Elsevier

Journal of Molecular Liquids

Volume 230, March 2017, Pages 175-189
Journal of Molecular Liquids

Toward genetic programming (GP) approach for estimation of hydrocarbon/water interfacial tension

https://doi.org/10.1016/j.molliq.2016.11.099Get rights and content

Highlights

  • Genetic programming (GP) algorithm is developed for accurate determination of water/hydrocarbon IFT.

  • Large data bank of experimental data reported in literature is used to develop and validate the GP model.

  • The GP model was compared with empirical correlations proposed in literature.

  • The developed tool is of great value for fast and improved estimation of water/hydrocarbon IFT.

Abstract

The interfacial tension (IFT) of hydrocarbon/water system is one of the most important parameters in various fields of chemical, petroleum and process industries. Laboratory measurement of interfacial tension is laborious, time demanding and involves costly experimental setup. Current study presents genetic programming (GP) as a powerful tool in order to develop a novel correlation for estimation of IFT in hydrocarbon/water systems under wide ranges of experimental conditions. To achieve this mission, a comprehensive databank comprising 1075 experimentally measured data points were acquired from the literature reports. Four influencing factors of hydrocarbon critical temperature, experiment temperature, pressure and hydrocarbon/water density difference were considered as independent correlating variables to design and develop the correlation. Comprehensive error analysis demonstrates the superiority of the proposed correlation with R2 = 0.91 and AARD = 4.38% in comparison with literature data. The predictability of the genetic model was further compared with a recently published model and other well-known empirical correlations reported in literature. The result suggests that the proposed tool is of great value for fast and precise estimation of hydrocarbon/water IFT.

Introduction

Interfacial forces are one of the important thermo-physical properties of immiscible fluids in contact [1], [2]. When the two immiscible liquids are in contact the acting forces at the interface are called interfacial tension (IFT), however, the general term of surface tension is used to describe a single liquid or single solid surface tendency in order to be contracted for resistance against the external forces [3]. The IFT or surface tension is defined as the applied forces at the interface plane per unit length which has the unit of energy per unit area or force per unit length [1].

IFT plays a major role in determining and characterizing the interfacial behavior which has been less studied in comparison with the other thermo-physical properties [4]. Because IFT is a connection bridge between the two immiscible phases and their characteristics whereas the other thermo-physical properties such as thermal conductivity, density and viscosity are dealing with bulk properties of a just single phase fluid [5]. In other words, in thermo-physics, IFT has a more complicated and more miscellaneous nature than the other properties [6]. Due to the noticeable differences in molecular density, molecular interactions and chemical nature of the two immiscible fluids in contact, a thin layer termed as the interface with dissimilar characteristics than these two fluids will be established between them as they come into contact [7], [8]. In this case, the heavier phase will lay below the lighter fluid for the reason of buoyancy forces and they would be separated by the pre-mentioned interface [9]. When the molecular differences between the two phases decrease, the interfacial layer will be weaker, consequently, lower amount of IFT would be allocated to this interface [10]. For miscible fluids this interface would be disappeared and IFT is equal to zero. Considerable differences between the oil and water phases will result in the formation of a strong interface between them [11].

Molecules of fluids are surrounded by repulsion and attraction forces. Among these intermolecular interactions, attraction forces are in charge of IFT [1]. In the bulk of each fluid, the resultant force on each molecule is zero because of the equal forces applied in the all directions on the molecule. Although the net attraction forces on each interface molecule is not zero leading to the imbalance of attraction forces at the interface [4], [10]. The numbers of each phase molecules on the both sides of the interface are not generally equal due to density difference. In a liquid-liquid contact, denser liquid has a greater number of molecules than the other phase leading to the creation of internal pressure in denser phase [4], [10]. Therefore, the interfacial area would be minimized. This tendency of fluids interface or IFT could be explicated by means of minimum energy principle. In accordance to this principle, minimum interface area could be attained by eliminating the numbers of high energy molecules at the interface [1].

In accordance to the abovementioned principals of IFT, widespread application of IFT has been proven in petroleum engineering, pharmacology, chemical engineering, and chemistry particularly in enhanced oil recovery (EOR), multiphase fluid flow, emulsion stability, designing petroleum production system, separation processes, sweetening of hydrocarbon stream, liquid-liquid extraction and the heat and mass transfer between two phases [7], [12], [13].

In petroleum reservoir engineering, IFT has a major role in EOR processes [12]. In other words, the oil mobility could be increased by lowering IFT between oil and water, and oil viscosity reduction for the reason that IFT has the most crucial contribution in capillary pressure leading to high oil trapping in porous media [14]. Therefore, determination of IFT can be of critical significance in determining ultimate oil recovery and oil production rate.

There are various experimental, theoretical and empirical methods for determining IFT. Among these methods, experimental measurements are the most precise way of IFT determination [15]. However, conducting an IFT experiment is time wasting, expensive, dependent to the availability of appropriate instrument and fluid sample quantity. In addition, theoretical models are in the need of phase properties such as constants of adsorption isotherms, partial molar surface area resulting in more complication and less popularity of these models [10]. Moreover, they use some assumptions for simplification purposes which may lead to noticeable prediction errors [16]. Therefore, the application of empirical correlations for fast estimation of IFT has been investigated by several researchers in last decades.

In last decades, several investigators have made considerable efforts to develop empirical correlations for IFT determination. In 1988, a graphical analysis for estimating IFT between water and hydrocarbon based on the density difference and reduced temperature was developed in the work of Firoozabadi and Ramey [17]. They concluded that this graphical correlation over-predicts the IFT value. A mathematical relation was established by Danesh [18] to get a better match with experimental data than the graphical correlation of Firoozabadi and Ramey [17]. Afterwards, Sutton [19] conducted a modification into the extended model by Danesh [18] and proposed new equation for IFT prediction. In continuum study, via non-linear regression analysis on a comprehensive databank Sutton [20] generated another equation for IFT prediction. More recently, Kalantari Meybodi et al. [4] suggested another IFT model for 32 hydrocarbon/water systems with temperature and pressure ranges of 252.44–550 K and 0.1–300 MPa, respectively. Despite these correlations, precise IFT estimation is still challenging in petroleum industry. Therefore, establishing a more reliable model is vital in which wide ranges of operational conditions could be covered.

Soft computation technique which has been developed during recent years, is a powerful tool for solving non-linear engineering difficulties [21], [22], [23], [24]. In the middle of all soft computation methods, wide varieties of investigations have employed genetic programming (GP) mathematical strategy for determining the best relationships among the dataset in several fields including water, transport, metaheuristics, geotechnical and civil engineering [25], [26], [27], [28]. Moreover, the successful applications of the GP scheme in chemistry, petroleum and chemical engineering have been strongly approved in recent decade. Recently, a comprehensive correlation for prediction of the dynamic viscosity of natural gases as a function of gas density, apparent molecular weight and pseudo-reduced critical properties was put forward by Abooali and Khamehchi [29] based on a large database with the total error of less than 3%. Subsequently, Khadem et al. [30] established a wide-ranging model estimating the interfacial tension (IFT) of the CO2/paraffin system as a function of diffusion coefficients, paraffin density, critical pressure and temperature with the use of GP framework analysis. They also verified that their model has an effective performance in comparison with the experimental data with the average absolute deviation percent of 5%. Moreover, Kaydani et al. [31] developed a GP-derived model for simulation of the wellhead choke flowrate as a function of gas-oil ratio, wellhead pressure and choke diameter for both critical and sub-critical states. In another study, an improved combinatory version of GP mathematical scheme was utilized by Kaydani et al. [32] for accurate determination of minimum miscibility pressure (MMP) during CO2 flooding into the oil reservoirs. More recently, due to the large requisite for accurate determination of natural gas viscosity the second GP-based model was created by Izadmehr et al. [33] in literature. They divided their databank including more than 6000 datapoints into the two groups of pure and impure natural gases, and then developed individual models for each group leading to the total error of less than 6%.

In current study, the GP mathematical scheme is implemented to derive a precise and trustworthy symbolic equation. For this purpose, a large number of datapoints are adopted from the open literature [15], [17], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79] to be sure about the comprehensiveness of our newly suggested model. Afterwards, the databank is divided into the three subsets of training, validation and testing for the aim of construction, optimization and testing the GP-based model. To the best of author's knowledge, there is no report on modeling the hydrocarbon/water IFT with GP technique in literature. Moreover, the performance of our newly suggested model was evaluated in comparison with formerly published correlations.

Section snippets

Danesh [18]

In 1988, Danesh [18] proposed the first mathematical relationship for correlating the IFT data between water and hydrocarbons as a function of hydrocarbon critical temperature (TC), reservoir temperature (TR), water/hydrocarbons density difference (∆ρ) and reservoir pressure (P). This correlation is as following:IFT=111Δρ1.024TRTC1.25where, the units of IFT, TC, TR and ∆ρ are mN/m, K, K and g/cm3, respectively.

Sutton [19]

In 2006, a modified version of Eq. (1) was proposed by Sutton [19]. His model is

Genetic programming (GP) tool as an IFT predictive model

One of the most powerful tools implemented in a wide variety of engineering and science applications are known as genetic programming (GP). GP has been developed on the basis of genetic algorithm (GA) for the purpose of creating accurate correlations and models [33]. For the first time, the GP mathematical strategy was established in the work of Koza [80] as an effective machine learning techniques in order to extend precise answers to the actual problems. The advantage of the GP approach over

Results and discussions

A comprehensive error analysis was carried out to evaluate the accuracy of the suggested GP-based model in compare with other correlations. Thus, various statistical quality measures including average relative deviation percent (ARD), average absolute relative deviation percent (AARD), root mean square error (RMSE) and determination coefficient (R2) were calculated for the all correlations. In continuum, several graphical visualizations like parity diagram, relative distribution plot and

Conclusions

In present study, a novel artificial intelligent based model called genetic programming (GP) was developed for accurate determination of hydrocarbon/water IFT. For this, a large number of datapoints from the open literature was utilized for training, optimization and testing purposes. In order to verify the superior performance and capability of the proposed model, the GP-based model was compared with some commonly used published correlations in literature. Therefore, a comprehensive error

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