Note
A novel method for evaluation of asphaltene precipitation titration data
Amir H.Mohammadi a,b,n,Ali Eslamimanesh a,Farhad Gharagheizi c,Dominique Richon a,b
a MINES ParisTech,CEP/TEP-Centre E´nerge´tique et Proce´de´s,35Rue Saint Honore´,77305Fontainebleau,France
b Thermodynamics Rearch Unit,School of Chemical Engineering,University of KwaZulu-Natal,Howard College Campus,King George V Avenue,Durban4041,South Africa
c Department of Chemical Engineering,Buinzahra Branch,Islamic Aza
d University,Buinzahra,Iran
a r t i c l e i n f o
Article history:
Received16February2012
Received in revid form
23April2012
Accepted7May2012
Available online18May2012
Keywords:
Evaluation of data
Leverage approach
Asphaltene precipitation
Outlier diagnostics
Scaling equation
Titration data
a b s t r a c t
In this work,we propo a mathematical method for detection of the probable doubtful asphaltene
precipitation titration data.The algorithm is performed on the basis of the Leverage approach,in which
the statistical Hat matrix,Williams Plot,and the residuals of the model results lead to identify the
probable outliers.This method not only contributes to outliers diagnostics but also defines the range of
applicability of the applied models and quality of the existing experimental data.Two available scaling
equations from the literature are ud to pursue the calculation steps.It is found from the obtained
results that:I.The applied models to reprent/predict the weight percent of asphaltene precipitation
are statistically valid and correct.II.All the treated experimental titration data em to be reliable
except one.III.The whole data points prent in the datat are within the domain of applicability of
the employed models.
&2012Elvier Ltd.All rights rerved.
1.Introduction
Saturates,aromatics,resins,and asphaltenes(SARA)are gen-
erally assigned as the portions of crude oils(Leontaritis and
Mansoori,1988;Leontaritis et al.,1992;Mohammadi and
Richon,2007,2008a,b;Thawer et al.,1990;Pan and Firoozabadi,
1996;Andern and Speight,2001;Mohammadi et al.,2012).
The latter fractions(asphaltenes)are normally toluene/benzene
soluble but n-heptane/n-pentane insoluble.It can be stated that
asphaltenes are the most aromatic with highest molecular weight
fraction of petroleumfluids that generally contain simple
heteroatoms(C,H,N,O,and S)or even particular metal constitu-
ents like Fe,Ni,and V(Mohammadi et al.,2012).Asphaltenes have
potential to be precipitated from the bulk of crude oils mainly due
to changes in pressure,temperature,andfluid composition.For九尾神狐
instance,there is a possibility of asphaltene precipitation as the oil
pressure drops during production of some crude oils.
It is currently well accepted that asphaltene precipitations/
depositions in petroleum rervoirs,production and/or process
facilities cau remarkable problems(Leontaritis and Mansoori,
1988;Leontaritis et al.,1992;Mohammadi and Richon,2007;
Thawer et al.,1990;Mohammadi and Richon,2008a,b;Pan
and Firoozabadi,1996;Andern and Speight,2001;Mohammadi
et al.,2012)Nevertheless,the real mechanism of asphaltene
agglomeration,flocculation,and precipitation has been not com-
pletely understood so far mainly due to its complexity
(Mohammadi and Richon,2007;Mohammadi et al.,2012)There
are still many debates on this subject(Mohammadi and Richon,
2007;Mohammadi et al.,2012).
To deal with clarification of this issue,many experimental
techniques have been propod in the literature.Perhaps,the
most widely ud ones are the titration tests.They are generally
performed using coreflood investigations accompanied by addi-
tion of different asphaltene precipitants such as n-alkanes
(mainly n-C5,n-C6,and n-C7).Different dilution ratios(the ratios
of solvents/precipitants to the weight of the live/dead oil samples)
are normally ud to precipitate or dissolve asphaltene fraction in
the bulk of crude at different temperatures(Andern and
Speight,2001;Ashoori et al.,2003;Rassamdana et al.,1996;
Rassamdana and Sahimi,1996).The common experimental
(filtration)procedure(which is generally performed on the basis
of IP-143procedure)is briefly as follows:(Rassamdana et al.,
1999).The crude oil sample accompanied by the precipitants are
mixed with each other(according to specified dilution ratios)in a
suitable vesl using agitation system.Later,an asphaltene solvent
(like toluene)is added to the system to dissolve the precipitated
asphalts.The solvent would then evaporate and the remaining
asphaltenes(precipitated asphaltenes)can be measured.
Although the available titration data em to be adequate to
investigate the amounts and onts of asphaltene precipitations
in various oil samples,no method has been propod to check
甄嬛后传小品台词
their reliability up to now.Furthermore,comparison between the
various titration data as a method for checking the quality of the
corresponding datats may be conrvative due to non-similar
Contents lists available at SciVer ScienceDirect
journal homepage:/locate/ces
Chemical Engineering Science
0009-2509/$-e front matter&2012Elvier Ltd.All rights rerved.
/10.s.2012.05.009
n Corresponding author at:MINES ParisTech,CEP/TEP-Centre E´nerge´tique et
Proce´de´s,35Rue Saint Honore´,77305Fontainebleau,France.
Tel.:þ33164694970;fax:þ33164694968.
E-mail hammadi@mines-paristech.fr
(A.H.Mohammadi).
Chemical Engineering Science78(2012)181–185
pha behaviors and/or structures of asphaltene fractions prent in different oil samples.
Apart from that,the scaling equation developed by Rassam-dana and co-workers(Rassamdana et al.,1996;Rassamdana and Sahimi,1996)has generated number of attractions in the past decade to reprent/predict the asphaltene precipitation titration data.Therefore,it is of much interest to propo a statistically-correct method for simultaneous detection of the doubtful titra-tion data and th
eir quality along with checking the validity and domain of applicability of the scaling equation.In this commu-nication,our aim is to u the Leverage approach(Rouuw and Leroy,1987;Goodall,1993;Gramatica,2007)for this purpo.To the best of our knowledge,this is thefirst time that this statistical method is ud for evaluation of such data which are of interest in petroleum industry.
2.Theory
2.1.Leverage approach
Outlier diagnostics(or detection)are of much importance in developing the mathematical models.As a matter of fact,outlier detection is to identify individual datum(or groups of data)that may differ from the bulk of the data prent in a datat (Rouuw and Leroy,1987).The corresponding methods gen-erally consist of numerical and graphical algorithms(Rouuw and Leroy,1987;Goodall,1993;Gramatica,2007;Gharagheizi et al.,2011).The Leverage approach(Rouuw and Leroy,1987; Goodall,1993;Gramatica,2007)is considered to be a reliable algorithm for outlier detection that deals with the values of the ,the deviations of a model results from the experi-mental data)and a matrix known as Hat matrix compod of the experimental
data and the reprented/predicted values obtained from a model.The primary application criterion of this method is to u a model,which is capable of acceptable calculation/ estimation of the data of interest.
The Leverage or Hat indices are calculated bad on Hat matrix (H)with the following definition:(Rouuw and Leroy,1987; Goodall,1993;Gramatica,2007;Gharagheizi et al.,2011)
H¼XðX t XÞÀ1X tð1Þwhere X is a(nÂk)matrix,in which n stands for the data(rows) and k denotes the parameters of the model(columns),and t stands for the transpo matrix.The Hat values of the data in the feasible region of the problem are,as a matter of fact,the diagonal elements of the H value.
Having evaluated the H values with Eq.(1),the Williams plot is sketched for graphical identification of the suspended data or outliers.This plot shows the correlation of Hat indices and standardized cross-validated residuals(R),which are defined as the difference between the reprented/predicted values and the implemented data.A warning Leverage(H)is generallyfixed at the value equal to3n/p,where n is number of training points and p is the number of model parameters plus one.The Leverage of three is normally considered as a‘‘cut-off’’value to accept the points within73range(two horizontal red
lines)standard deviations from the mean(to cover99%normally distributed data).Existence of the majority of data points in the ranges 0r H r H n andÀ3r R r3reveals that both model development and its predictions are done in applicability domain,which result in a statistically valid model.‘‘Good High Leverage’’points are located in domain of H n r H andÀ3r R r3.The Good High Leverage can be designated as the ones,which are outside of applicability domain of the applied model.In other words,the model is not able to reprent/predict the following data at all.The points located in the range of R oÀ3or3o R(whether they are larger or smaller than the H n value)are designated as outliers of the model or‘‘Bad High Leverage’’points.The erroneous reprentations/predictions may be attributed to the doubtful data.
2.2.Scaling equation
In1996,Rassamdana and co-workers(Rassamdana et al., 1996;Rassamdana and Sahimi,1996)stated that the titration data of asphaltene precipitation including the dilution ratio,the molecular weight of solvent/precipitant,and the weight percent of precipitated asphaltene can be collapd onto a single(and simple)equation(curve)(Rassamdana et al.,1996;Rassamdana and Sahimi,1996).As a conquence,they propod the following three-order polynomial for reprentation/prediction of the amounts/onts of asphaltene precipitations against addition of n-alk
anes:(Rassamdana et al.,1996).
Y¼aþbXþcX2þdX3ð2Þwhere,
X¼R d=M zð3Þand
Y¼W=R Z0
d
ð4ÞIn the preceding equations,W is the weight percent of the precipitated asphaltene,R d stands for the dilution ratio,and M denotes the molecular weight of the solvent/precipitant.They recommended the values of1/4andÀ2for z and z0after adjusting the parameters against the obtained experimental titration data.Later,Rassamdana et al.(1999)and Ashoori et al.(2003) modified one of the parts of the original scaling equation to account for the effects of temperature on the amount of pre-cipitations introducing a third parameter in Eq.(3)as follows:
X¼R d=T n M zð5Þwhere T is the temperature.The value of0.15for the n parameter in Eq.(5)shows acceptable results for reprentation of the experimental titration values reported by Ashoori et al.(2003).
3.Experimental data
The experimental asphaltene precipitation titration data obtained and reported in the original publications of Rassamdana et al.(1996)and Ashoori et al.(2003)have been treated in this work.
4.Results and discussion
Tables1and2show the absolute relative deviations of the results using the original(Rassamdana et al.,1996)and the modified scaling equation.(Ashoori et al.,2003).As can be en, the deviations of the models reprentations/predictions from the corresponding experimental data reported in the original articles (Ashoori et al.,2003;Rassamdana et al.,1996)are generally acceptable to be ud for the Leverage statistical approach.
The evaluation steps have been followed on the basis of the aforementioned procedure(Section2.1).
The H values have been calculated through Eq.(1).The Williams plots have been sketched in Figs.1and2for the results using thefirst model(Rassamdana et al.,1996)and corresponding experimental datat(Rassamdana et al.,1996)and the cond ones,(Ashoori et al.,2003),respectively.All the calculated H and R values are prented in Tables1and2.Two warning Leverages
A.H.Mohammadi et al./Chemical Engineering Science78(2012)181–185 182
Table1
The results of the applied model(Rassamdana et al.,1996)(the original scaling equation)and the Leverage approach(Rouuw and Leroy,1987;Goodall,1993; Gramatica,2007).
W exp*W rep/pred**Precipitant Hat Standardized
residuals
1.190.6n-C50.05
2.38
1.61 1.13n-C50.03 1.85
2.05 1.72n-C50.02 1.09
2.61 2.38n-C50.020.72
3.12 2.83n-C50.03 1.36
3.5 3.14n-C50.03 2.00
3.85 3.55n-C50.05 1.79
4.21 4.01n-C50.07 1.34
4.62 4.48n-C50.1 1.16
0.790.54n-C60.05À0.02
1.091n-C60.03À0.90
1.43 1.37n-C60.02À0.93
1.57 1.5n-C60.02À0.80
1.68 1.67n-C60.02À1.13
1.74 1.8n-C60.02À1.54
1.96 1.92n-C60.02À0.80
2.16 2.13n-C60.02À0.77
2.55 2.54n-C60.02À0.71
3.05 2.82n-C60.020.94
3.46 3.2n-C60.04 1.33
3.61 3.63n-C60.05À0.40
4.28 4.07n-C60.07 1.44
0.740.41n-C70.060.48
1.020.84n-C70.04À0.36
1.16 1.18n-C70.03À1.57
1.4 1.33n-C70.02À0.88
1.4 1.46n-C70.02À1.71
1.64 1.7n-C70.02À1.59
1.94 1.91n-C70.02À0.87
2.3 2.29n-C70.02À0.83
2.58 2.55n-C70.02À0.57
2.93 2.92n-C70.03À0.53
3.21 3.33n-C70.04À1.24
3.54 3.57n-C70.05À0.5
3.68 3.74n-C70.06À0.63
0.70.29n-C80.060.98
1.080.7n-C80.040.96
1.26 1.03n-C80.030.08
1.4 1.15n-C80.030.27
1.49 1.3n-C80.02À0.07
万能主持词开场白台词1.59 1.51n-C80.02À0.72
1.82 1.7n-C80.02À0.36
2.24 2.06n-C80.020.23
2.48 2.33n-C80.020.15
2.89 2.69n-C80.020.67
3.13 3.09n-C80.03À0.24
3.17 3.32n-C80.04À1.45
3.42 3.48n-C80.05À0.75
0.70.17n-C100.07 1.77
0.890.52n-C100.050.81
1.150.81n-C100.040.73
1.190.96n-C100.030.04
1.39 1.1n-C100.030.53
1.42 1.28n-C100.02À0.42
1.61 1.46n-C100.02À0.27
1.91 1.79n-C100.02À0.31
鬼字成语2.16 2.03n-C100.02À0.13
2.56 2.36n-C100.020.51
2.83 2.72n-C100.020.06
2.97 2.93n-C100.03À0.32
2.99
3.08n-C100.03À1.14
n Experimental weight percent of precipitated asphaltene(Rassamdana et al., 1996).The experiments have been done at approximately299.272K.The data have been taken from thefigures in the original publication(Rassamdana et al., 1996).
nn Reprented/predicted weight percent of precipitated asphaltene by the original scaling equation(Rassamdana et al.,1996).The values of the parameters in Eq.2are as follows:a¼1.18;b¼À14.9;c¼39.16;d¼0.92.Table2
The results of the applied model(Ashoori et al.,2003)(the modified scaling equation)and the Leverage approach(Rouuw and Leroy,1987;Goodall,1993; Gramatica,2007).
W exp*W rep/pred**Precipitant Temperature
(K)
Hat Standardized
residuals
00n-C7303.150.040.49
0.750.99n-C7303.150.03À0.27
善良的空姐1.2 1.24n-C7303.150.030.24
1.7 1.6n-C7303.150.020.57
4 3.76n-C7303.150.010.68
4.8 4.68n-C7303.150.010.26
6.6 6.55n-C7303.150.02À0.15pdf加页码
7.57.39n-C7303.150.02À0.09
87.73n-C7303.150.020.30
8.18.09n-C7303.150.03À0.44
8.38.46n-C7303.150.03À0.94
0.81 1.09n-C6303.150.03À0.39
1.23 1.36n-C6303.150.03À0.02
1.91 1.78n-C6303.150.020.63
4.16 4.21n-C6303.150.01À0.14
5.03 5.24n-C6303.150.01À0.69
7.037.33n-C6303.150.02À1.18
8.138.05n-C6303.150.03À0.25
8.688.41n-C6303.150.030.22
8.868.78n-C6303.150.03À0.33
9.089.17n-C6303.150.04À0.84
0.91 1.23n-C5303.150.03À0.52
1.42 1.53n-C5303.150.020.01
2.32 2.01n-C530
3.150.02 1.08
4.66 4.81n-C5303.150.01À0.48
5.83 5.99n-C5303.150.01À0.64
8.17.98n-C5303.150.03À0.13
9.258.9n-C5303.150.040.38
109.27n-C5303.150.04 1.36
10.29.66n-C5303.150.050.80
10.410.08n-C5303.150.050.16
0.60.81n-C7323.150.03À0.17
0.98 1.02n-C7323.150.030.26
1.35 1.3n-C7323.150.030.47
2.983n-C732
3.150.020.08
3.61 3.73n-C7323.150.01À0.27
5.07 5.2n-C7323.150.01À0.47
5.88
6.21n-C7323.150.01À1.12
6.32 6.52n-C7323.150.02À0.81
6.42 6.84n-C7323.150.02À1.44
6.58
受助学生感谢信7.18n-C7323.150.02À1.96
0.620.89n-C6323.150.03À0.34
1.01 1.12n-C6323.150.030.06
1.44 1.44n-C6323.150.030.32
3.33 3.35n-C6323.150.010.04
4.06 4.17n-C6323.150.01À0.3
5.77 5.83n-C6323.150.01À0.36
6.67 6.77n-C6323.150.02À0.58
7.227.09n-C6323.150.020.00
7.37.43n-C6323.150.02À0.73
7.467.78n-C6323.150.02À1.29
0.731n-C5323.150.03À0.35
1.18 1.26n-C5323.150.030.13
2.12 1.63n-C532
3.150.02 1.61
4.15 3.83n-C5323.150.010.89
5.16 4.76n-C5323.150.010.99
7.46 6.6n-C5323.150.02 2.01
8.587.49n-C5323.150.02 2.52
9.167.83n-C5323.150.02 3.13
9.258.18n-C5323.150.03 2.40
9.468.56n-C5323.150.03 1.90
0.50.7n-C7343.150.03À0.13
0.750.9n-C7343.150.03À0.02
1.5 1.14n-C7343.150.03 1.32
2.51 2.58n-C734
3.150.020.00
3.07 3.21n-C7343.150.01À0.26
4.2 4.47n-C7343.150.01À0.76
4.91
5.52n-C7343.150.01À1.79
5.36 5.82n-C7343.150.01À1.42
A.H.Mohammadi et al./Chemical Engineering Science78(2012)181–185183
(H n ¼0.147)and (H n ¼0.133)have been fixed at 3n /p for the first model and experimental data (Rassamdana et al.,1996)and the cond ones (Ashoori et al.,2003),respectively.In addition,the recommended cut-off value of three has been applied (Gharagheizi et al.,2011).
Accumulation of the whole datat in the ranges 0r H r 0:147and À3r R r 3for the data þmodel reported by Rassamdana et al.(1996)and 0r H r 0:133and À3r R r 3regarding the data þmodel of Ashoori et al.(2003)reveals that the applied models are statistically correct and valid.Furthermore,it shows that the whole data except one in the later datat are located within the applicability domains of the applied models.
Good High Leverage points are accumulated in the domains of 0:147r H and À3r R r 3for the first model þdata (Rassamdana et al.,1996)and 0:133r H and À3r R r 3for the cond ones (Ashoori et al.,2003).The points may be declared to be outside of applicability domains of the applied models.As can be en,there are no such points in the investigated datats.It should be noted that,in the ca of existence of the kinds of points,it is recommended to u/develop other models on the basis of different theoretical concepts for their calculations/estimations,in order to avoid estim
ation through biad model calculations.The points located in the range of R o À3or 3o R (ignoring their H values)are designated as outliers of the model or ‘‘Bad High Leverage’’points,as already mentioned.The erroneous reprentations/predictions can be attributed to the doubtful asphaltene precipitation data.There is only one point in the two treated datats (Ashoori et al.,2003;Rassamdana et al.,1996),which is within this domain and conquently we can state it as probable doubtful datum.
In the final analysis,we may conclude the following elements:
1.The applied scaling equations (Ashoori et al.,2003;Rassamdana et al.,1996)are statistically correct and valid.
2.All of the data points are within the applicability domains of the prented model.
3.There is only 1point,which may be designated as outlier from the datat of Ashoori et al.(2003)(e Table 2).
4.The quality of the treated data (even different data in the same datat)is different.The data with lower absolute R values (near R ¼0line)and lower H values may be declared as the more reliable ex
perimental data.It is worth it to point out that the reliability of experimental pha equilibrium data can be checked normally by performing the thermodynamic consistency tests.However,the kinds of tests may be just applicable for homogeneous phas or the non-heterogeneous ones with small amounts of (solubility of)the solutes in the mixture.However,this is not the ca for the studied systems.It may be the main reason why we
cannot
Fig.1.Detection of the probable doubtful experimental data (Rassamdana et al.,1996)and the applicability domain of the original scaling equation (Rassamdana et al.,1996).Squares,valid data;Horizontal (red)lines,Suspended data limit;Vertical (blue)line,Leverage limit.(For interpretation of the references to color in this figure legend,the reader is reffered to the web version of this
article.)
Fig.2.Detection of the probable doubtful experimental data (Ashoori et al.,2003)and the applicability domain of the modified scaling equation (Ashoori et al.,2003)Squares,valid data;Circular,Probable suspended data;Horizontal (red)lines,Suspended data limit;Vertical (blue)line,Leverage limit.(For interpretation of the references to color in this figure legend,the reader is reffered to the web version of this article.)
Table 2(continued )W
exp *
W
rep/pred **
Precipitant Temperature (K)Hat
Standardized residuals 5.53 6.12n -C 7343.150.01À1.85.65 6.44n -C 7343.150.02À2.380.510.78n -C 6343.150.03À0.330.670.99n -C 6343.150.03À0.491.2 1.26n -C 6343.150.030.182.67 2.89n -C 6
dnfss改版343.150.02À0.443.27 3.59n -C 6343.150.01À0.794.59 5.01n -C 6343.150.01À1.225.48 6.03n -C 6343.150.01À1.695.96 6.33n -C 6343.150.01À1.246.63 6.65n -C 6343.150.02À0.350.580.88n -C 5343.150.03À0.420.81 1.1n -C 5343.150.03À0.421.48 1.42n -C 5343.150.030.483.6 3.29n -C 5343.150.010.934.48 4.1n -C 5343.150.01 1.026.27 5.72n -C 5343.150.01 1.287.32 6.67n -C 5343.150.02 1.447.737n -C 5343.150.02 1.617.887.33n -C 5343.150.02 1.107.98
7.68
n -C 5
343.15
0.02
0.39
n
Experimental weight percent of precipitated asphaltene (Ashoori et al.,2003).
nn
Reprented/predicted weight percent of precipitated asphaltene by the
modified scaling equation (Ashoori et al.,2003).The values of the parameters in Eq.2are as follows:a ¼1.18;b ¼À14.9;c ¼39.16;d ¼0.92.
A.H.Mohammadi et al./Chemical Engineering Science 78(2012)181–185
184
extend our previous works(Eslamimanesh et al.,2011a–d,2012; Mohammadi et al.,2011a,b)on the data asssments tests for the treated experimental data in this work.
5.Conclusion
A method for evaluation of asphaltene precipitation titration data was propod on the basis of the Leverage statistical approach (Rouuw and Leroy,1987;Goodall,1993;Gramatica,2007).Two asphaltene precipitation titration datats from the literature (Ashoori et al.,2003;Rassamdana et al.,1996)were reprented/ predicted by the original scaling equation(Rassamdana et al.,1996) and the modified one(Ashoori et al.,2003)to pursue the calculation steps of the evaluation method.The results show that the applied models are valid and statistically correct.Furthermore,only one of the d
ata points was found to be outlier(doubtful experimental data) while all of the investigated precipitation data were interpreted to within the applicability of the employed models.The results can be further ud to conclude about the quality of the data points,which are suppod to be applied in tuning the asphaltene precipitation models(thermodynamic or numerical ones).
Acknowledgement
Ali Eslamimanesh is grateful to MINES ParisTech for providing him with a PhD scholarship.
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