Natural Gas Compressibility Factor Research Articles

Estimating the natural gas compressibility factor using a statistical correlations and machine learning approaches

Gas compressibility factor plays an critical role in petroleum engineering applications such as gas metering, pipeline design, reserve estimation, gas flow rate, material balance calculations, and many other significant tasks. Therefore, it is crucial to accurately estimate the gas compressibility factor. There have been a lot of studies on calculating the gas compressibility factor from laboratory data, which can be summarized into two main approaches: statistical correlations and machine learning algorithms. In this study, on statistical correlations the authors implement explicit and implicit method while on machine learning algorithms, we use Artificial Neural Network (ANN) and Least-Squares Support Vector Machine (LS-SVM). The data was collected from open literature. Implementing the two approaches mentioned above and comparing statistical parameters such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Coefficient of Determination (R2 ) found that machine learning algorithms give much more accurate estimation results than statistical correlations, and besides, the ANN algorithm has the most accurate prediction results with the lowest MSE and RMSE (0.000002 and 0.0016) and the highest R2 (0.9999). The high-precision calculation results show that the ANN algorithm mentioned above can be applied to estimate other real gas compressibility factor data sets. On the other hand, this study can be extended to another subset of machine learning algorithms, such as deep learning and ensemble learning.

Procedure for Natural Gas Compressibility Factor Determination

The article is devoted to the development of an experimental stand and a methodology for experimental determination of the gas compressibility factors, to ensure the possibility of obtaining reliable information about the values of natural gas compressibility factor within the temperature range 223 - 250 K. An overview of empirical assessment methods of the compressibility factor values of gas media and approaches used to organize the hardware design of experimental studies is given. The method of compressibility factor determination is proposed and the description of the developed experimental stand is given. The error of the proposed method was assessed by testing in media with known compressibility factors in a wide range of temperatures and pressures: air, nitrogen, argon, methane. The test results are presented in the form of experimentally obtained data deviations from the compressibility factor values published in literature. The air compressibility factor uncertain values obtained as a result of the study are in the range (-0.02 -0.07%), for nitrogen - (-0.06 - 0.02%), for argon - (- 0.04 - 0.04%), for methane - (-0.08 - 0.06%). The obtained empirical values are taken satisfactory with the information given in literary sources. The good agreement of the experimental and design data obtained for pure gases and air shows that the developed method of compressibility factor experimental determination is reliable, has the required accuracy and can be used to determine the natural gas compressibility factor of various component composition.

Applicability Evaluation of Natural Gas State Equations at Low Temperatures

The paper analyzes the possibility of operating range expanding of natural gas state equations for low temperatures. The state equations of natural gas and methods of estimating the compressibility factor, entrenched in modern national and international standards, were analyzed. It has been shown that the range of their applicability is limited to a temperature value of 250 K, however, these temperature limitations is not restricted bystate equations directly butstipulated by the lack of reliable data about natural gas compressibility factor values at temperatures below 250 K and methods for complementary errorcalculation that may arise. The results of comparison of values of natural gas compressibility factor as a function of temperature at pressure of 1.3 and 6 MPa calculated by means of the most widely used state equations are presented. It was found that the results of the calculation according to the considered methods have satisfactory convergence within the range of 220 K, that generally confirms the applicability of modern state equations for low temperatures. In its turn, the effect of assumptions applied nowadays to definegas volume flow rateon flow metering error showed that application of substitutive compressibility values may result in significant complementary systematic error. This indicates the practicability of expanding the database of compressibility factor values for natural gas for low temperatures, as well as developmentof a standard to assess the value of the corresponding complementary error.

Predicting the Compressibility Factor of Natural Gas by Using Statistical Modeling and Neural Network

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.

The Impact of Accurate Prediction of Natural Gas Compressibility Factor on the CO2 Replacement Method for Natural Gas Hydrate Exploitation

The Impact of Accurate Prediction of Natural Gas Compressibility Factor on the CO2 Replacement Method for Natural Gas Hydrate Exploitation

Experimental Determination of the Compressibility Factor of Natural Gas: Methods and Results

Experimental Determination of the Compressibility Factor of Natural Gas: Methods and Results

An accurate correlation for calculating natural gas compressibility factors under a wide range of pressure conditions

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.

COMPARATIVE STUDY OF EMPIRICAL CORRELATIONS AND EQUATIONS OF STATE EFFECTIVENESS FOR COMPRESSIBILITY FACTOR OF NATURAL GAS DETERMINATION

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.

A Novel Simplification for the Prediction of Natural Gas Compressibility Factor

The need for a simpler, effective and less expensive predictive tool for the estimation of natural gas compressibility factor cannot be exaggerated. An accurate prediction of gas compressibility factor is essential because it plays a definitive role in evaluating gas reservoir properties used in the estimation of gas reserves, custody transfer and design of surface equipment. In this present work, a novel explicit correlation and a highly sophisticated computer program were developed to accurately predict natural gas deviation factor. The research also aims to effectively capture the relationship between Pseudo-reduced temperature and pressure in relations to the Z-factor. In this study, 3972 digitized data points extracted from Standing and Katz’s Chart were regressed and analyzed using Microsoft Excel Spreadsheet, the extraction of this data was done using WebPlotDigitizer developed by Ankit Rohatgi of GitHub, Pacifica, CA, USA. The correlation was developed as a function of Pseudo-reduced temperature and pressure with tuned parameters distributed across 1.05 ≤ Tpr ≤ 3.0 and 0 < Ppr ≤ 8.0. Subsequently, the input (Tpr and Ppr values) of the feed data was used to validate the correlation and compare it with other known and published correlations. Statistical analysis of the results showed that a 99.8% agreement exists between the predicted and actual compressibility factors for the various test scenarios and case studies involving both sweet and sour gases. Also, the correlation was observed to outperform other models. Finally, the results were observed to perfectly mimic the Standing and Katz charts with an overall correlation coefficient of 99.76% and an adjusted R2 of 99.75%. The proposed correlation was subsequently used to develop a software using JavaScript. Undoubtedly, the proposed correlation and software are suitable for rapid and accurate simplification and prediction of natural gas compressibility factor.

Accurate determination of natural gas compressibility factor by measuring temperature, pressure and Joule-Thomson coefficient: Artificial neural network approach

Natural Gas (NG) compressibility factor as important property at any NG industrial applications determined by utilizing an intelligent approach precisely. Three thermodynamic properties include pressure, temperature and Joule-Thomson (JT) coefficient are selected as input parameters. These properties are chosen due to the measurement capabilities of available sensors. Unlike the traditional approaches, the current approach does not require NG compositions as input. The current intelligent approach is developed based on an Artificial Neural Network (ANN) method. Real-time measurement capability and very low cost are two main advantages of the developed approach. Big data sets of NG thermodynamic properties are created considering 30,000 random compositions for training, testing and validating the ANN. The GERG-2008 is utilized (as the most recent equation of state) to calculate thermodynamic properties to train the ANN. Validation of the developed ANN method compared to experimental data shows the Average Absolute Percent Deviation (AAPD) is about 0.33%. To show the accuracy of the developed approach, four different NG compositions are selected as case studies. The compressibility factor and JT coefficient are computed for various pressure and temperature range using the traditional approach. Then, the compressibility factor is determined using the intelligent approach when only pressure, temperature and JT coefficient are known. The AAPD of NG compressibility factor calculations for various natural gases show 0.385% for pure methane, 0.45% for the Khangiran gas, 0.58% for the Kangan gas, 0.78% for the Pars gas and is 1.12% for the Bidboland gas. The comparing results show that overall AAPD is less than 0.7% that shows the high accuracy of the intelligent approach.

THE INFLUENCE OF PRESSURE AND TEMPERATURE ON THE COMPRESSIBILITY FACTOR

The natural gas compressibility factor indicates the compression and expansion characteristics of natural gas under different conditions. It is a thermodynamic property used to take into account the deviation of the behaviour of real natural gases from that of an ideal gas. Compressibility factor, Z, values of natural gases are necessary for most petroleum gas engineering calculations. In this study, a comparison between five different calculation methods is presented to determine this critical parameter for the same natural gas at different conditions (pressure and temperature), using Canadian Association of Petroleum Producers, Azizi, Behbahani and Isazadeh, Dranchuk- Purvis- Robinson, Dranchuk-Abu-Kassem and Standing- Katz methods. The correlations are based on the equation of state are often implicit because they require iteration. Many correlations have been derived to enhance simplicity; however, no correlation has been developed for the entire range of pseudo-reduced pressures and temperatures. Azizi, Behbahani and Isazadeh’s method was found to have the biggest error as a result obtained for T=20° C, and p=20 bar is no longer in the field of applicability.

An intelligent approach for calculating natural gas compressibility factor and its application in ultrasonic flow meters

The current study presents an intelligent method for calculating natural gas compressibility factor. The method requires three easily measurable properties including pressure, temperature, and speed of sound as inputs. As sound speed could be measured with ultrasonic flow meters, temperature, and pressure with appropriate sensors, the real-time natural gas compressibility factor could be calculated easily. The presented method eliminates the high cost of determining compressibility based on measuring natural gas composition. Artificial Neural Network is employed to develop the method. The artificial neural network is trained in a way to accept pressure, temperature, and speed of sound as inputs. To train an artificial neural network, the 30,000 random datasets of natural gas compositions were utilized. To check the validity and accuracy of the developed artificial neural network, four different natural gas compositions are selected and the compressibility factor are compared with the GERG-2008 equation of state (as standard and accurate method for calculating natural gas properties) results. The results reported the average absolute percent deviation is less than 0.7% for the compressibility factor calculation by utilizing the proposed method.

NEW CORRELATIONS FOR THE PSEUDOCRITICAL PARAMETERS AND THE ACENTRIC FACTOR S OF THE HYDROCARBON COMPONENT OF THE DNIEPER-DONETS PETROLEUM BASIN’S NATURAL GAS

NEW CORRELATIONS FOR THE PSEUDOCRITICAL PARAMETERS AND THE ACENTRIC FACTOR S OF THE HYDROCARBON COMPONENT OF THE DNIEPER-DONETS PETROLEUM BASIN’S NATURAL GAS

Modeling natural gas compressibility factor using a hybrid group method of data handling

The natural gas compressibility factor indicates the compression and expansion characteristics of natural gas under different conditions. In this study, a simple second-order polynomial method based on the group method of data handling (GMDH) is presented to determine this critical parameter for different natural gases at different conditions, using corresponding state principles. The accuracy of the proposed method is evaluated through graphical and statistical analyses. The method shows promising results considering the accurate estimation of natural gas compressibility. The evaluation reports 2.88% of average absolute relative error, a regression coefficient of 0.92, and a root means square error of 0.03. Furthermore, the equations of state (EOSs) and correlations are used for comparative analysis of the performance. The precision of the results demonstrates the model’s superiority over all other correlations and EOSs. The proposed model can be used in simulators to estimate natural gas compressibility accurately with a simple mathematical equation. This model outperforms all previously published correlations and EOSs in terms of accuracy and simplicity.

A New Model of Displacement Efficiency of Gas Hydrate Considering the Influence of Temperature

The model of natural gas hydrate displacement failed to accurately analysis the influence degree of temperature, and it is not accurate enough to calculate the volume of gas under high pressure owing to the influence of compressibility factor, which leading to a result that the model has great error in calculating the displacement efficiency. In this paper, a new model of displacement efficiency affected by temperature is derived in the design of displacement experiment based on the law of conservation of mass, Multicomponent gas equation of state, Multicomponent thermodynamic phase equilibrium principle at the first. Next, several methods for calculating the compressibility factor of natural gas at different temperatures and pressures are compared by using Visual Basic software, and the Setzmann equation with the smallest error is selected. Finally, compared with the new model, the traditional model as well as the experimental data, the results show that the new model is closer to the experimental data. At the same time, the displacement efficiency of natural gas hydrate at different temperatures is analyzed. It is suggested that higher displacement efficiency can be obtained by reasonably increasing the temperature of the displacement reaction system.

Evaluation of Correlations of Compressibility Factor (z) of Natural Gas for Algerian Gas Reservoirs

The study of PVT properties of natural gas is essential for the development of its production and exploitation. The laboratory is considered the main source of data for these properties as it is also possible to compute these data using state equations and empirical correlations with variable error margins.This work aims to study experimentally an Algerian natural gas, concentrating on the calculation of the compressibility factor, using the relative correlations to calculate this factor, while trying to modify these with what corresponds better with Algerian natural gas based on statistical tools and experimental data.The results of this study show that it is possible to develop and update the correlation coefficients that correspond better with each geographic region in order to reduce the margin of error.

Measurement and control of natural gas mass flow in a dual-fuel engine operating at partial load through sonic nozzles

In this paper, the part load operation of a dual fuel engine operating at 1500 m above sea level and its control using sonic flow meters for natural gas fuelling are presented. Dual fuel operation was established by retrofitting the intake system of a commercial Diesel engine with a port-injected gaseous fuels system, which was comprised by calibrated orifices working under sonic flow conditions. Natural gas mass flow rates throughout the orifices were estimated assuming the isentropic one-dimensional theory for perfect gases. The effect of natural gas compressibility factor on the measured flow rates was established according to the recommendations of American Gas Association Report No. 10, evaluating the accuracy for the operating pressures and temperatures. Natural gas intake temperature was kept constant and the required flow rate was controlled by absolute intake pressure variations from 2 to 8.5 bar, according to the required diesel substitution. The maximum diesel substitution was close to 60% at 43% of full load, additional values were established for 6, 18, and 25% of full load. The absolute differences between the measured natural gas mass flow rates and those achieved by using the American Gas Association Report No. 10 were lower than 2%. A predictive correlation for natural gas mass flow rate was fitted depending on the required diesel substitution and the power output using the recommended methodology by the International Energy Agency Annex 42 for micro-cogeneration systems. The absolute errors between the measured flow rates and those achieved by the predictive correlation were lower than 3%.

Precise calculation of natural gas sound speed using neural networks: An application in flow meter calibration

The natural gas speed of sound (SoS) is needed for flowmeters calibration using sonic nozzles. To determine SoS of real gases, the compressibility factor (sometimes called Z-factor) should be calculated firstly. Historically, natural gas thermodynamic properties are determined by employing AGA8 equation of state (EOS). Although, AGA8 EOS could predict natural gas thermodynamic properties precisely but has a few limitations. The acceptable range of natural gas composition is the main limitation of employing AGA8 EOS. In this work, to overcome this limitation and also speed up the thermodynamic calculation procedure, the Artificial Neural Network (ANN) has been utilized to predict the compressibility factor of natural gas and SoS. The ANN training is performed by measured values of gas mixture and also training data obtained from AGA8 equation of state. The validity of the ANN methodology is carried out by comparing results with experimental values of natural gas mixtures. Analyzing the results indicate that the percentage of the relative difference for Z-factor and SoS prediction is almost within ± 5% (and even in some cases, much less than this amount). This shows a very high accuracy of the proposed method for calculating natural gas thermodynamic properties. Finally, the application of the calculations for natural gas flowmeter calibrating is applied to the different gas fields in the world as case studies.

Estimation of density and compressibility factor of natural gas using artificial intelligence approach

Natural gas density is commonly measured by Coriolis density meters and gas chromatographs, both of which are used to calculate the natural gas mass flow rate. In this study, two networks are proposed to predict the density and compressibility factor of natural gas. The first network (N1) uses temperature, pressure and Joule Thomson (JT) coefficient of natural gas as input variables and density of natural gas is selected to be the target. This network is proposed to predict the natural gas density at natural gas pressure drop stations (CGSs). For this network, the gas mixture compositions are unnecessary. The second network (N2) is proposed based on the pseudo reduced temperature and pressure as input variables that the network by using these two variables can predict the density and compressibility factor of natural gas. This model needs the gas mixture compositions. For these targets, a novel idea based on artificial intelligence is used. Five models of artificial intelligence are implemented that are fuzzy inference system (FIS), adaptive neuro-fuzzy inference system (ANFIS), ANFIS optimized with genetic algorithm (ANFIS-GA), multilayer feed-forward neural network (MLFFNN) and group method of data handling (GMDH). The results demonstrated that the ANFIS-GA and GMDH model performed better than the FIS, MLFFNN and ANFIS models. For N1, root mean square error (RMSE) for ANFIS-GA and GMDH models were obtained as 0.2405 and 0.2042 (kg/m3), respectively. For N2 (compressibility factor), the value of RMSE for ANFIS-GA and GMDH models consecutively was achieved 0.0061 and 0.0054. Also, for N2 (density), RMSE for ANFIS-GA and GMDH models was taken 2.2735 and 2.6113, respectively. These values of RMSE were reported for the testing phase of the models.

Submarine slope stability analysis during natural gas hydrate dissociation

ABSTRACTThe purpose of this paper is to analyze the stability of submarine slope during the natural gas hydrate dissociation. A model is deduced to calculate the excess pore fluid pressure. In addition, a new method is proposed to define and calculate the factor of safety (FoS) of the submarine slope. Case study is also performed, results of which show that dissociation of hydrates would decrease the stability of submarine slope. If the cohesion of the hydrate-bearing sediments is small, the submarine slope would become unstable because of the shear failure. If the cohesion of the hydrate-bearing sediments is large enough, the tensile failure would happen in the hydrate-bearing sediments and the excess pore pressure may explode the submarine slope. Under the drained condition, the submarine slope may remain stable because the buildup of excess pore fluid pressure could not take place. Moreover, FoS would be underestimated by the assumption that natural gas hydrates dissociate in the horizontally confined space, but would be overestimated by only taking into account of the base of the natural gas hydrate-bearing sediments. The compressibility factor of natural gas should also be considered because treating natural gas as ideal gas would underestimate the stability of submarine slope.