316 American Academic Scientific Research Journal for Engineering, Technology, and Sciences ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 http://asrjetsjournal.org/ Principal Component Analysis for the Study of Opening Underground Caverns in Salt Rocks Rayra Amorim a *, Leonardo Guimarães b , Oscar Melgar c a,b,c Dept. of Civil Engineering, Federal University of Pernambuco, Av. Prof. Moraes Rego,1235, Cidade Universitária, Recife, 50670-901, Pernambuco, Brazil a Email: rayra.amorimsilva@ufpe.br b Email: leonardo.guimares@ufpe.br c Email: oscar.melgar@ufpe.br Abstract The constant dynamism within the oil industry associated with the need for new technologies in terms of production and disposal of products were fundamental for the increase of studies about the use of underground caverns in salt rocks as an alternative for the storage of petroleum products. Salt rock is particularly useful for storage because of its low cost, low permeability, and its healing potential when compared to other rocks, including granite, mud, and basalt. The opening process and subsequent development of these cavities are complex activities and the variables involved in the process play a crucial role during the entire operation. In this sense, the present work aims to identify, through the PCA (Principal Component Analysis) statistical tool, the variables that most influence the process of opening a salt cavern by dissolution. For this, numerical simulations of the dissolution mining process for opening a cavern under typical conditions of water injection into a salt rock using the software SALGAS were developed considering different methods of saline water circulation, after that, the variables injection temperature, injection rate, radius, volume, pump power, cumulative energy, tubing loss, produced brine, pump pressure, injection pressure, and salt dissolution factor were interpreted using the multivariate statistical tool through software PAST. For the simulations generated, the results with the statistical tool were satisfactory, it was found that the brine injection rate contributes significantly to the process, in terms of x-axis, directly influencing the behavior of other variables, the temperature have a great importance to the y-axis. Regarding the total variability of the data, more than 97% of these could be represented in terms of the first two components for both scenarios studied. Keywords: cavern; salt rock; process variables; numerical simulations; statistical analysis. ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ mailto:rayra.amorimsilva@ufpe.br American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 317 1. Introduction The growing global energy demand requires the search for new techniques for the safe storage of products. In this sense, salt rock is considered the ideal material for underground storage dues to low permeability, healing capacity, and availability [1]. In addition, underground salt caverns can be built by solution mining techniques, which are cheaper than other conventional excavation techniques [2]. When compared to other rocks, including granite, mud, and basalt the cost of leaching caverns by dissolution in salt rock turns out to be lower. Another advantage is the ability to absorb harmful nuclear radiation (in a waste storage medium and water solubility, an ideal choice for the deep burial of nuclear waste and oil and gas storage) [3]. The dissolution of the salt rock contemplates the initial phase of opening of these cavities, being one of the first experimental studies on the subject, that of Durie & Jessen [4] who carried out a series of laboratory tests in order to evaluate the influence of the injection rate of water (fresh and salty) in the cavern formation rate and the salt removal rate. The injection rate of water was one of the main parameters in our study, being important to know works that approach the behavior of this and other variables. In addition to experimental studies, mathematical and numerical modeling were also developed in this field. Also, in the work of Durie & Jessen [4], a mathematical model was presented that describes the dissolution process as a function of the salinity of the water at any point on the vertical surface of the salt. It was found that at low injection rates, the induced flow does not significantly contribute to the salt removal rate, which means that it is the high injection rates that really influence the process. Saberian [5] developed a 5” tall cylindrical model to study the flow and expansion mechanisms of saline cavities during dissolution, the results combined into a generalized numerical model, where the prediction of cavity dissolution as a function of the time and also other physical parameters such as velocity, radius, and dissolution rate. These other parameters besides injection rater of water were also important in our study. More recently Yang et al. [6] presented a proposal for an analytical solution of a differential equation to calculate the dissolution rate of saline rocks subjected to an instantaneous diffusion process, the results showed a fit between the numerical model and the experiment of the salt concentration with concerning to time. As these are numerical aspects, the parameters involved in numerical simulations can also be interpreted from a statistical perspective. Multivariate data analysis can reduce data or carry out a structural simplification as well as investigate the dependency relationship between variables [7]. This set of statistical methods is widely used in various fields of science and encompasses different techniques, the most used being cluster analysis, factor analysis, principal component analysis, multiple regression, and logistic regression, each with its characteristics. In the present work, a finite difference code, SALGAS is used to predict response surfaces for these caverns, this method solves differential equations based on the finite difference derivative approximation. After the surface generation, the numerical data analysis was performed with the PCA (Principal Component Analysis) statistical tool through the software PAST. In this method, an orthogonal transformation is performed to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called Principal American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 318 Components (PC) that reveal the internal structure of the data in a way that best explains its variance [8]. In this context, this work aims to investigate the degree of influence that each variable has individually on the process of opening an underground cavern in salt rock. 2. Materials and methods Two hypothetical scenarios were considered for the study of the opening of an underground cavern in salt rock by dissolution, scenario D where water was injected at the bottom of the cavern and the brine was extracted from the top of it, through the so-called direct circulation method, and the scenario R where water was injected at the top of the cavern and the brine was extracted from the bottom of the cavern, in the so-called reverse circulation method. In Table 1 the respective injection and production heights are presented for the considered scenarios and in Figure 1 their schematic representation. Table 1: Injection and Production depths for the proposed hypothetical scenarios Figure 1: Scenarios of salt cavern opening by dissolution. Source: Adapted from [9] For the numerical modeling of the approached scenarios was used the SALGAS software, written in FORTRAN in the mid-1970s. This finite difference code developed by the Solution Mining Research Institute (SMRI) to simulate the dissolution of sodium chloride salt by water, optionally simulates the hydraulic properties and power requirements of the mining system. The main limitation of this software is the impossibility to simulate offshore scenarios, which limits the reach of the proposed scenarios. Both scenarios were based on example number 1 from the SALGAS Manual [10]. In this example, the SCENARIO ID (ft) ID (m) PD (ft) PD(m) SCENARIO D 3000 914.4 2500 762 SCENARIO R 2500 762 3000 914.4 American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 319 development of a new cavern is started from a hole with a blanket, which moves up once, with 3% insolubles, considering a constant brine injection rate and equal to 750 gpm (170.34 m³/h) and the SALGAS base temperature of 75°F (23.9°C) during 120 days. The hydraulic model has a short section of surface piping and divides each of the piping lines into two sections. From this base situation, new simulations were obtained in this study by varying the injection temperature and the brine injection rate. The injection pressure, P (MPa) is the difference between the pressure of the fluid to be injected, P1 (MPa) and the pressure of fluid in the massive, P2 (MPa). With P2 known, the Bernoulli equation, only valid for incompressible fluids, is used to find P1, through Equation 1: 𝑃1 𝛾 + 𝑣1 2 2𝑔 + 𝑧1 = 𝑃2 𝛾 + 𝑣2 2 2𝑔 + 𝑧2 (1) Where: g = gravity acceleration (m/s 2 ); P = pressure (Pa); v = velocity (m/s); z = height (m); γ = specific weight (N/m 3 ), and z; v = flow/area; γ = ρg. The initial brine specific gravity and the injection fluid specific gravity are input parameters for SalGas obtained from the Toolbox provided by SMRI. The brine pressure and temperature values are entered and the Toolbox automatically provides the parameters, to determine the brine produced, it is also necessary to inform the fluid saturation which is 4.05% in NaCl. According to Saberian [11], it is possible to obtain the dissolution rate of a brine, mT (cc/cm²/min x 10³), for different temperatures and salinities, as a function of the specific density of the brine, ρ (-), of the reference temperature, T0 (°F), and the initial production temperature, T (°F), according to Equation 2: 𝑚𝑇 =  0.22(1.2019 − 𝜌)1.42𝑒𝑥𝑝 [0.0119 ( 𝜌−1 1.2019−𝜌 ) 0.2 𝛥𝑇] (2) As in SalGas the reference temperature is 75°F and all the simulations performed are isothermal fixed for this temperature, the input data instead of being the dissolution rate is the dissolution factor which is the exponential term of Equation 2 for an ideal salt (T0=75°F and ρ=1.20). The dissolution factor, DF corrects the dissolution rate by compensating between a 75°F isothermal simulation of an “ideal salt”, which would generate a brine with the maximum specific gravity accepted by the software = 1.2, and the simulation that needs to be done, with temperature and specific densities different from the ideal. DF is given by Equation 3: 𝐷𝐹 = 𝑒𝑥𝑝 [0.0119 ( 𝜌−1 1.2019−𝜌 ) 0.2 𝛥𝑇] (3) The diameters of the external and internal piping were the same as those considered in the example, respectively 10¾” (273.05 mm) and 7” (177.8 mm). The mining module of SALGAS was used together with the hydraulic module to simulate the dissolution of the rock. Tables 2 and 3 present the parameters that were used in the SALGAS data input file for scenarios D and R respectively. American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 320 Table 2: Input parameters for Scenario D Table 3: Input parameters for Scenario R N° Injection Temperature (°C) Injection Rate (m³/h) Injection Pressure (MPa) Initial Brine Density Injected Fluid Density Salt Dissolution Factor 1 40 120 7.5600 1.195700 1.023330 1.25822596 2 40 200 7.7100 1.195800 1.023430 1.25850574 3 40 360 8.2300 1.196000 1.023530 1.25878481 4 40 400 8.4100 1.196000 1.023630 1.25906319 5 40 800 11.2200 1.197200 1.024830 1.26235126 6 40 1200 15.9000 1.199000 1.026730 1.26737505 7 60 120 7.5600 1.186800 1.013730 1.58127404 8 60 200 7.7100 1.186800 1.013830 1.58240401 9 60 360 8.2300 1.187000 1.014030 1.58464903 10 60 400 8.4100 1.187100 1.014130 1.58576420 11 60 800 11.2200 1.188200 1.015330 1.59878792 12 60 1200 15.9000 1.190100 1.017230 1.61821655 13 80 120 7.5600 1.178500 1.002230 1.63097469 14 80 200 7.7100 1.178500 1.002330 1.63810134 15 80 360 8.2300 1.178700 1.002530 1.65174855 16 80 400 8.4100 1.178800 1.002630 1.65829672 17 80 800 11.2200 1.179900 1.003830 1.72622905 18 80 1200 15.9000 1.181900 1.005730 1.80920606 N Injection Temperature (°C) Injection Rate (m³/h) Injection Pressure (MPa) Initial Brine Density Injected Fluid Density Salt Dissolution Factor 1 40 120 9.0500 1.196300 1.023930 1.25989419 2 40 200 9.1800 1.196400 1.024030 1.26016984 3 40 360 9.6700 1.196500 1.024230 1.26071911 4 40 400 9.8300 1.196600 1.024330 1.26099276 5 40 800 12.4200 1.197600 1.025430 1.26396075 6 40 1200 16.7400 1.199400 1.027130 1.26840665 7 60 120 9.0500 1.187400 1.014330 1.58798018 8 60 200 9.1800 1.187400 1.014530 1.59017741 9 60 360 9.6700 1.187600 1.014630 1.59126914 10 60 400 9.8300 1.187600 1.014730 1.59235636 11 60 800 12.4200 1.188700 1.015830 1.60403307 12 60 1200 16.7400 1.190500 1.017630 1.62214403 13 80 120 9.0500 1.179100 1.002830 1.67090079 14 80 200 9.1800 1.179100 1.002930 1.67697674 15 80 360 9.6700 1.179300 1.003130 1.68871982 16 80 400 9.8300 1.179400 1.003230 1.69440201 17 80 800 12.4200 1.180400 1.004330 1.75029718 18 80 1200 16.7400 1.182300 1.006130 1.82428703 American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 321 After running the cases in SALGAS, the production variables in addition to the volume and radius of the cave in the proposed final time (120 days) had their data selected together with the input variables injection temperature, brine injection rate, injection pressure, and salt dissolution factor to be statistically analyzed by the PAST software, through the technique of PCA. Table 4: Input parameters for the PAST software: Scenario D Injection Temperature (°C) Injection Rate (m³/h) Radius (m) Volume (m³) Pump Power (kW) Cumulative Energy (J) Tubing Loss (MPa) Produced Brine (m³) Pump Pressure (MPa) Injection Pressure (MPa) Salt Dissolution Factor 40 120 7.7694 37213.41616 658.4531 6.6829E+11 0.1502 334211.3423 1.7878 9.0500 1.25989419 40 200 9.4031 57141.62737 1429.5069 1.45308E+12 0.3816 557057.8557 2.3318 9.1800 1.26016984 40 360 11.8049 92203.71572 4639.7454 4.73274E+12 1.1280 1002038.7796 4.2044 9.6700 1.26071911 40 400 12.2682 99816.80821 5941.7376 6.06455E+12 1.3755 1109596.3469 4.8381 9.8300 1.26099276 40 800 15.8313 166230.4175 34571.3977 3.56105E+13 4.9684 2230660.5850 14.1687 12.4200 1.26396075 40 1200 17.9192 212801.6161 103292.8726 1.08158E+14 10.4662 3329176.0150 28.5650 16.7400 1.26840665 60 120 8.3972 41667.42743 709.9064 7.21642E+11 0.1507 334211.3423 1.9154 9.0500 1.58798018 60 200 10.0614 64858.28877 1518.9909 1.54811E+12 0.3818 557057.8557 2.4656 9.1800 1.59017741 60 360 12.7224 106726.4532 4892.5377 4.96045E+12 1.1425 1002038.7796 4.3844 9.6700 1.59126914 60 400 13.2466 116042.2662 6068.5066 6.2317E+12 1.3617 1109596.3469 4.9463 9.8300 1.59235636 60 800 17.4315 201898.7646 35147.0781 3.62468E+13 4.9725 2230660.5850 14.3342 12.4200 1.60403307 60 1200 20.0497 265475.1015 104578.4594 1.09958E+14 10.4731 3329176.0150 28.7718 16.7400 1.62214403 80 120 8.7325 44843.31677 750.9199 7.6468E+11 0.1501 334211.3423 2.0209 9.0500 1.67090079 80 200 10.4760 70250.0149 1599.5265 1.62383E+12 0.3832 557057.8557 2.5786 9.1800 1.67697674 80 360 13.2801 116354.5469 4988.733 5.07783E+12 1.1321 1002038.7796 4.4685 9.6700 1.68871982 80 400 13.8440 126798.4618 6128.9083 6.34018E+12 1.3383 1109596.3469 5.0077 9.8300 1.69440201 80 800 18.4038 225757.1488 36343.9266 3.67627E+13 5.0421 2230660.5850 14.6307 12.4200 1.75029718 80 1200 21.4213 305255.9144 108662.6583 1.1227E+14 10.6800 3329176.0150 29.4406 16.7400 1.82428703 American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 322 Table 5: Input parameters for the PAST software: Scenario R Injection Temperature (°C) Injection Rate (m³/h) Radius (m) Volume (m³) Pump Power (kW) Cumulative Energy (J) Tubing Loss (MPa) Produced Brine (m³) Pump Pressure (MPa) Injection Pressure (MPa) Salt Dissolution Factor (DF) 40 120 9.7384 41584.35672 624.1509 6.38849E+11 0.1605 334211.3423 1.6885 7.5600 1.25822596 40 200 11.7653 64401.4905 1395.9504 1.42797E+12 0.4075 557057.8557 2.2698 7.7100 1.25850574 40 360 14.5786 104419.1241 4654.6594 4.77441E+12 1.1997 1002038.78 4.2106 8.2300 1.25878481 40 400 15.0967 113043.1148 5985.7339 6.12315E+12 1.4576 1109596.347 4.8629 8.4100 1.25906319 40 800 19.0378 189170.0651 34992.7182 3.67585E+13 5.2835 2230660.585 14.2997 11.2200 1.26235126 40 1200 21.3787 244061.1218 107118.3136 1.1174E+14 11.3074 3329176.015 29.5027 15.9000 1.26737505 60 120 10.4638 45842.4658 659.9445 6.78539E+11 0.1609 334211.3423 1.7802 7.5600 1.58127404 60 200 12.7467 72203.79183 1457.0978 1.49936E+12 0.4087 557057.8557 2.3670 7.7100 1.58240401 60 360 15.9258 119336.2686 4803.7994 4.92558E+12 1.2045 1002038.78 4.3265 8.2300 1.58464903 60 400 16.5384 129867.4276 6131.8911 6.29215E+12 1.4638 1109596.347 4.9718 8.4100 1.58576420 60 800 21.1988 225099.0809 35408.0731 3.69047E+13 5.3159 2230660.585 14.5204 11.2200 1.59878792 60 1200 24.2286 300251.0434 110101.8593 1.13889E+14 11.3901 3329176.015 29.9646 15.9000 1.61821655 80 120 10.8692 48891.77127 693.501 7.13102E+11 0.1609 334211.3423 1.8643 7.5600 1.63097469 80 200 13.2862 77437.07788 1517.4995 1.55969E+12 0.4087 557057.8557 2.4518 7.7100 1.63810134 80 360 16.6634 128735.2716 4864.9468 5.02142E+12 1.2045 1002038.78 4.3906 8.2300 1.65174855 80 400 17.3401 140390.4591 6262.3886 6.42679E+12 1.4638 1109596.347 5.0566 8.4100 1.65829672 80 800 22.4516 248085.5009 35762.2806 3.71783E+13 5.3221 2230660.585 14.6031 11.2200 1.72622905 80 1200 26.0634 339761.6182 110544.8051 1.14688E+14 11.4108 3329176.015 30.0060 15.9000 1.80920606 American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 323 3. Results and discussions 3.1. Results with SALGAS Based on the simulations performed in the SALGAS software, it was possible to compare the D and R scenarios, through curves. The behavior of the cavern was analyzed considering the variation of the injection temperature and the brine injection rate along time of 120 days. Figures 2 and 3 bring the main simulations for scenario D. The comparison of the final contour of the cavern for the time of 120 days considering all analyzed cases was presented in figure 2, where it was possible to verify the geometry and the value of the radius reached. The maximum value reached for the time of 120 days was approximately 22 m of radius for the temperature of 80ºC and injection rate of 1200 m³/h. Analyzing the same rate value, the cavern radius increases with increasing temperature, but this seems to have less influence on the final diameter obtained than the rate. Figure 2: Comparison of final cavern contours: all simulations In addition to the cavern geometry, the evolution of its volume was evaluated. For the same temperature, the volume grows faster for higher rates. Figure 3 shows all cases analyzed (all rates and temperatures). Analyzing the influence of temperature, it is observed that for the same rate, the higher the temperature, the greater the volume of the cavern. American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 324 Figure 3: Comparison of final cavern volume evolution: all simulations Figures 4 and 5 bring the main simulations for scenario R. Similar to what happens in scenario D, for the same temperature, the higher the injection rate, the greater the radius of the cavern. The maximum value reached for the time of 120 days was approximately 26 m of radius for the temperature of 80ºC and injection rate of 1200 m³/h (Figure 4). Figure 4: Comparison of final cavern contours: all simulations American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 325 Figure 5 shows the evolution of the cavern volume for all cases analyzed (all rates and temperatures). Analyzing the influence of temperature, it is observed that for the same rate, the higher the temperature, the greater the volume of the cavern. Figure 5: Comparison of final cavern volume evolution: all simulations 3.2 Results with PCA For each of the scenarios studied, statistical analysis of the data was performed considering the principal components technique. The main results are presented below. For scenario D, Table 6 presents the respective eigenvalues and the percentages of variance explained by each one. In the study with 11 parameters of simulations for the opening of a cavern in salt rock by dissolution, it was found that only two principal components are sufficient to explain 97% of the total variance of the parameters, in which PC1 was responsible for 79,04% and the second, PC2, for 18,04% of the data variations. Comparatively, in a study with 7 criminality characteristics of some cities in the United States, it was found that with only two components it was possible to explain 68.13% of the total variance of the characteristics [12]. JOHNSON & WICHERN [13], emphasize that it is sufficient for the retained components to represent at least 80% of the total variability of the data. Despite the first component (PC1) representing 79.04% of the total variability of the data, according to Table 7, the injection temperature parameter data has significant weight for the second component (PC2), around 70%, which justifies that this component is also considered in the study of the data set. American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 326 Table 6: Principal Components (PCs), eigenvalues (λ), and percentage of variance explained by the components PC Eigenvalue % Variance 1 8.69491 79.045 2 1.98493 18.045 3 0.26294 2.3904 To understand the importance of each variable in the construction of the two components, two important relationships were shown in Table 7, the weighting coefficient, that is, the weight of each variable in the component under analysis and its correlation coefficients with the first two components main. As previously mentioned, the injection temperature variable has a significant weight in terms of the second component (PC2), not influence on the first component (PC1), the salt dissolution factor has similar comportment to injection temperature, it’s happened because this coefficient depends directly on the temperature according to Eq. (3), the other variables have almost similar weight for PC1, even in PC2, radius and volume also have a small weight for the second component. As for the correlation, the injection temperature and DF are directly correlated to the y axis, while the other variables are directly correlated to the x-axis. Table 7: Weighting coefficients of the characteristics and their correlation coefficients with the first two principal components Weighting Coefficient Correlation Principal Component PC 1 PC 2 PC1 PC2 Injection Temperature 0.026337 0.6988 0.07766 0.98453 Injection Rate 0.33591 -0.053025 0.9905 -0.074706 Radius 0.32133 0.094616 0.94752 0.1333 Volume 0.32742 0.096823 0.96546 0.13641 Pump Power 0.33103 -0.052234 0.97611 -0.073591 Cumulative Energy 0.33056 -0.054977 0.97473 -0.077455 Tubing Loss 0.3369 -0.056195 0.99341 -0.079172 Produced Brine 0.33582 -0.052931 0.99022 -0.074573 Pump Pressure 0.33701 -0.048399 0.99374 -0.068188 Injection Pressure 0.33588 -0.06052 0.99042 -0.085265 Salt Dissolution Factor 0.067061 0.68762 0.19774 0.96877 Through Figure 6, a PC1 x PC2 biplot, it is possible to observe a high correlation between the variables injection rate, pump power, cumulative energy, tubing loss, produced brine, injection pressure, and pump pressure, as they are almost overlapping each other, the radius and volume variables also show a high correlation with each other. From the position in the biplot, it is noted that the injection temperature variable is isolated, next to DF, quite close to the y-axis, although they are in the same quadrant of the radius and volume, the latter doesn’t seem to have a great contribution in terms of PC2. American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 327 Figure 6: PC1 x PC2 Biplot For scenario R, the results with the PCA technique were quite similar to those of scenario D, in Table 8, below, it is observed that 78,97% of the data are in terms of the first component (PC1), 17,88% in terms of the second (PC2), adding up to a total of almost 97% of variance in terms of the first two components. Similar to what happens in scenario D, the temperature and DF in scenario R also has a significant weight in terms of the second component, around 70%, as shown in Table 9. Therefore, both components (PC1 and PC2) must be considered in the data analysis of this population. Table 9 also shows that for PC1, the radius variable, which in scenario D had a weight and a correlation almost in the same proportion as the other variables, except injection temperature and DF, in this scenario appears to have slightly smaller participation. On the other hand, it increased its share in terms of the second component. Table 8: Principal Components (PCs), eigenvalues (λ), and percentage of variance explained by the components PC Eigenvalue % Variance 1 8.68696 78.972 2 1.96689 17.881 3 0.273911 2.4901 By the PC1 x PC2 Biplot, Figure 7, it is possible to observe that in terms of PC1, the variables injection rate, pump power, cumulative energy, tubing loss, produced brine, injection pressure, and pump pressure maintain a high correlation between them, also in the R scenario. The radius and volume variables decreased the correlation between them, compared to the D scenario. For PC2, the temperature and DF remained very close to the y axis, with the radius variable closer to the y axis as well. American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 328 Table 9: Weighting coefficients of the characteristics and their correlation coefficients with the first two principal components Weighting Coefficient Correlation Principal Component PC 1 PC 2 PC1 PC2 Injection Temperature 0.02688 0.69881 0.079224 0.98005 Injection Rate 0.33594 -0.054279 0.99012 -0.076124 Radius 0.31809 0.11815 0.93754 0.1657 Volume 0.32906 0.083291 0.96987 0.11681 Pump Power 0.33053 -0.059279 0.97419 -0.083137 Cumulative Energy 0.33056 -0.060614 0.97427 -0.085009 Tubing Loss 0.33682 -0.060065 0.99274 -0.084239 Produced Brine 0.33583 -0.054172 0.98983 -0.075975 Pump Pressure 0.33688 -0.054571 0.99291 -0.076534 Injection Pressure 0.33604 -0.062936 0.99044 -0.088265 Salt Dissolution Factor 0.076151 0.68349 0.22444 0.95856 Figure 7: PC1 x PC2 Biplot 3.3 Relation DF x Injection Temperature x Injection Rate Another important relation it’s DF x Injection Temperature x Injection Rate. Considering the temperatures of 40, 60, and 80°C for the respective injection rates and salt dissolution factors, it is possible to trace a graphic American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 329 analyzing each scenario. Figures 8 and 9 suggest low temperatures, 40°C, DF doesn’t change with an increase in injection rates, it’s possible to see any changes from the injection rate of 400 m³/h and injection temperature of 80°C. Similar behavior was observed in both scenarios. Therefore, one can consider in future studies, working with injection rates above 400 m³/h and injection temperatures above 60°C, since from that point, DF is really relevant. Table 10: Data of DF, Injection Temperature, and Injection Rate to Scenario D 40°C 60°C 80°C Q DF Q DF Q DF 120 1.259894 120 1.58798 120 1.670901 200 1.26017 200 1.590177 200 1.676977 360 1.260719 360 1.591269 360 1.68872 400 1.260993 400 1.592356 400 1.694402 800 1.263961 800 1.604033 800 1.750297 1200 1.268407 1200 1.622144 1200 1.824287 Table 11: Data of DF, Injection Temperature and Injection Rate to Scenario R 40°C 60°C 80°C Q DF Q DF Q DF 120 1.258226 120 1.581274 120 1.630975 200 1.258506 200 1.582404 200 1.638101 360 1.258785 360 1.584649 360 1.651749 400 1.259063 400 1.585764 400 1.658297 800 1.262351 800 1.598788 800 1.726229 1200 1.267375 1200 1.618217 1200 1.809206 Figure 8: DF x Injection Temperature x Injection Rate to Scenario D 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 120 200 360 400 800 1200 D F Injection Rate (m³/h) DF x Injection rate x Injection temperature 40 °C 60 °C 80 °C American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 330 Figure 9: DF x Injection Temperature x Injection Rate to Scenario R 4. Conclusion Taking into account the results obtained, the principal component analysis technique proved to be effective and allowed the removal of nine variables that were redundant because they were correlated with others of greater importance, that is, the 11 parameters of the numerical simulations in SalGas reduced its dimensionality to two principal components, the brine injection rate provided the most information for the x-axis and the injection temperature the largest for the y-axis, in this way, the modeling process for new scenarios can be streamlined and simplified, preserving most of the original data. Added together, the first two components represented about 97% of the total variability of the original data. As for the influence on the salt cavity opening process, in terms of PC1, the brine injection rate was the variable that most contributed to the process, being followed in the same proportion by the other variables, exception for the injection temperature and DF. These have a significant weight in terms of PC2. For the analysis of principal components, both scenarios presented almost similar results, as for the SALGAS simulations, in the proposed time of 120 days, the final geometry of the cave for the Scenario D resembled the appearance of a pear while for the Scenario R of a cone, the contour and the final volume of the cave were higher for the Scenario R, this does not imply that one scenario is more favorable than the other, since each one has its advantages and limitations. With the numerical simulations, it was also possible to conclude that the largest radius and the largest volume were found for the simulation of a higher production rate, 1200m³/h, and higher temperature, 80°C, that is, the higher the brine injection rate, the greater the radius and volume of the cave. Similar behavior is verified in relation the influence of the injection temperature, the higher the temperature, the greater the volume and radius of the cavern, although it influences to a lesser extent. Also, when analyzing the relation of DF with injection temperature and injection rate, it’s possible to see that the variable temperature influences in the behavior of cavern for high temperatures and injection rates. Acknowledgments The authors acknowledge the Graduate Program in Civil Engineering (PPGEC) and the final support from the Brazilian research agency CAPES (Coordination for the Improvement of Higher Education Personnel), Energi 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 120 200 360 400 800 1200 D F Injection Rate (m³/h) DF x Injection rate x Injection temperature 40°C 60°C 80°C American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2022) Volume 88, No1, pp 316-331 331 Simulation, and PETROBRAS (Brazilian Oil Company). References [1] H. 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