Natural Gas Compressibility Factor Research Articles

An intelligent approach to predict gas compressibility factor using neural network model

This research illustrates the utilization of a new model based on artificial neural networks (ANNs) in prediction of compressibility factor (z-factor) of natural gases using experimental data based on Standing and Katz z-factor diagram. Although equations of state and empirical correlations have been applied for predicting compressibility factor, the demands for the modern, more reliable and easy-to-use models encouraged the researchers to recommend modern facilities such as intelligent systems. This investigation describes a new technique for computing z-factor of natural gases. The base of the approach is ANN in which a 2:5:5:1 structure is used as an optimum network to predict the z-factor. The statistical results show that the developed ANN is an excellent tool for estimating z-factor values; therefore, it can be confidently used for natural gases with various compositions at a specific temperature and pressure.

Predicting the compressibility factor of natural gas

ABSTRACTKnowing compressibility factor (z-factor) values of natural gases is the basis of most petroleum engineering calculations. Shortage of available experimental data for the specified composition, temperature, and pressure conditions encourages researchers to propose efficient equations for calculating z-factor values.This investigation presents a useful empirical model for determining natural gases compressibility factor values. The advantages of this correlation are that it is explicit in terms of z-factor and the results of calculating compressibility factor values by this method reveal the supremacy of the new equation over the other widely used correlations.

Using Lee-Kesler equation of state to compute the compressibility factor of CO2-content natural gas

To improve the compressibility factor prediction of CO2-content natural gas, this short communication proposes a new combinational Stewart-Burkhardt-Voo (SBV) + Prausnitz-Gunn (PG) mixing rule for the Lee-Kesler equation of state. The rule suggests using SBV and PG mixing rules for the pseudocritical temperature and pressure computations, respectively, when the reduced temperature is higher than one and the reduced pressure is higher than five; otherwise, the pseudocritical temperature and pressure is calculated according to SBV mixing rule. Comparisons between experimental and calculation data show that the maximum average relative deviation is 1.56% when the mole fraction of CO2 is less than 50%.

New explicit correlation for the compressibility factor of natural gas: linearized z-factor isotherms

The compressibility factor (z-factor) of gases is a thermodynamic property used to account for the deviation of real gas behavior from that of an ideal gas. Correlations based on the equation of state are often implicit, because they require iteration and are computationally expensive. A number of explicit correlations have been derived to enhance simplicity; however, no single explicit correlation has been developed for the full range of pseudo-reduced temperatures $$\left( {1.05 \le T_{pr} \le 3} \right)$$ and pseudo-reduced pressures $$\left( {0.2 \le P_{pr} \le 15} \right)$$ , which represents a significant research gap. This work presents a new z-factor correlation that can be expressed in linear form. On the basis of Hall and Yarborough’s implicit correlation, we developed the new correlation from 5346 experimental data points extracted from 5940 data points published in the SPE natural gas reservoir engineering textbook and created a linear z-factor chart for a full range of pseudo-reduced temperatures $$(1.15 \le T_{pr} \le 3)$$ and pseudo-reduced pressures $$(0.2 \le P_{pr} \le 15)$$ .

Application of Wilcoxon generalized radial basis function network for prediction of natural gas compressibility factor

Gas compressibility factor is necessary in most of chemical and petroleum engineering calculations. Accurate and fast calculation of this property is of a vital importance in a large number of simulators used in petroleum and gas engineering. In this study, a large data bank (978 data points), covering a wide range of natural gases, was collected from open literature sources. Afterwards, one of the newest and most powerful modeling approach, namely Wilcoxon generalized radial basis function network (WGRBFN) was employed to predict the compressibility factor of natural gases. The results obtained from the proposed model were compared to those of nine empirical correlations and five equations of state. Statistical and graphical error analyses demonstrated that the developed model can satisfactorily predict the compressibility factor of natural gases with an average absolute percent relative error of 2.3%. Moreover, it was demonstrated that the proposed model outperforms all of the studied empirical correlations and equations of state. Finally, to identify the probable outliers the Leverage approach was performed. All of the experimental data seem to be reliable except 2%. Therefore, the developed model is reliable for the prediction of natural gas compressibility factor in its applicability domain.

An improved algorithm for calculation of the natural gas compressibility factor via the Hall‐Yarborough equation of state

The Hall‐Yarborough equation (H‐Y equation) of state has been favoured in natural gas engineering due to its accuracy and conciseness for many years. In this paper, the Adomian decomposition method (ADM) is employed to devise a novel algorithm for calculating the compressibility factors of natural gases through this reliable equation of state. A convergence accelerator technique, namely the efficient Shanks transform, is also exploited to further improve our scheme in terms of computational speed. Unlike most of the previous numerical solution strategies, our algorithm does not require an initial guess as the starting point and is computationally efficient. The proposed algorithm is found to be superior over the common Newton‐Raphson algorithm, where we have also demonstrated that the latter can easily lead to grossly erroneous solutions. For the sake of illustration, a number of real‐world case study problems are solved by our algorithm and relevant comparisons are provided.

A Methodology for Calculating the Natural Gas Compressibility Factor for a Distribution Network

This work describes a methodology that allows an accurate correlation for natural gas compressibility factor to be obtained. This methodology was applied to the Parana State natural gas distribution network in Southern Brazil, whose operating conditions were characterized by more than 14,000 pairs of pressure–temperature readings, measured along eight months. Compressibility factors calculated following Peng-Robinson, Patel-Teja-Valderrama, Shell Oil Company, Soave-Redlich-Kwong, and Van der Waals were compared to those given by the American Gas Association equation, which is used by most natural gas companies. Finally, an alternative correlation was proposed, which is highly accurate within the network operating range.

An accurate explicit form of the Hankinson–Thomas–Phillips correlation for prediction of the natural gas compressibility factor

The use of the Hankinson–Thomas–Phillips correlation for prediction of the natural gas compressibility factor is a common practice in natural gas engineering calculations. However, this equation suffers a serious deficiency from a computational viewpoint; in that it is not explicit with respect to the z-factor and hence is subject to time-consuming trial and error procedures. In this paper, we propose an explicit series expansion equivalent to the Hankinson–Thomas–Phillips equation by the aid of a powerful mathematical technique known as the Adomian decomposition method. Furthermore, we have enhanced our formula by a applying nonlinear convergence accelerator algorithm, namely the Shanks transform. The proposed equation is simple, easy to use, and is shown to be extremely accurate in reproducing the experimental PVT data of natural gases. Moreover, in contrast to the previous numerical algorithms such as the Newton–Raphson algorithm, the explicit nature of our formula obviates the need for any initial guess as an input for calculation of the z-factor. Such independence permits our formula to always quickly converge to the correct z-factor.

Efficient estimation of natural gas compressibility factor using a rigorous method

The compressibility factor (Z-factor) of natural gases is necessary in many gas reservoir engineering calculations. Accurate determination of this parameter is of crucial need and challenges a large number of used simulators in petroleum engineering. Although numerous studies for prediction of gas compressibility factor have been reported in the literature, the accurate prediction of this parameter has been a topic of debate in the literature. For this purpose, a new soft computing approach namely, least square support vector machine (LSSVM) modeling optimized with coupled simulated annealing optimization technique is implemented. The model is developed and tested using a large database consisting of more than 2200 samples of sour and sweet gas compositions. The developed model can predict the natural gas compressibility factor as a function of the gas composition (mole percent of C1–C7+, H2S, CO2, and N2), molecular weight of the C7+, pressure and temperature. The calculated Z-factor values by developed intelligent model are also compared with predictions of other well-known empirical correlations. Statistical error analysis shows that the developed LSSVM model outperforms all existing predictive models with average absolute relative error of 0.19% and correlation coefficient of 0.999. Results from present study show that implementation of LSSVM can lead to more accurate and reliable estimation of natural gas compressibility factor.

Prediction of sour gas compressibility factor using an intelligent approach

Compressibility factor (z-factor) values of natural gasses are essential in most petroleum and chemical engineering calculations. The most common sources of z-factor values are laboratory experiments, empirical correlations and equations of state methods. Necessity arises when there is no available experimental data for the required composition, pressure and temperature conditions. Introduced here is a technique to predict z-factor values of natural gasses, sour reservoir gasses and pure substances. In this communication, a novel mathematical-based approach was proposed to develop reliable model for prediction of compressibility factor of sour and natural gas. A robust soft computing approach namely least square support vector machine (LSSVM) modeling optimized with coupled simulated annealing (CSA) optimization tool was proposed. To evaluate the performance and accuracy of this model, statistical and graphical error analyses have been used simultaneously. Moreover, comparative studies have been conducted between this model and nine empirical correlations and equations of state. The obtained results demonstrated that the proposed CSA-LSSVM model is more robust, reliable and efficient than the existing correlations and equations of state for prediction of z-factor of sour and natural gasses.

Natural Gas Compressibility Factor Correlation Evaluation for Niger Delta Gas Fields

Natural gas compressibility factor (Z) is key factor in gas industry for natural gas production and transportation. This research presents a new natural gas compressibility factor correlation for Niger Delta gas fields. First, gas properties databank was developed from twenty-two (22) laboratory Gas PVT Reports from Niger Delta gas fields. Secondly, the existing natural gas compressibility factor correlations were evaluated against the developed database (comprising 22 gas reservoirs and 223 data sets). The developed new correlation was used to compute the z-factors for the four natural gas reservoir system of dry gas, solution gas, rich CO2 gas and rich condensate gas reservoirs, and the results were compared with some exiting correlations. The performances of the developed correction indicated better statistical ranking, good graph trends and best crossplots parity line when compared with correlations evaluated. From the results the new developed correlation has the least standard error and absolute error of (stdEr) of 1.461% and 1.669% for dry gas; 6.661% and 1.674% for solution; 7.758% and 6.660% for rich CO2 and 7.668% and 6.661 % for rich condensate gas reservoirs. The new correlation also show high correlation coefficient of: 93.39%, for dry gas; 89.24% for solution gas; 83.56% for rich CO2 and 83.34% for rich Condensate gas reservoirs. Also the proposed new model maintained good graphical trends for four z-factors matched it: experimental, estimated (Standing - Katz) and the best evaluated correlation when matched. Very good crossplots parity line performance when compared with the evaluated correlations. It could then be concluded that the new developed correlation and that of Papay correlation are most appropriate correlations for calculating natural compressibility for Niger Delta gas fields. Carr, Kobayashi, and Burrows (1954) and Wichert-Aziz (1972), correction factor methods; were applied to correct the presence of non-hydrocarbons. But the major setbacks on laboratory analyses for PVT behavior are sometimes expensive and time consuming. Correlations, which are used to predict gas compressibility factor, are much easier and faster than equations of state, invariably save cost.

A new correlation based on artificial neural networks for predicting the natural gas compressibility factor

In this study a new correlation of natural gas compressibility factor based on theory of Mohammadikhah-Mohebbi-Abolghasemi’s equation of state (MMA EOS) is developed using an artificial neural network. In MMA EOS, the compressibility factor as a function of M-factor (BP/RT) is expressed. An artificial neural network (ANN) is designed in which the M-factor, reduced temperature, and reduced pressure are selected as input variables, whereas the natural gas compressibility factor is selected as output. Then, a new correlation based on the weights of ANN is obtained. Results of this correlation are compared with some other equations and experimental data. Proposed correlation for 597 data points has an average absolute deviation (AAD%) of 0.6% and a correlation coefficient (R 2 value) of 0.9999.

Estimation of natural gas compressibility factors using artificial neural network approach

Prediction of compressibility factor of natural gas is an important key in many gas and petroleum engineering calculations. In this study compressibility factors of different compositions of natural gas are modeled by using an artificial neural network (ANN) based on back-propagation method. A reliable database including more than 5500 experimental data of compressibility factors is used for testing and training of ANN. The designed neural network can predict the natural gas compressibility factors using pseudo-reduced pressure and pseudo reduced temperature with average absolute relative deviation percent of 0.593. The accuracy of designed ANN has been compared to the mostly used empirical models as well as equations of state of Peng–Robinson and statistical association fluid theory. The comparison indicates that the proposed method provide more accurate results relative to other methods used in this work.

An accurate empirical correlation for predicting natural gas compressibility factors

The compressibility factor of natural gas is an important parameter in many gas and petroleum engineering calculations. This study presents a new empirical model for quick calculation of natural gas compressibility factors. The model was derived from 5844 experimental data of compressibility factors for a range of pseudo reduced pressures from 0.01 to 15 and pseudo reduced temperatures from 1 to 3. The accuracy of the new empirical correlation has been compared with commonly used existing methods. The comparison indicates the superiority of the new empirical model over the other methods used to calculate compressibility factor of natural gas with average absolute relative deviation percent (AARD%) of 0.6535.

Measurement and correlation of compressibility factor of high CO2-content natural gas

The JEFRI-PVT apparatus made in Canada by the Schlumberger company has been used to obtain accurate compressibility factor measurements on high CO2-content natural gasses so as to study the effect of different CO2 content on gas compressibility factor (range covered: temperature, 263.15K to 313.15K; pressure, 3MPa to 15MPa; CO2 content, 9.84, 28.86 and 50.99mol%). The results showed that gas compressibility factors reduce with increasing CO2 content in natural gasses and increase with increasing temperature. In addition, a non-integral power polynomial correlation was proposed without an iterative procedure whose coefficients were determined by fitting experimental data. The mixing rules used include: Kay's mixing rule combined with Wichert-Aziz correlations (Kay) and Stewart-Burkhardt-Voo mixing rule with Wichert-Aziz (SBV). Comparison of the DAK-SBV, DAK-Kay, and proposed correlations showed that the presented model yielded the most accurate predictions with the lowest average absolute deviation (0.42%) among them.

The Prediction of the Compressibility Factor of Sour and Natural Gas by an Artificial Neural Network System

In this study, a multilayer normal feed-forward artificial neural network with three layers has been developed for prediction of compressibility factors of gases with different compositions. This model was developed using 977 experimental data of compressibility factors obtained from the literature. In this model, some statistical criteria such as R2, root mean square error (RMSE), and average absolute deviation (AAD) are obtained 0.991, 0.024, and 0.965, respectively. Model validity was obtained by comparison between the experimental results and the results of various equations of state, such as van der Waals (1910), Redlich-Kwong (1949), Lawal-Lake-Silberberg (Lawal, 1999), Peng-Robinson (1976), and pseudo-experimental correlations such as Dranchuk-Abu-Kassem (1975), Dranchuk-Purvis-Robinson (1974), Hall-Yarborough (1973), Brill-Beggs (1974), Shell Oil Company (2003), Gopal (1977) obtained result of this model. It can be inferred that the results of this model are compatible with the experimental data and the obtained result of this model is more accurate than other correlations.

An efficient correlation for calculating compressibility factor of natural gases

Compressibility factor ( z-factor) values of natural gases are necessary in most petroleum engineering calculations. Necessity arises when there are few available experimental data for the required composition, pressure and temperature conditions. One of the most common methods of calculating z-factor values is empirical correlation. Firstly, a new correlation based on the famous Standing-Katz (S-K) Chart is presented to predict z-factor values. The advantage of this correlation is that it is explicit in z and thus does not require an iterative solution as is required by other methods. Secondly, the comparison between new one and other correlations is carried out and the results indicate the superiority of the new correlation over the other correlations used to calculate z-factor.

New correlations to predict natural gas viscosity and compressibility factor

This study proposed two new accurate simple explicit numerical methods for calculating the z-Factor and viscosity of natural gases. Results of these correlations are compared versus experimental data. Proposed correlation for z-Factor has 0.402 and 1.366 of Absolute Average Percent Error (AAE%) respectively versus Standing and Katz chart and experimental data. The output of this correlation can be directly assumed or be used as an initial value of other implicit correlations. In addition, this correlation is valid for gas coefficient of isothermal compressibility ( c g) calculations. The new method for viscosity accounts for the presence of heptane plus and non-hydrocarbon components. This model was derived from 1260 experimental measurement of gas viscosity of eleven different mixtures with AAE% of 2.083. This model is simpler and more efficient than published correlations, and the comparisons indicate superiority of the proposed model over other methods.

A novel correlation approach for prediction of natural gas compressibility factor

Gas compressibility factor (z-Factor) is one of the most important parameters in upstream and downstream calculations of petroleum industries. The importance of z-Factor cannot be overemphasized in oil and gas engineering calculations. The experimental measurements, Equations of State (EoS) and empirical correlations are the most common sources of z-Factor calculations. There are more than twenty correlations available with two variables for calculating the z-Factor from fitting in an EoS or just through fitting techniques. However, these correlations are too complex, which require initial value and more complicated and longer computations or have magnitude error. The purpose of this study is to develop a new accurate correlation to rapidly estimate z-Factor. Result of this correlation is compared with large scale of database and experimental data also. Proposed correlation has 1.660 of Absolute Percent Relative Error (E ABS) versus Standing and Katz chart and has also 3.221 of E ABS versus experimental data. The output of this correlation can be directly assumed or be used as an initial value of other implicit correlations. This correlation is valid for gas coefficient of isothermal compressibility (c g) calculations also.

A cubic interpolation algorithm for solving non-linear equations

A new Algorithm - based on cubic interpolation have been developed for solving non-linear algebraic equations. The Algorithm is derived from LaGrange's interpolation polynomial. The method discussed here is faster than the \Regular Falsi which is based on linear interpolation. Since this new method does not involve derivatives, it does not have the problem of non-convergence associated with the Newton - Raphson method, when a small derivative is encountered. The efficiency of the cubic interpolation method was ascertained by practical testing with Leonardo\'s cubic equation and Dranchuk, Purivis and Robinson method for calculating the Gas Compressibility Factor (z) of Natural Gases. The Watfor computer program (based on the new method) that was used to solve the Dranchuk Purivis and Robinson equation is also included in this paper. Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 317-324