Design and Implementation of an AI-Powered Sapient System for Maximum Efficiency of Fractionation Operations

Design and Implementation of an AI-Powered Sapient System for Maximum Efficiency of Fractionation Operations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Design and Implementation of an AI-Powered Sapient System for Maximum Efficiency of Fractionation Operations Behzad Amirsalari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5441475/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper introduces a multi-step and comprehensive data-intensive structure to optimize the control of petrochemical fractionation columns using big-data analysis. The case study involved 11 parameters categorized into five control (adjustable) inputs, four imposed (non-adjustable) inputs, and two target outputs. The results from a factorial-designed set of experiments on a simulated model of a functional de-Ethanizer distillation unit constructed the initial database, consisting of 5620 vectors. The generated big dataset then trained a feed-forward artificial neural network (FF-ANN) that predicts the characteristics of the produced Ethane in response to ten input parameters. Subsequently, this trained model provided the feasible region for a multi-objective particle swarm optimization (PSO) algorithm to predict 625 individual optimum control points in response to different combinations of the imposed parameters. Finally, these optimum operation conditions trained five dedicated individual ANNs to predict a continuous optimum operation log according to the imposed parameters. This multi-step architecture of optimization and ANNs forms a flexible data-driven sapient system for the optimum control of distillation columns. Artificial neural network Particle swarm optimization Optimum process control Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Introduction Gas refineries typically consist of interconnected process units, each having a specific role in carrying out a portion of the refining process. Crude gas (or so-called sour gas), coming from the off-shore platforms, first enters the gas reception facilities to separate the associated phases and calm the flow. The sweetening units separate some mingled components, such as light hydrocarbon compounds, and stabilize the accompanying gas condensate. Methane is the main product of the gas refinery plants, while Butane, Propane, and Ethane are some of the other by-products. Distillation facilities operate based on fundamental thermodynamic principles to produce various purified products by separating different hydrocarbons from an untreated feed. These units comprise three main sections: the process column (tower), the reboiler loop, and the reflux cycle. Fractionator trays are strategically installed at different heights within the process towers to facilitate the separation of products according to their boiling points. The multi-component mixture feed is introduced into the distillation tower at an upper-middle point, while low-pressure (LP) steam supplies the necessary heat to the reboiler system. The reboiler applies heat from the bottom of the tower, creating a temperature gradient with the hottest tray at the bottom and the coolest at the top. This configuration allows lighter components to be collected from the top of the tower. An external drum and reflux loop further enhance separation by cooling and condensing vapors. If the top purified product contains any heavier components, they accumulate in a pressure tank, known as the reflux drum, and are returned to the process tower. The schematics of a de-Ethanizer modification of this unit are illustrated in Figure 1. Achieving higher quality and higher flow of condensed Ethane with lower energy consumption is desirable. To ensure optimal performance, designers must consider dimensional, thermodynamic, chemical engineering, and metallurgical aspects. For simple feeds, analytical methods such as the McCabe-Thiele method or the Fenske equation are employed [1, 2], while multi-component feeds typically necessitate the use of simulation models such as Aspen HYSYS. However, because of the complexity of the process and the high number of independent parameters with non-linear relationships, it is too difficult or time-consuming to analyze the process explicitly or to use computational methods in real-time decisions. Hence, the solution appears to lie in employing artificial intelligence (AI) approaches to construct a coherent model of optimal process control that considers the complex interrelationships among the system's characteristics. These methods can fill the gap in the accurate and optimal execution of the designed process by enhancing the operation and amending product purity, equipment health, fuel consumption, energy efficiency, and environmental pollution. Soft computing and data modeling approaches have been increasingly employed in predicting the operation of distillation columns. The publications mostly include prediction, fault diagnosis, optimization, and operation control. The popularity of inferential approaches for process prediction can be attributed to their capacity to uncover correlations between parameters. Masnadi et al. [3] introduced a general data-driven framework to develop a statistical proxy model. They applied this methodology in the bottom-up life-cycle assessment (LCA) of an acid gas removal (AGR) unit. A large database comprising over 25000 simulated trials trained a reduced-order (RO) model to forecast the energy usage and product compositions. To assess the correctness of their findings, they employed the mean absolute percentage deviation (MAPD) evaluation technique. Compared to standard models, the aforementioned simple proxy model needed fewer input parameters and produced practically instantaneous predictions with great accuracy. However, since the predictive model is usually not used alone, their research could be more comprehensive by adding another practical section, such as optimization. Among various data modeling methods, artificial neural networks (ANNs) have been one of the favorites of many researchers. Bahar et al. [4] published their research to dynamically predict product compositions based on the temperature in various points of a De-Ethanizer column. They used the backward propagation (BP) method to train a multilayer perceptron (MLP) ANN with simulation data; and then fed it with a model predictive controller (MPC) to estimate the product chemical compositions based on temperature measurements. They evaluated predicted and simulated dynamic plots of the bottom and top compositions in response to the reflux and feed rate. They proved that their represented inferential composition control is reliable in predicting the product compositions with acceptable performance. However, they could improve their work by focusing on multiple outputs. The first step to implementing a data model with a firm base is deciding the most efficient methods to model, analyze, and visualize the data. Corona et al. [5] investigated the effectiveness of two different ANN methods in analyzing the data from a de-Ethanizer column. They represented a brief discussion on the Self-Organizing ability of Map (SOM) and MLP methods in modeling the fractionation process. They foretold the process modes with an unsupervised clustering technique in the SOM approach and then developed an MLP to cope with time delay matter and instrumentation costs. Their research represented a strategy to model the process of their achievements; however, it could have more clarification on the mechanism of the prediction methods. Solooki et al. [6] represented a method based on FF-ANNs to predict the collection outputs of the regenerator columns in a gas sweetening unit. For this purpose, they trained 145 experimental data to an ANN, and the results showed that ANNs can accurately predict the operation of these industrial units. Although using industrial data is one of the strengths of their work, they could add simulation data to have a firmer base for their study because the volume of their operational database is considerably limited. Because online monitoring of chemical components of the products in distillation towers is technically challenging, prediction of these compounds using data analysis methods is becoming popular among many researchers. Ramli et al. [7] used an ANN to predict the chemical composition of products in a Debutanizer tower. They combined the open-loop and closed-loop online data with the simulation results as three data sources in their research. However, since the column has many surrounding variables, important affecting ones were determined utilizing principal component (PCA) and partial least square (PLS) analyses before training the ANN. Eventually, they used the root mean square error (RMSE) to evaluate the model and then utilized the mentioned data to train, validate, and test the ANN. The highly accurate results with low amounts of errors between the predictions and the actual data, as the strength of their work, show that the ANN method is a reliable in-time inferential estimator for the product composition in the fractionation towers. However, mixing data from three completely different sources and training them in a single ANN seems like a risky decision because the errors and deviations of these sources can vary a lot, which could lead the ANN to have faults in its predictions. Concerning the integrated relationship between environmental constraints and conditions with facilities and other parameters, predicting the production trend is another issue of interest in applications of industrial data-based algorithms. Song et al. [8] published a paper on forecasting the production of fractured horizontal wells in a volcanic reservoir. They trained a long short-term memory (LSTM) ANN, whose configuration was optimized via particle swarm optimization (PSO) algorithm. Finally, they evaluated the mentioned method through two cases by comparing its performance with traditional ANNs, time-series forecasting approaches, and conventional decline curves. Different methods predict the behavior of industrial units, each with its strengths and weaknesses. One of the issues in predicting refinery units is the limited size of data and the need to use methods that are most efficient with small databases. Fatima et al. [9] examined the ability of the adaptive neuro-fuzzy inference systems (ANFIS) technique to model and predict the operation of a Debutanizer column with limited data. They trained an ANFIS algorithm with the actual operation data of the unit and compared its generalization performance with regular ANN. Regarding root mean square error (RMSE) criteria, the ANFIS method demonstrated a better prediction performance when training data samples were limited. One of the advantages of modeling industrial equipment data is the possibility of predicting errors and preventing unwanted stops or accidents. In many cases, fault diagnosis before failure occurs is crucial for industrial equipment. Determining an efficient strategy for preventive maintenance (PM) makes it possible to avoid financial and even human damage due to cessation of operations. In 2018, Yang et al. [10] proposed a method to implement an intelligent fault diagnosis system based on the ANN tool. They trained a long-short-term memory (LSTM) recurrent neural network (RNN) with the operation measurement signals of a wind turbine drivetrain diagnostics simulator (WTDDS). Therefore, they introduced a scheme to discover dependencies to both spatial and temporal circumstances plus potential faults. For industrial equipment, fault detection systems play a decisive role in production continuation. This importance becomes more apparent considering the complexity of operations in distillation columns. In 2019, Li et al. [11] published their research on fault diagnosis in a Depropanizer tower. They proposed a hybrid model based on convolutional neural networks (CNN) and deep auto-encoders (DAE) to classify and detect the operational faults in the vessel. They used simulation data to train and test the proposed model. Thanks to its hybrid nature, the introduced CNN-DAE method showed to be more powerful in feature extraction and classification compared to CNN, DAE, and deep belief network (DBN) methods. However, in many cases, the factors that are simplified in the simulations are the ones that cause errors in the system. Therefore, using simulation data solely could challenge the nature of this fault diagnostic system. Usually, distillation towers operate in steady-state operation conditions. Hence, the amplitude of affecting variables fluctuations is relatively slight. Despite their large values of available operation data, this stable operation limits the available labeled data for fault detection. In 2019, Li et al. [12] published an investigation proposing an intelligent anomaly identification approach based on a semi-supervised deep learning method. They implemented semi-supervised ladder networks (SSLN) based on a deep denoising autoencoder (DAE) to build an anomaly identification model with improved performance. In 2019, Maddah et al. [13] used a data modeling approach to analyze the working conditions of a steam boiler unit. They trained a data set with 95 operating points to an ANN and modeled the device performance dependencies on environmental parameters. Then, they used the response surface method (RSM) to optimize the boiler performance and introduced the optimal mode, leading to the highest efficiency. This study could be better if the authors used more powerful optimization methods, like PSO or GA (because of their ability to avoid getting locked in local optimum points), in their research. Shortage of labeled data is always a challenge in performing intelligent condition monitoring (CM) systems. In 2020, Li et al. [14] introduced a method of unsupervised learning to overcome this problem by representing it in a wind turbine case study. They performed this intelligent early anomaly detection structure in multiple steps. Firstly, they used unlabeled data to construct and pre-train a regular auto-encoder network with multiple restricted Boltzmann machines. Then, they fine-tuned the network parameters by transferring them into a deep small-world neural network (DSWNN) model. They compared the predictions of deep neural network (DNN) and deep belief network (DBN) with this combination of deep auto-encoder network and DSWNN, which showed this approach to be highly reliable in the accurate prediction of the wind turbine's dynamic behavior. However, it cannot be neglected that dynamic predictions may contain deviated points, which requires more advanced accuracy measurement methods for these cases. The applications of data modeling methods are not limited to production forecasting. These methods can also be used to predict consumption trends. In 2020, Yin et al. [15] forecasted the NG consumption trend in Myanmar by combining operational consumption data between 1990 and 2015 with supplementary data such as gross domestic product (GDP). They evaluated their predictions with the mean squared error (MSE) technique, which showed high accuracy. However, they could focus more on the developing industrial aspects, which neglecting them puts the reliability of the predictions under question. There are heated debates on the capability of different methods in industrial control and operation prediction. Each approach may be preferred depending on the expectations, like convergence pace, interpolating / extrapolating target area, and results' accuracy. In 2021, Jalanko et al. [16] published their research on three different models in dynamic modeling of an industrial ethylene splitter behavior. They used both simulated and operational data to develop and evaluate three modeling methods of subspace identification (SID), nonlinear autoregressive network with exogenous inputs (NARX), and recurrent neural network (RNN). They evaluated the results with the weighted mean squared error (WMSE) method. Concerning the convergence pace and prediction accuracy, the results revealed that the SID method is more reliable in prediction, especially in extrapolating the results. They also represented two adaptive strategies to enhance the training section in the system identification method. Having a brief comparison between the data modeling methods and discussing their abilities related to the expectations is one of the bold points of their investigations. However, they could add other factors like energy consumption and operation costs to the desired control parameters. Hydrocracking is one of the processes with in-time varying product requirements that determining the optimum operational points is essential. Due to the restricted ability of hydrocracking equipment for quick reaction and modification, optimizing the process using empirical methods or simulation models seems too idealistic. Dong-Hoon et al. [17] suggested an actor-critic reinforcement learning optimization technique in 2021 utilizing a Deep Neural Network (DNN) surrogate model, which was created from a validated mathematical model. They indicated that their model was highly accurate and that the suggested technique has the benefits of short response time, minimal computing load, and adaptability for online execution, all of which are crucial for real-world optimization problems. Multi-objective optimization algorithms have considerable potential for linking with deep learning models to predict the best operational points for petrochemical process plants. In 2021, Zapf et al. [18] used extracted process data from a refinery plant to train black-box and gray-box models and predict the process characteristics. They used a sequential-modular approach, fed by these models, to optimize the production margin and emissions. Their work showed the high capability of data-driven models in the prediction and optimization of in-field industrial process plants. Series, parallel, and series-parallel models are examples of hybrid modeling in petrochemical process simulation and optimization that combine the benefits of first principles and data-driven techniques. Wenjiang et al. [19] investigated the capability of these models in consistent optimization of petrochemical plants by modeling and optimization of a traditional hydrocracking unit using one first-principles model, one data-driven model, and three hybrid models. As a result, they divided the models into mechanism-dominated and data-dominated models based on their capacity for prediction rather than their structural characteristics. In addition, they developed the adaptive weighted hybrid model (AWHM) and achieved a better performance in prediction. Park et al. [20] integrated machine learning methods with optimization algorithms to predict and enhance steam flow in a commercial mixed butane distillation unit and minimize energy consumption consequently. They used a hold‐out cross‐validation method to ensure the accuracy of their model and then used it for a hyper‐parameter optimization approach. However, according to the structure of their work, these optimum results are not sensitive to the environmental and upstream conditions that affect the process in reality. By accurately modeling or recognizing the relevant Heat-Integrated Distillation Column (HIDC) composition of the fluid phase may be determined in petrochemical equipment. Abdul Jaleel et al. [21] presented an in-time HIDC modeling method system instead of relying on the traditional non-realistic steady-state models. They used HYSYS to model the process and MATLAB to run a Support Vector Regression (SVR) algorithm on the obtained dataset. Finally, they optimized the SVR variables using the PSO algorithm. They confirmed the high accuracy of this model with a case study and using multiple error measurement criteria. With the high standards of today, it is impossible to maintain product quality during the hydrocracking process using the classic feedback control techniques with their long response time and low accuracy. For an industrial hydrocracker, Iplik et al. [22] proposed a feed-forward model-based predictive control scheme. They experimented with state-space, auto-regressive exogenous (ARX), SVR, and DNN models. They found considerable increases in the quality of the product and energy efficiency after comparing the results with one another and with the site-measured data. The reviewed publications highlight diverse data modeling, optimization, and validation methods across various industrial fields. As mentioned before, traditional methods are often complex, time-consuming, and sometimes ineffective, making data-intensive applications attractive for optimizing operations. However, factors beyond operators' control impact distillation units, making a single optimal operation setting impractical, therefore, a flexible optimization in response to mandatory parameters is necessary. Despite the advancements, a research gap remains in developing a comprehensive control system that maintains ideal process conditions consistently. This research aims to design and implement a sapient optimizer system capable of enhancing processes under varying imposed conditions. Methodology The case study in this research is a de-Ethanizer unit located in a gas refinery that separates Ethane from the feed gas (Figure 1). The inlet gas is a sweetened multi-component dry gas that experienced Methane separation in earlier stages and now contains Ethane (C2) and heavier hydrocarbons (C2+). The distillation tower consists of 47 separator trays and the inlet feed line enters the 27th tray from the bottom. At the bottom of the column, a heat exchanger charged by low-pressure (LP) Steam applies thermal energy to the system to keep the lower-side temperature around 110°C. At the top of the tower, a liquid Propane condenser reduces the temperature of the released gas to about 10°C. This unit operates under various conditions for the inlet gas and the upstream units. The overarching goal is to reach a flexible optimization method for finding the best process control parameters in every potential working condition, ensuring maximum performance in real time. Here, a simulation model forecasts the process in a De-Ethanizer unit. Then, a data-driven method predicts and optimizes the process according to imposed conditions. Finally, prediction models use the generated optimum points to form a sapient optimizer system capable of forecasting the optimum operation for any feasible condition. The first step is to extract the affecting and objective parameters of the process with their allowable ranges. Then, all the possible working conditions are covered uniformly by simulating a factorial design of experiments (DoE) in Aspen HYSYS. Then, an ANN, whose structure is decided by evaluating the predictions of sample data, will learn the big dataset from simulations to predict the process. After that, the multi-objective optimization function is defined based on the problem expectations. In the next step, the PSO algorithm in factorial-designed conditions finds the best adjustable (control) parameters according to different combinations of the nonadjustable (imposed) circumstances. Finally, the resulting optimum points are trained to a separate set of individual ANNs, each responsible for predicting one control variable, to generate the optimum operation choices. Figure 2 depicts the overall architecture of the proposed methodology. The first step is to define the measurable input and output parameters for different stages of the study. Table 1 presents the involved input and output parameters along with their allowable range of change for the understudy De-Ethanizer unit with their nature and units of measurement. Table 1. Involved parameters No. Zone Index Description Range of operation Unit Control / Imposed parameter Adjustability Input / Output to … Min Max 1 st ANN Optimization 2 nd ANNs 1 Input feed Pi Feed pressure 30 35 bar Imposed Input Input Input 2 Ti Feed temperature 35 50 °C Imposed Input Input Input 3 Mi Feed flow 50 80 Ton/h Imposed Input Input Input 4 Ei Feed quality 30 40 % Imposed Input Input Input 5 Reboiler loop (bottom) Mp Bottom product flow 35 55 Ton/h Control Input Output Output 6 Ms Input LP steam flow 5 30 Ton/h Control Input Output Output 7 Mb Boil-up Ratio 0.7 10 - Control Input Output Output 8 Chiller / reflux (top) Mc Refrigerant fluid flow 2340 10750 Ton/h Control Input Output Output 9 Mr Reflux flow 35 150 Ton/h Control Input Output Output 10 Final product Mo Final product flow - - Ton/h output Output Output Output 11 Eo Final product quality - - % output Output Output Output Where the first to four rows include pressure, temperature, mass flow rate, and Ethane mass fraction in the inlet gas from the previous unit, respectively, these thermodynamic and chemical conditions of the feed gas are imposed on the process, and the control parameters are adjusted according to them in every process cycle. The five control parameters, which all fall under the mass flow type, are applied by pumps and valves placed in specific locations and adjust the desired conditions when manipulated. The two latter parameters are the product specifications to control the quality. The next step is to design the desired database with the factorial method and Aspen HYSIS simulations. This technique generated 5620 experiments to achieve uniform distribution in the feasible region. Figure 3 shows the schema of the used simulation model that simulated each of these experiments as a separate steady-state operation mode. The mentioned inputs could not independently vary in the simulation since it should converge all the petrochemical and thermo-dynamic equations simultaneously. The key point in implementing the simulations is that all the other affecting parameters should remain consistent during all experiments. Here, the temperatures of the Condenser and Reboiler sections were fixed at 10.3 and 111 °C, respectively. The generated dataset from simulations was validated with 50 operational data from a working similar unit in a gas refinery and showed an acceptable accuracy of 91.3% in average. In the next step, the predictive ANN algorithm uses the generated dataset to analyze the process. Multiple factors shape the structure of an ANN, including the shape form of the neural network, the number of hidden layers, and the number of neurons in each layer. Feed-forward (FF) and deep feed-forward (DFF) ANNs are long-standing members of the family whose operation generally follows the following rules: All neurons are fully connected. Activation flows from the input layer to the output without having a backward loop. There are one or more hidden layers between the input and output for FF or DFF neural networks. Each neuron in these networks receives values from the previous layer, processes them with the transferor or activation function, and passes the resulting values to the next layer. Here, the transferor function receives the sum of the weighted inputs and uses the bias value to produce the neuron output. The mechanism of a canonical neuron can be observed in Equation 1. The bias values and weights, pronounced as the learnable parameters, are related to the neurons and the links between them, respectively. The training operation, often the BP method for FF-ANNs, adjusts these parameters by updating them to predict the outputs based on the pre-learned data. Here, Levenberg-Marquardt (trainlm) is one of the most popular training functions used as a first-choice supervised learning algorithm. Another crucial factor in prediction accuracy is the activation or transferor function of the layers. There are multiple options for choosing the transfer function, and sigmoid functions (logsig, tansig, etc.) are basically the first choices for this purpose. MATLAB coding environment trained the ANN structures with the generated database from simulations. Firstly, the ANN structure with the best number of hidden layers, the number of neurons in each layer, and the transfer function in each layer should be defined. Therefore, the candidate configurations were trained three times with one specific sample dataset. Then, the most suitable structure was specified by comparing average R-squared, MSE, and MPE separately (Table 2). In the pre-processing step, the order of the data was randomized initially to prevent the formation of any unwanted patterns. The permissible range of all parameters was also normalized between [-1,+1], and the possible repetitive data were deleted to increase the training efficiency and the accuracy of the predictions. The next step is to create training, validation, and testing data sections. The dataset was divided into training, testing, and validation parts with a ratio of 70%, 15%, and 15%, respectively. Then, the new dataset trained MLP-ANN to predict the process and reveal the interrelationships between inputs and outputs. After calculating the coefficient of determination (R-squared) to ensure accuracy, the trained ANN was saved to fix the weights and biases. Figure 4 depicts the schema of the explained workflow of this step. Table 2. Selected ANN parameters in 1st stage of prediction Parameter Action zone Check Number of neurons Hidden layer 1 12 Hidden layer 2 7 Transfer function Hidden layer 1 Tansig Hidden layer 2 Tansg Training function ANN Levenberg-Marquardt Data division Train-Ratio 70 Val-Ratio 15 Test-Ratio 15 Divide mode Simple random Number of epochs ANN 1000 Performance Function MSE Goal 10e-7 Maximum fails 20 The PSO algorithm was employed to find the optimum operation states of the fractionation process. To ensure its functionality in finding optimum states, the written PSO code was first benchmarked with the Egg Crate function (Equation 2) as a multi-funnel function whose optimum point is known to be (0,0). Then, the algorithm was adjusted to the ranges of the current variables to find the best operation parameters for each combination of the mandatory inputs. The next task is to write the objective function before implementing the optimization algorithm. As mentioned before, the principal purpose of the optimization in this study is to increase profitability and reduce production costs simultaneously. Therefore, the objective function is considered as the difference between costs and revenues. Here, the recovery factor represents the profit. This parameter is the ratio of the total produced Ethane to the total Ethane in the input feed. These values are the product of the flow in the mass fraction of Ethane in that flow. The cost of the production process directly relates to the amount of consumed LP Steam and refrigerant liquid in the reboiler and condenser, respectively. Therefore, the algebraic sum of the profit and cost factors with the concord coefficients will form the objective function. Furthermore, to take the fixed operating costs into account, this function must be summed up with a fixed value (C) to increase the flexibility of the proposed solution method. Setting the objective function to zero when having the profit and cost factors on their mean value obtained the desired fixed coefficients. Since this algorithm inherently minimizes its objective function, this function was multiplied by -1 before being introduced to the algorithm. Finally, the objective function resulted to be as shown in Equation 3. The PSO algorithm is a population-based meta-heuristic optimization method that uses an evolutionary approach to calculate the optimum location vector for particles. This process creates multiple moving particles in the feasible region to use their location and speed, the best position experienced by each particle, and the best reported by the whole population. In this case, the PSO algorithm begins with creating the initial locations of the particles by assigning random values in the permissible range to 10-dimensional position vectors. Then, the cost function for each of these particles is calculated using the ANN predictions. After that, the algorithm locates the best particle with the lowest calculated amount for the objective function. In the next step, the velocity of the particles determines their location in the next iteration. Note that the mirror effect limits the location and speed of the particles to keep them in the allowable range. This operation repeats for a specified number of iterations, and the particle velocity is reduced in every step to achieve convergence. Equation 4 shows the method of determining particle positions, where W, C1, and C2 represent Inertia Weight, Personal Learning Coefficient, and Global Learning Coefficient, respectively. A hybrid method inks the optimization and prediction sections. This means the optimization values (the objective function and the particles' positions) were not calculated directly using mathematical equations but were recalled by the trained ANN and the dataset from the previous stages. Accordingly, the positions and the velocities were determined in the permissible range, and the objective function was calculated using the recalled ANN predictions throughout the code. Here, the particle positions and the predicted process model from the ANN were firstly de-normalized from the [-1,+1] range to the original form before being used by the PSO algorithm and calculating the objective function, which is because of the existing division operator in the function equations. Figure 5 illustrates the schema of the PSO method with further details. This research includes the optimization problem in two scenarios that differ in terms of input and output parameters. The first assumption is that operators have the authority to manipulate the pressure and temperature of the inlet feed by pre-processing treatments on the received gas (Scenario A). The second assumption is that no pre-processing treatment is accessible, and the inlet feed enters the fractionation unit as received from the previous process unit (Scenario B). Both scenarios require designing a loop in the optimization algorithm to repeat it several times. However, in both solutions, the elements of the particle position that refer to the mandatory parameters are fixed in the designed levels of experiments. Scenario A: If there are pre-processing facilities available to adjust the pressure and temperature of the received sweetened gas, the optimization process can be implemented in response to the inlet feed mass fraction and its mass flow rate, which are still mandatory. Therefore, by changing these two parameters in five levels through their allowable range ( Error! Reference source not found. ), 52=25 different optimization problems were defined and solved. Table 3 contains the parameters in the PSO algorithm. Table 3. PSO parameters in scenario A Parameter Name in code Check Population Size nPop 30 Inertia Weight w 5 Damping Ratio wdamp 0.9 Personal Learning Coefficient c1 2 Global Learning Coefficient c2 2 Iterations i 200 The outcome of this stage was stored in a 12x25 matrix which contains the best operation conditions based on various inlet feed mass fractions and mass flow rates. Hence, the optimum operation surfaces can be obtained by 3D plotting each available parameter concerning the two mandatory variables. Scenario B: Another potential approach in designing the optimizer system is to assume receiving inlet gas with no pre-processing treatments when all the four thermodynamic parameters of the inlet feed would not be adjustable to the operators. Here, pressure, temperature, mass flow, and mass fraction of the feed gas are varied in five equal steps in their permissible range, creating 5 4 =625 optimization problems. Therefore, the optimization process was repeated 625 times to cover all combinations of the four mandatory inputs and find the best operational parameters for each possible combination. The PSO parameters for this step were decided to be as mentioned in Table 4. Table 4. PSO parameters in scenario B Parameter Name in code Check Population Size nPop 40 Inertia Weight w 5 Damping Ratio wdamp 0.9 Personal Learning Coefficient c1 2 Global Learning Coefficient c2 2 Iterations i 150 The 625 optimal states obtained from the previous step created a 12x625 matrix. The final purpose is to predict the best operating conditions plus the conditions of the product based on the four mandatory parameters from the inlet feed. Therefore, the optimum feasible region was again predicted by modeling these optimum data in another set of ANNs. Here, the count of target parameters would be greater than that of the input. Hence, separate ANNs for each output were trained by this optimum dataset. At this stage, the four imposed parameters (rows 1 to 4 in Table 1) were considered inputs to predict the optimum value for the other ones (rows 5 to 11 in Table 1) individually. Therefore, the best control parameters that lead the operation to optimum production are predicted with this set of ANNs. Moreover, because the size of available data is much smaller than the first stage (625 compared to 5620), the training method is implemented in a while loop. This loop allowed reaching an acceptable accuracy in predictions, which was R-squared greater than or equal to 0.7. The ANN structure in this step is mentioned below in Table 5. The obtained eight ANNs can predict the best operation and production in response to mandatory circumstances. Therefore, this system can be pronounced as a flexible and wise optimizer system. Table 5. ANN parameters in 2nd stage of prediction Parameter Action zone Check Number of neurons Hidden layer 12 Transfer function Hidden layer tansig Training function ANN Levenberg Marquardt Data division TrainRatio 80 ValRatio 10 TestRatio 10 Divide mode Simple random Number of epochs ANN 1000 Performance Function MSE Goal 10e-7 Maximum fails 10 Evaluation In training the initial big dataset to the first ANN, MPE, MSE, and R-squared parameters evaluated the accuracy of predictions (Table 6). Moreover, Figure 6 and Figure 7 depict the performance validation for the trained ANN plus the accuracy of the predictions for each data division, respectively. Table 6. Prediction accuracy by trained ANN Evaluation parameter Product flow Product purity MPE 0.0228678822731286 0.0150541982466198 MSE 4.07192998150094e-05 3.25347716451295e-08 R 2 0.9999996446 0.9999978692 Scenario A: By converging the optimization process under the first scenario the best values for each control parameter can be plotted in response to the two considered mandatory inputs, which are the inlet feed mass fraction and its flow. Hence, interpolant surfaces with the cubic method fitted to the point clouds on the optimum operation surface for any desired parameter. Surface plots for optimum states of the cost function, product conditions (mass flow and mass fraction), and operation parameters (LP steam flow, refrigerant flow, reflux flow, bottom product flow, and boil-up ratio) are the available results. Figures 8 to 11 depict some of these optimum surfaces as examples. Scenario B: Here, the achieved enhancement by implementing the suggested wise system is evaluated. The optimization process was repeated 625 times, and the operation vectors' dimension is larger than the power of human perception. Therefore, showing the results in the form of plots and graphs would be impossible. However, the effectiveness of this optimization approach can be measured by evaluating the resulting enhancement by the optimization process. Here, the average cost function was calculated for the initial dataset with 5620 points and the optimum dataset with 625 points. The performance enhancement in the distillation unit resulting from the optimization process can be calculated as follows in Equation 5. Table 7. Optimum prediction accuracy Index Parameter description Prediction R-square Mp Bottom Product Flow (C2+) 0.77 Mr Reflux Loop - Mass Flow 0.75 Mc Refrigerant - Mass Flow 0.97 Mb Boil-up Ratio 0.65 Ms LP Steam - Mass Flow 0.72 Mo C2 - Mass Flow 0.91 Eo C2 - Phase Comp Mass Frac 0.85 Discussion As mentioned before, the design and implementation of a flexible/responsive optimizer control system for industrial units is a research gap in the literature. The proposed approach is not similar to the previously published literature. Therefore, the functionality and efficiency of the prediction and optimization steps are compared to peer research to have a more transparent overview of the results. The paper that Ma et al. [24] published is one of the closest studies to the present research regarding the implemented method and the practiced industrial unit. They modeled a high sulfur NG purification process in ProMax and simulated the experiments designed by the Uniform Design method. They selected eight parameters as input factors and five as output results. In that paper, the results were then trained to a BP-ANN, which was then used as the feasible region for GA optimization. Finally, they claimed that their approach could enhance the total energy consumption by 12.7% The experiments used in the present study provided a dataset with 5620 conditions, which is much larger than the 11 experiments used in the mentioned reference. Furthermore, Ma et al. selected eight parameters from many affecting ones in the whole refinery plant with various units. Therefore, there is no guarantee for the other factors to be fixed during the experiments, which causes the predictions to be unstable. However, the objected parameters in this study are from one fractionation unit, and all other affecting parameters have a fixed value. Another bold point is considering a practical method for selecting the optimization parameters. There are many dependencies between the measurable parameters in fractionation columns that cannot vary independently. Hence, picking parameters regardless of the relationships between them is not a technically proper approach. In the present research, the optimization parameters are all from operation factors that can be measured and manipulated independently. Moreover, the main improvement in the research approach is that the optimization results (625 conditions) were trained to second-stage ANNs to predict the optimum feasible region. Here, the resulting ANNs can suggest the optimum operation region as a continuous region. This is while in the peer research, the optimization results only represent one single optimum point for the operation. The reference paper presented the accuracy of the predictions for two different experiments separately. To have a better comparison between these two studies, the average relative error is calculated for two random experiments to be compared against peer results in the reference, (Table 8). Table 8. Prediction accuracy, reference vs present study Point 1 Point 2 Average Reference [24] 1.464% 2.186 1.825% Present study 0.0106% 3.9416E-03% 3.30816E-03% The effectiveness of the optimization process is also investigated here. The total energy consumption in the reference is claimed to have experienced a 12.7% reduction in the reference study. However, because consumed energy in fractionation columns has a direct relationship with the amount of consumed LP Steam and Refrigerant liquid, the reduction in the use of these resources would be a proper target for comparison. Hence, by calculating the average flow of LP Steam and Refrigerant liquid before and after the optimization process (5620 initial experiments and 625 optimum states, respectively) the enhancement in energy consumption is anticipated. Furthermore, the total enhancement resulting from the present study is calculated as the weighted average considering the cost function in Equation 3 (Table 9). Table 9. Enhancement in energy consumption, reference vs present study Target Optimization enhancement Total enhancement Reference [24] Total energy consumption 12.7% 12.7% Present study Consumed energy to maintain LP Steam flow 70.66% 58.21% Consumed energy to maintain Refrigerant liquid flow 57.65% Ultimately, this study introduced a responsive, flexible, and intelligent optimization system. Based on the obtained results, this data-driven system is able to suggest the control parameters of distillation towers (in this case, a De-Ethanizer tower) according to the measurable imposed parameters or any other mandatory conditions from outside. Declarations conflicts of interest The author declares no conflict of interest regarding the present research. Author Contribution This paper originates from an individual course project that I expanded into a journal paper format. All findings presented are original, and I am fully committed to transparency in my methodology. I would be pleased to provide further details, including access to my code, simulation files, database, and my professor’s contact information for verification, upon request. Acknowledgement The author wishes to thank Mr. Arash Ara (Eng.) for his kind cooperation and guidance in the simulation process. Data availability statement The supporting data for the findings of this study are available from the author upon reasonable request. References Green, D.W. and M.Z. Southard, Perry's chemical engineers' handbook . 2019: McGraw-Hill Education. Beychok, M., AN ALGEBRAIC SOLUTION OF MCCABE-THIELE DIAGRAM. Chemical Engineering Progress, 1951. 47 (5): p. 265-269. Masnadi, M.S., et al., Statistical proxy modeling for life cycle assessment and energetic analysis. Energy, 2020. 194 : p. 116882. Bahar, A., et al., Artificial neural network estimator design for the inferential model predictive control of an industrial distillation column. Industrial & engineering chemistry research, 2004. 43 (19): p. 6102-6111. Corona, F., et al., Data-derived analysis and inference for an industrial deethanizer. Industrial & engineering chemistry research, 2012. 51 (42): p. 13732-13742. Salooki, M.K., et al., Design of neural network for manipulating gas refinery sweetening regenerator column outputs. Separation and purification technology, 2011. 82 : p. 1-9. Ramli, N.M., et al., Online composition prediction of a debutanizer column using artificial neural network. Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 2017. 36 (2): p. 153-174. Song, X., et al., Time-series well performance prediction based on Long Short-Term Memory (LSTM) neural network model. Journal of Petroleum Science and Engineering, 2020. 186 : p. 106682. Fatima, S.A., et al., Prediction of industrial debutanizer column compositions using data-driven ANFIS-and ANN-based approaches. Neural Computing and Applications, 2021: p. 1-13. Yang, R., et al., Rotating machinery fault diagnosis using long-short-term memory recurrent neural network. IFAC-PapersOnLine, 2018. 51 (24): p. 228-232. Li, C., et al., Fault diagnosis for distillation process based on CNN–DAE. Chinese Journal of Chemical Engineering, 2019. 27 (3): p. 598-604. Li, C., et al., Anomaly identification with few labeled data in the distillation process based on semisupervised ladder networks. Process Safety Progress, 2020: p. e12206. Maddah, H., et al., Modeling and efficiency optimization of steam boilers by employing neural networks and response-surface method (RSM). Mathematics, 2019. 7 (7): p. 629. Li, M., et al., Anomaly Detection of Wind Turbines Based on Deep Small-World Neural Network. Applied Sciences, 2020. 10 (4): p. 1243. Yin, K.S. and S.S. Htay. Prediction of Natural Gas Final Consumption using Artificial Neural Networks . in 2020 International Conference on Advanced Information Technologies (ICAIT) . 2020. IEEE. Jalanko, M., et al., Adaptive System Identification of Industrial Ethylene Splitter: A Comparison of Subspace Identification and Artificial Neural Networks. Computers & Chemical Engineering, 2021: p. 107240. Oh, D.-H., et al., Actor-critic reinforcement learning to estimate the optimal operating conditions of the hydrocracking process. Computers & Chemical Engineering, 2021. 149 . Zapf, F. and T. Wallek, Case-study of a flowsheet simulation using deep-learning process models for multi-objective optimization of petrochemical production plants. Computers & Chemical Engineering, 2022. 162 . Song, W., et al., Adaptive Weighted Hybrid Modeling of Hydrocracking Process and Its Operational Optimization. Industrial & Engineering Chemistry Research, 2021. 60 (9): p. 3617-3632. Park, H., et al., A framework for energy optimization of distillation process using machine learning‐based predictive model. Energy Science & Engineering, 2022. 10 (6): p. 1913-1924. Jaleel, E.A., S.M. Anzar, and A.M. Koya, Machine learning based system identification of a realistic heat integrated distillation column using particle swarm optimization. Chemical Engineering Communications, 2022: p. 1-21. Iplik, E., I. Aslanidou, and K. Kyprianidis, A Feedforward Model Predictive Controller for Optimal Hydrocracker Operation. Processes, 2022. 10 (12). fuer kontinuierliche Regelungen, D.R.L., Deep Reinforcement Learning for Continuous Control. Ma, L., et al., Energy consumption optimization of high sulfur natural gas purification plant based on back propagation neural network and genetic algorithms. Energy Procedia, 2017. 105 : p. 5166-5171. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5441475","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":377496642,"identity":"b6fb247c-2db9-4a39-94dd-21276359eaed","order_by":0,"name":"Behzad 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17:23:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5441475/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5441475/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":71633024,"identity":"d496a81c-0731-479c-b1e9-8e29562a01e2","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":66656,"visible":true,"origin":"","legend":"\u003cp\u003eSchematics of fractionation system\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/8685abe1693d63c77d90ccbb.png"},{"id":71633038,"identity":"8780ef36-509a-4b47-bb17-8727d52b4c3f","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":96468,"visible":true,"origin":"","legend":"\u003cp\u003eThe high-level methodology schematics\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/3d4cd047ca31c93e4a71cbda.png"},{"id":71633042,"identity":"8fa78146-5446-48cf-bae1-3d9071a92ea1","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":35073,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation of the De-Ethanizer unit\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/c1c763f59774e4d6b701b888.png"},{"id":71633027,"identity":"5f5e0323-5ff6-4cbc-b27f-1d30908e7558","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":122671,"visible":true,"origin":"","legend":"\u003cp\u003eThe schema of the ANN algorithm\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/e9859e906f7911a549775e2e.png"},{"id":71633041,"identity":"0b5440cd-a6bc-4656-b594-d71df1e438bd","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":94507,"visible":true,"origin":"","legend":"\u003cp\u003eThe schema of the PSO algorithm\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/1873c42da568079326601e06.png"},{"id":71633045,"identity":"7419aa92-822f-4707-b060-6ffd01a76029","added_by":"auto","created_at":"2024-12-17 09:49:19","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":46690,"visible":true,"origin":"","legend":"\u003cp\u003eValidation performance\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/6ecca71604a392899172cd65.png"},{"id":71633033,"identity":"e1caf392-6e48-4406-a088-578ccd470aa0","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":85381,"visible":true,"origin":"","legend":"\u003cp\u003eAccuracy of predictions\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/d0eb3f6e36773ced8054c64d.png"},{"id":71633039,"identity":"8ad9a7bc-c21b-4bd4-a526-ffcd89db3251","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":240987,"visible":true,"origin":"","legend":"\u003cp\u003eBest cost function vs feed mass fraction and feed mass flow rate\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/fc13985a48315e511df55c56.png"},{"id":71634706,"identity":"f8948dbf-d700-446e-95e3-fc794632c869","added_by":"auto","created_at":"2024-12-17 09:57:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":220625,"visible":true,"origin":"","legend":"\u003cp\u003eBest Ethane product mass fraction vs feed mass fraction and feed mass flow rate\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/d652cc39fa997a34c97a56c0.png"},{"id":71635089,"identity":"7b52e14c-ff7f-46e8-88ce-22363ff33f85","added_by":"auto","created_at":"2024-12-17 10:05:18","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":267557,"visible":true,"origin":"","legend":"\u003cp\u003eBest Ethane product mass flow rate vs feed mass fraction and feed mass flow rate\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/0c812d3747810c8799f3efae.png"},{"id":71633025,"identity":"18bc529e-312b-4001-a19a-e4e5087d8ccf","added_by":"auto","created_at":"2024-12-17 09:49:18","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":137466,"visible":true,"origin":"","legend":"\u003cp\u003eBest refrigerant mass flow rate vs feed mass fraction and feed mass flow rate\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/5e74cf144283ebc460adfb3e.png"},{"id":72294059,"identity":"5c571e68-5caf-467f-954d-66f4da95821b","added_by":"auto","created_at":"2024-12-24 18:46:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2005524,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5441475/v1/15180bf2-5218-4f36-8afe-9e527b204768.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Design and Implementation of an AI-Powered Sapient System for Maximum Efficiency of Fractionation Operations","fulltext":[{"header":"Introduction","content":"\u003cp\u003eGas refineries typically consist of interconnected process units, each having a specific role in carrying out a portion of the refining process. Crude gas (or so-called sour gas), coming from the off-shore platforms, first enters the gas reception facilities to separate the associated phases and calm the flow. The sweetening units separate some mingled components, such as light hydrocarbon compounds, and stabilize the accompanying gas condensate. Methane is the main product of the gas refinery plants, while Butane, Propane, and Ethane are some of the other by-products.\u003c/p\u003e\n\u003cp\u003eDistillation facilities operate based on fundamental thermodynamic principles to produce various purified products by separating different hydrocarbons from an untreated feed. These units comprise three main sections: the process column (tower), the reboiler loop, and the reflux cycle. Fractionator trays are strategically installed at different heights within the process towers to facilitate the separation of products according to their boiling points. The multi-component mixture feed is introduced into the distillation tower at an upper-middle point, while low-pressure (LP) steam supplies the necessary heat to the reboiler system. The reboiler applies heat from the bottom of the tower, creating a temperature gradient with the hottest tray at the bottom and the coolest at the top. This configuration allows lighter components to be collected from the top of the tower. An external drum and reflux loop further enhance separation by cooling and condensing vapors. If the top purified product contains any heavier components, they accumulate in a pressure tank, known as the reflux drum, and are returned to the process tower. The schematics of a de-Ethanizer modification of this unit are illustrated in Figure 1.\u003c/p\u003e\n\u003cp\u003eAchieving higher quality and higher flow of condensed Ethane with lower energy consumption is desirable. To ensure optimal performance, designers must consider dimensional, thermodynamic, chemical engineering, and metallurgical aspects. For simple feeds, analytical methods such as the McCabe-Thiele method or the Fenske equation are employed\u0026nbsp;[1, 2], while multi-component feeds typically necessitate the use of simulation models such as Aspen HYSYS.\u0026nbsp;However, because of the complexity of the process and the high number of independent parameters with non-linear relationships, it is too difficult or time-consuming to analyze the process explicitly or to use computational methods in real-time decisions. Hence, the solution appears to lie in employing artificial intelligence (AI) approaches to construct a coherent model of optimal process control that considers the complex interrelationships among the system\u0026apos;s characteristics. These methods can fill the gap in the accurate and optimal execution of the designed process by enhancing the operation and amending product purity, equipment health, fuel consumption, energy efficiency, and environmental pollution.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSoft computing and data modeling approaches have been increasingly employed in predicting the operation of distillation columns. The publications mostly include prediction, fault diagnosis, optimization, and operation control. The popularity of inferential approaches for process prediction can be attributed to their capacity to uncover correlations between parameters. Masnadi et al. [3] introduced a general data-driven framework to develop a statistical proxy model. They applied this methodology in the bottom-up life-cycle assessment (LCA) of an acid gas removal (AGR) unit. A large database comprising over 25000 simulated trials trained a reduced-order (RO) model to forecast the energy usage and product compositions. To assess the correctness of their findings, they employed the mean absolute percentage deviation (MAPD) evaluation technique. Compared to standard models, the aforementioned simple proxy model needed fewer input parameters and produced practically instantaneous predictions with great accuracy. However, since the predictive model is usually not used alone, their research could be more comprehensive by adding another practical section, such as optimization.\u003c/p\u003e\n\u003cp\u003eAmong various data modeling methods, artificial neural networks (ANNs) have been one of the favorites of many researchers. Bahar et al. [4] published their research to dynamically predict product compositions based on the temperature in various points of a De-Ethanizer column. They used the backward propagation (BP) method to train a multilayer perceptron (MLP) ANN with simulation data; and then fed it with a model predictive controller (MPC) to estimate the product chemical compositions based on temperature measurements. They evaluated predicted and simulated dynamic plots of the bottom and top compositions in response to the reflux and feed rate. They proved that their represented inferential composition control is reliable in predicting the product compositions with acceptable performance. However, they could improve their work by focusing on multiple outputs.\u003c/p\u003e\n\u003cp\u003eThe first step to implementing a data model with a firm base is deciding the most efficient methods to model, analyze, and visualize the data. Corona et al. [5] investigated the effectiveness of two different ANN methods in analyzing the data from a de-Ethanizer column. They represented a brief discussion on the Self-Organizing ability of Map (SOM) and MLP methods in modeling the fractionation process. They foretold the process modes with an unsupervised clustering technique in the SOM approach and then developed an MLP to cope with time delay matter and instrumentation costs. Their research represented a strategy to model the process of their achievements; however, it could have more clarification on the mechanism of the prediction methods.\u003c/p\u003e\n\u003cp\u003eSolooki et al. [6]\u0026nbsp; represented a method based on FF-ANNs to predict the collection outputs of the regenerator columns in a gas sweetening unit. For this purpose, they trained 145 experimental data to an ANN, and the results showed that ANNs can accurately predict the operation of these industrial units. Although using industrial data is one of the strengths of their work, they could add simulation data to have a firmer base for their study because the volume of their operational database is considerably limited.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBecause online monitoring of chemical components of the products in distillation towers is technically challenging, prediction of these compounds using data analysis methods is becoming popular among many researchers. Ramli et al. [7] used an ANN to predict the chemical composition of products in a Debutanizer tower. They combined the open-loop and closed-loop online data with the simulation results as three data sources in their research. However, since the column has many surrounding variables, important affecting ones were determined utilizing principal component (PCA) and partial least square (PLS) analyses before training the ANN. Eventually, they used the root mean square error (RMSE) to evaluate the model and then utilized the mentioned data to train, validate, and test the ANN. The highly accurate results with low amounts of errors between the predictions and the actual data, as the strength of their work, show that the ANN method is a reliable in-time inferential estimator for the product composition in the fractionation towers. However, mixing data from three completely different sources and training them in a single ANN seems like a risky decision because the errors and deviations of these sources can vary a lot, which could lead the ANN to have faults in its predictions.\u003c/p\u003e\n\u003cp\u003eConcerning the integrated relationship between environmental constraints and conditions with facilities and other parameters, predicting the production trend is another issue of interest in applications of industrial data-based algorithms. Song et al. [8] published a paper on forecasting the production of fractured horizontal wells in a volcanic reservoir. They trained a long short-term memory (LSTM) ANN, whose configuration was optimized via particle swarm optimization (PSO) algorithm. Finally, they evaluated the mentioned method through two cases by comparing its performance with traditional ANNs, time-series forecasting approaches, and conventional decline curves.\u003c/p\u003e\n\u003cp\u003eDifferent methods predict the behavior of industrial units, each with its strengths and weaknesses. One of the issues in predicting refinery units is the limited size of data and the need to use methods that are most efficient with small databases. Fatima et al. [9]\u0026nbsp; examined the ability of the adaptive neuro-fuzzy inference systems (ANFIS) technique to model and predict the operation of a Debutanizer column with limited data. They trained an ANFIS algorithm with the actual operation data of the unit and compared its generalization performance with regular ANN. Regarding root mean square error (RMSE) criteria, the ANFIS method demonstrated a better prediction performance when training data samples were limited.\u003c/p\u003e\n\u003cp\u003eOne of the advantages of modeling industrial equipment data is the possibility of predicting errors and preventing unwanted stops or accidents. In many cases, fault diagnosis before failure occurs is crucial for industrial equipment. Determining an efficient strategy for preventive maintenance (PM) makes it possible to avoid financial and even human damage due to cessation of operations. In\u0026nbsp;2018,\u0026nbsp;Yang et al.\u0026nbsp;[10]\u0026nbsp;proposed a method to implement an intelligent fault diagnosis system based on the ANN tool. They trained\u0026nbsp;a long-short-term memory (LSTM) recurrent neural network (RNN) with the operation measurement signals\u0026nbsp;of a wind turbine drivetrain diagnostics simulator (WTDDS). Therefore, they introduced a scheme to discover dependencies to both spatial and temporal circumstances plus potential faults.\u003c/p\u003e\n\u003cp\u003eFor industrial equipment, fault detection systems play a decisive role in production continuation. This importance becomes more apparent considering the complexity of operations in distillation columns. In 2019, Li\u0026nbsp;et al.\u0026nbsp;[11]\u0026nbsp;published their research on fault diagnosis in a Depropanizer tower. They proposed a hybrid model based\u0026nbsp;on convolutional neural networks (CNN) and deep auto-encoders (DAE) to classify and detect the operational faults in the vessel. They used simulation data to train and test the proposed model. Thanks to its hybrid nature, the introduced CNN-DAE method showed to be more powerful in feature extraction and classification compared to CNN, DAE, and deep belief network (DBN) methods. However, in many cases, the factors that are simplified in the simulations are the ones that cause errors in the system. Therefore, using simulation data solely could challenge the nature of this fault diagnostic system.\u003c/p\u003e\n\u003cp\u003eUsually, distillation towers operate in steady-state operation conditions. Hence, the amplitude of affecting variables fluctuations is relatively slight. Despite their large values of available operation data, this stable operation limits the available labeled data for fault detection. In 2019, Li et\u0026nbsp;al.\u0026nbsp;[12]\u0026nbsp;published\u0026nbsp;an investigation proposing an intelligent anomaly identification approach based on a semi-supervised deep learning method. They implemented semi-supervised ladder networks (SSLN) based on a deep denoising autoencoder (DAE) to build an anomaly identification model with improved performance.\u003c/p\u003e\n\u003cp\u003eIn 2019, Maddah et al.\u0026nbsp;[13]\u0026nbsp;used\u0026nbsp;a data modeling approach to analyze the working conditions of a steam boiler unit. They trained a data set with 95 operating points to an ANN and modeled the device performance dependencies on environmental parameters. Then, they used the response surface method (RSM) to optimize the boiler performance and introduced the optimal mode, leading to the highest efficiency. This study could be better if the authors used more powerful optimization methods, like PSO or GA (because of their ability to avoid getting locked in local optimum points), in their research.\u003c/p\u003e\n\u003cp\u003eShortage of labeled data is always a challenge in performing intelligent condition monitoring (CM) systems. In 2020, Li et al.\u0026nbsp;[14]\u0026nbsp;introduced a method of unsupervised learning to overcome this problem by representing it in a wind turbine case study. They performed this intelligent early anomaly detection structure in multiple steps. Firstly, they used unlabeled data to construct and pre-train a regular auto-encoder network with multiple restricted Boltzmann machines. Then, they fine-tuned the network parameters by transferring them into a deep small-world neural network (DSWNN) model. They compared the predictions of deep neural network (DNN) and deep belief network (DBN) with this combination of deep auto-encoder network and DSWNN, which showed this approach to be highly reliable in the accurate prediction of the wind turbine\u0026apos;s dynamic behavior. However, it cannot be neglected that dynamic predictions may contain deviated points, which requires more advanced accuracy measurement methods for these cases.\u003c/p\u003e\n\u003cp\u003eThe applications of data modeling methods are not limited to production forecasting. These methods can also be used to predict consumption trends. In 2020, Yin et al.\u0026nbsp;[15]\u0026nbsp;forecasted the NG consumption trend in Myanmar by combining operational consumption data between 1990 and 2015 with supplementary data such as gross domestic product (GDP). They evaluated their predictions with the mean squared error (MSE) technique, which showed high accuracy. However, they could focus more on the developing industrial aspects, which neglecting them puts the reliability of the predictions under question.\u003c/p\u003e\n\u003cp\u003eThere are heated debates on the capability of different methods in industrial control and operation prediction. Each approach may be preferred depending on the expectations, like convergence pace, interpolating / extrapolating target area, and results\u0026apos; accuracy. In 2021, Jalanko et al.\u0026nbsp;[16]\u0026nbsp;published their research on three different models in dynamic modeling of an industrial ethylene splitter behavior. They used both simulated and operational data to develop and evaluate three modeling methods of subspace identification (SID), nonlinear autoregressive network with exogenous inputs (NARX), and recurrent neural network (RNN). They evaluated the results with the weighted mean squared error (WMSE) method. Concerning the convergence pace and prediction accuracy, the results revealed that the SID method is more reliable in prediction, especially in extrapolating the results. They also represented two adaptive strategies to enhance the training section in the system identification method. Having a brief comparison between the data modeling methods and discussing their abilities related to the expectations is one of the bold points of their investigations. However, they could add other factors like energy consumption and operation costs to the desired control parameters.\u003c/p\u003e\n\u003cp\u003eHydrocracking is one of the processes with in-time varying product requirements that determining the optimum operational points is essential. Due to the restricted ability of hydrocracking equipment for quick reaction and modification, optimizing the process using empirical methods or simulation models seems too idealistic. Dong-Hoon et al.\u0026nbsp;[17]\u0026nbsp;suggested an actor-critic reinforcement learning optimization technique in 2021 utilizing a Deep Neural Network (DNN) surrogate model, which was created from a validated mathematical model. They indicated that their model was highly accurate and that the suggested technique has the benefits of short response time, minimal computing load, and adaptability for online execution, all of which are crucial for real-world optimization problems.\u003c/p\u003e\n\u003cp\u003eMulti-objective optimization algorithms have considerable potential for linking with deep learning models to predict the best operational points for petrochemical process plants. In 2021, Zapf et al. [18] used extracted process data from a refinery plant to train black-box and gray-box models and predict the process characteristics. They used a sequential-modular approach, fed by these models, to optimize the production margin and emissions. Their work showed the high capability of data-driven models in the prediction and optimization of in-field industrial process plants.\u003c/p\u003e\n\u003cp\u003eSeries, parallel, and series-parallel models are examples of hybrid modeling in petrochemical process simulation and optimization that combine the benefits of first principles and data-driven techniques. Wenjiang et al. [19] investigated the capability of these models in consistent optimization of petrochemical plants by modeling and optimization of a traditional hydrocracking unit using one first-principles model, one data-driven model, and three hybrid models. As a result, they divided the models into mechanism-dominated and data-dominated models based on their capacity for prediction rather than their structural characteristics. In addition, they developed the adaptive weighted hybrid model (AWHM) and achieved a better performance in prediction.\u003c/p\u003e\n\u003cp\u003ePark et al. [20] integrated machine learning methods with optimization algorithms to predict and enhance steam flow in a commercial mixed butane distillation unit and minimize energy consumption consequently. They used a hold‐out cross‐validation method to ensure the accuracy of their model and then used it for a hyper‐parameter optimization approach. However, according to the structure of their work, these optimum results are not sensitive to the environmental and upstream conditions that affect the process in reality.\u003c/p\u003e\n\u003cp\u003eBy accurately modeling or recognizing the relevant Heat-Integrated Distillation Column (HIDC) composition of the fluid phase may be determined in petrochemical equipment. Abdul Jaleel et al. [21] presented an in-time HIDC modeling method system instead of relying on the traditional non-realistic steady-state models. They used HYSYS to model the process and MATLAB to run a Support Vector Regression (SVR) algorithm on the obtained dataset. Finally, they optimized the SVR variables using the PSO algorithm. They confirmed the high accuracy of this model with a case study and using multiple error measurement criteria.\u003c/p\u003e\n\u003cp\u003eWith the high standards of today, it is impossible to maintain product quality during the hydrocracking process using the classic feedback control techniques with their long response time and low accuracy. For an industrial hydrocracker, Iplik et al. [22] proposed a feed-forward model-based predictive control scheme. They experimented with state-space, auto-regressive exogenous (ARX), SVR, and DNN models. They found considerable increases in the quality of the product and energy efficiency after comparing the results with one another and with the site-measured data.\u003c/p\u003e\n\u003cp\u003eThe reviewed publications highlight diverse data modeling, optimization, and validation methods across various industrial fields. As mentioned before, traditional methods are often complex, time-consuming, and sometimes ineffective, making data-intensive applications attractive for optimizing operations. However, factors beyond operators\u0026apos; control impact distillation units, making a single optimal operation setting impractical, therefore, a flexible optimization in response to mandatory parameters is necessary. Despite the advancements, a research gap remains in developing a comprehensive control system that maintains ideal process conditions consistently. This research aims to design and implement a sapient optimizer system capable of enhancing processes under varying imposed conditions.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eThe case study in this research is a de-Ethanizer unit located in a gas refinery that separates Ethane from the feed\u0026nbsp;gas (Figure 1). The\u0026nbsp;inlet gas is a sweetened multi-component dry gas that experienced Methane separation in earlier stages and now contains Ethane (C2) and heavier hydrocarbons (C2+). The distillation tower consists of 47 separator trays and the inlet feed line enters the 27th tray from the bottom. At the bottom of the column, a heat exchanger charged by low-pressure (LP) Steam applies thermal energy to the system to keep the lower-side temperature around 110\u0026deg;C. At the top of the tower, a liquid Propane condenser reduces the temperature of the released gas to about 10\u0026deg;C. This unit operates under various conditions for the inlet gas and the upstream units. The overarching goal is to reach a flexible optimization method for finding the best process control parameters in every potential working condition, ensuring maximum performance in real time. Here, a simulation model forecasts the process in a De-Ethanizer unit. Then, a data-driven method predicts and optimizes the process according to imposed conditions. Finally, prediction models use the generated optimum points to form a sapient optimizer system capable of forecasting the optimum operation for any feasible condition.\u003c/p\u003e\n\u003cp\u003eThe first step is to extract the affecting and objective parameters of the process with their allowable ranges. Then, all the possible working conditions are covered uniformly by simulating a factorial design of experiments (DoE) in Aspen HYSYS. Then, an ANN, whose structure is decided by evaluating the predictions of sample data, will learn the big dataset from simulations to predict the process. After that, the multi-objective optimization function is defined based on the problem expectations. In the next step, the PSO algorithm in factorial-designed conditions finds the best adjustable (control) parameters according to different combinations of the nonadjustable (imposed) circumstances. Finally, the resulting optimum points are trained to a separate set of individual ANNs, each responsible for predicting one control variable, to generate the optimum operation choices. Figure 2 depicts the overall architecture of the proposed methodology.\u003c/p\u003e\n\u003cp\u003eThe first step is to define the measurable input and output parameters for different stages of the study. Table 1 presents the involved input and output parameters along with their allowable range of change for the understudy De-Ethanizer unit with their nature and units of measurement.\u003c/p\u003e\n\u003cp\u003eTable 1. Involved parameters\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"576\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003eNo.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eZone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eIndex\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 69px;\"\u003e\n \u003cp\u003eRange of operation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eUnit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eControl / Imposed parameter\u003c/p\u003e\n \u003cp\u003eAdjustability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 174px;\"\u003e\n \u003cp\u003eInput / Output to \u0026hellip;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003eMin\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003eMax\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003e1\u003csup\u003est\u003c/sup\u003e ANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOptimization\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e2\u003csup\u003end\u003c/sup\u003e ANNs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"4\" valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eInput feed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003ePi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eFeed pressure\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003ebar\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eImposed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eTi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eFeed temperature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003e\u0026deg;C\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eImposed\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eFeed flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eTon/h\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eImposed\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eEi\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eFeed quality\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003e%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eImposed\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"3\" valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eReboiler loop\u003c/p\u003e\n \u003cp\u003e(bottom)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eBottom product flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eTon/h\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eControl\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eInput LP steam flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eTon/h\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eControl\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eBoil-up Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e0.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eControl\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eChiller / reflux (top)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMc\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eRefrigerant fluid flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e2340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e10750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eTon/h\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eControl\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMr\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eReflux flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eTon/h\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eControl\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eFinal product\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eFinal product flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003eTon/h\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eoutput\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 30px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eEo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003eFinal product quality\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 36px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003e%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 70px;\"\u003e\n \u003cp\u003eoutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 48px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eWhere the first to four rows include pressure, temperature, mass flow rate, and Ethane mass fraction in the inlet gas from the previous unit, respectively, these thermodynamic and chemical conditions of the feed gas are imposed on the process, and the control parameters are adjusted according to them in every process cycle. The five control parameters, which all fall under the mass flow type, are applied by pumps and valves placed in specific locations and adjust the desired conditions when manipulated. The two latter parameters are the product specifications to control the quality.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe next step is to design the desired database with the factorial method and Aspen HYSIS simulations. This technique generated 5620 experiments to achieve uniform distribution in the feasible region. Figure 3 shows the schema of the used simulation model that simulated each of these experiments as a separate steady-state operation mode. The mentioned inputs could not independently vary in the simulation since it should converge all the petrochemical and thermo-dynamic equations simultaneously. The key point in implementing the simulations is that all the other affecting parameters should remain consistent during all experiments. Here, the temperatures of the Condenser and Reboiler sections were fixed at 10.3 and 111 \u0026deg;C, respectively. The generated dataset from simulations was validated with 50 operational data from a working similar unit in a gas refinery and showed an acceptable accuracy of 91.3% in average.\u003c/p\u003e\n\u003cp\u003eIn the next step, the predictive ANN algorithm uses the generated dataset to analyze the process. Multiple factors shape the structure of an ANN, including the shape form of the neural network, the number of hidden layers, and the number of neurons in each layer. Feed-forward (FF) and deep feed-forward (DFF) ANNs are long-standing members of the family whose operation generally follows the following rules:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eAll neurons are fully connected.\u003c/li\u003e\n \u003cli\u003eActivation flows from the input layer to the output without having a backward loop.\u003c/li\u003e\n \u003cli\u003eThere are one or more hidden layers between the input and output for FF or DFF neural networks.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eEach neuron in these networks receives values from the previous layer, processes them with the transferor or activation function, and passes the resulting values to the next layer. Here, the transferor function receives the sum of the weighted inputs and uses the bias value to produce the neuron output. The mechanism of a canonical neuron can be observed in Equation 1.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"614\" height=\"20\"\u003e\u003c/p\u003e\n\u003cp\u003eThe bias values and weights, pronounced as the learnable parameters, are related to the neurons and the links between them, respectively. The training operation, often the BP method for FF-ANNs, adjusts these parameters by updating them to predict the outputs based on the pre-learned data. Here, Levenberg-Marquardt (trainlm) is one of the most popular training functions used as a first-choice supervised learning algorithm. Another crucial factor in prediction accuracy is the activation or transferor function of the layers. There are multiple options for choosing the transfer function, and sigmoid functions (logsig, tansig, etc.) are basically the first choices for this purpose.\u003c/p\u003e\n\u003cp\u003eMATLAB coding environment trained the ANN structures with the generated database from simulations. Firstly, the ANN structure with the best number of hidden layers, the number of neurons in each layer, and the transfer function in each layer should be defined. Therefore, the candidate configurations were trained three times with one specific sample dataset. Then, the most suitable structure was specified by comparing average R-squared, MSE, and MPE separately (Table 2). In the pre-processing step, the order of the data was randomized initially to prevent the formation of any unwanted patterns. The permissible range of all parameters was also normalized between [-1,+1], and the possible repetitive data were deleted to increase the training efficiency and the accuracy of the predictions. The next step is to create training, validation, and testing data sections. The dataset was divided into training, testing, and validation parts with a ratio of 70%, 15%, and 15%, respectively. Then, the new dataset trained MLP-ANN to predict the process and reveal the interrelationships between inputs and outputs. After calculating the coefficient of determination (R-squared) to ensure accuracy, the trained ANN was saved to fix the weights and biases. Figure 4 depicts the schema of the explained workflow of this step.\u003c/p\u003e\n\u003cp\u003eTable 2. Selected ANN parameters in 1st stage of prediction\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eAction zone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eCheck\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eNumber of neurons\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eHidden layer 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eHidden layer 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTransfer function\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eHidden layer 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTansig\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eHidden layer 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTansg\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTraining function\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eLevenberg-Marquardt\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"4\" valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eData division\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTrain-Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eVal-Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTest-Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eDivide mode\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eSimple random\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eNumber of epochs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003ePerformance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eFunction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eGoal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e10e-7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eMaximum fails\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe PSO algorithm was employed to find the optimum operation states of the fractionation process. To ensure its functionality in finding optimum states, the written PSO code was first benchmarked with the Egg Crate function (Equation 2) as a multi-funnel function whose optimum point is known to be (0,0). Then, the algorithm was adjusted to the ranges of the current variables to find the best operation parameters for each combination of the mandatory inputs.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"618\" height=\"21\"\u003e\u003c/p\u003e\n\u003cp\u003eThe next task is to write the objective function before implementing the optimization algorithm. As mentioned before, the principal purpose of the optimization in this study is to increase profitability and reduce production costs simultaneously. Therefore, the objective function is considered as the difference between costs and revenues. Here, the recovery factor represents the profit. This parameter is the ratio of the total produced Ethane to the total Ethane in the input feed. These values are the product of the flow in the mass fraction of Ethane in that flow. The cost of the production process directly relates to the amount of consumed LP Steam and refrigerant liquid in the reboiler and condenser, respectively. Therefore, the algebraic sum of the profit and cost factors with the concord coefficients will form the objective function. Furthermore, to take the fixed operating costs into account, this function must be summed up with a fixed value (C) to increase the flexibility of the proposed solution method.\u003c/p\u003e\n\u003cp\u003eSetting the objective function to zero when having the profit and cost factors on their mean value obtained the desired fixed coefficients. Since this algorithm inherently minimizes its objective function, this function was multiplied by -1 before being introduced to the algorithm. Finally, the objective function resulted to be as shown in Equation 3.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"633\" height=\"98\"\u003e\u003c/p\u003e\n\u003cp\u003eThe PSO algorithm is a population-based meta-heuristic optimization method that uses an evolutionary approach to calculate the optimum location vector for particles. This process creates multiple moving particles in the feasible region to use their location and speed, the best position experienced by each particle, and the best reported by the whole population.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this case, the PSO algorithm begins with creating the initial locations of the particles by assigning random values in the permissible range to 10-dimensional position vectors. Then, the cost function for each of these particles is calculated using the ANN predictions. After that, the algorithm locates the best particle with the lowest calculated amount for the objective function. In the next step, the velocity of the particles determines their location in the next iteration. Note that the mirror effect limits the location and speed of the particles to keep them in the allowable range. This operation repeats for a specified number of iterations, and the particle velocity is reduced in every step to achieve convergence. Equation 4 shows the method of determining particle positions, where W, C1, and C2 represent Inertia Weight, Personal Learning Coefficient, and Global Learning Coefficient, respectively.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"626\" height=\"76\"\u003e\u003c/p\u003e\n\u003cp\u003eA hybrid method inks the optimization and prediction sections. This means the optimization values (the objective function and the particles\u0026apos; positions) were not calculated directly using mathematical equations but were recalled by the trained ANN and the dataset from the previous stages. Accordingly, the positions and the velocities were determined in the permissible range, and the objective function was calculated using the recalled ANN predictions throughout the code. Here, the particle positions and the predicted process model from the ANN were firstly de-normalized from the [-1,+1] range to the original form before being used by the PSO algorithm and calculating the objective function, which is because of the existing division operator in the function equations. Figure 5 illustrates the schema of the PSO method with further details.\u003c/p\u003e\n\u003cp\u003eThis research includes the optimization problem in two scenarios that differ in terms of input and output parameters. The first assumption is that operators have the authority to manipulate the pressure and temperature of the inlet feed by pre-processing treatments on the received gas (Scenario A). The second assumption is that no pre-processing treatment is accessible, and the inlet feed enters the fractionation unit as received from the previous process unit (Scenario B). Both scenarios require designing a loop in the optimization algorithm to repeat it several times. However, in both solutions, the elements of the particle position that refer to the mandatory parameters are fixed in the designed levels of experiments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eScenario A:\u0026nbsp;\u003c/strong\u003eIf there are pre-processing facilities available to adjust the pressure and temperature of the received sweetened gas, the optimization process can be implemented in response to the inlet feed mass fraction and its mass flow rate, which are still mandatory. Therefore, by changing these two parameters in five levels through their allowable range (\u003cstrong\u003eError! Reference source not found.\u003c/strong\u003e), 52=25 different optimization problems were defined and solved. Table 3 contains the parameters in the PSO algorithm.\u003c/p\u003e\n\u003cp\u003eTable 3. PSO parameters in scenario A\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003eName in code\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eCheck\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003ePopulation Size\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003enPop\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003eInertia Weight\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003ew\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003eDamping Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003ewdamp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e0.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003ePersonal Learning Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003ec1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003eGlobal Learning Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003ec2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003eIterations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003ei\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e200\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe outcome of this stage was stored in a 12x25 matrix which contains the best operation conditions based on various inlet feed mass fractions and mass flow rates. Hence, the optimum operation surfaces can be obtained by 3D plotting each available parameter concerning the two mandatory variables.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eScenario B:\u0026nbsp;\u003c/strong\u003eAnother potential approach in designing the optimizer system is to assume receiving inlet gas with no pre-processing treatments when all the four thermodynamic parameters of the inlet feed would not be adjustable to the operators. Here, pressure, temperature, mass flow, and mass fraction of the feed gas are varied in five equal steps in their permissible range, creating 5\u003csup\u003e4\u003c/sup\u003e=625 optimization problems. Therefore, the optimization process was repeated 625 times to cover all combinations of the four mandatory inputs and find the best operational parameters for each possible combination. The PSO parameters for this step were decided to be as mentioned in Table 4.\u003c/p\u003e\n\u003cp\u003eTable 4. PSO parameters in scenario B\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003eName in code\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003eCheck\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003ePopulation Size\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003enPop\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eInertia Weight\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003ew\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eDamping Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003ewdamp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003e0.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003ePersonal Learning Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003ec1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eGlobal Learning Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003ec2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 234px;\"\u003e\n \u003cp\u003eIterations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003ei\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 61px;\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe 625 optimal states obtained from the previous step created a 12x625 matrix. The final purpose is to predict the best operating conditions plus the conditions of the product based on the four mandatory parameters from the inlet feed. Therefore, the optimum feasible region was again predicted by modeling these optimum data in another set of ANNs. Here, the count of target parameters would be greater than that of the input. Hence, separate ANNs for each output were trained by this optimum dataset. At this stage, the four imposed parameters (rows 1 to 4 in Table 1) were considered inputs to predict the optimum value for the other ones (rows 5 to 11 in Table 1) individually. Therefore, the best control parameters that lead the operation to optimum production are predicted with this set of ANNs. Moreover, because the size of available data is much smaller than the first stage (625 compared to 5620), the training method is implemented in a while loop. This loop allowed reaching an acceptable accuracy in predictions, which was R-squared greater than or equal to 0.7. The ANN structure in this step is mentioned below in Table 5. The obtained eight ANNs can predict the best operation and production in response to mandatory circumstances. Therefore, this system can be pronounced as a flexible and wise optimizer system.\u003c/p\u003e\n\u003cp\u003eTable 5. ANN parameters in 2nd stage of prediction\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eAction zone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003eCheck\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eNumber of neurons\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eHidden layer\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTransfer function\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eHidden layer\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003etansig\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eTraining function\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003eLevenberg Marquardt\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"4\" valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eData division\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eTrainRatio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eValRatio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eTestRatio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eDivide mode\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003eSimple random\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003eNumber of epochs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e1000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" valign=\"top\" style=\"width: 156px;\"\u003e\n \u003cp\u003ePerformance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eFunction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eGoal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e10e-7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003eMaximum fails\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 152px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003ch1\u003eEvaluation\u0026nbsp;\u003c/h1\u003e\n\u003cp\u003eIn training the initial big dataset to the first ANN, MPE, MSE, and R-squared parameters evaluated the accuracy of predictions (Table 6). Moreover, Figure 6 and Figure 7 depict the performance validation for the trained ANN plus the accuracy of the predictions for each data division, respectively.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 6. Prediction accuracy by trained ANN\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 155px;\"\u003e\n \u003cp\u003eEvaluation parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003eProduct flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003eProduct purity\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 155px;\"\u003e\n \u003cp\u003eMPE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003e0.0228678822731286\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003e0.0150541982466198\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 155px;\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003e4.07192998150094e-05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003e3.25347716451295e-08\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 155px;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003e0.9999996446\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 164px;\"\u003e\n \u003cp\u003e0.9999978692\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eScenario A:\u003c/strong\u003e By converging the optimization process under the first scenario the best values for each control parameter can be plotted in response to the two considered mandatory inputs, which are the inlet feed mass fraction and its flow. Hence, interpolant surfaces with the cubic method fitted to the point clouds on the optimum operation surface for any desired parameter. Surface plots for optimum states of the cost function, product conditions (mass flow and mass fraction), and operation parameters (LP steam flow, refrigerant flow, reflux flow, bottom product flow, and boil-up ratio) are the available results. Figures 8 to 11 depict some of these optimum surfaces as examples. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eScenario B:\u0026nbsp;\u003c/strong\u003eHere, the achieved enhancement by implementing the suggested wise system is evaluated. The optimization process was repeated 625 times, and the operation vectors\u0026apos; dimension is larger than the power of human perception. Therefore, showing the results in the form of plots and graphs would be impossible. However, the effectiveness of this optimization approach can be measured by evaluating the resulting enhancement by the optimization process. Here, the average cost function was calculated for the initial dataset with 5620 points and the optimum dataset with 625 points. The performance enhancement in the distillation unit resulting from the optimization process can be calculated as follows in Equation 5.\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"629\" height=\"68\"\u003e\u003c/p\u003e\n\u003cp\u003eTable 7. Optimum prediction accuracy\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eIndex\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eParameter description\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003ePrediction R-square\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eBottom Product Flow (C2+)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.77\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMr\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eReflux Loop - Mass Flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMc\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eRefrigerant - Mass Flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eBoil-up Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eLP Steam - Mass Flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eMo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eC2 - Mass Flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 55px;\"\u003e\n \u003cp\u003eEo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 184px;\"\u003e\n \u003cp\u003eC2 - Phase Comp Mass Frac\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eAs mentioned before, the design and implementation of a flexible/responsive optimizer control system for industrial units is a research gap in the literature. The proposed approach is not similar to the previously published literature. Therefore, the functionality and efficiency of the prediction and optimization steps are compared to peer research to have a more transparent overview of the results.\u003c/p\u003e\n\u003cp\u003eThe paper that Ma et al. [24] published is one of the closest studies to the present research regarding the implemented method and the practiced industrial unit. They modeled a high sulfur NG purification process in ProMax and simulated the experiments designed by the Uniform Design method. They selected eight parameters as input factors and five as output results. In that paper, the results were then trained to a BP-ANN, which was then used as the feasible region for GA optimization. Finally, they claimed that their approach could enhance the total energy consumption by 12.7%\u003c/p\u003e\n\u003cp\u003eThe experiments used in the present study provided a dataset with 5620 conditions, which is much larger than the 11 experiments used in the mentioned reference. Furthermore, Ma et al. selected eight parameters from many affecting ones in the whole refinery plant with various units. Therefore, there is no guarantee for the other factors to be fixed during the experiments, which causes the predictions to be unstable. However, the objected parameters in this study are from one fractionation unit, and all other affecting parameters have a fixed value.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAnother bold point is considering a practical method for selecting the optimization parameters. There are many dependencies between the measurable parameters in fractionation columns that cannot vary independently. Hence, picking parameters regardless of the relationships between them is not a technically proper approach. In the present research, the optimization parameters are all from operation factors that can be measured and manipulated independently.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMoreover, the main improvement in the research approach is that the optimization results (625 conditions) were trained to second-stage ANNs to predict the optimum feasible region. Here, the resulting ANNs can suggest the optimum operation region as a continuous region. This is while in the peer research, the optimization results only represent one single optimum point for the operation.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe reference paper presented the accuracy of the predictions for two different experiments separately. To have a better comparison between these two studies, the average relative error is calculated for two random experiments to be compared against peer results in the reference, (Table 8).\u003c/p\u003e\n\u003cp\u003eTable 8. Prediction accuracy, reference vs present study\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 73px;\"\u003e\n \u003cp\u003ePoint 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003ePoint 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 107px;\"\u003e\n \u003cp\u003eAverage\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eReference [24]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 73px;\"\u003e\n \u003cp\u003e1.464%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003e2.186\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 107px;\"\u003e\n \u003cp\u003e1.825%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003ePresent study\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 73px;\"\u003e\n \u003cp\u003e0.0106%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003e3.9416E-03%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 107px;\"\u003e\n \u003cp\u003e3.30816E-03%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe effectiveness of the optimization process is also investigated here. The total energy consumption in the reference is claimed to have experienced a 12.7% reduction in the reference study. However, because consumed energy in fractionation columns has a direct relationship with the amount of consumed LP Steam and Refrigerant liquid, the reduction in the use of these resources would be a proper target for comparison. Hence, by calculating the average flow of LP Steam and Refrigerant liquid before and after the optimization process (5620 initial experiments and 625 optimum states, respectively) the enhancement in energy consumption is anticipated. Furthermore, the total enhancement resulting from the present study is calculated as the weighted average considering the cost function in Equation 3 (Table 9).\u003c/p\u003e\n\u003cp\u003eTable 9. Enhancement in energy consumption, reference vs present study\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eTarget\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eOptimization enhancement\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eTotal enhancement\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003eReference [24]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eTotal energy consumption\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e12.7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e12.7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003ePresent study\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eConsumed energy to maintain LP Steam flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e70.66%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e58.21%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eConsumed energy to maintain Refrigerant liquid flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 104px;\"\u003e\n \u003cp\u003e57.65%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eUltimately, this study introduced a responsive, flexible, and intelligent optimization system. Based on the obtained results, this data-driven system is able to suggest the control parameters of distillation towers (in this case, a De-Ethanizer tower) according to the measurable imposed parameters or any other mandatory conditions from outside.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003econflicts of interest\u003c/h2\u003e \u003cp\u003eThe author declares no conflict of interest regarding the present research.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThis paper originates from an individual course project that I expanded into a journal paper format. All findings presented are original, and I am fully committed to transparency in my methodology. I would be pleased to provide further details, including access to my code, simulation files, database, and my professor\u0026rsquo;s contact information for verification, upon request.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe author wishes to thank Mr. Arash Ara (Eng.) for his kind cooperation and guidance in the simulation process.\u003c/p\u003e\u003ch2\u003eData availability statement\u003c/h2\u003e \u003cp\u003eThe supporting data for the findings of this study are available from the author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eGreen, D.W. and M.Z. 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Htay. \u003cem\u003ePrediction of Natural Gas Final Consumption using Artificial Neural Networks\u003c/em\u003e. in \u003cem\u003e2020 International Conference on Advanced Information Technologies (ICAIT)\u003c/em\u003e. 2020. IEEE.\u003c/li\u003e\n\u003cli\u003eJalanko, M., et al., \u003cem\u003eAdaptive System Identification of Industrial Ethylene Splitter: A Comparison of Subspace Identification and Artificial Neural Networks.\u003c/em\u003e Computers \u0026amp; Chemical Engineering, 2021: p. 107240.\u003c/li\u003e\n\u003cli\u003eOh, D.-H., et al., \u003cem\u003eActor-critic reinforcement learning to estimate the optimal operating conditions of the hydrocracking process.\u003c/em\u003e Computers \u0026amp; Chemical Engineering, 2021. \u003cstrong\u003e149\u003c/strong\u003e.\u003c/li\u003e\n\u003cli\u003eZapf, F. and T. 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Koya, \u003cem\u003eMachine learning based system identification of a realistic heat integrated distillation column using particle swarm optimization.\u003c/em\u003e Chemical Engineering Communications, 2022: p. 1-21.\u003c/li\u003e\n\u003cli\u003eIplik, E., I. Aslanidou, and K. Kyprianidis, \u003cem\u003eA Feedforward Model Predictive Controller for Optimal Hydrocracker Operation.\u003c/em\u003e Processes, 2022. \u003cstrong\u003e10\u003c/strong\u003e(12).\u003c/li\u003e\n\u003cli\u003efuer kontinuierliche Regelungen, D.R.L., \u003cem\u003eDeep Reinforcement Learning for Continuous Control.\u003c/em\u003e\u003c/li\u003e\n\u003cli\u003eMa, L., et al., \u003cem\u003eEnergy consumption optimization of high sulfur natural gas purification plant based on back propagation neural network and genetic algorithms.\u003c/em\u003e Energy Procedia, 2017. \u003cstrong\u003e105\u003c/strong\u003e: p. 5166-5171.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Artificial neural network, Particle swarm optimization, Optimum process control","lastPublishedDoi":"10.21203/rs.3.rs-5441475/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5441475/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces a multi-step and comprehensive data-intensive structure to optimize the control of petrochemical fractionation columns using big-data analysis. The case study involved 11 parameters categorized into five control (adjustable) inputs, four imposed (non-adjustable) inputs, and two target outputs. The results from a factorial-designed set of experiments on a simulated model of a functional de-Ethanizer distillation unit constructed the initial database, consisting of 5620 vectors. The generated big dataset then trained a feed-forward artificial neural network (FF-ANN) that predicts the characteristics of the produced Ethane in response to ten input parameters. Subsequently, this trained model provided the feasible region for a multi-objective particle swarm optimization (PSO) algorithm to predict 625 individual optimum control points in response to different combinations of the imposed parameters. Finally, these optimum operation conditions trained five dedicated individual ANNs to predict a continuous optimum operation log according to the imposed parameters. This multi-step architecture of optimization and ANNs forms a flexible data-driven sapient system for the optimum control of distillation columns.\u003c/p\u003e","manuscriptTitle":"Design and Implementation of an AI-Powered Sapient System for Maximum Efficiency of Fractionation Operations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-17 09:49:12","doi":"10.21203/rs.3.rs-5441475/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"612afdae-e38a-42b5-bb04-551290c83cd2","owner":[],"postedDate":"December 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-24T18:38:12+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-17 09:49:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5441475","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5441475","identity":"rs-5441475","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}