Towards improved genetic programming based-correlations for predicting the interfacial tension of the systems pure/impure CO2-brine

https://doi.org/10.1016/j.jtice.2021.08.010Get rights and content

Highlights

  • The interfacial tension of the systems pure/impure CO2-brine was modeled using GP.

  • 2346 authenticated points were utilized for establishing the correlations.

  • The implemented correlations very satisfactory prediction performance.

Abstract

Background-

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).

Methods-

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.

Significant Findings-

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.

Introduction

Due to global energy demand and the resulted environmental issues, mainly climate change, recent decades have witnessed great importance and noticeable efforts towards using cleaner sources of energy and applying efficient strategies for mitigating the high atmospheric concentration of greenhouse gases [1], [2], [3], [4], [5], [6]. Among these latter, carbon dioxide (CO2) has turned into a hot topic due not only to its high impact on atmospheric pollution and contribution to the increased global surface average temperature, but also to its valuable applications such as in the oil industry as an enhanced oil recovery (EOR) technique while it is injected in depleted reservoirs [4,[7], [8], [9], [10], [11], [12], [13]]. In this context, another option, namely carbon capture and sequestration (CCS) in saline aquifers, is increasingly becoming a vital way for reducing the CO2 level in the atmosphere [14,15] owing to the availability and the storage capacity of this kind of geological formations [16,17].

To ensure better implementation of CO2 sequestration in saline aquifers, several vital parameters related to this operation should be determined correctly [5,18]. Among these latter, and due to its involvement in the capillary trapping phenomenon and the displacement process, the interfacial tension (IFT) of the systems pure/impure CO2-brine plays a primordial role in the monitoring of CO2 streams flooding in such geological formations [18], [19], [20]. Besides, this parameter affects greatly the minimization of leakage risk and the maximization of CO2 injections [21,22]. As some of the other parameters describing the systems CO2-brine, the IFT of these latter can be directly measured using experimental procedures or estimated using modeling techniques. From literature review standing point of view, there has been interesting recent works which shed light on the methods utilized for studying the IFT of CO2/brine and rock wettability [13,15]. As the experimental methods (such as Pendant Drop and Rising Drop) are expensive and time-consuming, researchers were oriented towards the development of predictive models for estimating the IFT of the systems CO2-brine using different approaches such as empirical/semi-empirical correlations and machine learning (ML) techniques.

Massoudi and King Jr [23] suggested an empirical correlation for estimating the IFT of the systems pure CO2-pure water. Their correlation was applicable for only one temperature, namely 25°C, and pressure range of 0.1 to 6.2 MPa. Hebach et al. [24], and after they performed an experimental investigation using the Pendant Drop method, proposed a regression-based function using their gained measurements for estimating the IFT of the systems CO2-water under the temperature and pressure ranges of 278 to 335 K and 0.1 to 20 MPa, respectively. Bennion and Bachu [25] established a correlation which depends on pressure (in MPa), temperature (in °C), and salinity (in mass percent) to estimate the IFT of CO2-brine systems. Their correlation was developed using a non-linear regression technique and considering 168 real datapoints that covered temperature range between 41 to 125°C and pressure range between 2 to 27 MPa. Chalbaud et al. [18] utilized their experimental results to develop a semi-empirical correlation that can compute the IFT of the systems pure CO2-brine under temperature and pressure values ranged between 27 to 100°C and 4.8 to 25.8 MPa, respectively. Their correlation is dependent on pressure, temperature, and salinity. Li et al. [26] implemented an empirical correlation as a function of temperature, pressure, and molality to predict IFT of the system pure CO2-brine. This correlation exhibits powerless prediction for pressure values below 2 MPa [27]. Another empirical correlation was suggested by Li et al. [28] for the systems impure CO2-brine within the pressure and temperature ranges of 0.1-60.05 MPa and 5.25-175°C, respectively.

Due to the limitations of the empirical/semi-empirical correlations, mainly the lack of generalization and the restriction in the considered operational conditions, some researchers have attempted to apply various ML base paradigm under extended conditions. In this regard, Zhang et al. [29] established an artificial neural network (ANN) based model for predicting the IFT of the systems CO2-brine using 1716 points covering pressures between 0.1–60.05 MPa and temperatures between 5.25–175°C. The authors claimed that their proposed intelligent model surpassed the previous empirical/semi-empirical correlation while predicting the IFT. Rashid et al. [30] proposed a hybrid model consisted of least square support vector machine (LSSVM) paradigm optimized with coupled simulated annealing (CSA). Their LSSVM-CSA model was developed using 1019 real points. Kamari et al. [19] implemented three soft computing techniques, namely LSSVM, decision tree (DT), and gene expression programming (GEP) to model the IFT of the systems CO2-bine. The authors utilized the same database employed by Zhang et al. [29]. Among their suggested paradigms, DT was the most reliable, while GEP exhibited the worst prediction performance. Feed forward artificial neural network (FFANN) was investigated by Madani et al. [31] who employed only 95 points to develop their paradigm. Amooie et al. [27] proposed a committee machine intelligent system (CMIS) by linking three of their best neural network schemes (consisted of multilayer perceptron (MLP) optimized with some backpropagation-based algorithms). Besides, the authors suggested an explicit correlation using group method of data handling (GMDH) technique. The models implemented by Amooie et al. [27] were gained using 2517 data points. Their findings revealed that CMIS approach outperformed the other ML-based paradigms as well as the existing models for predicting the IFT of the systems CO2-brine.

More recently, and for the same purpose, Zhang et al. [22] applied the extreme gradient boosting (XGBoost) trees. The authors utilized 2346 points for developing their models after removing some of the suspected points from the different existing references. The outcomes of their investigation demonstrated the superiority of their XGBoost model for the accurate prediction of CO2-brine IFT values. Table 1 summarizes the most relevant models that were proposed in the literature for estimating the IFT of the systems CO2-brine/water. However, although the robustness of the existing ML-based models for estimating the IFT of the systems CO2-brine, most of them are of black-box type, and this means that calculability efforts are needed for reproducing their results for other utilizations and extended simulation tasks. Besides, some prior paradigms were developed using limited databases. Therefore, it is suitable to consider more representative database and apply powerful data-driven and evolutionary methods, such as genetic programming (GP), which allows generating reliable and simple-to-use correlations for modeling of the interfacial tension of the systems pure/impure CO2-brine.

The aim of this study was to establish improved explicit correlations for estimating the IFT of the systems pure/impure CO2-brine. To this end, genetic programming (GP) was applied on the most authenticated IFT measurements of the systems pure/impure CO2-brine. Various statistical and graphical evaluation methods were employed for testifying the high accuracy of the newly implemented correlations. Furthermore, detailed trend analyses were performed on the predictions of the correlations in order to demonstrate their preservation of the physics sense while the input parameters change.

Section snippets

Genetic programming (GP)

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]. This rigorous ML techniques showed satisfactory results when modeling various parameters and phenomena, such as hydrogen production using

Data gathering

In order to establish reliable explicit correlations that can estimate precisely the IFT of the systems pure/impure CO2-brine, an extensive experimental data was gathered from the published literature [18,20,[24], [25], [26],[41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]]. As it was indicated in previous studies [22,29], the IFT of the systems CO2-brine is dependent on pressure (P), temperature (P), the total molalities of the monovalent

Results and discussion

As mentioned earlier, the aim behind applying GP approach in this study was to establish explicit and simple-to-use correlations that can predict the IFT of the systems pure/impure CO2-brine with high truthfulness. In order to improve the robustness of GP, this technique was run several times with different setting parameters. Besides, after performing some preliminary runs and evaluating the best resulted GP-based correlations, it was noticed that it was more proper to split the database into

Conclusions

In this study, genetic programming (GP) was applied for establishing improved correlations for estimating the interfacial tension (IFT) of the systems pure/impure CO2-brine at extensive operational conditions. To this end, a widespread database encompassing 2346 real measurements was considered while implementing the correlations. The main findings gained from the current research work are as follows:

  • 1

    The newly proposed GP-based correlations can estimate the IFT of the systems pure/impure CO2

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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