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## Artificial Intelligence-based Modeling of Interfacial Tension for Carbon Dioxide Storage | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Gas Processing Journal | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

دوره 8، شماره 1، فروردین 2020، صفحه 83-92 اصل مقاله (588.76 K) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نوع مقاله: Research Article | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

شناسه دیجیتال (DOI): 10.22108/gpj.2020.119977.1069 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نویسندگان | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Amir Hossein Hosseini^{1}؛ Hossein Ghadery-Fahliyany^{2}؛ David Wood^{*} ^{3}؛ Abouzar Choubineh^{4}
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^{1}Petroleum Department, Semnan University, Semnan, Iran | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{2}Petroleum Department, Shahid-Bahonar University, Kerman, Iran | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{3}DWA Energy Limited, Lincoln, United Kingdom | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{4}Petroleum Department, Petroleum University of Technology, Ahwaz, Iran | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

چکیده | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

A key variable for determining carbon dioxide (CO2) storage capacity in sub-surface reservoirs is the interfacial tension (IFT) between formation water (brine) and injected gas. Establishing efficient and precise models for estimating CO2 – brine IFT from measurements of independent variables is essential. This is the case, because laboratory techniques for determining IFT are time-consuming, costly and require complex interpretation methods. For the datasets used in the current study, correlation coefficients between the input variables and measured IFT suggests that CO2 density and pressure are the most influential variables, whereas brine density is the least influential. Six artificial neural network configurations are developed and evaluated to determine their relative accuracy in predicting CO2 – brine IFT. Three models involve multilayer perceptron (MLP) tuned with Levenberg-Marquardt, Bayesian regularization and scaled conjugate gradient back-propagation algorithms, respectively. Three models involve the radial basis function (RBF) trained with particle swarm optimization, differential evolution and farmland fertility optimization algorithms, respectively. The six models all generate CO2 – brine IFT predictions with high accuracy (RMSE | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

کلیدواژهها | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Interfacial Tension (IFT)؛ CO2 Storage؛ Multi-Layer Perceptron؛ Radial Basis Function؛ Neural Network Prediction؛ IFT Influencing Variables | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

اصل مقاله | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Storing in depleted oil and gas reservoirs or deep saline aquifers is an attractive technology with the potential for reducing CO 1. Capacity to accept high quantities of CO 2. Injectivity to absorb CO 3. Confinement (sealing) sufficient to avoid the dispersal and leakage of buoyant and portable CO Reservoirs at various depths can effectively store CO Storing carbon dioxide in subsurface reservoirs is vulnerable to potential problems and impacted by various uncertainties, some of which may occur during and/or after the injection stage (Damen, Faaij, & Turkenburg, 2003). The most important potential problem is leakage. Both reservoir pressure and the buoyancy of carbon dioxide once in the reservoir can be sufficient over time to penetrate the reservoir seals (both cap rock and lateral seals) (Ennis-King & Paterson, 2005). If is able to breach a seal at any point it will ultimately find a pathway out of the reservoir. At high injection rates and pressures, a capillary breakthrough of may cause leakage from a reservoir. Interfacial tension (IFT) between and reservoir fluids is known to play a vital role in the capillary breakthrough (De Lary, Loschetter, Bouc, Rohmer & Oldenburg, 2012). Therefore, detailed investigations of the IFT behavior between and formation fluids are required for each specific subsurface reservoir considered for long-term CO Researches focusing on IFT between and reservoir fluids have provided in recent years substantial experimental data. Early studies provided IFT measurements for pure water- systems in underground conditions dating back to 1957 (Hebach, Oberhof, Dahmen, Kögel, Ederer, & Dinjus, 2002). However, there are concerns about the accuracy of these earlier data measurements due to the questionable assumptions and equations applied (Ennis-King & Paterson, 2005). Yan, Zhao, Chen, & Guo (2001) applied linear-gradient theory to determine IFT for pure water- systems at specific temperatures. However, other researchers found out that method tended to underestimate IFT at high pressures and overestimate IFT at low pressures. For salt-water (brine) systems there are much more limited IFT measurements available. Yang & Gu (2004) determined IFT values for a brine- system. However, the salinity they studied used was constant and very low, resulting in their observation that salinity did not affect IFT. Previously, Aveyard & Saleem (1975) had reported, however, a linear connection between IFT of brine- systems and molal salt concentration under ambient conditions. Two frequently used techniques for measuring IFT of -brine solutions at high pressures and high temperatures are pendant drop and capillary rise methods (Georgiadis, Maitland, Trusler, & Bismarck, 2010). However, such experimental measurements are time-consuming and require expensive laboratory equipment and sophisticated interpretation procedures. Mahbob, & Sultan (2016) studied experimentally the changes of interfacial tension and wettability with dolomite rock in the presence of carbon dioxide due to various parameters, such as temperature, pressure, salinity and surfactant type. It was found that with increasing salinity and temperature IFT of brines increases but it decreases with an increase in pressure. These effects are due to the solubility of carbon dioxide in brine. They also concluded that the use of fluoro-surfactants gives the minimum (less than one) interfacial tension. Zhao, Chang, & Feng, (2016) measured the crude oil-carbon dioxide mixture IFT to assess the minimum miscibility pressure. Their research showed that under immiscible conditions, the oil extraction and storage capacity improve dramatically as the injection pressure increases. On the other hand, while the pressure is higher than the MMP, the rise in the injection pressure can only cause a slight increase in oil recovery and storage capacity. A series of slim tube experiments were planned and presented to measure the impact of cold CO The CO An empirical equation with an extended uncertainty of 1.6 mN·m Artificial neural networks (ANN) are widely used (Toghyani, S., Ahmadi, M. H., Kasaeian, A., & Mohammadi, A. H., 2016; Kahani, M., Ahmadi, M. H., Tatar, A., & Sadeghzadeh, M., 2018) for a variety of applications (Maddah, H., Ghazvini, M., & Ahmadi, M. H., 2019; Ramezanizadeh, M., Ahmadi, M. H., Nazari, M. A., Sadeghzadeh, M., & Chen, L., 2019) and continue to be refined and their prediction accuracy improved (Farzaneh-Gord,
107 published laboratory measurements of interfacial tension (24.78 to 47.87 mN/m) covering a broad range of conditions: temperatures from 27 to 100 °C; pressures from 48 to 258 bar; salinities from 0.085 to 2.75 M, brine densities from 0.97 to 1.105 g/ ; and, CO
Table 2 presents a correlation matrix for the six measured variables in the compiled dataset. It reveals that -brine IFT has relatively high negative correlations with CO
Six distinct neural network algorithms are developed to compare their IFT CO In all cases, the mean square error (MSE) was evaluated as the cost function to be minimized. Activation functions applied to the MLPs for the input layer to hidden layer 1, hidden layer 1 to hidden layer 2 and hidden layer 2 to the output layer were tensig, logsig and purelin, respectively. Each hidden later had only seven neurons. The following control variables were applied to the RBF networks: For RBF-DE: max neurons (35), spread parameter (1.2111), number of population (30), beta min (0.4), beta max (0.8) and crossover probability (0.2). Where: beta min = lower bound of scaling factor and beta max = upper bound of scaling factor. For RBF-FFA: max neurons (35), spread parameter (1.1429), number of population (49), 𝛼 (0.6), 𝛽 (0.4), W (1) and Q (0.5). Where: 𝛼, 𝛽, and Q are numbers between zero and one. W represents the farmland fertility control variable. The values of these variables used for initiating the algorithm are validated by sensitivity analysis. For RBF-PSO: max neurons (35), spread parameter (1.2129), number of particles in population (50), W (1), W Where: W is inertia weight, W
Four standard statistical measures of prediction accuracy, average percentage error (APRE), average absolute percentage error (AAPRE), root mean square error (RMSE) and coefficient of determination (R The AAPRE and RMSE values recorded for the independent testing data records (Table 3) reveal that the RBF neural network achieves higher IFT prediction accuracy than the MLP models. The RBF network optimized by farmland fertility algorithm (RBF-FFA) displays the lowest AAPRE for the testing records (1.04253), whereas the RBF-PSO model displays the lowest RMSE (0.510938 mN/m) for the testing records, and RBF-DE displays the highest R
Considering only the MLP networks, the MLP network optimized by Levenberg-Marquardt (MLP-LM) displays the lowest AAPRE (1.550892) and highest R Figure 2 illustrates the prediction accuracies achieved for IFT of -brine solutions by the six ANN models in terms of the cumulative frequency of the prediction errors of individual data records when arranged in ascending order for all data records. Whereas all six models display high prediction accuracies for IFT of -brine solutions, the best performing model in terms of absolute relative error is the RBF-FFA model. For that model, Figure 2 identifies that nearly 70% of the data records involve an absolute relative error of less than 1, and only 3% of the total data records exceeds an absolute relative error of 4. Figure 3 displays measured experimental IFT for -brine solutions versus predicted IFT values for each of the six neural network models evaluated for all data records. All data points for the models straddle a line with a 45-degree slope and passing through the origin. This demonstrates the high prediction accuracy achieved collectively by the models, particularly the RBF-FFA and RBF-PSO models. Figure 2 reveals that for the MLP models and the RBF-DE models the greatest dispersion about the unit slope line between measured and predicted data points occurs in the IFT range 26 to 31 mN/m. The RBF-FFA and RBF-PSO models fit the data in that range with much less error than the other models.
Table 4 displays the correlation coefficients (calculated with Excel’s CORREL function) between the input variables and the predicted IFT for -brine solutions. As should be expected, these are all in good agreement with the correlation coefficients displayed in the right-hand column of Table 2 (i.e. between input variable values and the experimentally measure IFT values). Clearly, CO
Interfacial tension (IFT) between carbon dioxide (CO | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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