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The EU's circular economy concept necessitates increasing the recycling ratio of municipal solid wastes. There are many existing mechanical–biological processing plants in Hungary for the preparation of residual municipal solid wastes (RMSWs). The two most important products of these plants are the bio-fraction and the refuse derived fuel (RDF). Currently, there are problems with both of these material streams in Hungary, since most of the bio-fraction is still landfilled, and the local thermal utilisation of the RDF has not been implemented yet. The high moisture content of the produced bio-fraction and RDF causes difficulties for the downstream operations; therefore, there is recent engineering interest in drying and agglomeration of these materials. The authors have carried out systematic and parallel drying and briquetting experimental series to study the effect of the material, material composition, mass (volume or surface) of the material, particle size distribution and pre-treatment with a cutting mill on drying intensity in a 1 m3 oven and their effect on briquettability by a laboratory briquette press. The initial slope of the relative moisture loss as function of time was determined. Process engineering design methods of convective hot air-drying can be further developed taking into account the research results. Results can be used for the design of the feed of a pyrolysis reactor once reactor experiments have provided the optimal feed requirements. [ABSTRACT FROM AUTHOR]

When designing compressors, it is necessary to take into account the reality of the working fluid, since when calculating the compressor using ideal gas models, strong deviations of the operating parameters from the calculated ones occur, which can lead to non-fulfillment of the technical specifications, as well as to the formation of non-stationary processes. The correct choice of the gas reality accounting methodology allows us to bring the calculated data as close as possible to the experimental ones. Thus, the choice of the most accurate method of accounting for the reality of gas makes it possible to predict the experimental characteristics of the designed compressor even before conducting physical tests. There are many methods that allow us to take into account the reality of gas, namely, to calculate the compressibility factor using empirical formulas. In this paper, a comparison of four methods is presented, and the calculation of a centrifugal compressor is performed taking into account the values of the compressibility factor obtained according to these methods. The calculated gas dynamic characteristics are compared with experimental data and discrepancies are revealed at different rotor speeds.

Cubic equations of state are utilized to model the behavior of substances in both liquid and gaseous states, incorporating cubic order terms in their variables. These equations are pivotal in describing the behavior of real substances, particularly their deviations from ideal behavior. Furthermore, they facilitate the prediction of a range of thermodynamic properties, including pressure, volume, temperature, and compressibility factors. This study was conducted with the objective of evaluating the compressibility factor using four distinct cubic equations of state: Van der Waals, Redlich–Kwong, Soave-Redlich–KwongRedlich–Kwong, and Peng–Robinson. The analysis focused on the dependency of these equations on temperature, pressure, and component fractions in binary mixtures. A numerical algorithm, featuring algebraic solutions, was developed on the Excel platform to enable graphical analysis of the mixtures in question. The results of this analysis led to the establishment of a parametric relationship for the compressibility factor, dependent on temperature, pressure, and concentration.The study's findings reveal significant discrepancies in the compressibility factors calculated using the Van der Waals (VDW) equation compared to those from the Redlich–Kwong (R–KR–K) and Peng–Robinson (P–R) equations, with deviations reaching as high as 16.13 %. Specifically, at the maximum pressure investigated, the compressibility factor derived from the VDW equation (1.519) significantly differed from that obtained via the Soave-Redlich–Kwong (S-R–K) equation (1.222), showing a 0.297 difference, or 19.55 %. This disparity is attributed to how temperature affects the repulsive forces term in the S-R–K, P–R, and R–K equations, leading to a closer approximation of the compressibility factor profile. Additionally, the P–R and S-R–K cubic state equations account for the acentric factor, a crucial parameter that influences compressibility factor behavior by considering the molecular size involved in the process. In conclusion, the Soave-Redlich–Kwong cubic equation of state was found to align most closely with experimental data and was therefore selected to explore the compressibility factor's behavior in relation to pressure across various fractions and temperatures within the examined systems.

The article is devoted to the analysis of compressibility factor calculation methods in the temperature range from 220 to 250 K. The AGA8-92DC (GOST 30319.2- 96), AGA8 Report Detail (GOST 30319.3-2015), GERG-2004/2008, NX19, GERG-91, ISO 20765-1 (GOST R 8.662-2009), GSSSD MR 118-05 (moderately compressed gas mixtures) and GSSSD MR 113-03 (Wet Oil Gas) methods are experimentally tested. Deviations of experimental data and calculated values of compressibility coefficient determined by the specified methods are shown. It is found out that the deviation of the calculated values of the compressibility factor according to the AGA8-92DC, AGA8 Report 1 Detail, GERG-2004/2008, ISO 20765-1 (GOST R 8.662-2009), GSSSD MR 13-03 methods from the experimental ones does not exceed 0,1 %. This fact confirms the possibility of using these methods in the temperature range from 220 to 250 K. The results obtained in the framework of this study are highly significant for flow metering, and in particular, provide an increase in the accuracy of the procedure for bringing the volume of natural gas to standard conditions at low temperatures.

To calculate the operating modes of gas pipelines and for the commercial metering of consumed or transported gas, it is necessary to take into account its compressibility factor, which is determined using equations of state or correlation dependencies. Equations of states are characterized by high calculation accuracy but require a significant amount of various data for calculations, so they are used for commercial gas metering. Correlation equations are usually used to calculate network parameters, which are less accurate but much easier to calculate. Gas transmission network operators use correlation equations for determining the compressibility factor based on carbon dioxide content or relative density, as given in SOU 60.3-0019801-100:2012. When these equations are applied to calculate the compressibility factor of natural gas-hydrogen blends with volumetric hydrogen content up to 20 %, an increase in error is observed with increasing hydrogen concentration. The equation based on the relative density is more accurate when calculating the natural gas-hydrogen mixture’s compressibility factor since the hydrogen content directly affects the density of the blend. The carbon dioxide equation is generally insensitive to changes in hydrogen concentration within the blend. Thus, it is worth adding a hydrogen variable to the equation to reduce calculation errors. In this article, the selection of the hydrogen variable coefficient is carried out by the classical regression method, in which the equations are modified by supplementing the existing equations for calculating the compressibility factor with the addition of the product of the hydrogen content in the mixture by the calculated coefficient, and the equation's bias adjustment. An alternative way to calculate the compressibility factor is to use artificial neural networks (ANNs). In the course of this work, a two-layer artificial neural network with back-propagation of error was developed. This ANN receives as input a set of values of carbon dioxide and hydrogen content, temperature, and pressure, and outputs the value of the compressibility factor. [ABSTRACT FROM AUTHOR]

For gas transportation through pipes in normal and emergency modes, a comparison of calculations based on mathematical models of various degrees of generality is presented. A mathematical model of a non-isothermal steady flow of a mixture of gases and its simplified versions are studied. For simplified options, simple analytical dependencies were obtained for calculating flow characteristics and calculating the lo cation of an emergency gas leak. Examples of calculations of pressure distributions, temperature and leakage coordinates in gas pipelines of medium pressures according to the general and simplified models are provided. The examples cover the parameter change area of practical interest. The conditions for the admissibility of using simplified models for calculating the coordinates of a leak of medium intensity and different lo cations are determined. [ABSTRACT FROM AUTHOR]

The assessment of gas behavior in chemical engineering systems necessitates a profound understanding of thermodynamic principles that govern the interactions among the components within a given system. To this end, the deviation from ideality in a single gas or gas mixture is associated with the disparity between the actual behavior of the gas or gas mixture and the behavior anticipated by the ideal gas model. This study is aimed at scrutinizing the deviation from ideal behavior in a gas mixture composed of CH4 and CO2. The analysis employs the cubic equations of state: Van Der Waals, Soave-Redlich-Kwong, and generalized Virial equations, truncated to the third term. These equations are widely recognized for their utility in characterizing substance behavior under specific thermodynamic conditions. The investigation involves an evaluation of the mixture's behavior by assessing variations in the compressibility factor concerning pressure, volume, and pressure, using a thermodynamic calculator at 296.15 K and 15 bar. The findings of this study reveal the prevalence of attractive intermolecular forces at higher pressures and repulsive interactions at lower pressures. An analogous examination of the effect of altering the composition of CH4 was undertaken using the Soave-Redlich-Kwong equation, which incorporates parameters allowing for an evaluation of the impact of molecule size and intermolecular interactions within the mixture. Furthermore, experimental data were employed to validate the results obtained in this study. Consequently, it can be inferred that these equations provide insight into the influence of pressure on molecular interaction forces, encompassing repulsive and attractive forces, which in turn can define the new volume of a real system. Thus, based on the corroboration established herein, these equations demonstrate a high degree of consistency and applicability, thereby expanding the realm of thermodynamic inquiry. [ABSTRACT FROM AUTHOR]

The paper presents a method for calculating the thermodynamic parameters of refrigerant vapors during their compression in a scroll compressor. The method takes the properties of a refrigerant as a real gas into account, as well as the process of mixing two vapor portions inside the scroll unit when the full geometric degree of compression is reached. [ABSTRACT FROM AUTHOR]

This work discusses an extension of the Redlich–Kwong (RK) equation of state for real gases that modifies its attractive part by introducing a third constant, fitted to the nearly-universal value of the compressibility factor at the critical point, Zc ≈ 0.27. From this, the model predicts a covolume b = V ¯ c / (6.33 ± 0.62) for 90% of all the gases, in terms of the critical molar volume V ¯ c. It is found that this b value is approximately the difference between the molar volume of a monodisperse fluid near its normal melting point and the interstitial space associated with the loose packing of spheres. In other words, in contrast to the covolume in the RK equation, the present b-parameter does correspond to a molecular excluded volume. Despite the intrinsic limitations of the cubic equations of state for fluids, the present model extends their phenomenological usefulness over a larger range of values for the molar volume. [ABSTRACT FROM AUTHOR]

Among the essential thermodynamic parameters of behavior, analysis (PVT) in natural gas engineering is the gas compressibility factor (Z). In this work, we improve the results of the compressibility factor (Z) prediction accurately after modifying the cubic equation coefficients for different gas types; the cubic equation of state (EOS) prediction model was tested using 149 experimental data under different conditions. In this study, the gas compressibility factor is calculated by Peng Robinson's equation of state (PR EOS). Additionally, the coefficients were updated to reflect a better representation of natural gas. The results are compared to the predictions of the original PR EOS and other equations of state in the literature. The statistical analysis shows an average absolute deviation percentage (AAD %) of 0,99% and a coefficient of determination (R²) of 0,9968 at pressure and temperature up to 16632,93 PSI (114,68 MPa) and 426,74K, respectively. The proposed model can effectively calculate (Z) for any type of gas, including condensate gas. [ABSTRACT FROM AUTHOR]

The behavior of the line of the unit compressibility factor in the region of low-temperature dense plasma of metals is studied for the first time. The shape of this line is universal in the density–temperature plane for many one-component gases and liquids at low temperatures, along with liquid metals. Using virial expansions and calculations within the framework of the chemical model, we demonstrate that such a similarity breaks apart upon transition to the region of low-temperature plasma of metals. Nevertheless, a weaker similarity expressed in the form of a power law is possible for the discussed line in this region at relatively low densities. [ABSTRACT FROM AUTHOR]

Due to the emergence of new technologies that make it possible to obtain hydrogen from associated petroleum gas, it has become necessary to store and transport it. As a solution to this problem, the possibility of hydrogen transportation as a methane-hydrogen mixture was considered, i.e. natural gas with a certain hydrogen content. The article considers the issues of methane-hydrogen mixture (MHM) transportation through existing main gas pipelines at various percentages of hydrogen to natural gas. As an example, the Urengoyskoye field was chosen, where it is possible to produce hydrogen from the associated gas of gas condensate fields, and a section of the Novopskovskiy corridor, through which it is possible to transport MHM. In the work, the influence of the hydrogen content in the methane-hydrogen mixture on the gas-dynamic characteristics of the pipeline, mainly on the pressure and throughput capacity of gas in the pipeline, as well as the influence of its content on the operating mode of the compressor station and the power of the gas turbine, when using MHM for the station's own needs, was studied. The obtained results show an insignificant effect of the hydrogen percentage in the mixture on the pressure and throughput of the gas pipeline, which is a weighty argument in favor of the possibility of transporting hydrogen through existing gas pipelines. [ABSTRACT FROM AUTHOR]

The injection of carbon dioxide ( CO 2 ) into gas reservoirs has become an important way to enhance gas recovery and reduce CO 2 emissions. Large discrepancies are observed when predicting natural gas compressibility factors with high CO 2 content by several well-known empirical correlations. An explicit correlation is proposed to improve the prediction accuracy in the estimation of compressibility factors on condensate gases with variable CO 2 contents. The analysis of the results is carried out on the basis of 202 experimental data from 9 various mixtures of natural gases. The results show that relative deviations of compressibility factors predicted by conventional empirical correlations increase with the increase in CO 2 mole fraction with an average error of 8%. The average error of the new method is less than 4%. The effect of compressibility factors on the estimations of dynamic reserves is studied and the compressibility factor causes a 3% reduction in dynamic reserves estimation. The proposed correlation has fewer uncertainties and more accurate results than other correlations that involve the iterative process in calculating compressibility factors of natural gases with variable CO 2 contents. [ABSTRACT FROM AUTHOR]

The natural gas compressibility factor is a vital parameter in petroleum engineering calculation. Currently, the calculation models for calculating natural gas compressibility factors in engineering are not accurate and efficient enough. To solve this problem, multivariate nonlinear regression is used to fit the 6988 data of the Standing–Katz chart, a novel empirical formula of natural gas compressibility factors is obtained, which is suitable for the pseudo-reduced pressure range of 0.2 to 30. The mean absolute error, mean relative error and root mean square error between the fitted values and the Standing–Katz chart values are 0.01140, 0.01282 and 0.01663 respectively, hence the fitted values accord well with the chart values. The proposed correlation is verified by 270 measured data of natural gas compressibility factors under low and medium pressure conditions and 219 measured data under high pressure conditions and compared with the other five representative calculation models. The verification result shows that the mean absolute error, mean relative error and root mean square error between the calculated values and the measured values are 0.01962, 0.01626 and 0.02511 respectively, and the proposed correlation is superior to the other five methods because of its higher calculation accuracy. The new correlation is practical and accurate for predicting the natural gas compressibility factor under an extensive range of pressure conditions.

Chromatographic and volumetric data are used to derive kinetic equations and calculate constants for catalytic reactions of the hydroformylation of isobutylene, the hydrocarboxylation of cyclohexene, and the hydrogenation of N-benzylideneaniline. It is found that the constants obtained using both ways of calculating are in good agreement. [ABSTRACT FROM AUTHOR]

An accurate value of compressibility factor, also called Z-factor or deviation factor, is essential for petroleum engineering, especially for reservoir simulation and material balance calculations. Standing and Katz (S-K) charts were published as an industry reference to calculate Z-factor since 1942. After that, many direct and indirect methods were implemented that can fit the Standing and Katz charts and extend the approach for high-range of pressure and temperature data. The problem arises from the difficulty of having accurate, direct, and quick correlations that can fit with low- and high-range pressure data. The objective of this study is to apply different machine learning (ML) techniques such as artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) to predict the gas compressibility factor within high and low-pressure ranges with high accuracy. Additionally, an empirical equation was extracted based on the ANN model to convert the black box model into a white box. It was concluded that the ANN-based model outperformed the other models with a correlation coefficient (R) of 0.99 and an average absolute percentage error (AAPE) of 0.159. The proposed correlation was validated using new experimental high-pressure range data for Z-factor and compared with existing correlations in the literature showing a lower error, which indicates that the proposed correlation can be used for low and high ranges of pressure and temperature and can be evaluated without having special programs to run the ANN model. [ABSTRACT FROM AUTHOR]

As an alternative to the construction of new infrastructure, repurposing existing natural gas pipelines for hydrogen transportation has been identified as a low-cost strategy for substituting natural gas with hydrogen in the wake of the energy transition. In line with that, a 342 km, 36″ natural gas pipeline was used in this study to simulate some technical implications of delivering the same amount of energy with different blends of natural gas and hydrogen, and with 100% hydrogen. Preliminary findings from the study confirmed that a three-fold increase in volumetric flow rate would be required of hydrogen to deliver an equivalent amount of energy as natural gas. The effects of flowing hydrogen at this rate in an existing natural gas pipeline on two flow parameters (the compressibility factor and the velocity gradient) which are crucial to the safety of the pipeline were investigated. The compressibility factor behaviour revealed the presence of a wide range of values as the proportions of hydrogen and natural gas in the blends changed, signifying disparate flow behaviours and consequent varying flow challenges. The velocity profiles showed that hydrogen can be transported in natural gas pipelines via blending with natural gas by up to 40% of hydrogen in the blend without exceeding the erosional velocity limits of the pipeline. However, when the proportion of hydrogen reached 60%, the erosional velocity limit was reached at 290 km, so that beyond this distance, the pipeline would be subject to internal erosion. The use of compressor stations was shown to be effective in remedying this challenge. This study provides more insights into the volumetric and safety considerations of adopting existing natural gas pipelines for the transportation of hydrogen and blends of hydrogen and natural gas.

Using the example of a ferromagnetic dielectric, an algorithm is proposed for calculating the Young modulus of elastically deformable solid bodies on the basis of the Holstein–Primakov transformations and the theory of spin waves. Due to the method of averaging over the ground state of a magnetic, a general expression is obtained for the temperature dependence of the Young modulus in a wide temperature range. [ABSTRACT FROM AUTHOR]

Summary: Nowadays, the gas chromatography (GC) method is vastly used in natural gas energy measurement but suffers from slow analysis, high capital investment, and high maintenance costs. With the advent of commercial calorimeters using new principles, the calorimeter measurement (CM) method has the ability to overcome the shortcomings of the GC method and is hoping to be an alternative method for energy measurement. To realize accurate energy metering of natural gas by the CM method, the standard GERG‐88 viral equation (denote hereafter as the SGERG‐88 algorithm) is needed to calculate the compressibility factors (Z‐factors). However, unlike the detailed characterization equation in American gas association report No.8 (denote hereafter as the AGA8‐92 DC algorithm) used in the GC method, the SGERG‐88 algorithm is seldom used since it was published in 1991, thus its applicability and accuracy is not so clear in the natural gas industry. In addition, the original SGERG‐88 algorithm coupled hydrogen and carbon monoxide together with a fixed relation, which is not applicable to natural gas blended with hydrogen (NatualHy) that will be widely used anymore. This paper firstly improves the original SGERG‐88 algorithm to make it applicable to NatualHy. Then, taking the Z‐factor calculated by the AGA8‐92 DC as references, the applicability of the improved SGERG‐88 algorithm to different gases is assessed for natural gas and NatualHy measurement. Results and related conclusions or further study suggestions are drawn to prompt the accurate energy measurement of natural gas by the CM method. [ABSTRACT FROM AUTHOR]

• Dissociation enthalpies of CH 4 hydrate in the absence/presence of ionic liquids using the Clausius-Clapeyron equation calculated. • The Clausius-Clapeyron equation was analyzed in the temperature and pressure range of 273 K – 290 K and up to 10 MPa, respectively. • The Peng-Robinson equation is preferred for the calculation of the compressibility factor. • The obtained methane hydrate enthalpies show overestimated values and temperature dependence compared to the experimental ones. • This approach can be used as a rule of thumb, but care should be taken to get molecular-level insights. The Clausius-Clapeyron (CC) equation is generally preferred to obtain dissociation enthalpies (ΔH) of hydrate-forming systems due to its ease of use. The application of other direct and indirect methods becomes more problematic if complex additives such as ionic liquids (ILs) are also present in the system. In this work, around 400 equilibrium data points for methane hydrates in the presence of over 80 ILs were collected from the literature in the temperature and pressure ranges of (272.10 – 306.07) K and (2.48 – 100.34) MPa, respectively. The ΔH of methane hydrates in the absence and presence of ionic liquids (ILs) have been calculated using the CC equation. The compressibility factor (z), required to calculate ΔH at each phase equilibrium condition has been obtained from three different approaches viz., Peng-Robinson (PR) equation of state, Soave-Redlich-Kwong (SRK) equation of state and Pitzer (Pz) correlation. The results were compared to the experimentally reported dissociation enthalpy (54.5 ± 1.5 kJ.mol−1) of methane hydrates. The role of the compressibility factor along with the slope of the equilibrium data set and the temperature/pressure range in determining the outcome of the CC equation has been discussed. The effect of molar mass, molar volume, and hydrate suppression temperature of the ILs on the ΔH of methane hydrates has been explored. The tested ILs do not show a systematic and significant influence on enthalpies, rather they show a large scattering in the ΔH values, which might mask any existing subtle effect of the ILs on the dissociation enthalpies. Therefore, this approach should be dealt with care to obtain molecular-level insights. [ABSTRACT FROM AUTHOR]

Introduction. Currently, for the treatment of gastric ulcer, drugs with a combined effect are used. To eliminate possible side effects of the drugs used, the search for new molecules to create more effective and safe histamine H2 receptors continues. As a possible solution to these problems, we investigated the substance dinitrate of 2-phenyl-9-diethylaminoethylimidazo[1,2-α]benzimidazole (DFDB).Aim. The aim of this study was to obtain 2-phenyl-9-diethylaminoethylimidazo[1,2-α]benzimidazole dinitrate tablets and develop methods for quality control.Materials and methods. The object of study was tablets based on the substance DF DB. The physicochemical and technological properties of the tablet dosage form were studied. Pharmaco-technological and physico-chemical indicators were determined according to the methods of the State Pharmacopoeia of the XIV edition. Identification and quantitative determination of DFDB in tablets was performed by HPLC.Results and discussion. Based on the physico-chemical properties and determination of the main technological indicators of DFDB, an optimal tableting technology has been developed. The optimal composition of tablets has been developed. Identification of tablets is proposed to be carried out using HPLC in comparison with the standard sample of DFDB. Related impurities, according to the data obtained, do not exceed 0.1 %. We found that the tablets do not have an antimicrobial effect. The analyzed tablets correspond to category 3A. The content of DFDB should be from 95 to 105 % of the declared amount in one tablet. During the analysis, we conducted biopharmaceutical and technological studies of the finished dosage form during storage under the conditions of long-term stability testing in polymer cans with screw-on lids. It is shown that the selected composition of excipients and the production technology ensure the stability of the finished dosage form for two years of storage under the observed conditions. To select the tableting technology, the main technological properties of the DFDB substance are analyzed. The choice of excipients and the composition of the film coating was carried out.Conclusion. The technology is developed and standardization of tablets based on the substance DFDB is proposed.

The article discusses the applicability of the equations of state for the gas phase of natural gas at temperatures below 250 K. To tackle this problem, highly accurate experimentally obtained values of the compressibility factor of natural gas are required. For this purpose, we developed a method to experimentally determine the compressibility factor of natural gas. The proposed method is based on the fact that, in order to assess the applicability of the equation of state, it is sufficient to obtain the relative value of the compressibility factor rather than determining its absolute value. This approach, which provides high accuracy in determining the compressibility factor, does not require sophisticated equipment. The method was tested on nitrogen, argon, air, and methane. The uncertainty in determining the compressibility factor did not exceed 0.1%. Two different compositions of natural gas were experimentally investigated. The method showed that the uncertainty in calculating the compressibility factor, according to the equations of state GERG-2004 and AGA8-DC92, was no more than 0.1% at a temperature of 220–250 K and a pressure of less than 5 MPa. [ABSTRACT FROM AUTHOR]

Ultrasonic parameters are very useful tools used to study the physic-chemical behavior and molecular interactions of various liquid mixtures. More than 50% problems of irrigated areas are associated with cultivated land and they frequently occur due to salinity. Application of fertilizers into agricultural land could be a remedy for soil salinity by providing essential nutrients to plants. In this research paper, ultrasonic and volumetric properties of phosphate based fertilizers of different molecular compositions at different temperatures have been studied. This is experimental based work; this knowledge can be employed in formulation of fertilizers according to the nature of their application which could enhance fertilizer’s activity either in terms of nutrients development or to control the salinity of soil. Results obtained from calculated ultrasonic and volumetric parameters indicated presence of strong interactions in aqueous fertilizer solutions which depends upon nature of molecules. Among presently studied phosphate fertilizers i.e. triple superphosphate, nitrophosphate and diammonium phosphate, maximum molecular interactions were observed in aqueous triple super phosphate solutions due to the presence of highly charged cationic specie i.e. calcium ions, which can also be used to control the salinity of soil using electrostatic interactions among saline salts and charged cationic species.

The injection of carbon dioxide (CO2) into gas reservoirs has become an important way to enhance gas recovery and reduce CO2 emissions. Large discrepancies are observed when predicting natural gas compressibility factors with high CO2 content by several well-known empirical correlations. An explicit correlation is proposed to improve the prediction accuracy in the estimation of compressibility factors on condensate gases with variable CO2 contents. The analysis of the results is carried out on the basis of 202 experimental data from 9 various mixtures of natural gases. The results show that relative deviations of compressibility factors predicted by conventional empirical correlations increase with the increase in CO2 mole fraction with an average error of 8%. The average error of the new method is less than 4%. The effect of compressibility factors on the estimations of dynamic reserves is studied and the compressibility factor causes a 3% reduction in dynamic reserves estimation. The proposed correlation has fewer uncertainties and more accurate results than other correlations that involve the iterative process in calculating compressibility factors of natural gases with variable CO2 contents.

In order to solve the problems of insufficient calculation accuracy, low calculation efficiency and small application range of the calculation method for natural gas compressibility factor currently used in engineering, the characteristics of the natural gas compressibility factor charts are analyzed. The nonlinear surface fitting method is used to fit the 6 988 data of Standing-Katz chart, and a new empirical formula of natural gas compressibility factor in the form of hook function is obtained, which is suitable for the pressure range of 0. 2 ≤ p ≤ 30. 0. The mean absolute error, mean relative error and root mean square error between the fitting values and the chart values are Cl. 012 51, Cl. 013 59 and 0. 017 57 respectively, so the fitting effect is good. The proposed method is verified by 237 measured data of natural gas compressibility factor under low and medium pressure conditions and 219 measured data under high pressure conditions, and compared with the other five common explicit or implicit methods. The verification result shows that the mean absolute error, mean relative error and root mean square error between the calculated values and the measured values are 0. 018 95, 0. 015 08 and 0. 024 19 respectively, and the method is superior to the other five methods because of its higher calculation accuracy. The new method c;m be used to predict the natural gas compressibility factor quickly and accurately in practice. [ABSTRACT FROM AUTHOR]

Introduction: Today, there are four main groups of methods for calculating the compressibility factor of natural gas: experimental measurements, equations of state, empirical correlations, modern methods based on genetic algorithms, neural networks, atomistic modeling (Monte Carlo method and molecular dynamics). A correctly chosen method can improve the accuracy of calculating gas reserves and predicting its production and processing. Aim: To find the optimal methods for calculating the z-factor following the characteristic thermobaric conditions. Methods: To determine the best method for calculating the compressibility factor, the effectiveness of using various empirical correlations and equations of state to predict the compressibility factor of hydrocarbon systems (reservoir gases and separation gases) of various compositions were evaluated by comparing numerical results with experimental data. Results and Discussion: Based on 824 experimental values of the compressibility factor for 235 various gas mixtures in the pressure range from 0.1 to 94 MPa and temperatures from 273 to 437 K, the optimal equation of state and empirical correlation dependence for accurate z-factor prediction was found. It is shown that for all gas mixtures the Peng-Robinson equation of state with the shift parameter and Brusilovsky equation of state allow achieving best results. For these methods, the average absolute relative error does not exceed 2%. Among the correlation dependences, the best results are shown by the Sanjari and Nemati Lay; Heidaryan, Moghadasi and Rahimi correlations with an error not exceeding 3%. Conclusions: It was found that for the proposed methods, the reduced pressure has a more significant effect on the accuracy of the calculated values than the reduced temperature. It is shown that when studying acid gas mixtures with a carbon dioxide content of more than 10%, the equations of state better describe the phase behavior of the system in comparison with empirical correlations. [ABSTRACT FROM AUTHOR]

The relevance of the work is caused by the need to determine the exact value of the compressibility factor for calculating gas reserves, forecasting technological indicators for development of gas and gas condensate fields, the behavior of hydrocarbon systems flow in wells, and preparation of well production and its transportation. The aim of the research is to develop a program for computation of the compressibility factor for the main components of natural gas to achieve more accuracy in determining z-factor in comparison with classical approach, based on the equations of state. Methods. To determine the z-factor the authors have used the technique based on the Peng–Robinson equation of state, its modification with a shift parameter, and a software module for molecular dynamic simulation developed by the authors that describes the behavior of the system at the molecular level. The potential of Lennard-Jones and NPT-ensemble is considered as a model of interatomic interaction of particles. Results. Based on the proposed methods of modeling, it was shown that the molecular dynamics simulations make it possible to accurately calculate the compressibility factor for the main components of natural gases. Based of the Peng–Robinson equation of state and its modification with a shift parameter, as well as using the molecular dynamics simulation for methane, ethane, propane, nitrogen and carbon dioxide, the dependencies of the compressibility factor on pressure were determined in the temperature range from 250 to 410 K. Lennard-Jones potential parameters for ethane, propane, nitrogen and carbon dioxide were specified that made it possible to improve the accuracy in calculating the compressibility factor. It is shown that the average absolute error of the molecular dynamics method in almost all calculations does not exceed 3 %.

Simulating the phase behavior of a reservoir fluid requires the determination of many parameters, such as gas–oil ratio and formation volume factor. The determination of such parameters requires knowledge of the critical properties and compressibility factor (Z factor). There are many techniques to determine the compressibility factor, such as experimental pressure, volume, and temperature (PVT) tests, empirical correlations, and artificial intelligence approaches. In this work, two different models based on statistical regression and multi-layer-feedforward neural network (MLFN) were developed to predict the Z factor of natural gas by utilizing the experimental data of 1079 samples with a wide range of pseudo-reduced pressure (0.12–25.8) and pseudo reduced temperature (1.3–2.4). The statistical regression model was proposed and trained in R using the “rjags” package and Markov chain Monte Carlo simulation, while the multi-layer-feedforward neural network model was postulated and trained using the “neural net” package. The neural network consists of one input layer with two anodes, three hidden layers, and one output layer. The input parameters are the ratio of pseudo-reduced pressure and the pseudo-reduced temperature of the natural hydrocarbon gas, while the output is the Z factor. The proposed statistical and MLFN models showed a positive correlation between the actual and predicted values of the Z factor, with a correlation coefficient of 0.967 and 0.979, respectively. The results from the present study show that the MLFN can lead to accurate and reliable prediction of the natural gas compressibility factor.

In the context of gas transportation, analytical solutions are helpful for the understanding of the underlying dynamics governed by a system of partial differential equations. We derive traveling wave solutions for the one-dimensional isothermal Euler equations, where an affine linear compressibility factor is used to describe the correlation between density and pressure. We show that, for this compressibility factor model, traveling wave solutions blow up in finite time. We then extend our analysis to networks under appropriate coupling conditions and derive compatibility conditions for the network nodes such that the traveling waves can travel through the nodes. Our result allows us to obtain an explicit solution for a certain optimal boundary control problem for the pipeline flow.

Ultrasonic parameters are very useful tools used to study the physic-chemical behavior and molecular interactions of various liquid mixtures. More than 50% problems of irrigated areas are associated with cultivated land and they frequently occur due to salinity. Application of fertilizers into agricultural land could be a remedy for soil salinity by providing essential nutrients to plants. In this research paper, ultrasonic and volumetric properties of phosphate based fertilizers of different molecular compositions at different temperatures have been studied. This is experimental based work; this knowledge can be employed in formulation of fertilizers according to the nature of their application which could enhance fertilizer's activity either in terms of nutrients development or to control the salinity of soil. Results obtained from calculated ultrasonic and volumetric parameters indicated presence of strong interactions in aqueous fertilizer solutions which depends upon nature of molecules. Among presently studied phosphate fertilizers i.e. triple superphosphate, nitrophosphate and diammonium phosphate, maximum molecular interactions were observed in aqueous triple super phosphate solutions due to the presence of highly charged cationic specie i.e. calcium ions, which can also be used to control the salinity of soil using electrostatic interactions among saline salts and charged cationic species. [ABSTRACT FROM AUTHOR]

By using the published accurate new virial coefficients B11∼B14 for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B2∼B13 at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy. [ABSTRACT FROM AUTHOR]

By taking carbon dioxide and hydrogen as lubricating gas, respectively, this paper presents an analysis on the pressure characteristics and temperature distribution of spiral groove dry gas seal which influenced by real gas effect under choked flow condition. Numerical results show that the deviation between real gas and ideal gas, which expressed by the deviation degree between compressibility factor Z and 1, is the main reason for real gas effect affecting sealing performance. Compared with ideal gas model, real gas effect raises exit pressure, opening force, leakage rate, Mach number in dam region, and temperature for carbon dioxide (Z < 1), while it decreases those characteristics for hydrogen (Z > 1) under the same operating conditions. In addition, choked flow effect increases opening force and reduces leakage rate and temperature-drop between entrance and exit of sealing clearance. Meanwhile, it may cause an unstable behavior for the seal. [ABSTRACT FROM AUTHOR]

An empirical equation is presented for the gas compressibility factor, Z, as a function of reduced temperature and reduced pressure. The average error of the equation is 2.5%, median error is 1.3%, and the coefficient of determination (R2) is 0.98. The equation is presented in a manner ready for use in software code. Comparison is made to the traditional generalized compressibility factor chart. The equation was found using genetic programing for symbolic regression coupled with the Levenburg-Marquardt algorithm for fitting-parameter optimization. [ABSTRACT FROM AUTHOR]

For H2S-containing natural gas with pressures higher than 70 MPa, closer the distance between natural gas molecules is, stronger the association between H2S molecules becomes. At such conditions, the traditional SRK, PR equations of state are difficult to accurately calculate the gas compressibility factors. In this paper, a total of 154 experimental compressibility factor data with pressure from 3.72 MPa to 97.58 MPa and H2S contents from 0%-70.03% are used to improve the binary interaction parameters between H2S and CH4,CO2 molecules for CPA(Cubic-Plus-Association)EoS and to evaluate the compressibility factor calculation accuracy of SRK, PR and CPA EoSs. Results show that the PR EoS has the highest accuracy and the average relative deviation is 1.12% for medium and low pressure natural gas (p<35 MPa). The CPA equation has the highest accuracy with average relative of -1.46% for the high pressure and ultra-high pressure natural gas (p>35 MPa). Furthermore, the ST PVT cell is applied to measure a total of 138 compressibility factors for four H2S-containing gas samples with pressures from 70 MPa to 131 MPa. The experimental results are used to verify the SRK, PR and CPA EoSs. Results demonstrate that CPA EoS has the highest accuracy for calculation of compressibility factors of ultra-high pressure and H2S-containing gas. [ABSTRACT FROM AUTHOR]