New correlations for predicting pure and impure natural gas viscosity

doi:10.1016/j.jngse.2016.02.026

Journal of Natural Gas Science and Engineering

Volume 30, March 2016, Pages 364-378

https://doi.org/10.1016/j.jngse.2016.02.026 Get rights and content

Highlights

•
New correlations for predicting pure (CH₄) and impure natural gas viscosity.
•
Good agreements for wide range of pressure, temperature and specific gravity.
•
Design of experiment is utilized to obtain the effective input model parameters.
•
Doubtful data points are determined based on Leverage Statistics approach.
•
Both statistical and graphical analyses are applied to the results.

Abstract

Accurate determination of natural gas viscosity is important for successful design of production, transportation, and gas storage systems. However, most of available models/correlations suffer from complexity, robustness, and inadequate accuracy especially when wide range of pressure and temperature is applied. Present study illustrates development of two novel models for predicting natural gas viscosity for pure natural gas (CH₄) as well as natural gas containing impurities. For this purpose, 6484 data points have been gathered and analyzed from the open literature covering wide range of pressure, temperature, and specific gravity levels, temperature ranges from −262.39 to 620.33 °F (109.6 to 600 K), pressure ranges from 1.4508 to 29,000 psi (0.0100–199.94801 MPa), and gas specific gravity ranges from 0.553 to 1.5741. Sensitivity analysis on the collected data points through design of experiments algorithm showed that pseudo reduced pressure and pseudo reduced temperature are the most effective parameters as the inputs of the models. The Leverage Value Statistics is applied and doubtful data points are determined.

The average absolute relative error and the coefficient of determination of the proposed models for predicting pure/impure natural gas viscosity on a wide range of conditions are 5.67% and 1.87%, 0.9826 and 0.9953, respectively. Reliable accuracy of proposed models in comparison to eight commonly used correlations makes them attractive for possible implementing in natural gas simulation/modeling applications.

Introduction

Abundance, easily accessible, wide usage and clean burning of natural gas make its demand increasing in the world (Wang and Economides, 2013). The human needs to extract this vital fuel from the underground reservoir to the location of usage. It is worth bearing in mind that the most dominant portion of natural gas is constructed from methane (McCain, 1990). Through single-phase and multiphase flow in gas and oil reservoirs, wellbore, separator, turbine, compressor, surface operation devices and transportation pipelines, the knowledge of the thermo-physical properties of natural gas is indispensable (Kamari et al., 2013), which is covered in various fields of study such as gas production, gas injection, and carbon dioxide injection in oil wells (AlQuraishi and Shokir, 2011, Carr et al., 1954, Fayazi et al., 2013, Iverson and Denlinger, 2001, Shams et al., 2015). Natural gas is composed of complex mixtures of light hydrocarbons, heavy hydrocarbons with low viscosity and density and a minor amount of inorganic/non-hydrocarbon components such as hydrogen sulfide, carbon dioxide and nitrogen. Natural gas is a subcategory of petroleum fluids but its specifications are different from that of liquid hydrocarbon. Natural gas physical properties vary widely with pressure, temperature and composition (Davani et al., 2013, McCain, 1990).

One of the most used properties of natural gas is viscosity. Viscosity is the measure of fluid flow resistance (Carr et al., 1954, Geertsma, 1974). It plays an important role in the study of dynamics of fluids flow processes such that described above and in simulation application especially in porous spaces in chemical and petroleum engineering (Iverson and Denlinger, 2001). According to Newton's expression, viscosity is a constant proportional parameter (μ) which is used in following expression: $τ=μ \frac{\partial v}{\partial y}$ τ is shear stress between bordering layers of fluid, $\frac{\partial v}{\partial y}$ is velocity gradient, perpendicular to layers direction. Practically, there is no exact theory that explains viscosity as a function of pressure, temperature and composition (Vesovic, 2001). Hence, one who needs to calculate accurate gas viscosity at desirable conditions should design an experiment, using apparatus such as vibrating wire viscometer (Wilhelm and Vogel, 2000), rolling-ball viscometer (Heidaryan et al., 2011), falling-body viscometer (Chan and Jackson, 1985, Heidaryan et al., 2010b), capillary tube viscometer (Jarrahian et al., 2015, Yusibani et al., 2011) or oscillating-piston viscometer (Davani et al., 2013). In addition, the gas viscosity is much more difficult to measure compared to the oil viscosity (AlQuraishi and Shokir, 2011).

A suitable viscosity model for implementation in simulators must: 1. trace the viscosity for full range condition of operation 2. be accurate, simple and fast; 3. forecast both pure component and mixture viscosities; 4. be reliable across the critical point.

The best of our knowledge, accurate experimental procedure needs to satisfy above conditions in measurement of viscosity. As well as, the various possible mixtures of natural gas and different operating conditions of interest hind acquisition of the pertinent data by experimental means alone. In addition, accurate measurement of natural gas viscosity is difficult and is necessary to optimize the number of wells in gas reservoirs, especially in high pressure/high temperature condition (Hu, 2013).

Consequently, in the absence of experimentally measured viscosity, it is essential to determine the viscosity from equations of state (EOSs), empirically derived correlations, and novel soft computing techniques.

As a result, using the EOSs to calculate the PVT properties of hydrocarbon fluids (Benedict et al., 1940) show that EOSs have poor capability to estimate the volumetric-properties of natural gas mixtures (Danesh et al., 1991, Elsharkawy, 2004, Younglove and Ely, 1987). As a standard approach, two steps are required to derive gas viscosity, the first step is to calculate gas viscosity at atmospheric condition then by using a graph, determine viscosity at desired condition (McCain, 1990). Up to now, several corresponding state models and empirical correlations have been introduced for calculating the gas viscosity under various pressure, temperature and composition. Some models that are used to predict the viscosity are under limited operating condition and sometimes have significant deviation and error, Some other are too complex and difficult to use (Danesh et al., 1991, Elsharkawy, 2004, Farasat et al., 2013, Younglove and Ely, 1987). Other category is soft computing methods. These models are based on black boxes, such as LS-SVM and ANN based models. In black box models (AlQuraishi and Shokir, 2011, Fayazi et al., 2013), there is no visual relationship between inputs and outputs. In order to use these models we should utilize a toolbox which maybe it is not easy to use in several cases, because the user usually need other software, which are not conventional.

Consequently, as one of several efforts by authors to present viscosity correlation for pure natural gas and mixtures, the main objective of the current work is to develop a useful, fast, accurate and simple viscosity correlation as a function of pressure, temperature and composition (Bicher Jr and Katz, 1943). In this study two correlations have been developed, one for pure (CH₄) natural gases and one for impure (sour (with H₂S) and sweet (without H₂S)) natural gases, respectively.

To achieve these objectives, we accomplish following steps: Review several existing open literature, which contain a wide range of natural gas compositions, experimental conditions and viscosity data. Finally gather them as a comprehensive data bank. Investigate accuracy of gathered data by implementing Leverage Value Statistics. Build a new, exact, and trustworthy correlation for estimating the natural gas viscosity using the obtained data set. Investigate the reliability, performance and preciseness of the developed correlations by statistical parameters and visual error examination. To reach this aim, we use several impressiveness criteria such as the coefficient of determination (R²), average relative error (ARE %) and average absolute relative error (AARE %). Confirm validity of the constructed correlation by comparison with widely used correlations.

Section snippets

Review on previous studies

There are numerous correlations, which are developed to predict natural gas viscosity. It is suitable to introduce and investigate the eight well-known empirical correlations to be aware of effectiveness and accuracy of newly proposed correlations. In a characteristic manner, these correlations are functions of pressure, temperature and gas composition. For quickness view only, essential factors of these eight correlations are demonstrated as follows.

Genetic programming

Genetic programming (GP) is a powerful tool based on the genetic algorithm (GA); however, it is used for correlating and modeling projects. GP is functionally very similar to GA and evolves tree structures to perform a task. This method was introduced and gradually developed by Koza (1992).

GP is one of the few efficient machine-learning methods used to find solutions of complicated real problems. Furthermore, the main problem of other intelligent structures such as artificial neural networks is

Data acquisition and evaluation

6484 experimental natural gas viscosity data points were collected from 11 different studies from 1966 to 2013 (Assael et al., 2001, Atilhan et al., 2010a, Atilhan et al., 2010b, Davani et al., 2013, Friend et al., 1989, Goodwin, 2008, Kashefi et al., 2013, Langelandsvik et al., 2007, Lee et al., 1966, Schley et al., 2004, Younglove and Ely, 1987), the description of collected data is presented in Table 2. The collected data includes many different compositions ranging from sour natural gas

Theory

Accuracy and simplicity can be assumed as two main parameters affecting the efficiency of viscosity prediction model. Most of developed models are able to predict natural gas viscosity with an acceptable accuracy for their data banks. However comparison of the results of NGV prediction outside the application range of each model and even for new experimental data which were not previously used for model development, might lead to high errors. Moreover, most of models need complicated and

Result and discussion

The new NGV prediction model only consists of six terms, including simple functions and coefficients. Moreover, there is no need to determine gas density prior to viscosity calculations, the NGV can be predicted using simply one equation, and there is no need to calculate coefficients separately. In addition, there is only one set of coefficients for the whole range of pressure and gas gravity variations. Despite this simplicity, the correlation shows to be the most accurate one among other

Conclusion

In this study, two new models were developed and used for predicting gas viscosity for both cases pure natural gas and natural gas containing impurities. To do such, 6484 data points were collected and analyzed from literature covering temperature range of −262.39–620.33 °F (109.6–600 K), pressure range of 1.4508–29,000 psi (0.0100–199.94801 MPa), and gas gravity range from 0.553 to 1.5741. The Leverage Value Statistics is applied and doubtful data points are determined. Based on the results

References (60)

Danial Abooali et al.
Estimation of dynamic viscosity of natural gas based on genetic programming methodology
J. Nat. Gas Sci. Eng.
(2014)
Abdulrahman A. AlQuraishi et al.
Artificial neural networks modeling for hydrocarbon gas viscosity and density estimation
J. King Saud Univ. Eng. Sci.
(2011)
M. Behjoomanesh et al.
Assessment of total oil production in gas-lift process of wells using Box–Behnken design of experiments in comparison with traditional approach
J. Nat. Gas Sci. Eng.
(2015)
A. Danesh et al.
Comparative study of cubic equations of state for predicting phase behaviour and volumetric properties of injection gas-reservoir oil systems
Fluid Phase Equilibr.
(1991)
Ehsan Davani
HPHT viscosities measurements of mixtures of methane/nitrogen and methane/carbon dioxide
J. Nat. Gas Sci. Eng.
(2013)
Adel M. Elsharkawy
Efficient methods for calculations of compressibility, density and viscosity of natural gases
Fluid Phase Equilibr.
(2004)
Amir Farasat
Toward an intelligent approach for determination of saturation pressure of crude oil
Fuel Process. Technol.
(2013)
Ehsan Heidaryan
Viscosity of pure carbon dioxide at supercritical region: measurement and correlation approach
J. Supercrit. Fluids
(2011)
Ehsan Heidaryan et al.
New correlations to predict natural gas viscosity and compressibility factor
J. Pet. Sci. Eng.
(2010)
Ehsan Heidaryan et al.
A new and reliable model for predicting methane viscosity at high pressures and high temperatures
J. Nat. Gas Chem.
(2010)

Azad Jarrahian et al.

On the viscosity of natural gas

Fuel

(2015)

Arash Kamari

Prediction of sour gas compressibility factor using an intelligent approach

Fuel Process. Technol.

(2013)

Khalil Kashefi

Viscosity of binary and multicomponent hydrocarbon fluids at high pressure and high temperature conditions: measurements and predictions

J. Pet. Sci. Eng.

(2013)

Chirdpong Preechakul et al.

Modified genetic algorithm with sampling techniques for chemical engineering optimization

J. Industrial Eng. Chem.

(2009)

Ehsan Sanjari et al.

An accurate empirical correlation for predicting natural gas viscosity

J. Nat. Gas Chem.

(2011)

Reza Shams

An intelligent modeling approach for prediction of thermal conductivity of CO 2

J. Nat. Gas Sci. Eng.

(2015)

Mostafa Vatani et al.

Application of Genetic Algorithm to the calculation of parameters for NRTL and two-suffix margules models in ternary extraction ionic liquid systems

J. Ind. Eng. Chem.

(2012)

Keelan Adamson

High-pressure, high-temperature well construction

Oilfield Rev.

(1993)

Mohammad ali Ghayyem et al.

Developing a simple and accurate correlation for initial estimation of hydrate formation temperature of sweet natural gases using an eclectic approach

J. Nat. Gas Sci. Eng.

(2014)

Mark J. Anderson et al.

DOE Simplified: Practical Tools for Effective Experimentation

(2015)

M.J. Assael et al.

Viscosity of natural-gas mixtures: measurements and prediction

Int. J. Thermophys.

(2001)

Mert Atilhan

Viscosity measurements and data correlation for two synthetic natural gas mixtures

J. Chem. Eng. Data

(2010)

Mert Atilhan

On the viscosity of natural gases from Qatari north field reservoir

J. Chem. Eng. Data

(2010)

Manson Benedict et al.

An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures I. Methane, ethane, propane and n-butane

J. Chem. Phys.

(1940)

B. Bicher Leo et al.

Viscosities of the methane-propane system

Ind. Eng. Chem.

(1943)

Max Born et al.

A general kinetic theory of liquids. I. The molecular distribution functions

G.E.P. Box et al.

Empirical Model-building and Response Surfaces

(1987)

Norman L. Carr et al.

Viscosity of hydrocarbon gases under pressure

J. Pet. Technol.

(1954)

R.K.Y. Chan et al.

An automated falling-cylinder high pressure laser-Doppler viscometer

J. Phys. E Sci. Instrum.

(1985)

David E. Dean et al.

The viscosity of nonpolar gas mixtures at moderate and high pressures

AIChE J.

(1965)

Cited by (24)

Smart predictive viscosity mixing of CO2–N2 using optimized dendritic neural networks to implicate for carbon capture utilization and storage
2024, Journal of Environmental Chemical Engineering
Crucial for carbon capture, utilization, and storage (CCUS) initiatives and diverse industries, heat transfer underscores the need for a precise assessment of carbon dioxide (CO₂) and nitrogen (N₂) viscosities in gaseous blends across various temperatures. This research pioneers an intelligent model by enhancing the dendritic neural regression (DNR) framework, employing the Seagull Optimization Algorithm with Marine Predator Algorithm (SOAMPA) for optimal predictions. Leveraging recent advancements in metaheuristic optimization techniques, the study reveals the superior performance of the novel SOAMPA approach in predictive accuracy, marking a significant breakthrough in predicting CO₂-N₂ mixture viscosities with implications for advancing CCUS projects and diverse industries. The optimized DNR model, empowered by the modified SOAMPA optimization technique, contributes to estimating the viscosity of N₂-CO₂ mixture gases. Utilizing inputs like pressure, temperature, mole fraction of N₂, and model fraction of CO₂, the models are trained and tested on a dataset comprising over 3030 data samples from public literature. Key contributions encompass proposing an optimized DNR approach, introducing the modified SOAMPA technique, and demonstrating its superiority over established optimization methods in conjunction with the traditional DNR model for predicting viscosity based on real experimental datasets.
Toward smart correlations for predicting in-situ stress: Application to evaluating subsurface energy structures
2023, Geoenergy Science and Engineering
The precise calculation of the in-situ stress tensor is a crucial factor in addressing the challenges associated with the development of subsurface energy structures. To establish a consistent relationship between breakout shapes and the in-situ stress using nonlinear or coupled process assumptions through numerical methods, effective techniques are required. In this regard, three white box algorithms, namely gene expression programming (GEP), genetic programming (GP), and the group method of data handling (GMDH), were developed to predict the maximum horizontal stress. To develop a robust correlation using the white box algorithms, 662 data points were obtained from numerical analysis using an elastoplastic model across a wide range of wellbore pressures. Input parameters were breakout width and depth, wellbore pressure, and minimum horizontal stress. The study results indicated that the GP algorithm demonstrates higher accuracy compared to the GEP and GMDH, with a root mean square error (RMSE) of 0.9977 and a determination coefficient (R²) of 0.97564. Additionally, both SHAP values (SHapley Additive exPlanations) and sensitivity analysis were employed. The sensitivity analysis revealed that breakout width has a greater influence on predicting the maximum in-situ stress compared to other parameters. Furthermore, the Leverage technique indicated that the GP model can be considered a reliable tool for accurately estimating the in-situ stress, making it suitable for use in the subsurface energy structures.
Towards improved genetic programming based-correlations for predicting the interfacial tension of the systems pure/impure CO<inf>2</inf>-brine
2021, Journal of the Taiwan Institute of Chemical Engineers
Citation Excerpt :
Genetic programming (GP) is a reliable machine learning (ML) technique which allows generating explicit and user-friendly correlations to rely input/output parameters that define complex systems. This approach belongs to the family of genetic algorithms which is inspired from the genetic and evolution theories [32]. GP was proposed and developed by [33].
Accurate knowledge of the interfacial tension (IFT) of the systems pure/impure CO₂-brine has significant importance for satisfying the dichotomy of maximizing CO₂ injections and minimizing leakage risks during injection of CO₂ in deep saline aquifers for carbon capture and sequestration (CCS).
In this study, new explicit correlations were implemented using the genetic programming (GP) approach for estimating the IFT of the systems pure/impure CO₂-brine under widespread operational conditions. In this regard, 2346 authenticated IFT measurements for these systems were utilized by considering pressure, temperature, monovalent cation molality, bivalent cation molality, and the mole fractions of CH₄ and N₂ as the correlations’ inputs.
The obtained results showed that the outcomes of GP-based correlations were in high agreement with the real IFT measurements. Moreover, GP-based correlations achieved overall coefficient of determination (R²) and root mean square error (RMSE) values of 0.9519 and 3.30, respectively. Besides, the GP-based correlations outperformed the best existing explicit correlations for estimating the IFT of the systems pure/impure CO₂-brine. Lastly, the performed trend analyses revealed that these newly implemented correlations preserved correctly the physics sense with respect to changes in the independent variables.
Data-driven model for ternary-blend concrete compressive strength prediction using machine learning approach
2021, Construction and Building Materials
Ternary-blend concrete is a complex composite material, and the nonlinearity in its compressive strength behavior is unquestionable. Entirely many models have been developed to accurately predict the ternary-blend concrete compressive strength, such as ANN, SVM, random forest, decision tree, to mention but a few. This study underscores the better predictive performance and successful application of the least square support vector machine (LSSVM), a machine learning model for predicting the compressive strength of ternary-blend concrete. Coupled simulated annealing (CSA) was applied to the LSSVM model as an optimization algorithm. In addition, the genetic programming (GP) model was used as a benchmark model to compare the performance of the LSSVM-CSA model. The predictive performance of the LSSVM-CSA was compared with that of some of the proposed models in well-known studies where the same datasets were used. The model proposed in this study outperformed other studies, yielding an R² value of 0.954.
Prediction of cementation factor for low-permeability Iranian carbonate reservoirs using particle swarm optimization-artificial neural network model and genetic programming algorithm
2021, Journal of Petroleum Science and Engineering
cementation factor is a crucial parameter that has a significant influence on the estimation of reservoir parameters. Laboratory measurements for cementation factor are available for occasional cases because experimental special core analyses for determination of cementation factor values are expensive and time-consuming. While this factor plays a significant role in determining water saturation, there is no comprehensive and precise relationship for the case of Iranian carbonate reservoirs. In this article, a unique model was used based on a powerful combination of artificial neural network (ANN) and particle swarm optimization (PSO) algorithm to model the cementation factor. In the second phase of simulation, a correlation for the cementation factor was discovered by genetic programming (GP) algorithm. Both the PSO-ANN model and GP algorithm are trained by input variables such as porosity, permeability, and grain density derived from 175 routine core analysis (RCAL) samples of 21 carbonated oil fields. To determine the relative impact of the independent variables on cementation factor the sensitivity analysis was carried out for both models. The comparison between the PSO-ANN model output and the experimental cementation factor data clearly demonstrated that the built model can predict the cementation factor with great precision; the mean square error between the model predictions and the experimental data was less than 0.07. The root mean square error of training and testing data sets for the new developed correlation using GP algorithm were 0.0902 and 0.0727 respectively. Finally, to evaluate the validity and reliability of the developed models, a comparison was implemented between these two models and other empirical models over an external employment data set (21 data point). This comparison revealed that the GP algorithm and PSO-ANN model deliver a higher performance capacity compared to other proposed correlations for predicting cementation exponent.
On the evaluation of solubility of hydrogen sulfide in ionic liquids using advanced committee machine intelligent systems
2021, Journal of the Taiwan Institute of Chemical Engineers
Ionic Liquids (ILs) are increasingly emerging as new innovating green solvents with great importance from academic, industrial, and environmental perspectives. This surge of interest in considering ILs in various applications is owed to their attractive properties. Involvements in the gas sweetening and the reduction of the amounts of sour and acid gasses are among the most promising applications of ILs. In this study, new advanced committee machine intelligent systems (CMIS) were introduced for predicting the solubility of hydrogen sulfide (H₂S) in various ILs. The implemented CMIS models were gained by linking robust data-driven techniques, namely multilayer perceptron (MLP) and cascaded forward neural network (CFNN) beneath rigorous schemes using group method of data handling (GMDH) and genetic programming (GP). The proposed paradigms were developed using an extensive database encompassing 1243 measurements of H₂S solubility in 33 ILs. The performed comprehensive error investigation revealed that the newly implemented paradigms yielded very satisfactory prediction performance. Besides, it was found that CMIS-GP provided more accurate estimations of H₂S solubility in ILs compared with both the other intelligent models and the best-prior paradigms. In this regard, the developed CMIS-GP exhibited overall average absolute relative deviation (AARD) and coefficient of determination (R²) values of 2.3767% and 0.9990, respectively. Lastly, the trend analyses demonstrated that the tendencies of CMIS-GP predictions were in excellent accordance with the real variations of H₂S solubility in ILs with respect to pressure and temperature.

View all citing articles on Scopus

View full text

New correlations for predicting pure and impure natural gas viscosity

Highlights

Abstract

Introduction

Section snippets

Review on previous studies

Genetic programming

Data acquisition and evaluation

Theory

Result and discussion

Conclusion

J. Nat. Gas Sci. Eng.

J. King Saud Univ. Eng. Sci.

J. Nat. Gas Sci. Eng.

Fluid Phase Equilibr.

J. Nat. Gas Sci. Eng.

Fluid Phase Equilibr.

Fuel Process. Technol.

J. Supercrit. Fluids

J. Pet. Sci. Eng.

J. Nat. Gas Chem.

Fuel

Fuel Process. Technol.

J. Pet. Sci. Eng.

J. Industrial Eng. Chem.

J. Nat. Gas Chem.

J. Nat. Gas Sci. Eng.

J. Ind. Eng. Chem.

High-pressure, high-temperature well construction

Oilfield Rev.

Developing a simple and accurate correlation for initial estimation of hydrate formation temperature of sweet natural gases using an eclectic approach

J. Nat. Gas Sci. Eng.

DOE Simplified: Practical Tools for Effective Experimentation

Viscosity of natural-gas mixtures: measurements and prediction

Int. J. Thermophys.

Viscosity measurements and data correlation for two synthetic natural gas mixtures

J. Chem. Eng. Data

On the viscosity of natural gases from Qatari north field reservoir

J. Chem. Eng. Data

An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures I. Methane, ethane, propane and n-butane

J. Chem. Phys.

Viscosities of the methane-propane system

Ind. Eng. Chem.

A general kinetic theory of liquids. I. The molecular distribution functions

Empirical Model-building and Response Surfaces

Viscosity of hydrocarbon gases under pressure

J. Pet. Technol.

An automated falling-cylinder high pressure laser-Doppler viscometer

J. Phys. E Sci. Instrum.

The viscosity of nonpolar gas mixtures at moderate and high pressures

AIChE J.