Accurate prediction of water dewpoint temperature in natural gas dehydrators using gene expression programming approach

Accepted Manuscript Accurate prediction of water dewpoint temperature in natural gas dehydrators using Gene Expression Programming approach

Alireza Rostami, Amin Shokrollahi PII: DOI: Reference:

S0167-7322(17)32685-5 doi: 10.1016/j.molliq.2017.08.045 MOLLIQ 7753

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

19 June 2017 8 August 2017 11 August 2017

Please cite this article as: Alireza Rostami, Amin Shokrollahi , Accurate prediction of water dewpoint temperature in natural gas dehydrators using Gene Expression Programming approach, Journal of Molecular Liquids (2017), doi: 10.1016/ j.molliq.2017.08.045

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ACCEPTED MANUSCRIPT Accurate Prediction of Water Dewpoint Temperature in Natural Gas Dehydrators Using Gene Expression Programming Approach Alireza Rostamia2, Amin Shokrollahib1 a

Department of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran Young Researchers and Elites Club, North Tehran Branch, Islamic Azad University, Tehran, Iran

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b

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Abstract

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Triethylene Glycol (TEG) is one of the most frequently applied liquid desiccants in natural gas dehydration. For this purpose, minimum concentration of TEG is necessary to achieve the outlet gas water dewpoint specification. Several empirical models have been developed to predict the equilibrium established between water vapor and TEG; however, the existing models requires numerous input parameters needing to longer and more complicated calculations. Thus, in present study, the most recent and powerful mathematical strategy known as, Gene Expression Programming (GEP), was applied to develop an easy-to-use and a simple mathematical expression for prognostication equilibrium water dewpoint temperature as a function of contactor temperature and TEG purity in water. For absolute pressures up to 10300 kpa (10.3 MPa), equilibrium water dewpoint temperature is nearly independent of operating pressure. For this, 167 datapoints were collected from the open literature, then the database was divided into the two sets of training (about 80% of the databank) and test (about 20% of the databank). Comprehensive error analysis and diverse graphical illustration were employed to show the performance of the developed empirically derived correlation in this study. The results of the GEP model was also compared with the previously published correlation available in literature, which leads to this consequence that the proposed model in this study is a more efficient approach with higher simplicity than the prementioned literature correlation. GEP-based model gives an acceptable agreement with experimental databank reported in the open literature in terms of determination coefficient (R2) of 0.9820 and Root Mean Square Error (RMSE) of 3.5018. With respect to cumulative frequency analysis, it is understood that about 80% of the whole databank used in this study have estimation error equal or less than 0.2. The results of sensitivity analysis approved that the TEG purity is the most affecting variable on the natural gas dehydration. At last, it can be concluded that the suggested GEP-based empirically-derived correlation is an efficient tool for experts working in gas industry to have a quick check on equilibrium water dewpoint temperature at various TEG concentrations and temperatures.

Keywords: Natural gas dehydration; Triethylene glycol; Equilibrium water dewpoint temperature; Gene expression programming; Correlation; Error analysis.

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Introduction

During natural gas transmission and processing, the existence of water vapor has been identified as the main causes of serious operational difficulties when they appear at outlet of subterranean hydrocarbon reservoirs [1]. The hydrate related issues are corrosion, decrease in heating value of natural gas, capacity reduction of transmission lines caused by the presence of free water, and

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plugging of lines as a consequence of gas hydrates formation [1]. Therefore, safe operation of

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gas industry requires the proper implementation of the so-called technology of dehydration

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processes. A number of techniques such as liquid and solid desiccants, can be used for inhibiting gas hydrate formation; however, liquid desiccants are more commonly applied to fulfill the

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economic aspect of dehydration process [2].

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In the midst of all absorption liquids, glycols are of great significance where 15 to 49 oC depression of dewpoint is desirable [3]. In a countercurrent mass transfer system, Triethylene

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Glycols (TEG) have been most commonly applied inside a contactor so that the suitable water content in the gas stream will be achieved [4]. An example of a dehydration system by utilization

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of TEG is illustrated in Fig. 1 [2]. In a countercurrent system to the gas flow, the regenerated TEG solution is pumped to the contactor top tray in order to absorb water vapors. The glycol,

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which is water-rich, is taken out of the absorber column (contactor), then most of the soluble gas will be flashed off by passing over the reflux condenser coil and rich-lean heat exchanger. Afterwards, TEG will flow toward regenerator, in which the absorbed water is removed from glycol by the use of distillation process at nearby atmospheric condition. This lean TEG will also pass through the surge drum, and then will be cooled by going over the lean-rich exchanger and glycol cooler before TEG recirculation to the contactor [5]. At first step of simulating dehydration process, it is highly demanded to establish the minimum TEG concentration for optimizing the process [6]. For this, a number of investigations have been implemented on natural gas processes by TEG dehydration system so as to develop empirically2

ACCEPTED MANUSCRIPT derived and equilibrium correlations for estimating equilibrium water dewpoint temperature [713]. In the main, the proposed correlations by Parrish et al. [7], Rosman [11] and Worley [10] work acceptably and are appropriate for plenty of TEG system designs; even though, along with literature [1], the main drawback of aforementioned published correlations is their limited ability for accurate estimation of equilibrium water vapor concentration above the TEG solution. At

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unlimited dilution, equilibrium water vapor concentration was determined by the correlations

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extended in the work of Won [13] and Parish et al. [7]. By means of extrapolating data at lower

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concentrations the authors presented other correlations in 100% TEG purity. For pressures equal or less than 2000 psi (13.8 MPa), the pressure impact on water-TEG system equilibrium can be

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ignored. More recently, Bahadori and Vuthaluru [2] developed an equilibrium polynomial equation for water dewpoint prediction as a function of contactor temperature and TEG purity in

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water. They divided the TEG purity in water into three ranges, and reported three sets of tuned coefficients for their proposed correlation. Despite the considerable efforts conducted in

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literature for simulation of dehydration process, there is still a large requisite for development of strong models estimating water dewpoint temperature with high accuracy. Afterwards, Ahmadi

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et al. [1] proposed an Artificial Neural Network (ANN) model for predicting water dewpoint temperature in equilibrium condition with respect to the TEG purity in water and contactor

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temperature. Using Particle Swarm Optimization (PSO) and Back-Propagation (BP) algorithms, the authors have trained their smart strategy, and consequently understood that ANN-PSO gives more precise estimates than that of ANN-BP. Lately, two new types of ANN-based numerical schemes termed as Multilayer Perceptron (MLP) and Radial Basis Function (RBF) networks, was established in the work of Tatar et al. [14] with the same databank used by Ahmadi et al. [1]. Then, it was found out the MLP results is more accurate than the RBF technique in prognosticating water formation temperature in dehydration process.

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ACCEPTED MANUSCRIPT In this work, a new evolutionary algorithm termed as, Gene Expression Programming (GEP), was utilized to construct an empirically derived correlation to predict water dewpoint temperature in equilibrium condition as a function of TEG purity in water and contactor temperature for the first time in literature. Based on the previous researches focusing on this mathematical strategy, GEP scheme has been successfully applied in wide varieties of chemical

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and petroleum engineering areas [15-19]. For this, a comprehensive databank [7, 12] was

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collected from the open literature for modeling. Then, several statistical quality measures like

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Root Mean Square Error (RMSE) and determination coefficient (R2), and graphical illustrations including cross plot, error distribution diagrams and cumulative frequency figure were employed

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to show the supremacy of the proposed GEP-based empirically derived correlation. Moreover, the performance of the GEP-based model was also compared with the formerly published

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correlation of Bahadori and Vuthaluru [2]. Finally, the sensitivity analysis was implemented to

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Data Collection

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explore the impact of each input variable on the output of the model.

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A bulk of previous investigations concerning on mathematical and numerical modeling approaches, has been proved that a large database including wide ranges of operational

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conditions is necessary for implementing a comprehensive modeling [20-24]. So, a wide-ranging databank was adopted from the existing open literature [7, 12] to develop the GEP-based empirically-derived model in this study. The utilized databank consists of 167 datapoints of equilibrium water dewpoint temperature as a function of TEG purity in water and contactor temperature. Table 1 shows the operational ranges of the used databank as well as their standard deviation and average values. As can be seen, contactor temperature varies in the range of 10 to 75 oC, TEG purity in water from 90 to 99.997%, and equilibrium water dewpoint temperature between -78 to 20 oC.

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Gene Expression Programming (GEP)

3.1 Background One of the latest strategies, which has been proposed for creating powerful equations, is known as Gene Expression Programming (GEP). In GEP [25] scheme, the disadvantages of Genetic Programming (GP) [26] and Genetic Algorithm (GA) approaches have been modified, to explore

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the best solution for highly nonlinear engineering and scientific problems by applying advanced

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regression strategy. In this powerful mathematical scheme, no specific equation format will be

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supposed, and it is the major function of computer program in order to determine the optimum relationship by testing all the predefined algebraic operators between the input and output

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parameters. The model, which gives the lowest prediction error defined in the program or software will be given to the user [27]. GEP [25] mathematical strategy has two key components

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comprising of chromosome and Expression Tree (ET). Similar to biological genes, chromosomes have the role of putting into code the candidate solution, which will be converted to the real

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candidate solution (i.e., ET) [17, 28]. It should be noted that the genetic operations in GEP

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strategy are applied on chromosomes, directly. Reproduction of almost always valid ETs obtained in GEP is mainly due to genes’ novel arrangement, reproduction approach, chromosomes structural organization, and translation process into ET [28]. As a results of

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literature studies, the convergence speed and calculation efficiency of GEP is two to four orders of magnitude higher than that of GP technique in order to establish a symbolic equation during regression analysis [29]. Each gene is composed of a head comprising of functions and terminals, and a tail containing terminals [28]. The tail length (t) can be computed as a function of the head length (h) and the largest arity function (n), as follows:

t  h (n 1) 1

(1)

A typical chromosome with two genes composed of four operators (i.e., ×, +, /, terminals a, b, c, is indicated in Fig. 2 [17]. 5

) and three

ACCEPTED MANUSCRIPT 3.2 Correlation Development By implementation of highly complicated GEP [25] computation, an accurate, symbolic and easy-to-use equation will be produced showing the optimum behavior of the studied phenomenon. According to the preceding investigations, the equilibrium water dewpoint temperature (Td) has a functionality of contactor temperature (T) and TEG purity in water (W) [1,

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building the GEP-based empirically-derived model, as follows:

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2]. Therefore, the abovementioned parameters can be selected as the correlating variables for

(2)

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Td  f (T ,W )

To construct a new model for effective estimation of water dewpoint temperature in equilibrium

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with TEG, the following procedure is advised [30]:

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At first, the program randomly generates chromosomes to initialize a particular number of population individuals. By using the following Objective Function (OF), a fitness value will be

100 N Tdiexp Tdiest N  Tdiexp i

(3)

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OF(i ) 

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computed for each population:

in which, the superscripts exp and est, and the symbol N specify, respectively, the real

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equilibrium water dewpoint temperature value, the estimated values by the established GEPbased empirically-derived correlation, and the number of the data points used in modeling [29]. On the basis of these fitness values, subsequent modifications will be applied. Afterwards, the chosen population individuals will be processed by the application of selection environment, confrontation of the genomes expression, and reconstruction with modification. Finally, the procedures mentioned above will be repeated to fulfill the defined criterion for convergence during GEP modeling.

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ACCEPTED MANUSCRIPT 4

Results and Discussions

A GEP mathematical strategy has been established employing the before mentioned calculation procedure. The total databank has been split into the two group of training (nearly 80% of the entire databank) and test (nearly 20% of the entire databank) for building the model and testing the prediction capability of the model. By the use of a random computer-based selection, the

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process of databank division was performed. For this, a lot of databank divisions with different

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distributions was implemented, then the division with homogeneous feature was accepted

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inhibiting the data local gathering in possible problem area. The utilized technique in this study can determine the effective correlating variables leading to development of sufficiently precise

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model with respect to the input parameters (T, W). Hence, the researchers can present a number of independent variables as the input data for a typical problem and achieve the influencing

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parameters on the target output parameter. The ultimate correlation obtained in this study is as follows:

A2  A3 

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A1 T 

(4)

1  27.0885513811173 100.033063778086 W

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where

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Td  A1  A2  A3

(5)

1.80123526661289 1.23630193779173T W 3.218777155

(6)

1 W ln(ln( )) 37.3855344958176

(7)

In above equations, Td is computed in oC, T in oC, and W in weight percent (%). During optimization process, the number of digits in these equations are determined by conducting simultaneous sensitivity analysis between the estimates of GEP and target values of equilibrium water dewpoint temperature. Table 2 reports the settings of implemented GEP scheme in this 7

ACCEPTED MANUSCRIPT study such as head size, numbers of genes and chromosomes, mutation and inversion coefficients, Insertion Sequence (IS) transposition and Root IS (RIS) transposition, one- and twopoint recombination coefficients, and used algebraic operators.

4.1 Evaluation of the Developed Model

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4.1.1 Analytical Analysis For assessing the capability, numerous statistical approaches like statistical quality measures and

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graphical analyses are implemented. The main statistical parameters used in this study are

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Average Absolute Deviation (AAD), Average Relative Deviation (ARD), Root Mean Square Error (RMSE), Standard Deviation (SD), and determination coefficient (R2). The definitions of

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the applied error parameters in this study are indicated in Table 3. The comprehensive error

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analysis of the GEP-based empirically-derived model for three ranges of TEG purity in water including 90 to 99%, 99 to 99.9% and 99.9 to 99.997%, are fully studied in Table 4. For the

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whole ranges of TEG purity in water, the values of AAD, ARD, AARD, RMSE, and SD, are, respectively, less than 3.0, 0.3, 0.5, 4.0, and 1.1. Moreover, the R2 values are greater than 0.94

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showing the prediction acceptability of the developed model (i.e., Eq. (4)). As shown, the principal parameters of AAD, AARD, ARD, and SD demonstrate that for the highest TEG purity

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range (i.e., 99.9 to 99.997% TEG) the proposed GEP-based correlation gives the best result. A different way of examining Eq. (4) is conducted by detailed analysis of the databank used in this study for various operational conditions, which is indicated in Table 5. In this table, prediction range of equilibrium water dewpoint temperatures are compared with the corresponding experimental range as well as their estimation errors. In nearly all operating conditions, the estimation range of GEP model has a satisfactory agreement with that of experimental range of equilibrium water dewpoint temperatures with AAD<4.5, RMSE<5.5 and R2>0.99.

4.1.2 Graphical Analysis

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ACCEPTED MANUSCRIPT In addition, some graphical tools like cross plot analysis, relative error distribution plot, and cumulative frequency diagram are used to show the superiority of the model in different manners. Cross plot comparison of GEP estimates with target values of equilibrium dewpoint temperatures for different ranges of TEG purity, are illustrated in Fig. 3. According to this figure, datapoints are mainly accumulated around the unit slope line. This is due to the high

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determination coefficient (R2>0.98) sufficiently low estimation error (e.g., AAD<3.0) resulting

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in the good fit of predicted outputs with target values. Thus, GEP estimates will give the least

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possible deviation from 45o line, which is illustrative of ideal fitness. Simultaneous exhibition of estimated values by Eq. (4) and measured datapoints versus the data index are shown in Fig. 4.

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This figure confirms the good coincidence of predicted datapoints with the experimental line. Fig. 5 describes the relative error distribution of GEP model versus experimental equilibrium

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dewpoint temperature in subplot Fig. 5(a), versus TEG purity in water in subplot Fig. 5(b), and versus contactor temperature in subplot Fig. 5(c). The higher concentration of the dataset around

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the zero horizontal line in this plot is another indication for good performance of Eq. (4) for

processes.

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efficient prediction of equilibrium condition existing between TEG-water system in dehydration

The performance of Eq. (4) is analyzed through the calculating RMSE parameter for different

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ranges of contactor temperature from 10 to 75 oC Fig. 6. It is interesting to see that in all ranges the RMSE value is less than 5. The highest accuracy of GEP-based empirically derived model is obtained when contactor temperature varies from 20 to 30 oC. Calculation of AAD for individual TEG purity in water leads to the plot of Fig. 7. At the worst condition, this diagram demonstrates that the GEP-based model gives the AAD value less than 7. Moreover, the developed correlation is incredibly efficient at TEG purities of 99.9, 99.95, 99.97, and 99.98%. For various TEG concentrations, equilibrium water dewpoint temperature against contactor temperature is displayed in Fig. 8. An increase in contactor temperature leads to the incremental growth of 9

ACCEPTED MANUSCRIPT dewpoint temperature; however, the water dewpoint will be decreased by increasing TEG purity. In all TEG purities, GEP prediction lines show satisfactory agreement with the measured datapoint. This trend analysis conducted in Fig. 8 can give the readerships a good view of the GEP effectiveness for predicting the water-TEG equilibrium in this study. Fig. 9 represents the cumulative frequency of the databank versus the absolute relative error for

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different TEG purity ranges. For example, about 80% of GEP estimates have estimation error

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equal or less than 0.2 for the total TEG purity range. This figure also shows that increasing TEG

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purity leads to the higher cumulative frequency. The more cumulative frequency means that higher portion of the databank has estimation errors equal or less than a typical value verifying

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the greater model capability in accurate output prediction.

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4.2 Comparison with Previously Developed Correlation The performance of the GEP-based empirically-derived correlation is compared with the recently

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published correlation of Bahadori and Vuthaluru [2] in Fig. 10. For the total range of TEG purity, Eq. (4) gives R2>0.98, although the R2 value for Bahadori and Vuthaluru [2] is less than

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0.53. It means that correlation of Bahadori and Vuthaluru [2] is much less accurate than the proposed Eq. (4) in this study. Moreover, Bahadori and Vuthaluru [2] divided the TEG purity

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into the three ranges and reported three sets of tuned coefficient; however, a unique GEP-based empirically-derived model is proposed for the entire range of TEG purity in this study. Clearly, the GEP model in this study is much simpler than the that of Bahadori and Vuthaluru [2] with less number of constant values in its equation.

4.3 Sensitivity Analysis In this section, the so-called sensitivity analysis is executed to find the quantitative impact of TEG purity on water and contactor temperature on the equilibrium water dewpoint temperature. The relative dependency value for each variable is computed by equation of correlation

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ACCEPTED MANUSCRIPT coefficient (R) inserted in Table 3 and known as Pearson technique [31]. The results of sensitivity analysis are illustrated in Fig. 11. As can be seen, TEG purity in water has a negative effect and contactor temperature has a positive impact on the trend of equilibrium water dewpoint temperature. Totally, the equilibrium water dewpoint temperature has more dependency to TEG purity in water because of its higher relative impact value calculated by

Conclusions

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Pearson technique [31].

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In this modeling study, an empirically-derived correlation is developed by means of state-of-theart mathematical strategy known as, Gene Expression Programming (GEP), for straightforward

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determination of equilibrium water dewpoint temperature of 167 datapoints at various contactor

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temperature (10 to 75 oC) and TEG purity in water (90 to 99.997%) as correlating variables, which were undertaken from the open literature. About 80% and 20% of the whole database

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were assigned, respectively, for developing and testing the model. The most commonly used statistical quality measures like Average Absolute Deviation (AAD), Root Mean Square Error

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(RMSE) and Standard Deviation (SD), as well as, graphical tools like cross plot comparison and relative error distribution plot, were utilized in order to conduct a comprehensive error analysis

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in this study. The relative impact of each variable is detected quantitatively by applying Pearson technique [31]. As a result, it is found out the proposed GEP-based empirically-derived correlation is simpler and more accurate than the published correlation by Bahadori and Vuthaluru [2] with lower numbers of tuning parameters for the whole range of TEG purity in water. The GEP model gives satisfactory agreement with the target values with determination coefficient (R2) of 0.9820 and Root Mean Square Error (RMSE) of 3.5018. Moreover, it is demonstrated that the equilibrium water dewpoint temperature has more dependency on the TEG purity than the contactor temperature. To this end, the developed tool in this study can be of immense practical value for reliable and rapid estimate of equilibrium water dewpoint 11

ACCEPTED MANUSCRIPT temperature accurately for engineers dealing with natural gas dehydration in academic researches

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and industrial processes.

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ACCEPTED MANUSCRIPT References

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ACCEPTED MANUSCRIPT Table Captions Table 1. Specification of the databank applied for modeling Table 2. Optimized parameters of the proposed GEP model Table 3. Definitions of statistical quality measures applied for error analysis conducted in this

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study

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Table 4. Comprehensive error investigation of the proposed GEP tool estimating equilibrium

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water dewpoint temperature for different ranges of TEG purity in water

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Table 5. The performance evaluation of the developed GEP model for prediction of the

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equilibrium water dewpoint temperature in different operational conditions

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Symbol

Unit

Min.

Avg.

Max.

STDEVa

TEG purity in water

W

%

90

98.983

99.997

2.128

Contactor temperature

T

o

C

10

39.174

75

19.220

Equilibrium water dewpoint temperature

Td

o

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-78

-32.531

25.660

20

STDEV refers to the standard deviation, which can be calculated as follows:





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a

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Parameter

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Table 1

1

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2 2  1 N STDEV   xi x    N 1 i 1 

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where, x is a typical data sample and N shows the number of dataset.

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Number of chromosomes

3

Head size

7

Number of genes

3

Linking function

+

Generations without change

2000

Fitness function

RMSE

Mutation

0.00138

Inversion

0.00546

IS transposition

0.00546

RIS transposition

0.00546

One-point recombination

0.00277

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Two-point recombination

0.00277 0.00277

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Gene recombination Gene transposition

0.00277

Constants per gene

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+, -, *, /, EXP, X2, INV, LN

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Operators used:

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Value

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GEP algorithm parameters

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Table 2

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ACCEPTED MANUSCRIPT Table 3 Error Minimum deviation Maximum deviation

Formula D min  min(Td iexp Td est i ) max exp D  max(Td i Td est i )

Average deviation

AD 

T N

1 N

i 1 N

1 N 1 ARD  N

AAD 

Average absolute deviation

exp di

T

exp di

i 1





Td est i

Td iexp Td est  i    exp Td i i 1   exp est 1 N  T T AARD   d i exp d i N i 1  Td i

1 N

PT

T N

SC

Average absolute relative deviation

N

RI

Average relative deviation

MSE 

Mean square error

i 1

NU

1 RMSE   N

exp di

exp di

i 1



2

Td est i

T N

  

1 2 est 2 di

 

T

1

 1 N T exp T est 2 2 di di SD       exp  N 1 i 1  Td i    SD CV  

MA

Root mean square error

Standard deviation

 T N

R

EP T

ED

Coefficient of variation

Correlation coefficient

Td est i

  T  .T N

 T 

 Td iexp Td . Td esti Td i 1 N

exp di

i

i 1 2 N

est di

d

i





2

d



2



2

N  N  exp est   Td i Td    Td i Td    i 1  R 2   i 1

AC C

Determination coefficient

T N i

18

exp di

  2 N

Td . Td est i Td i



2

ACCEPTED MANUSCRIPT Table 4 For 90 to 99% TEG

For 99 to 99.9% TEG

For 99.9 to 99.997% TEG

N

46

40

81

Td min

-30

-52.5

-78

Td

-0.8646

-25.1537

-52.4928

Td max

20

4.5

-22.5

D min

-6.6163

0.6662

-10.0929

D max

5.5941

15.8997

AD

-0.4700

2.8834

AAD

2.8943

2.8834

ARD

0.2187

0.0348

AARD

0.4927

MSE

11.5358

RMSE

3.3964

SD

0.8485

CV R

MA

RI

NU

SC

2.5917

-1.5771 2.5544 0.0334 0.0508

13.7290

12.1595

ED

0.3957

3.4870

1.0592

0.0697

-0.9814

-0.0421

-0.0013

0.9733

0.9893

0.9749

0.9788

0.9504

EP T

3.7053

AC C

R2

PT

Parameter

0.9473

19

ACCEPTED MANUSCRIPT Table 5 W, %

T, oC

Td, exp, o C

Td, est, oC

AAD

RMSE

R2

6

90

10–37

-6–20

-0.2300– 16.3996

2.7587

3.2646

0.9993

7

95

10–45

-12–19

-5.383– 16.1732

3.3242

3.9972

0.9992

10

97

10–55

-18–19.5

-11.5316– 16.1843

3.2135

3.6246

0.9987

11

98

10–60

-22 – 17.5

-17.4481– 13.3474

2.5967

12

99

10–70

-30–14.5

-28.2991– 8.6555

10

99.5

10–55

-37.5– -6 -38.1662– -10.4503

14

99.8

10–75

-46.5– -5.5

14

99.9

10–75

-52.5– -14

14

99.95

10–75

14

99.97

10–75

14

99.98

14

99.99

13 Overall

RI

2.9004

2.8083

3.0910

0.9994

2.8372

2.8955

0.9991

-54.7781– -14.7440

1.7396

1.8017

0.9992

-59– -22.5

-61.0462– -21.0121

1.0498

1.2260

0.9988

-63– -28

-65.5917– -25.5576

1.4213

1.6585

0.9994

10–75

-66.5– -32.5

-68.9505– -28.9164

1.7427

1.9820

0.9991

10–75

-72– -39.5

-73.7016– -33.6675

2.4696

3.0071

0.9993

NU

SC

0.9997

-48.3534– -8.3202

MA

ED

EP T

2.6420

0.9993

3.3046

AC C

14

PT

N

99.995

10–75

-77– -44

-76.9412– -36.9071

4.3544

5.3053

0.9984

99.997

10–70

-78– -51.5

-78.4742– -41.5196

4.4222

5.3640

0.9978

90– 99.997

10–75

-78–20

-78.4742– 16.3995

2.7786

3.5018

0.9820

20

ACCEPTED MANUSCRIPT Figure Captions Fig. 1. Typical TEG-Natural Gas Dehydration System [2] Fig. 2. A typical two-gene chromosome with its corresponding mathematical expression [17] Fig 3. Comparison of GEP estimates with experimental values of equilibrium water dewpoint

PT

temperature

RI

Fig. 4. Experimental and GEP predicted values of equilibrium water dewpoint temperature

SC

versus data index

NU

Fig. 5. Distribution of relative deviation for GEP model predictions when relative deviation is drawn versus various parameters of: (a) Experimental equilibrium water dewpoint temperature,

MA

(b) TEG purity in water, and (c) Contactor temperature

Fig. 6. Root mean square error (RMSE) of GEP model for various contactor temperature ranges

ED

Fig. 7. Average absolute deviation (AAD) of GEP model for various range of TEG purity in

EP T

water

Fig. 8. Comparison of the experimental, GEP prediction values of equilibrium water dewpoint

AC C

temperature versus contactor temperature for TEG purity in water of 98 to 99.98% Fig. 9. Comparison of the determination coefficent (R2) of the developed GEP model with the previously published correlation of Bahadori and Vuthaluru in diverse ranges of TEG purity in water Fig. 10. Cumulative frequency versus the absolute relative deviation for the developed GEP tool in this study for different operational conditions Fig. 11. Relative dependency of equilibrium water dewpoint temperature to contactor temperature and TEG purity in water 21

MA

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

Fig. 1. Typical TEG-Natural Gas Dehydration System [2]

22

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

NU

SC

Fig. 2. A typical two-gene chromosome with its corresponding mathematical expression [17]

23

ACCEPTED MANUSCRIPT

20

PT

-10

-40

Unit slope line

RI

GEP for 90 to 99% TEG -70

GEP for 99 to 99.9% TEG

SC

Estimated water dewpoint temperature, °C

50

GEP for 99.9 to 99.997% TEG

-100

-70

-40

-10

NU

-100

20

50

Experimental water dewpoint temperature, °C

AC C

EP T

ED

MA

Fig 3. Comparison of GEP estimates with experimental values of equilibrium water dewpoint temperature

24

ACCEPTED MANUSCRIPT

20

Experimental data

GEP for 90 to 99% TEG

GEP for 99 to 99.9% TEG

GEP for 99.9 to 99.997% TEG

0

PT

-20

-40

RI

-60

-80 0

20

40

60

80

SC

Equilibrium water dewpoint temperature, °C

40

100

120

140

160

180

NU

Data index

AC C

EP T

ED

MA

Fig. 4. Experimental and GEP predicted values of equilibrium water dewpoint temperature versus data index

25

ACCEPTED MANUSCRIPT

(a) Zero line GEP for 90 to 99% TEG GEP for 99 to 99.9% TEG GEP for 99.9 to 99.997% TEG

3

4

2 1 0 -1

3 2 1 0 -1

-2

-2

-3

-3

-4

-4 -100

-70

-40

-10

20

90 91 92 93 94 95 96 97 98 99 100

50

TEG purity in water, %

SC

Experimental water dewpoint temperature, °C

(c)

NU

6

Zero line GEP for 90 to 99% TEG GEP for 99 to 99.9% TEG GEP for 99.9 to 99.997% TEG

5

MA

4 3 2 1 0

ED

Relative deviation

PT

4

Zero line GEP for 90 to 99% TEG GEP for 99 to 99.9% TEG GEP for 99.9 to 99.997% TEG

5

Relative deviation

5

Relative deviation

(b) 6

RI

6

-1 -2

EP T

-3 -4

0

10

20

30

40

50

60

70

80

Contactor temperature, °C

AC C

Fig. 5. Distribution of relative deviation for GEP model predictions when relative deviation is drawn versus various parameters of: (a) Experimental equilibrium water dewpoint temperature, (b) TEG purity in water, and (c) Contactor temperature

26

ACCEPTED MANUSCRIPT

5 4.5

3.5

PT

3 2.5

RI

2 1.5

SC

Root mean square error (RMSE)

4

1

NU

0.5 0 10.0-20.0

20.0-30.0

30.0-40.0

40.0-50.0

50.0-60.0

60.0-75.0

MA

Contactor temperature, °C

AC C

EP T

ED

Fig. 6. Root mean square error (RMSE) of GEP model for various contactor temperature ranges

27

ACCEPTED MANUSCRIPT

6 5

PT

4

RI

3 2

SC

Average absolute deviation (AAD)

7

1

NU

0

MA

TEG purity in water, %

AC C

EP T

ED

Fig. 7. Average absolute deviation (AAD) of GEP model for various range of TEG purity in water

28

ACCEPTED MANUSCRIPT

GEP, TEG=99.98% GEP, TEG=99.9% GEP, TEG=98% Data, TEG=99.95% Data, TEG=99%

GEP, TEG=99.95% GEP, TEG=99% Data, TEG=99.97% Data, TEG=99.8%

10

RI

PT

-10

SC

-30

-50

-70 10

20

30

40

MA

0

NU

Equilibrium water dewpoint temperature,°C

30

GEP, TEG=99.97% GEP, TEG=99.8% Data, TEG=99.98% Data, TEG=99.9% Data, TEG=98%

50

60

70

80

Contactor temperature,°C

AC C

EP T

ED

Fig. 8. Comparison of the experimental, GEP prediction values of equilibrium water dewpoint temperature versus contactor temperature for TEG purity in water of 98 to 99.98%

29

ACCEPTED MANUSCRIPT

1 0.9 0.8

PT

0.6

RI

0.5 0.4

SC

Cumulative frequency

0.7

Total

0.3

NU

For TEG=90 to 99%

0.2

MA

0.1 0 0

0.1

0.2

0.3

For TEG=99 to 99.9% For TEG=99.9 to 99.997%

0.4

0.5

ED

Absolute relative deviation

AC C

EP T

Fig. 9. Cumulative frequency versus the absolute relative deviation for the developed GEP tool in this study for different operational conditions

30

ACCEPTED MANUSCRIPT GEP

Bahadori and Vuthaluru

1

0.8 0.7

PT

0.6 0.5 0.4

RI

Determination coefficient (R2)

0.9

0.3

SC

0.2

0 90-99

99-99.9

NU

0.1

99.9-99.997

Overall

MA

TEG purity in water, %

AC C

EP T

ED

Fig. 10. Comparison of the determination coefficent (R2) of the developed GEP model with the previously published correlation of Bahadori and Vuthaluru in diverse ranges of TEG purity in water

31

ACCEPTED MANUSCRIPT 1 TEG purity in water 0.8

Contactor temperature

0.4

PT

0.2 0 -0.2

RI

Relative dependency factor

0.6

SC

-0.4

-0.8

NU

-0.6

99-99.9%

99.9-99.997%

Overall range

-0.504777569

-0.309224616

-0.452625726

-0.66078668

Contactor temperature

0.610834711

0.855966602

0.895686359

0.258201195

MA

90-99%

TEG purity in water

ED

Range of TEG purity in water, %

AC C

EP T

Fig. 11. Relative dependency of equilibrium water dewpoint temperature to contactor temperature and TEG purity in water

32

ACCEPTED MANUSCRIPT Research Highlights 

A new efficient correlation based on GEP algorithm for modeling the natural gas dehydration process has been introduced



For assessing the capability of developed correlation statistical quality measurement and graphical analyses are implemented The relative impact of each variable is detected quantitatively by applying Pearson

EP T

ED

MA

NU

SC

RI

PT

technique

AC C



33