An assessment test for phase equilibrium data of water soluble and insoluble clathrate hydrate formers

Accepted Manuscript Title: An Assessment Test for Phase Equilibrium Data of Water Soluble and Insoluble Clathrate Hydrate Formers Author: Poorandokht Ilani-Kashkouli Saeedeh Babaee Farhad Gharagheizi Hamed Hashemi Amir H. Mohammadi Deresh RamjugernathTel.: + 33 1 64 69 49 70; fax: + 33 1 64 69 49 68. PII: DOI: Reference:

S0378-3812(13)00455-X http://dx.doi.org/doi:10.1016/j.fluid.2013.08.016 FLUID 9723

To appear in:

Fluid Phase Equilibria

Received date: Revised date: Accepted date:

24-5-2013 15-8-2013 19-8-2013

Please cite this article as: P. Ilani-Kashkouli, S. Babaee, F. Gharagheizi, H. Hashemi, A.H. Mohammadi, D. Ramjugernath, An Assessment Test for Phase Equilibrium Data of Water Soluble and Insoluble Clathrate Hydrate Formers, Fluid Phase Equilibria (2013), http://dx.doi.org/10.1016/j.fluid.2013.08.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

An Assessment Test for Phase Equilibrium Data of Water Soluble and Insoluble Clathrate Hydrate Formers Poorandokht Ilani-Kashkouli,a Saeedeh Babaee,a Farhad Gharagheizi,a Hamed Hashemi,a Amir H. Mohammadi,a,b,* Deresh Ramjugernatha* a

Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France.

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Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa.

Abstract - In this communication, the validity of experimental data reported in the

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literature for structure II and H hydrate dissociation conditions in the presence of water soluble/insoluble promoters are assessed. Outliers in the hydrate dissociation data are identified using a statistical method. The Leverage mathematical based approach is employed for determination of the statistical Hat matrix, sketching of the Williams Plot, and computation of residual values (difference between calculated and experimental data) for a specific model. In addition, the range of applicability of the applied model and quality of the available experimental data is determined. Because of the high accuracy of the Least Squares Support Vector Machine (LSSVM) method which has been used in previous studies, this method has been used for the prediction of dissociation conditions of clathrate hydrates of methane, carbon dioxide, nitrogen, and hydrogen in the presence of water soluble organic promoters (tetrahydrofuran (THF), 1,4-dioxane, and acetone) and twenty one water insoluble hydrocarbon promoters. It is expected that the results reported in this study would provide a better understanding of the reliability of hydrate equilibrium data. This would enable the development of more accurate thermodynamic models based on reliable experimental data.

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Keywords: Gas hydrate, Clathrate hydrate, Promoter, Assessment test, Hat, LSSVM.

________________________________________________________________________ *: Corresponding author, Email: [email protected] Tel.: + (33) 1 64 69 49 70. Fax: + (33) 1 64 69 49 68. *: Corresponding author, Email: [email protected] Tel.: + (27) 312603128. Fax: + (27) 312601118.

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1. Introduction

Gas hydrates (or clathrate hydrates) are crystalline compounds, consisting of water and

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guest molecules which have small molecular diameter, that form at suitable conditions of temperature and pressure (normally at low temperature and high pressure). In these

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structures, small guest molecules of appropriate gases and/or volatile liquids are trapped in

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the cavities which are constructed from water molecules by hydrogen bonding [1]. Depending on the size of guest molecules and the temperature and pressure conditions, there are

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typically three types of hydrate structures, viz. structure I (sI), structure II (sII) and structure

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H (sH) [1, 2].

Clathrate hydrates have been considered in the past few decades in many studies for gas

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storage applications [2-26] because of their several advantages, viz. low storage volume, low

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cost of transportation compared to LNG [3], reversibility, and safety. The major problem with gas hydrate storage, however, is the slow kinetic rate for formation of the hydrate, as well as

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the formation conditions (e.g. high pressure and low temperature) [4, 26]. One solution to this problem is the use of promoters which have been studied widely. A promoter is a large molecule which produces the gas hydrate by occupying large cavities, while smaller cavities are occupied by small gas molecules such as methane and hydrogen. For instance, tetrahydrofuran (THF) as a promoter can stabilize H2 in H2 + THF structure II hydrates at lower pressure than pure hydrogen hydrates [1].

When one considers gas hydrate structures (sI, sII and sH) it has been shown that gas hydrate storage capacity can be increased significantly in structure H hydrates compared with sI and sII hydrates at reasonable pressure conditions. There are three types of cavities in sH:

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three small cavities (512), two medium cavities (435663), and one large cavity (51265). In this structure (sH), small gas molecules can occupy both small and medium cavities and the large cavity is occupied by a large molecule such as cycloalkanes, cycloalkenes, etc as a promoter

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[26]. Since in sII, small gas molecules can be stored in only the small cages (512) and the large cages (51264) are occupied by a large molecule (e.g. THF), gas hydrate occupancy is

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decreased in comparison with structure I in which that small gas molecules can occupy both small and large cavities (512 and 51262) at high pressure conditions. Kang et al. [27] and Linga

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et al. [28] found that the dissociation pressure of hydrates in the presence of THF is lower

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than the case without this promoter.

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In addition, promoter additives can be used in gas separation, such as CO2 capture, to increase the rate of hydrate formation and decrease the dissociation pressure of gas hydrates;

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thus the capability of the gas hydrate storage method will be improved [29].

In this study, the quality of experimental equilibrium data of gas hydrates in the

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presence of large molecules (promoters) is assessed. As it has been mentioned in previous studies [4, 30], there are two groups of gas hydrate promoters which consist of water soluble and water insoluble chemicals. Typically, water-soluble promoters are categorized as kinetic and thermodynamic promoters [4, 29, 30]. Thermodynamic promoters are organic compounds which shift the equilibrium conditions of hydrate formation to higher temperatures or lower pressures and are divided into two types of molecules, viz.

molecules which do not

participate in the structure of the hydrate cavities, such as tetrahydrofuran (THF), acetone and 1,4-dioxane and 1,3-dioxalane [31-36] and those which participate in hydrate structures, e.g., tetra-n-butylammonium bromide (TBAB) and tetrabutyl phosphonium bromide (TBPB) which produce semi-clathrate hydrates [37-51]. Kinetic water soluble promoters generally

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include surfactant molecules (e.g. sodium dodecyl sulfate (SDS)) which have an effect on the rate of hydrate formation [1, 29, 52]. Water insoluble promoters consist of heavy hydrocarbons such as methyl cyclohexane, cyclopentane, etc which can be placed in the large

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cavity of the H structure, except for cyclopentane and cyclohexane which produce structure II

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hydrates [1, 4, 5, 29, 30, 36].

The existing thermodynamic models in the literature for the prediction of gas hydrate

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phase equilibria in the presence of promoters are based on the solid solution theory of van der

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Waals and Platteeuw [53]. The models are applied with the equilibrium criterion that the fugacity/chemical potential of water in the various phases must be equal [26, 35, 54-58].

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When the promoters are dissolved in water, the aqueous phase becomes highly polar, and as known, few models are capable of estimating the water activity coefficient correctly. In order

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to improve the thermodynamic models for the prediction of gas hydrate dissociation

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conditions in the presence of different promoters, the equilibrium solubility data of promoters in water are needed. This data is scarce in the literature and this limits the use of

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thermodynamic models [4, 26, 30]. Of course there are some solutions to this problem, such as the use of the UNIFAC group contribution model [4, 26, 36]. However, such methods are complicated, especially for application to molecules for which parameters are not easily available. Furthermore, the existing thermodynamic models based on the van der Waals and Platteeuw theory [53] have studied equilibrium conditions of gas hydrates in the presence of only a few promoters and the effects of a wider range of promoters has as yet not been undertaken. An additional problem with regard to thermodynamic modeling is related to the influence of the water insoluble promoter and the existence of four equilibrium phases consisting of liquid hydrocarbon (LHC), liquid water (LW), vapour (V), and hydrate phase (H) which leads to difficulties in computation and performing flash calculations.

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In order to develop a reliable thermodynamic model for the prediction of methane hydrate dissociation conditions in the presence of water insoluble promoters, without the

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problems mentioned above, Eslamimanesh and co-workers [4] proposed a method based on the quantitative structure property relationship (QSPR) method. For the estimation of the

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parameters used in their model, two mathematical algorithms consisting of the geneticalgorithm-based multivariate linear regression (GA-MLR) and the least square support vector

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machines (LSSVM) methods were applied and good results were obtained.

In order for researchers to propose an accurate model and also to adjust the parameters

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of the model to experimental data, precise and reliable phase equilibrium data are needed. In order to check the domain of applicability of their model, Eslamimanesh et al. [59] used an

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approach based on a statistically-correct method [59-63] for assessment of doubtful pressure

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and/or temperature data for simple clathrate hydrates such as methane, ethane, propane, carbon dioxide, nitrogen and hydrogen sulphide. In this study, a novel statistical method and

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approach is applied to evaluate the quality of the gas hydrate equilibrium data in the presence of water soluble/insoluble promoters.

2. Experimental Database

Available experimental gas hydrate dissociation data in the presence of water soluble

[54, 56-58, 64-77] and water insoluble promoters [72, 78-92] in liquid water-hydrate-vapour (LW-H-V) and liquid water-liquid hydrocarbon-hydrate-vapour (LW-LHC-H-V) regions, respectively, have been tested in this study. Table 1 reports the ranges of the experimental data as well as their references.

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3. Theory

LSSVM Model

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3.1.

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In mathematical approaches, appropriate methods are needed to propose the best

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relationship between the input information of the models and desired outputs. For solving such a problem, some mathematical models based on artificial neural network (ANN) or

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Support Vector Machine (SVM) or Least-Squares Support Vector Machine (LSSVM) can be

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used [93-100].

Because of random initialization of the networks and change of the stopping criteria

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during the model parameter optimization process, the ANN method has some problems in

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prediction [93-97] outside the range of data used in the model development. A way to solve this problem is in using another strong mathematical method which was developed from the

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machine learning community, viz. Support Vector Machine (SVM). This method is considered as a non-probabilistic binary linear classifier. There is a greater probability of the SVM method to converge to the global optimum, and to find a quick solution by a standard algorithm. It does not require numerous adjustable parameters, as well as a priori determination of the network topology. There are no over-fitting complications, and there is no need to choose hidden node numbers. The satisfactory generalization performance of the SVM method is considered an advantage of the SVM method over the traditional ANN method. In addition to the points above, as a result of the specific formulation of the SVM method, both linear and nonlinear regressions can be performed [93-96].

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In 1999, Suykens and Vandewalle [95] proposed a faster and much easier method than SVM by solving a set of linear equations, which they named the Least-Squares Support Vector Machine (LSSVM) method. It can be considered as an alternative method to the

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conventional SVM algorithm [93-96].

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As mentioned earlier, the hydrate dissociation conditions in the presence of water soluble and insoluble promoters using LSSVM algorithm, have been modelled in previous

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studies [4, 30], with good results having been achieved. Because of the high accuracy of this

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approach, these results [4, 30] have been applied in the development of mathematical nonlinear relationships between the available experimental information considered as inputs

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of the models and the desired outputs. For this purpose, four molecular descriptors, and the gas hydrate dissociation temperature for the systems which included water insoluble

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promoters were used. The weight fractions of water-soluble promoters in aqueous solution

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and the gas hydrate dissociation temperature in the systems including water soluble promoters have been considered as input information and the hydrate dissociation pressures

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considered as the output of the model.

For optimization using the LSSVM mathematical algorithm, it is required to minimize a

cost function [95] as shown below [93-95, 101]:

Q LSSVM 

N 1 T w w    e k2 k 1 2

(1)

with the following constraint:

y k  wT  ( xk )  b  ek

k=1, 2,…, N

(2) 7

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where w shows the slope of the linear regression (regression weight), γ indicates the relative weight of the summation of the regression errors and ek is the regression error for N training

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objects. In addition, in Eq.2, xk indicates the input vector including the input elements (molecular descriptor of water insoluble promoter or weight fractions of water-soluble

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promoters and gas hydrate dissociation temperature) and yk is the output vector (gas hydrate dissociation pressure in this work). b indicates the linear regression intercept of the model, φ

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indicates the feature map, and finally superscript T indicates the transpose matrix.

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Using the Lagrange function, the regression weight (w) in Eqs. 1 and 2 can be defined

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as shown below [93-95, 101]:

N

w    k xk

(3)

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k 1

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where,

 k  2  ek

(4)

As a result of linear regression between the independent and dependent variables of the

LSSVM method [95], Eq. (2) can be revised as follows [93-95, 101]:

N

y    k xk x  b

(5)

T

k 1

In Eq. 5 the value of x is equal to the value of xk in k = 1. By inserting Eq. 4 and 5 into Eq. 1, the value of the  k (the Lagrange multipliers) can be defined as:

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k 

( yk  b) x x  ( 2  ) 1

(6)

T k

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The Kernel function can be applied to convert the linear regression to a nonlinear form as

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shown below [93-95, 101]:

N

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f ( x)    k K ( x, xk )  b k 1

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and

(8)

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K ( x, x k )  Φ ( x )T .Φ ( x k )

(7)

where K(x,xk) is the Kernel function which is composed of the inner product of the vectors

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Ф(x) and Ф(xk). Applying a radial basis function (RBF) Kernel, the following expression can

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be used for computing the Kernel function [93-95, 101]:

K ( x, xk )  exp(  xk  x /  2 )

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(9)

where σ is the decision variable which deals with the external optimization algorithm during the internal LSSVM [95] calculations. The mean square error (MSE) of the LSSVM [95] results can be defined as follows:

n

MSE 

 (p i 1

pred. i

 p exp .i ) 2

(10)

ns  nn

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where ppred. is the predicted hydrate dissociation pressure which is achieved by minimization of the cost function, pexp. is the experimental hydrate dissociation pressure, ns denotes the number of samples from the initial population, and nn is the number of model parameters.

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Two optimization values of the LSSVM algorithm consist of  and  , in Eqs. 6 and 9 respectively, have been reported in previous studies [4, 30]. In this study, these reported

 and   have

been used for the assessment of the quality of

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optimized parameters

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experimental data of gas hydrate structure H in the presence of water soluble and insoluble

Leverage Method

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3.2.

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promoters.

As presented in previous studies [59, 60, 102], prior to the estimation of experimental

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data using a model, it is essential to identify a group or groups of data that may differ from

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the bulk of data presented in a dataset. Simultaneous numerical and graphical methods [59, 60, 102] can be applied for this identification. The Leverage statistical approach [59-63, 102],

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which is used in this work, consists of a definition of the values of the residuals (i.e. deviations of the model results from the related experimental data) and a matrix, named as the Hat matrix which includes the experimental data and the estimated values given by the model [59, 60, 102]. For employing the aforementioned algorithm, an appropriate mathematical model is needed.

The Hat matrix used in the Leverage method is defined as shown below [59-63, 102]:

H  X ( X t X ) 1 X t

(11)

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where X stands for a two-dimensional matrix consisting of n data (rows), k parameters ‎of the model (columns), and t is the transpose matrix. The Hat values of the chemicals in the feasible region of the problem are the ‎diagonal elements of the H matrix. In order to

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undertake graphical diagnostics of the suspect experimental data or outliers, the Williams plot has been sketched based on the calculated H values from Eq. 1. The Williams plot indicates

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the correlation of the Hat indices and standardized cross-validated residuals (SR), which are defined as the difference between the predicted values and the corresponding data [59, 60,

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102].

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A warning Leverage (H*) is generally equal to 3n/p, ‎which n is number of training points

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(represented data) and p is the number of model (or correlation) input parameters plus one. [59, 60, 102]. A leverage value of 3 is appointed as a boundary value to accept the points

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within a ± 3 range (the region between the two horizontal red lines in the figures) standard

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deviations from the mean (covering 99% of distributed data). Existence of most of the experimental data points in the acceptable ranges ( 0  H  H  and ‎  3  R  3 )‎ indicates that

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the model has a wide capability domain to include data points. “Good High Leverage” points are ‎placed in the H   H ‎and  3  R  3 ‎ domain range. In addition, the data points which are outside of applicability domain of the model used can still be considered as “Good High Leverage data points”. In the other words, the model does not have the capability to represent the following data at all. The outliers of the model or “Bad High Leverage” points are located in the range of R < - 3 or 3 < R (whether they are larger or smaller than the H  value). They can be attributed to doubtful data [59, 60, 102].

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4. Results and discussion

The absolute relative deviation percentage (ARD%) of the represented model results

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from the experimental hydrate dissociation pressure in the presence of water soluble and insoluble promoters are shown in Tables S.1 and S.2 in the supplementary material,

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respectively. As can be seen in these tables, there is an acceptable deviation between the

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model predictions and the corresponding experimental data which indicates use of the

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Leverage statistical approach correctly.

Using Eq. 1, the H values have been calculated. As can be seen, the Williams plots for

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structure H gas hydrate in the presence of water soluble promoters are shown in Figures 1 to 11 using the LSSVM model. In addition, the Williams plot for systems in the presence of

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water insoluble promoters is shown in Figure 12. The H and R values are listed in Tables S.1

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and S.2 in the supplementary materials for all of the data series. The warning Leverages (H*) have been fixed at 3n/p for all data series and have been presented in Figures 1 to 12. In

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addition, the recommended cut-off value of three has been applied [59, 60, 102].

As can be seen, the majority of the data, which is approximately around 98% of the

1022 gas hydrate experimental data points in the presence of water soluble/insoluble promoters are presented in 0  H  H * and ‎  3  R  3 ‎. These results show that the model used is satisfactorily accurate and correct for prediction of the experimental dataset.

As previously mentioned, good high leverage points are gathered in the domains of

H*  H ‎and  3  R  3 . However, these points may lie outside the applicability domain of the applied model such as the triangles point in Figures 4, 6 and 7. In the case of dealing with 12

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these kinds of points, it would be better to use a different kind of theoretically based model in order to prevent estimation through biased model calculations.

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As explained earlier, another group of data points which include bad high leverage points are in the range of R < - 3 or 3 < R (ignoring their H values). These erroneous

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predictions can be classified as suspect or doubtful data. As can be considered in Figures 1 to 12 and Tables S.1 and S.2 in the supplementary materials, approximately 98% of all the

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hydrate dissociation data points are presented in acceptable ranges, except for one point for

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hydrate dissociation pressure data of the CO2+ THF system in the LW +V+H region, 4 points for CH4 + 1,4 dioxane hydrate dissociation pressure data in the LW +V+H region, three points

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related to CH4 + acetone hydrate dissociation pressure data in the LW +V+H region, one point related to CH4 + THF hydrate dissociation pressure data in LW +V+H region, one point for N2

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+ 1,4 dioxane hydrate dissociation pressure data in the LW +V+H region, and finally 2 points

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for CH4 + 2,2-dimethylpentane hydrate dissociation pressure data in LW+LHC+V+H region. These twelve suspect or doubtful data which are presented as bold-highlighted data in Tables

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S.1 and S.2 in the supplementary material, as well as red circular points in figures 1 to 12 constitute approximately 2% of all the data.

The data points in the ranges H*  H and ‎ R < - 3 or 3 < R can be classified as either

out of the domain of the applied model, or suspect or doubtful data. There are two points in these region: one point for CH4 + acetone hydrate dissociation pressure data in LW+ V+H region and another point for CH4 + 2,2 dimethylpentane hydrate dissociation pressure data in LW+LHC+ V+H region system which are presented in figures with square points. The applied model cannot estimate these suspect data points.

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As shown in Tables S.1 and S.2 in the supplementary materials and Figures 1 to 12, there is definitely a difference in the quality of experimental data. The experimental data which have lower absolute R values (near R=0 line) and lower H value regions may be

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considered to be of higher reliability.

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In this study, a mathematical assessment test has been developed and the quality of some selected data from the literature, as well as the capability of the model applied has been

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evaluated. The results indicate that some experimental data may be regarded as suspect or

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doubtful. The reason for the suspect data may be because of the inaccurate experimental measurements or the experimental technique that has been used in that corresponding

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experimental measurement. The data assessment tool presented in this study merely provides a warning for suspect data and it is advised that a thorough investigation of suspect

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before the data is discarded.

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experimental data with regard to the reliability of measurement method should be undertaken

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Apart from the mathematical assessment which is used in this study, a thermodynamic

consistency test is another method used to check the reliability of experimental phase equilibrium data. The consistency test indicates to what extent the experimental data satisfies the Gibbs-Duhem equation [103-108]. The thermodynamic consistency test is a necessary, but not sufficient test in that data that does not pass the test is not necessarily incorrect. The mathematical assessment test then serves as a further reliability test. It is advisable to not use experimental data which cannot satisfy both tests (consistency and mathematical assessment test).

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5. Conclusions

In this study, a statistical approach based on the Leverage statistical method has been

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proposed to assess the quality of structure H and II gas hydrate dissociation pressure data in the presence of water soluble and insoluble promoters. The assessment test applied is model

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dependent. However, the model used viz. the Least Squares Support Vector Machine

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(LSSVM) algorithm has been successful applied in previous studies and therefore was used with reasonable confidence to predict the hydrate dissociation dataset in this study. The

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majority of experimental data (approximately 98%) were determined to fall within the applicability domain of the model used. Twelve hydrate dissociation pressure data may be

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classified as suspect or doubtful experimental data.

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Acknowledgement

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This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation.

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[1] E.D. Sloan, C.A. Koh, Clathrate Hydrates of Natural Gases, in, CRC Press, 2007. [2] A.A. Khokhar, J.S. Gudmundsson, E.D. Sloan, Gas storage in structure H hydrates, Fluid Phase Equilibria, 150–151 (1998) 383-392. [3] A. Børrehaug, J.S. Gudmundsson, Gas Transportation in Hydrate Form, in: EUROGAS 96, 1996, pp. 35-41. [4] A. Eslamimanesh, F. Gharagheizi, A.H. Mohammadi, D. Richon, Phase Equilibrium Modeling of Structure H Clathrate Hydrates of Methane + Water “Insoluble” Hydrocarbon Promoter Using QSPR Molecular Approach, Journal of Chemical & Engineering Data, 56 (2011) 3775-3793. [5] C. Sun, W. Li, X. Yang, F. Li, Q. Yuan, L. Mu, J. Chen, B. Liu, G. Chen, Progress in Research of Gas Hydrate, Chinese Journal of Chemical Engineering, 19 (2011) 151-162. [6] X. Lang, S. Fan, Y. Wang, Intensification of methane and hydrogen storage in clathrate hydrate and future prospect, Journal of Natural Gas Chemistry, 19 (2010) 203-209. [7] A. Celzard, V. Fierro, Preparing a Suitable Material Designed for Methane Storage:
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[107] A. Eslamimanesh, S. Babaee, A.H. Mohammadi, J. Javanmardi, D. Richon, Experimental data assessment test for composition of vapor phase in equilibrium with gas hydrate and liquid water for carbon dioxide + methane or nitrogen + water system, Ind. Eng. Chem. Res., 51 (2012) 3819–3825. [108] A. Eslamimanesh, S. Babaee, F. Gharagheizi, J. Javanmardi, A.H. Mohammadi, D. Richon, Assessment of Clathrate Hydrate Phase Equilibrium Data for CO2 + CH4/N2 + Water System, Fluid Phase Equilibria, 349 (2013) 71-82.

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List of Tables

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Table 1. The range of experimental hydrate dissociation pressure and temperature tested in

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this study.

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Captions of Figures: Figure 1. Detection of the probable doubtful experimental data [64-68] and the applicability domain of the LSSVM model for the CO2 structure H hydrate in the presence of 1,4 dioxane in the Lw–H–V region. The H* value is 0.428. Stars, valid data; Horizontal (red) lines, Suspended data limit; Vertical

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(blue) line, Leverage limit.

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Figure 2. Detection of the probable doubtful experimental data [64-68] and the applicability domain of the LSSVM model for the CO2 structure H hydrate in the presence of Acetone in the Lw–H–V

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region. The H* value is 0.15. Stars, valid data; Horizontal (red) lines, Suspended data limit; Vertical

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(blue) line, Leverage limit.

Figure 3. Detection of the probable doubtful experimental data [64-68] and the applicability domain of the LSSVM model for the CO2 structure H hydrate in the presence of THF in the

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Lw–H–V region. The H* value is 0.209. Stars, valid data; Circular, suspected data;

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Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit. Figure 4. Detection of the probable doubtful experimental data [69, 70] and the applicability

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domain of the LSSVM model for the H2 structure H hydrate in the presence of Acetone in the Lw–H–V region. The H* value is 0.321. Stars, valid data; Triangle, out of leverage;

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Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit. Figure 5. Detection of the probable doubtful experimental data [69, 71] and the applicability domain of the LSSVM model for the H2 structure H hydrate in the presence of THF in the Lw–H–V region. The H* value is 0.643. Stars, valid data; Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit. Figure 6. Detection of the probable doubtful experimental data [56, 58, 64, 72, 73] and the applicability domain of the LSSVM model for the CH4 structure H hydrate in the presence of 1,4 dioxane in the Lw–H–V region. The H* value is 0.069. Stars, valid data; Circles, suspected data; Triangles, out of leverage; Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit.

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Figure 7. Detection of the probable doubtful experimental data [56, 57, 64, 70, 72-75] and the applicability domain of the LSSVM model for the CH4 structure H hydrate in the presence of Acetone in the Lw–H–V region. The H* value is 0.049. Stars, valid data; Circles, suspected data; Triangles, out of leverage; Squares, out of leverage and suspected data;

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Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit. Figure 8. Detection of the probable doubtful experimental data [54, 56, 64, 72-74] and the

cr

applicability domain of the LSSVM model for the CH4 structure H hydrate in the presence of THF in the Lw–H–V region. The H* value is 0.094. Stars, valid data; Circles, suspected data;

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Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit.

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Figure 9. Detection of the probable doubtful experimental data [56, 76, 77] and the applicability domain of the LSSVM model for the N2 structure H hydrate in the presence of 1,4 Dioxane in the Lw–H–V region. The H* value is 0.225. Stars, valid data; Circle,

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suspected data; Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit.

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Figure 10. Detection of the probable doubtful experimental data [56, 76, 77] and the

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applicability domain of the LSSVM model for the N2 structure H hydrate in the presence of Acetone in the Lw–H–V region. The H* value is 0.219. Stars, valid data; Horizontal (red)

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lines, Suspended data limit; Vertical (blue) line, Leverage limit. Figure 11. Detection of the probable doubtful experimental data [56, 76, 77] and the applicability domain of the LSSVM model for the N2 structure H hydrate in the presence of THF in the Lw–H–V region. The H* value is 0.155. Stars, valid data; Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit. Figure 12. Detection of the probable doubtfulxperimental data [72, 78-92] and the applicability domain of the LSSVM model for the CH4 structure H hydrate in the presence of insoluble promoters in the LW–LHC-H–V region. The H* value is 0.064. Stars, valid data; Circles, suspected data; Squares, out of leverage and suspected data; Horizontal (red) lines, Suspended data limit; Vertical (blue) line, Leverage limit.

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Table 1.

(Lw+H+V)

274.2-326.8

Methane+THF Nitrogen+1,4 dioxane Nitrogen +Acetone Nitrogen +THF Methane+ Isopentane Methane+ Neopentane Methane+ Neohexane Methane+2,3 Dimethyl butane Methane+2,2,3-Trimethylbutane Methane+2,2-Dimethylpentane Methane+ Methylcyclopentane

(Lw+H+V) (Lw+H+V) (Lw+H+V) (Lw+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V)

274.2-326.8 274.5-309.4 274.5-309.4 274.5-309.4 274.0-279.0 276.6-292.8 244.8-288.2 275.9-286.4 275.6-289.4 274.8-290.0 275.2-287.8

Methane+ Methylcyclohexane

(Lw+LHC+H+V) 251.5-290.4

1.2-1000

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Methane+ cis-1,2Dimethylcyclohexane Methane+2,3-Dimethyl-1-butene Methane+3,3-Dimethyl-1-butene Methane+3,3-Dimethyl-1-butyne Methane+ Cycloheptene Methane+ cis-Cyclooctene Methane+ Adamantane Methane+ Ethylcyclopentane Methane+1,1Dimethylcyclohexane Methane+cis-1,4Dimethylcyclohexane Methane+ Ethylcyclohexane Methane+ Cycloheptane Methane+ Cyclooctane

Ref.C [64-68] [64-68] [64-68] [69, 70] [69, 71] [56, 58, 64, 72, 73] [56, 57, 64, 70, 7275] [54, 56, 64, 72-74] [56, 76, 77] [56, 76, 77] [56, 76, 77] [79, 80] [78] [79-83] [81, 84] [81, 84] [81, 84] [81, 84-86] [72, 79, 81, 83, 87, 88]

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Methane+ Acetone

274.8-282.5 269.2-282.8 272.6-291.0 265.6-273.9 267.20-282.03 274.2-326.8

Pb range / MPa 1.080-4.360 0.93-4.36 0.20-4.36 10.84-258.9 2.09-258.9 1.1-1000

cr

T a range / K

Carbon dioxide+ 1,4 Dioxane Carbon dioxide +Acetone Carbon dioxide +THF Hydrogen +Acetone Hydrogen +THF Methane+1,4 Dioxane

Equilibrium region (Lw+H+V) (Lw+H+V) (Lw+H+V) (Lw+H+V) (Lw+H+V) (Lw+H+V)

System

0.3-1000 3.701-439.0 19.1-439.0 2.5-439.0 2.24-4.15 0.4-4.9 0.5-5.2 2.07-8.19 1.47-7.55 1.73-7.28 1.75-11.47 0.52-11.20 1.57-11.32

[72, 81, 84]

(Lw+LHC+H+V) (Lw+LHC+H+V (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V) (Lw+LHC+H+V)

2.53-4.80 2.02-3.87 2.85-4.57 2.11-3.81 2.08-3.56 1.78-3.00 3.59-9.13

[84] [84] [89] [84, 89] [84] [84] [81]

(Lw+LHC+H+V) 274.7-293.2

1.07-11.53

[81, 91]

(Lw+LHC+H+V) 274.1-287.9

1.62-9.13

[92]

(Lw+LHC+H+V) 283.6-286.0 (Lw+LHC+H+V) 281.4-290.4 (Lw+LHC+H+V) 274.1-290.4

6.30-8.90 3.29-10.93 1.60-11.65

[81] [81] [81, 86]

Ac ce p

(Lw+LHC+H+V) 274.2-290.0 275.7-280.8 276.2-281.4 275.8-279.6 275.1-281.0 276.9-281.3 275.1-280.2 280.2-287.4

a

Temperature Pressure c Reference of experimental data b

26

Page 26 of 39

ip t us

5

an

0

-5

-10 0

0.2

M

sl a u di s e R d e zi dr a d n at S

cr

10

0.4

valid data suspected limit leverage limit

0.6

0.8

d

Hat

Ac ce p

te

Figure 1.

27

Page 27 of 39

cr

5

0

us

sl a u di s e R d e zi dr a d n at S

ip t

10

-5

valid data suspected limit leverage limit

0

0.05

an

-10 0.1

0.15

0.2

0.25

0.3

Hat

Ac ce p

te

d

M

Figure 2.

28

Page 28 of 39

10

ip t

5

cr

0

-5

valid data suspected data suspected limit leverage limit

us

sl a u di s e R d e zi dr a d n at S

0

0.1

0.2

an

-10

0.3

0.4

M

Hat

Ac ce p

te

d

Figure 3.

29

Page 29 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

ip t

10

valid data out of leverage suspected limit leverage limit

0

0.1

0.2

0.3

an

-10 0.4

0.5

0.6

Hat

Ac ce p

te

d

M

Figure 4.

30

Page 30 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

ip t

10

valid data suspected limit leverage limit

0

0.2

0.4

0.6

an

-10 0.8

1

1.2

Hat

Ac ce p

te

d

M

Figure 5.

31

Page 31 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

ip t

10

valid data suspected data out of leverage suspected limit leverage limit

0

0.02

0.04

0.06

an

-10 0.08

0.1

0.12

Hat

Ac ce p

te

d

M

Figure 6.

32

Page 32 of 39

10

ip t

5

-5

cr

0

valid data sus pected data

us

sl a u di s e R d e zi dr a d n at S

out of leverage and sus pected data out of leverage sus pected limit leverage limit

0

0.02

an

-10 0.04

0.06

0.08

Hat

Ac ce p

te

d

M

Figure 7.

33

Page 33 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

ip t

10

valid data suspected data suspected limit leverage limit

0

an

-10 0.05

0.1

0.15

Hat

Ac ce p

te

d

M

Figure 8.

34

Page 34 of 39

cr

5

us

0

-5

valid data suspected data suspected limit leverage limit

-10 0

0.1

0.2

an

sl a u di s e R d e zi dr a d n at S

ip t

10

0.3

0.4

M

Hat

Ac ce p

te

d

Figure 9.

35

Page 35 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

ip t

10

valid data suspected limit leverage limit

0

0.1

0.2

an

-10

0.3

0.4

Hat

Ac ce p

te

d

M

Figure 10.

36

Page 36 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

ip t

10

valid data suspected limit leverage limit

0

0.05

an

-10 0.1

0.15

0.2

0.25

0.3

Hat

Ac ce p

te

d

M

Figure 11.

37

Page 37 of 39

5

cr

0

-5

us

sl a u di s e R d e zi dr a d n at S

0.02

an

-10 0

ip t

valid data valid data suspected data sus pected data out of leverage suspected out ofand leverage and sus pecteddata data sus pected limit suspected limit leverage limit leverage limit

10

0.04

0.06

0.08

0.1

0.12

Hat

Ac ce p

te

d

M

Figure 12.

38

Page 38 of 39

 A novel assessment test is proposed for evaluating the quality of clathrate hydrate data.  Test is applied to a compiled database of hydrate equilibrium data.  Test is based on the Leverage statistical method.

ip t

 Based on the assessment test some experimental data were determined to be

Ac ce p

te

d

M

an

us

cr

doubtful.

39

Page 39 of 39