical in situ investigations and laboratory testing carried out in the Institute for Development of Water Resources "Jaroslav Cerni" in Belgrade were used for making the models.
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Xiaolong, Tong, Yan Liangjun, and Xiang Kui. "Modifying the generalized effective-medium theory of induced polarization model in compacted rocks." GEOPHYSICS 85, no. 4 (June 15, 2020): MR245—MR255. http://dx.doi.org/10.1190/geo2019-0718.1.
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The generalized effective-medium theory of the induced polarization model (GEMTIP) is a mathematical-physical model derived from the Maxwell equations based on the effective-medium approach. Compared to the Cole-Cole model, the GEMTIP parameters are better related to the structural parameters of reservoir rocks, such as rock composition, mineral particle size, porosity, and specific surface; therefore, it can better describe the induced polarization (IP) characteristics of tight oil and gas reservoirs. However, GEMTIP is not suitable for high-resistivity perturbed media, and it does not account for interfacial polarization, which occurs between two media that share the same resistivity. Starting from the theoretical assumptions of the GEMTIP model, we derived an extended GEMTIP model (MGEMTIP) by adding an equivalent surface current term into the Maxwell equations for a heterogeneous medium. The complex resistivity parameters predicted by two models are compared through numerical simulation, and the results demonstrate that MGEMTIP can more accurately predict the DC resistivity and the chargeability of heterogeneous media. MGEMTIP is suitable for characterizing the polarization phenomena of rock with high salinity, low porosity, low hydraulic permeability, and a disseminated perturbed medium. Furthermore, the testing of rock samples for the inversion of IP parameters with MGEMTIP revealed that the predicted chargeability is higher than the inverted chargeability from the experimental data. This difference is strongly correlated with rock hydraulic permeability. MGEMTIP provides a petrophysical basis for the forward modeling and inversion of IP parameters of compacted rocks. The quantitative relationships between model IP parameters and reservoir parameters also provide a theoretical foundation for predicting reservoir permeability using electromagnetic methods.
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Denny, Mark W., and Ben B. Hale. "Cyberkelp: an integrative approach to the modelling of flexible organisms." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (August 11, 2003): 1535–42. http://dx.doi.org/10.1098/rstb.2003.1341.
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Biomechanical models come in a variety of forms: conceptual models; physical models; and mathematical models (both of the sort written down on paper and the sort carried out on computers). There are model structures (such as insect flight muscle and the tendons of rats' tails), model organisms (such as the flying insect, Manduca sexta ), even model systems of organisms (such as the communities that live on wave–swept rocky shores). These different types of models are typically employed separately, but their value often can be enhanced if their insights are integrated. In this brief report we explore a particular example of such integration among models, as applied to flexible marine algae. A conceptual model serves as a template for the construction of a mathematical model of a model species of giant kelp, and the validity of this numerical model is tested using physical models. The validated mathematical model is then used in conjunction with a computer–controlled tensile testing apparatus to simulate the loading regime placed on algal materials. The resulting information can be used to create a more precise mathematical model.
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Skakal's'ka, L. "Physical and reservoir properties prediction for reservoir rocksin unconventional gas-bearing geological structures." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 1 (64) (2014): 35–40. http://dx.doi.org/10.17721/1728-2713.64.07.35-40.
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Research into the behavior of elastic waves in thin-layered gas-bearing geological structures depends on the choice of geophysical and mathematical models of natural geological media and the numerical methods of problem solving. Hence the efficiency of a quasi-homogeneous, isotropic fractured-porous two-phase medium with given physical and mechanical properties. We have suggested a method of calculating empirical relationships between volumetric compression, porosity and pressure in porous rocks of an arbitrary geological region. Data on Zaluzhany wells were used to calculate the correlation and empirical relationships between reservoir properties and parameters of elastic waves and to distinguish dry and oil-gas saturated rocks. The least square technique made it possible to determine the correlation between the compressibility factor of fluid-saturated rocks and their porosity and pressure. Discrimination between oil and water was based on the density parameter. An algorithm has been suggested to do the corresponding calculations. The theoretical and practical implications of this study are as follows: – developing a numerical analytical predictive model for interpreting acoustic data on thin-layered rocks which is based on the correlations between their dynamic physical (effective wave propagation velocities, amplitude attenuation coefficients and their energy absorption) and reservoir (porosity, fracturing, compressibility) properties; – applying the proposed model and software products in geophysical exploration to interpret the geological and geophysical data on the structure and physical characteristics of sections and the physical properties of gas-bearing basins. In seismic acoustic exploration, the numerical model has to include experimental geological and geophysical data on the peculiarities of rock occurrence in the investigated area, with the physical and mechanical properties of different territories showing considerable variation. Such input data, as well as structural features and scattering properties of rocks (density, bedding, microporosity), ensure a significant increase in the accuracy of the numerical analysis. Preliminary testing was based on the data on the elastic moduli and S-wave velocities for dry and fluid-saturated rocks. Calculations were made of the elastic moduli and P-wave velocities for dry and fluid-saturated rocks of the Western oil and gas region of Ukraine (Zaluzhany-18 and Zaluzhany-19 wells). The aim of this work was to demonstrate the efficiency of the predictive method by examining the reservoir rock properties of the wells and to evaluate their gas saturation using the acoustic logging, geophysical and petrophysical data.
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Shahani, Niaz Muhammad, Barkat Ullah, Kausar Sultan Shah, Fawad Ul Hassan, Rashid Ali, Mohamed Abdelghany Elkotb, Mohamed E. Ghoneim, and Elsayed M. Tag-Eldin. "Predicting Angle of Internal Friction and Cohesion of Rocks Based on Machine Learning Algorithms." Mathematics 10, no. 20 (October 19, 2022): 3875. http://dx.doi.org/10.3390/math10203875.
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The safe and sustainable design of rock slopes, open-pit mines, tunnels, foundations, and underground excavations requires appropriate and reliable estimation of rock strength and deformation characteristics. Cohesion (𝑐) and angle of internal friction (𝜑) are the two key parameters widely used to characterize the shear strength of materials. Thus, the prediction of these parameters is essential to evaluate the deformation and stability of any rock formation. In this study, four advanced machine learning (ML)-based intelligent prediction models, namely Lasso regression (LR), ridge regression (RR), decision tree (DT), and support vector machine (SVM), were developed to predict 𝑐 in (MPa) and 𝜑 in (°), with P-wave velocity in (m/s), density in (gm/cc), UCS in (MPa), and tensile strength in (MPa) as input parameters. The actual dataset having 199 data points with no missing data was allocated identically for each model with 70% for training and 30% for testing purposes. To enhance the performance of the developed models, an iterative 5-fold cross-validation method was used. The coefficient of determination (R2), mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and a10-index were used as performance metrics to evaluate the optimal prediction model. The results revealed the SVM to be a more efficient model in predicting 𝑐 (R2 = 0.977) and 𝜑 (R2 = 0.916) than LR (𝑐: R2 = 0.928 and 𝜑: R2 = 0.606), RR (𝑐: R2 = 0.961 and 𝜑: R2 = 0.822), and DT (𝑐: R2 = 0.934 and 𝜑: R2 = 0.607) on the testing data. Furthermore, to check the level of accuracy of the SVM model, a sensitivity analysis was performed on the testing data. The results showed that UCS and tensile strength were the most influential parameters in predicting 𝑐 and 𝜑. The findings of this study contribute to long-term stability and deformation evaluation of rock masses in surface and subsurface rock excavations.
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Inkin, O., N. Dereviahina, P. Volk, and Yu Hriplivec. "Estimation of parameters of gas storage operation in inhomogeneous aquifers." Collection of Research Papers of the National Mining University 69 (June 2022): 23–34. http://dx.doi.org/10.33271/crpnmu/69.023.
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The purpose of the article is development and testing of a mathematical model of gas storage in a layered aquifer with a low permeabilityinterlayer for a case of plane-parallel and axial-symmetric filtration. Methodology. One of the most common models of anisotropy of rocks is a model of a layered seam, which is explained by geological conditions of sedimentation, which lead to stratification of layers with different collecting properties. In the practice of underground gas storage, consideration of such a model is of particular importance.This is due to possible significant difference in advancing a boundary of gas-water contact through the interlayers with different filtration characteristics caused by changes in a position of a gas zone. A comprehensive approach is applied, which includes collection, systematization and analysis of actual data on filtration and physical and mechanical properties of host rocks that affect the formation of natural and technogenic deposits, as well as analytical and numerical methods for solving equations of gas-water contact in different conditions. Results. Gas-hydrodynamic model of underground gas storage in an inhomogeneous aquifer is justified for calculation of its cyclic operation in a three-layer seam considering cross-flows through a low permeability interlayer.The results can be used in evaluation calculations at a design stage of gas storage facilities in aquifers. Scientific novelty. A mathematical model of gas storage in a layered aquifer with a low permeability interlayerfor a case of plane-parallel and axial-symmetric filtration is developed and tested. A new method of linearization of a system of differential equations for determining pressures in a collectingseamis obtained in the article and it is a generalization of previously used methods, with an introduction of "boundary schemes". Practical significance. Calculation results indicate a significant influence of characteristics of a layered porous medium on the advance of gas-water contact along individual layers. The results can be used in the evaluation calculations at a design stage of gas storage facilities in aquifers.
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Thompson, J. Michael T. "Introduction. Progress in Earth science and climate studies." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1885 (September 25, 2008): 4503–8. http://dx.doi.org/10.1098/rsta.2008.0215.
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In this introductory paper, I review the ‘visions of the future’ articles prepared by top young scientists for the second of the two Christmas 2008 Triennial Issues of Phil. Trans. R. Soc. A , devoted respectively to astronomy and Earth science. Topics covered in the Earth science issue include: trace gases in the atmosphere; dynamics of the Antarctic circumpolar current; a study of the boundary between the Earth's rocky mantle and its iron core; and two studies of volcanoes and their plumes. A final section devoted to ecology and climate covers: the mathematical modelling of plant–soil interactions; the effects of the boreal forests on the Earth's climate; the role of the past palaeoclimate in testing and calibrating today's numerical climate models; and the evaluation of these models including the quantification of their uncertainties.
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Doan, Luong T. A., Murat Karakus, Giang D. Nguyen, Scott Smith, Chris Chester, and Robert Hawker. "Estimating the Hydraulic Conductivity of jointed rock mass using Genetic Programming." IOP Conference Series: Earth and Environmental Science 1124, no. 1 (January 1, 2023): 012001. http://dx.doi.org/10.1088/1755-1315/1124/1/012001.
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Abstract Ground engineering through injection of cementitious grouts or polymer resins is an integral part of fractured rock mass stabilisation by improving its maximum load carrying capacity, stiffness, cohesiveness and reduction in permeability. To optimise product delivery and achieve a high penetrability of product into the rock mass, it is imperative to understand the permeability characteristics or hydraulic conductivity of the rock mass. The hydraulic conductivity of the rock mass also dictates the type of polyurethane (PU) or cement-based products to be injected. For this purpose, a Packer test has to be conducted to measure the hydraulic conductivity of a rock formation which is an expensive and time-consuming process. Alternatively, a number of empirical methods that use rock mass classifications and rock joint properties Rock Quality Designation (RQD), Q-system (Q), Geological Strength Index (GSI), Joint Spacing (JS), Joint Aperture (a) proposed by a number of researchers that are capable of predicting hydraulic conductivity (HC). In this research, a predictive model between rock mass properties and HC is proposed using new approach - genetic programming (GP). For this purpose, a database of rock mass parameters including RQD, Q, GSI, JS, Joint Aperture (a), Second Permeability Index (SPI) and Packer test results available in the literature is established. The database is split into randomly selected training and testing sets. To assess the fitting quality, the sum of the absolute difference is used, while maximum depth on trees is set to control the bloat of the model. The performance is assessed with four statistical criteria and three GP models using different input combinations are proposed. These models have been converted into simple mathematical equations to calculate HC based on collected input data. In summary, two out of three models have successfully predicted HC with high correlation to the actual HC (R2 of testing sets ≈ 0.92). Therefore, this study has shown the feasibility of applying GP models into future prediction of HC for the initial phase of rock grouting design.
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Zhou, Desheng, and Andrew K. Wojtanowicz. "Analysis of Leak-off Tests in Shallow Marine Sediments." Journal of Energy Resources Technology 124, no. 4 (November 20, 2002): 231–38. http://dx.doi.org/10.1115/1.1506322.
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Typical analysis of the Leak-off testing (LOT) in wells assumes elastic wellbore and involves identification of diversion points from linear trends of the recorded plots. However, LOTs from wells in the shallow marine sediments (SMS) are inherently nonlinear and their analysis becomes a problem. The paper presents mathematical models of the pressure-volume behavior for two different possible failures around the casing shoe, annular crack (cement-rock parting) and formation fracture. The study submits that these two failure modes would control abnormal LOT patterns. A general pressure-volume model of LOT has been developed including volumetric effects of wellbore expansion, mud loss into the rock, and propagation of an annular crack or plastic fracture. A diagnostic method is proposed to identify LOT-control mechanisms (i.e., formation fracture, annular crack, or mud loss) by analyzing the shut-in section of the LOT’s plot.
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Clifton, R. J., and F. P. Chiang. "Experimental Mechanics." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1279–81. http://dx.doi.org/10.1115/1.3143691.
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Mechanical failure of machine parts, structures, and microelectronic components has a strong negative impact on the safety, security, and productivity of our people. Prevention of these failures is a principal focus of solid mechanics, which uses analysis, experiment, and computation to provide the understanding necessary for failure reduction through improved design, fabrication, and inspection. Experimental mechanics plays a critical role in this effort since it provides the data base for the calculations and the means for testing the validity of proposed theoretical models of failure. Current trends in experimental mechanics show increased use of optical methods for monitoring the displacements, velocities, and strains of surfaces. This trend has gained impetus from the attractiveness of noncontact methods for hostile environments and dynamically loaded bodies. Advances in laser technology have enhanced the instrumentation associated with these methods. Another trend is the investigation of material behavior under more complex loading conditions, made possible by the availability of servo-controlled testing machines with computer interfaces. Still another trend is the increased attention given to defects, such as inclusions, cracks, and holes, because of their importance in failure mechanisms. Opportunities for future contributions from experimental mechanics appear to be great and to occur across a broad range of technological problems. A central theme of future research appears to be increased emphasis on measurements at the micron and submicron scale in order to advance the understanding of material response and failure at the micromechanical level. Increased attention will also be given to internal measurements of defects, deformations and residual stresses because of their importance in developing a fundamental understanding of failure. Automated data reduction and control of experiments will greatly increase the information obtained from experiments and its usefulness for the development of mathematical models. Other important research directions include improved methods for measurements of in situ stresses in rocks, improved measurements of displacements and physiological parameters in biological systems, capability for long-term monitoring of the integrity of structures, and improved sensors for feedback control of mechanical systems.
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Wang, Pan. "Modeling and Estimation of Production Rate in Ornamental Stones Sawing Based on Brittleness Indexes." Mathematical Problems in Engineering 2019 (February 13, 2019): 1–12. http://dx.doi.org/10.1155/2019/3232517.
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As for estimating the cost and planning the process of the rock sawing plants, it is significant to predict the production rate of ornamental stones sawing. To promote the efficiency in planning these rock sawing projects, scholars have been trying to find a high-accuracy method of production rate estimation. Moreover, targeting at the 28 granite and carbonates stone in the nature, this study examined the connection between two various brittleness indexes in statistics, including the ratio of compressive strength to tensile strength (B1) and places below the line of compressive strength and the line of tensile strength (B2) in rocks and production rate had been studied. Through the results of cross plots analysis, it was indicated that there existed a strong connection between production rate and the brittleness B1 and B2. Finally, in this thesis, through adding B1 factor, it has improved the estimation model for production rate which Mikaeil et al. (2013) have established. What’s more, by virtue of brittleness about B1 and B2, this production rate estimation model has been established successfully for natural stone sawing. Actually, the way of estimating the production rate of 28 rock samples is to utilize the two kinds of models described before. Through the result, it is showed that the production rate estimated by the improved model corresponds to the value of production rate of rock testing. Meanwhile, the precision has been greatly improved with comparison to the model of estimating the production rate designed by Mikaeil et al. (2013). Thus, on the basis of the new model, a dependable prediction for ornamental stones production is put forward in this paper. And it is required to do a further study involving different rock types since limited rock types were used in this study.
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Sadchikov, A., N. Zhelaeva, J. Tokusheva, and M. Ponomareva. "APPLICATION OF SEISMOTOMOGRAPHY METHODS FOR SOLVING VARIOUS PROBLEMS IN THE MINING AND GEOLOGICAL DIRECTION." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 1 (92) (2021): 50–54. http://dx.doi.org/10.17721/1728-2713.92.07.
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The Karaganda coal basin is characterized by a complex structure. The presence of geological inconsistencies such as tectonic disturbances, washouts, variable reservoir hypsometry, etc. makes it difficult to conduct underground mining operations. Currently, in the world practice, mine seismic exploration is widely used for the purpose of studying the geological structure and solving various mining problems. Safe and productive operation of treatment faces in underground coal mining requires a timely and reliable forecast of the mining and geological conditions of the structure and condition of the coal-bearing mass from the mine workings. The most accurate and reliable picture of the tectonic structure of the Carboniferous massif can be obtained using methods of mine seismic exploration to study the geological structure and conditions of the coal bed and host rocks. The main goal of implementing modern methods of mine seismic exploration was to conduct mathematical modeling to assess the possibility of identifying tectonic disturbances with an offset amplitude of the order of magnitude and higher than the reservoir capacity using various methods of underground seismic exploration - the seismic transmission method (STM) and the reflected wave method (RWM). For this purpose, physical models of sections of the Carboniferous massif were developed, including a geometric description of geological structures, the distribution of rock densities, velocities, wave propagation and their influence on compression, and the shift of the mountain range. One of the models corresponded to a section of the formation without geological disturbances, and the second one - to a section with tectonic disturbances with displacement amplitudes from 5 to 15 m. The results obtained can be used in the development of modern effective methods for predicting the state of the mountain range in complex mining and geological conditions of both the Karaganda coal basin and other coal basins with a complex geological structure. Initially, seismic surveys were performed using the method of reflected waves using the common depth point method. However, the problem of obtaining an objective image of the geological environment is still relevant, due to the peculiarities of elastic wave excitation in mine conditions (features of the generated wave field, patterns of its propagation, the direction of the source). The method of mine seismic survey based on channel and boundary waves registration was developed and applied. This method allows obtaining a detailed geological and geophysical model of the field site. Due to the processing of both types of waves, the resolution of the method is increased to obtain information about both the coal bed and the host rocks, and, in particular, the state of the roof of the formation. The method of measurements in mine conditions is presented, the results of testing the method of performing field work in mine conditions are shown, and seismic characteristics with high contrast and clear traceability of reflecting boundaries are obtained.
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Elkatatny, Salaheldin. "Real-Time Prediction of Rate of Penetration in S-Shape Well Profile Using Artificial Intelligence Models." Sensors 20, no. 12 (June 21, 2020): 3506. http://dx.doi.org/10.3390/s20123506.
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Rate of penetration (ROP) is defined as the amount of removed rock per unit area per unit time. It is affected by several factors which are inseparable. Current established models for determining the ROP include the basic mathematical and physics equations, as well as the use of empirical correlations. Given the complexity of the drilling process, the use of artificial intelligence (AI) has been a game changer because most of the unknown parameters can now be accounted for entirely at the modeling process. The objective of this paper is to evaluate the ability of the optimized adaptive neuro-fuzzy inference system (ANFIS), functional neural networks (FN), random forests (RF), and support vector machine (SVM) models to predict the ROP in real time from the drilling parameters in the S-shape well profile, for the first time, based on the drilling parameters of weight on bit (WOB), drillstring rotation (DSR), torque (T), pumping rate (GPM), and standpipe pressure (SPP). Data from two wells were used for training and testing (Well A and Well B with 4012 and 1717 data points, respectively), and one well for validation (Well C) with 2500 data points. Well A and Well B data were combined in the training-testing phase and were randomly divided into a 70:30 ratio for training/testing. The results showed that the ANFIS, FN, and RF models could effectively predict the ROP from the drilling parameters in the S-shape well profile, while the accuracy of the SVM model was very low. The ANFIS, FN, and RF models predicted the ROP for the training data with average absolute percentage errors (AAPEs) of 9.50%, 13.44%, and 3.25%, respectively. For the testing data, the ANFIS, FN, and RF models predicted the ROP with AAPEs of 9.57%, 11.20%, and 8.37%, respectively. The ANFIS, FN, and RF models overperformed the available empirical correlations for ROP prediction. The ANFIS model estimated the ROP for the validation data with an AAPE of 9.06%, whereas the FN model predicted the ROP with an AAPE of 10.48%, and the RF model predicted the ROP with an AAPE of 10.43%. The SVM model predicted the ROP for the validation data with a very high AAPE of 30.05% and all empirical correlations predicted the ROP with AAPEs greater than 25%.
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Germay, C., T. Richard, E. Mappanyompa, C. Lindsay, D. Kitching, and A. Khaksar. "The Continuous-Scratch Profile: A High-Resolution Strength Log for Geomechanical and Petrophysical Characterization of Rocks." SPE Reservoir Evaluation & Engineering 18, no. 03 (July 17, 2015): 432–40. http://dx.doi.org/10.2118/174086-pa.
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Summary Knowledge of rock properties is essential to predict and optimize the performance of oil and gas reservoirs by means of the reduction of the uncertainty pertaining to standard subsurface issues such as the mechanical integrity of the borehole (Tiab and Donaldson 1996; Moos et al. 2003), the risk of sanding (Tronvoll et al. 2004), and the geometry and efficiency of hydraulic fractures. These properties are evaluated by combining different field-measurement techniques (wireline logs, results of well tests, seismic surveys) and laboratory-test results (Archie 1942, 1950; Serra 1986; Bassiouni 1994). When cores are available, empirical models are built from correlations derived between well logs and laboratory measurements to estimate rock properties in noncored wells. The validity of these empirical models is often limited to specific litho-facies (see reviews by Chang et al. 2006; Blasingame 2008; Khaksar et al. 2009), which makes the identification of lithofacies a necessity before applying the model for predictions in uncored wells (Massonnat 1999). Because of the heterogeneity of rocks (Haldorsen 1996), with characteristic length scales commonly smaller than the resolution of wireline logs or even the core-plug size, the robustness of correlations is determined by how plug samples capture the dispersion in rock properties over the lithofacies under consideration. The correlation between a very localized core-plug measurement and a low-resolution wireline log with inherent low-pass filtering properties raises issues related to the upscaling of a property from one length scale (few centimeters for core plugs) to another (up to 1 m for wireline log). As an illustration, consider the high-resolution, continuous profile X, where the variations of the measured property are quantified for length scales smaller than typical plug sizes. We filter this data to produce the profiles X5 and X50 (the subscript stands for the length scale in centimeters at which the signal is averaged out) with lower spatial resolutions similar to the plug and the well-log resolutions, respectively (Fig. 1). The resulting crossplot, shown in Fig. 2, of X5 vs. X50 exhibits a cloud of points in which the dispersion is governed by the properties of the signal (the degree of heterogeneity or the frequency content) and the difference between the two resolution length scales. Two linear-fit optimizations were carried out with the low-resolution-data X50 and the high-resolution-data X5 as the dependent variables, respectively. It is interesting to note that these linear fits yield different results, with a slope of 0.96 in the first case and 0.69 in the second case. This is a mathematical artifact caused by the minimization process inherent in the search for the best linear fit, which is most commonly a minimization of the vertical distance between the representative data points and the best-fit line. On the basis of this result, it should always be advisable to select the high-resolution data (plug) as the dependent variable. Discrete sampling (i.e., plugging) and the dispersion caused by the difference in resolution scales of two measurements are two important root causes of the errors often seen in correlations between two variables. The examples shown in Fig. 2 illustrate how the correlations derived from several sampling schemes can deviate from the expected one-to-one relation between the two variables. To circumvent these issues, petrophysicists usually select large quantities of plugs to build representative statistical data sets, with the hope that they are large enough to attenuate the effects listed previously. However, extensive plugging strategies imply longer lead times and higher costs, and are therefore not always viable (e.g., in the cases of rock-mechanics testing or special-core-analysis programs). As an illustration, consider the modeling of the variations of rock strength, one of the key geomechanical properties along a well trajectory. Such an exercise relies heavily on correlations derived between well logs and laboratory tests (uniaxial or triaxial compressive tests), because there is no wireline log providing a direct measure of a mechanical property related to strength. In their comprehensive review of existing literature, Khaksar et al. (2009) listed approximately 40 models designed to derive strength properties from wireline logs. The authors showed that the relevance of these as empirical is limited to specific rock types. A broader application of these models would require the considerations of additional complexity such as the coexistence of several facies within the same data set or the impact of diagenesis on petrophysical variability within one facies. The elements of reflection introduced previously all suggest that a continuous measure of a physical property such as the strength profiles generated from the scratch test, which provides some useful elements for the mapping of rock heterogeneity, could partially fill the gap between measurements on plugs and well logs and help with the optimization of the selection of plug samples. In the main sections of this paper, we first describe briefly the scratch test and outline the key intrinsic benefits of the test. We then discuss how standard and special core analysis could benefit most from all the features of the scratch test when introduced at a very early stage of the work flows. In particular, we illustrate with some examples how rock-strength profiles averaged to the relevant length scale can be correlated with other petrophysical properties either measured on core plugs or inferred from well logs.
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Chen, Ying, Shirui Chen, Zhengyu Wu, Bing Dai, Longhua Xv, and Guicai Wu. "Optimization of Genetic Algorithm through Use of Back Propagation Neural Network in Forecasting Smooth Wall Blasting Parameters." Mathematics 10, no. 8 (April 11, 2022): 1271. http://dx.doi.org/10.3390/math10081271.
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With the continuous development in drilling and blasting technology, smooth wall blasting (SWB) has been widely applied in tunnel construction to ensure the smoothness of tunnel profile, diminish overbreak and underbreak, and preserve the tunnel’s interior design shape. However, the complexity of the actual engineering environment and the deficiency of current optimization theories have posed certain challenges to the optimization of SWB parameters under arbitrary geological conditions, on the premise that certain control targets are satisfied. Against the above issue, a genetic algorithm (GA) and back propagation (BP) neural network-based computational model for SWB design parameter optimization is proposed. This computational model can comprehensively reflect the relation among geological conditions, design parameters, and results by training and testing the 285 collected sets of test data samples at different conditions. Moreover, it automatically searches optimal blasting design parameters through the control of SWB targets to acquire the optimal design parameters based on specific geological conditions of surrounding rocks and under the specified control targets. When the optimization algorithm is compared with other current optimization algorithms, it is shown that this algorithm has certain computational superiority over the existing models. When the optimized results are applied in practical engineering, it is shown that in overall consideration of the geological conditions, control targets, and other influencing factors, the proposed GA_BP-based model for SWB parameter optimization has high feasibility and reliability, and that its usage can be generalized to analogous tunneling works.
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Chandra, Suandy, and Daulat Debataraja Mamora. "Improved Steamflood Analytical Model." SPE Reservoir Evaluation & Engineering 10, no. 06 (December 1, 2007): 638–43. http://dx.doi.org/10.2118/97870-pa.
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Summary The Jones (1981) steamflood model incorporates oil displacement by steam as described by Myhill and Stegemeier (1978), and a three-component capture factor based on empirical correlations. The main drawback of the model, however, is the unsatisfactory prediction of the oil production peak: It is usually significantly lower than the observed value. Our study focuses on improving this aspect of the Jones model. In our study, we simulated the production performance of a five-spot-steamflood-pattern unit and compared the results against those based on the Jones model (1981). To obtain a satisfactory match between simulation and Jones-analytical-model results, at the start and height of the production peak, the following refinements to the Jones model were necessary. First, the dimensionless steam-zone size AcD was modified to account for the decrease in oil viscosity during steamflood and its dependence on the steam injection rate. Second, the dimensionless volume of displaced oil produced VoD was modified from its square-root format to an exponential form. The modified model gave very satisfactory results for production performance for up to 20 years of simulated steamflood, compared to the original Jones model. Engineers will find the modified model an improved and useful tool for the prediction of steamflood-production performance. Introduction Steamflooding is a major enhanced-oil recovery (EOR) process applied to heavy oil reservoirs. A steamflood typically proceeds through four development phases: reservoir screening, pilot tests, fieldwide implementation, and reservoir management (Hong 1994). Steamflood-performance prediction is essential to provide information for the proper execution of each development phase. Three mathematical models (statistical, numerical, and analytical models) are often used to predict steamflood performance. Statistical models are based on the historical data of steamflood performance from other reservoirs which have similar oil and rock properties. A statistical model, however, does not include all the flow parameters, and thus may be inaccurate for a particular reservoir. Numerical models usually require a large amount of data input with lengthy calculations using computers; and they are usually CPU-, manpower- and time-consuming and also expensive. They may be extremely comprehensive and better serve as tools for research or advanced reservoir analysis. Meanwhile, analytical models are more economical, but at the expense of accuracy and flexibility. They serve as tools for engineering screening of possible reservoir candidates for field testing (Hong 1994). For many years, attempts have been made to provide analytical models for steamflood-production-performance prediction (Marx and Langenheim 1959; Boberg 1966; Mandl and Volek 1969; Neuman 1975; Myhill and Stegemeier 1978; Gomaa 1980; Jones 1981; van Lookeren 1977; Farouq Ali 1970; Miller and Leung 1985; Rhee et al. 1978; Aydelotte et al. 1982). None of these analytical models gives a comparison with simulation results. Miller and Leung (1985) presented comparison between their analytical model and simulation results for cumulative production vs time, but the comparison for production rate vs time is not available.
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Wac-Wlodarczyk, A., R. Goleman, D. Czerwinski, and T. Gizewski. "Mathematical models applied in inductive non-destructive testing." Journal of Magnetism and Magnetic Materials 320, no. 20 (October 2008): e1044-e1048. http://dx.doi.org/10.1016/j.jmmm.2008.04.179.
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Pshenichny, I. "MODELS AND METHODS OF GEOCHEMICAL ASSESSMENT OF THE RISK OF ROCK DUMPS INTERACTION WITH ENVIRONMENTAL FACTOR." TRANSBAIKAL STATE UNIVERSITY JOURNAL 28, no. 3 (2022): 21–27. http://dx.doi.org/10.21209/2227-9245-2022-28-3-21-27.
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Models and methods of geochemical testing and evaluation of the influence of rock dumps on environmental factors are considered. The object of testing are samples of ores and rocks in the tailings dump formed during the extraction of porphyry-copper ores by an open method. The purpose of testing is to assess the risk of rock dumps" interaction with environmental factors, to determine the content of harmful substances in dust, as well as the formation of drainage of acidic rocks and leached metals. The task of testing is to analyze the average content of sulfur and sulfur sulfide in dump rocks and ores, to analyze the acid-neutralizing potential in these rocks and the potential for acid neutralization, as well as to assess the risk of rock dumps" interaction with environmental factors. Based on the acid base accounting indicators, characterizing the amount of acid-producing (sulfides) and acid-neutralizing (carbonates) minerals, as well as their ratios, an accelerated predictive assessment of the risk of acid drainage and mine water formation has been performed. With the help of geochemical testing of rock samples and dumps, the contents of sulfur, sulfur sulfide, acid-neutralizing potential and acid neutralization potential are determined. With the help of geochemical testing of rocks and ores, the impact of rock dumps on the external environment has been assessed, the content of harmful substances in dust and the influence of porphyry-copper ores on the formation of acidic drainage rocks and leached metals are determined. The data obtained made it possible to determine the level of saturation of watercourses with acidic products harmful to environmental factors. Based on the results of geochemical tests, options for the location of rock dumps and the construction of mining and processing industries during the development of the deposit are proposed
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Feinberg, Alec. "Accelerated Reliability Growth Models." Journal of the IEST 37, no. 1 (January 1, 1994): 17–23. http://dx.doi.org/10.17764/jiet.2.37.1.f2u73m8022207868.
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Extending reliability growth so that it can be applied in the area of accelerated testing will enable one to apply all the reliability growth tools and their planning advantages. This paper describes linking these two areas together into what is termed accelerated reliability growth testing (ARGT). Mathematical equations of ARGT for both iso-stress and step-stress accelerated testing are modelled.
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Purwanto, Burhan Eko, Icha Jusmalisa, Indah Permata Sari, Agus Jatmiko, and Andika Eko Pasetiyo. "Learning Models to Improved Mathematical Communication Skills." Desimal: Jurnal Matematika 3, no. 1 (January 23, 2020): 7–16. http://dx.doi.org/10.24042/djm.v3i1.5650.
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The problem faced by students in slow learning is in terms of communication. The use of Auditory, Intellectually, Repetition (AIR) and Cooperative Think Pair Share (TPS) types is needed to help students communicate mathematically in expressing mathematical ideas. This study aims to determine whether or not there are differences in mathematical communication skills of students using the Auditory, Intellectually, Repetition (AIR) learning model with students who use Think Pair Share (TPS) Cooperative learning models. This research uses a quantitative approach using the Quasi Experiment method. The research design is in the form of posttest only, non-equivalent group design. Testing data using the T test with Independent Samples T-Test. Based on the results of hypothesis testing obtained p-value> α 0.05. So it was concluded that there were indications of differences between Auditory, Intellectually, Repetition (AIR) learning models with (TPS) Cooperative learning models and superior (AIR) learning models compared to Cooperative learning models of (TPS) Type in influencing students' mathematical communication skills.
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Cui, Jiangfeng, and Long Cheng. "Liquid Storage Characteristics of Nanoporous Particles in Shale: Rigorous Proof." Energies 12, no. 20 (October 19, 2019): 3985. http://dx.doi.org/10.3390/en12203985.
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Different from conventional reservoirs, a significant proportion of oil is in an adsorbed or even immobile state in shale and tight rocks. There are established comprehensive mathematical models quantifying the adsorbed, immobile, and free oil contents in shale rocks. However, the conclusions of the monotonicity of the complicated models from sensitivity analysis might not be universal, and rigorous mathematical derivation is needed to demonstrate their rationale. In this paper, the models for oil/water storage in the nanoporous grains in shale, i.e., kerogen and clay, are achieved based on the aforementioned storage models. Rigorous analytical derivations are employed to strictly prove the monotonicity of the immobile and adsorbed models, which is the main purpose of this work. This work expands the applicability of the storage models, is fundamental and important for mobility analysis in shale reservoirs, and can shed light on its efficient exploration and development.
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Peeters, Bart, Herman Van der Auweraer, and Patrick Guillaume. "Modal Survey Testing and Vibration Qualification Testing: The Integrated Approach." Journal of the IEST 46, no. 1 (September 14, 2003): 110–18. http://dx.doi.org/10.17764/jiet.46.1.y542012501w0701q.
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In the assessment of the structural integrity and launch-environment survivability of satellite structures, dynamic mathematical models are used for load prediction. These analytical models are test-verified by a modal survey test. Once the vibration environment is specified, the satellite equipment is subjected to shaker excitation in order to reproduce this environment. This paper investigates the possibilities to integrate both the modal survey and the vibration qualification test.
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Figoń, Piotr. "Mathematical models of single-phase long lines." Bulletin of the Military University of Technology 68, no. 4 (February 28, 2020): 119–37. http://dx.doi.org/10.5604/01.3001.0013.9735.
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Most simulation packages provide long line models containing only two input terminals and two output terminals. These models allow testing transient states initiated by the occurrence of interference at the ends of the line. For this reason, it is not possible to study disorders occurring at any point of the electrical network. The article describes in detail the mathematical models of the long line, their implementation in the Matlab environment and exemplary results of computer simulations. Keywords: power line, state variables, differential scheme
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Repko, Alexandr, Milan Sága, Boris Sentyakov, and Vladislav Sviatskii. "Development and Testing of a Block Hydrocyclone." Processes 8, no. 12 (November 30, 2020): 1577. http://dx.doi.org/10.3390/pr8121577.
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The study aimed to theoretically substantiate the efficiency of liquid purification and obtain corroborating experimental data for a hydrocyclone, consisting of several blocks. Mathematical models of the process of hydrodynamic fluid filtration were developed with the use of screw swirlers. The obtained mathematical models characterize all the main processes of fluid movement in various zones of the functioning of the hydrocyclone. Formulas for calculating the structures of hydrocyclone blocks are included. A block for swirling the flow of the liquid to be cleaned has been made in the form of a three-way screw. For the first time, wear-resistant and high-strength plastic ZEDEX ZX-324 has been used as a material. An experimental study was conducted and the change in the Reynolds number and the coefficient of fluid consumption was shown, using different constructions of the three-way screw. The research results confirmed the correctness and sufficiency of mathematical models for the development and production of block hydrocyclones.
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Kravchenko, Alexander, Boris Gerasimov, Evgeniy Loskutov, Alexander Okrugin, Larisa Galenchikova, and Vasily Beryozkin. "Statistical Models of the Distribution of Chemical Elements in Precambrian Rocks of the Siberian Craton." Separations 8, no. 3 (February 25, 2021): 23. http://dx.doi.org/10.3390/separations8030023.
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Natural chemical systems are an excellent object for studying the properties of various elements. The most diverse and informative geological complexes are crystalline rocks of the Precambrian. These rocks are exposed near the northern and southern margins of the Siberian craton. The chemical composition of rocks, the contents of impurity elements, and metals were studied by us using chemical and spectral analysis methods. Microprobe studies were performed. Using regression and multivariate statistical methods of analysis, the regularities of the distribution of chemical elements were found. It is shown that the distribution of precious metals and carbon dioxide in rocks is attributed to their chemical properties and comparable with close in-chemical properties’ rock-forming elements. It is found that the factor analysis reflects the uniform regularities of the distribution of elements in different regions and rocks. These regularities are similar on macro and micro levels. Comparison of the distribution patterns with the results of geochemical and petrological studies of other authors shows the leading role of the redox potential and acidity of the environment in the formation of rocks and minerals. The role of mathematical statistics for solving problems of chemical petrology and chemical systems analysis is underlined.
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Stovpnik, Stanislav Nikolaevich. "FRAC PERFORMANCE EVALUATION OF SIMULATION OF BRITTLE ROCKS ON TESTING SAMPLES AND MODELS." Theoretical & Applied Science 30, no. 10 (October 30, 2015): 58–64. http://dx.doi.org/10.15863/tas.2015.10.30.15.
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Tennant, Marc, and Estie Kruger. "A Mathematical Simulation Approach to Testing Innovative Models of Dental Education." Journal of Dental Education 74, no. 3 (March 2010): 261–67. http://dx.doi.org/10.1002/j.0022-0337.2010.74.3.tb04871.x.
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Vigneswaran, S., and Jing Song Chang. "Experimental testing of mathematical models describing the entire cycle of filtration." Water Research 23, no. 11 (November 1989): 1413–21. http://dx.doi.org/10.1016/0043-1354(89)90081-x.
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Chernienkov, EM, A. Yu Primychkin, and L. Yu Belozertseva. "Energy efficiency evaluation of high-pressure DTH hammers." IOP Conference Series: Earth and Environmental Science 991, no. 1 (February 1, 2022): 012030. http://dx.doi.org/10.1088/1755-1315/991/1/012030.
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Abstract The design of a domestically produced DTH hammer for drilling holes in rocks of medium and high strength is presented. Using the mathematical modeling method, the serviceability of the hammer at an energy source pressure of 2.4 MPa is proved. The results of DTH hammer prototype testing at lab and full scale are presented.
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Olszak, Artur, Karol Osowski, Zbigniew Kęsy, and Andrzej Kęsy. "Modelling and testing of a hydrodynamic clutch filled with electrorheological fluid in varying degree." Journal of Intelligent Material Systems and Structures 30, no. 4 (January 6, 2019): 649–60. http://dx.doi.org/10.1177/1045389x18818780.
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The article concerns steady-state characteristics of a hydrodynamic clutch with electrorheological working fluid controlled by changes in strength of electric field and changes in the filling degree. The characteristics were obtained by experimenting, as well as calculations based on one-dimensional mathematical models. While creating the mathematical models, factors taken into consideration included differences between methods controlling the clutch, as well as various ways the working fluid flows in the clutch’s working space, depending on the relation of angular speed of rotors. The resultant mathematical models were verified with experimental research.
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Vikulov, A. G. "Mathematical simulation of heat transfer in spacecraft." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 2 (June 30, 2017): 61–78. http://dx.doi.org/10.38013/2542-0542-2017-2-61-78.
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We implemented a systemic scientific approach to thermal vacuum development of spacecraft, which integrates the problems of thermal calculations, thermal vacuum tests and accuracy evaluation for mathematical models of heat transfer by means of solving identification problems. As a result, the following factors increase the efficiency of spacecraft ground testing: reducing the duration of thermal vacuum tests, making autonomous thermal vacuum testing of components possible, increasing the accuracy of thermal calculations
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Sturniolo, Simone, William Waites, Tim Colbourn, David Manheim, and Jasmina Panovska-Griffiths. "Testing, tracing and isolation in compartmental models." PLOS Computational Biology 17, no. 3 (March 4, 2021): e1008633. http://dx.doi.org/10.1371/journal.pcbi.1008633.
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Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.
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Samaei, Masoud, Timur Massalow, Ali Abdolhosseinzadeh, Saffet Yagiz, and Mohanad Muayad Sabri Sabri. "Application of Soft Computing Techniques for Predicting Thermal Conductivity of Rocks." Applied Sciences 12, no. 18 (September 14, 2022): 9187. http://dx.doi.org/10.3390/app12189187.
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Due to the different challenges in rock sampling and in measuring their thermal conductivity (TC) in the field and laboratory, the determination of the TC of rocks using non-invasive methods is in demand in engineering projects. The relationship between TC and non-destructive tests has not been well-established. An investigation of the most important variables affecting the TC values for rocks was conducted in this study. Currently, the black-boxed models for TC prediction are being replaced with artificial intelligence-based models, with mathematical equations to fill the gap caused by the lack of a tangible model for future studies and developments. In this regard, two models were developed based on which gene expression programming (GEP) algorithms and non-linear multivariable regressions (NLMR) were utilized. When comparing the performances of the proposed models to that of other previously published models, it was revealed that the GEP and NLMR models were able to produce more accurate predictions than other models were. Moreover, the high value of R-squared (equals 0.95) for the GEP model confirmed its superiority.
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Wu, L. M., Nan Hui Lai, and G. T. Wang. "Measurement and Simulation of Automotive Eddy Current Retarder Based on Virtual Reality." Key Engineering Materials 392-394 (October 2008): 93–97. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.93.
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Structure and working principles of eddy current retarder (ECR) are discussed, as well as performance requirements of real-time virtual testing and simulation. On the basis of hardware testing platform, virtual models of vehicle and retarder are embedded into application program. In the testing system, Vega API function library is used for second development to control the 3D models, and Visual C++ is used for mathematical models call from MATLAB to simulate the working condition. Integrated with virtual instrument and virtual environment, the limitation of former simulation is broken through. Monitoring and testing on eddy current retarder are achieved efficiently and visually. Besides, the virtual test data is not only compared with the practical vehicle test data to correct the technical parameter of eddy current retarder, but also compared with the simulation of mathematical models for further study. The testing system gives evaluation on the performance of the retarder in different vehicles, so it expands application range and heightens testing efficiency.
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Chowdhury, M. R., and F. Y. Testik. "Laboratory testing of mathematical models for high-concentration fluid mud turbidity currents." Ocean Engineering 38, no. 1 (January 2011): 256–70. http://dx.doi.org/10.1016/j.oceaneng.2010.10.020.
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Katanov, Yu E. "A probabilistic and statistical model of rock deformation." E3S Web of Conferences 266 (2021): 03011. http://dx.doi.org/10.1051/e3sconf/202126603011.
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A new approach to the study of strength characteristics of the rocks on the basis of probabilistic and statistical models of the deformation processes (models of dilatancy initiation processes) under conditions of uncertainty is presented. The main purpose of the study is to create geological and mathematical tools, which could be used to study the development of volumetric deformation (dilatancy, disintegration) of reservoirs at a constant tension, acting on the array. The information and analytical basis of the performed study consists of methods of mathematical statistics and probability theory and the sedimentary rocks research methods. The probabilistic-statistical approach is formed in the study of deformation processes of the productive stratum structure, taking into account the degree of heterogeneity of the reservoirs. The obtained analytical expressions allow us to determine the moment of the beginning of the volumetric deformation process (dilatancy, disintegration) in the rock, similar to the identification of the bifurcation point in the development of geological and dynamic systems
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Mussina, Alla A. "BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 3 (211) (September 30, 2021): 25–31. http://dx.doi.org/10.18522/1026-2237-2021-3-25-31.
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The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.
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GRIYZEV, M. V., and A. N. KACHURIN. "PHYSICAL MODEL AND MATHEMATICAL DESCRIPTION OF METHANE MOTION IN MINING MASSIF TAKING INTO ACCOUNT FINAL PRESSURE SPEED." News of the Tula state university. Sciences of Earth 2, no. 1 (2020): 235–47. http://dx.doi.org/10.46689/2218-5194-2020-2-1-235-247.
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The physical model and the mathematical description of the methane movement in the rock massif are substantiated, taking into account the final pressure propagation velocity. It is proved that the mathematical model of gas filtration in coal seams and host rocks is based on an equation of hyperbolic type and it is shown that the use of parabolic type equations is physically justifiedfor long periods of time. It is proposed to use the law of resistance, which is a functional relationship between the gas flow and the gas pressure gradient and the local rate of change of the gas flow for an arbitrarily selected point in the considered region of the rock mass. The derivation of non-linear equations of the hyperbolic type for modeling methane filtration in coal seams and host rocks is presented. Variants of linearized equations of hyperbolic type for modeling methane filtration are presented and their use as approximate mathematical models is recommended.
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Aitkazinova, Sh, O. Sdvyzhkova, N. Imansakipova, D. Babets, and D. Klymenko. "Mathematical modeling the quarry wall stability under conditions of heavily jointed rocks." Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no. 6 (December 25, 2022): 18–24. http://dx.doi.org/10.33271/nvngu/2022-6/018.
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Purpose. To develop techniques for estimating the pit wall stability in terms of occurring of a zone of heavily jointed rock mass during ore mining at the Akzhal deposit (Kazakhstan), to work out measures to strengthen the rock opening and to verify the effectiveness of the developed measures. Methodology. The finite element analysis of the rock stress-strain state is implemented on the basis of the elastic-plastic model and the generalized Hoek-Brown failure criterion. The rock mass quality was assessed using the RMR and GSI rating classifications. This made it possible to simulate a zone of intense fracturing by changing the characteristics of the jointed surface. The shear strength reduction procedure was used to determine the safety factor for the quarry wall. Findings. The strain distributions in the rock mass forming the quarry wall have been obtained in terms of the Akzhal polymetallic ore deposit (Kazakhstan). The case of creating a zone of heavily jointed rocks in the area of a tectonic fault was considered. The safety factor of the quarry wall was determined under conditions of increased rock fracturing, as well as after carrying out measures to strengthen the rocks with a hardening solution. Originality. The effect of intense jointness on the pit wall stability is demonstrated. A method for the consistent evaluation of the quarry wall stability is proposed considering the change in the rock properties due to natural factors and artificial reinforcement. It is shown that a change in the joint surface quality due to the hardening injection reduces the shear strains in the sliding zone. Practical value. The pit wall stability was predicted considering the formation of a zone of intense fracturing under mining and geological conditions of the Akzhal deposit. The possibility of testing the effectiveness of rock strengthening measures based on mathematical modeling was shown.
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KARNACHEV, I. P., V. G. NIKOLAEV, V. V. BIRYUKOV, and S. A. GUSAK. "THE THERMAL MODE OF LARGE-SPAN EXCA VATIONS DURING THE CONSTRUCTION OF NUCLEAR POWER FACILITIES." News of the Tula state university. Sciences of Earth 2, no. 1 (2020): 289–301. http://dx.doi.org/10.46689/2218-5194-2020-2-1-289-301.
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The paper observes particular experimental research results on increase of stability of mining excavations in a permafrost area under low positive temperatures. The authors discuss the tasks on determining the temperature field parameters around the different-section excavations of underground small nuclear power plants at the construction stage. The mathematical models were designed for heat transfer processes in frozen rocks. The rocks were simulated as pore media filled with water with phase transfer under heating. This allowed creating virtual computing stands on which it became possible to work out the thermal modes of excavation driving.
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Xing, Guangchi, and Tieyuan Zhu. "A viscoelastic model for seismic attenuation using fractal mechanical networks." Geophysical Journal International 224, no. 3 (November 17, 2020): 1658–69. http://dx.doi.org/10.1093/gji/ggaa549.
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SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.
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Lima, Enzo Lenine. "Models, explanation, and the pitfalls of empirical testing." Estudos Internacionais: revista de relações internacionais da PUC Minas 6, no. 3 (December 19, 2018): 82–97. http://dx.doi.org/10.5752/p.2317-773x.2018v6n3p82.
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Formal models constitute an essential part of contemporary political science and International Relations. Their recent history is tightly tied to the developments of Rational Choice Theory, which is considered to be the only deductive theory in the social sciences. This unique character, especially its manifestation through mathematical symbolisms, has caused profound schisms and criticisms in the discipline. Formal models have constantly been accused of being built on unrealistic assumptions of human behaviour and social structure, rendering as a result either trivial predictions or no empirical prediction at all. Nevertheless these criticisms frequently ignore essential elements of the concept of explanation and how it is applicable to formal modelling. In this paper, I provide an approach to mathematical modelling that considers the challenges of designing and performing empirical tests of predictions generated by formal models. Rather than disqualifying or falsifying models, empirical tests are paramount to the tailoring of more grounded explanations of political phenomena and should be seen as a tool to enhance modelling. In this sense, I scrutinise two examples of formal modelling in IR, and derive lessons for the empirical testing of models in the discipline.
Os modelos formais constituem uma parte essencial da ciência política contemporânea e das Relações Internacionais. Sua história recente está fortemente ligada aos desenvolvimentos da teoria da escolha racional, que é considerada a única teoria dedutiva nas ciências sociais. Este caráter único, especialmente sua manifestação por meio de simbolismos matemáticos, causou profundas divisões e críticas na disciplina. Os modelos formais têm sido constantemente acusados de serem construídos com base em suposições irrealistas do comportamento humano e da estrutura social, resultando em previsões triviais ou nenhuma previsão empírica. No entanto, essas críticas frequentemente ignoram elementos essenciais do conceito de explicação e como o mesmo é aplicável à modelagem formal. Neste artigo, forneço uma abordagem à modelagem matemática que considera os desafios de conceber e executar testes empíricos de previsões geradas por modelos formais. Em vez de desqualificar ou falsificar modelos, os testes empíricos são fundamentais para a adaptação de explicações mais fundamentadas dos fenômenos políticos e devem ser vistos como uma ferramenta para aprimorar a modelagem. Nesse sentido, analiso dois exemplos de modelagem formal em RI e extraio lições para o teste empírico de modelos na disciplina.
Palavras-chave: modelos formais, teoria da escolha racional, teste empírico, explicação
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Gamal, Hany, Salaheldin Elkatatny, Ahmed Alsaihati, and Abdulazeez Abdulraheem. "Intelligent Prediction for Rock Porosity While Drilling Complex Lithology in Real Time." Computational Intelligence and Neuroscience 2021 (June 14, 2021): 1–12. http://dx.doi.org/10.1155/2021/9960478.
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Rock porosity is an important parameter for the formation evaluation, reservoir modeling, and petroleum reserve estimation. The conventional methods for determining the rock porosity are considered costly and time-consuming operations during the well drilling. This paper aims to predict the rock porosity in real time while drilling complex lithology using machine learning. In this paper, two intelligent models were developed utilizing the random forest (RF) and decision tree (DT) techniques. The drilling parameters include weight on bit, torque, standpipe pressure, drill string rotation speed, rate of penetration, and pump rate. Two datasets were employed for building the models (3767 data points) and for validating the developed models (1676 data points). Both collected datasets have complex lithology of carbonate, sandstone, and shale. Sensitivity and optimization on different parameters for each technique were conducted to ensure optimum prediction. The models’ performance was checked by four performance indices which are coefficient of determination (R2), average absolute percentage error (AAPE), variance account for (VAF), and a20 index. The results indicated the strong porosity prediction capability for the two models. DT model showed R2 of 0.94 and 0.87 between the predicted and actual porosity values with AAPE of 6.07 and 9% for training and testing, respectively. Generally, RF provided a higher level of strong prediction than DT as RF achieved R2 of 0.99 and 0.90 with AAPE of 1.5 and 7% for training and testing, respectively. The models’ validation proved a high prediction performance as DT achieved R2 of 0.88 and AAPE of 8.58%, while RF has R2 of 0.92 and AAPE of 6.5%.
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Ezangina, T., S. A. Gayvoronsiy, and S. Sobol. "Modeling a Microgravity System for Ground Testing of Transformable Space Structures." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012144. http://dx.doi.org/10.1088/1742-6596/2096/1/012144.
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Abstract The article develops a mathematical model of a microgravity system that simulates the conditions of weightlessness during ground tests of spacecraft. The microgravity system consists of vertical and horizontal control channels, providing a link opening in a twodimensional coordinate system. The channels are two-mass electromechanical systems with elastic connections. To simulate the microgravity system, mathematical models of these channels are obtained. To check the adequacy of the obtained models in Simulink Matlab, we simulated the opening of a link of a mechanical system. As a result of modeling, the permissible indicators of the accuracy of simulating weightlessness were obtained.
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Bažant, Zdeněk P. "Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2224 (April 2019): 20180617. http://dx.doi.org/10.1098/rspa.2018.0617.
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The objective in materials or structure design has been to maximize the mean strength. However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10 −6 per lifetime. But this objective is not the same. Indeed, a quasibrittle material or structure with a superior mean strength can have, for the same coefficient of variation, an inferior strength at the less than 10 −6 tail. This tail is unreachable by histogram testing. So, one needs a rational theory, physically based and experimentally verified indirectly, which is feasible by size effect. Focusing on the results at the writer's home institution, this inaugural article (written three years ex post facto ) reviews recent results towards this goal, concerned with quasibrittle materials such as concretes, rocks, tough ceramics, fibre composites, bone and most materials on the micrometer scale. The theory is anchored at the atomic scale because only on that scale the failure probability is known—it is given by the frequency of breakage of bonds, governed by the activation energy barriers in the transition rate theory. An analytical way to scale it up to the macroscale representative volume element (RVE) has been found. Structures obeying the weakest-link model are considered but, for quasibrittle failures, the number of links, each corresponding to one RVE, must be considered as finite. The result is a strength probability distribution transiting from Weibullian to Gaussian, depending on the structure size. The Charles-Evans and Paris laws for subcritical crack growth under static and cyclic fatigue are also derived from the transition-rate theory. This yields a size-dependent Gauss–Weibull distribution of lifetime. Close agreement with numerous published test data is achieved. Discussed next are new results on materials with a well-defined microscale architecture, particularly biomimetic imbricated (or staggered) lamellar materials, exemplified by nacre, a material of astonishing mean strength compared to its constituents. This architecture is idealized as a diagonally pulled fishnet, which is shown to be amenable to an analytical solution of the strength probability distribution. The solution is verified by million Monte Carlo simulations for each of the fishnets of various shapes and sizes. In addition to the classical weakest-link and the fibre-bundle models, the fishnet is found to be the third strength probability model that is amenable to an analytical solution. The nacreous architecture is shown to provide an additional major (greater than 100%) strengthening at the 10 −6 failure probability tail. Finally, it is emphasized that the most important consequence of the quasibrittleness, and also the most effective way of calibrating the 10 −6 tail, is the size effect on the mean structural strength, which permeates all formulations.
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Baikov, V. A., M. V. Rykus, Ye A. Ryzhikov, and Ch R. Akhmetov. "Use of mathematical technologies for processing geophysical logging to build facial models of terrigenous reservoir rocks." Neftyanoe khozyaystvo - Oil Industry 9 (2019): 12–15. http://dx.doi.org/10.24887/0028-2448-2019-9-12-15.
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Сазонова, Светлана, Svetlana Sazonova, Сергей Николенко, S. Nikolenko, Максим Манохин, and Maksim Manohin. "DEVELOPMENT OF MATHEMATICAL MODELS FOR MONITORING WATER HEAT HEATING WITH SALES OF VALUABLE ROCKS OF FORESTS." Forestry Engineering Journal 8, no. 3 (September 10, 2018): 30–35. http://dx.doi.org/10.12737/article_5b97a15e9393c4.46673542.
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Volkov, Victor E. "Mathematical and information models of decision support systems for explosion protection." Applied Aspects of Information Technology 5, no. 3 (October 25, 2022): 179–95. http://dx.doi.org/10.15276/aait.05.2022.12.
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This paper is dedicated to the issue of mathematical and information modeling of the combustion-to-explosion transition that makes it possible to create an adequate mathematical and information support for decision support systems (DSS) for automatedcontrol of explosive objects.A simple mathematical model for the transition of combustion to explosion is constructed. This model is based on solving mathematical problems of the hydrodynamic stability of flames and detonation waves. These problems are reduced to solving eigenvalue problems for linearized differential equations of gas dynamics. Mathematical model is universal enough. It provides opportunities for making simple analytical estimates for the explosive induction distance and the time of the shock wave formation. The possibilities of the transition of slow combustion to both a deflagration explosion and a detonation wave are considered. Theoretical estimates of the explosive induction distance and the time of the combustion-to-explosion transition are obtained. These estimates are expressed by algebraic a formula, the use of which save computer resources and does not require significant computer time. The application of fuzzy logic makes it possible to use the proposed mathematical model of the combustion-to-explosion transition for real potentially explosive objects in industry and transport.Mathematical models of potentially explosive objects are based on combination of the fuzzy logic and classical mathematical methods. These models give possibilities for creating corresponding information models. Thus mathematical and information support of DSS for automated control systems of explosive objects is developed. The main advantage of these DSS is that it makes it possible for decision makers to do without experts. In particular, developed mathematical and information models create the base forsoftware of DSS for explosion safety of grain elevators. Appropriate software is developed and some calculations are performed. These calculations are useful not only from the point of view of testing the proposed method of mathematical modeling of a grain elevator as a potentially explosive object or testing the software itself, but also from the point of view of the grain elevator designing.
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Junevičius, Raimundas, and Marijonas Bogdevičius. "MATHEMATICAL MODELLING OF NETWORK TRAFFIC FLOW." TRANSPORT 24, no. 4 (December 31, 2009): 333–38. http://dx.doi.org/10.3846/1648-4142.2009.24.333-338.
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The article describes mathematical models of traffic flows to initiate different traffic flow processes. Separate elements of traffic flow models are made in a way to be connected together to get a single complex model. A model of straight road with different boundary conditions is presented as a separate part of the network traffic flow model. First testing is conducted in case the final point of the whole modelled traffic line is closed and no output from that point is possible. The second test is performed when a constant value of traffic flow speed and traffic flow rate is entered. Mathematical simulation is carried out and the obtained results are listed.
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Sherstyuk and Musayev. "Data Warehouses Application in the Automated Testing and Verification System for Mathematical Models." SPIIRAS Proceedings, no. 4 (March 17, 2014): 163. http://dx.doi.org/10.15622/sp.4.11.
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