State-of-the-Art Least Square Support Vector Machine Application for Accurate Determination of Natural Gas Viscosity Amir Fayazi, † Milad Arabloo, † Amin Shokrollahi,* ,† Mohammad Hadi Zargari, ‡ and Mohammad Hossein Ghazanfari † † Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran ‡ Department of Petroleum Engineering, Petroleum University of Technology, Ahwaz, Iran ABSTRACT: Estimation of the viscosity of naturally occurring petroleum gases is essential to provide more accurate analysis of gas reservoir engineering problems. In this study, a new soft computing approach, namely, least square support vector machine (LSSVM) modeling, optimized with a coupled simulated annealing technique was applied for estimation of the natural gas viscosities at different temperature and pressure conditions. This model was developed based on 2485 viscosity data sets of 22 gas mixtures. The model predictions showed an average absolute relative error of 0.26% and a correlation coefficient of 0.99. The results of the proposed model were also compared with the well-known predictive models/correlations available in the literature. It has been observed that the proposed model correctly captures the physical trend of changing the natural gas viscosity as a function of the temperature and pressure. Finally, sensitivity analysis was performed to assess the effect of the gas viscosity uncertainty on the cumulative gas production for a synthetic natural gas reservoir, using a numerical reservoir simulation. Results revealed that applications of LSSVM modeling can lead to a more accurate and reliable estimation of the gas viscosity over a wide range of reservoir conditions. 1. INTRODUCTION The role of natural gas in meeting the world energy demand has been increasing because of its versatility, abundance, and clean burning. 1 An accurate knowledge of the thermophysical properties of natural gas is necessary for basic petroleum and chemical engineering calculations. One of these properties is the viscosity, which is an important parameter that is frequently used in the equations for single-phase and multiphase flow in gas and oil reservoirs, tubing, and transportation purposes. 2 Thus, the viscosity of a natural gas has to be evaluated for wide ranges of temperature, pressure, and composition. 3 The most reliable and accurate way to obtain thermophysical properties is from accurate experimental measurements. However, the wide range of possible natural gas mixtures and of conditions of interest impede obtainment of the relevant data by experimental means alone. 4 Therefore, in the absence of experimentally measured properties, it is essential for the gas reservoir engineers to determine the properties from equations of state (EOSs), empirically derived correlations, and soft computing techniques. Many comparative studies have been carried out to ascertain the EOSs ability to estimate the PVT properties of reservoir fluids. 5-8 The general conclusion is that EOSs have poor ability to predict the volumetric properties of hydrocarbon gas mixtures. 9 Several empirical correlations and corresponding state models have been developed for estimating the gas viscosity under various pressure and temperature conditions. 10-17 However, correlations that are used to estimate the gas viscosity are sometimes too complex and also have significant error. Hence, introducing a more powerful, fast, and accurate method than the traditional ones is necessary. The complexity, fuzziness, and uncertainty existent in addition to the nonlinear behavior of most reservoir parameters require a powerful tool to overcome these challenges. 18 In the last decades, various prediction models have been proposed that include conventional and hybrid artificial neural network models, 19-27 adaptive neuro-fuzzy inference system mod- els, 28,29 and least-squares support vector machine (LSSVM). 30-34 The recent development and success of applying LSSVM modeling to solve various difficult engineering problems has drawn attention to its potential applications in the petroleum industry. 8,18,35 However, to the best of the authors’ knowledge, no work has been published on the subject of modeling of the gas viscosity with the LSSVM approach. Hence, the main objective of the present work is to develop an intelligent model based on the LSSVM algorithm for accurate prediction of the natural gas viscosity. To this end, this study is aimed at the following objectives: (1) To acquire a comprehensive, large-scale databank, covering a wide range of natural gas compositions and experimental conditions from the existing open literature. (2) To develop a novel, accurate, and reliable computer- based model for predicting the natural gas viscosity based on the LSSVM modeling approach using the acquired database. (3) To evaluate the performance and accuracy of the newly proposed model as well as previously published correlations by statistical and graphical error analyses. For this purpose, various routinely implemented effectiveness criteria such as the coefficient of determination (R 2 ), average relative error (ARE %), average absolute relative error (AARE %), and root-mean- square error (RMSE) were introduced to figure out the performance of various correlations/models. Received: August 28, 2013 Revised: November 25, 2013 Accepted: December 12, 2013 Article pubs.acs.org/IECR © XXXX American Chemical Society A dx.doi.org/10.1021/ie402829p | Ind. Eng. Chem. Res. XXXX, XXX, XXX-XXX