Pressure and temperature functionality of paraffin-carbon dioxide interfacial tension using genetic programming and dimension analysis (GPDA) method
Introduction
Enhanced oil recovery (EOR) methods are essential in today's petroleum industry. The research on EOR always emphasizes the surface and interfacial phenomena. These phenomena change based on the pressure, temperature, and composition of reservoir crude oil. Carbon dioxide (CO2) injection is one of the prevalent methods in EOR that reduces interfacial tension and increases displacement of oil by gas (Wang and Gu, 2011, Abedini and Torabi, 2013, Li et al., 2012a, Zanganeh et al., 2012, Suebsiri et al., 2006). The maximum recovery occurs when there is no interfacial tension between the injected gas and reservoir crude oil, which means the two fluids are miscible together (Rao and Lee, 2003). The determination of interfacial tension between CO2 and hydrocarbon at different pressures and temperatures has been studied over the years for EOR processes (Hemmati-Sarapardeh et al., 2014, Nobakht et al., 2008, Nobakht et al., 2007, Yang and Gu, 2005, Rusanov and Prokhorov, 1996). To obtain precise values of the interfacial tension at different pressures, an apparatus capable of high pressure and temperature is needed. However, producing valid experimental data is usually time-consuming, expensive, and with probable high uncertainties due to harsh experimental conditions. Different theoretical methods are used to measure interfacial tension between two immiscible fluid phases. A comprehensive investigation conducted by Rusanov and Prokhorov reviews the technical literature on the interfacial tension techniques, both theoretically and instrumentally, in details (Rusanov and Prokhorov, 1996). Furthermore, there are other comprehensive sources on the interfacial tension measurement methods (Shah, 1981, Hirasaki and Zhang, 2004, Zolghadr et al., 2013). Some of the mentioned important methods are density functional theory, (Dominik et al., 2006, Ohnesorge et al., 1994, Ebner et al., 1976) gradient theory, (Miqueu et al., 2005, Dee and Sauer, 1992, Gupta and Robinson, 1987) corresponding states theory, (Mousazadeh and Faramarzi, 2011, Holcomb and Zollweg, 1993) thermodynamic correlations, (Janz, 1988, Harris et al., 1973, Clever and Chase, 1963) and the Parachor model (Tjahjono and Garland, 2010, Ayirala and Rao, 2004, Li et al., 2012b).
A recent study has shown that paraffin components in a hydrocarbon mixture have a key role in the interfacial tension of a carbon dioxide and hydrocarbon mixture (Zolghadr et al., 2014). There are other studies focused on the explanation of vapor-liquid phase behavior for CO2-hydrocarbon mixtures using thermodynamic models (Turek et al., 1984, Lin, 1984, Sahimi et al., 1985, Mohebbinia et al., 2012). The perturbation chain statistical associating fluid theory (PC-SAFT) could describe the vapor-liquid equilibria (VLE) of CO2-light hydrocarbon and CO2-heavy n-alkane by optimizing the binary interaction parameters (kij) (Llovell et al., 2010, Fu and Wei, 2008). Most of the thermodynamic properties are applied in individual fluid phases; also, interfacial tension is a property of the interface between two fluid phases. The IFT, which is a property of the interface, strongly depends on the temperature, pressure, and compositions of the interacting fluid phases, and is mostly governed by the mass transfer interactions between the phases (Zolghadr et al., 2014). The density of two immiscible fluids has a key role in the calculation of interfacial tension in the existing theoretical methods. The pressure and temperature factors do not directly affect the interfacial tension in the existing methods, and usually, the effect of pressure applies in IFT through the density values. The purpose of this study is to apply a symbolic regression methodology to obtain the interfacial tension between the carbon dioxide and paraffin group, based on the explicit functionality of pressure and temperature. A powerful, new symbolic regression genetic programming (GP) has become available to develop correlations of material properties; however, this technique is very time-consuming and needs a supercomputer to expedite the timing; further, it produces a complex relation between the parameters of correlation (Vladislavleva et al., 2009, Koza, 1992, McKay et al., 1995, Hoai et al., 2002, Uy et al., 2011).
To overcome this limitation, in this study the combination of genetic programming (GP) and dimension analysis (DA), known as (GPDA), is used to introduce a correlation that has explicit functionality of temperature and pressure to obtain interfacial tension of heptane (C7) + CO2, decane (C10) + CO2, dodecane (C12) + CO2, and hexadecane (C16) + CO2, for the first time.
Section snippets
Database
The experimental data of interfacial tension (approximately 600 data points) between the paraffin component and carbon dioxide at different pressures and temperatures have been used to develop and then validate the developed correlation for the calculation of equilibrium interfacial tension (Zolghadr et al., 2014, Georgiadis et al., 2010) (See Tables S1–S5 of the Supplementary).
Symbolic regression via GP and DA (GPDA)
To obtain a correlation as an explicit functionality of temperatures and pressures, so as to calculate the interfacial tension between the carbon dioxide and paraffin group, the technique of symbolic regression (SR) (Duffy and Engle-Warnick, 2002, Davidson et al., 2003, Muzny et al., 2013) is used. Symbolic regression from genetic programming (GP) was used in different studies to discover arbitrary functional forms to fit data (Gharagheizi et al., 2012a, Vladislavleva, 2008).
The main branches
Results and discussion
The GP method introduces an exact functional form; however, because this method is time-consuming and due to the complexity of the correlation results, the GPDA method is presented here. In this method, the primary functional form is obtained from the GP method, which determines the type of correlation (e.g., polynomial, logarithmic). The symbolic regression is stopped when the position of the variables does not change—at least for N = 50 generation and—AAD % is below ɛ = 40%. At this point,
Conclusion
In this article, a combination of genetic programming and dimension analysis (GPDA) was introduced to develop a correlation for measuring the interfacial tension between carbon dioxide and the paraffin group based on the explicit functionality of pressure and temperature. The GPDA method is very fast, and it produces a monotonic relation between the parameters of the correlation. In the GPDA method, at first, a functional form was obtained from the GP program (symbolic regression), and then the
Associated content
The authors wish to acknowledge the discussions with Prof. Prausnitz, University of California, Berkeley.
Conflicts of interest
The authors declare no competing financial interest.
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